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IRRADIANCE FORECASTING AND DISPATCHING CENTRAL STATION PHOTOVOLTAIC
POWER PLANTS
by
Badrul Hasan Chowdhury
Dissertation submitted to the Faculty of the
Virginia Polytechnic Institute and State University
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
1 )(r~n7G. Phadke
Subhash C. Sarin
in
Electrical Engineering
APPROVED:
tSaifur Rahman, Chairman
August, 1987
Blacksburg, Virginia
loannis. M. Besieris
Charles E. Nunnally
IRRADIANCE FORECASTING AND DISPATCHING CENTRAL STATION PHOTOVOLTAIC
POWER PLANTS
by
Badrul Hasan Chowdhury
Saifur Rahman, Chairman
Electrical Engineering
(ABSTRACT)
This dissertation introduces a new operational tool for integrating a photovoltaic (PV) system
into the utility's generation mix. It is recognized at the outset, that much of the existing
research concentrated on the central PV system and its operations have concluded that
technical problems in PV operation will override any value or credit that can be earned by a
PV system, and that penetration of a PV plant in the utility will be severely limited. These are
real problems and their solutions are sought in this dissertation. Judging from the drawbacks
of the static approach, it is felt that a new approach or methodology needs to be developed
which would give a central station PV plant its due share of credit. This dissertation deals
mainly, with the development and implementation of this new approach -- a dynamic
rule-based dispatch algorithm which takes into account the problems faced by the dispatch
operator during a dispatch interval and channels those into a knowledge base.
The new dynamic dispatch requires forecasts of photovoltaic generations at the beginning of
each dispatch interval. A Box-Jenkins time-series method is used to model the sub-hourly
solar irradiance. The irradiance data at any specific site is stripped of its periodicities using
a pre-whitening process which involves parameterization of certain known atmospheric
phenomena. The pre-whitened data series is considered stationary, although some
non-stationarity might be introduced by the discontinuities in the data collection during night
hours. This model is extended to yield forecast equations which are then used to predict the
photovoltaic output expected to occur at certain lead times coinciding with the economic
dispatch intervals.
An rule-based (RB) dispatch algorithm is developed in this dissertation. The RB is introduced
to operate as a substitute for the dispatch operator. Some of the dispatcher's functions are
routine jobs, while some require specialized knowledge or experience. The RB is given these
two qualities through a number of rules. This algorithm works in tandem with a conventional
economic dispatch algorithm. The functions of the two are coordinated by another algorithm
which oversees the now of information and records them.
The RB gives one of 16 possible solutions as and when required. These solutions are written
as rules which manipulate the non-committable generation to achieve an optimal solution. The
RB system during its operation supervises the fact that the PV generation are kept at the
maximum level possible under all constraints. The case study revealed that the thermal
generating units which are scheduled by the unit commitment are able to absorb most of the
small to medium variations present in the PV generations. In cases of large variations during
a single interval, the thermal generators reach their response limits before they can reach
their maximum or minimum generation, thus causing mismatches in the load and generation.
The mismatches are then picked up by the non-committable sources of generation, comprised
of pumped storage units, hydro generation plant, or by interconnection tie-lines. If none of
these are sufficient, changes are made in the PV generation schedule.
It is concluded that results depend on the time of the year and the specific utility. The time of
the year information is reflected in the load demand profile. Most utilities in the U.S. have
single peaks in summer and double peaks in winter. Also, the time of the peak load
occurrence, varies with season. The utility generating capacity mix influences the results
greatly.
Acknowledgements
It gives me great pleasure to write this piece mainly because it does not contain any equations
or any technical jargon. Writing this small section also means that the job I had set out to do
some years ago, is now almost complete. I can actually see a streak of sunshine at the end
of the tunnel.
It has been my privilege and honor to have been associated with Dr. Saifur Rahman at Virginia
Tech. He has been my advisor, mentor, guide and friend for the past few years. My research
was initiated under his kind supervision, some six years ago. His persistence, insight and
devotion to research has helped me build my character. I am grateful to him for the support
he has shown me and the independence he has allowed me in structuring my research. Now,
that I move along into my own career, his ideals will always serve as a guiding light.
I would like to thank Dr. Arun Phadke, Dr. Charles Nunnally, Dr. loannis Besieris and Dr.
Subhash Sarin for serving on my committee. Their constant encouragement and interest in
my work has helped me a great deal. I have pestered them on so many occasions, the
runaway winner being the scheduling of my defense on a weekend. But everyone had
accommodated me without the slightest hint of objection.
Acknowledgements Iv
This dissertation is the product of years of struggle. Struggle with the research, with the mind
and body and in certain ways, the amazingly capricious phenomenon called the computer. A
lot has been said and done about the computer and I shall leave it at that. I will only remark
that it is a wonderful feeling, now that I have the final product in my hands.
It would be remiss, if I did not mention my fruitful association with the department. When I look
back to the days when I had my first days of classes, everything seemed distant and
unfriendly. Over the years, the relationship has grown. After my offices had moved from
temporary cubicles in various buildings on campus, I finally got a nice little room in an
expanded Whittemore hall. Now that I am getting ready to part from this relationship, I have
only fond memories.
I have been involved with the Energy Systems Research Laboratory in this department, since
its infancy. I have therefore developed a special feeling toward it. I extend my thanks to all the
people associated with the laboratory.
Finally, I would like to take this opportunity to express my deep gratitude to my wonderful
parents who have stood by me through thick and thin. They have been a constant source of
strength and motivation for me. I also thank the other members of my family, all of whom have
shown me great support and love.
Acknowledgements v
Table of Contents
Introduction • • • • • • . . • • • • . . • . • • • . . . • • • . . . • . • • . • • . . • • • . • . • . • • • . • . . • • • . . . . • 1
1.1 Historical Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Present PV Status & Future Trends ...................................... 3
1.3 Central Station Photovoltaics ........................................... 4
1.3.1 Utility Point of View . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.2 Economics ...................................................... 6
1.3.3 Operating Characteristics .......................................... 7
1.4 PV Dispatchability ................................................... 9
1.5 Resource Forecast .................................................. 11
Recent Advances In Utility Integration . • . . . . • • • • . • • . . • • • • . . • • • • . • • . . • . . • . . . • . 12
2.1 Systems Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2 Operational Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3 Planning and Reliability Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4 Economic Dispatch With PV Plants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Table of Contents vi
Optimizing PV Output in the Utility • . . . . . . . • • . . . . • • • • • • . . • . . . • • • • • . • • • • . . • . . . 39
3.1 Array Orientation Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.1.1 South-facing array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.1.2 Optimal-Surface-Azimuth Oriented Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.1.3 Two-axis Tracking Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.2 PV Performance Simulation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.2.1 Translation of Horizontal lrradiance on the Plane of Array . . . . . . . . . . . . . . . . . 52
3.2.1.1 Liu and Jordan Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.2.1.2 Duffie and Beckman Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2.1.3 Klucher Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.2.1.4 Perez Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.2.1.5 Results of the Comparative Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.3 Energy Storage With Central Station PV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.3.1 Potential For A Combined Photovoltaic/Battery System . . . . . . . . . . . . . . . . . . . 64
3.3.2 Battery Plant Consideration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.3.3 PV/Battery Operating Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.3.4 Comparative Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.3.5 Relative Performance of Array Orientation Strategies . . . . . . . . . . . . . . . . . . . . 76
Resource Forecast . . . . . • . • . • . . . . . • . . . • . . • . • • . • • • . • • • • • • • . . • • . . . • . . . • . • • . 82
4.1 Background Information .............................................. 83
4.2 Time Series Modeling in lrradiance Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.2.1 Choosing the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.2.2 The Pre-whitening Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.2.2.1 Parameterization for the Prewhitening Process . . . . . . . . . . . . . . . . . . . . . . 88
4.3 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.3.1 Predicting the Output from a Photovoltaic System . . . . . . . . . . . . . . . . . . . . . . . 93
4.3.2 Programming Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Table of Contents vii
4.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.4.1 Identification of the ARIMA Model (p,d,q) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.5 Conclusions on the Forecast Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Unit Commitment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.1 Solving the Unit Commitment problem .................................. 119
5.2 EPRl's Unit Commitment Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5.2.1 Input Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.2.2 Priority List Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.2.3 Hourly Generation Maximum Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
5.2.4 Reserve capacity From Non-committable Sources . . . . . . . . . . . . . . . . . . . . . . 122
5.2.5 Precommitment of Peaking Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.2.6 Hourly Regulation Requirement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.2.7 Committable Unit Commitment Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Economic Dispatch .•••••.••.•••.••.••.••••••••••••••••••••••••...•..•. 126
6.1 AGC and Economic Dispatch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.1.1 Load Frequency Control .......................................... 131
6.2 Formulating the Economic Dispatch Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
6.3 Solving the Economic Dispatch Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
Implementing PV Dispatch in a New Economic Dispatch Algorithm •.••.•.••...••.. 138
7.1 Need For a New Approach to Economic Dispatch . . . . . . . . . . . . . . . . . . . . . . . . . . 138
7.2 Proposed Rule-based System Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
7.2.1 Present Functions of the Dispatcher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
7.2.2 A Rule Base Replacing the Dispatcher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
7.2.2.1 PV Dispatch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
7.2.3 Rules in the Rule Base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Table of Contents viii
7.3 Programming Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
7.3.1 Interface With EPRl's GPUC Program ................................ 156
7.3.2 Interface With the Solar Resource Forecast Program . . . . . . . . . . . . . . . . . . . . 159
7.3.3 The Dispatch Combined With the RB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Case Study: Results . . . . • . . . . . • . • . • • . . . . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . • . 164
8.1 Continuous Simulation Run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
8.1.1 Generator Data ................................................ 166
8.1.2 Load Data .................................................... 166
8.1.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
8.2 Effect of PV Penetration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
8.3 Static Versus the Dynamic Dispatch Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
Summary and Recommendation 191
9.1 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
Bibliography . . . . . . . • . . . . . . • . . . • . • . . . . . . . . . • . . . . . . . . . • . . . . . . • . . . . • . . . . 198
Solar Geometry . . . . . • . . . . . . . . . . . • . . . . . . . . . . • . . • . . . . . . . . . . . . . . • . . . . . . . . 216
Selected Input-Output for Dispatch Model . . . . . . . . • . . . . . . . . . . . . • . . . . . • • . . . . . . 221
Sample Run . . . . . . . . . . . . . . . . . . . • . . • . • . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . 231
Vita . . . . . . • . • . . . . . . . . . . . . . . . . . • . . . . . . . . . . • . . . • . . . • . . . . . . . . . . . . . . . . • . 255
Table of Contents Ix
List of Illustrations
Figure 1. Utility Integration Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Figure 2. System simulation models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Figure 3.
Figure 4.
Figure 5.
Figure 6.
Figure 7.
Figure 8.
Figure 9.
Figure 10.
Figure 11.
Figure 12.
Figure 13.
Figure 14.
Figure 15.
Figure 16.
Solar irradiance components. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Position of the sun relative to an inclined plane . . . . . . . . . . . . . . . . . . . . . . . 42
Array orientation options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
PV output comparisons for fixed tilt, azimuth-optimized and fully tracking arrays for August at Raleigh, NC ....................................... 46
PV output comparisons for fixed tilt, azimuth-optimized and fully tracking arrays for November at Hesperia, CA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Functional blocks in a PV simulation model . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Battery capacity requirement for percent peak load supplied. Site is Raleigh, NC ........................................................ 68
Battery capacity requirement for percent peak load supplied. Site is Hesperia, CA ........................................................ 69
Comparison of depth of charge and discharge of battery with and without PV power at Raleigh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
The simulation process to forecast global irradiance . . . . . . . . . . . . . . . . . . . 94
Execution of the FORECST module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
ACF of March Data in Raleigh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
ACF of the Differenced Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
PACF of the Differenced Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
Figure 17. ACF of the residuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Figure 18. Global irradiance comparison at Raleigh in March 107
List of Illustrations x
Figure 19. PV output comparison at Raleigh in March . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Figure 20. Global irradiance comparison at Raleigh in June . . . . . . . . . . . . . . . . . . . . . 109
Figure 21. Global irradiance comparison at Richmond in March . . . . . . . . . . . . . . . . . . 110
Figure 22. lrradiance comparisons with updates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
Figure 23. A case of model inaccuracy. . ................................... 113
Figure 24. A four-level hierarchy in production control . . . . . . . . . . . . . . . . . . . . . . . . . 117
Figure 25. Relationship of unit commitment to other programs in the control center . . . 118
Figure 26. AGC and economic dispatch functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
Figure 27. System frequency characteristic versus tie-line flow 133
Figure 28. The three computer modules in the proposed operation scheme . . . . . . . . . 144
Figure 29. Operational scenario with PV system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
Figure 30. Rule-set 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Figure 31. Rule-set 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
Figure 32. Rule-set 8
Figure 33. Functional properties of the new dynamic economic dispatch
Figure 34. Components of unit commitment
Figure 35. Execution of the DRIVER module
154
157
158
160
Figure 36. Information exchange in the three modules . . . . . . . . . . . . . . . . . . . . . . . . . 162
Figure 37. Continuous simulation run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
Figure 38. Sample modified load profile and PV output for a day in January . . . . . . . . . 169
Figure 39. Effect of PV output on thermal generation . . . . . . . . . . . . . . . . . . . . . . . . . . 177
Figure 40. Effect of PV output on combustion turbine generation . . . . . . . . . . . . . . . . . . 178
Figure 41. Effect of PV output on spinning reserves
Figure 42. Effect of PV output on system lambda
Figure 43. Effect of PV output on production costs
179
181
182
Figure 44. Effect of PV output on some specific thermal units . . . . . . . . . . . . . . . . . . . . 183
Figure 45. Effect of PV output on some specific CT units . . . . . . . . . . . . . . . . . . . . . . . . 184
Figure 46. Effect of PV penetration on system production cost . . . . . . . . . . . . . . . . . . . 188
List of Illustrations xi
Figure 47. Position of the sun relative to an inclined plane . . . . . . . . . . . . . . . . . . . . . . 217
Figure 48. Generator input data {Generating unit identification) 222
Figure 49. Generator input data {Generating unit performance characteristics) . . . . . . . 223
Figure 50. Generator input data {Generating unit cost data and hourly load) 224
Figure 51. Unit commitment output used as input to the model {Generator unit schedule) 225
Figure 52. Unit commitment output used as input to the model {Partial CT generation data) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
Figure 53. Generator response rates
Figure 54. Partial thermal generator output during simulation
Figure 55. Sample of model output at each interval
Figure 56. Sample of model output at each interval ............................
List of Illustrations
227
228
229
230
xii
List of Tables
Table 1. Some Characteristics of the Four Models ............................ 60
Table 2. Ratio of lrradiance in Raleigh, NC and Orlando, FL . . . . . . . . . . . . . . . . . . . . . 61
Table 3. Ratio of lrradiance in Hesperia, CA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Table 4. Peak shaving characteristics in the four seasons for typical utility in the south-east (assuming 7000 MW annual peak). . . . . . . . . . . . . . . . . . . . . . . . . . 73
Table 5. Peak shaving characteristics in the four seasons for typical utility in the west (assuming 7000 MW annual peak) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Table 6. Comparisons of the three PV array orientation strategies for the south-eastern utility. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Table 7. Comparisons of the three PV array orientation strategies for the western utility. 80
Table 8. Fitted ARIMA (p,d,q) Models in Raleigh, NC. . . . . . . . . . . . . . . . . . . . . . . . . . 105
Table 9. Fitted ARIMA (p,d,q) Models in Richmond, VA.
Table 10. Thermal generator data for the synthetic utility
106
167
Table 11. Combustion turbine generator data for the synthetic utility .............. 168
Table 12. System operation without PV during 1st time period ................... 171
Table 13. System operation without PV during 2nd time period ................... 172
Table 14. System operation without PV during 3rd time period . .................. 173
Table 15. System operation with PV during 2nd time period ..................... 174
Table 16. System operation with PV during 3rd time period ..................... 175
Table 17. System regulation limit violations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
Table 18. System operation summary with and without PV . . . . . . . . . . . . . . . . . . . . . . 186
Table 19. Static versus dynamic dispatch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
List of Tables xiii
CHAPTER 1
Introduction
Solar photovoltaics is now an acceptable form of power generation. The clean, simple and
renewable nature of this type of generation is highly desirable, particularly in the context of
depleting conventional fossil fuel resources. Photovoltaics can provide power for electric
utilities, homes, boats, water pumping, and small electronic consumer products. Tremendous
progress has been made in developing PV as a cost effective electrical option for many
diverse applications.
1.1 Historical Perspective
Photovoltaics (PV) has come a long way since being a mere laboratory curiosity in the
1950's,when the Silicon solar cell was discovered at Bell Laboratories in New Jersey. The
beginning of the Space Age in the late 1950s was also the beginning of extensive research
and development into the photovoltaic device. Space satellites needed a light weight, long
Introduction 1
lasting energy source. Photovoltaics were an ideal match to this need, depending only on the
sun for fuel. The age of the PV power source in space began with the launching of the
Vanguard satellite.
Photovoltaics quickly proved themselves to be an ideal source for earth and extraterrestrial
applications. Research improved the device performance and decreased weight. By the early
1970's, large arrays were being developed. While proven as an energy source for space,
photovoltaic cells still remained too expensive for terrestrial use. It was not until the oil
embargo of 1973, that the current program to develop a terrestrial energy source began in
earnest. In the short time since that beginning, tremendous strides in efficiency, reliability and
cost effectiveness have been made. PV is now cost-effective over a wide range of applications
and shows promise for becoming a major world supply source in the future. The advent of
micro-electronics industry has resulted in the use of many megawatts of photovoltaics in
millions of calculators, watches, and other small devices. Battery chargers, auxiliary power
supplies, emergency radio power sources are just some of the new applications of
photovoltaics now being brought on to the market.
Before the end of this century, PV should achieve its long-term goal of becoming a major
power source in the industrialized countries. Its promise of a clean, secure energy source,
combined with its simplicity and modularity make it ideal for future utility connected
applications. Large installations already operating in the United States have verified the
practicality of the energy source. Systems such as the first 1-megawatt (of the planned two
megawatts) installed at the electric utility at Sacramento, CA, have demonstrated that the
systems can indeed operate compatibly with the electric grid producing valuable energy.
Collector costs remain a major obstacle to large scale use of PV on the U.S. utility system.
However, the progress already made in this area has led many utilities as well as third party
investment groups to begin to investigate large scale PV systems today. As a result of these
efforts, it has been possible to verify that today's commercial collectors are extremely reliable.
Introduction 2
The first major utility connected non-utility owned photovoltaic system is the megawatt-sized
Lugo facility installed in Southern California by ARCO Solar in 1982. The plant feeds power into
the Southern California Edison's grid. Another multi-megawatt PV plant was installed by ARCO
Solar, shortly afterward (1983-84) at Carissa Plains, CA. The plant in now interconnected to the
Pacific Gas & Electric Co.
In approximately thirty years, PV has progressed from the laboratory to a proven power
source for both terrestrial and space applications. The modularity of the source allows the
same technology to power calculators or entire cities. Continued research has resulted in a
commercial technology that is used in high reliability applications in space and on earth. PV
is probably the optimal choice for a remote location where it is difficult to get fuel to, or which
may be inaccessible to utility service extensions. Provided some technological problems are
solved, PV will find increased use as a utility power source in the very near future.
1.2 Present PV Status & Future Trends
The basic principles of converting sunlight directly to electricity are well known. However,
there are many photovoltaic materials and devices and their design, fabrication, optimization
and performance vary a great deal from one photovoltaic material to another. The basic power
element of a photovoltaic system is the solar cell. Typical solar cells are made of crystalline
silicon, the material of the semiconductor revolution. Crystalline silicon technology continues
to be an important area of research and development in the photovoltaic community. Recent
achievements in increasing cell and module efficiencies point to silicon's continued potential
as a cost effective technology. Researchers have made impressive progress in identifying,
developing and optimizing new single-crystal cell structures and in improving the performance
of conventional cell structures. For example, over the past five years, the one-sun efficiency
Introduction 3
of laboratory cells has increased from 18% to 22%, while module life expectancy has
increased from less than 10 years to approximately 20 years. However, even though industry
has used the technology base to reduce module costs to less than $500/m 2, the cost of silicon
materials and of processing cells made from single-crystal wafers, remain obstacles to
achieving cost effective crystalline silicon systems for utility applications. On the other hand,
thin film technologies show considerable potential, and must be considered major
competitors. These include amorphous silicon and its alloys, copper Indium diselenide and its
alloys, and thin film, single crystal gallium arsenide. Multijunction devices in flat-plate and
concentrator systems also look like viable options. Amorphous silicon and polycrystalline thin
film cells, which are about a hundred times thinner than crystalline silicon cells use very little
semiconductor material and offer a long term potential for significantly lower cost. Further,
entire thin film modules, rather than individual cells, can be fabricated in an automated
production process.
As a result of advances in these and other technologies, the cost of PV-generated electricity
has decreased from an estimated $1.50 per kilowatt-hour in 1980 to approximately 35 cents
per kilowatt-hour today. Although significant progress has been made in reducing the cost
of PV electricity, commercially available systems and designs are cost effective only for
remote and special high-value applications. The cost of PV-generated electricity must be
reduced approximately six fold to achieve the long term goal of cost competitiveness in the
U.S. bulk power markets.
1.3 Central Station Photovoltaics
There is a growing number and types of remote applications of PV around the world today.
PV systems are pumping water, grinding grain, protecting bridges and pipes from corrosion,
Introduction 4
aiding navigation, helping communications and powering entire buildings or villages. There
is also an increasing number of modern homes that are installing PV systems as a primary
source, as a backup or auxiliary source to the utility, or who want to sell excess power to the
utility. The first type of application is termed stand-alone systems in as much as no utility
interaction is conceived in the design framework. These systems are essentially isolated and
meant to supply the entire load. The second type of application is known as a utility
interactive distributed system. There could be multitudes of such power generations, all
connected to the same power grid.
There is yet another conceivably potential application of photovoltaics. It is the central station
mode of operation of the plant which is either owned by a utility or a third party investor, and
supplies all its power to the utility's grid. It is generally felt in the photovoltaic community, that
the ultimate application of PV will be its use for bulk power generation. Already, large
MW-sized installations are operating in the U.S and Japan. Some are in the construction
phase and some are in the design and planning stages. Southern California Edison Co., Pacific
Gas & Electric Co. and Tennessee Valley Authority among others, are large utilities having a
substantial solar powered generation component in their generation mixes.
1.3.1 Utility Point of View
Within a large utility company, solar technology is viewed in different ways. There are those
who see solar variously as a resource to be planned for, a system to be designed, a
perturbation on the future load curve, and a technology to be developed. In addition, different
utilities see solar differently, depending on their load, and their size and geographic location.
Some see it as an opportunity to ease a critical future problem of fuel cost and availability.
Many utilities, particularly in the Southwest, are actively engaged in collecting solar radiation
Introduction 5
data for their areas. This is evidence that the utilities are looking into the future and strongly
believe that solar applications have real potentials.
At this time, utilities are concerned about a number of problems related to solar photovoltaic
technology. These are economics and operating characteristics.
1.3.2 Economics
An electric utility is an economically driven entity. Therefore, its primary need is to determine
how to supply the load at the least cost, and then arrange to do so. The economic optimization
must be based on a detailed characterization of future electricity usage patterns, the capital
cost, fuel cost, maintenance requirements, efficiency and reliability of various types of power
plants. Evaluating the economic value of a PV system is a difficult job, to say the least. To be
comparable to a utility, two power plants have to be capable of doing the same job. This
means, they not only must produce the same amount of electric energy annually, but they
must have the same effective capacity or power output capability in kilowatts. The problem
with PV is that its effective capacity is not easily related to its peak output, as with other types
of plants. The effective capacity of solar generation depends on how the operation of the PV
plant affects the load on the remainder of the generating system. This, in turn depends on the
relative amount of solar generation as well as on its reliability and availability during periods
of high demands. Load patterns vary from utility to utility and PV plant reliability and
availability are dependent on irradiance patterns which vary geographically. Thus, no two PV
plants will have the exact same effective capacity. The economic value of a PV plant is
calculated as a part of a utility system and then compared to its costs. The economic value
of a PV installation is sensitive to the amount of installed solar capacity as a percentage of the
total generating capacity. The more a utility relies on PV, the less each individual increment
of PV capacity is worth.
Introduction 6
1.3.3 Operating Characteristics
PV power generation from a central station PV plant effects the operation of all existing
generating units in the system. For the PV plant to integrate successfully into the electric
energy system under circumstances which now exist, it becomes necessary to provide the
PV generating plant with control regimes adequate to the demands that will be placed on
them, and the development of such control regimes becomes an integral part of the
integration process. The first step in such a development is the determination of the conditions
under which the controlled plant will operate. When connected to a large power system, PV
plants become an integral part of that system, and are affected by conditions which would not
occur if they were serving an isolated load. Some of these conditions are directly related to
basic physical laws, while others arise because of the manner in which the power systems
are operated. A power system never attains a steady state, so it is always characterized by
dynamic phenomena.
The basic requirement is that of maintaining a balance between energy being absorbed by the
connected loads and energy being provided by the generating units. In addition, since most
power systems are composed of equipment required to operate at given voltage and
frequency, the system is designed to supply energy within constraints of voltage and
frequency. The Automatic Generation Control (AGC) mechanism in the system takes care of
these problems.
The existing conventional generating units, through the use of AGC, are capable of operating
under the dynamic response required to supply the random variations in system load. Such
is not the case with central station PV plants. Frequent weather changes may translate into
extremely high variations in the power generations from the plant. If the plant is constantly
connected to the distribution system, this causes operational problems like load following,
spinning reserve requirements, load frequency excursions, system stability, etc., which the
Introduction 7
conventional AGC system is unable to handle. This calls for modifications of the existing
schedule and control algorithms to incorporate the random variations in PV output.
This dissertation deals with the development of a new strategy for dynamic economic dispatch
that allows the control of PV plant generations and therefore, avoids the penalties because
of load following and spinning reserve requirements and other related real-time operational
problems. Until now, most researchers have used a static analysis of PV generations in the
central station utility concept. In this method, the total system load is modified by the
generations and the net load is scheduled for dispatch by the conventional generating system.
A major disadvantage of the static approach is that, there is no way of knowing ahead of time,
the potential effects the high variations in PV generations might have on generations from the
cycling units in the system.
Judging from the above two points, clearly the real-time operations perspective is just as
important as the economical aspect of central station PV. While economics are constantly
improving and it is only a matter of time before central station PV plants can compete
favorably against conventional peaking or intermediate fossil fuel plants, questions still
remain to be answered in the real-time operations framework and continues to be the weak
link between the PV plant and the utility. An attempt is made in this dissertation to devise an
algorithm that does everything that a standard AGC program accomplishes, with the
additional capability of treating the PV plant as a dispatchable unit, comparable to the dispatch
operation of a combustion turbine unit.
Dispatchability of a central station PV plant is introduced in the next section.
Introduction 8
1.4 PV Dispatchability
Why is dispatchability of a PV plant so Important In the framework of modern AGC? The
answer to that question is rather simple. It provides controllability to an otherwise random
source of generation.
In most power system computer control, which include AGC and economic dispatch (ED)
functions, the ED program computes an economic base value for designated units every few
minutes based on the load change over the time since the last execution of the ED program.
In between computations of this economic base, the frequency deviation and inadvertent
interchange is controlled by an algorithm which distributes the area control error (ACE) over
certain designated regulating units, and linearly distributes the deviation of the units from their
economic limits. In using this approach, the economic base value calculated is usually
restricted not only by the dispatcher-entered economic high and low limits, but also by the rate
at which the unit can respond over the nominal period of the economic dispatch (5 minutes).
Hence, a unit with a response rate of 5 MW/minute, economic high and low limits of 200 and
100 MW respectively, an actual power of 100 MW and an economic dispatch period of 5
minutes, will be restrained in the on-line economic dispatch, by an effective upper and lower
limits of 135 MW and 100 MW respectively. The result of doing this is that each unit is
assigned an economic base, which can be achieved by moving it at its sustained rate of
response from the present value and hence controlling the system in a smooth manner. An
extension to this method, which is now becoming common in power systems, is that of
including a constraint into the ED problem to guarantee that sufficient regulating and/or
reserve margin is maintained over a short (5 minute) period. This method ensures that the
economic base values assigned to the units will be achievable within 5 minutes of operation
and will, if possible, maintain sufficient short term regulating reserve.
Introduction 9
Under the strategy described above, it is well known that the least expensive units will be
allocated close to their limits during the early stages of the load pickup.leaving the more
expensive units for the final stages. This may result in the utility company not being able to
meet its load pickup in the later stages, except by purchasing energy from a neighboring
utility. At present, this is handled by the dispatcher's ramping of the more expensive units
above their economic assignment early in the load pickup period and thus keeping some less
expensive units below their operational limits in the early stages, so that they can help satisfy
the load pickup required at later stages. This requires of course, the dispatcher to make these
decisions at his own discretion. He will tend to choose a safe solution rather than an
economical one.
The problem of dispatching PV under these circumstances, adds a new facet to the entire
problem. First, the dispatcher has no knowledge about the amount of generation, which will
be available at any economic dispatch interval. Secondly, actual observations at various PV
sites in the Southeastern U.S. shows high amount of fluctuations in the solar irradiance within
a 3-minute interval. This variation translates into constantly fluctuating PV generations posing
a serious decision-making problem for the dispatcher. These problems can be resolved by
using a rule-based system approach, which will comprise of all the decision process of an
expert dispatcher plus the speed of a computer processor. The new proposed methodology
provides the following:
• A prediction of the short term sub-hourly solar irradiance thus, giving a look ahead
capability at the PV generations.
• An economic dispatch.
• Decisions on steps to take in case of operating problems
• Area control error correction.
An introduction to the forecast of solar irradiance which is an integral part of the methodology,
follows.
Introduction 10
1.5 Resource Forecast
Dispatch of photovoltaic power is a difficult problem. This is largely due to the fact that short
term prediction of solar irradiance is difficult to predict. The wide variability of the cloud cover
and to some extent, the atmospheric condition makes it hard for any attempt at
parameterization of these phenomena. On the other hand, observed hourly global irradiance
data is available at many locations throughout the SOLMET network [206]. These data, as well
as the typical meteorological year (TMY) [207] data which provide the data for typical months
of a synthetic year, have proven to be useful in the past for PV array performance prediction
[228]. Such weather data are known to be used in many PV performance analysis models.
These models rely for their analysis on the past historical data and are therefore accurate only
in a most general sense with possibilities of wide statistical variability between the actual and
the predicted data.
It therefore seems only logical to assume that a typical synthetic year or a number of years
of historical data may only be useful to predict the average monthly or even daily PV array
performance. A time scale smaller than the day requires knowledge of the cloud cover and
their expected instantaneous changes. Chapter 4 of this dissertation discusses a novel
approach for the prediction of the solar irradiance in the sub-hourly time frame (3-10 minutes)
by means of a Box and Jenkins time-series analysis [37].
Introduction 11
CHAPTER 2
Recent Advances in Utility Integration
A considerable amount of work has been done on the integration of photovoltaic (PV) systems
with the electric utility. Such PV systems studied vary from simple residential systems to large
MW-sized central stations. The existing literature may be divided into three general categories
according to the nature of the study. These are:
• Systems Study
• Operations Study
• Planning and reliability study
Systems study belongs to a group where only the photovoltaic system is examined in the light
of the solar resource. Operational study comprises of the investigation into the specific nature
of the impact of the PV systems into the utility's existing network. Such effects may be
harmonics and power factor effects, generation scheduling effects, frequency control effects,
etc., all of which relate to the short term impacts. Planning and reliability study on the other
hand refers to the long-term impact on the utility. Factors that are of interest in this study are
Recent advances In utility Integration 12
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Avo.llo.lolllty Modeling
Annuo.l Production
Cost
Co.po.city Credit
long term expansion planning , capacity credit, reliability study, etc. The relationship among
these three avenues of research are illustrated in Figure 1.
The following discussion exemplifies the research literature available in each of these areas.
2.1 Systems Research
The survey is initiated with a number of reports from large central station power projects
which are already operating in interconnected mode with electric utilities. Other aspects of the
systems research are then explored.
PATAPOFF (212) discusses the design and construction process for three large photovoltaic
facilities in Lugo, Carissa Plains and Sacramento, California. These plants are operating as
central station power plants providing their host utilities with additional resources in their
energy mix. The Lugo facility is rated at 1 MW built by ARCO Solar and is interfaced with a
12 ·KV distribution system of the Southern California Edison Company at Hesperia, CA. The
monthly capacity factor of this plant has varied between 21% and 37% during its operation.
The author points out an important feature of the system - that of the coincidence of peak load
matching between the Edison company's summer loads and the PV output.
The plant at Carissa Plains is reported by the author to be a 6 MW rated system, also
constructed by ARCO Solar. The design is similar to the plant at Lugo, except that the system
uses reflector enhancements on its two-axis tracking arrays. Use of reflection mirrors
enhances the solar radiation incident on the modules by 80%. The net effect is reduction in
the number of modules needed. The plant is connected to the Pacific Gas & Electric
Recent advances In utility Integration 14
Company's 115 KV grid. The PV system shows a good match with summer-time peak demands
at this site as well.
The plant at Sacramento is rated at 1 MW and is supplying power to the Sacramento Municipal
Utility District (SMUD). The plant consists of one-axis tracking arrays and was constructed by
Acurex Corp. The author concludes that although some issues remain to be resolved, none
of them represent impediments to widespread use of PV. Low annual capacity factors are not
detrimental if availability is high when demand is the highest.
SPENCER [262) describes the SMUD project as being only a phase of the bigger 100 MW
project which was to be completed in 12 years period. At present, two of the phases are
operating and feeding power into the 12.47 KV SMUD distribution grid. Further development
has essentially been discontinued. The entire project was expected to cost $3.2 million per
MW. Each MW of PV power corresponds to roughly 9 acres of land area.
ARNETT et al. [9) describe the conceptual design, prototype testing, production, assembly and
installation of two MW-sized plants constructed by ARCO Solar. The two plants being the one
at Lugo, CA and the other at Carissa Plains, CA. The facilities employ structural mounting
systems for the photovoltaic modules which provide a means of tracking to enhance the daily
energy production of the PV power plants. Estimates of increased annual energy production
of upto 45% for the two-axis tracking over the fixed tilt arrays were projected.
CHEATHAM et al. [62) in elaborating on the Lugo plant and the Carissa Plains plant,
emphasize on advantages of a large MW-sized central station power plant. These are: (a)
Modularity, (b) environmentally benign, (c) low operating and maintenance costs, (d)
predictable reliability, (e) speed of installation and (f) system life expectancy.
LEONARD [183) attempts to answer some of the questions that need to be addressed before
PV can become economically and technically attractive. The author begins with an overview
Recent advances In utility Integration 15
of six existing utility interconnected projects and leads to the design study of a 100-200 MW
utility interconnected plant. It is pointed out that although the projected cost of completion of
the 1 MW SMUD plant at Sacramento was $12 million, actual costs incurred were less. This
data provides strong evidence that projections of the cost of a PV plant are likely to be quite
reliable in the future mainly because the cost of PV modules are on a downward trend. The
large-scale system design studies confirm that array fields in PV plants will almost certainly
be divided into a number of subfields, each with its own power conditioning subsystem (PCS).
With only a few exceptions, failure of a component will lead to the shutdown of no more than
one subfield and the loss of only 5-10% of the total plant output. Another conclusion of the
author is that no generally preferred array field design can be defined, because different array
concepts will be optimal in different utility systems (with different diurnal or seasonal demand
profiles).
A study conducted by SHUSHNAR et al [253) reveals that PV and area-related
Balance-of-System (BOS) costs make up 75% to 85% of the total costs in all cases considered
in the study. The study results indicate the high sensitivity of BOS costs to PV efficiency,
system configuration design and identify efficiency and configuration (fixed, tracking, etc.) as
the most effective avenues for system cost reduction.
SMITH (260) examines the economics of large-scale photovoltaic power generation and a
projected break-even cost for photovoltaic cell systems in the light of an electric utility's hourly
energy profile. The author concludes by saying that the PV system may prove to be
economical for utility systems where a substantial reduction in conventional power generation
is realized and the total PV system costs approach $0. 75 per peak watt. The analysis is based
on a 19% cell efficiency.
A number of papers have been devoted to improvements in power conditioning subsystems.
CHU et al (72) have studied several options for central station utility interactive power
conditioning. They have compared the development potential for two PCS designs, 50-500 KW
Recent advances In utility Integration 16
and 1-10 MW. The 1-10 MW sized PCS employs new switching devices which are faster and
can be switched at higher rates than those existing. Through the use of Pulse Width
Modulation (PWM), chopper waveshaping techniques, the need for magnetic filtering is
significantly reduced. Total harmonic currents are limited to 5% and the power factor is
maintained between 0.95 leading and 0.95 lagging during normal operation. Projected PCS
efficiencies are reportedly greater than 96% from one quarter to full load. PCS cost
projections are made at $0.07 to $0.12/W for the most probable combination of volume,
voltages and ratings.
In a similar study, KEY et al. (161) study and compare the designs of PCS units ranging from
ratings of 2 KW to 5 MW. Both line and self-commutated inverter designs for single and
three-phase applications are described. Both types of inverter designs have been used
successfully. The 1 MW line-commutated unit at SMUD achieved 97% efficiency and power
quality has been reported to be good.
KRAUTHAMER et al. [173) predict that the technical viability and to some extent, the economic
viability of central station PV generation will depend on the availability of large power
conditioners that are efficient, safe, reliable, and economical. The authors go on to overview
the technical cost requirements that must be met to develop economically viable PCS.
PICKRELL et al. (220) discuss the optimization of an inverter/controller design as part of an
overall photovoltaic power system (PPS) designed for maximum energy extraction from the
solar array. The special design requirements for the inverter/controller include: (a) a power
system controller (PSC) to control continuously the solar array operating point at the
maximum power level based on variable solar irradiance and cell temperatures and (b) an
inverter designed for high efficiency at rated load and low losses, at light loadings to conserve
energy. The authors found that although good overall immunity to transients is achieved in
utility line voltages, oscillations in the injected utility line power and solar array voltage are
Recent advances In utility Integration 17
encountered at low irradiance levels. The hardware manufacture of such a system is
realizable.
WOOD (290] proposes a new scheme for power conditioning in a central station PV plant.
Instead of each array subfield being served by an inverter, the author proposes that the
subfields be served by a de-to-de converter, a boost converter. The de voltage is increased
by a factor of 4-6 through the converter, and the transformed de is collected by an
underground distribution. A single transformation is then used to tie into the utility
sub-transmission or transmission system.
Several authors have discussed detailed design considerations for a multimegawatt-sized
central station photovoltaic system. STRANIX et al. (268] present a conceptual design of a 50
MW PV power plant based on the technology of thin film amorphous silicon (A-si) panels. The
design is for a location in New Jersrey; the performance evaluation based on actual
irradiance. The design criterion minimizes the installed plant cost per annual kilowatt-hour of
energy generated. Based on a design and performance evaluation, the input de voltage is 2000
Vdc while the ac output is 34 KV, 3 phase; the PCS delivers power at unity power factor over
the operating range; the annual energy production is 85.5 GWh at a capacity factor of 19.4%;
the costs are projected at 0.93-1.55 $/Wp (1982 dollars) intermediate and near term goals.
SIMBURGER et al. [255] presents a similar design study for a 200 MW rated central station
PV plant. The plant located at Barstow, CA (southwestern U.S.), uses fixed-tilt Oat plate panels
consisting of 8X20 ft arrays, with single crystal silicon cells. According to the authors, the basic
plant size for a commercial scale central station power plant is in the range of 200 to 300 MW.
The reason for this size selection is that the output of the PV plant is expected to be similar
to an intermediate load conventional fossil-fuel generating station.
JONES et al. (154) discusses a number of guidelines to be followed in the design of large
photovoltaic systems. The guidelines include considerations related to the selection of
Recent advances In utility Integration 18
collector type, array field configuration, hardware specifications, system installation and
checkout.
LEONARD (184] uses the basic computer simulation approach for the design of a central
station PV plant. The central element of the design process is a computer simulation of the
operation of the photovoltaic system at the assumed location. Hour-by-hour computation of
system performance are carried out with the aid of a mathematical model of the system and
an hourly representation of the irradiance to be expected at the site. The simulations are
carried out for a full year of simulated operations and yield as a figure of merit, the capacity
factor.
DEMEO et al. (89] describes a procedure for estimating capital costs of non-conventional, flat
plate photovoltaic central stations. According to results obtained by the study, acceptable
plant economics will require photovoltaic panel efficiencies in excess of 10%, and panel costs
near $10-$20/m2• Also, a key overall factor affecting the plant economics is the array cost per
unit area per unit plant efficiency. Any modification which reduces the factor without an
offsetting reduction in average irradiance will lower the plant capital cost. Another conclusion
that the authors derive is the fact that concentrator arrays may not be cost effective when
employed solely to reduce required cell areas.
POST et al. [224] provide detailed cost comparisons of five competing photovoltaic system
options for large sized PV power plants. The options include fixed tilt, one-axis tracking and
two-axis tracking flat-plate collectors as well as concentrators, utilizing linear and point-focus
fresnel optics. For a high insolation location, such as the southwest U.S., concentrator systems
offer a slight cost estimate for current PV technology. For the same location, however none
of the competing system options is a clear winner over the others for tomorrow's technologies
(mid 1990s). The system options depend on the site being considered for the installation.
Recent advances In utility Integration 19
ROSEN (238) calls for attention toward the balance-of-system costs as the next most important
cost element after the array cost. The author discusses development requirements with
regard to array design, de voltage level, array field grounding, power conditioning, operating
and maintenance requirements and system prediction. THOMAS et al. (274] reasserts the fact
that utility owned central station PV plant will constitute a major potential application in the
foreseeable future. The authors also point that solar availability dictates the allowable cost
of the PV system.
TAYLOR (99) in an EPRI report, states that after reaching compatibility between allowable
costs and achievable performance and price, the ultimate limits to penetration are likely to
be set by operational issues, like system reliability, dispatch, etc. The author lists a number
of implications of PV research and development. Among these, an important issue is the
establishment of a better solar data base, which can be used to determine requirements for
regulating capacity. These requirements can also be used to more accurately establish
generation expansion scenarios.
In another EPRI report (98) the authors discuss a new microcomputer based evaluation model
to determine the value of a PV plant to the electric utility. The model consists of a simplified
utility production cost code and a simplified PV system performance code. The model accepts
data on the existing generation mix(unit rating, fuel type, heat rate, forced outage rate and
monthly dispatch order), the electrical demand (hourly demand profile for a typical week in
each month) and the contribution from an alternative generation source (hourly for a typical
day in each month). For any given hour. the model dispatches units in a pre-specified order
to meet the hourly electrical demand (dispatch order in the analysis is based on the principle
of least cost generation). Upon meeting the load, the model checks the amount of available
contribution from the PV plant and displaces an equal amount of the last unit dispatched (the
marginal generation). The procedure is reiterated hour-by-hour for each typical week. The
simulation gives an estimate of the type and quantity of fuels displaced. Using the value
Recent advances In utility Integration 20
determined from the simplified production cost model, the authors obtain the allowable cost
of PV generation in cents per KWh.
A number of photovoltaic system simulation models are now existing in the literature. Shown
in Figure 2 are some of the better known models with their origins. Most of these models take
as input, the hourly irradiance and weather parameters at any particular site and simulate
hourly or daily photovoltaic output.
2.2 Operational Research
This phase of central station PV plants refers to the situation which is brought about when the
utility has already decided to install the PV plant and the problem is to find out the optimal
way to operate and control the output in real time. The problems associated are manifold.
The more important of those are: generation dispatch, load frequency control, power factor
control and system protection.
SIM BURGER et al. [254] present a new model which was synthesized in order to simulate the
operation of an entire electric power system. This model simulates the operation of the
generation system and the automatic generation control in response to changes in net
demand. When a large, widely varying power generation source like the PV system is added
to an existing system, the impact on this system would be the same as reducing the total
energy required from the remainder of the system while increasing the short term swings in
net system demand. A 24 hour simulation shows that with a 500 MW wind system, some
changes in base operating system need to be made. For example, a peaking unit of 500 MW
capacity would have to operate under AGC for the entire 24-hour period to accommodate the
Recent advances in utility integration 21
Model PV Performance Model Photovoltaic F-Chart Lifetime Cost & Performance Engineering & Reliability TRNSYS/MIT
Photovoltaic Analysis Model PVFORM - System Analysis Program Solar Cell Model (SOLCEL-11) Solar Energy System Analysis TRNSYS/ASU
PV Transient Analysis Prog.
Solar Reliability
Figure 2. System simulation models
Recent advances In utility Integration
Originator Electric Power Research Institute (EPRI) University of Wisconsin Jet Propulsion Laboratory (JPL) JPL University of Wisconsin MIT Lincoln Laboratory Solar Energy Research Institute (SERI) Sandia National Laboratory Sandia National Laboratory Sandia National Laboratory University of Wisconsin Arizona State University Sandia National laboratory BDM Corporation Sandia National Laboratory Battelle-Columbus Laboratory Sandia National Laboratory
22
wind power system. Also, some unscheduled interconnected power will have to be
interchanged, which might create area control error problems.
THOMAS et al. [275) investigate the potential impact of photovoltaic systems on the utility
operations. The results show that a small (1-4%) penetration of photovoltaic systems will not
adversely affect the utility operations even under the "worst case", which is a rapidly moving
cloud front. As individual plant size approaches ;:::- 5% of the control area capacity, difficulties
might arise. Some of the authors' recommendation for alleviating the problems are:
• Reduced energy density of the array field i.e., install 50 MW/mi2 as opposed to 100 MW/
mi2•
• Disperse the array field. Install four 25 MW fields instead of one 100 MW field.
• Forecast approaching cloud fronts via National Weather Service type data or from sensors
located in close proximity of the array field.
• Alter the generating types used for regulation to give an improved ramp rate during times
of problematic cloud movement.
PATAPOFF et al. [213) present the utility experience in the operation of a MW-sized plant. The
plant is the 1 MW PY station at Lugo, CA. The facility is interfaced with the Southern California
Edison utility company through a 12 KV/480 V delta-wye 1 MVA transformer. Protection
equipment include over and under voltage, over and under frequency and overcurrent relays.
During normal operation, either the two 500 KVA self-commutated inverters are operated in
parallel, or the 1000 KVA line-commutated inverter unit is operated. The total harmonic
distortion values ofthe self-commutated inverters are lower than those of the line-commutated
inverter at all power levels, for both current and voltage, but the level is not much of a concern
to the utility.
LEE et al. [182) p~esent a method for estimating the load following and spinning reserve
requirements for a power system containing intermittent generation. The authors incorporate
Recent advances In utility Integration 23
the generations in an optimal generation expansion planning model which evaluates the effect
of such requirements on the generation mix and the production costs. The authors use the
"negative load" concept in which intermittent generation is deducted from the load demand
at each hour. Load following and spinning reserve requirements are evaluated for the two
cases of with and without intermittent generations. The requirements increase linearly with
penetration of intermittent generations. According to the authors, the overall effect of
integrating the intermittent generations were: it increased the annual production costs,
decreased the annual fixed costs, and substantially reduced the energy and capacity credits
otherwise attributable to intermittent generations.
A number of studies have been devoted solely to the harmonics and power factor effects of
PV systems on the operation of electric utilities. CAMPEN (48], TAKEDA [270], TAKIGAWA et
al. (271], all report analysis of the effect of harmonics at different PV sites. COKKINIDES et al
(76] conducted experiments and simulation studies to investigate problems of interface, such
as harmonic generation and propagation, and safety assessment during faults. The authors
conclude that present technology of power conditioning units generate lower level harmonics
than those existing in the system from other sources. GUESS et al. [123]present the result of
a conceptual design study for a central station PV power conditioning system. The authors
propose promising methods for the power converters to minimize subsystem costs, harmonic
currents, and size, while maximizing efficiency.
2.3 Planning and Reliability Research
This phase of the research on central station PV applications is concerned with incorporation
of the new system into the various utility planning and reliability models. These models are
required prior to making decisions regarding the planning of electric power components,
Recent advances in utility integration 24
constructing components, continuing or delaying construction, etc. Two basic objectives have
to be satisfied in any such planning models.
• To serve the load most reliably, that is, with the least probability of losing the load or
failing to serve the entire energy requirement during the period of study.
• To accomplish the above with the least cost of generation.
The following is a discussion of the advances made in the field of incorporation of PV systems
in the planning and reliability models.
DAY et al. [88) discuss model extensions implemented to assist in determining the potential
value and reliability impact of solar plants. The principal computer programs used in the
study are: A production costing model, a reliability model, and a solar plant model. This
general procedure is useful in estimating the lifetime value of a solar plant to a utility system.
The framework provides a vehicle for assessing the value of either a single solar plant or a
number of them, independent of their cost projections. The initial step in the evaluation
process is to project future loads for all years in the expansion period. An optimal generation
expansion program is used to expand the conventional system without any solar plant
installations. The next phase involves the optimal expansion of conventional units in the
presence of a forced solar plant. Comparisons are then made between non-solar and solar
expansion plan installation schedules, capital and operating costs, and present worth of plan
revenue requirements.
SISSINE [257) discusses the issue of capacity credit for wind and other renewable power
sources. Although the paper deals mostly with wind systems, some of the suggestions made
by the author are equally valid for photovoltaic systems. Capacity credit for a conventional
thermal plant is determined on the basis of its capacity factor which ranges between 70 and
80%. However, the traditional capacity factor approach would be erroneous in determining the
capacity credit of wind systems. The major shortcoming of this approach is reportedly, its
Recent advances In utility Integration 25
failure to capture correlations of wind resource availability with utility loads. It is more
appropriate to use a method based on the reliability of the entire generating system.
Reliability analysis examines the difference in loss-of-load probability (LOLP) between two
arrangements of utility equipment: the existing arrangement (base case) and an expansion
arrangement that adds wind facilities to the base case. The change in LOLP due to the
addition of wind facilities gauges the reliability improvements which is equated to an increase
in system capacity. The ratio of this change in system capacity to the wind facilities' total rated
capacity is defined as their effective load carrying capability (ELCC) and represents their
capacity credit.
PESCHON et al. [219] discuss the development of new mathematical models for the economic
evaluation of intermittent sources of power. The purpose of these mathematical models are
to answer questions related to real-time operational problems, operating savings, economic
characteristics over a typical 20-25 year planning horizon and level of penetration. The
computer model makes feasible the simulation of the hourly operation of the combined system
for a complete snapshot year with and without the non-conventional source. With the reliability
criteria satisfied by the generation mixes with and without the non-conventional source, the
capacity credit is determined.
KU et al. [175] describe a methodology used for and the results obtained from a study for
assessment of the economic viability of long-range applications of PV generations in the
Public Service Electric & Gas (PSE&G) Co. at New Jersey. The authors develop a
mathematical and statistical process to convert actual irradiance data to hourly electric
energy production patterns for average days of each season. Using the PSE&G electric system
as a basis, they develop a long-range generation expansion scenario including advanced
design for combustion turbines (CT). The authors then substitute various amounts of CT
capacity additions with PV generating capacity which corresponds to different levels of PV
penetration. The authors then determine the amount of PV kw capacity required to replace
each kw of CT capacity in order to provide the same level of system reliability.
Recent advances In utility Integration 26
JORDAN et al. (155] describe the methodology developed for evaluating capacity factor,
effective capacity and total economic value of a PV system, when combined with other
generating units in an electric utility. The authors adopt a total system performance model
which consists of three models: the source performance model (wind or photovoltaics), the
reliability model, and the production costing model. The source model evaluates the total PV
power generations for a given system; the reliability model makes use of the long-established
loss-of-load probability method with modification to represent hourly variations in both load
and PV plant output, and the production cost simulation model is a standard production cost
program which has been in use for years.
DAPKUS et al. (80) describe a planning method which considers the uncertain and dynamic
nature of the decision process. A stochastic dynamic program is used to model uncertainty in
demand, the date of new technology (PV plant) commercialization, and the possible loss of
service of existing technologies due to accident, regulatory action or lack of fuel. In this
methodology, the state of the system at any time is completely defined by the number of units
of each type of technology, the availability status of each technology and the peak level of
demand.
CARAMANIS (50) discusses the methodology used in the software package, Electric
Generation Analysis System (EGEAS) developed for EPRI, by the Massachusetts Institute.of
Technology. EGEAS is a comprehensive planning package which can analyze
"non-dispatchable" (NOT) options in the utility. NOT refers to those generations which depend
on the weather, or nature, e.g., wind, solar, hydrothermal, etc. The author addresses the issue
of an additional source of uncertainty in NDT, besides equipment failure. The uncertainty is
due to energy source availability fluctuations arising from the stochastic nature of wind speed,
irradiance, river flow, etc., affecting the output from a particular NDT. This random variable is
interdependent with system load fluctuations. This particular relationship is identified in the
methodology. The rest of the methodology follows any standard optimal expansion program.
Recent advances In utility Integration 27
FINGER [109] presents a production costing methodology which can also model solar power
generations as well as other non-conventional sources or energy. The treatment or solar
generations is deterministic. In other words, the hourly load demands are modified
chronologically by solar generations.
SINGH et al. [256] discuss a methodology which evaluates the reliability of electric power
systems having PV plants. Two groups are created, one each for the conventional generation
system and the other for the non-conventional generation system. A generation system is
created for each group. The models of the non-conventional group are modified hourly
depending on the limitations of energy. All the models are combined hourly to find the loss
of load expectations and the frequency of capacity deficiency for the hour in question. This
procedure is accomplished using a discrete state algorithm as well as the method of
cumulants.
STEMBER [265] presents two techniques for modeling the availability and maintenance costs
of photovoltaic power systems. The term 'availability' refers strictly to the hardware system.
The two basic availability models are: a simulation technique using the GASP-IV language,
and an analytical approach using state space techniques. The simulation model developed is
SOLREL [266]. It uses event-by-event simulation to represent the 30 year life of the system
with individual reliability and maintenance events modeled with statistical distributions.
UNIONE et al. [278] discuss the availability as a measure for estimating the expected
performance for solar and wind powered generation systems and for identifying causes of
performance loss. The authors discuss models ranging from simple system models to
probabilistic fault-tree analysis. They develop a methodology incorporating typical availability
models for estimating reliable plant capacity.
Recent advances In utility Integration 28
2.4 Economic Dispatch With PV Plants
Economic dispatch is defined as the process of allocating generation levels to the generating
units in the mix, so that the system load may be supplied entirely and most economically. A
general survey of the economic dispatch methods now existing, is done along with the studies
done on integration of photovoltaic systems into these dispatch algorithms. The research
study shown here are those published after the comprehensive survey done by HAPP [125)
which was published in 1977. Since then, substantial work has been published in this area,
particularly in the area of modernizing the AGC.
HAPP [125) reviews the progress of optimal dispatch from its inception to its present day
status. As presented by the author, economic dispatch dates back to the early 1920's or even
earlier when engineers already concerned themselves with the problem of the economic
allocation of generation or how to properly divide the load among the generating units
available. Prior to 1930, various methods were in use, such as: (a) the base load method
where the next most efficient unit is loaded to its maximum capability, then the second most
efficient unit is loaded, etc., (b) "best point loading", where units are successively loaded to
their lowest heat rate point, beginning with the most efficient unit and working down to the
least efficient unit, etc. It was recognized as early as 1930, that the incremental method, later
known as the equal incremental method, yielded the most economic results. The theoretical
work on optimal dispatch later led to the development of analog computers for properly
executing the coordination equations in a dispatching environment. A transmission loss
penalty factor computer was developed in 1954 and was used by AEP in conjunction with an
incremental loading slide rule for producing daily ger:ieration schedules in a load dispatching
office. An electronic differential analyzer was developed for use in economic scheduling for
off-line or on-line use by 1955. The use of digital computers for obtaining loading schedules
was investigated in 1954 and is used to this day.
Recent advances in utility Integration 29
BOSE [35) examines the impact of new generation technologies on utility operation practices.
While not dealing in extent with any particular technology, the author discusses the general
characteristics of each potentially viable new generation source. The scheduling practices
considered, range from load frequency control and economic dispatch to the weekly (short
term) and yearly (long term) scheduling of generating units. The impact of new technologies
is predicted to be significant, the exact effects depending on the level of penetration, the
extent of dispersion, ownership, and the weather dependency of the technologies selected.
WAIGHT et al. (285) have used the Dantzig-Wolfe decomposition method to resolve the
economic dispatch problem into a master problem and several smaller linear programming
subproblems. The algorithm that that they have followed is as follows:
• Decompose the problems into n subproblems and a master problem.
• Choose the initial basis of the master problem by introducing artificial variables and
setting up the appropriate Phase I (feasibility) and Phase II (optimality) objective
functions.
• Compute an objective function for each subproblem and solve each subproblem using the
revised simplex method.
• Calculate the relative cost factors for all subproblems. If all are positive, stop since
optimality has been reached. Otherwise, reiterate with new simplex multipliers.
The authors claim that with this decomposition technique, a significant advantage can be
achieved in terms of computer timing and storage.
ISODA (144) recognizes the response limitations of generation units in the mix and assesses
its impact as well the impact of short term load demand forecast on the economic dispatch
scheme. The author claims that with short term load forecasts available, the manual operation
(by operator) to regulate the power generations of the thermal units when the load changes
steeply for a long time is reduced. According to the authors, the optimum forecast period is
Recent advances In utility Integration 30
approximately one hour in which the load demand should be forecast for a total of 4 to 6
points. Application of the method is also possible in an on-line dispatching control in electric
utilities.
LEE et al. (182] have investigated the load following and spinning reserve penalties for
intermittent generation in the economic evaluation of such sources in the presence of a
conventional generation mix. They present an approach estimating the load following and
spinning reserve requirements for a power system containing intermittent generation. They
incorporate this in an optimal generation expansion planning model which evaluates the effect
of such requirements on the generation mix and the production costs. The authors claim that
the penalties are too high due to the presence of intermittent generation and that all energy
and capacity credits are eliminated due to such penalties. According to a case study
performed by the authors, increasing penetration of intermittent generation (wind powered
system in the case study), causes an increase in the spinning reserve requirements and the
load following requirements, the increase being linear. The effect of penetration on system
costs is found to be non-linear. For their case study, below 5% penetration, the load following
requirement is satisfied by the optimal generation mix, the penalty cost arising primarily due
to increase in spinning reserve requirement. Beyond 5% penetration, the load following
requirement begins to alter the generation mix, with the consequence that the penalty cost is
greatly increased due to the combined effect of higher spinning reserve and the departure
from the optimal generation mix, imposed by the load following constraint.
STADLIN [263] incorporates an additional constraint into the economic dispatch optimization
process, that of regulating margin. He introduces the term µ to be the Lagrange multiplier
representing the incremental cost of regulating margin in dollars per megawatt-hour. This is
used in addition to the Lagrange multiplier A. which is defined' as the incremental cost of
delivered power in dollars per MWh, in the classical /..-dispatch solution of the economic
dispatch problem. Modification of the conventional incremental cost is therefore accomplished
by introducing a regulating margin cost penalty. For example, an increase in µ causes an
Recent advances In utility Integration 31
increased incremental bus cost for high load levels which will tend to retard normal economic
loading to produce extra "raise" regulating margin.
RAITHEL et al. (230) introduce a successive approximation dynamic programming to obtain
the optimal unit generation trajectories that meet the predicted area load. They use "dynamic"
optimization as compared to the "static" case, as the dispatch program determines the
economic allocation of generation for the entire future period of interest, using knowledge of
both the present and the predicted load . The look-ahead capability provides the advantage
of responding to sudden severe changes in load demand. They adapt the successive
approximations dynamic programming algorithm to handle valve-point loading of units.
Valve-point loading is accomplished via the representation of the valve point in the unit
production cost function.
CHALMERS et al. [60) evaluate the effect on utility operation of photovoltaic generations that
is interconnected to an electric utility grid. The authors study various PV concentrations and
performance characteristics on generation control. Their results show that PV generation can
be integrated into the utility system in substantial amounts without creating any unusual
problems in system operation and control. The most severe condition as reported by the
authors is created when the entire PV array is completely covered and uncovered by a fast
moving cloud cover. Their simulation results show that the NERC limit is exceeded for PV
sizes of 100 MW (5.5% penetration) or more, in the winter, during conditions of the cloud cover
moving away from the sun. The penetration limit for the PV system is somewhat higher for
the case when the sun gets covered suddenly by a large cloud cover.
SAMUAH et al. (243] reformulates the economic dispatch problem by introducing an added
constraint on maximum frequency deviation following a postulated disturbance. The significant
improvement in average system frequency deviation response is found to be at the expense
of increased operating cost. The main difference between the frequency deviation constrained
dispatch and the conventional economic dispatch is the allocation of the total system margin.
Recent advances in utility Integration 32
In the latter case, the margin allocation is made without explicit consideration of the minimum
frequency following a specified disturbance. The margin is usually carried by a few units. On
the other hand, with a tight minimum frequency limit imposed, the allocation is made so that
the system margin is distributed among more units with the faster units carrying relatively
larger portions. The method of solution adopted by the authors is a Dantzig-Wolfe
decomposition technique followed by several linear programming solutions. An algebraic
formula is developed for the maximum frequency deviation.
KAMBALE et al. (156) discuss the problem of tracking economic target curves, produced by
an economic program. In tracking the target curves, unit dynamics including boiler dynamics,
are taken into account. The problem is decomposed in such a way that the slower bulk control
is based on a fully non-linear and dynamic model of the unit while faster load fluctuations are
traced by fast, dynamic vernier control based on a linearized model. This, according to the
authors, results in fuel economy coupled with tight and smooth control, which demands
moderate computational load. Three stages of control are identified arising out of three
components of load. The first stage has a 24-hour horizon and load needs to computed once
in 24 hours. Stage 2 has a 0.5-1 hour time horizon and the load component estimate is
recomputed every 2-5 minutes on line. The third stage is represented by the random load
generation component having a time horizon of 15-30 seconds. The load component in this
stage is recomputed once every 2-4 seconds. All control operations are divided into these
three stages.
LIN et al. (186) present a real time economic dispatch method by calculating the penalty
factors from a base case data base. The basic strategy of the proposed method assumes that
a base case data base of economic dispatch solution is established according to statistical
average of system operation data of the daily demand curve. Solutions in the data base can
either be calculated by the B-coefficients method or other existing methods in the literature.
Recent advances In utility Integration 33
PATTON (214) introduces the concept of dynamic optimal dispatch as opposed to the static
optimization, which does not consider the effect of change related costs. The dynamic optimal
dispatch method uses forecasts of system load to develop optimal generator output
trajectories. Generators are then driven along the optimal trajectories by the action of a
feedback controller. Optimal trajectories are first calculated for nominal load forecasts using
quadratic programming or gradient projection methods; then they are updated using
neighboring optimum methods as load forecasts are revised through time. Studies of small
system indicate that the dynamic optimal dispatch may be economically attractive. Savings
of upto 1 % of total fuel consumption is possible with this approach over the static approach.
WOOD (291) proposes a new methodology to incorporate· reserve constraints and goes on to
prove that this methodology is more efficient than that introduced by (Stadlin]. He shows a
technical solution to the reserve constrained problem which can be achieved with a very
efficient use of computer resources. The problem is expressed as a dynamic programming
scheduling problem and a feasible, but suboptimal solution is proposed which eliminates the
usual search space problem. This method reduces the problem to a backward sequence of
dispatch problems, with the generator limits being carefully adjusted between each time
interval in the solution sequence.
BOSCH (35) also presents a solution to a dynamic optimal dispatch constrained by reserve
and power rate limits. The solution is obtained with a special projection having conjugate
search directions that quickly and accurately solves the associated non-linear programming
problem with upto 9600 constraints. The proposed methodology reduces fuel costs by about
0.5%.
RAMANATHAN (231) discusses a fast solution technique for economic dispatch, based on the
penalty factors from Newton's method. The algorithm uses a closed form expression for the
calculation of Lambda (Lagrangian multiplier), as well as takes care of total transmission loss
changes due to generation change, thereby avoiding any iterative processes in the
Recent advances in utility Integration 34
calculations. In this algorithm, a major portion of the calculation time is spent on performing
penalty factor calculations and is the same regardless of the calculation technique. Since, no
iterations are involved, there are no oscillations or convergence problems in the execution
of the algorithm.
ROSS et al. (239) discuss the application of a dynamic economic dispatch algorithm to AGC.
When coupled with a short term load predictor, look-ahead capability is provided by the
dynamic dispatch, that coordinates predicted load changes with the rate of response
capability of generation units. The dispatch algorithm also enables valve-point loading of
generation units. The method that the authors use in their dispatch algorithm makes use of
successive approximations dynamic programming. The authors claim that the algorithm is an
improvement over the existing dynamic dispatch algorithms, in that the computer resources
required are modest.
AOKI et al. [6] present a new method to solve an economic load dispatch problem with de load
flow type network security constraints. The network security constraints represent the branch
flow limits on the normal network and the network with circuit outages. Hence, the problem
contains a large number of linear constraints. In power systems, only a small number of flow
limits may become active. Computationally, since it is inefficient to deal with such constraints
simultaneously. the authors have extended the quadratic programming technique into the
parametric quadratic programming method using the relaxation method. The memory
requirements and execution times suggest that the method is practical for real-time
applications.
BECHERT et al. [19) point out the problems of applying solutions of static optimization
techniques used for solving economic load allocation, into the feedback control of dynamic
electric power networks. Their research attempts at overcoming the disadvantages of such
controllers by combining economic load allocation and supplementary control action into a
single dynamic optimal control problem. Power interconnection is partitioned into the
Recent advances In utility Integration 35
electrical network subsystem plus separate control area subsystems, each of which then
constitutes a separate control problem. The electrical network subsystem is solved to find the
shaft power required from each control area, such that network frequency and tie-line power
errors may be minimized. The demand signal then serves as a target toward which each
control area's power output is driven.
BRAZZELL et al. [41) present a computerized algorithm of scheduling generation for
contingency load flows, used in planning studies taking into account the operating constraints
such as economic dispatch and regulating reserves.
VIVIANI et al. (283) present an algorithm to incorporate the effects of uncertain system
parameters into optimal power dispatch. The method employs the multivariate Gram-Charlier
series as a means of modeling the probability density function which characterize the
uncertain parameters. The sources of uncertainty are identified as those emanating from long
and short term forecast errors; measurement or telemetering errors and system configuration
error. The energy system parameters are grouped into state vectors and control vectors. The
Gram-Chartier series is employed to statistically model the control vector, which consists as
elements, the generator power and voltages at each bus.
INNORTA et al. (142) discuss a method of redefining the optimal and secure operation
strategies, a very short period in advance by exploiting the availability of the on-line state
estimation and load forecasting. An H Advance Dispatching" (AD) activity is added in the
system control hierarchy between the day before scheduling and the on-line economic
dispatch. The authors prove that AD can be very effective for supplying security constrained
participation factors to the regulating units when economic dispatch is operating and also
improves system operation when economic dispatch is not available. More precisely, AD
modifies the day before scheduling by supplying the optimal trajectories of the thermal units
over very short time periods, taking into due account, the load predictions (30 minutes ahead)
and the actual security constraints which include dynamic limitations upon the rates of change
Recent advances in utility integration 36
of the thermal generator MW outputs. The authors use an on-line parametric linear
programming algorithm for the AD model.
CARPENTIER [54) reviews the potential applications of modern proposals for AGC as opposed
to the conventional methods. The conventional implementations generally use
integro-proportional control derived from the servo-mechanism theory. The modern proposals
employ optimal power flow techniques. The author discusses the primary, secondary (LFC)
and tertiary (ED) controls in a single system using conventional AGC. During the tertiary
control, economic dispatch owns the cost curves in its memory, receives the electric powers
of these units and computes the economic participation factors for each units, in order that
resulting operation should be the most economic possible. The computation is static and is
usually taken into account but not transmission security. Modern AGC systems, on the other
hand, allows system constraints to be taken into account, particularly transmission security
while improving economy and even transients, e.g., through solving the LFC-ED interface
problems. Moreover, optimal power flow techniques may be combined with the results of
optimal control theory to further increase the quality of the transients.
2.5 Conclusions
Two points are very clear from the survey of the recent advances in integration of PV systems
in an electrical utility's generation system.
• Although PV economics, dictated by array costs, has been targeted as a primary concern
for increasing penetration, it is obvious, that many technical problems need to be
answered, particularly in the area of real-time operation of PV systems with a
conventional system.
Recent advances In utility Integration 37
• At present, the PV generations, if any exist are handled in a static manner in utility
operation. In other words, they are forced on the power system and the latter is expected
to accomodate the presence of PV. Most studies consider hourly PV output during their
operation in the utility and these are assumed to be constant throughout the hour.
Although, this procedure may be adequate on a clear day, it is likely to create problems
on a cloudy or partly cloudy day, when hourly estimates of PV output produces large
errors when compared to the instantaneous values, because of high amount of variations
in the solar irradiance.
• Advanced automatic generation control algorithms utilizing state-of-the-art control
technology are now available. These algorithms may not be appropriate for handling
intermittent power generations from PV systems. Modifications need to be made on the
existing algorithms or new and efficient algorithms need to be developed.
There is no question that the overall utility system planning, including reliability and capacity
credits will depend on the real-time operating characteristics of the PV plants. At this point,
as it stands, central station PV systems have been limited to less than 5% penetration of the
generation capacity before operational problems become significant. This translates to a PV
plant capacity of less than 500 MW or less for large electric utility systems. Although, in the
light of present day's technology standards, this figure seem relatively high, it certainly would
look quite modest in a few years time.
Recent advances In utility Integration 38
CHAPTER 3
Optimizing PV Output in the Utility
Solar radiation, also termed as irradiance, reaching the surface of the earth is a general term
for the global horizontal lrradiance received on the ground. Global horizontal irradiance can
be decomposed into two general components, the direct normal irradiance component and the
diffuse irradiance component. The relationship is depicted more clearly in Figure 3.
Extraterrestrial radiation refers to the solar radiation above the atmosphere of the earth. The
transmission of solar radiation through the atmosphere is mainly dependent on three factors:
• scattering by the molecules (Rayleigh scattering),
• scattering and absorption by solid and liquid particles, and
• selective absorption by gaseous constituents.
As shown in the figure, the scattered radiation is called diffuse radiation. A portion of this
diffuse radiation goes back to space and a portion reaches the ground. The radiation arriving
on the ground directly in line from the solar disk is the direct normal or beam radiation. A
knowledge of both direct and diffuse irradiance components is very essential for the design
of photovoltaic systems. Unfortunately, solar data availability around the U.S. has been a
Optimizing PV output 39
I I Extra terres t ri a I
Radiation
. . . . . . . . :··Diffuse:.·
: Scattering ... 11·· ...... ·.·· Reflected \ \ Direct
Radiation
Atmospheric Absorption Warming of Air
by Surface Diffuse Raid1ta~tion ____ ... Total
~,___ )-Rad1at1on
Direct, Diffuse, and Total Solar Radiation
Figure 3. Solar lrradiance components.
Optimizing PV output 40
major constraint in the design of such systems. At most sites, only the global horizontal
irradiance data is measured, at the hourly or daily time scale. Direct and diffuse components
are rarely recorded anywhere. PV system designers therefore have to rely on estimates of the
diffuse irradiance given by prediction techniques. The basic procedure is to develop
correlations between the global irradiance and its diffuse component using measured values
of these two components at those sites which do record both quantities, and then to apply
such correlations at locations where diffuse radiation data are not available. The quantities
which are generally correlated can be divided into the four following groups:
1. Correlations between the daily global irradiance H a~d its diffuse component Hd.
2. Correlations between the monthly mean daily global irradiance Fi and its diffuse
component Hd.
3. Correlations between the monthly mean hourly global irradiance i and its diffuse
component Id.
4. Correlations between the hourly global irradiance I and its diffuse component Id.
Such correlations have been studied by a number of authors over the past few years.
References [77, 103, 187) provide detailed discussion of these relationships.
The diurnal variation of solar irradiance depends on the position of the sun relative to the
receiving plane throughout the day. The seasonal variation is brought about by the difference
in the orientation relative to the sun as seasons change. Figure 4 shows the relationship of
the sun's position with an inclined plane. As will be obvious later in this section, an inclined
plane receives more energy throughout the day, than a horizontal receiving plane.
Mathematical relationships govern the specific geometry shown in the figure. The
relationships are different for the different array orientation employed. Equations governing
this sun-earth geometry are given in Appendix A.
Optimizing PV output 41
Sun
~ r.e 01 s.1;r.t to the sun-coserver at 0
Figure 4. Position of the sun relative to an Inclined plane
Optimizing PV output
!-'cr1zonta1 suriace
\ \
Hcrizontal ;i1ane c.:i
eartn s st..:r~ace
42
3.1 Array Orientation Strategy
Realistic PV systems are oriented at particular tilt angles so as to optimize the solar
irradiance. There are a number of options that the designer might choose for the system.
These options are generally dictated by cost-benefit ratios. Figure 5 shows the options that
may be used to configure the PV array. Besides, among the systems options, the designer
may choose one of two types: (a) flat plate and (b) concentrators. The choice of the right
option in both the orientation and the system is a matter of simulating the relative
performances throughout the year with long term data at any location. The performance
characteristics are believed to vary considerably from location to location. While the
southwestern U.S is well suited for concentrator technology, the same is not true for the
southeast or northeast. The reason is that, the southwest receives more direct normal
irradiance annually. Array orientation strategies may strictly be based on array structure
costs. While the two-axis tracking array orientation requires a computer controlled automatic
tracker system, the simple fixed surface orientation does not incur the extra costs of tracking.
On the other hand, energy collected by a 2-axis tracking system may prove to be twice as
much as the fixed surface array during the year.
Two mathematical relationships which figure prominently in simulating the performance of an
array oriented in one of the ways described in Figure 5 are shown below:
1. Angle of incidence of solar radiation on a horizontal surface:-
cos eh = sin 0 sin <p + cos 0 cos <p cos co = sin a = cos 0z (3.1)
Optimizing PV output 43
Option
1. Fixed surface
2. Monthly tilt on Fixed surface
3. Monthly tilt on 2-axis fixed surface
4. North-south axis tracking
5. East-west axis tracking
6. Polar-axis tracking
7. Monthly tilted with vertical axis tracking
8. Two-axis tracking
Figure 5. Array orientation options
Optimizing PV output
Description
PV modules mounted horizontal to the surface
Monthly tilt adjusted on modules facing south
Monthly tilt and azimuth adjustment on PV modules
Modules track the sun about a north-south axis with the entire plane tilted
Modules track the sun about an east-west axis
Modules track the sun about a polar axis
Modules track east-west on a vertical axis with optimal monthly tilts applied on the modules
PV modules constantly updated maintaining it parallel with sun's rays
44
where:
eh = incidence angle on horizontal.
ez = zenith angle.
a = elevation angle of the sun.
5 = solar declination.
<p = latitude at the site.
co = hour angle = cos- 1( - tan <p tan 5)
2. Angle of incidence of solar radiation on a tilted surface:-
COS et = COS a sin p COS(y5 - y) + sin a COS p
where:
e, = incidence angle (angle between direction of the
sun and normal direction of the surface).
Ys = solar azimuth angle.
= sin-1[ cos 5 sin co] cos a
y = surface azimuth angle.
p = slope of the planar array.
(3.2)
(3.3)
Three of the most important array orientations for central station PV systems and results of
actual simulations are discussed next.
3.1.1 South-facing array
Optimizing PV output 45
320
i 240 ~
~ a.. ~
0
> 0... 160
80
S oulh facing 2 axis traclang
;\ I \ /"-:;
I \t. \ I I I I I I I I I
Op!1mal az1mulhm
\ ~
\ ('.\ '(
'.\
'.\
'.\
'\ '\ \ \
0 .._~..._~..__~..r..:-~...._~....._~_,_~_._~_._~_.__.__._~_._~_, 0 4 8 12 16 20 24
Holl' or day
Figure 6. PV output comparisons for fixed tilt, azimuth-optimized and fully tracking arrays for August at Raleigh, NC
Optimizing PV output 46
320
i 240 ~
~ a.. ~
0
> a. 160
80
4
s oulh racing 2 axis traclang
I f I i I i I i i
8
/. r
\
12 Ho1r or day
\ \ \ \ I I I \ \
16
I \ \ \
20 24
Figure 7. PV output comparisons for fixed tilt, azimuth-optimized and fully tracking arrays for November at Hesperia, CA
Optimizing PV output 47
This is the most typical orientation for PV arrays in the northern hemisphere. The installation
requires only a simple tilting structure. Use of the solar geometry and weather data at
Raleigh, NC, latitude 35.75 ° , shows the fact that the optimal tilt angle varies for each month
from 60 ° in January to 5 ° in June and back up to 60 ° in December. The surface azimuth angle
in each case is held at O 0 • Therefore in order to obtain the maximum available solar energy
every month, it is required to change the tilt angles according to the figures obtained. On the
other hand, it may be desirable to leave the array facing south at one specific tilt angle
throughout the year. Then a new tilt angle may be found which optimizes the annual output.
In this case for Raleigh, this angle is 30 °. The curve in Figure 6 shows, among other things
the PV output from a south facing array on a typical day in the month of August at Raleigh.
To show the effect of site diversity , similar results are also shown for a site at Hesperia, CA
in Figure 7. The month shown here is November. An annual tilt angle also of 30 ° is used at
this site as well.
3.1.2 Optimal-Surface-Azimuth Oriented Array
Since maximizing PV output at noon time may not necessarily be of primal importance to a
utility with a load shape peaking at another hour besides noon, it is only natural to try and
maximize the PV output at or close to the hour of peak demand. It is found that this can be
done by changing the surface azimuth angles as required to an angle suitable for maximizing
the PV generations at any prescribed hour of peak load. This strategy is a special case of
option 3 shown in Figure 5. The orientation strategy is of course inherently linked with the fact
that the overall energy generated during the day is less than that generated by a south-facing
array. Also because of the diurnal nature of the solar radiation, optimal orientation is not
possible for peak demands occurring after 1600 hrs and in these situations it is better to leave
the array facing a direction optimal for the 4 PM peak.
Optimizing PV output 48
Results of maximizing the irradiance at the 16th hour of the day in August at Raleigh is shown
in Figure 6. Similar results of maximizing at the 13th hour of the day in November at the
Hesperia site is shown in Figure 7. Needless to say that the reason why these particular hours
are chosen for maximization is the occurrence of the peak demands at those hours. For the
Raleigh site, the optimal tilt angle and the optimal surface azimuth angle are found to be 40
0 and 80 ° west of south respectively for the month shown in the figure. At the Hesperia site,
these angles are determined to be 50 ° and 10 ° west of south respectively.
3.1.3 Two-axis Tracking Arrays
In this orientation strategy, the array is always facing the direction of the sun for maximum
solar radiation at every hour. In other words, the incidence angle is constantly held at O 0 • This
strategy requires the use of expensive tracking mechanism in both the horizontal and vertical
axes.
The output from a two-axis tracking array model at the Raleigh and Hesperia sites are shown
in Figure 6 and Figure 7 along with the outputs from the other two strategies of array
orientation. From the figures, it is obvious that two-axis tracking provides much more energy
during the day than either the south-facing or the optimal fixed surface azimuth arrays.
However, the peak power generations are the same for all three. It will be seen in a later
analysis that the peak generation at a desired hour is of greater importance than the total
energy generated during the day in the case of utility integrated PV systems combined with
a battery plant meant specifically for supply side load management. More specifically, to
shave an equal percentage of the peak load, the battery size requirement actually increases
with a two-axis tracking array option than either of the other two.
Optimizing PV output 49
3.2 PV Pet1ormance Simulation Model
Simulation programs are essential for evaluation of the hourly performance of PV systems
given the historically observed irradiance data, the ambient temperature data and in some
cases, the wind speed data. The purpose of the simulation model is to calculate hourly
plane-of-array irradiance at pre-specified tilt and azimuth orientations of PV arrays. Thermal
models are then used to model cell temperatures at each interval of the simulation and
various efficiencies are then calculated with the help of reference efficiencies. DC power
output is calculated as a product of these efficiencies and the modular area of the PV array.
DC/AC inversion efficiencies are either input as a curve or in the form of a regression
polynomial. The major blocks of the performance simulation model are shown in Figure 8.
Block A in the figure, is concerned with the availability of atleast a full year's worth of
irradiance and weather data at the site. The translation of horizontal irradiance on to tilted
surfaces is accomplished in block B. The irradiance on a tilted surface is also known as
plane-of-array irradiance. Each component of the horizontal global irradiance get translated
in a different way. While the direct normal irradiance on the plane-of-array depends only on
the solar zenith angle, the same is not true for the diffuse irradiance component. There are a
number of techniques proposed by different authors for this purpose. Some of the more widely
used models are discussed in the following section.
Block C is the cell temperature model. A cell temperature model is required because the
currents and voltages developed in a solar cell is a function of the cell temperature. Solar
irradiance, ambient temperature and wind speed have a combined effect on the cell
temperature. Some researchers do not consider wind speed in their modeling, and predict a
linear relationship between cell temperature and the solar irradiance. A commonly used
relationship is:
Optimizing PV output 50
Hourly Gloloo.I Hortzonto.I lrro.dlcrnce, 1 Direct Irraolto.nce, AMlolent T eMpero:ture
o.nd \/Ind Speed
CoMpute Plo.ne-of-o.rro.y 2 Irro.cllo.nce
I CoMpute Module TeMperature 3 I
4 CoMpute DC Power
CoMpute AC Power 5 Using PCU EfflClency Curv1r
Figure 8. Functional blocks in a PV simulation model
51 Optimizing PV output
Tc= Ta+ 0.3A (3.4)
where:
Tc = cell temperature
T. = ambient temperature
A = plane-of-array irradiance
Some consider a more complex thermodynamic relationship between these parameters and
also the wind speed. One of such study is reported by FUENTES (185).
Block D is the array electrical model. This model calculates currents, voltages and peak power
using the output from block C. The power conditioning model is incorporated in block E. Here
de power is converted to ac for use in supplying directly to the grid or after a voltage boost.
3.2.1 Translation of Horizontal lrradiance on the Plane of Array
The plane-of-array irradiance models play a vital role in the design, simulation and
operational studies of a solar photovoltaic system. These models are developed to calculate
the amount of energy available from the sun at a given hour on a surface tilted at any angle
from the horizontal and facing a given direction. The electrical output from a PV system is
directly effected by the amount of insolation received on an inclined plane.
Almost all factors other than the plane-of-array irradiance, are either constants or vary
predictably depending on cell structure, ambient temperature, area of the array, etc. The final
optimal array orientation strategy that must be decided upon, is influenced by the prediction
available from a plane-of-array irradiance model. For example one has to choose one from the
eight array orientation options shown in Figure 5. All of those orientations need translation
of horizontal irradiance onto tilted surfaces. Knowing the importance of plane-of-array
Optimizing PV output 52
irradiance, it becomes imperative to find a model which can accurately predict the irradiance
on such surfaces.
For design analysis, long-term monthly plane-of-array irradiance models have been found to
be adequate. But analytically, the performance of these models is not known when operational
considerations become important. A change in the time frame is therefore required and daily
and hourly models need to be assessed for their performance. The study sequence adopted
is mentioned below for clarity:
• Four models are compared to determine their applicability on a monthly basis.
• After an acceptable model is found whose predicted output matches the field
observations, a shorter term analysis is performed using models on a daily or hourly
basis to find the best model which matches the observed data.
In choosing the models for study, care is taken so as to include both isotropic and anisotropic
models which are also well known and have been widely used in the literature for solar energy
design and operational studies. The models selected for this study are:
• Liu & Jordan (188)
• Duffie & Beckman (94)
• Klucher [169], and
• Perez (218].
Generally, the direct normal irradiance on a horizontal surface is translated onto tilted
surfaces by multiplying with a factor, (cos i/ cos i) (188), where i is the incidence angle on a
horizontal surface and it, the incidence angle on the tilted surface. The diffuse sky component
is where most authors differ in their opinions. Some have suggested a simplistic isotropic sky
condition (188), and many have presented different forms of anisotropy for the diffuse sky
(169,218,273). It would seem that the translation models ought to be of the split transposition
Optimizing PV output 53
type where direct and diffuse irradiances are modeled separately assuming the availability
of both types of data. But unfortunately, both the direct and the diffuse irradiance data are
rarely available throughout the U.S., much less the rest of the world. In this situation, only the
global horizontal irradiance (a commonly measured item at numerous locations) are used in
various estimation models given in references (77], (188] to estimate the diffuse component.
Under these circumstances, all translation models are effectively reduced to simple
transposition models considering the global-on-horizontal to global-on-slope relationship
used.
3.2.1.1 Liu and Jordan Model
This model [188] is used in the daily and monthly time frames. This model is valid only for
surfaces facing the equator. The conversion factor R for the daily total radiation is given as;
Hr Hd Hd R = - = (1 - -)Ro + -Rd + R H H H P
where
R0 = conversion factor for the direct normal irradiance
= cos(q> - P) [ si.n C05 - C05 cos co'5 J cos <p sin co5 - co5 cos co5
= cos(<p - P> [ si~ ro'5 - co'5 cos co'5 ]
COS <p Sin C05 - C05 COS C05
Rd = conversion factor for the diffuse sky component
= _!_(1 + cos p) 2
and RP = conversion factor for the ground reflected component
Optimizing PV output
(3.5)
(3.6)
(3.7)
(3.8)
54
= ~ (1 - cos p)p; (3.9)
p = reflectivity (albedo) of ground.
The conversion factor R for the monthly average daily irradiance is the same as 3.10, except
that the daily terms are replaced by the monthly average terms.
3.2.1.2 Duffie and Beckman Model
Duffie and Beckman (94) have presented a model for estimating factor R. They have used an
isotropic diffuse sky model and in contrast to the Liu and Jordan model, this model is claimed
to be able to handle any surface orientations including south-facing, east or west facing arrays
or any other surface azimuth angles. This model, like the Liu and Jordan model also requires
long-term historical data for global irradiance. The diffuse component on the horizontal
surface is determined from equations 3.5 and 3.6, similar to the Liu-Jordan model. The
difference in the two models lies in the treatment of the direct term. Klein and Theilacker
(167), have developed an algorithm for this term. The model is given as follows:
- Fid R =D+-Rd+R H P (3.10)
where
max{O, G(ross,ros,)}
D = (3.11)
Optimizing PV output 55
Hd a'= a - -=-H
(3.12)
a = 0.409 + 0.5016 sin(ros - 60°) (3.13)
b = 0.6609 - 0.4767 sin(ros - 60°) (3.14)
d . 7t = sin ros - ~s cos ros (3.15)
A = cos p + tan q> cosy sin p (3.16)
B = cos cos cos P + tan o sin P cosy (3.17)
C = sin p sin y/ cos q> (3.18)
i = incidence L = arcos [cos o cos q>{A cos ro - B + C sin ro}] (3.19)
lrosrl = rnin{ros,[arcos(AB + c.J A2 - 8 2 + c2 )/(A 2 + c2)]} (3.20)
- I COsr I if (A > 0 & B > 0) or (A ~ 8)
+ I rosr I otherwise.
lrossl = rnin{ros, [arcos(AB - c.J A2 - a2 + c2 )/(A 2 + C2)]} (3.21)
+ lrossl if(A > O&B > O)or(A ~ B)
COss = - I ross I otherwise.
Optimizing PV output 56
3.2.1.3 Klucher Model
Klucher (169) developed a model for predicting the irradiance on inclined surfaces using an
anisotropic diffuse sky model. The model he presents is a modification of the Temps and
Coulson model [273) which he found to be valid only for clear sky conditions. The Klucher
model uses hourly measured irradiance data for the global irradiance. The diffuse part of the
model is given below:
where F is the so-called modulating factor defined as
Id 2 F = 1.0 - (-1 )
(3.22)
(3.23)
The second and third terms represent the horizon brightening and the circumsolar brightening
respectively. The direct and ground reflected parts are given by 3.24 and 3.25.
I - I D0 = H. d cos "'
srn a (3.24)
where "' = incidence angle on the inclined plane
(3.25)
It is noteworthy here that under overcast skies when the ratio of diffuse to global irradiance
!JI is unity, the Klucher all sky model reduces to the Liu and Jordan isotropic model, shown
in equation 3.10.
Optimizing PV output 57
3.2.1.4 Perez Model
Perez, et al. [218) developed a model which uses the anisotropy of the diffuse irradiance by
superimposing upon an isotropic radiance field both a disc and a horizontal band with
increased radiance. This is an attempt to replicate circumsolar and horizon brightening.
The radiance enhancements within these areas were determined by Perez et al. [218) by
analyzing the direct radiation and the global radiation incident upon seven inclined and one
horizontal sensor. The enhancement parameters F1 and F2 are functions of the ratio I/Id, Id and
the zenith angle. The equation for the diffuse component on the inclined surface is given in
terms of the following;
o.5(1 + cos p) + 2(1 - cos WHF1 - 1)Xc(9) cos e· + ~~'(F2 - 1) Ds= ~~~~~~~~~~~~~,;..._~___:,~~~~~~=--~-1 + 2(1 - cos P'HF1 - 1)Xh(z) cos z' + 0.5(1 - cos 2~)(F2 - 1)
where
F, = diffuse irradiance enhancement factor for circumsolar brightening.
F2 = diffuse irradiance enhancement factor for horizon brightening.
W = half angle width of circumsolar disc (assumed equal to 15°)
~ = horizon band angular thickness (assumed equal to 6.5 ° )
~· = altitude of the horizon bandwidth with respect to the sloping plane.
p = slope of the plane.
z = solar zenith angle.
z' = equal to the solar zenith angle if the circular region is totally visible
(3.26)
from the horizontal or equal to the average incidence angle if only partially visible.
Xh = fraction of the circular region visible from the horizontal
e = equivalent of z for the sloping surface.
e· = equivalent of z' for the sloping surface
Xe = equivalent of Xh for the sloping surface.
Optimizing PV output 58
The direct and the ground reflected parts are identical to Klucher's.
3.2.1.5 Results of the Comparative Study
Three sites representing three regions of the U.S. are selected for evaluating the four models.
These sites are, Raleigh, NC representing eastern U.S., Orlando, FL representing
southeastern U.S. and Hesperia, CA representing the western U.S. General information about
these sites and PV arrays are provided in Appendix B. Data for the Raleigh site comprised
of 3-minute observations for the months of March through July, 1985. That for the Orlando site
are 6-minute observations during the month of December, 1985. Observations for the Hesperia
site are taken at 10-minute intervals for the entire year of 1985.
Some special features of the four models are kept in mind when comparisons are made.
These are shown in Table 1. Table 2 and Table 3 show the comparisons of results obtained
from using the four models. The numbers presented in these tables reflect the monthly
average daily ratios of the irradiance on a tilted surface and that on the horizontal.
Comparisons are made only for the months for which actual data are available at this time.
The column labeled 'Actual' represents the ratios between (measured) plane-of-array and
horizontal irradiances. The four columns that follow represent the same ratio when calculated
by these models using historical data. Table 2 shows the performance comparison of the four
models in Raleigh, NC and Orlando FL. It is seen from this table that the isotropic model of
Liu-Jordan comes close to estimating the actual data in the summer months of June and July
but underestimates by a considerable margin during March. The Klucher model does better
in March but overestimates in June and July. Perez model seems to do better overall. the
comparison at Orlando, FL in December shows that the Duffie-Beckman model is very close
to the actual value while Liu-Jordan overestimates. This is to be expected, because the
Duffie-Beckman model was developed as an improvement over the Liu-Jordan model which
Optimizing PV output 59
Table 1. Some Characteristics of the Four Models
MODEL NAME
LIU-JORDAN
DUFFIE-BECKMAN
KLUCHER PEREZ
Optimizing PV output
MODELING CHARACTERISTICS
• Monthly average of daily ratios R predicted. • Daily ratio R predicted. • Requires long-term historical data. • Requires only global irradiance data. • Diffuse component on horizontal plane is estimated
• Only monthly average of daily ratios R predicted.
• Requires long-term historical data. • Requires only global irradiance data. • Diffuse component on horizontal plane is estimated
• Hourly ratios RH predicted. _ • Monthly average of daily ratio R predicted. • Daily ratio R predicted. • Does not require long-term historical data if either
direct or diffuse component is available. • Diffuse component is estimated if no observed
data is available.
60
Table 2. Ratio of lrradiance in Raleigh, NC and Orlando, FL
RALEIGH
MONTH ACTUAL KLUCHER PEREZ LIU-JORDAN DUFFIE
MARCH 1.1954 1.188 1.151 1.139 1.125
JUNE 0.9202 0.970 0.955 0.927 0.942
JULY 0.9425 0.982 0.940 0.940 0.953
ORLANDO
MONTH ACTUAL KLUCHER PEREZ LIU-JORDAN DUFFIE
DEC 1.2739 1.324 1.256 1.305 1.269
Optimizing PV output 61
Table 3. Ratio of lrradiance in Hesperia, CA
MONTH ACTUAL KLUCHER PEREZ
JANUARY 2.210 2.794 2.201
FEBRUARY 1.862 2.026 1.856
MARCH 1.605 2.086 1.472
APRIL 1.491 1.867 1.499
MAY 1.429 1.747 1.405
JUNE 1.400 1.611 1.407
JULY 1.395 1.678 1.362
AUGUST 1.563 1.967 1.554
SEPTEMBER 1.553 1.717 1.584
OCTOBER 1.677 2.215 1.828
NOVEMBER 1.944 2.168 1.649
DECEMBER 2.403 2.767 2.308
Optimizing PV output 62
was claimed to have come short of accurately estimating the irradiance on tilted surfaces
during the winter. The Perez model provides the next best scenario.
The next site examined is Hesperia which has two-axis tracking arrays. Since
Liu-Jordan and Duffie-Beckman models do not have the capability of modeling tracking arrays,
comparisons for the Hesperia site are confined only to the Klucher and the Perez models.
Table 3 presents the respective irradiance ratios which are compared with the field
measurements for every month of the year. It is seen that the Klucher model always
overestimates the actual data. This is because the Klucher model happens to overestimate
values on clear days when diffuse sunlight is almost negligible. And Hesperia gets more direct
sunlight than any of the other sites in the east or the southeast. On the other hand, Perez
model seems to provide better estimate of the irradiance ratios in Hesperia. However, Perez
model is somewhat off in the month of March.
3.3 Energy Storage With Central Station PV
With the availability of advanced batteries, it is now possible to store large amounts of energy
during off-peak periods of the day for use during the peak periods. This process is called load
leveling. The rationale for this entire scheme revolves around the fact that energy during
off-peak periods is cheaper and easily available whereas that during the peak periods of the
day is very expensive and is derived from fossil fuel. Considerable amount of research and
development work has been performed at the battery test facility (BEST) in New Jersey [221).
Storage batteries are now looked at seriously by electric utilities for load leveling. The
proposed 10 MW battery load leveling project for the Southern California Edison Co. at Chino,
California, is a case in point.
Optimizing PV output 63
As the storage technology matures and becomes available for electric utility load leveling,
there may be other ways to make it more viable. One such option may be to integrate
batteries and photovoltaic (PV) energy system. Since utilities are in fact looking for the ideal
PV plant which can be as effective as a conventional peaking generating unit, only because
with such a plant, the effective load carrying capacity is the highest. The objective of the
optimization is then to perform a comparative analysis of the benefits of the battery alone
versus the battery-PV hybrid system for load-leveling applications. In order to study the effects
of such a hybrid system in different geographical regions, two different sites - one in the
southeastern and the other southwestern U.S. have been looked at. Results of the study follow
shortly.
3.3.1 Potential For A Combined Photovoltaic/Battery System
The PV plant may be generating power during low-demand periods when the lower
incremental cost machines are operating as base or intermediate capacity. This may not be
the most desirable form of operation as it cannot justify the high installation cost of the PV
plant at certain sites. In cases like this, CHINERY (64) states that it is quite possible that the
operating cash now of some utilities can be adversely affected. This is because they sell
power to many of their customers (especially residential) at the same rate regardless of
whether the sale takes place during on-peak or off-peak periods. Cutting their load during
off-peak periods forces them to sell less power when their profit margin is the greatest. This
act reduces their revenues significantly without reducing their operating expenses.
These problems lead to the general belief that a combined PV and energy storage system set
up with an objective of reshaping the peak demand curve might prove to be an attractive
option for the utility. Photovoltaics, in conjunction with a battery under the peak load
management scheme, would have a unique application in utility peak load restructuring.
Optimizing PV output 64
Whereas, PV power combined with energy storage in stand-alone mode attempts to supply
all of the load, the central station application of PY/energy storage combination attempts to
shave the peak load where the most fuel savings can be earned by the combined system.
From the point of view of economics, SCHUELER, et al. [248] claim that utility owned energy
storage perform better than dedicated storage for photovoltaic central station application.
Therefore, utilities already planning on having PV power in the generation mix and further
contemplating advanced battery energy storage for peak-shaving might be better off bringing
the two technologies together for a more effective utilization. Details of the performance of
such a system as well as the effect of the nature of PV array orientation on battery
performance are discussed.
3.3.2 Battery Plant Consideration
Sizing a suitable battery adequate for shaving the peak demand hours in every month of the
year is tantamount to determining the size of the battery required to supply the peak load of
the month which contains the annual peak. However, this may not be true for low
peak-shaving requirements. For example, if the month of August contained the annual peak
and assuming that this month had a single daily peak occurring in the afternoons, then for a
peak shaving requirement of upto 6% of the peak load, this particular month will always need
the largest battery size. Any further reduction in the peak shaving requirement will shift the
worse conditions to another month which most probably has double peaks in a day and
therefore the size of the battery is determined according to that required in that month.
For load leveling purposes, advanced batteries are required. These batteries should have the
following features: high efficiency, 70-75%; high cycle life, 3000-4000 cycles; discharge should
be at constant power for 5-8 hours; low demand cost ($/MW) and low capacity cost ($/MWh).
Optimizing PV output 65
Although, all of these criteria are not met by any of the existing batteries, the following provide
good choices:
1. Sodium-Sulfur,
2. Zinc-Bromine,
3. Hydrogen-Nickel, and
4. Lead-acid.
Out of the above four, only the lead-acid battery has been the front runner in the application
of load leveling. A cycle life of 1000-1500 may easily be reached with the present technology.
For the simulation results presented in this paper, an advanced lead-acid battery
characteristics are used.
Needless to say that the actual size of the battery will depend on the amount of peak-shaving
desired. Some utilities have load profiles which will not allow peak shaving beyond a certain
limit, the constraint being the depth of discharge limitations on the battery itself. A second
factor is the fact that the costs of batteries are largely dependent on the MWh size of the plant
rather than the MW size. Thus, utility planners would opt for a low MWh to MW ratio in sizing
a battery plant. That means a small period of discharge. Also figuring prominently in the
fixation of an optimal amount of peak shaving is the limitation on the total base capacity
available for charging the battery. It so happens that the daily utility load experiences a low
demand period during the early morning hours. Therefore, this period is suitable for charging
the battery with the generating capacity which is available at this time. The operating costs
of this generation, called here, as the base capacity, is minimal. On the other hand, there is
also a limited amount of capacity to be spared, wherefore comes the limitation on the exact
amount of peak shaving possible.
A third constraint on the lower limit of the peak shaving comes from the presence of
photovoltaic power in the grid. The best possible use of PV generation, as pointed out earlier,
Optimizing PV output 66
is in its utilization during the peak shaving period. This decreases the capacity needed from
battery discharge during these hours and is therefore conducive to the battery sizing.
Reducing the peak load shaving amount certainly precludes the PV power from being
optimally utilized and therefore works against the economics of the utility.
Once the peak shaving period/s has been fixed within the limitations as pointed out,
some additional constraints must be kept in mind before arriving at a final size of the battery.
These are:
1. Battery discharge should be deep enough to supply an entire peak load duration.
2. Base capacity (power taken from the reserve generation during the lowest daily demand
periods on top of any available photovoltaic power) to charge the battery should be
enough for charging at the specific charging rate of the battery.
3. Back-up power, i.e. power outside of the combined capacity of the PV/battery system to
shave the peak should be zero.
4. Usage of PV power outside the peak demand region should be minimized. This is done
in order to earn more fuel and capacity credit.
An iterative computer optimization method to satisfy the above constraints with the maximum
possible peak shaving possible, is employed to yield the results enumerated below. In the two
case studies performed on the typical utilities in the south-east and in the west, it is found that
5% peak load shaving is the optimal amount of load management possible under the
constraints. The size of the battery of course depends on the orientation strategy of the PV
arrays. Figure 9 and Figure 10 illustrate the change in battery capacity for percent peak load
shaved in the southeastern and the western parts of the U.S. respectively. Steeper slopes of
these curves signify the fact that for each percent increase of peak shaving desired, the
Optimizing PV output 67
,.... c:: :c
4550
~ 3600 >°"' ~ u Ill Q.. nl u
~2650 --nl co
1700
South facing array ~----~~, Optimal array onenbt.1011 0---------.t> T vo axis t.raclang
No PV array
750 ...._~--~---~~-'-~~--~--~~--~~--~--~~....._~_. 0 2 4 6 8 10
Percent. peak load
Figure 9. Battery capacity requirement for percent peak load supplied. Site is Raleigh, NC
Optimizing PV output 68
4550
...... c:: I i 3600 >-
-t! u
"' 0..
"' u
t2650 --"' co
1700
Soll'lh facing array ))(-(-----"")( Opt.rmal array onent.at.ron ~-----'Z> Tvo axu; !raclang "+"'-------'-P No PV array
750 '--~ ......... ~-......_~-'-~--''--~ ........ ~--'~~ ......... ~-...~~...a.....~~ 0 4 6 8 10
Percent peak load
Figure 10. Battery capacity requirement for percent peak load supplied. Site is Hesperia, CA
Optimizing PV output 69
number of peak hours increases faster in the case of the western utility thereby requiring
higher battery capacity. This also gives an indication that the peak periods in the western
utility are more flat.
3.3.3 PV/Battery Operating Strategy
Duty Cycle
It is found that a daily duty cycle rather than a weekly cycle would best suit the peak shaving
purposes. This is agreed upon because of the excessive amount of battery capacity required
for longer hours of storage in the weekly cycle application.
Cycle Life
One of the general concerns in battery operation for peak shaving is preserving the cycle life
of the battery. The depth of discharge (DOD) of the batteries has a direct affect on the cycle
life. Generally, an advanced lead-acid battery will last 3000 cycles if its cycling is limited to
50% DOD (99). On the other hand an 80% DOD limits the cycle life to only 1500 cycles.
Besides, temperature also has an affect on the life of the battery. Owing to the dependence
of cycle life on the DOD, it is necessary to maintain the discharge level to a minimum possible.
It will be proved later that PV power can help in preserving the cycle life of the battery through
a combined operation of the two plants for peak shaving.
Combined Operation
The following steps describe how the combined operation of the PY and battery system
is envisaged:
Optimizing PV output 70
1. During the early morning hours, it is natural to find the battery State Of Charge (SOC)
down to a low level. This is from the preceding day's discharge during peak periods.
Therefore, apply constant power to charge the battery to as high a level possible before
the discharge cycle begins. The charging power is composed of base capacity and
photovoltaic power generation, available only after sunrise, during the charge cycle.
2. Apply all the photovoltaic generations to the peak load during the load management
period. If not sufficient, discharge the battery.
3. The daily duty cycle of the battery consists of one of the following possibilities:
a. Two charge cycles; two discharge cycles:-
• charging is done in the early morning hours.
•charging again done by photovoltaic power in the mid-afternoons when the morning
peak has been shaved and the evening peak is ahead.
• discharge in the morning peak period.
• discharge in the evening peak period.
b. Two charge cycles; one discharge cycle:-
• same as in (a) except that only the morning peak is required to be shaved.
c. One charge cycle; one discharge cycle:-
• charging is done in the early morning hours.
• discharging during one long extended period.
4. During charge periods, if the battery SOC reaches 100%, then all photovoltaic power
available is diverted to supply the load demand at that time even if the load is not within
the peak load period. This is because the PV operating cost is zero and therefore any
available power is an addition to the overall generation capacity with a higher dispatch
priority over the other dispatchable generation.
Optimizing PV output 71
3.3.4 Comparative Study
Two model utilities from the south-eastern and the western regions of the U.S are selected for
analysis of the load management strategy described in preceding sections. The Load profiles
for these utilities are produced from (98]. The peak load occurs in the month of August for both
utilities and are assumed to be 7000 MW in both cases. The assumption for the annual peak
demand is actually immaterial. The most important factor influencing load management
strategies is the shape of the daily load curve.
The PV array site representing the south-east is chosen to be Raleigh, NC and that
representing the west is Hesperia, CA. Simulations concerning the PV power output itself are
done by using the program PVFORM (198] developed at the Sandia National Laboratories.
Battery (Lead-acid) charging and discharging characteristics are taken from HOOVER (137].
Specifications of the PV battery system can be found in CHOWDHURY and RAHMAN (68].
The optimal load management strategies for both sites are determined by an optimization
routine to be 5% peak shaving for the worst month (in terms of energy capacity requirement).
Because of lower energy requirement in some other months particularly in the spring season,
this translates into a higher (upto 8%) peak shaving capability by the same PY/battery system.
Four representative months, viz., February, May, August and November representing the
winter, spring, summer and fall respectively are chosen for presenting the results of the study.
Table 4 shows the nature of the systems used in the peak load management scheme in the
southeastern utility. Similar results for the western utility are shown in Table 5. The following
observations may be made from these tables:
1. Photovoltaic power combined with battery storage makes a large difference in battery
size compared to the case with no PV power assumed. The differences are:-
Optimizing PV output 72
Table 4. Peak shaving characteristics In the four seasons for typical utility In the south-east (assuming 7000 MW annual peak).
c Percent Battery Base Cap· A PV array peak Capacity. acity for s orientation. load MW/MWh charging. E shaved. 1 MW
5% - WI 150 - WI 1 South- 6% - SP 350/2050 50 - SP
Facing 5% - SU 50 - SU 6% - FA 0 - FA
5% - WI 125 - WI 2 Optimal 6% - SP 350/1925 50 - SP
surface 5% - SU 75 - SU azimuth 5% - FA 0 - FA
5% - WI 125 - WI 3 Two-axis 6% - SP 350/1925 25 - SP
tracking 5% - SU 50 - SU 5% - FA 0 - FA
5% - WI 175 - WI 4 No PV 5% - SP 350/2350 200 - SP
array 5% - SU 325 - SU 7% - FA 250 - FA
1 WI-Winter; SP-Spring; SU-Summer; FA-Fall
Optimizing PV output 73
Table 5. Peak shaving characteristics in the four seasons for typical utility in the west (assuming 7000 MW annual peak)
c Percent Battery Base Cap· A PV array peak Capacity acity for s orientation load MW/MWh charging E shaved. 1 MW
5% • WI 0 • WI 1 South- 7% - SP 350/1925 125 - SP
Facing 6% - SU 150 - SU 5% - FA 150 - FA
6% - WI 50 - WI 2 Optimal 7% - SP 350/2025 100 - SP
surface 6% - SU 125 - SU azimuth 5% - FA 150 - FA
6% - WI 25 - WI 3 Two-axis 8% - SP 350/2075 150 - SP
tracking 6% - SU 0 - SU 5% - FA 150 - FA
7% - WI 325 - WI 4 No PV 5% - SP 350/3400 300 - SP
array 5% - SU 475 - SU 5% - FA 225 - FA
1 WI-Winter; SP-Spring; SU-Summer; FA-Fall
Optimizing PV output 74
• Case 1 vs. case 4:
• Case 2 vs. case 4:
• Case 3 vs. case 4:
Saving of 300 MWh in S-E utility
Saving of 1475 MWh in W utility
Saving of 425 MWh in S-E utility
Saving of 1375 MWh in W utility
Saving of 425 MWh in S-E utility
Saving of 1325 MWh in W utility
Obviously, photovoltaics has a bigger impact on load management in the western utility
in terms of battery size requirement.
2. PV/battery combination also has a large impact on base capacity required for charging
the battery as opposed to the case with no PV power assumption. These are as follows:
• For S-E utility:
• For W utility:
25 - 50 MW saving in winter.
150 - 175 MW saving in spring.
275 - 300 MW saving in summer.
250 MW saving in fall.
275 - 325 MW saving in winter.
150 - 175 MW saving in spring.
325 - 475 MW saving in summer.
75 MW saving in fall.
The reductions in base capacity for cases 1,2 and 3 should be examined in the light of
total PV installed capacity. Both utilities had 350 MW of rated PV power in these
Optimizing PV output 75
simulations, and looking at the above comparisons, the turnaround is quite attractive,
particularly in spring and summer. The savings in summer for the typical western utility
which comes to 475 MW should be compared to the 350 MW of installed PV capacity. The
savings in combined PV/battery case stems from the fact that less base generation
capacity is required to charge a battery with smaller capacity size required compared to
the stand-alone battery case.
3. The fact that PV power can cause low depth of discharge of the battery is evident from the
comparison shown in Figure 11. The "no PV" case shows that the DOD can reach over
70% on a typical day in the month of August at Raleigh while the PV/battery combined
case exhibits a more preferable discharge characteristic, the DOD not reaching 50%.
Similar characteristics are also seen in all the other months at both sites.
4. Another important issue of concern is the cycle life of the battery versus the PV array size.
It is found that the number of charge-discharge cycles do not change significantly for
small changes in the PV array size. Large changes in the latter is not possible in such
applications without losing much of benefits earned in terms of percent of peak load
shaved and amount of base generation capacity saved.
3.3.5 Relative Performance of Array Orientation Strategies
After comparing the attractiveness of PV/battery combination over the battery system
alone, i.e. cases 1,2 and 3 versus case 4, it is useful to compare cases 1,2 and 3 against one
another. In other words, to find out what array orientation strategy is the best for load
management.
Once again from Table 4 (S-E utility):
Optimizing PV output 76
1.0
0.8 GI f' nl
..&; u
0 0.6 ll .... nl ....
U)
0.4
0.2
4 8
No PV array Opl1mal az1mulh array
.. - - - - - - - -
12 16 20 Ho1r of day
0.0
0.2
0.4
0.6
0.8
Figure 11. Comparison of depth of charge and discharge of battery with and without PV power at Raleigh
Optimizing PV output
GI E'9 nl
..&; u UI
-6 .... 0
..&; ...... D.. GI
0
77
• Case 2 vs. case 1:
• Case 3 vs. case 2:
From Table 5 (W utility):
• Case 2 vs. case 1:
• Case 3 vs. case 2:
Saving in battery capacity of 125 MWh.
Saving in base capacity of 25 MW
in winter and 25 MW in summer.
Almost identical in all respects to case 2.
Increase in battery capacity of 100 MWh.
Saving in base capacity of 25 MW
in spring and 25 MW in summer.
Increase in battery capacity of 50 MWh.
Saving in base capacity of 25 MW
in winter, 50 MW in spring and
125 MW in summer.
While optimal surface azimuth oriented arrays are better than others in the southeast,
south-facing arrays provide a better perspective of load management strategy in the west. Of
course the final choice of the orientation strategy would have to depend on the economics
involved.
Table 6 and Table 7 show the comparisons for the simulation runs involving the three
strategies for PV array orientation. The indices to look for are the "peak effectiveness ratio"
(column 4) and the "charging effectiveness ratio" (column 6). The former is defined here as the
ratio of array energy supplied by the array to the grid during the peak period to the total
energy supplied by the array to the grid. The "charging effectiveness ratio" is defined as the
ratio of the energy supplied by the PV array to charge the battery to the total energy required
Optimizing PV output 78
Table 6. Comparisons of the three PV array orientation strategies for the south-eastern utility.
Total Total Peak Total Charging PV array array effec· energy effec· array energy energy tiveness to charge tiveness orient- to load. during ratio battery. ratio a ti on MWh 1 peaks. MWh
MWh
Case 1. 32200 - WI 11200 - WI 0.35 - WI 16770 - WI 0.53 South- 46100 - SP 37100 - SP 0.80 - SP 20460 - SP 0.61 facing 41300 - SU 25900 - SU 0.63 - SU 24570 - SU 0.69
27800 - FA 10500 - FA 0.38 - FA 14000 - FA 1.00
Case 2. 29800 - WI 14000 - WI 0.47 - WI 13270 - WI 0.48 Optimal 47400 - SP 37000 - SP 0.78 - SP 20220 - SP 0.61 azimuth 42700 - SU 31900 - SU 0.75 - SU 18700 - SU 0.41 orient. 29100 - FA 10700 - FA 0.37 - FA 8700 - FA 1.00
Case 3. 43400 - WI 14600 - WI 0.34 - WI 12970 - WI 0.47 2-axis 61600 - SP 45800 - SP 0.74 - SP 17320 - SP 0.77 tracking 61700 - SU 33700 - SU 0.55 - SU 19530 - SU 0.63
41900 - FA 11100-FA 0.26 - FA 9300 - FA 1.00
1 WI-Winter; SP-Spring; SU-Summer; FA-Fall
Optimizing PV output 79
Table 7. Comparisons of the three PV array orientation strategies for the western utility.
Total Total Peak Total Charging PV array array effec· energy effec· array energy energy tiveness to charge tiveness orient· to load. during ratio battery. ratio a ti on MWh 1 peaks. MWh
MWh
Case 1. 35400 - WI 10300 - WI 0.29 - WI 25600 - WI 1.00 South- 78600 - SP 66900 - SP 0.85 - SP 24500 - SP 0.28 facing 75700 - SU 6090 - SU 0.80 - SU 23800 - SU 0.20
48200 - FA 37900 - FA 0.79 - FA 13000 - FA 0.18
Case 2. 38000 - WI 16900 - WI 0.44 - WI 29200 - WI 0.75 Optimal 78700 - SP 70200 - SP 0.89 - SP 22500 - SP 0.36 azimuth 7520 - SU 62900 - SU 0.84 - SU 21800 - SU 0.22 orient. 50100 - FA 39600 - FA 0.79 - FA 13200 - FA 0.20
Case 3. 50500 - WI 18200 - WI 0.36 - WI 31000 - WI 0.88 2-axis 111000- SP 91200 - SP 0.82 - SP 31700 - SP 0.44 tracking 99100 - SU 75700 - SU 0.76 - SU 21900 - SU 1.00
59000 - FA 44100 - FA 0.75 - FA 12800 - FA 0.18
1 WI-Winter; SP-Spring; SU-Summer; FA-Fall
Optimizing PV output 80
for charging. Column 3 in The tables also show the total energy supplied by the PV array
during the period of load management. Column 2 presents the PV energy used to supply the
overall load and column 5 shows the PV and base energy used to charge the battery. Column
4 is the ratio of column 3 over column 2 whereas column 6 is the ratio of the PV array energy
used to charge the battery over column 5.
Higher values in columns 4 and 6 indicate a more desirable feature. A higher "peak
effectiveness ratio" means that the array power is used more effectively during the load
management period in terms of the amount of energy being supplied. A higher "charging
effectiveness ratio" signifies the fact that lesser base capacity is used for charging the battery
and that most of the charging power came from the existing PV array. Evidently, from
Table 6 and Table 7, case 2 in which the array is optimally oriented for maximum power
during peak shaving periods, is the best option in this perspective.
Optimizing PV output 81
CHAPTER 4
Resource Forecast
The dispatching of photovoltaic power has always posed a major problem to electric utility
system operators. This has been largely due to the fact that the short term prediction of solar
irradiance is difficult to predict. The wide variability of the cloud cover and to some extent, the
atmospheric condition makes it hard for any attempt at parameterization of these phenomena.
On the other hand, observed hourly global irradiance data is available at many locations
throughout the SOLMET network [206). These data, as well as the typical meteorological year
(TMY) [207] data which provide the data for typical months of a synthetic year, have proven
to be useful in the past for PV array performance prediction [198). Such weather data are
known to be used in many PV performance analysis models. Examples of such models are
shown in Figure 2 on page 22. These models rely for their analysis on the past historical data
and are therefore accurate only in a most general sense with possibilities of wide statistical
variability between the actual and the predicted data (Refer to Reference [228) for a detailed
comparative analysis).
It therefore seems only logical to assume that a typical synthetic year or a number of years
of historical data may only be useful to predict the average monthly or even daily PV array
Resource Forecast 82
performance. A time scale smaller than the day requires knowledge of the cloud cover and
their expected instantaneous changes.
In applications such as utility grid connected systems. it is important to be able to dispatch the
PV output in the same fashion as any conventional generators. like coal and oil-fired units.
That means the dispatcher has to have the information about the general availability of PV
power plant 24 hours in advance (for unit commitment), and expected fluctuations in PV output
in 10 minute time frame (for economic dispatch). The expected weather conditions of the next
day, will determine the availability of PV power in the 24-hour time frame. However, for the
economic dispatch considerations the prediction of PV output in 10 minute (or less) intervals
is necessary. Failure to do so will cause the PV power to remain non-dispatchable and will
inhibit its penetration in the utility grid.
This was the incentive for undertaking a study which would enable prediction of sub-hourly
solar irradiance and prove its usefulness to not only the photovoltaic community, but the
electric utility industry as well. In this chapter, A novel approach is presented, for the
prediction of the solar irradiance in the sub-hourly time frame (3-10 minutes) by means of a
Box and Jenkins time-series analysis [37).
4.1 Background Information
A number of authors have previously presented models to estimate the global solar
irradiance. Of these some are stochastic in nature and the rest use some form of
parameterization of known phenomena. GLANH et al. [117), have used Model Output
Statistics (MOS) to predict, among other weather variables, the variation of the cloud amount.
MOS is a weather forecasting technique which consists of determining a statistical
Resource Forecast 83
relationship between a predictand and variables forecast by a numerical model at some
projection time. The lead time of projection varied from 6 hours to a day. The predictions
depend on empirical relationships derived from observations of numerous weather variables
on the hour.
PURI [225) has introduced a statistical Markovian irradiance model for predicting the
time-sequence of half-hour solar radiation values on a horizontal surface, which uses hourly
irradiance values. He finds a half-hour transition density function from the hourly transition
density function and predicts the joint cumulative distribution function for several successive
normalized half-hour values.
ATWATER, et al. [12). have developed a parametric model which accounts for atmospheric
phenomena. Parameterizations were used to account for Rayleigh and Mie scattering and for
absorption by permanent gases, water vapor and aerosols. Cloud cover was incorporated into
their model by using cloud transmission functions developed by HAURWITZ (128). Their
models estimate the global horizontal irradiance at any time of the day with an a-priori
assumption that cloud cover amount at every layer is known.
BRINKWORTH (44) recognizes the sequential characteristics in the past solar irradiance data
and introduces a stochastic model which generates future irradiance sequences. He uses the
autocorrelation function of the irradiance time-series based on long-term averaged data. This
model is dependent on a reference year of irradiance measurement and although useful for
solar-thermal system design, may not be very useful for the photovoltaic performance study
as pointed out earlier.
Resource Forecast 84
4.2 Time Series Modeling in lrradiance Prediction
4.2.1 Choosing the Model
The most fundamental time series models are the autoregressive model and the moving
average model (37). In the autoregressive model AR(p), the current value of the process is
expressed as a linear combination of p previous values of the process and a random shock.
(4.1)
In order to write this in a more convenient form, the following operators are introduced.
So that equation (4.1) can be written as:
(4.2)
In the moving average model MA(q), the current value of the process is expressed as a linear
combination of q previous random shocks.
(4.3)
Resource Forecast 85
Introducing the operator
equation (4.3) can be written as:
(4.4)
The general mixed autoregressive-moving average model ARMA (p, q) is a combination of (4.2)
and (4.4)
(4.5)
Writing (4.5) is the operator notation
(4.6)
Equation (4.6) can only be used to model stationary processes where the roots of the
polynomial q>(B) and 0(8) lie outside the unit circle. Non-stationary processes can be modeled
by differencing the original process i; to obtain a stationary process, wt . Multiple differencing
may sometimes be required in order to achieve stationarity. This results in an autoregressive
integrated moving average ARIMA (p,d,q) model, which is expressed as:
(4.7)
where Vd is the differencing operator of order d.
Resource Forecast 86
It is a well known fact that the hourly solar irradiance data presents a diurnal as well as an
annual periodicity. To model such data in its raw form would mean using a seasonal ARIMA
model which recognizes the dependence of a particular hour's data on the same hour of all
the previous day's and all previous year's data. Needless to say, the dimensionality of this
seasonal modeling appears to have unwieldy proportions. To make things less complicated,
it becomes necessary to pre-whiten the solar irradiance data so that all periodicities may be
stripped. The underlying principle is the recognition of the fact that the randomness found in
the global solar irradiance data received on earth's surface is caused by changes in the cloud
cover and the aerosol content in the air. A clear day's (cloudless sky) irradiance data may
be estimated accurately by atmospheric parameterization (85], and is therefore deterministic
in nature. It is the stochastic behavior of constant cloud movement which makes the radiation
on a cloudy day difficult to predict. It was therefore decided to model the cloud cover, or in
computational terms, the cloud transmissivity coefficients by an ARIMA (p,d,q) model of the
form shown in equation 4. 7 where i; represents the transmission coefficients.
4.2.2 The Pre-whitening Process
This is the process of obtaining i; as described above from past observations of the global
solar irradiance. Global irradiance under cloudless skies is written as the sum of a direct
beam component 18 and diffuse components from Rayleigh scatter l0 R and scattering by
aerosol 10 A (85]:
18 = S' cos 9z[T,(O)T,(R) - awJT,(a) (4.8)
loR = S' cos 9zT,(0)[1 - T,(R)]/2 (4.9)
loA = S' cos 9z[T,(O)T,(R) - aw][1 - T,(a)]ro0 f (4.10)
Resource Forecast 87
where: S' = the solar constant (1353 W/m2)
corrected for departure of the actual
Sun-Earth distance from the mean value
ez = the solar zenith angle
aw = the absorptivity of water vapor
co0 = the spectrally averaged single scattering
albedo for aerosol
f = the ratio of forward to total scatter by
aerosol.
T,(O) = the transmissivity after absorption by ozone
T,(R) = the transmissivity after Rayleigh scatter
T,(a) = the transmissivity after extinction by aerosol
The parameterization used in the prediction strategy follows in part, that used in the MAC
model [84), which has been used in the estimation of solar irradiance and its components.
The derivation of these parameters are described in the following sub-section.
4.2.2.1 Parameterization for the Prewhitening Process
Optical Air-mass
m, = ____ 35 ___ _
(1224 cos2 ez + 1) 112 (4.11)
Transmittance after Ozone Absorption
0.1082 X0 0.00658 X0 0.002118 X0 T,(O) = 1 - + ___ __..;;_ + ______ ....:.,_ __ _ (1 + 13.86 X0 )o.sos 1 + (10.36 X0 )3 1 + 0.0042 X0 + 0.00000323 X!
(4.12)
X0 = m,U0 , U0 = 3.5mm
Resource Forecast 88
Water Vapor Absorptivity
Water vapor absorption is given by the equation:
a = w (1 + 141.5 Xw)0'635 + 5.925 Xw
In Uw = (0.1133 - In(/... + 1)) + 0.0393td
(4.13)
(4.14)
Where td is the dew point temperature (°F) and A. is a variable exponent by which the
atmospheric water vapor path length is modified. A. is a variable depending on the season and
the latitude of the site. Values of A. for different seasons and latitudes have been computed
and reported in (259).
Transmissivity after Extinction by Aerosol
The transmissivity after extinction by aerosol is calculated from:
T,(a) = exp( - µ8 m,) = kmr (4.15)
Values of the extinction coefficient µ. for a particular site is found by using an equation given
in reference (279). This equation is:
µ8 = - ~ In [l/1(0)) r
(4.16)
where I is the measured direct beam flux density for the whole spectrum and 1(0) is the
spectrally integrated value of /"(/...), which is the flux density beneath an aerosol free
atmosphere. 1(0) can be calculated [277) as:
Resource Forecast 89
1(0) = S[T,(R)T,(O) - Bw] (4.17)
Rayleigh Scatter
Davies et al [85) have presented the following table for relating the Rayleigh scatter and the
optical air mass:
m, 0.5 1.0 1.2 1.4 1.6 1.8 2.0 3.0
T,(R) 0.9385 0.8973 0.8830 0.8696 0.8572 0.8455 0.8344 0.7872
m, 3.5 4.0 4.5 5.0 5.5 6.0 10.0 30.0
T,(R) 0.7673 0.7493 0.7328 0.7177 0.7037 0.6907 0.6108 0.4364
Aerosol Scatter
The aerosol scatter is calculated from a relationship of the ratio of the forward to total scatter
for aerosol. This relationship is also found in a tabular form in (85).
25.8 36.9 45.6 53.1 60.0 66.4 72.5 78.5 90.0
f 0.92 0.91 0.89 0.86 0.83 0.78 0.71 0.67 0.60 0.60
Since global irradiance le on a clear (cloudless) sky assumption is given by
le = Is + loA + loR (4.18)
we have,
Resource Forecast 90
T (0) le= S' cos 0z[T,(O)T,(R) - aw)T,(a) + Tl1 - T,(R)]
(4.19)
Also, since
(4.20)
where 10 = extraterrestrial irradiance
'ta = total transmissivity on a clear day.
Comparing (4.20) with (4.19),
T (0) 'ta= T,(a)[T,(O)T,(R) - aw][1 - roof]+ T(1 - T,(R)) + 2T,.(R)roof - awroof (4.21)
For a cloudy sky, 'ta is modulated by the transmissivity of the clouds at any given instant of
time. Therefore the total all-sky transmissivity 't, on a cloudy day would be
(4.22)
where 'tc = transmissivity of the cloud.
If 't is already known, and since 't• may be calculated as described in equations 4.8 to 4.21,
we already have the input time-series 'tc, to the ARIMA (p,d,q) model.
Commensurate with equation 4.18, we may also write the all-sky global irradiance, IA on
earth's surface as:
Resource Forecast 91
(4.23)
Using long-term historical observations of IA at any site, t may then be found from equation
4.23.
We can now generate the stationary time series tc = _.!... which is Gaussian by nature. t.
4.3 Simulation
The pre-whitened time-series tc is used in the ARIMA (p.d.q) model given by equation 4.7 to
estimate the values of the autoregressive and moving average parameters. The latter are
used in a forecast model originating directly from the ARIMA model itself. The forecast model
requires at least one previous hour's data and the data at the top of the hour at which
simulation is desired. Simulation continues for all the sub-intervals within the hour. Forecast
updates may be done at any interval during simulation. The forecasted values of the solar
irradiance at those intervals is found by the anti-mapping technique which is the reverse of
the transformation described in equations 4.22 and 4.23.
The entire simulation process consists of separate simulations for the direct beam irradiance
component, the irradiance component after Rayleigh scattering and the irradiance component
after aerosol absorbtion and scattering. These are described next.
• Beam Component
1. Optical air mass.
Resource Forecast 92
2. Ozone path length (for transmissivity through ozone layer).
3. Dew point temperature (to determine atmospheric water vapor path length).
4. Spectrally averaged single scattering albedo ro0 for aerosol.
For scattering aerosols: ro0 = 1
For absorbing aerosols: ro0 = 0
For urban areas: ro0 = 0.75
5. Aerosol extinction coefficient which depends on the climatic conditions at the site.
6. Sun-earth geometrical relationships.
• Diffuse Component After Rayleigh Scatter
1. Optical air mass.
• Diffuse Component After Aerosol Scatter
1. Optical air mass.
2. Single scattering albedo for aerosol.
3. Aerosol extinction coefficient.
4. Sun-earth geometrical relationships.
The flow chart in Figure 12 shows the simulation process.
4.3.1 Predicting the Output from a Photovoltaic System
The computer simulation program PVFORM (198) is modified to take in the sub-hourly
irradiance data generated, and to calculate the output from a given photovoltaic system.
Additional input requirements for PVFORM are temperature and wind speed measurements.
Resource Forecast 93
SYNTHETICALLY J GENERATED
IRRADIANCE DATA
H PRE - 'JHJTEN I 3
HISTORICALL ye:. OBSERVED STATlONARY
lRRADlANCE DAT A TIME-SERIES CLOUD i.--
TRANSHISSIVI TIES 4
I AR IMA MODELS I t
SUB-HOURLY FORECASTED
CLOUD TRANSH1SSIVITIES 6
SUB-HOURLY FDRECASTED GLOBAL INVERSE 7
IRRADIANCE TRANSFDRHA TIDN DATA 8
Figure 12. The simulation process to forecast global irradiance
Resource Forecast 94
Although the program also requires observed direct irradiance data, these are synthetically
generated as shown in box 1 of Figure 12.
4.3.2 Programming Considerations
The PV output forecast strategy is an integral part of an extended scheme, that of dispatching
the PV generations in the electric utility's power system operation. the PV output forecast is
coded into a computer module called FORECST. The latter consists of two sub-modules called
SIMUL and PREDIC. The relationship between these computer modules and their input and
output are shown in Figure 13. SIMUL generates a simulated global irradiance and direct
normal irradiance data on clear days during the period of interest. Input for SIMUL consists
of:
• Dew point temperature at the site
• Turbidity at the site
• Actual direct normal data (if turbidity at the site is not known)
• Actual global irradiance
Output from the sub-module SIMUL consists of:
• Simulated global irradiance on clear days
• Simulated direct normal irradiance data
• Simulated cloud cover data at the site
Sub-module PREDIC generates the forecasted sub-hourly PV generations which is used
by the DRIVER module. The inputs for sub-module PREDIC are the following:
Resource Forecast 95
Irro.dlo.nce Do. to. SIMulo. t1on
I TAPE
Dew point tel"lpero.ture
a.t site
Turbidity o.t site
l l ACTUAL DIRECT NDRHAl DATA
DATA BAS!
I TAPE
+
SIM UL
PV a.rro.y TeMpero.ture
Wind speed
TAPE I
PV output forcrco.sts
Sub-hourly PV Output Foreco.s-t
Figure 13. Execution of the FORECST module
Resource Forecast 96
• Time series parameters at the site
• PV array data
• Wind speed and temperature at the site
• Simulated global irradiance on clear days
• Simulated direct normal irradiance data
• Simulated cloud cover data at the site
The forecasts generated by SIMUL are based on the specific ARIMA (p,d,q) model applicable
for the site and period of the month. According to reference [37), the forecast equation is
derived from the ARIMA (p,d,q) model as follows:
Equation 4.7 can be written as:
(4.24)
where '1'(8) is called the generalized autoregressive operator. It is a non-stationary operator
with d of the roots of the polynomial '1'(8) equal to unity.
Equation 4.8 can be written directly in terms of the difference equation [37) by:
Substituting t + I in (4.25), we have
(4.26)
Taking conditional expectations at time t, in (4.26), we obtain,
(4.27)
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To calculate conditional expectations, we note that if j is a non-nagative integer
[Zt+ j1 = E[Zt+ j1 = ~t(J); j = 0, 1,2, ...
(at-11 = E[at-11 = at-l = Zt-l - ~t-j- 1 (1); j = 0,1,2, ...
(at+ 11 = E[Bt+ 11 = 0; j = 0, 1,2, ...
Therefore, to obtain forecasts ~(/), one would write down .the model for z.+ 1 in the form shown
in equation 4.26 and treat the terms on the right according to the following rules (371:
• The z._1 U = 0,1,2, .. ) which have already happened at origin t, are left unchanged.
• The z.+1 U = 0,1,2, .. ) which have not yet happened, are replaced by their forecasts~(/)
at origin t. /\ • The a1 _ 1 U = 0,1,2, .. ) which have happened are available from z._1 - z._1_ 1(1).
• The a,+1 U = 0,1,2, .. ) which have not yet happened are replaced by zeroes.
4.4 Simulation Results
Two sites representing the Southeastern United States were selected for evaluating the
forecast model. These sites are, Raleigh, NC and Richmond, VA. General information about
these sites and PV arrays are provided in Appendix B.
Data for the Raleigh site comprised of 3-minute observations for a 12-month period, March
1985 through February 1986. That for the Richmond site were 10 minute observations during
Resource Forecast 98
the months of June 1986 through March 1987. The Virginia Power site has the Sandia National
Laboratory designed on-site data acquisition system (ODAS). The Carolina Power and Light
site has an industry standard data acquisition system very similar to the ODAS. To assure
proper data quality, some reasonableness checks on the observed data are made and missing
data are filled in by interpolation.
4.4.1 Identification of the ARIMA Model (p,d,q)
For a better presentation of existing conditions, the time series data are resolved into weeks
rather than an entire season's or a full month's data. This gives a more realistic and accurate
estimate of the parameters in the model. Techniques for preliminary identification of time
series models rely on the analysis of autocorrelation function (ACF) and partial autocorrelation
functions (PACF). Figure 14 shows the ACF of the undifferenced time-series data for the 1st
week of March in Raleigh.
The non-decaying function indicates that differencing is required. The reason for persistence
of non-stationarity of the pre-whitened data is the discontinuity in the series during night-time
and early morning hours, during which times, irradiance is obviously inexistent. Figure 15
shows the ACF of the same data after differencing of the first order (V 1) is applied to the data.
Figure 15 shows the PACF of the same data. These figures suggest a moving average model
of order 2, considering the relatively large autocorrelations at lags 1 and 2. No autoregressive
parameters need to be included as is apparent from these figures. The parameters in the
initial model are estimated using maximum likelihood techniques and the model is checked
for goodness of fit. An accurate model produces residuals (one-step ahead forecasting errors)
that are white and will therefore have zero autocorrelations at lags 1 to oo. Figure 17 shows
that ACF of the residuals. From the figure it is evident that the fitted model is adequate except
Resource Forecast 99
1. 0] 0.8
0.6
~ O. LI
.... 0.2 < -' ~ -0.0 ~ 8 -0.2 .... :::> < -0.Ll
-0.6
-0.8
-1. 0 0 3 6 9
Figure 14. ACF of March Data in Raleigh.
Resource Forecast
12 LAGS
15 18 21 2Y
100
I. 0
0.8
0.6
~ 0.4
... < 0.2 ...J
~ -0.0 ~ 8 -0.2 ... ::::> < -0.li
-0.6
-0.8
-1. 0 0 3 6
Figure 15. ACF of the Differenced Data
Resource Forecast
9 12 LAGS
15 18 21
101
I. 0
0.8
0.6
0:: 0.4 0:: 0 <.> 0.2 0 t-::> < -0.0 _, < ;: -0.2
11 I I ~ Q. -0.4
-0.6
-0.8
- i. 0 0 3 6
Figure 16. PACF of the Differenced Data
Resource Forecast
9 12 LAGS
1 5 18 21
102
1. 0
0.8
0.6
~ 0.4
.... 0.2 < _, ~ -0.0 ~ 8 -0.2 .... ::> < -0. Li
-0.6
-0.8
-1. 0 0 3 6 9 12 15 18 21
LAGS
Figure 17. ACF of the residuals
Resource Forecast 103
that the model needs autoregressive factors at lags 4, 7 and 19, suggested by the spikes at
these lags.
Similar procedure was followed for all months of data available at each site. Table 8 and
Table 9 show the models fitted for the data in Raleigh and Richmond respectively.
Forecasted global irradiance are compared against the actual data at both sites. Also, the
photovoltaic power output as simulated by PVFORM are compared against actual PV output
data at both sites.
Figure 18 shows the comparison of the global irradiance data as forecasted by the ARIMA
model and measured global irradiance data at Raleigh for the 1st week of March. The figure
shows simulations at hours 12, 13 and 14. Forecasts are issued at the top of each hour for
all the ensuing intervals throughout the hour. For the site at Raleigh, each interval
corresponds to 3 minutes.
Figure 19 shows the predicted PV output for the same time intervals at the same site. Both
figures suggests that the forecasts are accurate most of the time except when there are
sudden transitional changes in the cloud cover moving across the sun. In other words, the
randomness involved in sudden extreme changes in the sun's intensity (e.g. bright sun to fully
shaded sun and back to bright sun again) during an interval will not be picked up by the
forecast model.
Figure 20 shows the comparison of modeled and observed data in the month of June at
Raleigh. The intervals in the figure are also equal to 3 minutes and the hours shown are 9, 10
and 11. Figure 21 provides the same comparative information for Richmond in March.
Forecasts are issued at intervals of 10 minutes at this site. The figure shows comparison for
the hours of 11,12 and 13. The transitional change from a clol!dY to a clear sky is evident but
Resource Forecast 104
Table 8. Fitted ARIMA (p,d,q) Models In Raleigh, NC.
Week Month d Autoregressive Moving Average Parameters Parameters
MAR 1 q>, = 0.085 (j)7 = 0.059 01 = 0.331 (j)19 =0.091 02= 0.163
1 q>5=0.089 q>8 =0.089 01 =0.491 JUN 1 q>,=0.092 q>g=0.117
(j)11 =0.086 MAR 1 q>5=0.102 01 = 0.332
02= 0.221 2 JUN 1 None 01=0.577
02 =0.212 (j)3 =0.123 (j)9 =0.093 01 =0.462
MAR 1 q>7=0.091 (j)14 =0.118 (j)15=0.090
3 JUN 1 q>3=0.085 01 =0.482 (j)g =0.120
MAR 1 q>4 =0.102 q>8 =0.106 01=0.391 (j)19 =0.070 02=0.132
4 JUN 1 q>2=-0.191 01 =0.415 q>5=0.110 02=0.397 q>8 =0.121 q>7=0.135 01=0.445
MAR 1 q>g=0.171 q>1,=0.108 02 =0.186 5 q>,g=0.147
JUN 1 q>3=-0.149 0, =o.306 <P12 = -0.148 02=0.181
Resource Forecast 105
Table 9. Fitted ARIMA (p,d,q) Models In Richmond, VA.
Week Month d Autoregressive Moving Average Parameters Parameters
1 MAR 1 None 01 = 0.265
2 MAR 1 q>, = 0.093 <p5 = 0.099 None <Jl11 =-.099 <j)19 =-.110
3 MAR 1 <Jl2 = 0. 143 <p5 = 0.078 None q>14 = 0.115 <p18 =-.099
4 MAR 1 <p4 = 0.093 <p8 = 0.157 None <p13 =-0.167
5 MAR 1 None 01 =0.189 02=0.249
Resource Forecast 106
N I: ...... :!
GI ~ Ill
-ij
~ -Ill ..c ,.Sil l.!J
800
600
400
200
Ob;erved - - - - Forecast
-\)\f'v
\\/ \ /"-- '\
0 '--~~~-'-~~~--I'--~~~-'-~~~-"~~~~-"-~~~-' 0 20 40 60
Intervals
Figure 18. Global lrradiance comparison at Raleigh In March
Resource Forecast 107
3750
3000
~ 2250 ~
0
> a.. 1500
750
-v----.:..
Observed - - - - Forecast
----
0 ...._~~~ ........ ~~~~--~~~---~~~~--~~~~.._~~~--0 20 40 60
I nlervals
Figure 19. PV output comparison at Raleigh in March
Resource Forecast 108
800
N ~
600 ' ;;§
II ~ 111
-6
~ - 400 111 ..ll _g l!)
200
I I I
\-v /\,-1
Observed ---- Forecast
0 '--~~~ ........ ~~~---'"--~~~..Jo-~~~--'~~~~_._~~~-' 0 20 40 60
Intervals
Figure 20. Global irradiance comparison at Raleigh in June
Resource Forecast 109
N l: ..... ;;s
Cll ~ RI
-ij
~ RI
...0
.Ji! l.!J
BOD
600
400
200
Ob;erved - - - - Forecast
3 6 9 Intervals
Figure 21. Global irradiance comparison at Richmond in March
Resource Forecast
12 15 18
110
is not very abrupt, and the forecasts therefore, follow the actual data with a fair amount of
accuracy.
Figure 22 shows the improvement in the accuracy of the forecasts when forecast updates are
applied at the half-hour mark. Hours 10, 11 and 12 are shown in the figure. Each interval
corresponds to 3 minutes. The RMSE (Root Mean Squared Errors) for the months of March
and June at Raleigh are 21.82% and 20.93% respectively. The MBE (Mean Bias Errors) for the
same two months at this site are 2.5% and 2.57%. At Richmond, the RMSE for the month of
March is 19.7%, while the MBE is 1.88%.
4.5 Conclusions on the Forecast Strategy
The following observations can be made about the predictive model and the results presented
in this chapter.
1. An accurate and relatively simple method (compared to other statistical methods) to
predict solar irradiance is proposed.
2. A comprehensive model is presented which can forecast the irradiance value for any lead
time from a few minutes to an hour.
3. Input requirements are not very restrictive. Only requirements are past global horizontal
irradiance measurement at a site.
4. Results show that when compared to actual data measured at several locations, the
forecasts are quite accurate and the model is site independent.
Resource Forecast 111
--N l:: ...... ~
cu g Ill
-6
~ Ill ...c _g
l!J
800
600
400
200
/\
Obi:erved - - - - Forecast
0 ,__~~~--'-~~~~..._~~~--"~~~~ ........ ~~~~..__~~~-' 0 20 40 60
Intervals
Figure 22. lrradiance comparisons with updates
Resource Forecast 112
800
N
~ 600 :!
Cll ~ Ill
-ij
~ Ill 400
...0
...5il l!l
200
Obi;;erved - - - - Forecast
0 '--~--'~~ ......... ~~--~~.L-~--'---~.....L.~~-'-~~..&.-~---JL...-~-' 0 4 8 12 16 20
Intervals
Figure 23. A case of model Inaccuracy.
Resource Forecast 113
5. Forecasts are found to be inaccurate only when there are sudden transitional changes in
the cloud cover moving across the sun. In other words, the randomness involved in
sudden extreme changes in the sun's intensity (e.g. bright sun to fully shaded sun and
back to bright sun again) during an interval will not be picked up by the forecast model
and is generally considered impossible to predict by any forecast model. Figure 23
illustrates an example of model inaccuracy. The hour shown is 10 A.M. It starts as a very
clear day and within one interval dark clouds cover the sun. As obvious, the model cannot
predict this situation.
6. One of the many applications of the forecast methodology is that, it may effectively be
used to predict photovoltaic power output at a lead time tL assuming a certain origin t0.
A PV plant may therefore be considered as a dispatchab/e generation unit comparable to
the operation of a combustion turbine unit in the generation scheduling scheme of electric
utilities.
Resource Forecast 114
CHAPTER 5
Unit Commitment
Unit commitment is the process of selecting a combination of generating units that will supply
a future expected load of the system over a required period of time, at minimum cost as well
as provide a specified margin of the operating reserve known as the spinning reserve. The
determination of the units to be operated in parallel in a given interval depends on their
operating costs as well as technical merits. While the operating cost consists of fuel and
maintenance costs, the technical merits include governor characteristic, stability limitation,
voltage regulation, etc., of the units.
As a matter of practice, generating units are broadly divided into two groups: (a) thermal and
(b) hydro. The operation of thermal units involves both fuel and maintenance cost, but that of
hydro generators require only maintenance costs. Thermal units include conventional steam
plants, nuclear plants, and diesel and gas turbine units. Of these four categories, the latter two
types are mostly used as peaking units, i.e., units are put to service during peak load periods
only. The other two types based on fossil and nuclear fuel respectively, run throughout the
load cycle, and are called base load units.
Unit Commitment 115
Unit commitment is a part of the production control scheme in power systems. The main
objective of production control is to minimize the cost of generated power while maintaining
its quality and satisfying the system security constraints. This implies directly that losses in
both the generation and the transmission of electrical energy must be as small as possible.
All participating generators are run at high efficiencies, the mix of production resource is
exploited economically and the energy is transmitted optimally.
The activities in the production control field have traditionally been based on planning. The
aim is to break down the overall objectives into detailed plans, normally on an hourly basis,
that can be carried out by the operator in the control center. Thus, several steps are taken
in a hierarchical scheme to support the operator's ambition always to have production
resources available to meet the load demand and guide him to operate the generating units
so that the most economic alternatives are chosen.
The long term off-line production planning takes all available generating plants into
consideration - hydro power plants, oil and coal-fired power plants as well as nuclear power
units; and then determines the set of generating units which meets the expected load demand.
This implies the requirement of load prediction functions to predict the future load demands,
both in the long and short term basis.
The active power production control is accomplished by the cooperation of several on-line and
off-line application functions in a four level hierarchy as outlined in Figure 24. Other programs
such as data acquisition, state estimation, security management functions, etc., are also part
of the production control package. Production control thrives on data transfer between each
level of the hierarchy and is therefore dependent on error-free operation of each of the
functions.
In most modern power system control centers, all functions are part of a man-machine
interface, the man being the dispatcher and the machine being a number of digital computers.
Unit Commitment 116
UlCAL CDHTRllL
RESOURCE SCHEDULING • Time interval - year/weeks • Weekly hydro generation • Fuel management.
UNIT COMMITMENT •Time interval - day/hours. •Hourly generation schedule. •Interchange schedule.
AGC •Time interval - minute/seconds. •Set points for plants or units. •Control of inadvertent tie-line flow.
ECONOMIC DISPATCH •Time interval - hour/minutes. •Base points selection. •Participation factors.
LOCAL CONTROL •Time interval - seconds/milliseconds. •Control orders for units. •System frequency control.
Figure 24. A four-level hierarchy In production control
Unit Commitment 117
c ::I ;::; 0 0 3 3 ;::; 3 111 a
..... CD
Dn-lln• CoMput•r Bo.ck-up CoMputer
St!curlt:t:'. Functions SysteM Support
Alo.rMs Logging AutoMo. tic Genera. tlon Control Buy I sell Ne go tlo. tlon
Sto. te Estll'lo. tton Un11: COMMl1:Ment
Contingencies I I I Loo.d Flow
EconoMlc Dlspo. tch Loo.d F oreco.stlng
Supervisory Control o.nd Do. to. Acquisition
<SCADA>
Short Circuit
I Sto.blllty
Figure 25. Relationship of unit commitment to other programs In the control center
Figure 25 shows a functional block diagram of the control center. The relationship between
unit commitment and the other programs in the production control hierarchy is evident from
the figure.
5.1 Solving the Unit Commitment problem
At present, unit commitment algorithms consider the following generic constraints:
• Initial unit operating conditions
• Unit maximum/minimum output levels
• Unit minimum up-time and minimum down-time
• Crew constraints
• Must-run and must-out constraints
• Spinning reserve constraints
While the purpose of this dissertation is not to solve the unit commitment problem, it will be
worthwhile to mention the existing solution techniques. The most talked about techniques for
the solution of the unit commitment problem are linked to six types of methods:
1. partial enumeration method (of the branch and bound type)
2. dynamic programming (DP) method
3. Benders partitioning method
4. heuristic method (e.g. priority list scheme)
5. Lagrangian relaxation method
6. Mixed integer-linear programming (MILP) method
Unit Commitment 119
Of these methods, the priority list scheme is the most popular. DP algorithms are the only
ones that approach an optimum solution for large systems. MILP algorithms are just
beginning to be researched and are not widely used on large system problems. Besides the
above solution techniques, a new solution methodology has been introduced in (194). The
author proposes an expert system approach in this methodology.
Results of a unit commitment program are an integral part of this dissertation. This is used in
the proposed economic dispatch program discussed in a later chapter. In the development
of this model for incorporating central station PV systems, a priority based unit commitment
program was used. The specific program used is the "Unit Commitment and Production
Costing Program (GPUC)" developed by Boeing Computer Services for the Electric Power
Research Institute (EPRI), (29,30). A brief discussion of the program is given below, details can
be found in (29,30).
5.2 EPRl's Unit Commitment Program
The program is designed to analyze the operations of generation and transmission systems
consisting primarily of thermal committable generating units and with possible additional
capacity in the form of non-committable combustion turbines, pumped storage hydro and
hydro units. Its main function is to schedule generation and interchange on an hourly basis
for periods ranging upto a week. Given a profile of the expected integrated hourly loads, a
description of the generation system and a set of scheduling constraints, the program
generates a unit commitment schedule such that the expected system load is met at suitably
low cost without violating any of the numerous operating constraints. Once a schedule has
been determined, the total production costs (fuel plus any start-up costs) are estimated. The
Unit Commitment 120
program also monitors fuel consumption by generating unit, station and fuel type and
compares this usage with any fuel usage constraints.
The following subsections highlight the scheduling process used by the program.
5.2.1 Input Data
The input data required by GPUC consists of:
• processing options such as spinning reserve requirements, priority list generation
options, load specification option, etc.
• unit identification, cost and performance data such as unit id, heat rate curve, startup
time, minimum downtime, maximum up time, boiler cool down time, etc.
• load models for a week. The load for each 24 hour period is assumed to start at 8:00 a.m.
and the loads specified have to be hourly integrated loads.
• manual scheduling data for hydro, pumped hydro and thermal units and interchange.
• transmission loss data appropriate to the option exercised. GPUC allows three options for
this purpose:
• ignore transmission losses;
• compute transmission losses using the 8-constants provided; or
• use a quadratic function of the load for computing losses.
5.2.2 Priority List Generation
Commitment of dispatchable units proceeds on the basis of a single priority list which may
be provided by the user or generated by GPUC. The priority list generation is based on the
Unit Commitment 121
operating cost of a unit at a user specified fraction of the generator set capacity. Units are
removed from the set as their priorities are assigned. The process stops when the capacity
of the reduced generator set is a specified fraction of the total generation capacity. The units
remaining in the set are then assigned priorities based on the relative operating costs at their
maximum capacity.
5.2.3 Hourly Generation Maximum Capacity
This quantity is central to the scheduling of non-committable capacity. It is determined as the
summation of:
1. the maximum capacities of all on-line committable units
2. the maximum capacities of any combustion turbines which are user-scheduled to be
on-line; and
3. any user-scheduled interchange and hydro capacity.
5.2.4 Reserve capacity From Non-committable Sources
All non-committable sources contribute to two types of reserves (ten minute and spinning
reserves) as a function of the unit type and status during the hour. The reserve capacity from
non-committable sources is required in order to compute:
1. the ten minute and spinning reserve capacity from such sources; and
2. an estimate of the additional reserve capacity from the committable sources.
Unit Commitment 122
5.2.5 Precommitment of Peaking Units
The purpose of this process is to schedule combustion turbines and interchange on an hourly
basis such that, for each hour:
1. there is sufficient on-line generating capacity and interchange to meet the expected load
plus losses;
2. if possible there is sufficient capacity and interchange to meet the load plus losses and
reserve requirements; and
3. if desired by the user, peaking units are scheduled to displace the more expensive
thermal units.
For each hour, two inflated estimates of required capacity are made:
1. an estimate of load plus losses computed by multiplying the hourly load by a user
specified factor. This estimate is denoted as TLOAD1.
2. TLOAD1 is further inflated to TLOAD2 by the addition of
• a user-specified non-negative factor called ADDPK which can cause GPUC to
schedule combustion turbines to displace the more expensive committable units; and
• a measure of potential spinning reserve deficit for the hour.
Peaking capacity or interchange is then scheduled according to whether GMAX, the hourly
maximum dispatchable capacity, lies above, below or between TLOAD2 and TLOAD1.
Unit Commitment 123
5.2.6 Hourly Regulation Requirement
GPUC does not require ramp rate inputs for the generating units. However, it attempts to
provide sufficient regulating margin during periods of load pickup. The policy followed in the
program is, that 'in the average system, bringing additional capacity on-line at a given hour,
equal to the load pickup the next hour, should ensure a system response rate sufficient to
meet the increased demand'. The regulation requirement for hour h is found by calculating
the increase in the dispatchable load, DELPWR.
DELPWR = (FL(h + 1) - FL(h)) x GENMIN + PNON(h) - PNON(h + 1) (5.1)
and
DISREG(h) = REGFAC x DELPWR, forDELPWR > 0
or
DISREG(h) = 0 for DELPWR < 0
where
FL(I) = the integrated MW load for hour I
PNON(I) = the total non-committable generation for hour I
DISREG(I) = regulation requirement for hour I
REGFAC = user-input regulation factor.
Unit Commitment
(5.2)
124
5.2.7 Committable Unit Commitment Schedule
The dispatchable unit commitment schedule is basically arrived at by considering a shutdown
decision for each unit on an hour by hour basis. The default status of all dispatchable units
is the Economic Run status. Then at every hour a decision is made whether to shut down a
unit or not. The decision is first based on a comparison of GMAX versus the load, loss,
reserve and regulation requirement for each hour that the unit would be shutdown, upto its
minimum down time. If this comparison allows the unit to be shut down, an economic
comparison is made. This is done by prorating the unit's startup cost over the shutdown
period and the up-time. A comparison of an hour's fuel costs plus the hour's prorated value
of start-up costs will allow the determination of the most economical set of on-line generators.
Once the schedule of committable and non-committable units has been determined, an
economic dispatch is done and production costs are calculated and fuel usage is logged.
Unit Commitment 125
CHAPTER 6
Economic Dispatch
Among the major economic-security functions in power systems operation, economic dispatch
is unanimously ranked very high by most power system engineers. This is a procedure for the
distribution of total thermal generation requirements among alternative sources for optimal
system economy with due consideration of generating costs, transmission losses, and several
recognized constraints imposed by the requirements of reliable service and equipment
limitations.
It is important to emphasize that the problem to be considered in this chapter is the problem
of minimizing production costs in real-time under the assumption that the generators available
have already been specified {i.e., we know which generators are on-line or committed at a
given moment) by a unit commitment program. The optimization is therefore concerned with
a particular set of generators. The economic dispatch problem has historically been the most
researched topic in power systems operation [125). One of the earliest methods to be adopted
is the base load procedure, whereby units are successively loaded to their lowest heat rate
point beginning with the most efficient unit.
Economic Dispatch 126
The incremental cost method was first formally derived by STEINBERG and SMITH (264) in
1934, even though it was recognized as early as 1930. The idea is that the next increment in
the load should be picked up by the unit with the lowest incremental cost. Loss inclusion in
the formulation and solution, received a boost in 1943 by the publication of the derivation of
a loss formula by GEROGE (116). The classic coordination equations were discovered by
KIRCHMAYER and STAGG (165), in 1951. These results form the backbone of today's economy
operation methodology. The classic book by KIRCHMAYER (166), published in 1958, gives a
comprehensive treatment of the loss formula derivations and the conventional economic
dispatch problem. Chapter 2 of this dissertation discusses in detail, the current status of
economic dispatch and the inclusion of PV systems in such algorithms.
The developments cited so far find their mathematical background in the classical
optimization results employing classical theory of maxima and minima in the static case and
variational calculation in the dynamic case. The solution of further problems has been
enhanced by the development of powerful optimization and computational techniques.
Bellman's principle of optimality and dynamic programming in 1950's, gave an impetus to
problems involving discrete and discontinuous variables. The introduction of Kuhn-Tucker
theorem in 1951 to the optimization literature, made it possible to include inequality
constraints in the problem formulation.
6.1 AGC and Economic Dispatch
Today's major power systems are not isolated entities. They are usually connected to a
number of neighboring utilities' power system and therefore power flows in all directions.
Needless to say, there are legal constraints and agreements enforced to govern the power
Economic Dispatch 127
flow over the tie-lines. Yet, inadvertent flows are not uncommon and consequently cause
departures of the area control error (ACE) from its zero setting.
Let Pd denote the demand power, 'P;. the total system losses, and P5 , the total intertie power
(P5 > 0 implies net injection of active power flow). Then one would expect that P9.,n, the total
power generation required from the economic dispatch routine will be:
(6.1)
With inadvertent intertie flows, then,
(6.2)
becomes non-zero for short periods of time. If the ACE is positive, there is excessive
generation and machines will accelerate, while negative ACE results in machine deceleration.
The ACE, expressed in megawatts is a very important system parameter. It is usually
displayed to the dispatch operator together with system lambda.
There is a relationship between the ACE and system frequency. The ACE can also be
expressed as:
ACE= M - S +BM (6.3)
where
M = metered interchange, MW
S = scheduled interchange, MW
B = frequency bias, MW/HZ [74)
~f = frequency deviation from 60 HZ (system frequency), HZ
It is a function of the automatic generation control (AGC) algorithm of the power system to
take remedial measures to correct the ACE back to zero within a stipulated period of time.
Economic Dispatch 128
m n 0 ~ 0 3 er c iii
"C I» -n ':S'
.... w 0
Load Precl1ct1on
Predicted
Bus Loads
EconoMlc Dispatch
Base Points Po.rtlclpo. tlon
Fo.ctors
'-------• Bus loads ._ __ ..,. ___ _
Unit CoMMltMent or Opero.tor Entered
Vo.lues
Bo.lo.nee
AutoMo.tlc Genera. tlon
Control
Bo.se Points to o.ll other
Production Units
Figure 26. AGC and economic dispatch functions
Generator Setpolnts to Plo.nts
f>o.rt1c1po. ting In AGC
6.1.1 Load Frequency Control
The load frequency control (LFC) system, deals with the control of loading of the generating
units vis-a-vis the system frequency. The loading in a power system is never constant and the
system frequency remains at its nominal value only when there is matching between the
active generation and the active demand. During changing demand condition, the frequency
error, that is, the deviation of frequency from its nominal value, is therefore, an index of
mismatch and can be utilized to send the appropriate command to adjust generation.
The function of the LF system is to basically control the opening of the inlet valves of the prime
movers according to the loading condition of the system. In the case of a multi-area system,
the above control system also maintains the specified interchanges between the participating
areas. In smaller and simpler systems, the control is generally exerted manually, but in large
systems, automatic control devices are used in the loop of the LFC system.
Single-area system
A single-area system is one which is not connected to any other system and hence the
demand on the system is fully met by its own generation. Sudden load changes are
accommodated in such systems in the following way:
1. Change in stored energy - The sudden load increment is initially supplied from the stored
energy of the spinning capacity of the system by bringing down the frequency of the
system.
2. Change in effective load - Due to the drop of the frequency, the total load on the system
effectively decreases (due to the frequency dependence nature of the load), thus allowing
the already available generation to partly serve the added demand.
Economic Dispatch 131
3. Change in generation - The reduced frequency actuates the inherent speed-governing
system of the generating units which then increases the input to the prime-movers
causing increased generation which prevents any further drop in frequency. The units
behave coherently, thereby maintaining equal frequency deviations among them.
For a sudden drop in demand, the above behavior follows a reverse sequence, i.e., the
frequency will increase and thereby the effective load on the system will be slightly increased.
These will then be followed by decreased generation due to the actuation of the governing
system of the units.
Multi-area system
In the operation of areas interconnected to one another, a step-load change in any area
belonging to the system, causes a non-zero static error of the frequency and area interchange.
For such systems, a control strategy that will set both frequency and interchange deviations
ultimately to zero, is therefore, needed. An integral control scheme is usually applied with an
input to the integral controller of each area, of the form:
The above input is known as the area control error of area i. B; represents the frequency bias
of the area, and ~S; indicates the interchange error. The above control scheme is known as
the tie-line frequency bias control. The control causes each area to absorb its own load
changes during the normal operating condition and thus to take part in the control of the
system frequency. During emergency, when one or more areas are unable to absorb their own
load changes, the remaining areas assist the affected areas by permitting power transfer
beyond scheduled values, provided the interconnection remains synchronous. The frequency
will be deviated from normal to the extent needed to provide the necessary assistance.
Economic Dispatch 132
ZDNE-2 ZDNE-1 N c I
:>. ~ f O Q.I ::s 0- N Cl.I t.
Li..
ZDNE-3 ZDNE-4 c
1 IN - TO ., OUT
Are<l net lntercha.nge, M\J
Figure 27. System frequency characteristic versus tie-line flow
Economic Dispatch 133
The frequency bias 8, is generally expressed in MW per 0.1 per Hz and its recommended
value varies from 0.5 ~ (~ = area frequency response characteristic) to ~ of the area. The
characteristic of the tie-line frequency bias control, which operates to reduce the area control
error to zero, is shown by the straight line CC in Figure 27. The line CC has a slope given by
the reciprocal of 8, the frequency bias. The horizontal line through fo (nominal frequency) and
the vertical line through T0 (scheduled interchange) cross at the point N on the line CC and
thus N defines the scheduled net interchange at the normal frequency. When the operating
condition of the concerned area is such that it falls on the line CC, the ACE will be zero. But
if the point does not fall in the line, then its horizontal distance from CC represents ACE. To
actuate the control, the point should be in the proper zone. Thus, for an area which is sending
power out of the area, zone 4 in the figure is an inoperative area. This is because the errors
in the zone are of opposite sign - the frequency error is negative while the interchange error
is positive. Hence, such an operating condition of the area, although not normal, will not
actuate its control. On the other hand, when the point falls in zone 3, such as N', the control
will act to increase the area generation. Similarly, zone 1 is an operating zone and the control
will act to reduce the area generation.
6.2 Formulating the Economic Dispatch Problem
The classical approach to formulating the economic dispatch problem is the calculation of
generator outputs from on-line (committed) units to satisfy the system load plus losses at the
minimum cost. The cost of operating a unit may be expressed as the product of fuel cost and
heat rate:
(6.4)
Economic Dispatch 134
where F1 = fuel cost and H1 = heat rate (input to the unit as heat energy requirements).
The heat rate of a thermal unit relates the unit's efficiency to the unit's total MW generation.
One popular method of representing this relationship relates the required energy input to the
MW output by an quadratic expression of the form:
- 2 H; - a; + bf; + cf 1 (6.5)
where a,, b1 and c, are the heat rate coefficients and P1 is the MW output of the unit. This results
in the following relationship between the cost of a unit and its MW output:
The economic dispatch problem can now be stated as:
n Minimize z = ! C,{P;)
i=1
such that !P1 - system load = 0
(6.6)
(6.7)
(6.8)
Realistic dispatching requires consideration of many more constraints than the primary power
balance constraint shown in equation 6.8. These are:
1. GENERATION LOSSES Considering line losses, the power balance constraint shown in
equation 6.8 is modified to:
p ! p;. - system load - losses = 0
I
where PF1 = penalty factor for unit i
= 1 (PL = systemload) 1 - oP/oP,
2. SPINNING RESERVE
Economic Dispatch
(6.9)
135
n l: min(G; - P1 S;) :::?: R j I
(6.10)
Where G1 = capacity of unit i
S; = maximum spinning reserve allowed on unit I
R = total spinning reserve required for the system.
3. UP-RAMP CONSTRAINT
(6.11a)
4. DOWN-RAMP CONSTRAINT
(6.11b)
Where llT = the economic dispatch interval.
y,1 .Yu = increase and decrease response rates in %/min.
5. CAPACITY LIMITS
P min,i S:: P;j S:: P max,/ (6.12)
6.3 Solving the Economic Dispatch Problem
An examination of the economic dispatch problem formulated in equations 6.7 through 6.12,
it is clear that it is a non-linear optimization problem. Several methods have been introduced
for its solution [289).
1. Penalty methods
Economic Dispatch 136
2. Gradient projection
3. Linearizing
4. Lagrangian methods
5. Direct search
Of the above five, perhaps the most widely used method is on that belongs to the fourth
category. Also known as /..-dispatch, the Lagrangian multiplier method is based on the
Incremental cost rule. The rule states that the minimum generation cost occurs when the
incremental costs of all units are equal. In other words, the cost of generating an aditional MW
is the same for all units.
A.= dC1 = dC2 = ... = dCn (6.13) dP1 dP2 dPn
Equation 6.13 portrays the essential significance of the incremental cost rule. Iterative
algorithms to solve the economic dispatch problem may be found in reference (289).
Economic Dispatch 137
CHAPTER 7
Implementing PV Dispatch in a New Economic
Dispatch Algorithm
In this chapter, the proposed strategy for the dynamic economic dispatch incorporating
photovoltaic (PY) generations is discussed in detail. The strategy is a combination of a
conventional economic dispatch and a rule-based system replacing the dispatcher. A case
study using the proposed strategy will be presented in the next chapter.
7.1 Need For a New Approach to Economic Dispatch
Optimal dispatch of photovoltaic (PY) power in its true meaning, is actually non-existent in the
current status of the research on the integration of this relatively new technology in the utility's
power system. This fact is clearly portrayed in the survey done in Chapter 2. The most
effective utilization of PV power can be envisaged in the three following roles:
Implementing PV In an ED Program 138
• Directly serving the load
• Reliability service (equivalent to spinning reserve)
• Load frequency control
For a thermal plant, these functions are inherently built-in, but for a PV plant, with the present
technology, it has not been possible to play all the above roles, simply because of lack of
control.
The need for definite control strategies becomes evident when one examines the role of PV
plants at present. PV operation in power systems has essentially been limited to hourly
system load modifications by PV output and then scheduling the conventional generations to
supply the net load. In other words, PV generation is only used to get a modified unit
commitment output (88,175,245). The unit commitment programs generally provide the
information on thermal, hydro and combustion turbine (CT) units scheduled for a period of 24
hours to a week. Besides, a production costing sub-program computes the cost of generation
to supply the expected loads during the same period. The program is executed twice, once
with PV power output and then again without the same. The difference in production costs
revealed by these two runs, indicates the fuel credit attributable to the PV system. This
approach has several disquieting characteristics. These are:
1. PV output over the day or week of the unit commitment period is simulated using typical
weather data at the site. While load forecasts during this period follow a particular trend
and are generally considered accurate to a certain degree, the same cannot be said for
the PV output. The reason is that, PV plant performance depends on the highly variable
weather phenomena and are liable to extreme changes during the week. Weather
forecasts as far ahead as one week can not be considered reliable. Therefore, the amount
of uncertainty introduced into the unit commitment program output is considerably
increased because of the presence of PV power.
Implementing PV In an ED Program 139
2. With this approach, PV power is considered to be forced on the system. No care is taken
to see whether the PV plant might be operating during a period of time when the
base-load units are operating. The latter are required to operate at the same level of
generation throughout the day, in order to be most economic. Also, no care is taken to
see whether there is enough cycling capacity available at any time during which the net
load changes substantially because of the forced PV generations.
3. The penetration level (capacity rating of PV plant compared to total system capacity) of
PV power is not well defined. Apparently, the phrase "the more the better" applies to this
case. Increased PV generations causes increased fuel savings. Therefore, the larger the
PV plant, the better or more economic it is for the entire system as a whole. But with
increasing amount of PV power, there comes a situation when some conventional
dispatch units will not be scheduled by the unit commitment (UC) program which
otherwise would have been scheduled because the UC program is led to believe there is
enough firm capacity. This change in the generation schedule is not acceptable because
of uncertainties involved with PV plant operation and the potential severity in the system
security because of loss of valuable spinning reserve. As mentioned in (1), PV power is
only as reliable as the weather, and decommitting a unit means loss of valuable spinning
reserve and possible regulating capacity for a number of successive hours. (Once a
steam unit is brought down, it cannot be brought back up immediately). Considering this
probable outcome, we are led to the contradictory statement that PV penetration should
be limited. (In (164) though, the authors using a static approach, have found that the
penetration of a PV plant is prevented from increasing beyond a certain limit because of
adverse economic affects.)
Implementing PV In an ED Program 140
7.2 Proposed Rule-based System Approach
Clearly a more qualitative approach is desirable for treating the presence of PV power in the
power system. PV plants are capital intensive and the cost of producing energy from such
plants can only be justified if the energy produced is used to serve more functions than just
reducing the load by a small amount, which in most cases, appears to be mere noise in the
presence of large utility loads. Whenever PV penetration exceeds 5% of the total system
capacity, it is no longer considered to be just noise and definite control regimes must be set
in order to accomplish trouble-free operation of the integrated system.
7.2.1 Present Functions of the Dispatcher
Dispatchers (operators) have to make decisions regularly when they operate and control the
power system. Even in the absence of unusual and emergency situations, many of the
decisions still are non-trivial in their nature. Therefore, a successful operation depends on the
ability of the dispatcher to interpret information and to execute proper control orders.
Today, the work of the system operator is eased in many ways, for example, a computerized
control system can improve the interpretation of the vast amounts of data which are
transmitted and collected in control centers. Application functions of various types also
contribute to helping the dispatcher in the decision making process, but the requirement is
that he must have the expertise or experience to use them.
An economic dispatch program is run at every 3-10 minute interval. The dispatcher has to
work from the hourly committed dispatch units and use standard procedures to allocate
generation levels, maintain the right amount of regulating capacity, maintain the system
Implementing PV In an ED Program 141
frequency, maintain the area control error at zero in case of interconnected systems, bring
up fast start-up units like peaking hydro or gas turbines in case of emergencies, etc. The work
of the power system dispatcher has changed significantly due to technical developments
which have taken place in the field of computerized control systems. Routine and tedious data
manipulations are handled automatically and application functions are introduced
successively into the control systems repertoire. Hence, the world of the dispatcher becomes
confined to more and more unique abilities which humans possess. For example, he is
required:
• To distinguish known patterns among large amounts of data and thereby to choose
appropriate strategies and approaches; and
• To inject intuition and common sense into the control of the power system.
To master his task skillfully, the dispatcher must be taught:
• Basic facts
• Methodological knowledge
• Active competence
Using these features, which are developed with time, the dispatcher makes his decisions. An
example of a situation where his experience is called upon is during the morning load pick-up
period when the constraints of power balance and operating reserve are stretched to their
limits. The situation is handled by the dispatcher's ramping of the more expensive units above
their economic assignment early in the load pick-up period and thus keeping some less
expensive units below their operational limits in the early stage, so that they can help satisfy
the load pick-up required at the later stages. In this case, the dispatcher chooses to go with
the safe solution than an economical one.
Implementing PV In an ED Program 142
It is conceivable to represent the knowledge of the dispatcher as a rule-based computer
algorithm. The decision making process of the dispatcher renders itself perfectly to a set of
*If-Then" rule structures for use by a rule-based system. This rule base (RB) approach to
economic dispatch becomes almost a necessity when the dispatch algorithm has to deal with
the operation of a photovoltaic system. This is discussed next.
7.2.2 A Rule Base Replacing the Dispatcher
A rule base will be defined as an intelligent combination of procedures that uses knowledge
and inference techniques of the human expert to solve problems in an algorithmic manner.
In narrow problem domains, the rule base can provide high performance, equalling or even
exceeding that of human individual experts.
In the proposed dynamic economic dispatch incorporating PV, a rule base is introduced to
operate, either by itself or in tandem with a conventional economic dispatch algorithm. The
functions of the two are coordinated by another algorithm which overlooks the flow of
information and records them. This functional relationship between the three computer
program modules are shown in Figure 28. Details of each module are discussed later in this
chapter. At this time, it is worthwhile to examine the nature of the problem introduced by the
presence of PV power in the mix before rules are established for an RB approach to the
solution.
7.2.2.1 PV Dispatch
The treatment of PV generations is considered, in this economic dispatch approach to be
similar to that of combustion turbines (CT). The essential similarities are the fact that CTs can
be brought on-line within a very short period of time whenever there is need for extra capacity,
Implementing PV In an ED Program 143
ECDl\JDMIC DISPATCH
DRIVER
RULE BASE
Figure 28. The three computer modules in the proposed operation scheme
Implementing PV in an ED Program 144
and they can be backed off whenever desired. Proceeding along those lines, provided PV
power is forecasted to be available at say 100 MW, the PV plant may be controlled to produce
anywhere from Oto 100 MW as and when required. Dissimilarities exist in the operation of the
two plant types though. Whereas, a CT plant operates on a low capacity factor (average
capacity of operation over the rated capacity) because of high cost of fuel, a PV plant is
expected to run on as high a capacity factor as possible in order to compete favorably against
conventional thermal units. Therefore, the PV plant will be required to not only supply the peak
loads as CTs, but also during intermediate load periods.
Unquestionably, the single most important parameter that is the cause of PV dispatch
problems is the response rate of thermal units. During dispatch, the fundamental constraint
becomes:
At any time t, expected power generation required from the thermal generators must equal expected load at t minus the sum of generation from non-conventional sources minus the PV output at t.
(7.1)
implying:
(7.2)
where G, = the total thermal generation at time t
G,_, = the total thermal generation at time t-1
D, = the total demand at time t
D,_, = the total demand at time t-1
4 = the total losses at time t
4-, = the total losses at time t-1
lmplementlng PV In an ED Program 145
c, = the total combustion turbine generation at time t
c,_ 1 = the total combustion turbine generation at time t-1
H, = the total hydro generation at time t
H,_ 1 = the total hydro generation at time t-1
PSH, = the total pumped-storage hydro generation at time t
PSH,_ 1 = the total pumped-storage hydro generation at time t-1
IC, = the total interconnected power flow at time t
IC,_ 1 = the total interconnected power flow at t-1
PV, = the total photovoltaic generation at time t
PV,_ 1 = the total photovoltaic generation at time t-1
Normally, differences in losses and other load-generation mismatches in the absence of PV
power are easily picked up by cycling (load following) units and the system maintains a
matched load condition. With PV power on the other hand, large variations in PV output can
cause the thermal plants to reach their response limits before load matching constraint is met.
Therefore, two conditions might arise:
• Thermal generation increase not possible in the dispatch interval.
This situation may arise because of a sudden drop in PV power in the mix, causing the
thermal generators to attempt to make up the loss. Using the up-ramp response
constraint of each cycling thermal unit, the total system response capability (regulating
capacity) in the Hup" direction should be greater than or equal to the change in generation
required of the units. Mathematically,
(7.3)
where l!.T = dispatch interval
Pit_, = MW output of unit i at interval t-1
Implementing PV in an ED Program 146
y,; = response rate of unit i In the raise direction (%/min)
Violation of equation 7.3 implies corrective action has to be taken to reach optimality.
• Thermal generation decrease not possible in the dispatch interval.
This situation is brought about when there is a sudden increase in PV generation in the
mix possibly by movement of clouds away from the area. The thermal generators are
expected to back-off part of their generations (unload) in order to accommodate the
additional PV power. Once again, the response rate of the thermal generators plays an
important role, this time in the "lower" direction. According to the down-response rate of
each unit, the total system response capacity in the lower direction should be greater
than or equal to the change in generations required from the generators. Mathematically,
(7.4)
where y11 = response rate of unit i in the lower direction (%/min.)
Violation of equation 7.4 once again implies corrective action has to be taken, by the
dispatcher.
The corrective actions are channeled into "rules" or "if-then" logic structures. These rules are
described next.
7.2.3 Rules in the Rule Base
Problems in operation require corrective actions so that the system may be brought back to
an optimal state. Figure 29 shows the situations where rules are applied for corrective action.
The following is a list of the set of rules written for the RB.
Implementing PV in an ED Program 147
THERMAL UNITS UNABLE TO PICK UP INCREASED NET DEMAND
1. Increase PV generation input 2. Increase hydro generation 3. Increase pumped storage plant output 4. Increase CT generation 5. Start-up unscheduled hydro unit 6. Start-up unscheduled PSH unit 7. Start-up unscheduled CT unit 8. Buy more unscheduled interconnected power
THERMAL UNITS UNABLE TO UNLOAD
1. Decrease CT generation 2. Decrease pumped storage output 3. Decrease hydro generation 4. Shut-down scheduled CT unit 5. Shut-down scheduled PSH unit 6. Shut-down scheduled hydro unit 7. Release scheduled interconnection 8. Decrease PV generation input
Choose the 'best' option
Redo the Dispatch Program. Get new system Lambda Set artificial maximums and minimums Recalculate reserve capacity Change status of units if applicable
Figure 29. Operational scenario with PV system
Implementing PV In an ED Program 148
RULE-SET 1 If thermal units are unable to pick up the increased net demand of the system, and
if the PV plant was operating at below maximum capacity in the last interval of the dispatch,
then increase PV generation.
RULE-SET 2 If thermal units are unable to pick up the increased net demand of the system, and
if RULE-SET 1 is not satisfied, then increase hydro generation.
RULE-SET 3 If thermal units are unable to pick up the increased net demand of the system, and
if RULE-SET 2 is not satisfied, then increase pumped storage hydro generation.
RULE-SET 4 If thermal units are unable to pick up the increased net demand of the system, and
if RULE-SET 3 is not satisfied, then increase combustion turbine generation.
RULE-SET 5 If thermal units are unable to pick up the increased net demand of the system, and
if RULE-SET 4 is not satisfied, then start-up unscheduled hydro unit(s).
RULE-SET 6 If thermal units are unable to pick up the increased net demand of the system, and
if RULE-SET 5 is not satisfied, then start-up unscheduled pumped storage unit(s).
RULE-SET 7 If thermal units are unable to pick up the increased net demand of the system, and
if RULE-SET 6 is not satisfied, then start-up unscheduled CT unit(s).
RULE-SET 8 If thermal units are unable to pick up the increased net demand of the system,
and if RULE-SET 7 is not satisfied, then buy unscheduled interconnected power.
RULE-SET 9 If thermal units are unable to unload the extra generation because of a decrease
in net system demand, then decrease CT generation.
Implementing PV In an ED Program 149
RULE-SET 10 If thermal units are unable to unload the extra generation because of a decrease
in net system demand and if RULE-SET 9 is not satisfied, then decrease pumped storage hydro
generation.
RULE-SET 11 If thermal units are unable to unload the extra generation because of a decrease
in net system demand and if RULE-SET 10 is not satisfied, then decrease hydro generation.
RULE-SET 12 If thermal units are unable to unload the extra generation because of a decrease
in net system demand and if RULE-SET 11 is not satisfied, then shut down scheduled CT
unit(s).
RULE-SET 13 If thermal units are unable to unload the extra generation because of a decrease
in net system demand and if RULE-SET 12 is not satisfied, then shut down scheduled pumped
storage hydro unit(s).
RULE-SET 14 If thermal units are unable to unload the extra generation because of a decrease
in net system demand and if RULE-SET 13 is not satisfied, then shut down scheduled hydro
unit(s).
RULE-SET 15 If thermal units are unable to unload the extra generation because of a decrease
in net system demand and if RULE-SET 14 is not satisfied, then decrease tie-line interchange
flow.
RULE-SET 16 If thermal units are unable to unload the extra generation because of a decrease
in net system demand and if RULE-SET 15 is not satisfied, then decrease photovoltaic power.
The set of rules 1 through 8 are valid for the situation when there is a significant reduction in
the non-committable generations causing the thermal generators to attempt to pick up
Implementing PV In an ED Program 150
Comment Check to see if PV plant is present in the generation mix. If (PV_STATUS = 0) then
else
begin Comment No PV plant is present. Therefore, set flag to false
and go to rule 2. FLAG1 : = false; end
begin Comment PV plant is present in the mix. Check if the plant
is running at maximum capacity. If (PV_GEN_NOW = PV_GEN_MAX) then
begin
endif
Comment Change in PV generation not possible. Diagnosis: plant is running at full capacity or plant is down.
FLAG1 : = false; end
If (PV_GEN_MAX - PV_GEN_NOW < INC_AMOUNT) then begin
else
Comment Possible increase in PV generation is less than the increase required by the system (INC_AMOUNT). So increase PV power by whatever amount possible and go to rule-set 2.
FLAG1 : = false; PV_GEN_NOW := PV_GEN_MAX; end
begin Comment Increase in PV generation is possible. PV GEN NOW : = PV GEN NOW + INC AMOUNT; FLAG1 : ;, true; - - -end
end If end
endif
Figure 30. Rule-set 1.
Implementing PV In an ED Program 151
generation. Response limitations of thermal units therefore require other measures to be
taken. Rule-set 1 receives the highest priority as logical reasoning dictates that PV power
ought to be optimally utilized. Therefore, it will be the purpose of the RB to supervise the
presence of maximum possible PV power which is the most favorable scenario from the
production costs point of view. Rule-set 1 is illustrated in Figure 30. Although, the rules are
written in FORTRAN, the style of a declarative language is used to represent the logic.
Rule-set 2 through 4 are similar although concerning different unit types. Hence these are not
repeated here. Rule-set 5 through 8 are apparently violations of the optimal solution given by
the unit commitment program. There is nothing so alarming about this violation. The only
concern under this action, that of departure from optimality, is quite unwarranted, because the
system is already in a sub-optimal state considering the fact that the thermal units are not
able to follow the economic trajectory. The only legitimate concern under this situation should
be that starting up unscheduled units may violate some constraints, e.g., minimum up-time
or minimum down-time requirements. The rules to be established are therefore required to
examine these constraints before starting unscheduled units. As for start-up time itself, the
units to be considered by the RB for start-up are fast-start units, like peaking hydro, pumped
storage hydro and combustion turbines, which need little warm-up time. Figure 31 shows the
logic for rule-set 5. Once again, for avoiding repetition of similar characteristics, rule-sets 6
and 7 are not shown. The logic for these set of rules is centered on locating the optimal
capacity unit which matches the generation increment requirement INC_AMOUNT. If that is
not possible, multiple units are searched for, whose combined capacity adds up to the variable
INC_AMOUNT. A sub-program called PRIORITY locates these units and "pushes" these units
into a "stack", with the highest priority unit residing at the top of the stack. A sequential "pop"
operation then brings out these units from the "stack".
Rule-set 8 is somewhat different from other rules, as it involves buying unscheduled power
from interconnected systems. This action advocates caution because it involves more than
one area. Area control error (ACE) problem is one criterion that must be looked into before
Implementing PV in an ED Program 152
Comment Check to see If a hydro plant Is present in the generation mix. If (NUM HYDRO = 0) then
begin
else
Comment No hydro plant Is present. Therefore, set flag to false and go to rule 6.
FLAG2 : = false; end
begin Comment Hydro plant is present In the mix. Search for units which are down.
If found, locate the unit with a capacity which matches the MW amount of increase required by the system.
UNIT FOUND:= O; NUM-LOOP := 1; N := -NUM HYDRO; While (N >-0) do
begin If (UP _HYD_STATUS(NUM_LOOP) = 1) then
begin Comment The hydro unit is up. Check the next one. NUM LOOP := NUM LOOP + 1; N:=-N-1; -end
else begin Comment Check for up-time and down-time constraint violations. call UNIT_VIOLATE (NUM_LOOP, VIO_FLAG); If (VIO FLAG = true) then
begin Comment Constraint violated. Check next unit. NUM LOOP:= NUM LOOP + 1 N := -N - 1; -end
else begin UNIT FOUND:= UNIT FOUND + 1; CONTRIB (UNIT_FOUND) := MAX_CAP (NUM_LOOP); NUM LOOP:= NUM LOOP + 1; N:=-N-1; -end
end if end
endif end
end endif If (UNIT FOUND = 0) then
FLAG2 : = false; else
begin Comment Prioritize the hydro units selected. call PRIORITY (CONTRIB, INC_AMOUNT, UNIT_ORDER) Comment The order of the selected hydro units according to descending order
of capacity is stacked in the UNIT _ORDER stack. This stack is popped sequentially to schedule the units.
TOTAL CAP:= O; While (TOT_CAP < > INC_AMOUNT) do
begin UNIT:= pop (UNIT_ORDER); TOTAL_CAP := TOTAL_CAP + MAX_CAP (UNIT) Comment Upgrade status of the unit to ·up· mode. STATUS (UNIT):= 1; end
end endif
Figure 31. Rule-set 5
Implementing PV In an ED Program 153
Comment Check to see if tie-lines are present. If (NUM_ TIES = 0) then
else
begin Comment No tie-lines are present. Therefore, set flag to false. FLAGS : = false; end
begin Comment Tie lines are present. Search for tie lines not scheduled at this hour. TIE_FOUND : = O; NUM_LOOP := 1; N : = NUM TIES; While (N >-0) do
begin If (UP _TIE_STATUS(NUM_LOOP) = 1) then
begin Comment The tie line is already scheduled. Check the next one. NUM_LOOP: = NUM_LOOP + 1; N:=N-1; end
else begin Comment Tie-line is available. Get out of loop TIE FOUND : = NUM LOOP; N : ;,, O; -end
endif end
end end if If (TIE_FOUND = 0) then
FLAGS : = false; else
begin Comment Check if area control error can be controlled. UNIT (TIE_FOUND): = INC_AMOUNT call ACE (SCHED, INC_AMOUNT, ACE_FLAG) If (ACE_FLAG = true) then
begin Comment ACE is not controllable with the interchange. Set flag. FLAGS : = false; UNIT (TIE_FOUND) : = O; end
endif end
endif
Figure 32. Rule-set 8
Implementing PV In an ED Program 154
scheduling any interchange company or a tie-line. The set of rules governing these actions is
shown in Figure 32.
The RB follows these sets of rules sequentially whenever there is not enough regulating
capacity in the system. At any point in time, a part of any set of rules may be satisfied, in which
case a coordinated decision is taken. For example, during dispatch operation, it was found
that thermal generation could not be increased any further to match the total load demand.
The RB finds a hydro unit to be scheduled which can only satisfy part of the increase in
generation required. None of the other rule-sets 1 through 7 can be satisfied. In this case, the
RB will schedule interconnected power to make up the rest of the increment. In situations like
these, human interaction produces delay and may take longer than the dispatch interval itself.
The RB provides solutions within seconds.
It should be noted that a tie-line may be receiving power from a number of interchange
companies. The sub-program ACE checks for NERC (North-American Electric Reliability
Council) regulation violations related to area control error. The tie-line bias [75), should be
such that the ACE is brought back to zero within the dispatch interval.
Rule-sets 9 through 16 employ inverse logic to what is used in rule-sets 1 through 8. For
example rule-set 14 is concerned with shutting down a scheduled hydro unit as compared to
rule-set 5 which is valid for starting up unscheduled hydro units. The set of rules effecting
change in the photovoltaic operation in the scenario of the presence of "unloadable
generation" is given a low priority. Following along the same reasoning as before, one would
like to maintain as much PV generation in the system, until it comes down to a "last resort"
to reduce the PV generation level.
Implementing PV In an ED Program 155
7.3 Programming Considerations
Summing up the functions of the dynamic economic dispatch as proposed in the dissertation,
there are a number of possible steps to take in case the system reaches a point where the
economic trajectory cannot be followed. Figure 33 illustrates the flow of information in the
dispatch algorithm. It is clear from the figure that as a result of the presence of photovoltaic
systems, the solution of the unit commitment may have to be modified in order to arrive at
an economic solution.
7.3.1 Interface With EPRl's GPUC Program
It was explained earlier that the dynamic economic dispatch algorithm proposed here starts
from a given unit commitment (UC) solution provided by EPRl's computer program namely,
Generation Production Unit Commitment. The UC program is slightly modified in order to
produce a particular set of data in a form which is useful to the dispatch program. The data
in question, comprises of the unit schedule throughout the commitment period, and the
amount of non-committable generation every hour, from units such as combustion turbines,
hydrothermal units, pumped storage units and also the hourly interchange schedule. The
period of UC considered most effective for this application is 24 hours. Figure 34 illustrates the
application of EPRl's GPUC program in the proposed scheme. Input to GPUC are hourly load
data and the generator data. The hourly load data are simulated by a computer module called
AVHR which takes in the raw sub-hourly load data input and produces a) the dispatchable
sub-hourly load data, and b) normalized hourly load data. Output (b) is directly input to GPUC
and the latter yields commitment schedules for all hours in the schedule and the participation
Implementing PV in an ED Program 156
3 .,, ii" 3 Ill ::I -:; cc "V < :; DI ::I m c "V ... 0 cc ... DI 3
.... "' ......
I
OPTIMAL PV OUTPUT
prHR/VfEK LOAD H DAILY/WEEKLY FORECAST UNIT COMMllMENT
I -11 SHORT-TERM DYNAUIC ECONOMIC I~ SUB-HOURLY
LOAD FORECAST LOAD DISP ATCl-1 PHOTOVOLTAIC
OPTIMAL THERMAL
GENERATION
I
OP11MAL COMBUSllON
TURBINE GENERATI~
* OPllMAL HYDRO (RUN-OF-RIVER'
PLANT GENERATION
OUTPUT PREDICllONS
* PUMPED-STORAGE
PLANT GENERATION
Figure 33. Functional properties of the new dynamic economic dispatch
rt
BUY/SEU POWER
Hourly Loo.d SiMulo. tlon
AVHR
Unit CoMMitMent
GPUC
Figure 34. Components of unit commitment
Implementing PV In an ED Program
To DRIVER
CoMMltMent Schedule
158
factors from combustion turbines, hydro units, pumped storage units and the interchange
schedule.
7.3.2 Interface With the Solar Resource Forecast Program
Figure 13 on page 96 shows the input output requirements for the FORECST module used for
forecasting PY output during the dispatch interval. The module is linked to the DRIVER module
described tater. The FORECST module consists of two sub-modules, SIMUL and PREDIC.
SIMUL generates a simulated global irradiance and direct normal irradiance data on clear
days during the period of interest. Sub-module SIMUL generates:
• global irradiance on clear days
• direct normal irradiance data
• cloud cover data at the site
Sub-module PREDIC takes in as input, the output of sub-module SIMUL and generates the
forecasted sub-hourly PV generations which is used by the DRIVER module.
The prediction of the photovoltaic power generations for the economic dispatch period is
dependent on the forecast of the global irradiance. The dispatch program accepts data from
this forecast generating algorithm. The tatter has been explained in Chapter 4. The resource
forecast is updated at the beginning of every dispatch interval.
7.3.3 The Dispatch Combined With the RB
Implementing PV In an ED Program 159
3 .,, ii" 3 CD a S" ca ~ S" Ill ;:,
"' 0 -a .. 0 ca Dl 3
.. °' 0
Sp1nn1n9 reserves Po.rt1c1po. tlon fo.ctors
Col"ll'll"trlen-t sch&dule C Therl'lo.l 9enero.t100
Sub-hourly loo.ct do. to.
Genera.tor do.to.
CT o.nd Hydro genera. tlon
PV output f oreco.s-ts
lntercho.nge
Figure 35. Execution of the DRIVER module
In order to be compatible with the UC program, the generation data input requirement for the
dispatch algorithm is quite similar to EPRl's GPUC program. The input data for both programs
is shown in greater detail, in Appendix C. Figure 35 provides an insight into the operation of
the DRIVER module which is the heart of the proposed dynamic economic dispatch scheme.
Input to the module consists of:
• Generator participation factors
• Commitment schedule for all generators
• Sub-hourly load data
• Generator data
• Forecasted PV output for the dispatch interval.
The output from the program consists of the following:
• Spinning reserve
• Thermal generation
• PV generation
• Production costs
• Pumped storage hydro generation
• Hydro generation
• Combustion turbine generation
• Interchange
Figure 36 shows the combined operation of the dynamic economic dispatch and the rule base
which can be used as a dispatcher's aid. The operations of the economic dispatch and the
rule base are coordinated by the module called DRIVER. The module makes sure that there
is enough reserve margin as required by the system. It computes the contributions from all
non-committable sources, computes artificial minimum and maximum limits dictated by
Implementing PV In an ED Program 161
3 "1:1 ii' 3 CD :;, -S" ca ~ S" DI :;,
"' c .,, 0 ca DI 3
.... 0 N
I --- D R I VE R
I I I
,-----____,1 Inter-cho.nge
CT Genera. taon
Hydro Genero. taor
Reserve Mo.rgln
P. Storo.ge Genera. taon
PV .Genero. t101
Ro.Mp Conditions
TherMo.l G.rnero. tlon
L_ ----- ---~ :;Ql -::s ~Sy=" =b: i-;1 11 -:hQ:-hy= ::rQ:ns - i I I C I Loss Estl"Q tlon i I I 1
1 [ Cho.nge puMped storo.ge gen. I I
0 s I R .. B I RequlreMent f'or
1 1 U I Cho.nge CT genera. taons I A 1 M I cllspo. tcho.ble genera. tlons DISREQ P _ ~
0
M
Mo.xlMuM avo.llo.ble A I I L ( Cho.nge PV genero.taons IS I dlspo. tenable genero. taon DISHAX --.._._._._._._ ______ _.T E E
MlsMo. tches between o.ctual I I ( Modlf'y unit coMMl1:Ment schedulel I I dlspo. tcho.lole genero. taon a. DISREQ C
I __ J
I C ( 1 H I I I Ch4n9e 1nterch4n9e schedule i _ Syst•" lo.Mlodo. ~ -L ______ J L ---
Figure 36. Information exchange In the three modules
response rates of thermal units and passes the information to ECONOMIC DISPATCH module.
The driver then, receives back information on the mismatches between the possible
dispatchable generation under constraints and that required by the system. This is then
passed on to the RULE-BASE module which makes the necessary decisions to correct the
situation. The RB at this stage communicates directly with the ED module.
An example of the operation of the PV plant in the proposed dispatch scheme follows. This
will illustrate the maximum potential of the plant in combined operation with other plants in
the mix.
During normal operation of the dispatch algorithm, assume a sudden drop in instantaneous
load by an amount of 60 MW at the beginning of the dispatch interval. Assuming that the total
non-committable generation output (consisting of combustion turbine units, hydro units,
pumped storage units and the PV plant), as well as system losses remain constant throughout
the interval, it is found that that the system on-line regulating capacity at this time is not
enough to unload the thermal generations during the interval. The RB takes over control and
decides that the PV generation may be reduced by 15 MW to bring the system back to a
balanced state. This is an illustration of how the PV plant may be used for maintaining system
security. Detailed results of a case study are presented in Chapter 8.
Implementing PV In an ED Program 163
CHAPTER 8
Case Study: Results
This chapter presents results of a case study using the PV output forecast strategy and the
rule based dispatch algorithm. The data used for the study represents a location in Virginia.
This is a typical location in the southeastern United States and has moderate weather
throughout the year.
The generation mix used for the study is derived from the EPRI synthetic utility system [98],
southeastern U.S. integrated by personal communication with a number of utility operations
personnel in the region. The results presented in this chapter are targeted toward bringing
out the differences in a power system with and without a photovoltaic power plant. Also the
differences in a static approach and a dynamic rule based strategy are pointed out.
8.1 Continuous Simulation Run
Case Study Results 164
l. 0 ~-d d > ... l. d ., ,,~ ,, ., d .c _g ....
Updo.te PV foreco.sts
No
START
Reo.d dlspo.tch 1ntervo.l T
Reo.d sto.rt "tlMe for SIMulo. t1on 10
=
Issue PV f oreco.sts for the next hour
o.t eo.ch lntervo.l
Do o.n econoMIC dlspo. tch
1Jr1te results for thtr lntervo.l
IncreMent lnterco.l count l = I + T
Figure 37. Continuous simulation run
Case Study Results
No
Yes
Yes
165
For the purpose of presenting the results, a continuous simulation procedure was followed.
The algorithm of this process is shown in Figure 37. At the outset, parameters such as,
generator data, generator schedule, dispatch interval, etc., are read in. PV output forecasts
are issued only if the interval of simulation falls within the daytime hours. After reading in the
interval's load demand, an economic dispatch calculation is performed. In case of any
dispatch problems, e.g., inadequate regulating capacity or spinning reserve, the rule-based
system takes over and matches the generation and demand maintaining system security, and
an economic dispatch calculation is redone. When there are no problems, the results are
written out for the interval and the time counter is incremented by one interval. If the time
coincides with the end of the hour, program control is handed back to the PV output forecast
routine which issues new forecasts for the upcoming hour of simulation. If on the other hand,
the time is within the hour, PV generation forecasts are updated with the newly available
actual irradiance in the last interval before control is transferred directly to the economic
dispatch program.
8.1.1 Generator Data
Table 10 and Table 11 list the characteristics of generators and combustion turbine
generators respectively, that are used in the study. Also shown in the figures are the minimum
and maximum generations possible as well as the ramp (response) rates for each generator.
It should be mentioned here that only the dis patchable thermal units belonging to the synthetic
utility are listed in Table 10. The base load units are supposed to run almost throughout the
day and are therefore considered non-dispatchable for all practical purposes.
8.1.2 Load Data
Case Study Results 168
Table 10. Thermal generator data for the synthetic utility
NAME TYPE OF UNIT PMAX(MW) PMIN(MW) LOAD/UNLOAD RATE TUNIT1 COAL 760 250 3%/MIN TUNIT2 COAL 760 174 3%/MIN
TUNIT3 COAL 420 125 5%/MIN TUNIT4 COAL 190 50 7%/MIN
TUNIT5 COAL 190 50 7%/MIN
TUNIT6 COAL 270 65 5%/MIN
TUNIT7 COAL 210 70 5%/MIN TUNIT8 COAL 210 70 5%/MIN TUNIT9 COAL 115 35 7%/MIN TUNIT10 COAL 450 136 3%/MIN TUNIT11 COAL 450 136 3%/MIN
TUNIT12 COAL 110 35 7%/MIN
TUNIT13 COAL 110 35 7%/MIN
TUNIT14 COAL 90 25 10%/MIN
TUNIT15 COAL 55 25 10%/MIN
TUNIT16 COAL 55 25 10%/MIN
TUNIT17 COAL 85 33 10%/MIN
TUNIT18 COAL 55 25 10%/MIN
TUNIT19 COAL 55 25 10%/MIN
TUNIT20 COAL 90 35 10%/MIN
TUNIT21 COAL 90 35 10%/MIN TUNIT22 COAL 76 25 10%/MIN
TUNIT23 COAL 80 25 10%/MIN TUNIT24 COAL 85 33 10%/MIN
Case Study Results 167
Table 11. Combustion turbine generator data for the synthetic utility
NAME TYPE OF UNIT PMAX(MW) PMIN(MW) LOAD/UNLOAD RATE CUNIT1 OIL 18 12 100%/MIN CUNIT2 GAS 18 12 100%/MIN CUNIT3 OIL 18 12 100%/MIN CUNIT4 GAS 44 16 100%/MIN
CU NITS GAS 44 16 100%/MIN CUNIT6 GAS 64 46 100%/MIN
CUNIT7 GAS 64 46 100%/MIN
CUNIT8 GAS 64 46 100%/MIN
CUNIT9 GAS 64 46 100%/MIN CUNIT10 OIL 17 11 100%/MIN CUNIT11 OIL 17 11 100%/MIN CUNIT12 OIL 17 11 100%/MIN
CUNIT13 OIL 17 11 100%/MIN
CUNIT14 GAS 42 28 100%/MIN CUNIT15 OIL 18 22 100%/MIN
CUNIT16 OIL 32 21 100%/MIN
CUNIT17 GAS 33 22 100%/MIN
Case Study Results 168
3700
~ 2900
l! .. E II
-0
-0
~ 2100
1300
1 I nlerval • 10 M rules
,, 1
1,1 I
I 1' 1 I 1 I 1' , 1
1' 1'
I
, , I I I I I , , I
I I I I I I I I I I I I I ; I I I I
v
Load ---------- PV
800
600
400
200
500'--~--~--~----~------~--~--~~---~--~-- 0 o 29 58 87 116 145 I nlervak
Figure 38. Sample modified load profile and PV output for a day In January
Case Study Results
::r ~ ~ .. 0... ~ D
> 0.
169
Load demand data at 30 seconds interval are available from a Virginia utility. These are used
to create an hourly load data (for generation scheduling purposes) and a sub-hourly load data
base (for the dynamic economic dispatch program). The sub-hourly data consists of load
demands at every 3 to 10 minute intervals.
Figure 38 shows the sub-hourly load demand and PV plant generations for a sample day in
the month of January. This day is particularly selected to show the variable nature of the PV
generations. Such extreme variations in PV output may occur during sudden movement of
thick, dark clouds covering the sun for several minutes before moving away again. It should
be mentioned here that the figure shows only the dispatchable load. In other words, the base
load is subtracted from the total load.
8.1.3 Simulation Results
The day is divided into three time spans for presenting the results. These three time spans
represent the three important regions of the daily load profile. Hour 0 (midnight) through hour
8 (8 AM) is used to fill in the first time span. This period consists of the base period of the day
during which mostly the base load units are operating. The demand profile experiences its
first valley period (winter loads may have a second valley later in the day). The end of this
period is marked by a sharply increasing load shape indicating the morning load pick-up. The
next time span comprises of hours 8 through 16. This is the period which experiences high
variability in the demand and at the same time, photovoltaic generations are increasing with
the sun gradually approaching its noon-time position of maximum radiation. Hours 16 through
24 (midnight) represents the third time span of the day. This period normally means a rapid
reduction in load demand during summer-time in most parts of the U.S., or a second increase
in demand during winter.
Case Study Results 170
Table 12. System operation without PV during 1st time period
INT 1 LOAD LOSS DISP CT GEN PV GEN SPIN A. COST X1 boo$ 1 2110.00 105.50 2215.50 0.00 0.00 2030.50 19.19 7.61 2 1997.00 99.85 2096.78 0.00 0.00 1014.10 19.01 7.23 3 1982.00 99.10 2081.03 0.00 0.00 894.53 18.99 7.19 4 1964.00 98.20 2062.19 0.00 0.00 895.46 18.96 7.13 5 1945.00 97.25 2042.25 0.00 0.00 893.99 18.93 7.06 6 1912.00 95.60 2007.60 0.00 0.00 905.97 18.87 6.95 7 1891.00 94.55 1985.54 0.00 0.00 888.65 18.84 6.88 8 1872.00 93.60 1965.60 0.00 0.00 883.52 18.81 6.82 9 1847.00 92.35 1939.35 0.00 0.00 887.10 18.77 6.74
10 1833.00 91.65 1924.64 0.00 0.00 871.97 18.75 6.69 11 1821.00 91.05 1912.05 0.00 0.00 867.85 18.73 6.65 12 1804.00 90.20 1894.20 0.00 0.00 871.39 18.70 6.60 13 1792.00 89.60 1881.59 0.00 0.00 863.70 18.68 6.56 14 1789.00 89.45 1878.45 0.00 0.00 852.53 18.67 6.55 15 1787.00 89.35 1876.34 0.00 0.00 851.05 18.67 6.54 16 1774.00 88.70 1862.70 0.00 0.00 862.31 18.65 6.50 17 1761.00 88.05 1849.05 0.00 0.00 860.45 18.63 6.46 18 1765.00 88.25 1853.25 0.00 0.00 840.73 18.64 6.47 19 1765.00 88.25 1853.25 0.00 0.00 845.51 18.64 6.47 20 1765.00 88.25 1853.25 0.00 0.00 845.51 18.64 6.47 21 1778.00 88.90 1866.90 0.00 0.00 831.86 18.66 6.51 22 1781.00 89.05 1870.05 0.00 0.00 844.22 18.66 6.52 23 1791.00 89.55 1880.55 0.00 0.00 837.30 18.68 6.56 24 1792.00 89.60 1880.55 0.00 0.00 849.24 18.68 6.56 25 1807.00 90.35 1897.34 0.00 0.00 832.44 18.70 6.61 26 1835.00 91.75 1926.74 0.00 0.00 822.13 18.75 6.70 27 1845.00 92.25 1937.24 0.00 0.00 845.05 18.77 6.73 28 1872.00 93.60 1965.60 0.00 0.00 828.63 18.81 6.82 29 1903.00 95.15 1998.14 0.00 0.00 828.31 18.86 6.92 30 1953.00 97.65 2049.63 0.00 0.00 813.81 18.94 7.09 31 2038.00 101.90 2139.89 0.00 0.00 977.07 18.78 7.55 32 2154.00 107.70 2261.57 0.00 0.00 794.84 18.97 7.94 33 2238.00 111.90 2349.02 0.00 0.00 845.70 19.10 8.21 34 2320.00 116.00 2435.99 0.00 0.00 858.31 19.22 8.49 35 2427.00 121.35 2548.35 0.00 0.00 845.09 19.39 8.85 36 2533.00 126.65 2659.65 0.00 0.00 859.47 19.56 9.21 37 2691.00 134.55 2825.54 0.00 0.00 856.71 19.73 9.86 38 2900.00 145.00 3046.46 0.00 0.00 768.61 20.09 10.59 39 3100.00 155.00 3256.13 0.00 0.00 801.16 20.42 11.30 40 3287.00 164.35 3453.14 0.00 0.00 765.18 20.79 11.97 41 3462.00 173.10 3636.31 0.00 0.00 710.94 21.38 12.61 42 3580.00 179.00 3759.00 0.00 0.00 741.67 21.80 13.05 43 3700.00 185.00 3358.00 527.00 0.00 684.89 20.32 18.58 44 3886.00 194.30 3554.42 527.00 0.00 278.00 21.08 19.25 45 3977.00 198.85 3648.65 527.00 0.00 270.14 21.36 19.58 46 3992.00 199.60 3662.84 527.00 0.00 306.40 21.40 19.63 47 3980.00 199.00 3653.21 527.00 0.00 323.67 21.37 19.60 48 3954.00 197.70 3624.70 527.00 0.00 347.00 21.28 19.50
1 1 interval = 10 minutes. Interval 1 = > 0:10 A.M.
Case Study Results 171
Table 13. System operation without PV during 2nd time period
INT 1 LOAD LOSS DISP CT GEN PV GEN SPIN /.. COST X1 :>OO $
49 3905.00 195.25 3572.95 527.00 0.00 383.37 21.13 19.32 3~4.00
50 3908.00 195.40 3576.28 527.00 0.00 352.69 21.14 19.33 3~4.00
51 3866.00 193.30 3533.89 527.00 0.00 396.75 21.02 19.18 3~4.00
52 3835.00 191.75 3500.82 527.00 0.00 397.97 20.93 19.06 53 3814.00 190.70 3478.34 527.00 0.00 388.24 20.87 18.99 54 3805.00 190.25 3468.50 527.00 0.00 376.18 20.84 18.95 55 3775.00 188.75 3562.58 402.00 0.00 397.52 21.10 17.41 56 3763.00 188.15 3549.20 402.00 0.00 499.57 21.06 17.36 57 3753.00 187.65 3538.67 402.00 0.00 500.04 21.03 17.33 58 3731.00 186.55 3515.58 402.00 0.00 512.88 20.97 17.25 59 3694.00 184. 70 3476.64 402.00 0.00 529.32 20.86 17.11 60 3675.00 183.75 3456.84 402.00 0.00 511.19 20.80 17.04 61 3650.00 182.50 3499.43 334.00 0.00 517.38 20.92 16.18 62 3648.00 182.40 3496.33 334.00 0.00 561.90 20.92 16.17 63 3645.00 182.25 3493.18 334.00 0.00 562.03 20.91 16.16 64 3632.00 181.60 3479.29 334.00 0.00 572.84 20.87 16.11 65 3608.00 180.40 3454.13 334.00 0.00 584.48 20.80 16.03 66 3584.00 179.20 3429.49 334.00 0.00 584.71 20.72 15.94 67 3550.00 177.50 3586.10 142.00 0.00 596.43 21.17 14.31 68 3545.00 177.25 3579.88 142.00 0.00 740.68 21.15 14.28 69 3482.00 174.10 3514.10 142.00 0.00 803.35 20.97 14.05 70 3456.00 172.80 3484.81 142.00 0.00 779.71 20.88 13.95 71 3414.00 170.70 3442.65 142.00 0.00 793.33 20.76 13.80 72 3394.00 169.70 3422.29 142.00 0.00 772.89 20.71 13.73 73 3347.00 167.35 3514.35 0.00 0.00 804.75 20.97 12.18 74 3280.00 164.00 3443.82 0.00 0.00 962.95 20.77 11.94 75 3252.00 162.60 3415.55 0.00 0.00 922.74 20.69 11.84 76 3229.00 161.45 3390.45 0.00 0.00 923.71 20.64 11.76 77 3221.00 161.05 3382.05 0.00 0.00 913.66 20.62 11.73 78 3208.00 160.40 3369.48 0.00 0.00 920.05 20.59 11.68 79 3187.00 159.35 3346.35 0.00 0.00 935.22 20.56 11.60 80 3445.00 172.25 3617.91 0.00 0.00 650.07 21.74 12.55 81 3219.00 160.95 3378.49 0.00 0.00 1120.93 20.61 11.71 82 3201.00 160.05 3361.55 0.00 0.00 925.37 20.58 11.66 83 3207.00 160.35 3367.35 0.00 0.00 909.56 20.59 11.68 84 3195.00 159.75 3354.74 0.00 0.00 925.57 20.57 11.63 85 3162.00 158.10 3320.10 0.00 0.00 952.81 20.52 11.51 86 3123.00 156.15 3279.14 0.00 0.00 973.41 20.45 11.37 87 3097.00 154.85 3251.85 0.00 0.00 976.64 20.41 11.28 88 3095.00 154.75 3249.74 0.00 0.00 962.72 20.40 11.27 89 3060.00 153.00 3213.00 0.00 0.00 998.22 20.34 11.15 90 3041.00 152.05 3193.05 0.00 0.00 996.59 20.31 11.08 91 3030.00 151.50 3181.49 0.00 0.00 996.42 20.29 11.04 92 3070.00 153.50 3223.50 0.00 0.00 947.63 20.36 11.19 93 3030.00 151.50 3181.49 0.00 0.00 1014.31 20.29 11.04 94 3017.00 150.85 3167.85 0.00 0.00 1003.28 20.27 11.00 95 3004.00 150.20 3154.20 0.00 0.00 1008.91 20.25 10.95 96 3046.00 152.30 3198.30 0.00 0.00 956.79 20.32 11.10
1 1 interval = 10 minutes. Interval 1 = > 0:10 AM
Case Study Results 172
Table 14. System operation without PV during 3rd time period
INT 1 LOAD LOSS DISP CT GEN PV GEN SPIN A. COST Tl N SP
97 3042.00 152.10 3194.10 0.00 0.00 986.91 20.31 11.09 98 3085.00 154.25 3239.24 0.00 0.00 939.29 20.39 11.24 99 3124.00 156.20 3280.20 0.00 0.00 924.86 20.45 11.38
100 3157.00 157.85 3314.85 0.00 0.00 914.26 20.51 11.50 101 3168.00 158.40 3326.39 0.00 0.00 923.08 20.53 11.54 102 3224.00 161.20 3386.39 0.00 0.00 869.86 20.63 11.74 103 3001.00 150.05 3152.18 0.00 0.00 1140.54 20.24 10.94 104 3412.00 170.60 3547.91 36.00 0.00 570.00 26.82 12.80 105 3302.00 165.10 3432.50 36.00 0.00 961.98 20.73 12.38 106 3334.00 166.70 3464.61 36.00 0.00 826.80 20.83 12.50 107 3393.00 169.65 3526.65 36.00 0.00 795.66 21.00 12.71 108 3437.00 171.85 3572.84 36.00 0.00 809.90 21.13 12.87 109 3469.00 173.45 3373.21 270.00 0.00 812.71 20.59 15.02 110 3514.00 175.70 3419.87 270.00 0.00 598.59 20.70 15.18 111 3597.00 179.85 3506.88 270.00 0.00 540.45 20.95 15.48 112 3646.00 182.30 3560.29 270.00 0.00 569.19 21.10 15.67 113 3651.00 182.55 3563.65 270.00 0.00 615.98 21.10 15.68 114 3662.00 183.10 3575.45 270.00 0.00 605.86 21.14 15.72 115 3671.00 183.55 3519.93 334.00 0.00 603.29 20.98 16.26 116 3671.00 183.55 3519.93 334.00 0.00 558.27 20.98 16.26 117 3679.00 183.95 3529.12 334.00 0.00 549.08 21.01 16.29 118 3678.00 183.90 3529.12 334.00 0.00 558.03 21.01 16.29 119 3652.00 182.60 3500.10 334.00 0.00 587.05 20.93 16.19 120 3631.00 181.55 3478.09 334.00 0.00 580.79 20.86 16.11 121 3612.00 180.60 3586.98 206.00 0.00 578.45 21.17 15.04 122 3599.00 179.95 3572.32 206.00 0.00 684.68 21.13 14.98 123 3594.00 179.70 3567.48 206.00 0.00 682.17 21.12 14.97 124 3549.00 177.45 3520.45 206.00 0.00 726.78 20.98 14.80 125 3512.00 175.60 3481.60 206.00 0.00 725.10 20.87 14.67 126 3457.00 172.85 3424.82 206.00 0.00 744.04 20.71 14.47 127 3404.00 170.20 3574.54 0.00 0.00 746.42 21.14 12.40 128 3375.00 168.75 3543.74 0.00 0.00 913.02 21.05 12.29 129 3340.00 167.00 3507.00 0.00 0.00 928.40 20.95 12.16 130 3279.00 163.95 3442.79 0.00 0.00 956.81 20.76 11.94 131 3197.00 159.85 3356.85 0.00 0.00 980.46 20.57 11.64 132 3122.00 156.10 3278.10 0.00 0.00 996.04 20.45 11.37 133 3074.00 153.70 3228.10 0.00 0.00 934.78 20.45 11.11 134 3040.00 152.00 3191.99 0.00 0.00 970.89 20.39 10.99 135 2968.00 148.40 3116.39 0.00 0.00 1025.28 20.27 10.73 136 2901.00 145.05 3046.04 0.00 0.00 1051.22 20.15 10.49 137 2812.00 140.60 2952.05 0.00 0.00 1087.48 20.00 10.18 138 2750.00 137.50 2887.63 0.00 0.00 1053.51 19.90 9.96 139 2706.00 135.30 2841.30 0.00 0.00 1026.41 19.82 9.81 140 2627.00 131.35 2758.34 0.00 0.00 1058.57 19.70 9.54 141 2582.00 129.10 2711.10 0.00 0.00 1021.49 19.63 9.38 142 2517.00 125.85 2642.85 0.00 0.00 1041.71 19.53 9.16 143 2428.00 121.40 2549.39 0.00 0.00 1065.79 19.39 8.86 144 2291.00 114.55 2405.54 0.00 0.00 1114.64 19.18 8.39
1 1 interval = 10 minutes. Interval 1 = > 0:10 AM
Case Study Results 173
Table 15. System operation with PV during 2nd time period
INT 1 LOAD LOSS DISP CT GEN PV GEN SPIN A. COST X1 t>oo s 49 3905.00 195.25 3155.87 527.00 416.73 800.45 19.61 17.89 50 3908.00 195.40 3023.61 527.00 553.08 641.51 19.94 17.44 51 3866.00 193.30 2962.83 527.00 569.19 537.82 19.94 17.24 52 3835.00 191.75 2922.32 527.00 578.07 512.08 19.87 17.10 53 3814.00 190.70 2885.61 527.00 592.83 502.66 19.82 16.98 54 3805.00 190.25 2872.12 527.00 596.13 477.00 19.80 16.94 55 3775.00 188.75 2944.59 402.00 618.45 515.82 19.91 15.31 56 3763.00 188.15 2894.64 402.00 656.31 643.99 19.83 15.14 57 3753.00 187.65 2865.18 402.00 673.47 618.13 19.79 15.04 58 3731.00 186.55 2860.49 402.00 655.05 592.87 19.78 15.03 59 3694.00 184.70 2791.07 402.00 685.62 657.52 19.68 14.80 60 3675.00 183.75 2782.92 402.00 673.83 595.11 19.66 14.77 61 3650.00 182.50 2810.21 334.00 688.29 627.52 19.70 13.86 62 3648.00 182.40 2810.21 334.00 687.21 655.27 19.70 13.86 63 3645.00 182.25 2803.39 334.00 689.85 662.09 19.69 13.83 64 3632.00 181.60 3186.55 558.00 67.85 48.00 27.31 18.21 65 3608.00 180.40 3162.54 558.00 67.85 467.30 20.26 18.11 66 3584.00 179.20 3167.99 558.00 37.21 434.01 20.27 18.12 67 3550.00 177.50 2947.43 142.00 638.46 1073.77 19.91 12.13 68 3545.00 177.25 2947.43 142.00 633.93 854.43 19.91 12.13 69 3482.00 174.10 3322.10 334.00 0.00 287.77 22.73 15.58 70 3456.00 172.80 3294.76 334.00 0.00 658.77 20.47 15.48 71 3414.00 170.70 3250.69 334.00 0.00 652.98 20.40 15.33 72 3394.00 169.70 3229.69 334.00 0.00 648.09 20.37 15.26 73 3347.00 167.35 3309.70 0.00 205.66 889.74 20.50 11.48 74 3280.00 164.00 2880.49 0.00 564.77 1365.96 19.04 10.04 75 3252.00 162.60 2731.24 0.00 681.96 1167.59 19.46 9.55 76 3229.00 161.45 2709.80 0.00 680.64 1015.76 19.56 9.48 77 3221.00 161.05 2700.92 0.00 681.12 996.49 19.54 9.45 78 3208.00 160.40 2672.58 0.00 695.82 1015.81 19.50 9.36 79 3187.00 159.35 2658.39 0.00 687.96 1001.18 19.48 9.31 80 3445.00 172.25 2939.05 0.00 679.32 706.09 20.05 10.23 81 3219.00 160.95 2697.87 0.00 682.08 1240.18 19.54 9.44 82 3201.00 160.05 2680.01 0.00 681.03 1005.27 19.51 9.38 83 3207.00 160.35 2690.28 0.00 677.07 976.85 19.53 9.41 84 3195.00 159.75 2683.41 0.00 671.34 994.15 19.52 9.39 85 3162.00 158.10 2646.83 0.00 673.26 1023.75 19.46 9.27 86 3123.00 156.15 2608.91 0.00 670.23 1024.49 19.41 9.15 87 3097.00 154.85 2585.13 0.00 666.72 1009.72 19.37 9.07 88 3095.00 154.75 2577.45 0.00 672.30 993.23 19.36 9.05 89 3060.00 153.00 2557.07 0.00 655.92 1005.61 19.33 8.98 90 3041.00 152.05 2524.19 0.00 668.85 1015.27 19.28 8.88 91 3030.00 151.50 2521.53 0.00 659.97 980.46 19.28 8.87 92 3070.00 153.50 2570.25 0.00 653.25 928.70 19.35 9.02 93 3030.00 151.50 2523.66 0.00 657.84 1030.83 19.28 8.87 94 3017.00 150.85 2508.57 0.00 659.28 992.80 19.26 8.83 95 3004.00 150.20 2508.57 0.00 645.81 975.61 19.26 8.83 96 3046.00 152.30 2560.55 0.00 637.74 923.62 19.34 8.99
1 1 interval = 10 minutes. Interval 1 = > 0:10 AM.
Case Study Results 174
Table 16. System operation with PV during 3rd time period
INT 1 LOAD LOSS DISP CT GEN PV GEN SPIN A. COST X1 t>oo s 97 3042.00 152.10 2925.95 270.00 0.00 347.48 22.79 13.53 98 3085.00 154.25 2969.99 270.00 0.00 689.49 19.96 13.66 99 3124.00 156.20 3009.99 270.00 0.00 689.92 20.02 13.79
100 3157.00 157.85 3044.85 270.00 0.00 700.37 20.07 13.91 101 3168.00 158.40 3056.40 270.00 0.00 728.66 20.09 13.95 102 3224.00 161.20 3115.20 270.00 0.00 682.94 20.19 14.14 103 3001.00 150.05 3151.04 0.00 0.00 970.55 20.24 10.94 104 3412.00 170.60 3547.24 36.00 0.00 570.00 26.83 12.80 105 3302.00 165.10 3432.46 36.00 0.00 961.32 20.73 12.38 106 3334.00 166.70 3464.61 36.00 0.00 826.77 20.83 12.50 107 3393.00 169.65 3526.65 36.00 0.00 795.66 21.00 12.71 108 3437.00 171.85 3572.84 36.00 0.00 809.90 21.13 12.87 109 3469.00 173.45 3373.21 270.00 0.00 812.71 20.59 15.02 110 3514.00 175.70 3419.87 270.00 0.00 598.59 20.70 15.18 111 3597.00 179.85 3506.88 270.00 0.00 540.45 20.95 15.48 112 3646.00 182.30 3560.29 270.00 0.00 569.19 21.10 15.67 113 3651.00 182.55 3563.65 270.00 0.00 615.98 21.10 15.68 114 3662.00 183.10 3575.45 270.00 0.00 605.86 21.14 15.72 115 3671.00 183.55 3519.93 334.00 0.00 603.29 20.98 16.26 116 3671.00 183.55 3519.93 334.00 o".oo 558.27 20.98 16.26 117 3679.00 183.95 3529.12 334.00 0.00 549.08 21.01 16.29 118 3678.00 183.90 3529.12 334.00 0.00 558.03 21.01 16.29 119 3652.00 182.60 3500.10 334.00 0.00 587.05 20.93 16.19 120 3631.00 181.55 3478.09 334.00 0.00 580.79 20.86 16.11 121 3612.00 180.60 3586.98 206.00 0.00 578.45 21.17 15.04 122 3599.00 179.95 3572.32 206.00 0.00 684.68 21.13 14.98 123 3594.00 179.70 3567.48 206.00 0.00 682.17 21.12 14.97 124 3549.00 177.45 3520.45 206.00 0.00 726.78 20.98 14.80 125 3512.00 175.60 3481.60 206.00 0.00 725.10 20.87 14.67 126 3457.00 172.85 3424.82 206.00 0.00 744.04 20.71 14.47 127 3404.00 170.20 3574.54 0.00 0.00 746.42 21.14 12.40 128 3375.00 168.75 3543.74 0.00 0.00 913.02 21.05 12.29 129 3340.00 167.00 3507.00 0.00 0.00 928.40 20.95 12.16 130 3279.00 163.95 3442.79 0.00 0.00 956.81 20.76 11.94 131 3197.00 159.85 3356.85 0.00 0.00 980.46 20.57 11.64 132 3122.00 156.10 3278.10 0.00 0.00 996.04 20.45 11.37 133 3074.00 153.70 3228.10 0.00 0.00 934.78 20.45 11.11 134 3040.00 152.00 3191.99 0.00 0.00 970.89 20.39 10.99 135 2968.00 148.40 3116.39 0.00 0.00 1025.28 20.27 10.73 136 2901.00 145.05 3046.04 0.00 0.00 1051.22 20.15 10.49 137 2812.00 140.60 2952.05 0.00 0.00 1087.48 20.00 10.18 138 2750.00 137.50 2887.63 0.00 0.00 1053.51 19.90 9.96 139 2706.00 135.30 2841.30 0.00 0.00 1026.41 19.82 9.81 140 2627.00 131.35 2758.34 0.00 0.00 1058.57 19.70 9.54 141 2582.00 129.10 2711.10 0.00 0.00 1021.49 19.63 9.38 142 2517.00 125.85 2642.85 0.00 0.00 1041.71 19.53 9.16 143 2428.00 121.40 2549.39 0.00 0.00 1065.79 19.39 8.86 144 2291.00 114.55 2405.54 0.00 0.00 1114.64 19.18 8.39
1 1 interval = 10 minutes. Interval 1 = > 0:10 AM
Case Study Results 175
Table 12, Table 13 and Table 14 show the parameters involved during operation of the power
system during the three time periods respectively. These tables show results of the case
before PV is added. Column 1 in these tables lists the intervals during the period with interval
1 being 10 minutes after midnight. Column 2 shows the modified load demand at each interval
while column 3 gives the transmission losses, both in MW. The latter is determined by
providing constant penalty factors for each unit. Column 4 provides information on
dispatchable generation. Columns 5 and 6 show the generations in MW, from combustion
turbines and the PV plant respectively. The spinning reserve (MW) at each interval is listed in
column 7 while the system lambda ($/MWh) is shown in column 8. Production cost (1000 $)
appears in column 9.
Table 15 and Table 16 are introduced to bring out the differences if a photovoltaic plant is
added to the system. These tables are counterparts ofTable 13 and Table 14 which shows the
"no PV" case. The PV plant is rated at 750 MW de.
A graphical representation of the net effect of having a PV plant in the generation mix is shown
in Figure 39. The particular feature shown in the figure is the effect on the dispatchable
thermal generations during the entire 24 hour period. Also shown in the figure are the load
profile and the photovoltaic generation on the same scale. The thermal generations follow the
load (transmission losses not shown in the figure) consistently until the PV plant starts
generating power. Dispatch problems that cannot be handled by the thermal units are picked
up by combustion turbine units as shown in Figure 40.
The effect of PV output on the spinning reserve is evident in Figure 41. The obvious impact is
during high variations in the PV plant output. In the morning, when the plant starts up, there
is a sudden decrease in thermal generation which contributes to an increase in the spinning
reserve. This happens during a time when the system is experiencing a shortage in reserves
without the PV plant being considered. In the afternoon, when the PV plant shuts off, the
Case Study Results 176
:x ~
3200
~ 2400 ....... Ill ... ~ Cll t7l
..Jl
...c Ill ~ 1600 Ill Q.. !!
0
800 1 I ntervaJ. 10 miMes
' I\. I
--------------
r> I\ r~\ r \ /1 I
\ \
Without PV With PV Load PV output
~ \
\
Li I 0 .__~---~--~~ .......... ~--~---~--'------~---~-----___,
0 29 58 87 116 145 Intervals
Figure 39. Effect of PV output on thermal generation
Case Study Results 177
1-u
800
600
400
200
1 I nt.erval- 1 amvles
I' I I I I I I I I
I
Wrlhout PV - - - - - - - - - - w 1th p v
~ - I I
0 .._~~....__~~.__~_....._~__..__~__.,__~__..___...~..._~__..__~ ............... ~__.J D 29 58 87 116 145
I nt.ervals
Figure 40. Effect of PV output on combustion turbine generation
Case Study Results 178
QI
~ QI LI
E en c ~ a.
U1
1500
1200
900
600
300
0 0
1 I nterval- 1
29
111rutes
~ II
1'.
: I f\ ~ /~ I I I 11 V I
----+--'- __..___ I I I
I ',1 I I I
58
I ~I ,, 11
,, 11 11 ,,
I nlervals
Figure 41. Effect of PV output on spinning reserves
Case Study Results
87
1thoul PV With PV Req11red
116 145
179
reverse condition of that of the morning start-up occurs, thus reducing the reserves
significantly for a short period of time.
Figure 42 provides a look at the change in system lambda because of the presence of PY
generations. System lambda goes up whenever the thermal generations cannot follow the
economic trajectory. In other words, lambda increases when there are sudden changes in the
PY generations. Figure 43 shows the effect on the overall production costs incurred by the
system. Figure 44 and Figure 45 show the net impact of PY output on some specific thermal
and combustion turbine units respectively.
Shown in Table 17, is a list of the system regulating capacity violations during the day. Also
evident from the table are the reasons of the violations which may be PY induced or
otherwise. These violations occur when inadequate generation capacity is present in the
system during times when the net load varies by a large amount during two successive
intervals. Net load is derived from the actual load minus the non-committable (CT, hydro,
pumped storage and interchange) generations minus the PY generations (if present). In
columns 2 and 3 are shown the total number of thermal units which have either reached their
minimum limit or maximum limit set by their response rates. Also shown in column 3 within
parentheses, are the changes in PY generations from the previous interval and the changes
in actual loads from the previous interval. It is seen that only in extreme variations of PY plant
output does the system experience loading or unloading problems. Other than that, the only
cases when the system might have problems are when the load itself varies during the
interval, by a large amount.
Table 18 gives a summary of the operation of the power system with and without the addition
of the PY plant. Total dispatchable thermal generation is reduced by 6.7% with the addition
of the 750 MW PY plant. On the other hand, CT picks up by 18.4%. The PY plant operates with
a capacity factor of 58.4%. The daily total spinning reserves is increased somewhat and the
production costs fall by about 3.5% indicating a saving of more than $60,000 during the day.
Case Study Results 180
111
" ..D E
..Ill
24
e 12 .S 1 I nt.ervaJ. 10 m1nule; Ill >-
Ul
6
ii /I
I I .... I .... ' ,- - ....... _, .... \ /\ ,, - - -- -- '
W1thou! PV ---------- w 1th p v
0 '--~--'~~-"'~~--~~--~~--~~--~-----~--~~--~~-0 29 58 87 116 145
I ntervak:
Figure 42. Effect of PV output on system lambda
Case Study Results 181
f ~
0 C>
24
C> 18 C> C> d -+"
I.II 0 u c 1! 12 ~
""'C e a.
6
0 0
1 I nlerval- 10 111nulec
29
W1thoui PV - - - - -- - - - - w 1th p v
\ 1' -.... \. -
58 87 116 I nt.ervals
Figure 43. Effect of PV output on production costs
Case Study Results
145
182
.JI ..c I'll
640
ij 320 -+' I'll 0.... !!
0
160
1 I nlerval- 10 111111ies
c:Jf------El TUN I T 2 v1lhout P V C9 e:i TUN I T2 v1lh PV 6 6 TUN I T3 v1lhout PV -+------------+- TUN I T 3 v1lh P V
>-< ------>( TUN I T '1 v1lhout P V <!>----<> TUN IT '1 v1lh PV
0 ,__~_._~__.,__~_._~__..__~ ......... ~--'~~ ......... ~--'~~-'-~--' 0 29 58 87 116 145
I nlerval&
Figure 44. Effect of PV output on some specific thermal units
Case Study Results 183
100 1 I nlervalo 10 111rlltei: cg E'.J CUN IT 1 vrthout PV
Ql e:J CUNITl vrth PV 6 6 CUNITS vrlhout PV
CUN ITS vrlh PV 80 )( >< CUNI T7 vrlhout PV
0 ~ CUNIT1 vrlh PV
:x 60 ~ c 0
...j:i
~ ~ Cll en
~ 40 u
20
58 87 116 I nlervals
Figure 45. Effect of PV output on some specific CT units
Case Study Results 184
Table 17. System regulation limit violations
Time Total Thermal Units Affected Remarks CASEI CASE II Without PV With PV
6:20 AM 3 3 (0 1) (209 2) No system problem 6:30 AM 1 1 (0) (200) No system problem 6:50 AM 3 3 (0) (175) No system problem 7:10 AM 7 7 (0) (120) No system problem 8:10 AM 0 12 (416)(-59) PV starts producing. No system problem 8:20 AM 0 2 (136)(+3) No system problem
10:40 AM 0 20 (-622)(-13) Thermal loading problem in Case II 11:30 AM 0 20 (-634)(-63) Thermal loading problem in Case II 12:20 PM 0 14 (360)(-67) Thermal unloading problem in Case II 1:20 PM 7 5 (-9) (258) No system problem 4:10 PM 0 21 (-638) (-4) PV plant shuts off. Thermal loading problem 4:20 PM 0 1 (0) (43) No system problem 5:20 PM 18 18 (0) (411) Thermal loading problem 6:10 PM 2 2 (0) (32) No system problem
1 MW change in PV generation from last interval; ( + = > increase) 2 MW change in load demand from last interval; ( + = > increase)
Case Study Results 185
Table 18. System operation summary with and without PV
Parameter No PV With PV Total daily dispatchable generation 72757.50 MWhr 67866.24 MWhr Total daily CT generation 2772.00 MWhr 3282.00 MWhr Total daily PV generation 0.00 MWhr 4381.54 MWhr Total daily pumped storage generation 0.00 MWhr 0.00 MWhr Total daily hydro generation 0.00 MWhr 0.00 MWhr Total daily interchange 0.00 MWhr 0.00 MWhr Total daily spinning reserve 19144.49 MWhr 19267.19 MWhr Total energy under daily load curve 71931.00 MWhr 71931.00 MWhr Total daily losses 3596.50 MWhr 3596.50 MWhr Total daily production costs $1, 725,526.90 $1,664,892.80 Total daily CT schedule 76 (Unit-hrs) 83 (Unit-hrs) Total daily Hydro schedule 0 (Unit-hrs) 0 (Unit-hrs) Total daily pumped storage schedule 0 (Unit-hrs) 0 (Unit-hrs) Total daily interchange schedule 0 (Unit-hrs) O (Unit-hrs)
Case Study Results 186
The extra operation time seen by the combustion turbines in the absence of hydro or pumped
storage generators is evident from the statistic on unit-hrs of operation time in the two cases.
8.2 Effect of PV Penetration
An important factor to be considered in the integrated operation of PV plants and conventional
generating units is the effect of the PV plant rating as a fraction of the system capacity on the
overall production costs. This is shown in Figure 46. In the figure, each percent of penetration
represents 56.5 MW of generating capacity. The fact that production costs decrease with each
additional penetration of PV plant is evident in the figure. Also featured in the figure is the fact
that the costs level off after the penetration reaches a certain limit. The limit in the case study
is found to be 13.27%. Beyond this point, system operational problems make it more
expensive than the base case, to run a PV plant.
8.3 Static Versus the Dynamic Dispatch Case
A static dispatch algorithm would be one where no PV output forecasts are available. A typical
day's irradiance data is selected in this case to yield PV output which would be expected on
a typical day during the month. (Solar irradiance data for typical days of the year may be found
in TMY weather tapes (207)). Therefore no care is taken to include the instantaneous changes
in the weather. Under this strategy, hourly expected PV generations are subtracted from
hourly load data and the thermal and non-thermal generations are forced to follow the net
Case Study Results 187
1740
...... ~
,.!I 0 -a
-g 1680 " ~ D
_r;
t; .....
UI 0 u c 1620 D
.+i g -a e a_
1560
1 Percent penetration • 56 MW 1500 .__~....._~__..~~-'-~-i..~~.i.......~ ......... ~--i~~...._~_._~__,
a 3 6 9 12 15 Percent penehbon
Figure 46. Effect of PV penetration on system production cost
Case Study Results 188
Table 19. Static versus dynamic dispatch
Parameter Static Case Dynamic Case Total daily dispatchable generation 70786.00 MWhr 67866.24 MWhr Total daily CT generation 2467.00 MWhr 3282.00 MWhr Total daily PV generation 2041.44 MWhr 4381.54 MWhr Total daily pumped storage generation 0.00 MWhr 0.00 MWhr Total daily hydro generation 0.00 MWhr 0.00 MWhr Total daily interchange 0.00 MWhr 0.00 MWhr Total daily spinning reserve 28455.00 MWhr 19267.19 MWhr Total energy under daily load curve 71793.00 MWhr 71931.00 MWhr Total daily losses 3488.00 MWhr 3596.50 MWhr Total daily production costs $1,659,572.00 $1,664,892.80 Total daily thermal schedule 497 (Unit-hrs) 497 (Unit-hrs) Total daily CT schedule 46 (Unit-hrs) 76 (Unit-hrs) Total daily Hydro schedule 0 (Unit-hrs) 0 (Unit-hrs) Total daily pumped storage schedule O (Unit-hrs) O (Unit-hrs) Total daily interchange schedule 0 (Unit-hrs) 0 (Unit-hrs)
Case Study Results 189
load. The proposed dynamic dispatch case has already been described in Chapter 7 and
results presented in this chapter. A comparison of the two cases in shown in Table 19. Both
cases assume the existence of a 750 MW PV power plant operating in the same generation
mix. Day shown in the figure is January 15th. The PV plant output in the static case during the
day is found to be more than 53% less than what is actually generated. The thermal
generations are up by 4% in the static case compared to the dynamic case. Rest of the
parameters show an overly optimistic scenario. CT generations in the static case are lower
by about 25% than the dynamic case; spinning reserves are up by about 52% and the
production cost is lower than the dynamic case. Another statistic in the comparison is the daily
thermal schedule measured in unit-hours. The two cases show similar schedules mainly
because the same hourly load data is used. The conclusion that is derived from these results
is that, although the dynamic dispatch case shows a more conservative result, these are more
realistic figures and are to be expected in real-time operation in the power system. The static
case is adequate for planning and reliability studies with PV plants in the generation mix. But,
for real-time integrated operation, a dynamic study as proposed in this chapter is required.
Case Study Results 190
CHAPTER 9
Summary and Recommendation
The value of solar photovoltaics to an electric utility will remain a widely debated topic in
research circles for the next few years. But before the "value" can be established, it is
imperative that the operation of the PV plant be studied in the context of the utility's
generation scenario. The utility's power system operations is a complex scheme to say the
least and to add the highly variable PV generations in the pot, obviously makes it more
complicated. But a solution needs to be found in order to make PV more competitive against
other emerging new technologies, or even against conventional fossil fuel-based generation
systems.
This dissertation has put forward a new operational tool for integrating a PV system with the
utility. It is recognized at the outset, that much of the existing research concentrated on the
central PV system and its operations have concluded that technical problems in PV operation
will override any value or credit that can be earned by a PV system, and that penetration of
a PV plant in the utility will be severely limited. These are real problems and their solutions
are sought in this dissertation. The following points are believed to be the major obstacles
Conclusions 191
that are plaguing the cause of PV systems, and for that matter, all renewable sources which
depend on the weather or any random phenomenon. These are:
• At present, the PV generations, if any exist in the generation mix, are handled in a static
manner in utility operations. PV output over the day or week of the commitment period is
simulated using typical weather data at the site. While typical load demand trends during
this period follow a particular trend and are generally considered accurate to a certain
degree, the same cannot be said for the PV output. The reason is that, PV plant
performance depends on the highly variable weather phenomena and are liable to
extreme changes during the week. Weather forecasts as far ahead as one week cannot
be considered reliable. Therefore, the amount of uncertainty introduced into the unit
commitment output is considerably increased because of the presence of PV power.
• With the static approach, PV power is considered to be forced on the system. No care is
taken to see whether the PV plant might be generating during a period of time when the
base load units are operating. The latter are required to operate at the same level of
generation throughout the day, in order to be most economic. Also, no care is taken to
see whether there is enough cycling capacity available at any time during which the net
load changes substantially because of the forced PV generations.
Judging from the drawbacks of the static approach, it seems obvious that a new approach or
methodology needs to be developed which would give a central station PV plant its due share
of credit.
This dissertation dealt mainly, with the development and implementation of this new approach
- a dynamic rule-based dispatch algorithm which takes into account all the problems faced
by the dispatch operator during a dispatch interval and channels those into a knowledge base
for use by a rule base (RB).
Conclusions 192
The new dynamic dispatch requires forecasts of photovoltaic generations at the beginning of
each dispatch interval to build the more realistic scenario. A Box-Jenkins time-series method
was used to model the sub-hourly solar irradiance. The irradiance data at any specific site can
be stripped of its periodicities using a pre-whitening process which involves parameterization
of certain known atmospheric phenomena. The pre-whitened data series can be considered
stationary, although some non-stationarity might be introduced by the discontinuities in the
data collection during night hours. This model is extended to yield forecast equations which
are then used to predict the photovoltaic output expected to occur at certain lead times
coinciding with the economic dispatch intervals. The following observations can be made
about the predictive model:
1. An accurate and relatively simple method (compared to other statistical methods) to
predict solar irradiance.
2. A comprehensive model which can forecast the irradiance value for any lead time from
a few minutes to an hour.
3. Input requirements are not very restrictive. Only requirements are past global horizontal
irradiance, wind speed and temperature measurements.
4. Results show that when compared to actual data measured at several locations, the
forecasts are quite accurate and the model is site independent.
5. Forecasts are found to be inaccurate only when there are sudden transitional changes in
the cloud cover moving across the sun. In other words, the randomness involved in
sudden extreme changes in the sun's intensity (e.g. bright sun to fully shaded sun and
back to bright sun again) during an interval will not be picked up by the forecast model
and is generally considered impossible to predict by any forecast model.
In the rule-based dispatch algorithm that was developed in this dissertation, the rule based
system is introduced to operate as a substitute for the dispatch operator. A dispatcher works
from the hourly committed dispatch units and uses standard procedures to allocate generation
levels, to maintain the system frequency, to maintain the area control error at zero in case
Conclusions 193
of interconnected systems and to bring up fast start-up units like peaking hydro or gas
turbines in case of emergencies. Some of these are routine jobs, while some require
specialized knowledge or experience. The RB is given these two qualities through a number
of rules. The RB works in tandem with a conventional economic dispatch algorithm. The
functions of the two are coordinated by another algorithm which overlooks the flow of
information and records them.
With the sub-hourly PV output forecasts available, the treatment of PV plants in the economic
dispatch algorithm becomes similar to that of combustion turbines (CT). The essential
similarities are the fact that CT's can be brought on-line within a very short time, whenever
there is need for extra capacity, and they can be backed off whenever desired. Dissimilarities
in the operation of the two plant types are that a CT plant operates at a low load factor,
whereas, a PV plant is expected to run at as high a load factor as possible in order to compete
favorably against conventional units.
It was found that inclusion of PV generations caused two forms of the same problem - that
of response limitation of thermal units. The problems were:
• Thermal generations were not able to increase and attain the economic trajectory as
dictated by the unit economics and net load.
• Thermal generations were not able to decrease and attain the economic trajectory as
dictated by the unit economics and net load.
The RB gives one of 16 possible solutions as and when required. These solutions are written
as rules which manipulate the non-committable generation to achieve an optimal solution. The
RB during its operation overlooks the fact that the PV generation are kept at the maximum
level possible under all constraints. The case study revealed that the thermal generating units
which are scheduled by the unit commitment are able to absorb most of the small to medium
variations present in the PV generations. In cases of large variations during a single interval,
Conclusions 194
for example, when the PV plant starts up from zero to a substantial amount in the morning,
or when the plant shuts-off in the evening, the thermal generators reach their response limits
before they can reach their maximum or minimum generation, thus causing mismatches in the
load and generation. The mismatches are then picked up by the non-committable sources of
generation (in the case study, combustion turbine units only), comprised of pumped storage
units, hydro generation plant, or by interconnection tie-lines. If none of these are sufficient,
changes are made in the PV generation schedule.
The effect on spinning reserve is markedly present during high variations in PV plant output.
In the morning when the PV plant starts up, there is a sudden decrease in thermal generation
which contributes to an increase in the spinning reserve. This is beneficial to the system
because, the time of PV plant start-up coincides with the morning load pick-up and therefore,
the system would experience a potential reserve shortage without PV at this particular time.
the situation reverses in the evening when the PV plant shuts off, and the load is also dropping
significantly, so that the thermal units would have to pick up generation, thus reducing the
reserves.
The case study revealed that during a single day's operation:
1. thermal plant generation was reduced by 6.7%,
2. CT generations picked up 18.4%,
3. the PV plant operated with a load factor of 58.4%,
4. total spinning reserves increased insignificantly,
5. production costs fell by 3.5%, indicating a saving of $60,000 during the day, and
6. the worst situation occurred when the demand decreased, but at the same time, the PV
generations increased substantially from one interval to another and vice versa.
The results obviously depend on the time of the year and the specific utility. The time of the
year information is reflected in the load demand profile. Most utilities in the U.S. have single
Conclusions 195
peaks in summer and double peaks in winter. Also, the time of the peak load occurrence,
varies with season. The utility generating capacity mix influences the results a great deal. A
utility with a generation mix having a combination of a number of non-committable plant types,
for example, pumped storage, CT, hydro, and interconnection, would incur lower production
costs since the extra non-committable generation required because of the presence of PV
could be shared by all the plant types.
For the utility selected in the case study, penetration of PV was limited to 13.27% before
operating mismatches were no longer possible to be resolved. Once again, the penetration is
a function of the utility and the location.
9.1 Recommendations
The concepts and algorithms developed in the dissertation are part of an integration process
dealing with photovoltaic power plants and electric utilities. Although, central station
photovoltaics is not a new concept, the methodology of integration presented here is. An effort
has been made to develop a model of power system operations incorporating the dispatch of
PV generations. The model, while serving to concretize the ideas presented and providing
validity, requires more development to be regarded as an operational tool.
Some issues which need to be researched further are:
• Resource forecast strategy
1. A more extensive data base may be created.
2. Grouping of similar days into day types may prove to be useful as irradiance
forecasts may become more accurate.
Conclusions 196
• Rule-based dispatch algorithm
1. Number of rules used in the rule base needs to be increased in order to make the
algorithm site independent.
2. A random firing of the rules in the rule base may be explored. This approach will
certainly have a distinct advantage over the hierarchical approach followed in this
dissertation. An expert system may be employed for this purpose.
• Overall Methodology
1. An economic analysis of the integration of PV systems with utilities needs to be
performed over the lifetime of the PV plant, before any value can be established for
the plant in the planning context.
2. Statistical availability and reliability modeling for the PV plant should be done in
order to perform the next stage of the value determination process -- that of
long-term planning in the utility's planning process.
Conclusions 197
Abbreviations
AIEE ASH RAE
EMNEA EPES EPRI IECEC ISES PAS PES PICA PSCC PVSC PWRS SERI
Bibliography
American Institute of Electrical Engineers American Society of Heating, Refrigerating & Air-Conditioning Engineers Energy Modeling & Net Energy Analysis Electrical Power & Energy Systems Electric Power Research Institute lntersociety Energy Conversion Engineering Conference International Solar Energy Society Power Apparatus & Systems (transactions) Power Engineering Society Power Industry Computer Applications Power Systems Computation Conference Photovoltaic Specialist Conference Power Systems (transactions) Solar Energy Research Institute
[1] M.A. ABDELRAHMAN. M.A. ELHADIDY (1986) "Comparison of Calculated and Measured Values of Total Radiation on Tilted Surfaces in Dhahran, Saudi Arabia. " Solar Energy , Vol. 37(3): 239-243.
[2] E.A. ALSEMA, A.J.M. VAN WIJK, W.C. TURKENBURG (1983) "The Capacity Credit of Grid Connected Photovoltaic Systems. " Proc. 5th Int. Solar Energy Conf. Athens, Greece. Pp. 382-392.
(3) B.A. ANDERSON, et al. (1984) "Potential applications for a dynamic hour by hour production simulator." Proc. American Power Conference. , Vol. 46: 403-407.
(4) A. ANGSTROM (1961) Techniques of Determining the Turbidity of the Atmosphere. "TELLUS XIII": 214-223.
Bibliography 198
[5] W.R. ANIS, R.P. MERTENS, R.J. VAN OVERSTRAETEN (1983) "Calculation of solar cell operating temperature in a flat plate PV array. " Proc. 5th Int. Solar Energy Conf., Athens, Greece Pp 520-524
[6] K. AOKI, T. SATOH (1982) "Economic Dispatch With Network Security Constraints Using Parametric Quadratic Programming." IEEE PAS, Vol. 101(12): 4548-4556.
[7] S.A. ARAFEH (1977) "Real-time Security Assessment With Fast Optimum Generation Shift Control" 1977 PICA Conference, Toronto, Canada: 360-368.
[8] Y. ARIGA (1984) "Optimum Capacities of Battery Energy Storage System for Utility Network and Their Economics." 19th IECEC: 1075-1080.
[9] J.C. ARNETT, J. SHUSHNAR, R. TOLBERT (1984) "Design Optimization of Tracking Photovoltaic Arrays". 19th IECEC: 2162-2166.
[10) E.A. ARONSOR, D.L. CASKEY (1981) "The Value of Prediction to Grid Connected Photovoltaic Systems With Storage" Proc. /st Workshop on Terrestrial Solar Resource Forecasting and on Use of Satellites for Terrestrial Solar Resource Assessment. Washington, D.C.
[11) D.F. ARPS, V.N. SMILEY (1977) "Total, Direct, Diffuse and Turbidity Measurements in Nevada" Proc. 1977 American Section of/SES Orlando, FL.
[12) M.A. ATWATER, P.S. BROWN (1974) "Numerical Computations of the Latitudinal Variation of Solar Radiation for an Atmosphere of Varying Opacity" Journal of Applied Meteorology: Vol. 13: 289-297.
[13) M.A. ATWATER, J.T. BALL (1978) "A Numerical Solar Radiation Model Based on Standard Meteorological Observations." Solar Energy, Vol. 21(3): 163-170.
[14) M.A. ATWATER, J.T. BALL (1981) "Effects of Clouds on lnsolation Models". Solar Energy, Vol. 27(1): 37-44.
[15) A.K. AYOUB, A.O. PATTON (1971) "Optimal thermal Generating Unit Commitment" IEEE PAS, Vol. 90(4): 1752-1756.
(16) A. BALOUKTSIS, P.H. TSALIDES (1986) "Stochastic Simulation Model of Hourly Solar Radiation" Solar Energy Vol 37(2): 119-126.
(17] P. BALTAS, et. al. (1986) "Evaluation of Power Output for Fixed and Step Tracking Photovoltaic Arrays" Solar Energy, Vol. 37(2): 147-163.
[18) R.J. BARON, L.G. SHAPIRO (1980) Data Structures and Their Implementation. Van Nostrand Reinhold Co., 1980.
[19) T.E. BECHERT, H.G. KWATNY (1972) "On the Optimal Dynamic Dispatch of Real Power" IEEE PAS Vol 91(3): 889-898.
(20) I. BENNETT (1969) "Correlation of Daily lnsolation With Daily Sky Cover, Opaque Sky Cover and Percentage of Possible Sunshine" Solar Energy, Vol. 12(3): 391-393.
[21) P. BEREANO, B. HYMAN, R.H. WATSON (1982) "Selecting desirable technologies for decentralized electricity generation." Proc. IEEE Int. Conf. on Cybernetics & Society.
(22) A.R. BERGEN (1986) Power System Analysis Prentice-Hall, Inc.
Bibliography 199
[23] D.A. BERGMAN, M.C RUSSELL (1985) "Off-azimuth Photovoltaic Performance and lnsolation Study" 18th PVSC: 240-245.
[24] R.H. BEZDEK, A.B. CAMBEL (1981) "The Solar energy/ Utility interface. " Energy Vol 6: 479-484
[25] A.J. BIGA, R. ROSA (1981) "Statistical Behavior of Solar Irradiation Over Consecutive Days" Solar Energy Vol 27(2): 149-157.
[26] R. BIRD, R. HULSTROM (1981) "A simplified clear sky model for direct and diffuse insolation on horizontal surfaces" SERllTR-642-761 SERI.
[27] R. BIRD, R.L. HULSTROM (1981) "Direct insolation models" SERllTR-335-344 SERI.
[28] R. BIRD (1984) "A Simple, Solar spectral Model for Direct Normal and Diffuse Horizontal lrradiance." Solar Energy, Vol. 32(4): 461-471.
[29] BOEING COMPUTER SERVICES CO. (1982) "EPRI Generating Unit Commitment Production Costing Program. Vol. 1: User's Guide", EPRI EL-2455 EPRI June 1982.
[30] BOEING COMPUTER SERVICES CO. (1982) "EPRI Generating Unit Commitment Production Costing Program. Vol. 2: Programmer's Guide", EPRI EL-2455 EPRI June 1982.
[31] E. C. BOES (1975) "Estimating the direct component of solar radiation. " SAND75-0565 Sandia National Labs.
[32] J. BOLTON (1983) "Solar Cells: A Technology Assessment". Solar Energy, Vol. 31(5): 483-502.
[33] G.J. BONK, G.J. JONES, M.G. THOMAS (1983) "The Effects of Future Energy Scenarios on Photovoltaic Energy Value." SAND83-1283 August 1983.
[34] C.S. BORDEN (1981) "Lifetime Cost and Performance model for distributed photovoltaic systems., Vol. 1: Summary. " JPL-5220-12 Sandia National Labs.
[35] A. BOSE, P.M. ANDERSON (1984) "Impact of new energy technologies on generation scheduling. " IEEE PAS Vol.103(1): 66-71.
[36] J.N. BOUCHER (1979) "Real-time Energy Control" 1979 PICA Conference, Ohio: 177-184.
[37] G.E.P. BOX, G.M. JENKINS (1970) Time Series Analysis: Forecasting and Control. Holden-Day.
[38] N. BRASLAU, J.V. DAVE (1973) "Effect of Aerosols on the Transfer of Solar Energy Through Realistic Model Atmospheres. Part I: Non-absorbing Aerosols". Journal of Applied Meteorology, Vol. 12: 601-615.
[39] G.W. BRAUN (1976) "Solar photovoltaic conversion - electric utility point of view." 12th PVSC Pp 658-660.
[40] J.E. BRAUN, J.C. MITCHELL (1983) "Solar Geometry for Fixed and Tracking Surfaces" Solar Energy, Vol. 31(5): 439-444.
[41] F.S. BRAZZELL, N.J. BALLI (1977) "An Algorithm for Dispatching in Contingency Load Flows in Power Systems Planning Studies" 1977 PICA Conference Toronto, Canada: 100-105.
Bibliography 200
[42] R. BRIGHT, H. DAVITIAN (1981) "Application of WASP to the analysis of solar and cogenerating technologies in the context of PURDA" Proc. Electric Generation System Exp. Analysis Conf. OSU.
(43] R.N. BRIGHT, R.W. LEIGH (1984) "Photovoltaics and electric utilities." Solar Energy, Vol. 9(2): 125-147.
(44] B.J. BRINKWORTH (1977) "Autocorrelation and stochastic modelling of insolation sequences." Solar Energy, Vol.19(4): 343-347.
(45] J.T. BROWN, J.H. CRONIN (1974) "Battery Systems for Peaking Power Generation" 9th IECEC: 903-910.
(46] L.L. BUCCIARELLI, B.L. GROSSMAN, E.1. LYON (1980) "Battery systems for peaking power generation." 9th IECEC Pp. 903-910.
(47] A.O. BULAWKA (1984) "Power Conditioner Sub-systems - DOE Technology Development Status." 19th IECEC: 2190-2194.
(48] G.L. CAMPEN (1982) "An Analysis of the Harmonics and Power Factor Effects at a Utility lntertied Photovoltaic System" IEEE PAS, Vol. 101(12): 4632-4639.
(49] C. CARAMANIS, R. D. TABORS, F. C. SCHWEPPE (1981) "The introduction of non-dispatchable technologies as decision variables in long-range capacity planning. " Proc. Electric Generation System Exp. Analysis Conf. OSU
(50] M. CARAMANIS, R. D. TABORS, K. S. NOCHUR (1982) "The introduction of non-dispatchable technologies as decision variables in long-term generation expansion models." IEEE PAS, Vol.101(8): 2658-2667.
(51] M. CARAMANIS (1983) "Analysis of Non-dispatchable Options in the Generation Expansion Plan." . IEEE PAS, Vol. 102(7): 2098-2103. ·
(52] CARNEGIE-MELLON UNIVERSITY (1986) "Artificial Intelligence Technologies for Power Systems Operations." EPRI EL-4323 EPRI Jan. 1986.
(53) J. CARPENTIER, A. MERLIN (1982) "Optimization Methods in Planning and Operation" EPES, Vol. 4(1): 11-18.
(54) J. CARPENTIER (1984) "A Link Between Short Term Scheduling and Dispatching: "Separability of Dynamic Dispatch"." 8th PSCC, Helsinki, Finland. Aug. 1984.
(55) J. CARPENTIER (1985) "To Be Or Not To Be Modern, That is the Question for Automatic Generation Control (Point of View of a Utility Engineer)" EPES, Vol. 7(2): 81-91.
(56) J.J. CARROLL (1985) "Global Transmissivity and Diffuse Fraction of Solar Radiation for Clear and Cloudy Skies Measured and as predicted for Bulk Transmissivity Models". Solar Energy, Vol. 3592): 105-118.
(57) C. CEGRELL (1986) Power System Control Technology., Prentice-Hall International.
(58) P. CEPPI, M. CAMANI (1983) "Analysis of the first year of operation of the photovoltaic utility interface plant TISO." Proc. 5th Int. Solar Energy Conf. Athens, Greece. Pp. 378-382.
(59) S.M. CHALMERS, et al. (1984) "The effect of photovoltaic power generation on utility operation." IEEE Power Engineering Society Summer Meet.
Bibliography 201
[60] S. CHALMERS (1984) "Status Report of Standards Development for Photovoltaic Systems Utility Interface". 19th IECEC: 2195-2196.
[61] S. CHAN, D.C. POWELL, M. YOSHIMURA, D.H. CURTICE (1983) "Operations Requirements of Utilities With Wind Power Generations". IEEE PAS, Vol. 102(9): 2850-2860.
[62] J.B. CHEATHAM, M.C. RECCHUITE (1984) "Photovoltaic Opportunities in Large Grid Connected Applications." 19th IECEC: 2152-2155.
[63] G.T. CHI NERY, J.M WOOD (1985) "TVA's photovoltaic activities." IEEE Power Engineering Society Winter Meet.
[64] G.T. CHINERY, J.M. WOOD (1985) "Photovoltaics From an Electric Power Systems Perspective" 20th IECEC: 3.421-3.426.
[65] B. CHOUDHURY (1982) "A Parameterized Model for Global lnsolation Under Partially Skies." Solar Energy, Vol. 29(6): 479-486.
[66] N.K.O. CHOUDHURY (1963) "Solar Radiation at New Delhi" Solar Energy, Vol. 7(2): 44-52.
[67] B.H. CHOWDHURY, S. RAHMAN (1987) "Forecasting Sub-hourly Global Solar lrradiance for Prediction of Photovoltaic Output." 19th PVSC, New Orleans, LA., May 1987.
[68] B.H. CHOWDHURY, S. RAHMAN (1987) "Analysis of Interrelationships Between Photovoltaic Power and Battery Storage for Electric Utility Load Management." Presented at the IEEE PES Summer Power Meeting, San Francisco, CA, July 1987.
[69] B.H. CHOWDHURY, S. RAHMAN (1987) "Comparative Assessment of Plane-of-array lrradiance Models." To be published in a forthcoming issue of Solar Energy
[70] C.R. CHOWANIEC, et al. (1977) "Solar Photovoltaic Power Stations" Proc. 1977 American Section of /SES Orlando, FL.
[71] C.R. CHOWANIEC, et al. (1978) "Energy storage operation of combined photovoltaic/ battery plants in utility networks." 13th PVSC Pp. 1185-1189.
[72] D. CHU, T.S. KEY (1984) "Assessment of Power Conditioning for Photovoltaic Central Power Stations" 17th PVSC: 1246-1251.
[73] A.S. CLORFEINE (1980) "Economic feasibility of photovoltaic energy systems." 14th PVSC Pp. 986-989.
[74] N. COHN (1957) "Some Aspects of Tie-line Bias Control on Interconnected Power Systems" A/EE, Vol. 75, Part Ill: 1415-1436.
[75) N. COHN (1971) Control of Generation and Power Flow on Interconnected Power Systems John Wiley & Sons.
(76] G. COKKINIDES, et al. (1984) "Investigation of utility interface problems of photovoltaic systems: Experimental and simulation studies." 17th PVSC Pp. 1234-1241.
(77] M. COLLARES-PEREIRA, A. RABL (1979) "The Average Distribution of Solar Radiation -Correlations Between Diffuse and Hemispherical and Between Daily and Hourly lnsolation Values". Solar Energy Vol 22(2): 155-164.
Bibliography 202
[78) A.J. COX (1980) "The Economics of Photovoltaics in the Commercial, Institutional and Industrial Sectors." 14th PVSC Pp. 252-258.
[79) D.H. CURTICE, T.W. REDDOCH (1983) "An Assessment of Load Frequency Control Impacts Caused by Small Wind Turbines". IEEE PAS, Vol. 102(1): 162-170.
(80] W.D. DAPKUS, T.R. BOWE (1984) "Planning for New Electric Generation Technologies: A Stochastic Dynamic Programming Approach. " IEEE PAS, Vol.103(6): 1447-1453
[81] J.V. DAVE, N. BRASLAU (1975) "Effect of Cloudiness on the Number of Solar Energy Through Realistic Model Atmospheres". Journal of Applied Meteorology, Vol. 14: 388-392.
[82] J.V. DAVE (1978) "Extensive Datasets of the Diffuse Radiation in Realistic Atmospheric Models With Aerosols and Common Absorbing Gases." Solar Energy, Vol. 21(5): 361-369.
[83] A.K. DAVID "Power System Contol in the Presence of Large Stochastic Sources." 8th PSCC, Helsinki, Finland. Aug. 1984.
[84) J.A. DAVIES, J.E. HAY (1980) "Calculation of the Solar Radiation Incident on a Horizontal Surface." Proc. First Solar Radiation Data Workshop.: 32-58.
[85] J.A. DAVIES, D.C. McKAY (1982) "Estimating Solar lrradiance and Components". Solar Energy, Vol. 29(1): 55-64.
[86] J.A. DAVIES, M. ABDEL-WAHAB (1983) "Evaluation of Models for Simulating Solar Radiation Incident on Horizontal Surfaces''. Report to Atmospheric Environment Service, Canada.
[87] J.T. DAY (1971) "Forecasting minimum production costs with linear programming." IEEE PAS, Vol.90(2): 814-823.
[88] J.T. DAY, M.J. MALONE (1982) "Electric utility modelling extensions to evaluate solar plants." IEEE PAS, Vol.101(1): 120-126.
[89] R. DESHMUKH, R. RAMAKUMAR (1982) "Reliability Analysis of Combined Wind-electric and Conventional Generation Systems". Solar Energy, Vol. 28(4): 345-352.
[90] M. DEVINE, H. KUMIN, A. ALY (1978) "Operations research problems in the economic design and operation of solar energy systems. " EMNEA Pp 619-638.
[91] R.N. DHAR (1982) Computer Aided Power System Operation and Analysis. McGraw-Hill.
[92] H.W. DOMMEL, W.F. TINNEY (1968) "Optimal Power Flow Solutions" IEEE PAS, Vol 87(10): 1866-1876.
(93] W. DUB, H. PAPE (1983) "Utility Operating Strategy and Requirements for Wind Power Forecast". Journal of Energy, Vol. 7(3): 231-236.
(94] J.A. DUFFIE, W.A. BECKMAN (1980) Solar Engineering of Thermal Processes. John Wiley & Sons.
[95] M.W. EDENBURN, G.R. CASE, L.H. GOLDSTEIN (1976) "Computer simulation of photovoltaic systems. " 12th PVSC Pp 667-672.
[96] A.H. EL-ABIAD (ed) (1983) Power Systems Analysis, Hemisphere Publishing Corporation.
Bibliography 203
[97] M.E. EL-HAWARY, G.S. CHRISTENSEN (1979) Optimal Economic Operation of Electric Power Systems, Academic Press.
[98] ELECTRIC POWER RESEARCH INSTITUTE (1981) "The EPRI Regional Systems." EPRI P-1950-SR, EPRI July 1981.
[99] ELECTRIC POWER RESEARCH INSTITUTE (1983) "Photovoltaic System Assessment: An Integrated Perspective." EPRI AP 3176-SR EPRI Sept. 1983.
[100] L. ELTERMAN (1968) "UV, Visible and IR Attenuation for Altitudes to 50 km". Environmental paper # 285, Air Force Cambridge Research Laboratories.
[101] ENERGY DEVELOPMENT SUB-COMMITTEE, PES (1985) "Utility industry outlook for emerging energy systems. "IEEE PAS Vol 104(12): 3321-3328.
[102] J.D. ENGELS, S. POLLOCK, J.A. CLARK (1981) "Observations on the Statistical Nature of Terrestrial Irradiation". Solar Energy, Vol. 26(1): 91-92.
[103] D.G. ERBS, S.A. KLEIN, J.A. DUFFIE (1982) "Estimation of the diffuse radiation function for hourly, daily and monthly average global radiation. " Solar Energy, Vol.28(4): 293-302.
[104] D.N. EWART (1975) "Automatic Generation Control: Performance Under Normal Conditions." System Engineering for Power: Status & Prospects.
[105] W.A. FACIANELLI (1983) "Modeling and Simulation of Lead-acid Batteries for Photovoltaic Systems". 18th IECEC: 1582-1588.
[106] G.R. FEGAN, C.D. PERCIVAL (1980) "Integration of intermittent sources into Baleriaux-Booth production cost models. " IEEE PES Winter meet.
[107] E.M. FEIGELSON (1984) Radiation in a Cloudy Atmosphere, D. Reidel Publishing Co.
[108] L.H. FINK, W.E. FEERO (1982) "Effective Integration of New Technologies into Electric Energy Systems." IEEE PAS, Vol 101(7): 1833-1842
[109] S. FINGER (1979) "Electric power system production costing and reliability analysis including hydroelectric, storage and time-dependent power plants. 11 MIT Energy Laboratory MIT-EL-79-006
[110] R. FISCL, et al. (1979) "Design of Integrated Electric Solar Utility System for Peak load Shaving. 11 1979 IEEE PES Winter Power Meeting.
[111] L. FRANCHI, et al. (1980) "Centralized Generation Control of Real Power for Thermal Units by a Parametric Linear Programming Procedure." Automatic Control in Power Generation, Distribution and Protection: 51-60.
[112] M.K. FUENTES, J.P. FERNANDEZ (1984) "Performance evaluation of large-scale photovoltaic systems. 11 17th PVSC Pp. 1060-1065.
[113] M.K. FUENTES (1985) "Thermal Characterization of Flat-plate Photovoltaic Arrays." SAND85-1163C, Sandia National Labs.
[114] M.K. FUENTES (1987) "A Simplified Thermal Model for Flat-plate Photovoltaic Arrays." SAND85-0330, Sandia National Labs. May 1987.
Bibliography 204
[115) J.D. GARRISON (1985) "A Study of the Division of Global lrradiance into Direct and Diffuse lrradiance at Thirty-three U.S. Sites." Solar Energy, Vol. 35(4): 341-351.
[116) E.E. GEORGE (1943) "lntrasystem Transmission Loses." A/EE Transactions, Vol. 62: 153-158.
[117) H.R. GLAHN, D.A. LOWRY (1972) "The Use of Model Output Statistics (MOS) in Objective Weather Forecasting." Journal of Applied Meteorology, Vol. 11: 1203-1211.
[118) H. GLAVITSCH, J. STOFFEL (1980) "Automatic Generation Control". EPES, Vol 2(1): 21-28.
[119) T.N. GOH, K.J. TAN (1977) "Stochastic Modeling and Forecasting of Solar Radiation Data". Solar Energy, Vol. 19(6): 755-757.
[120) L.H. GOLDSTEIN, G. R. CASE (1977) "PVSS- A Photovoltaic System Simulation program users manual. " SAND77-0814:
[121) J.M. GOODRICH, B. KENDALL, G. NAGEL (1974) "Use of Interactive Programs in Daily Dispatch Operations". Proc. American Power Conference, Vol. 36: 848-855.
[122) C.A. GROSS (1986) Power System Analysis, John Wiley & Sons.
[123) R.H. GUESS, et al. (1984) "Central Station Advanced Power Conditioning Technology, Utility Interface and Performance." 19th IECEC: 2210-2215.
[124) H.H. HAPP (1972) "Diakoptics and System Operations: Automatic Generation Control in Multi-areas." Conference on Computers in Power Systems Operation & Control,: 208-225.
[125) H.H. HAPP (1977) "Optimal Power Dispatch - A Comprehensive Survey". IEEE PAS, Vol. 96(3): 841-854.
· [126) G.W. HART, P. RAGHURAMAN (1982) "Electrical aspects of photovoltaic system simulation." DOEIET/20279-207
[127) J. HASLETI, M. DIESEN DORF (1981) "The Capacity Credit of Wind Power: A Theoretical Analysis." Solar Energy, Vol. 26(5): 391-401.
[128) B. HAURWITZ (1948) "lnsolation in Relation to Cloud Type." Journal of Meteorology, Vol. 5(June): 110-113.
[129) J.E. HAY (1979) "Calculation of monthly mean solar radiation for horizontal and inclined surfaces. " Solar Energy, Vol.23(4): 301-307.
[130) J.E. HAY (1985) "Estimating solar lrradiance on inclined surfaces: A review and assessment of methodologies." Int. Journal of Solar Energy, Vol.3: 203-240.
[131) J.E. HAY, D.C. McKAY (1985) "Estimating Solar lrradiance on Inclined Surfaces: A Review and Assessment of Methodologies" International Journal of Solar Energy, Vol. 3: 203-240.
(132) J.E. HAY, R. PEREZ, D.C. McKAY (1986) "Addendum and Errata to the Paper #Estimating Solar lrradiance on Inclined Surfaces: A Review and Assessment of Methodologies•", International Journal of Solar Energy, Vol. 4: 321-324.
Bibliography 205
(133) H.M. HEALEY, G.L. BIRDWELL (1984) "Photovoltaic systems interconnection requirements from the utility perspective. " 17th PVSC Pp. 535-540.
(134) E. HERNANDEZ, N. RISSER (1982) "Utility operation of a flat-plate photovoltaic system. " 16th PVSC Pp. 1002-1006.
(135) G.T. HEYDT (1986) Computer Methods for Power Systems, Macmillan Publishing Company.
(136) T. HOFF, C. JENNINGS (1985) "Match Between PG & E's Peak Demand and lnsolation Availability." 18th PVSC: 235-239.
(137) E.R. HOOVER (1980) "SOLCEL-11: An Improved Photovoltaic System Analysis Program." Report - SAND 79-1785 Sandia National Labs. Feb. 1980.
(138) F.C. HOOPER, et al. (1975) "The Canadian Solar Radiation Data Base." ASHRAE journal, Vol. 85(2): 497-506.
(139) D.V. HOYT (1978) "A model for the calculation of solar global insolation. " Solar Energy, Vol.21(1): 27-35.
(140) D.J. HUGHES, R.E. HEIN, B.W. HELLER (1983) "Photovoltaic central power stations: Opportunity analysis and technology status." 18th IECEC Pp. 1301-1306.
(141) IEEE Committee Report (1971) "Present Practices in the Economic Operation of Power Systems". IEEE PAS, Vol. 90(4): 1768-1775.
(142) M. INNORTA, P. MARANNINO (1986) "Advance Dispatch Procedures for the Centralized Control of Real Power." IEEE PWRS, Vol. 1(2): 233-240.
(143) S.A. ISARD (1986) "Evaluation of Models for Predicting lnsolation of Slopes Within the Colorado Alpine Tundra." Solar Energy, Vol. 36(6): 559-564.
(144] H. ISODA (1982) "On-line Load dispatching Method Considering Load Variation Characteristics and Response Capabilities of Thermal Units." IEEE PAS, Vol. 101(8): 2925-2930.
(145) M. IQBAL (1983) An Introduction to Solar Radiation, Academic Press.
(146) M. IQBAL (1980) "Prediction of Hourly Diffuse Solar Radiation From Measured Hourly Global Radiation on a Horizontal Surface." Solar Energy, Vol. 24(5): 495-503.
(147) L.D. JAFFE (1985) "Availability of solar and wind generating units. " IEEE PAS, Vol.104(5): 1012-1016.
(148) S.H. JAVID, et al. (1985) "A Method for Determining How to Operate and Control Wind Turbine Arrays in Utility Systems. "IEEE PAS, Vol.104(6): 1335-1341.
(149) J.S. JENSENIUS, Jr., G.F. COTTON (1981) "The Development and Testing of Automated Solar Energy Forecasts Based on the Model Output Statistics (MOS) Techniques". Proc. /st Workshop on Terrestrial Solar Resource Forecast and on Use of Satellites for Terrestrial Solar Resource Assessment, Washington, D.C., February 1981.
(150) E.E. JOHANSON (1978) "An economic model to establish the value of WECS to a utility system. " Proc. Annual meet. Am. section of /SES. Pp. 580-587.
Bibliography 206
[151) G.J. JONES, D.G. SCHUELER (1978) "Status of the DOE photovoltaic systems engineering and analysis project. " 13th PVSC Pp. 1160-1165.
[152) G.J. JONES (1980) "Energy storage in grid-connected applications. " 14th PVSC Pp. 1025-1028.
[153) G.J. JONES (1984) "A Comparison of Concentrating Collectors to Tracking Flat Panels." 17th PVSC: 1190-1195.
[154) G.J. JONES, H. POST, J. STEVENS, T.S. KEYS (1985) "Design Considerations for Large Photovoltaic Systems" 18th PVSC: 1307-1313.
[155) G.A. JORDAN, W.D. MARSH, J.L. OPLINGER (1978) "Application of Wind and Photovoltaic Power Plants in Electric Utility Systems." Proc. 1978 Annual Meeting of American Section of /SES, Denver CO.
(156) P. KAMBALE, et al. (1983) "A Reevaluation of the Normal Operating State Control (AGC) of the Power System Using Computer Control and System Theory. Part Ill: Tracking the Dispatch Targets With Unit Control". IEEE PAS, Vol. 102(6): 1903-1912.
[157] V. KAPUR, A. CHU (1981) "Battery Requirement for Photovoltaic Energy Storage." 16th /ECEC: 685-688.
[158) W.R. KAUFMAN (1984) "Photovoltaic Balance of System experience from an engineering design and construction perspective. " 17th PVSC Pp. 1153-1158.
(159) J. KERN. I. HARRIS (1975) "On the Optimum Tilt of a Solar Collector." Solar Energy, Vol. 17(2): 97-102.
(160) E.C. KERN (1984) "Photovoltaics, Wind & Small Hydro Power Generation: Comparative Costs and performance." 17th PVSC: 1196-1201.
[161) T.S. KEY, S. KRAUTHAMER (1985) "Status of Utility-interactive Photovoltaic Power Conditioning Technology." 20th IECEC: 3.444-3.449.
[162) T. KEY, D. MENICUCCI (1987) "Photovoltaic Electrical System Design Practice: Issues and Recommendations." 19th PVSC, New Orleans, LA; May 1987.
[163) M. KHALLAT, S. RAHMAN (1985) "A Probabilistic Approach to Photovoltaic Generator Performance Prediction." IEEE Summer Power Meeting, Vancouver, Canada.
[164) M. KHALLAT, S. RAHMAN (1987) "A Model for Capacity Credit Evaluation of Grid-connected Photovoltaic Systems With Fuel cell Support." Paper 87SM 478-1. IEEE Summer Power Meeting, San Francisco. July, 1987.
[165] L.K. KIRCHMAYER (1951) "Analysis of Total and Incremental Loses in Transmission Systems." A/EE Transactions, Vol. 70 Part II: 1197-1205.
[166) L.K. KIRCH MAYER (1958) Economic Operation of Power Systems, John Wiley & Sons.
(167) S. A. KLEIN, J. C. THEILACKER (1980) "An algorithm for calculating monthly average radiation on inclined surfaces." Journal of Solar Energy Engineering, Vol.103: 29-33.
(168) S.A. KLEIN, J.A. DUFFIE (1978) "Estimation of montly average diffuse radiation. " Proc. Annual meet. Am. section of /SES. Pp. 729-735.
Bibliography 207
(169] T.M. KLUCHER (1979) "Evaluation of models to predict insolation on tilted surfaces." Solar Energy, Vol. 23(2):111-114.
[170] U.G. KNIGHT (1972) Power Systems Engineering and Mathematics, Pergamon Press.
[171] C. KO, et al. (1982) "Development and Application of Linear Programming Methods for Pumped Storage Hydro." IEEE PAS, Vol. 101(8):2649-2655.
[172] P.S. KORONAKIS (1986) "On the Choice of the Angle of Tilt for South-facing Solar Collectors in the Athens Basin Area''. Solar Energy, Vol. 36(3): 217-225.
[173] S. KRAUTHAMER, R. DAS, A. BULAWKA (1985) "Power Conditioning Sub-systems for Photovoltaic Central Station Power Plants: Technology and Performance." 20th IECEC: 3.438-3.443.
(174] F. KRIETH, J.F. KRIEDER (1978) Principles of Solar Engineering, McGraw-Hill.
[175] W.S. KU, et al. (1983) "Economic evaluation of photovoltaic generation applications in a large electric utility system. "IEEE PAS, Vol. 102(8):2811-2816.
(176] G.L. KUSIC, H.A. PUTNAM (1985) "Dispatch and Unit Commitment Including Commonly Owned Units." IEEE PAS, Vol. 104(9): 2408-2412.
(177] G.L. KUSIC (1986) Computer-aided Power System Analysis, Prentice-Hall.
[178] H.G. KWATNY, T.A. ATHAY (1979) "Coordination of Economic Dispatch and Load Frequency Control in Electric Power Systems." Proc. 18th IEEE Conference on Decision & Control: 703-714.
(179] A.A. LACIS, J.E. HANSEN (1974) "A Parameterization for the Absorption of Solar Radiation in the Earth's Atmosphere." Journal of Atmospheric Sciences, Vol. 31(Jan): 118-133.
[180] L.J. LANTZ, C.B. WINN (1978) "Validation of Computer Models Used for Predicting Radiation Levels." Proc. Annual Meeting of the American Section of /SES, Denver, CO.
[181] K.D. LE, B.L. COOPER, E.W. GIBBONS (1983) "A global Optimization Method for Scheduling Thermal Generation, Hydro Generation and Economy Purchases." IEEE PAS, Vol. 102(7): 1986-1993.
(182] S.T. LEE, Z.A. YAMAYEE (1981) "Load-following and spinning reserve penalties for intermittent generation." IEEE. PASVol.100(3): 1203-1211.
[183] S.L. LEONARD (1985) "Photovoltaic power generation for utilities: The implications of some recent projects and design studies." IEEE PES winter power meet.
(184] S.L. LEONARD (1978) "Central station power plant applications for photovoltaic solar energy conversion." 13th PVSC Pp. 1190-1195.
(185] T.E.D. LIACCO (1975) "System Control Center Design." Systems Engineering for Power: Status & Prospects, New Hampshire, Aug. 1975.
(186] C.E. LIN, Y.Y. HONG, C.C. CHUKO (1987) "Real-time Fast Economic Dispatch." 1987 IEEE Winter Power Meeting, New Orleans, LA; May 1987.
Bibliography 208
(187) B.Y.H. LIU, R.C. JORDAN (1960) "The inter-relationship and characteristic distribution of direct, diffuse and total solar radiation." Solar Energy, Vol. 4(3): 1-19.
(188) B.Y.H. LIU, R.C. JORDAN (1961) "Daily insolation on surfaces tilted toward the equator." ASHRAE Journal, Vol.3(10): 53-59.
[189) C. LIU (1986) "Expert systems in the Power Industry: A Short Course." 1986 IASTED International Conference, Montana State University
(190) M. LOTFALIAN, R. SCHLUETER (1985) "Inertial, Governor and AGC/Economic dispatch Load Flow Simulations of Loss of Generation Contingencies." IEEE PAS, Vol. 104(11): 3020-3028.
(191) C.C.Y. MA, M. IQBAL (1983) "Statistical Comparison of Models for Estimating Solar Radiation on Inclined Surfaces". Solar Energy, Vol. 31(3): 313-317.
(192) L. MAGID (1985) "Prospects for Photovoltaic Energy Technologies". 20th IECEC: 3.394-3.397.
(193) A. MANI, S. RANGARAJAN (1983) "Techniques for the Precise Estimation of Hourly Values of Global and Direct Solar Radiation." Solar Energy, Vol. 31(6): 577-595.
(194) S. MOKHTARI, et al. (1985) "A Unit Commitment Expert System". PICA Conference, Montreal, Canada. May 1985.
(195) GENERAL ELECTRIC CO. (1978) "Requirement assessment of photovoltaic power plants in electric utility systems." EPRl-ER-685-SY Vol. 1 EPRI June 19778.
[196) GENERAL ELECTRIC CO. (1978) "Requirement assessment of photovoltaic power plants in electric utility systems." EPRl-ER-685 Vol. 2 EPRI June 19778.
(197] GENERAL ELECTRIC CO. (1978) "Requirement assessment of photovoltaic power plants in electric utility systems." EPRl-ER-685 Vol. 3 EPRI June 19778.
(198) D.F. MENICUCCI (1984) "PVFORM- Photovoltaic system analysis program." Draft Report Sandia National Labs.
[199) A. MERLIN, P. SANDRIN (1983) "A New Method for Unit Commitment at Electricite de France." IEEE PAS, Vol. 102(5): 1218-1225.
(200) W.C. MERRILL, R.J. BLAHA, R.L. PICKRELL (1978) "Performance analysis and stability analysis of a photovoltaic power system." DOEINASA/1022-78130
(201) J. MILLER, et al. (1983) "Testing and Evaluation of Advanced Lead-acid Batteries for Utility Load-leveling Applications". 18th IECEC: 1595-1598.
(202) R.H. MILLER (1970) Power System Operation, McGraw-Hill Book Company.
(203) H. MUKAI et al. (1981) "A Reevaluation of the Normal Operating Control of the Power System Using Computer Control and System Theory. Part II: Dispatch Targeting." IEEE PAS, Vol. 100(1): 309-317.
(204) C. MUSTACCHI, V. CENA, M. ROCCHI (1979) "Stochastic Simulation of Hourly Global Radiation Sequences." Solar Energy, Vol. 23(1): 47-51.
Bibliography 209
[205) R.A. McCLATCHEY, et al. (1971) "Optical Properties of the Atmosphere". Environmental Research Paper #354. Air force Cambridge Research Laboratories.
[206) NATIONAL CLIMATIC CENTER (1982) "SOLMET Volume 1- User's Guide", January 1982.
[207) NATIONAL CLIMATIC CENTER (1982) "Typical Meteorological Year - User's Manual", September 1982.
[208) D.J. NORRIS (1968) "Correlation of solar radiation with clouds." Solar Energy, Vol.12(1): 107-112.
[209) J.F. ORGILL, K.G.T. HOLLANDS (1977) "Correlation Equations for Hourly Diffuse Radiation on a Horizontal Surface." Solar Energy, Vol. 19: 357.
[210) G.W. PALTRIDGE, C.M.R. PLATT (1976) Radiative Processes in Meteorology and Climatology, Elsevier Scientific Publishing Co.
[211) N.W. PATAPOFF (1980) "Evaluation of impact on utility of photovoltaic cost breakthrough." 14th PVSC Pp. 235-239.
[212) N.W. PATAPOFF, D.R. MATT JETZ (1985) "Utility interconnection experience with an operating central station MW-sized photovoltaic plant." IEEE PES winter meeting, New York, NY., February, 1985.
[213) N.W. PATAPOFF (1985) "Photovoltaic Power Plants in Utility Interactive Operations." 20th IECEC: 3.413-3.417.
[214) A.D. PATTON (1973) "Dynamic Optimal Dispatch of Real Power for Thermal Generating Units." 8th PICA Conference, Minneapolis, MN; June 1973.
[215) D. PERCIVAL, J. HARPER (1981) "Electric utility value determination for wind energy., Vol. 1: A methodology. " SERllTR-732-604 SERI, CO.
[216) M.V.F. PEREIRA, L.M.V.G. PINTO (1987) "Economic Dispatch With Security-constrained Rescheduling." EPES, Vol. 9(2): 97-104.
[217) R. PEREZ, J. T. SCOTT, R. STEWART (1983) "An anisotropic model for diffuse radiation incident on slopes of different orientations and possible application to CPCs." Proc. ASES, Minneapolis, MN Pp.883-888.
[218) R. PEREZ, et al. (1986) "An Anisotropic Hourly Diffuse Radiation Model for Sloping Surfaces: Description, Performance Validation and Site Dependency Evaluation." Solar Energy, Vol. 36(6): 481-497.
[219) J. PESCHON, S. T. Y. LEE (1978) "Mathematical models for economic evaluation of non-conventional electric power sources." EMNEA Pp. 735-752.
[220) R.L. PICKRELL, G. O'SULLIVAN, W.C. MERRILL (1978) "An inverter/controller sub-system optimized for photovoltaic applications." DOEINASA/1022-78131
(221) A. PIVEC, et al. (1983) "The Battery Energy Storage Test Facility - First Year of Operation". 18th IECEC: 1658-1664.
[222) J.K. PLASTIRAS (1978) "Capacity displacement for solar plants." Proc. Annual meet. Am. section of /SES. Pp. 562-563.
Blbliography 210
[223) POWER MATH ASSOCIATES, INC. (1986) "Automatic Generation Control simulation: User's Guide." SAND86-7044 Sandia National Lab; Dec. 1986
[224) H.N. POST, D.E. ARVIZU, M.G. THOMAS (1985) "A Comparison of Photovoltaic System Options for Today's and Tomorrow's Technologies." 18th PVSC: 1353-1358.
[225) V.M. PURI (1978) "Estimation of Half-hour Solar Radiation Values From Hourly Values". Solar Energy, Vol. 21: 409-414.
[226) V.M. PURI et al. (1980) "Total and Non-isotropic Diffuse lnsolation on Tilted Surfaces." Solar Energy, Vol. 25(1): 85-90.
[227) J.E. QUINN, A. LANDGREBE (1985) "The Mission and Status of the U.S. Department of Energy's Battery Energy Storage Program." 20th IECEC: 2.3-2.10.
[228) S. RAHMAN, B.H. CHOWDHURY (1987) "Simulation of Photovoltaic Power Systems and Their Performance Prediction". Paper 87SM 425-2. Presented at the IEEE PES Summer Power Meeting, San Francisco, CA, July 1987.
[229) S. RAHMAN, R. BHATNAGAR (1987) "An Expert System Based Algorithm Algorithm for Short-term Load Forecasting." Paper 87WM 082-1. 1987 IEEE Winter Power Meeting, New Orleans, LA. Feb. 1987.
[230) R. RAITHEL, et al. (1981) "Improved Allocation of Generation Through Dynamic Economic Dispatch." Proc. 7th PSCC, Lausanne, Switzerland; July.
[231) R. RAMANATHAN (1985) "Fast Economic Dispath Based on the Penalty Factors from Newton's Method." IEEE PAS, Vol. 104(7): 1624-1629.
[232) N.E. RASMUSSEN, H.M. BRANZ (1981) "The dependence of delivered energy on power conditioner electrical characteristics for utility-interactive PV systems" 15th PVSC Pp. 614-620.
[233) T.W. REDDOCH (1975) "Load Frequency Control Performance Criteria With Reference to the Use of Advanced Control Theory." Proc. Systems Engineering for Power: Status & Prospects, New Hampshire. Pp 15-26
(234) F.J. REES, R.E. LARSON (1971) "Computer-aided Dispatching and Operations Planning for an Electric Utility With Multiple Types of Generation." IEEE PAS, Vol. 90(2): 891-899.
[235) RESEARCH TRIANGLE INSTITUTE (1982) "Photovoltaic Cell and Module Status Assessment. Vol. 2: Technology Basis". EPRI AP-2473 EPRI Oct. 1982.
[236) C.H. RIETAN (1963) "Surface Dew Point and Water Vapor Aloft." Journal of Applied Meteorology, Vol. 2(Sep): 776-779.
[237) D.J. ROSEN, D. THORPE, R. SPENCER (1985) "Design, construction and storage of the SMUDPV1 1 MWAC photovoltaic central station power plant." IEEE PES winter power meet.
(238) D. ROSEN (1984) "Photovoltaic Balance of System Development Requirements for Large Terrestrial Power Plants." 19th IECEC: 2113-2116.
[239) D.W. ROSS, S. KIM (1980) "Dynamic Economic Dispatch of Generation." IEEE PAS Vol. 99: 2060-2068.
Blbllography 211
[240) N.D. SADANANDAN, et al. (1983) "Impact Assessment of Wind Generation on the Operations of a Power System". IEEE PAS, Vol. 102(9): 2905-2911.
[241) G.W. SADLER (1970) "Measurement of Apparent Solar Constant and Apparent Extinction coefficient at Edmonton (Alberta), Canada." Solar Energy, Vol. 13(1): 35-41.
(242) G.W. SADLER (1977) "Turbidity of the Atmosphere at Solar Noon for Edmonton (Alberta), Canada." 1977 Annual meeting of American Section of /SES, Orlando, FL.
[243) C.B. SAMUAH, F.C. SCHWEPPE (1981) "Economic Dispatch Reserve Allocation." IEEE PAS, Vol. 100(5): 2635-2642.
(244) S.V. SAVULESCU (1976) Computerized Operation of Power Systems., Elsevier Scientific Publishing Company.
(245) K.F. SCHENK, S. CHAN, P. UKO. N.S. RAU (1980) "Evaluation of production cost and capacity credits of a wind energy conversion system supplying an electric utility." Proc. 3rd Miami Int. Conf. on Energy Sources.
(246) R.A. SCHLUETER, et al. (1983) "Modification of Power System Operation for Significant Wind generation Penetration." IEEE PAS, Vol. 102(1): 153-161.
[247) R.A. SCHLUETER, et al. (1985) "A modified unit commitment and generation control for utilities with large wind generation penetrations." IEEE PAS Vol. 104(7): 1630-1636.
(248) D.G. SCHUELER, G.J. JONES (1978) "Energy storage considerations in photovoltaic central station utility applications." Proc. Annual meet. Am. section of /SES. Pp. 322-326.
(249) SCIENCE APPLICATIONS INC. (1983) "Photovoltaic Requirements Estimation". EPRI AP-2475 EPRI Feb. 1983.
(250) E.B. SHAHRODI, A. MORCHED (1985) "Dynamic Behavior of AGC Systems Including the Effects of Nonlinearities." IEEE PAS, Vol. 104(12): 3409-3415.
[251) J.E. SHERRY, C.G. JUSTUS (1984) "A Simple Hourly All-sky Solar Radiation Model Based on Meteorological Parameters." Solar Energy, Vol. 32(2): 195-204.
(252) R.R. SHOULTS, et al. (1980) "A Practical Approach to Unit Commitment, Economic Dispatch and Savings Allocation for Multiple Area Pool Operation With Import Export Constraints." IEEE PAS, Vol. 99(2): 625-635.
(253) G.J. SHUSHNAR, et al. (1985) "Balance of System Costs for a 5 MW Photovoltaic Generating System." 1985 IEEE PES Winter Power Meeting, New York, NY, February 1985.
(254] E.J. SIMBURGER, C.K. CRETCHER (1985) "Load Following Impacts of a Large Wind Farm on an Interconnected Electric Utility System." IEEE PAS, Vol. 102(3): 687-692.
(255) E.J. SIMBURGER, R. B. FLING (1983) "Engineering Design for a Central Station Photovoltaic Power Plant." IEEE PAS, Vol. 102(6): 1668-1677.
(256) C. SINGH, A. LALO-GONZALEZ (1985) "Reliability Modeling of Generation Systems Including Unconventional Energy Sources." IEEE PAS, Vol. 104(5): 1049-1056.
(257) F. SISSINE (1984) "Wind Power and Capacity Credits: Research and Implementation Issues Arising From Aggregation With Other Renewable Power Sources and Utility
Bibliography 212
Demand Management Measures." European Wind Energy Conference, Hamburg, FRG, October 1984.
[258) J.H. SMITH, L.R. RIETER (1985) "A Non-numerical Approach for the Review of Photovoltaic System Performance Models." Solar Engineering: 220-226.
[259) W.L. SMITH (1966) "Note on the Relationship Between Total Precipitable Water and Surface Dew Point." Journal of Applied Meteorology, Vol. 5(0ct): 726-727.
[260) D.W. SOBIESKI, M.P. BHAVARAJU (1985) "An economic assessment of battery storage in electric utility systems." IEEE PAS, Vol.104(12): 3453-3459.
[261) J.W. SPENCER (1982) "A Comparison of Methods for Estimating Hourly Diffuse Solar Radiation from Global Solar Radiation." Solar Energy, Vol. 29(1): 19-32.
[262) R. SPENCER (1984) "Array Field Optimization for Central Station Photovoltaic Power Plants". 19th IECEC: 2167-2170.
[263) W.O. ST AD LIN (1971) "Economic Allocation of Regulating Margin." IEEE PAS, Vol. 90(4):1776-1781.
[264) M.J. STEINBERG, T.H. SMITH (1934) "The Theory of Incremental Rates and their Practical Applications to a Load Division." Electrical Engineering, Vol. 53: 432-445, 571-584.
[265) L.H. STEMBER (1982) "Reliability, availability and maintenance-costs models for use in the design of photovoltaic systems." 16th PVSC Pp. 1036-1040.
[266) L.H. STEMBER, W.R. HUSS, M.S. BRIDGMAN (1982) "Reliability-Economic Analysis Models for Photovoltaic Power Systems: Vol. 1 ". SAND82-7126/1 Sandia National Labs; Nov. 1982.
[267) R. STEWART. D. SPENCER (1978) "The Analysis of Minute by Minute lnsolation Data and its Structural Implications". Proc. 1984 Annual Meeting of the American Section of /SES, Anaheim, CA.
[268) A.J. STRANIX, A.H. FIRESTER (1983) "Conceptual Design of a 50 MW Photovoltaic Power Plant." IEEE PAS, Vol. 102(9): 3218-3223.
[269) M. TAKAHASHI, et al. (1985) "Development of 1MW Photovoltaic Power System for Centralized Array Location." 18th PVSC: 1466-1471.
[270) Y. TAKEDA, K. TAKIGAWA, H. KAMINOSONO (1981) "Operating Characteristics of Photovoltaic Power System". 15th PVSC Pp. 1245-1250.
[271) S.N. TALUKDAR, F.F. WU (1981) "Computer-aided Dispatch for Electric Power Systems." Proceedings of the IEEE, Vol. 69(10).: 1212-1231.
[272] C.W. TAYLOR, R.L. CRESAP (1976) "Real-time Power System Simulation for Automatic Generation Control." IEEE PAS: 375-384.
[273) R.C. TEMPS, K.L. COULSON (1977) "Solar Radiation Incident Upon Slopes of Different Orientations". Solar Energy, Vol. 19(2): 179-184.
[274] M.G. THOMAS, G.J. JONES (1984) "Grid-connected PV systems." 17th PVSC Pp. 991-996
Bibliography 213
(275) M.G. THOMAS, et al. (1984) "The Effect of Photovoltaic Systems on Utility Operations." 17th PVSC: 1229-1233.
(276) K. TSUKAMOTO, K. TANAKA (1981) "Photovoltaic Power System Interconnected With Utility." American Power Conference, Vol. 48.
[277) T.C. UBOEGBULAM, J.A. DAVIES (1983) "Turbidity in Eastern Canada". Journal of Climate and Applied Meteorology, Vol. 22(8): 1384-1392.
[278) A. UNIONE, E. BURNS, A. HUSSEINY (1981) "Availability Modeling Methodology Applied to Solar Systems." Solar Energy, Vol. 26(1): 55-64.
[279) M.H. UNSWORTH, J.L MONTEITH (1972) "Aerosol and Solar Radiation in Britain". Quarterly Journal of the Royal Meteorological Society, Vol 98: 778-797.
[280) U.S. WEATHER BUREAU (1949) "Mean Precipitable Water in the United States." Technical Paper #10
[281) G.J. VACHTSEVANOS, K.C. KALAITZAKIS (1985) "Penetration of wind electric conversion systems into the utility grid." IEEE PAS, Vpl. 104(7): 1677-1683.
[282) L. VERGARA-DOMINGUEZ, et al. (1985) "Automatic Modeling and Simulation of Daily Global Solar Radiation Series." Solar Energy, Vol. 35(6): 483-489.
[283) G.L. VIVIAN NI, G.T. HEYDT (1981) "Stochastic Optimal Energy Dispatch." IEEE PAS, Vol. 100(7): 3221-3228.
[284) J.G. WAIGHT, A. BOSE, G.B. SHEBLE (1981) "Generation Dispatch With Reserve Margin Constraints Using Linear Programming. 11 IEEE PAS, Vol. 100(1): 252-258.
[285) J.G. WAIGHT, F. ALLAEYEH, A. BOSE (1981) "Scheduling of Generation and Reserve Margin Using Dynamic and Linear Programming." IEEE PAS, Vol. 100(5): 2226-2230.
[286) D.B. WALLACE (1985) "PV Power Conditioner Harmonics. 11 Solar Engineering: 237-243.
[287) X. WANG, H. DAI, R. J. THOMAS (1984) "Reliability modelling of large windfarms and associated electric utility interface systems. " IEEE PAS, Vol. 103(3): 509-575.
[288) C.J. WILMOTI (1982) "On the Climatic Optimization of the Tilt and Azimuth of Flat plate Solar Collectors." Solar Energy, Vol. 28(3): 205-216.
[289) A.J. WOOD, B.F. WOLLENBERG (1984) Power Generation, Operation & Control. John Wiley & Sons.
[290) P. WOOD (1984) "Central Station Advanced Power Conditioning Technology, Utility Interface and Performance." 19th IECEC: 2216-2219.
[291) W.G. WOOD (1982) "Spinning Reserve Constrained Static and Dynamic Economic Dispatch." IEEE PAS, Vol. 101(2): 381-388
(292) Z. A. YAMAYEE (1984) "Modelling intermittent generation in a Monte Carlo regional system analysis model" IEEE PAS, Vol. 103(1): 174-182.
[293) J. ZABORSZKY, A.K. SUBRAMANIAN, K.M. LU (1975) "Control Interfaces in Generation Allocation." Systems Engineering for Power: Status & Prospects, New Hampshire, Aug. 1975.
Bibliography 214
(294) J. ZAHAVI (1985) "Probabilistic Simulation Incorporating Single and Multiple Hydroelectric Units with Stochastic Energy Availabilities." EPES, Vol. 7(4): 229-232.
(295) H. ZWIBEL, et al. (1981) "A 20 KW photovoltaic flat-panel power system: An overview." 15th PVSC Pp. 1447-1452.
Bibliography 215
Appendix A
Solar Geometry
In order to calculate the solar irradiance reaching a horizontal surface on the earth, it is
necessary to write down the trigonometric relationships between the solar position in the sky
and the surface coordinates on earth. The position of the sun is expressed in terms of the
following solar angles as illustrated in Figure 47which is the same figure as Figure 4 on page
42 and is repeated here for convenience.
1. Solar elevation angle (Solar altitude): The angular distance of the sun above the horizon
at a specified time of the year and time of day from a particular location. This is angle f3
in the figure.
where B = declination
L = latitude
ro = hour angle
Solar Geometry
sin f3 = sin L sin B + cos L cos B cos ro (A.1)
216
L..r.e JI 5,gnt :o :ne sun-ocserver at 0
~-
Figure 47. Position of the sun relative to an Inclined plane
Solar Geometry
\ Hcrizontal ;>1ane c.:i
~arth s :urrace
217
2. Solar azimuth: The angular distance from due south to the sun's projection on the horizon,
measured from due south (northern hemisphere). This is angle <p in the figure. It is
measured east positive, west negative and south zero.
cos o sin ro sin<p =----cos p (A.2)
3. Surface azimuth: (angle required for tilted surfaces) Angular distance from due south to
the normal to a vertical surface. This is angle 'I' in the figure.
4. Solar declination: Angular distance of the sun north latitudes (positive) or south latitudes
(negative) of the equator at a specified time of the year.
(A.3)
where dn = julian date
5. Sun's hour angle: (apparent solar time) Angular distance in degrees of the sun from its
highest position at solar noon. Mornings are considered positive and evenings negative.
Apparent solar time = local standard time + longitude correction + equation of time
6. Zenith angle: Angle between the local zenith and the line joining the observer and the
sun. This is eH In the figure.
COS 0H =sin~ (A.5)
7. Sunrise and sunset angles: The hour angle at sunrise and sunset.
cos ros = - tan L tan o (A.6)
8. Incidence angle: The incidence angle i is defined as the angle between the normal to a
surface and a line collinear with the sun's rays.
Solar Geometry 218
• South-facing Horizontal and Vertical Surfaces (Fixed):
cos i = - sin o cos L + cos o sin L cos ro (A.6)
• South-facing Titled Surfaces
cos i = sin(L - r) sin o + cos(L - r) cos o cos ro (A.7)
where r = tilt angle
• Non-south-facing Titled Surfaces: If a tilted surface has a direction other than due
south, the following equation is used to calculate the incidence angle:
cos i = cos(q> - 'Vl cos P sin r + sin P cos r (A.8)
• Generalized Equation for Fixed Planar Surfaces
cos i = sin o( sin L cos r - cos L sin r cos 'Vl
+ cos o cos ro( cos L cos r + sin L sin r cos 'I')
+ cos o sin r sin 'I' sin ro (A.9)
9. Extraterrestrial lrradlance: The irradiance on a horizontal surface on top of the
atmosphere.
10 = lscE0( sin o sin L + cos o cos L cos ro1)
where /0 = extraterrestrial irradiance for 1 hour
centered around the hour ro;
lsc = solar constant = 1353 w/m2
E0 = eccentricity correction factor of the earth's orbit
Solar Geometry
(A.10)
219
= (rof r)2 = 1 + 0.033 cos[(27td,,f365)] (A.11)
r0 = mean earth-sun distance.
Solar Geometry 220
Appendix B
Selected Input-Output for Dispatch Model
Selected Input-Output for Dispatch Model 221
1 101 1. 24. 13. 1.1 1. 20. 102 1. 1. 1. 1. 1. 1. 1. 103 3915. 3915. 3915. 3915. 3915. 3915. 3915. 104 1. 10. 5. 107 1. 109 50.
2 2 1 TUNIT1 1 1 1 760. 250. 2 2 TUNIT2 1 1 1 760. 174. 2 3 TUNIT3 1 1 1 420. 125. 2 4 TUNIT4 1 2 1 190. 50. 2 5 TUNIT5 1 2 1 190. 50. 2 6 TUNIT6 1 3 1 270. 65. 2 7 TUNIT7 1 4 1 210. 70. 2 8 TUNIT8 1 4 1 210. 70. 2 9 TUNIT9 1 5 1 115. 35. 2 10 TUNIT10 1 5 1 450. 136. 2 11 TUNIT11 1 5 1 450. 136. 2 12 TUNIT12 1 5 1 110. 35. 2 13 TUNIT13 1 5 1 110. 35. 2 14 TUNIT14 1 5 1 90. 25. 2 15 TUNIT15 1 6 1 55. 25. 2 16 TUNIT16 1 6 1 55. 25. 2 17 TUNIT17 1 6 1 85. 33. 2 18 TUNIT18 1 6 1 55. 25. 2 19 TUNIT19 1 6 1 55. 25. 2 20 TUNIT20 1 3 1 90. 35. 2 21 TUNIT21 1 3 1 90. 35. 2 22 TUNIT22 1 7 1 76. 25. 2 23 TUNIT23 1 8 1 80. 25. 2 24 TUNIT24 1 6 1 85. 33. 2 25 CUNIT1 2 9 1 3 18. 12. 2 26 CUNIT2 2 2 2 2 18. 12. 2 27 CUNIT3 2 1 3 3 18. 12. 2 28 CUNIT4 2 10 4 2 44. 16. 2 29 CUNIT5 2 10 5 2 44. 16. 2 30 CUNIT6 2 10 6 2 64. 46. 2 31 CUNIT7 2 10 7 2 64. 46. 2 32 CUNIT8 2 10 8 2 64. 46. 2 33 CUNIT9 2 10 9 2 64. 46. 2 34 CUNIT10 2 7 10 3 17. 11. 2 35 CUNIT11 2 7 11 3 17. 11. 2 36 CUNIT12 2 7 12 3 17. 11. 2 37 CUNIT13 2 7 13 3 17. 11. 2 38 CUNIT14 2 6 14 2 42. 28. 2 39 CUNIT15 2 3 15 3 18. 12. 2 40 CUNIT16 2 3 16 3 32. 21. 2 41 CUNIT17 2 5 17 2 33. 22.
Figure 48. Generator Input data (Generating unit Identification)
Selected Input-Output for Dispatch Model 222
3 3 1 680.941472 7.189709 0.00185289 24. 24. 3 2 702.962766 7.681645 0.00137080 24. 24. 3 3 401.805713 7.245143 0.00425294 24. 24. 3 4 118.276158 8.117995 0.00448263 8. 8. 3 5 120.276158 8.117995 0.00448263 8. 8. 3 6 162.333586 7.643047 0.00326549 24. 24. 3 7 269.422099 6.091183 0.00938761 24. 24. 3 8 248.665264 6.544131 0.01010862 24. 24. 3 9 156.272943 6.122496 0.02577877 8. 8. 3 10 391.128891 7.463225 0.00306321 24. 24. 3 11 396.128891 7.463225 0.00306321 24. 24. 3 12 117.296959 7.903477 0.01579254 8. 8. 3 13 117.296959 7.903477 0.01579254 8. 8. 3 14 49.930167 13.002987 0.00435611 8. 8. 3 15 32.600426 10.016945 0.01324790 8. 8. 3 16 32.600426 10.016945 0.01324790 8. 8. 3 17 85.080842 7.489352 0.01736940 8. 8. 3 18 32.600426 10.016945 0.01324790 8. 8. 3 19 32.600426 10.016945 0.01324790 8. 8. 3 20 118.552580 7.590891 0.02703001 8. 8. 3 21 103.900210 7.517778 0.02761267 8. 8. 3 22 52.503344 12.188683 0.01718860 8. 8. 3 23 47.585357 8.994592 0.01746156 8. 8. 3 24 85.080842 7.489352 0.01736940 8. 8. 3 25 87.876 9.217 3 26 87.468 9.245 3 27 87.036 9.259 3 28 236.716 8.631 3 29 236.716 8.631 3 30 236.716 8.631 3 31 236.716 8.631 3 32 236.716 8.631 3 33 236.716 8.631 3 34 71.181 10.862 3 35 71.181 10.862 3 36 71.181 10.862 3 37 71.181 10.862 3 38 291.83 9.745 3 39 87.876 9.217 3 40 135.828 9.943 3 41 262.112 9.363
Figure 49. Generator input data (Generating unit performance characteristics)
Selected Input-Output for Dispatch Model 223
4 4 1 2.11 4000. 24. 4 2 2.11 4000. 24. 4 3 2.11 2000. 12. 4 4 2.11 450. 10. 4 5 2.11 450. 10. 4 6 2.11 750. 10. 4 7 2.11 530. 10. 4 8 2.11 430. 10. 4 9 2.11 2800. 10. 4 10 2.11 3600. 24. 4 11 2.11 3600. 24. 4 12 2.11 2250. 10. 4 13 2.11 2250. 10. 4 14 2.11 300. 10. 4 15 2.11 100. 10. 4 16 2.11 100. 10. 4 17 2.11 300. 10. 4 18 2.11 100. 10. 4 19 2.11 100. 10. 4 20 2.11 460. 10. 4 21 2.11 300. 10. 4 22 2.11 300. 10. 4 23 2.11 300. 10. 4 24 2.11 300. 10. 4 25 5.90 100. 4 26 5.53 100. 4 27 5.90 100. 4 28 5.53 100. 4 29 5.53 100. 4 30 5.53 100. 4 31 5.53 100. 4 32 5.53 100. 4 33 5.53 100. 4 34 5.90 100. 4 35 5.90 100. 4 36 5.90 100. 4 37 5.90 100. 4 38 5.53 100. 4 39 5.90 100. 4 40 5.90 100. 4 41 5.53 100. 7 7 1 1 30 -1 8 8 1 0.507 0.471 0.454 0.454 0.477 0.584 0.810 1.000 0.985 0.953 0.927 0.887 0.832 0.828 0.791 0.775 0.800 0.846 0.917 0.936 0.908 0.839 0.747 0.645
12 VA. TECH SAMPLE SYSTEM (FROM EPRI REGIONAL SYSTEM S.E. AND CP&L DATA).
Figure 50. Generator Input data (Generating unit cost data and hourly load)
Selected Input-Output for Dispatch Model 224
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Figure 51. Unit commitment output used as input to the model (Generator unit schedule)
Selected Input-Output for Dispatch Model 225
0.00 0.00 0.00 0.00 0.00 0.00 0.00 18.00 18.00 18.00 18.00 18.00 0.00 0.00 0.00 0.00 0.00 0.00
18.00 18.00 18.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 18.00 18.00 18.00 18.00 18.00 0.00 0.00 0.00 0.00 0.00 0.00
18.00 18.00 18.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 18.00 18.00 18.00 18.00 18.00 0.00 0.00 0.00 0.00 0.00 0.00
18.00 18.00 18.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 44.00 44.00 44.00 44.00 44.00 0.00 0.00 0.00 0.00 0.00 0.00
44.00 44.00 44.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 44.00 44.00 44.00 44.00 44.00 0.00 0.00 0.00 0.00 0.00 0.00
44.00 44.00 44.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 64.00 64.00 64.00 64.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
64.00 64.00 64.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 64.00 64.00 64.00 64.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
64.00 64.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 64.00 64.00 64.00 64.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 64.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 64.00 64.00 64.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 17.00 17.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 17.00 17.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 17.00 17.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 17.00 17.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Figure 52. Unit commitment output used as Input to the model (Partial CT generation data)
Selected Input-Output for Dispatch Model 226
UP DOWN
TUNIT1 .03 .03 TUNIT2 .03 .03 TUNIT3 .05 .05 TUNIT4 .07 .07 TUNIT5 .07 .07 TUNIT6 .05 .05 TUNIT7 .05 .05 TUNIT8 .05 .05 TUNIT9 .07 .07
TUNIT10 .03 .03 TUNIT11 .03 .03 TUNIT12 .07 .07 TUNIT13 .07 .07 TUNIT14 .10 .10 TUNIT15 .10 .10 TUNIT16 .10 .10 TUNIT17 .10 .10 TUNIT18 .10 .10 TUNIT19 .10 .10 TUNIT20 .10 .10 TUNIT21 .10 .10 TUNIT22 .10 .10 TUNIT23 .10 .10 TUNIT24 .10 .10 CUNIT1 1.0 1.0 CUNIT2 1.0 1.0 CUNIT3 1.0 1.0 CUNIT4 1.0 1.0 CUNIT5 1.0 1.0 CUNIT6 1.0 1.0 CUNIT7 1.0 1.0 CUNIT8 1.0 1.0 CUNIT9 1.0 1.0
CUNIT10 1.0 1.0 CUNIT11 1.0 1.0 CUNIT12 1.0 1.0 CUNIT13 1.0 1.0 CUNIT14 1.0 1.0 CUNIT15 1.0 1.0 CUNIT16 1.0 1.0 CUNIT17 1.0 1.0
Figure 53. Generator response rates
Selected Input-Output for Dispatch Model 227
HRINT UNIT# GEN CHANGE MORE REQD. STATUS
7 2 2 0.59809E + 02 0.50698E+01 ramp-up limit 7 2 10 0.27933E + 02 0.22856E + 00 ramp-up limit 7 2 11 0.27933E +02 0.22856E + 00 ramp-up limit 7 3 2 0.63461E +02 0.37961E +01 ramp-up limit 7 5 10 0.40542E +02 0.54078E + 01 ramp-up limit 7 5 11 0.40542E + 02 0.54078E +01 ramp-up limit 7 5 23 0.75663E +01 0.6631 SE-01 ramp-up limit 8 1 3 -. 73862E + 02 -.19441E+02 ramp-down limit 8 1 8 -.31076E +02 -.29781E +01 ramp-down limit 8 1 10 -.84423E + 02 -.43923E +02 ramp-down limit 8 1 11 -.84423E +02 -.43923E +02 ramp-down limit 8 1 12 -.19891E +02 -.37502E + 01 ramp-down limit 8 1 13 · -.19891E +02 -.37502E+01 ramp-down limit 8 1 23 -.13272E + 02 -.17904E + 01 ramp-down limit 8 1 2 -.80593E +02 -.12193E+02 ramp-down limit 8 2 2 0.68400E +02 0.61562E+01 ramp-up limit 8 2 4 0.34790E +02 0.21956E +01 ramp-up limit 8 2 5 0.34790E +02 0.21956E +01 ramp-up limit 9 1 2 -.69601E +02 -.12014E +01 ramp-down limit 9 1 3 -.50089E + 02 -.14989E + 01 ramp-down limit 9 1 10 -.69543E + 02 -.32270E + 02 ramp-down limit 9 1 11 -.69543E + 02 -.32270E +02 ramp-down limit 9 1 4 -.42900E + 02 -.29996E + 01 ramp-down limit 9 1 5 -.42900E + 02 -.29996E + 01 ramp-down limit 9 1 8 -.27883E + 02 -.22383E +01 ramp-down limit 9 1 12 -.17847E + 02 -.39048E +01 ramp-down limit 9 1 13 -.17847E+02 -.39048E + 01 ramp-down limit 9 1 7 -.33984E + 02 -.27511E +01 ramp-down limit 9 2 10 -.48620E +02 -.14701E+02 ramp-down limit 9 2 11 -.48620E +02 -.14701E +02 ramp-down limit
11 4 2 0.15745E +03 0.10322E + 03 ramp-up limit 11 4 3 0.55359E + 02 0.18529E + 02 ramp-up limit 11 4 4 0.52522E +02 0.24048E + 02 ramp-up limit 11 4 5 0.52522E + 02 0.24048E +02 ramp-up limit 11 4 8 0.23291E +02 0.25946E +01 ramp-up limit 11 4 10 0. 76860E + 02 0.49383E + 02 ramp-up limit 11 4 11 0. 76860E + 02 0.49383E + 02 ramp-up limit 11 4 12 0.14908E + 02 0.53997E +01 ramp-up limit 11 4 13 0.14908E+02 0.53997E + 01 ramp-up limit 11 4 7 0.37303E + 02 0.11399E +02 ramp-up limit 11 4 9 0.39247E +02 0.26168E + 02 ramp-up limit 11 4 15 0.25580E +02 0.18080E + 02 ramp-up limit 11 4 16 0.25580E + 02 0.18080E + 02 ramp-up limit 11 4 17 0.31911E +02 0.15984E+02 ramp-up limit 11 4 18 0.25580E +02 0.18080E + 02 ramp-up limit 11 4 19 0.25580E +02 0.18080E + 02 ramp-up limit 11 4 20 0.34667E +02 0.24167E +02 ramp-up limit 11 4 21 0.34521E +02 0.24021E +02 ramp-up limit 11 4 23 0.42649E + 02 0.35149E +02 ramp-up limit
Figure 54. Partial thermal generator output during simulation
Selected Input-Output for Dispatch Model 228
VA. TECH SAMPLE SYSTEM (FROM EPRI REGIONAL SYSTEM S.E.)
ECONOMIC DISPATCH AND PRODUCTION COST SUMMARY
11:00 AM 11:10AM 11:20 AM 11:30 AM 11:40 AM
LOAD DEMAND (MW) 3584.00 3550.00 3545.00 3482.00 3456.00 TRANSMISSION LOSSES (MW) 179.20 177.50 177.25 174.10 172.80 DISPATCHABLE GEN (MW) 3167.99 2947.43 2947.43 3322.10 3294.76 COMBUST. TURB. GEN (MW) 558.00 142.00 142.00 334.00 334.00 PV POWER GENERATION (MW) 37.21 638.46 633.93 0.00 0.00 PUMPED STORAGE GEN (MW) 0.00 0.00 0.00 0.00 0.00 HYDRO GENERATION (MW) 0.00 0.00 0.00 0.00 0.00 INTERCHANGE (MW) 0.00 0.00 0.00 0.00 0.00 SPINNING RESERVES (MW) 434.01 1073.77 854.43 287.77 658.77 TEN MINUTE RESERVES (MW) 1318.00 2502.00 2502.00 2502.00 2502.00 SYSTEM LAMBDA ($/MWH 20.27 19.92 19.92 22.73 20.47 FUEL COSTS ($/H) 18124.20 12127.99 12127.99 15582.55 15478.89 CUMULAT. PROD.COST ($) 729933.62 742061.56 754189.50 769772.00 785250.87
11:50AM 12:00 PM 12:10 PM 12:20 PM 12:30 PM
LOAD DEMAND (MW) 3414.00 3394.00 3347.00 3280.00 3252.00 TRANSMISSION LOSSES (MW) 170.70 169.70 167.35 164.00 162.60 DISPATCHABLE GEN (MW) 3250.69 3229.69 3309.70 2880.49 2731.24 COMBUST. TURB. GEN (MW) 334.00 334.00 0.00 0.00 0.00 PV POWER GEN (MW) 0.00 0.00 205.66 564.77 681.96 PUMPED STORAGE GEN (MW) 0.00 0.00 0.00 0.00 0.00 HYDRO GENERATION (MW) 0.00 0.00 0.00 0.00 0.00 INTERCHANGE (MW) 0.00 0.00 0.00 0.00 0.00 SPINNING RESERVES (MW) 652.98 648.09 889.74 1365.96 1167.59 TEN MINUTE RESERVES (MW) 2502.00 2502.00 3546.00 3546.00 3546.00 SYSTEM LAMBDA ($/MWH) 20.40 20.37 20.50 19.04 19.46 FUEL COSTS ($/H) 15328.77 15257.42 11478.66 10043.20 9548.11 CUMULAT.PROD.COST ($) 800579.62 815837.00 827315.62 837358.81 846906.87
Figure 55. Sample of model output at each Interval
Selected Input-Output for Dispatch Model 229
Characteristics of the two selected sites.
Site Latitude Altitude Location Climate Longitude
RALEIGH 35.46 °N 134 m South-east Moderate 78.38 °W U.S
RICHMOND 37.75 °N 50 m South-east Moderate 77.33 °W U.S
Characteristics of the two PV Arrays.
Site Size Array Azimuth Operated of Orientation by
PV Array
RALEIGH 4KW Fixed Monthly South CP & L Tilt
RICHMOND 25KW 2-axis Tracking N/A VA POWER
Figure 56. Sample of model output at each interval
Selected Input-Output for Dispatch Model 230
= = = > Enter dispatch interval
10
Appendix C
Sample Run
= = = > Input status of PV plant. 0 - None; 1 - Present; Default: 0
1
= = = > Enter multiplication factor for PV plant
30.0000000
Sample Run
More non-thermal generation required
Hour: 11 Minute: 40. Amount 109.19 MW
231
= = = > Switch to manual (Y/N)
y
= = = > Choose a number from the following choices
1. Display status of the entire system
2. Increase PV generation input
3. Increase hydro generation
4. Increase pumped storage plant output
5. Increase CT generation
6. Start-up unscheduled hydro unit
7. Start-up unscheduled PSH unit
8. Start-up unscheduled CT unit
9. Buy more unscheduled interconnected power
1
SYSTEM STATUS
TOTAL LOAD: 3632.00 MW. LOSSES: 181.60 MW.
VA. TECH SAMPLE SYSTEM (FROM EPRI REGIONAL SYSTEM S.E. ).
Sample Run 232
Thermal Generation summary for 10:40 A.M.
NAME STATUS POWER
1 ROXBOR03 UNIT DOWN 0.00
2 ROXBOR04 ART MAXIMUM 656.78
3 ROXBOR01 ART MAXIMUM 282.36
4 ROBNSON1 ART MAXIMUM 164.06
5 ROBNSON2 ART MAXIMUM 164.06
6 LEEUNIT3 ART MAXIMUM 270.00
7 ASHEVLE1 MAXIMUM GEN 210.00
= = = > Review more screens (Y /N)
y
VA. TECH SAMPLE SYSTEM (FROM EPRI REGIONAL SYSTEM S.E. ).
Thermal Generation summary for 10:40 A.M.
NAME STATUS POWER
8 ASHEVLE2 ART MAXIMUM 158.67
9 SUTTON 2 DIS PATCHABLE 101.53
10 SUTTON 3 ART MAXIMUM 332.77
11 SUTTON 4 ART MAXIMUM 332.77
12 SUTTON1B ART MAXIMUM 54.79
13 SUTTON 1 ART MAXIMUM 54.79
14 SUTTON1A MINIMUM GEN 25.00
15 WTHSPN 1 DIS PATCHABLE 50.58
16 WTHSPN 2 DIS PATCHABLE 50.58
17 WTHSPN 3 MAXIMUM GEN 85.00
18 WTHSPN 4 DIS PATCHABLE 50.58
19 WTHSPN 5 DIS PATCHABLE 50.58
Sample Run 233
20 LEE UNT2 DISPATCHABLE 69.67
21 LEE UNT1 DISPATCHABLE 69.52
22 BLEWETT1 MINIMUM GEN 25.00
23 CFHREC DISPATCHABLE 67.65
= = = > Review more screens (Y /N)
y
VA. TECH SAMPLE SYSTEM (FROM EPRI REGIONAL SYSTEM S.E. ).
Thermal Generation summary for 10:40 A.M.
NAME STATUS POWER
24 WTHSPN 7 MAXIMUM GEN 85.00
Total Thermal Generation: 3411.74 MW
= = = > Review more screens (Y/N)
y
VA. TECH SAMPLE SYSTEM (FROM EPRI REGIONAL SYSTEM S.E. ).
Non-dispatchable Generation Summary for 10:40 A.M.
NAME STATUS POWER
25 MOREHD1A MAXIMUM GEN 18.00
26 ROBNSN1A MAXIMUM GEN 18.00
27 ROXBR01A MAXIMUM GEN 18.00
28 DRLNGTN1 MAXIMUM GEN 44.00
29 DRLNGTN2 MAXIMUM GEN 44.00
30 DRLNGTN3 MAXIMUM GEN 64.00
31 DRLNGTN4 MAXIMUM GEN 64.00
Sample Run 234
32 DRLNGTNS MAXIMUM GEN 64.00
33 DRLNGTN6 UNIT DOWN 0.00
34 BLEWET1A UNIT DOWN 0.00
35 BLEWET2A UNIT DOWN 0.00
36 BLEWET3A UNIT DOWN 0.00
37 BLEWET4A UNIT DOWN 0.00
38 WTSPNIC1 UNIT DOWN 0.00
39 LEE IC1 UNIT DOWN 0.00
40 LEE IC2 UNIT DOWN 0.00
= = = > Review more screens (Y/N)
y
VA. TECH SAMPLE SYSTEM (FROM EPRI REGIONAL SYSTEM S.E. ).
Non-dispatchable Generation Summary for 10:40 A.M.
NAME
41 SUTONIC2
STATUS
UNIT DOWN
POWER
0.00
Non-dispatchable Generation at this point: 334.00 MW
Photovoltaic Plant Generation: 67.85 MW
Total Non-dispatchable Generation: 401.85 MW
= = = > Review more screens (Y/N)
y
System Summary
Sample Run 235
System Load:
System Losses:
Thermal Generation Capacity:
Total Thermal Generation:
Total Non-dispatchable Gen:
Total Combustion Turbine Gen:
Total Hydro Gen:
Total Pumped Hydro Gen:
Total lntertie:
Total Photovoltaic Gen:
Last System Lambda:
Spinning Reserve:
Choose a number from the following choices
1. Display status of the entire system
2. Increase PV generation input
3. Increase hydro generation
4. Increase pumped storage plant output
5. Increase CT generation
6. Start-up unscheduled hydro unit
7. Start-up unscheduled PSH unit
8. Start-up unscheduled CT unit
9. Buy more unscheduled interconnected power
2
3632.00 MW
181.60 MW
3612.06 MW
3411.74 MW
401.85 MW
334.00 MW
0.00 MW
0.00 MW
0.00 MW
67.85 MW
0.25 $/MWh
257.00 MW
PV plant generating 67.85 MW. Increment desired 109.19 MW
Sample Run 236
•••••• Change in PV generation not possible. ••••••
•••••• Plant is down or running at full capacity ••••••
Choose a number from the following choices
1. Display status of the entire system
2. Increase PV generation input
3. Increase hydro generation
4. Increase pumped storage plant output
5. Increase CT generation
6. Start-up unscheduled hydro unit
7. Start-up unscheduled PSH unit
8. Start-up unscheduled CT unit
9. Buy more unscheduled interconnected power
4
••• No PSH plant present in the system •••
••• Try another choice ...
Choose a number from the following choices
1. Display status of the entire system
2. Increase PV generation input
Sample Run 237
3. Increase hydro generation
4. Increase pumped storage plant output
5. Increase CT generation
6. Start-up unscheduled hydro unit
7. Start-up unscheduled PSH unit
8. Start-up unscheduled CT unit
9. Buy more unscheduled interconnected power
5
•••••• Change in CT generation not possible. ••••••
•••••• Units are down or running at full capacity ••••••
Choose a number from the following choices
1. Display status of the entire system
2. Increase PV generation input
3. Increase hydro generation
4. Increase pumped storage plant output
5. Increase CT generation
6. Start-up unscheduled hydro unit
7. Start-up unscheduled PSH unit
8. Start-up unscheduled CT unit
9. Buy more unscheduled interconnected power
8
Sample Run 238
••• CT unit DRLNGTN6 Rescheduled •••
••• CT unit BLEWET1A Rescheduled •••
•••CT unit BLEWET2A Rescheduled •••
••• CT unit BLEWET3A Rescheduled •••
More non-thermal generation required
Hour: 11 Minute: 40. Amount 95.19 MW
Switch to manual (Y /N)
y
Choose a number from the following choices
1. Display status of the entire system
2. Increase PV generation input
3. Increase hydro generation
4. Increase pumped storage plant output
5. Increase CT generation
Sample Run 239
6. Start-up unscheduled hydro unit
7. Start-up unscheduled PSH unit
8. Start-up unscheduled CT unit
9. Buy more unscheduled interconnected power
1
SYSTEM ST A TUS
TOTAL LOAD: 3632.00 MW. LOSSES: 181.60 MW.
VA. TECH SAMPLE SYSTEM (FROM EPRI REGIONAL SYSTEM S.E. ).
Thermal Generation summary for 10:40 A.M.
NAME STATUS POWER
1 ROXBOR03 UNIT DOWN 0.00
2 ROXBOR04 ART MAXIMUM 656.78
3 ROXBOR01 ART MAXIMUM 282.36
4 ROBNSON1 ART MAXIMUM 164.06
5 ROBNSON2 ART MAXIMUM 164.06
6 LEEUNIT3 ART MAXIMUM 270.00
7 ASHEVLE1 ART MAXIMUM 198.60
= = = > Review more screens (Y /N)
y
Sample Run 240
VA. TECH SAMPLE SYSTEM {FROM EPRI REGIONAL SYSTEM S.E. ).
Thermal Generation summary for 10:40 A.M.
NAME STATUS POWER
8 ASHEVLE2 ART MAXIMUM 158.67
9 SUTTON 2 ART MAXIMUM 75.36
10 SUTTON 3 ART MAXIMUM 332.77
11 SUTTON 4 ART MAXIMUM 332.77
12 SUTTON1B ART MAXIMUM 54.79
13 SUTTON 1 ART MAXIMUM 54.79
14 SUTTON1A MAXIMUM GEN 90.00
15 WTHSPN 1 ART MAXIMUM 32.50
16 WTHSPN 2 ART MAXIMUM 32.50
17 WTHSPN 3 ART MAXIMUM 69.02
18 WTHSPN 4 ART MAXIMUM 32.50
19 WTHSPN 5 ART MAXIMUM 32.50
20 LEE UNT2 ART MAXIMUM 45.50
21 LEE UNT1 ART MAXIMUM 45.50
22 BLEWETT1 DIS PATCHABLE 70.99
23 CFHREC ART MAXIMUM 32.50
= = = > Review more screens (Y/N)
y
VA. TECH SAMPLE SYSTEM (FROM EPRI REGIONAL SYSTEM S.E. ).
Thermal Generation summary for 10:40 A.M.
NAME STATUS POWER
24 WTHSPN 7 ART MAXIMUM 69.02
Sample Run 241
Total Thermal Generation: 3297.54 MW
= = = > Review more screens (Y/N)
y
VA. TECH SAMPLE SYSTEM (FROM EPRI REGIONAL SYSTEM S.E. ).
Non-dispatchable Generation Summary for 10:40 A.M.
NAME STATUS POWER
25 MOREHD1A MAXIMUM GEN 18.00
26 ROBNSN1A MAXIMUM GEN 18.00
27 ROXBR01A MAXIMUM GEN 18.00
28 DRLNGTN1 MAXIMUM GEN 44.00
29 DRLNGTN2 MAXIMUM GEN 44.00
30 DRLNGTN3 MAXIMUM GEN 64.00
31 DRLNGTN4 MAXIMUM GEN 64.00
32 DRLNGTN5 MAXIMUM GEN 64.00
33 DRLNGTN6 MAXIMUM GEN 64.00
34 BLEWET1A MAXIMUM GEN 17.00
35 BLEWET2A MAXIMUM GEN 17.00
36 BLEWET3A MAXIMUM GEN 17.00
37 BLEWET4A UNIT DOWN 0.00
38 WTSPNIC1 UNIT DOWN 0.00
39 LEE IC1 UNIT DOWN 0.00
40 LEE IC2 UNIT DOWN 0.00
= = = > Review more screens (Y/N)
y
VA. TECH SAMPLE SYSTEM (FROM EPRI REGIONAL SYSTEM S.E. ).
Sample Run 242
Non-dispatchable Generation Summary for 10:40 A.M.
NAME
41 SUTONIC2
STATUS
UNIT DOWN
POWER
0.00
Non-dispatchable Generation at this point: 449.00 MW
Photovoltaic Plant Generation: 67.85 MW
Total Non-dispatchable Generation: 626.05 MW
= = = > Review more screens (Y /N)
y
System Summary
System Load:
System Losses:
Thermal Generation Capacity:
Total Thermal Generation:
Total Non-dispatchable Gen:
Total Combustion Turbine Gen:
Total Hydro Gen:
Total Pumped Hydro Gen:
Total lntertie:
Total Photovoltaic Gen:
Last System Lambda:
Spinning Reserve:
Sample Run
3632.00 MW
181.60 MW
3302.55 MW
3297.54 MW
626.05 MW
449.00 MW
0.00 MW
0.00 MW
0.00 MW
67.85 MW
0.25 $/MWh
257.00 MW
243
Choose a number from the following choices
1. Display status of the entire system
2. Increase PV generation input
3. Increase hydro generation
4. Increase pumped storage plant output
5. Increase CT generation
6. Start-up unscheduled hydro unit
7. Start-up unscheduled PSH unit
8. Start-up unscheduled CT unit
9. Buy more unscheduled interconnected power
0
Invalid Choice 0
Choose a number from the following choices
1. Display status of the entire system
2. Increase PV generation input
3. Increase hydro generation
4. Increase pumped storage plant output
5. Increase CT generation
6. Start-up unscheduled hydro unit
7. Start-up unscheduled PSH unit
Sample Run 244
8. Start-up unscheduled CT unit
9. Buy more unscheduled interconnected power
8
... CT unit BLEWET4A Rescheduled •••
••• CT unit WTSPNIC1 Rescheduled •••
••• CT unit LEE IC1 Rescheduled •••
••• CT unit LEE IC2 Rescheduled •••
More non-thermal generation required
Hour: 12 Minute: 30. Amount 60.24 MW
Switch to manual (Y/N)
N
PV plant generating 0.00 MW. Increment desired 60.24 MW
...... Change in PV generation not possible ...... .
•••••• Plant is down or running at full capacity ••••••
Sample Run 245
••• No hydro present in the system •••
••• Try another choice •••
••• No PSH plant present in the system •••
••• Try another choice •••
•••••• Change in CT generation not possible. ••••••
•••••• Units are down or running at full capacity ••••••
••• No hydro present in the system •••
••• for rescheduling •••
••• No PSH plant present in the system •••
••• for rescheduling •••
••• CT unit DRLNGTN3 Rescheduled •••
Sample Run
More non-thermal generation required
Hour: 12 Minute: 30. Amount 97.24 MW
246
Switch to manual (Y/N)
N
PY plant generating 0.00 MW. Increment desired 97.24 MW
•••••• Change in PY generation not possible. ••••••
•••••• Plant is down or running at full capacity ••••••
••• No hydro present in the system •••
••• Try another choice •••
••• No PSH plant present in the system •••
••• Try another choice •••
•••••• Change in CT generation not possible. ••••••
•••••• Units are down or running at full capacity ••••••
••• No hydro present in the system •••
••• for rescheduling •••
Sample Run 247
••• No PSH plant present in the system •••
••• for rescheduling •••
••• CT unit DRLNGTN4 Rescheduled •••
••• CT unit DRLNGTNS Rescheduled •••
Excessive non-thermal generation present
Hour: 13 Minute: 20. Amount 110.74 MW
Switch to manual (Y/N)
N
•••••• Change in CT generation not possible. ••••••
•••••• Units are down or running at minimum capacity ••••••
••• No PSH plant present in the system •••
••• Try another choice •••
Sample Run 248
*** No hydro present in the system ***
*** Try another choice ***
****** Change in CT schedule not possible. ******
****** Reason: Violation of up-time constraints ******
*** No PSH plant present in the system ***
*** for rescheduling ***
... No hydro present in the system ***
*** for rescheduling ***
*** No tie lines present in the system ***
*** for rescheduling ***
PV plant generating 675.51 MW. Reduction desired 110.74 MW
*** Generation in PV plant decreased ***
Sample Run
More non-thermal generation required
Hour: 17 Minute: 10. Amount 140.67 MW
249
Switch to manual (Y/N)
N
PV plant generating 0.00 MW. Increment desired 140.67 MW
...... Change in PV generation not possible. ••••••
•••••• Plant is down or running at full capacity ••••••
••• No hydro present in the system •••
••• Try another choice •••
••• No PSH plant present in the system •••
••• Try another choice •••
•••••• Change in CT generation not possible. ••••••
•••••• Units are down or running at full capacity ••••••
••• No hydro present in the system •••
••• for rescheduling •••
Sample Run 250
••• No PSH plant present in the system •••
*** for rescheduling *"*
••• CT unit MOREHD1A Rescheduled •••
**" CT unit ROBNSN1A Rescheduled •••
**" CT unit ROXBR01A Rescheduled *"*
*"* CT unit DRLNGTN1 Rescheduled *"*
*"* CT unit DRLNGTN2 Rescheduled •••
More non-thermal generation required
Hour: 17 Minute: 10. Amount 99.67 MW
Switch to manual (Y/N)
N
PV plant generating 0.00 MW. Increment desired 99.67 MW
...... Change In PV generation not possible. ••••••
•••••• Plant is down or running at full capacity ***"**
Sample Run 251
••• No hydro present in the system •••
••• Try another choice •••
••• No PSH plant present in the system •••
••• Try another choice •••
•••••• Change in CT generation not possible. ••••••
•••••• Units are down or running at full capacity ••••••
••• No hydro present in the system •••
••• for rescheduling •••
••• No PSH plant present in the system •••
••• for rescheduling •••
••• CT unit DRLNGTN3 Rescheduled •••
••• CT unit DRLNGTN4 Rescheduled •••
More non-thermal generation required
Sample Run 252
Hour: 18 Minute: 20. Amount 20.36 MW
Switch to manual (YIN)
N
PV plant generating 0.00 MW. Increment desired 20.36 MW
...... Change in PV generation not possible ...... .
•••••• Plant is down or running at full capacity ••••••
••• No hydro present in the system •••
... Try another choice •••
*** No PSH plant present in the system ***
••• Try another choice •••
•••••• Change in CT generation not possible. ••••••
•••••• Units are down or running at full capacity ******
*** No hydro present in the system ***
••• for rescheduling •••
Sample Run 253
... No PSH plant present in the system •••
... for rescheduling •••
••• CT unit MOREHD1A Rescheduled ...
••• CT unit ROBNSN1A Rescheduled ...
Sample Run 254
The vita has been removed from the scanned document
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