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IEEE Transactions on Power Systems, Vol. 3, No. 4, November 1988
An Expert System for Voltage and Reactive Power Control of a Power System S.J. Cheng O.P. Mal& G.S. Hope
Department of Electrical Engineering The University of Calgary
Calgary Alberta Canada T2N lN4
Keywords: Expert System; Voltage Control; VAr Control; Power System Control
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Abstract A methodology, called the sensitivity tree, which CM be easily
used to form an expert system for real-time control is proposed in this paper. Based on this methodology, an expert system for control of voltage and reactive power of a power system is developed. The main objective of this expert system is to help the operator detect buses experiencing abnormal conditions, select the most effective control measures and calculate the control actions required to over- come the voltage violation. The control measures qsed to alleviale the voltage problem are capacitor compensation, transformer tap and generator terminal voltage changes. By keeping the bus voltage in the entire system within limits, system security is increased. The expert system is written in PROLOG language. Simulation studies with this expert system applied to a 30 bus power system show satisfactory results.
1. INTRODUCTION
Conventional computer programs can have huge data base, but because of the limitations of sequential programming and the primi- tive structure of these data base, no real "reasoning" can be carried out. Artificial intelligence techniques on the other hand, incorporate a general set of 'rules' to represent a 'dynamic' programming solution.
Expert systems, as one kind of artificial intelligence, have attracted large interest in recent years. Early applications of expert systems were in medical diagnosis and therapy [l], and computer system configuration and troubleshooting [2]. Other applications include electrical circuit analysis and synthesis, and computer-aided control system design [3]. However, application of expert systems to power systems is a new area. Some attempts made in this area include: solving the problem of fast power system voltage con- tingency analysis 141, automatic control of a power system in the restorative state [5], assisting decision-making of reactive powedvoltage control 161, and intelligent load flow engine [7]. Application of the expert systems to power systems is still in the early stage, and much research is needed to bring this new technique into practical use. The research reported in this paper is a step towards that end.
The strength of an expert system can be exploited fully when it is used in conjunction with a data base, Changes in the system operating conditions are reflected in the data base. The expert sys- tem, that draws its data from the data base, thus automatically trach the system operating conditions. In this paper a methodology for use in the expert system only is proposed. The aspect of data base management is not discussed.
The proposed methodology based on the sensitivity tree is found to be very effective in the development of an expert system to
88 WM 153-9 by the IEEE Power System Engineering Commtttee of the IEEE Power Engineering Society for presentation at the IEEE/PES 1988 Winter Meeting, New York, New York, January 31 - February 5, 1988. Manuscript submitted June 10, 1987; made available €or printing January 7, 1988.
A paper recommended and approved
deal with a large, complex, interconnected system, especially when the system onl linearity is not large. An expert system used con- trol the voltage and reactive power based on this metho&logy is developed,
It is well known that power systems are usually large, complex interconnected systems. The importance of the voltage and reactive power control to power system operation, the main control measures and their contributions are given in Appendix I. The sensitivity technique used to analyze power systems is given in Appendix 11.
The developed expert system identifies the system operating configuration, selects the appropriate knowledge from the knowledge base, detects the bus or buses at which certain constraints have been violated, sequentially selects the most effective control measure, calculates the appropriate control action according to some selected strategy and system constraints, and checks the predicted recovery of voltage against the necessity to relocate reactive power distribution for large disturbances.
By using the PROLOG facility, an efficient man-machine interface has also been developed.
The expert system shell (including the inference engine and the man-machine communication) combined with the knowledge developed from a 30 bus power system has been tested on the system. Results obtained are very satisfactory. The expert system shell has features that allow easy expansion to large power systems.
2. EXPERT SYSTEM An expert system is a computer program that behaves like an
expert in some, usually w w , domain of application. Each system has knowledge in a particular domain and is capable of solving problems that require that knowledge. Therefore, expert gystems are also called knowledge-based systems [8].
Expert systems derive their power from the problem domain knowledge they possess and from their use of "rules of thumb" in going about their problem solving activities. They can be used as computer-based consultants to humans in the performarme of complex tasks. Typical applications include tasks such as medical diagnosis, location of a failure in certain kinds of equipment, or interpretation of measurement data.
Development of an expert system can be conveniently divided into three main modules, i.e.,
a knowledge base, an inference engine, a user interface.
' h e structure of an expert system in a general block diagram form is shown in Fig. 1.
The knowledge base comprises knowledge that is specific to the domain of application, including such things as simple facts about the domain, rules that describe relations or phemmena in the domain, and possibly methods, heuristics and ideas for solving problems in the domain. The inference engine actively uses the knowledge in the base. The user interface provides smooth communication between the user and the system. It also provides the user with an insight into the problem-solving process executed by the inference engine. It is convenient to view the inference engine and the interface as one module, usually called an expert system shell.
.
0885-8950/88/11W-1449$01 .WO1988 IEEE
1450
I
Base Engine I
Knowledge , I h f ~ ~ e ~ c e
I
j User User - Interface - I
VI
I I . - -J Shell I _ _ ~ _ ~ _ - ~
Fig. 1 Block Diagram of Expert System
3. KNOWLEDGE BASE All known knowledge about the system or domain forms the
knowledge base. In the voltage and reactive power control expert system developed, the following knowledge is needed to form the knowledge base:
The upper and lower limits of voltage at each bus. The upper and lower limits of each control measure. The upper and lower reactive power limits of each load bus. The possible selection of the discontinuous control measures. A sensitivity factor table for each bus voltage and the control measure pair. As the generator bus voltage itself is a control measure, the sensitivity factors between a generator bus and all other control measures are zero, and the sensitivity factor of this bus to the control measure itself is equal to one.
The system may operate in different configurations for which the sensitivity factors may be quite different. For this reason it is necessary to include sensitivity tables for a range of possible operating configurations. A weighting factor for each control measure. A sensitivity table for the reactive power control and the voltage variations for a range of possible system operating configurations. The above mentioned knowledge base, except for the
sensitivity tables (5 ) and (7). can be easily obtained for-a particular power system. The tables can either be collected from the experts or from a numerical analysis using load flow calculations. All knowledge is represented in the knowledge base as simple facts in the form of "List" or "Tree".
4. INFERENCE ENGINE - USE OF THE SENSITIVITY TREE
The inference engine is used to chain the facts given in the knowledge base and the basic rules. The fundamental ideas for the development of the basic rules and the inference engine of the proposed expert system are outlined here.
In order to easily analyze the relationship between the bus voltage and the control measures, Fig6 from the Appendix is redrawn in a slightly different form in Fig.2. NI sensitivity trees, equal to the number of load buses in the power system, are used to represent system relationships. Each tree represents the entire relationship between a particular bus voltage and all control measures and secondary variations of the other bus voltages.
The root of the tree is the controlled bus voltage. Each root connects the control measures through branches. The sensitivity factor associated with the controlled bus voltage and the control measure is given on the corresponding branch. The second level of the tree gives the effect of the control measures on all other load bus voltages. In the second level, each control measure is connected to the other bus voltages by sub-branches. The sensitivity factors between the control measures and the bus voltages are shown at the sub-branches.
Similar trees can be made for the reactive power dispatch control. In these trees, the reactive powers drawn at each load bus become the control measures.The roots and the second level leave are the same as the voltage control sensitivity trees. Appropriate sensitivity factors corresponding to the reactive power dispatch and the bus voltage are used.
Fig. 2 A Sensitivity Tree
Based on the sensitivity tree, the basic rules and the inference engine of the proposed voltage and reactive power control expert system are developed. By recursively using predicate calculus rules in cooperation with numerical and logical calculations, the following procedure is realized in PROLOG language.
The expert system is started by any bus voltage violation. Next, the expert system identifies the system operating configuration and makes voltage control and reactive power dispatch sensitivity trees by using the associated sensitivity factor table of the knowledge base.
Read in the current voltage value at each bus through the monitor or the input/output interface. Compare the current voltage values with their limits, find the buses with abnormal voltage and the magnitude of the voltage violations. For each bus voltage violation, sequentially search for the most effective (the highest weighted sensitivity) control measure by using the sensitivity tree and calculate the control action needed to recover the voltage violation. Check the calculated control action from the view point of the controllers' constraints. If the control action exceeds the limit, the control limit is chosen as the control action. Check the control action from the view point of the other bus voltage limits by using the sensitivity tree. This is used to guarantee that recovering proper voltage level at one bus does not cause bus voltage violations on other buses. As the real power system is a nonlinear system, some tolerances are introduced. By using these tolerances, the voltage at the fault bus is over-corrected by a factor and the other bus voltage limits used to check the control action are reduced by a factor. Test results show that this is an effective way to overcome the system nonlinear error problem. Output the search procedures and the recommended control action through the U 0 interface on the monitor. According to the selected control action, estimate the voltage variations at each bus using the sensitivity tree and recalculate the new bus voltages after the control action.
(10) Repeat the procedure from (4) to (9) until the bus voltage violation has been overcome.
(11) For large disturbances it may happen that even after all the possible voltage control measures have been used, the bus voltage violation still can not be overcome. In this case, a reactive power dispatch procedure is needed.
Procedures using the reactive power dispatch to control the bus voltage are similar to that in (4) to (10). In this case, the reactive power dispatch sensitivity trees are used.
(12) Repeat the above procedure for each load bus of the system until all bus voltages are within limits. The search procedure of the proposed expert system makes use
of the "depth-first" search strategy. This strategy provides the most
145 1
efficient utilization of the reactive power control sources. This is because the sensitivity tree is formed in such a way that the most weighted sensitive controller has the highest priority.
The inference engine developed involves a series recursive search procedure. This is the main reason the PROLOG language is chosen for this.expert system. PROLOG provides very powerful automatic back-tracking, pattern matching and tree-based data structuring capabilities. In addition, the recursive search procedures can also be easily realized by the PROLOG language.
Fig.3 shows the detailed configuration of the developed expert system. -
K N 0 W L E D G E
B A S E
-
and form the sensitivity trees
Input current voltagcs & oontrolr I #
Find the abnormal bus I -- I -
I 1 Select & calculate the
: I I ' I I I
I I t
-t-
Output coamlla
elect the next controller until all controllers an king used or the violation is oveccomc
1 - 1 I ? i L s -
I Volt Corn. I
Reacnve power d i s p a t E h c o n o o l - (similar procedurt as for c
voltage control) I
Find the next abnormal bus until all buses arc normal
INFERENCE ENGINE
-
I N P U T
0 U T P U T
I N T E R F A C E
- Fig. 3 System configuration of the developed expert system
S. RESULTS The proposed expert system has been tested on the JEEE 3(
bus power system with some modifications. The power system is shown in Fig.4. System parameters are given in Appendix 111.
Five studies have been performed and the results are given below:
Case 1: Condition: System is fully connected. Fault:
Action: (1)
Bus#26 voltage is 0.93972 or 0.01028 pu below its lower limit of 0.95 pu.
Controller #8 is chosen fist. As controller #8 has reached its upper limit already, this controller is not available. Control #3 is chosen. The expert system indicates that this controller be increased from 0 to 0.0989645.
Result: After changing controller #3, the voltage violation is overcome. The load flow results are given in Table I.
(2)
B26
Case 2:
c11
U85
c10
9
JfZ7lB3ll Fig. 4 30 Bus Power Systems
. 3
Condition: System is fully connected. Fault: Action:
Bus #12 voltage is above its upper limit by 0.00996 pu. In order to overcome the Bus #12 voltage violation, it is first suggested that controller #6 be decreased from 1.05 to 1.02. This reduces the voltage violation from 0.00996 to 0.00833416. It is further suggested that controller #14 be decreased from 1.091 to 1.06. After the control action, the voltage violation is overcome. Load flow results for both before and after the control action are shown in Table I.
Result:
Case 3 and Case 4 are used to test the capability of the expert system tuning itself to the system operation configuration change.
Case 3: Condition: System is fully connected. Fault: Lower voltage limit on Bus #23 is violated by 0.01718 pu,
on Bus #24 by 0.00555 pu and on Bus #26 by 0.00468 pu. Action: Control #3 is chosed at first and required to be increased
from 0.0 to its upper limit of 0.16. In addition, control #4 is suggested to be increased from 0.0 to 0.02. By doing this, all bus voltages are recovered to within acceptable limits. The results are shown in Table I.
Result:
Case 4:
Condition:
Fault:
Action:
The transmission line between Bus #23 and Bus #24 is switched-off.
Lower voltage limit on bus #23 is violated by 0.0230103 Pu.
Control #4 is chosen at first. It is indicated that control #4 be increased from 0.02 to its upper limit of 0.18. As the voltage violation continues to exist, it is then suggested that control #14 be increased from 1.071 to 1.07334. The voltage violation is overcome. The results are shown in Table I.
Result:
It can be seen from the results of Cases 3 and 4 that as the
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system operation configuration changes, the expert system selects different control actions to deal with the same kind of voltage violation problem. Case 5:
In this example, with the power system operating normally initially, one transmission line is switched-off. As a result, the voltage on some buses drops considerably so that reactive power control is needed to recover the voltages. Condition: System is initially operating normally in the fully
connected operating configuration. One of the transmission lines (Bus #27 to Bus #30) is switched-off which causes voltages at some buses to fall significantly below their lower limits.
Fault: Lower voltage limit on Bus #29 is violated by 0.01987 and on Bus #30 by 0.0731 1 pu.
Action: In order to recover the voltage on Bus #29, the following measures are indicated by the expert system:
maintain control #8 at its original value of 1.04 because of other bus voltage constraints. increase control #12 from 1.01 to 1.052 pu.
(1)
(2) In order to recover the voltage on Bus #30, the following measures are indicated:
keep control #8 at its original value of 1.04. increase control #12 from 1.052 to the upper limit of 1.087 pu. retain control #3 at 0.16. raise control #1 from 0.0 to its upper limit of 0.2 pu. keep control #2 at 0.0. keep control #4 at 0.02. increase control #14 from 1.071 to 1.0711 pu. keep control # I O at 1.045. keep control #I3 at 1.082. retain control #6 at 1.05. retain control #7 at 1.07. keep control #11 at 1.01. keep control #5 at 1.05. retain control #9 at 1.06. decrease the reactive power load at Bus #30 by at least 0.02237 pu.
Result: The load flow results in the four situations are given in Table I. Before the disturbance, the power system is operating normally, all the bus voltages are within their limits. After the disturbance, voltages on Bus #27 and Bus #30 violate their limits. By the use of the voltage control measures the voltage violations are decreased considerably. With the help of the reactive power control, all the bus voltages are recovered.
The monitor record of the action of the expert system dealing with case 5 is given in FigS. This figure shows a typical problem solving process and the man-machine communications.
...........................................
1 ?- expert.
Read in the operating condition cord. op cord=2. Is it true, op cord=2? y.
Read in the current bus voltages.
Read in the current controllers.
Bus #29 voltage is low by 0.0198698.
......
......
The violation is equal to -0.0248698 now. Control #8 is chosen.
The current control of C#8 is 1.04. From the constraints of the other buses,
this control is unavailable.
The violation is equal to -0.0248698 now. Control #12 is chosen.
The current control of #12 is 1.01. Considering the constraints, this generator
voltage should be equal or near but greater than the recommended value 1.05166.
What value do you want to chose?
Is it true, C#12=1.052? y. C#12=1.052.
This voltage violation has been overcome.
Bus #30 voltage is low by 0.0469017. ...... The violation is equal to -0.0300618 now. Control #3 is chosen.
The current control of #3 is 0.16. As this controller hits the upper limits,
it is unavailable.
The violation is equal to -0.0300618 now. Control #1 is chosen.
The current control of #1 is Q. The possible selection are:
0.02, 0.04, 0.06, 0.08, 0.1, 0.12,0.14, 0.16, 0.18, 0.20
Considering the constraints, this capacitor shou!d be equal or near but less than the recommended value 0.0208877.
What value do you want to chose? C#1=0.02. Is it true, C#1=0.02? y.
...... The violation is equal to -0.0290746 now. Control #5 is chosen.
The current control of #5 is 1.05. From the constraints of the other buses,
this control is unavailable. ...... A11 the measures for this bus have been used. The violation at this bus still exists.
The reactive power load should be rearranged. It is suggested that the reactive power at
this bus decrease at least by 0.0223651. What value do you want to chose? Dec. of R.P. on Bus #30 =0.023. Is it me , Dec. of R.P. on Bus #[email protected]? y.
This voltage violation has been overcome.
All the other bus voltages have been checked. They are normal. No further control is needed.
Fig.5 Monitor record of the expert system for Case 5
6. CONCLUDING REMARKS An expert system for the power system voltage and reactive
power control is developed in this paper. It has the following main features:
(a) The inpurloutput interface facilities give a friendly user inter-
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Table 1
2 case 5 mi& lower 0.9 0.95 0.95 0.95 0.95 0.9 0.95 0.95 0.9 0.95 0.9 0.95 0.9 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95
- -
-
1
1.06 1.045 1.022 1.013 1.01 1.007 1 .o 1.01 1.038 1.023 1.052 1 .a37 1 .os 1 1.022 1.017 1.024 1.018 1.007 1.004 1.008 1.012 1.012 1 .008 1.004 0.991 0.956 1 .OOo 1.001 0.973 0.962
- rffer
-
3 after 1.06 1.045 1.022 1.013 1.01 1 .a07 1 .o 1.01 1.044 1.019 1.082 1.035 1.07 1 1.01 1 1 .o 1.021 1.014 0.994 0.994 0.999 1404 1.004 0.958 0.981 0.99 0.972 1.004 1.002 0.984 0.972 -
Volt. 4 after 1.06 1.045 1.024 1.015 1.01 1.009 1.001 1.01 1 .os2 1.033 1.082 1.046 1.075 1.026 1.018 1.033 1.027 1.011 1.01 1.015 1 .a21 1.021 0.959 1.01 1 1.011 0.993 1.02 1.005 1 .o 0.988
-
-
Car - before 1.06 1.045 1.022 1.013 1.01 1.008 1.0 1.01 1.047 1.024 1.082 1.03 1.071 1.002 0.987 1.02 1.018 0.988 0.991 0.999 1.012 1.013 0.927 1.003 1.006 0.988 1.016 1.003 0.9% 0.984
Ca before 1.06 1.045 1.021 1.012 1.01 1.006 0.999
1.034 1.015 1.052 1.032 1 .os 1 1.016 1.010 1.018 1.010 0.999 0.996 1 .Ooo 1.001 1.001 0.995 0.983 0.975 0.940 0.989 0.999 0.961 0.95 1
-
1.01
Bus #
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
CrU before 1.06 1.045 1.025 1.017 1.01 1.01 1.02 1.01 1 .OS4 1.037 1.082 1.060 1.09 1 1.043 1.037 1.043 1.034 1.025 1.021 1.024 1.024 1.025 1.022 1.01 1 1.01 1 0.993 1.019 1.005 0.999 0.988
- -
Cai - before 1.06 1.045 1.020 1.011 1.01 1.005 0.999 1.01 1.037 1.005 1.082 1.027 1.07 1 0.999 0.984 1.001 1.001 0.978 0.979 0.984 0.985 0.984 0.933 0.945 0.964 0.94s 0.986 0.998 0.965 0.953
- upper 1.1 1.1 1.05 1 .os 1.01 1.1 1 .os 1.1 1.1 1 .os 1.1 1 .os 1.1 1.05 1 .os 1 .os 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05
-
-
EL 1.06 1.04s 1.024 1.015 1.01 1.01 1.002 1.01 1.040 1.023 1.082 1.041 1.06 1.025 1.019 1.026 1.019 1.008 1.005 1.009 l.Dl0 1.01 1 1.006 0.997 1.002 0.984 1.013 1.005 0.993 0.982 -
fault 1.06 1.045 1.0213 1.0125 1.01 1 .a066 0.9997 1.01 1.0433 1.0175 1.082 1.034 1.071 1.01 0.9977 1.0197 1.0127 0.9921 0.992 0.9976 1.0016 1.0012 0.955 0.9762 0.9794 0.961 0.9905 0.9999 0.9301 0.877
v. & r. cont. 1.06 1.045 1.0453 1.0417 1.01 1 .os 1.0256 1.087 1.0495 1.0473 1.082 1.0488 1.0711 1.0299 1.02 1.0422 1.0404 1.0173 1.0189 1.0252 1.0327 1.0325 0.984 1.0119 1.0269 1.0094 1.0449 1.049 0.9993 0.9615
aOrinal 1.06 1.045 1.0214 1.0128 1.01 1.0068 0.9999 1.01 1.0437 1.0181 1.082 1.0343 1.071 1.0104 0.9983 1.0201 1.0132 0.9927 0.9926 0.9982 1.0024 1.002 0.9561 0.9778 0.9828 0.9645 0.995 1.0005 0.9698 0.9528
v. cont. 1.06 1.045 1.045 1 1.0414 l.O€ 1.0497 1 .OX4 1.087 1 . a 8 9 1.046 1.082 1.048 1.0711 1.029 1.0189 1.0414 1.0394 1.0162 1.0178 1.0240 1.0312 1.03 1 0.9821 1.009 1.0206 1.003 1.0369 1.0482 0.9798 0.9297
face to the power system. (2) It can be used to assist in decision-making for power system voltage and reactive control. It can also be used to train power system operators.
(3) It can be used to assist in system planning. The sensitivity tree, a methodology &veloped in this paper, is
effective in the development of an expert system used to control a large interconnected system especially when the system nonlinearity is not large.
(b) The expert system automatically tunes to the new system operating configuration when the system operating codguration changes.
(c) The expert system contains both voltage and reactive power conml, and can restore the system to desired limits even when the system is subjected to large disturbances. The expert system has been tested on an IEEE 30 bus power.
system. Test results show very satisfactory results. The technique proposed is based on the use of sensitivity factors. In general, many bus voltages and control measures pairs have very small sensitivity factors as explained in Appendix II. Most of these can be eliminated by introducing a threshold value when forming the tree. Such a simplified sensitivity tree will require little computation time and die
7. ACKNOWLEDGMENTS The authors acknowledge the financial suppdrt provided by the
University of Calgary under research-grant no.851407.
8. REFERENCES P. Szolovits and S. Pauker, "Categorical and Probabilistic Reasoning in Medical Diagnosis". Anificial Intelligence Vol.
J. McDemtt , "Rl: A Rule based Configurer of Computer System", Artificial Intelligence Vol. 19, 1982, pp. 39-88. R. Duda, J. Gaschning and P. Hart, "Model Design in the Prospector Consultant System for Mineral Exploration, in: D.Michie(Ed.), Expert systems in the Microelectronic Age", (Edinburgh University Press, Edinbufgh, 1979) pp. 153-167. E.C. McClelland and P.R. Van Home, "Fast Voltage Prediction Using a Knowledge Based Approach", IEEE Trans. Vol. PAS- 102, No.2, Feb. 1983, pp. 315-319. T. Sakaguchi and K. Matsumoto, "Development of a Knowledge Based System for Power System Restoration", IEEE Trans. Vol. PAS-102, No.2, Feb. 1983, pp. 320-329. C.C. Liu and K. Tomsovic, "An expert System Assisting Decision-Making of Reactive PowerNoltage Control", IEEE
11, 1978, pp. 115-144.
proposed expert system can easily be applied to very large systems. The use of the threshold in simplifying the sensitivity tree
enhances the possibility of using the expert system with large sys- terns in real time as c o r n p W to the optimization techniques which are more suited to off-line analysis because of large cornputation requirements. Off-line information obtained from the optimizadon techniques can be used to enrich the knowledge base and the two methods can complemeht each other.
Expert systems also have other advantages. Whereas the con- ventional programs indicate to the system operator the actions required but not the reasoning behind them, the expert systems have the capability of providing the reasoning procedure leading to the proposed actions. Using skeletal systems call 'shells', it is easy to develop an expert system for another similar task as only the knowledge base needs to be built for that task.
The expeh system described in this paper is useful at least in the following three aspects: (1) It can be used as an on-line controller in co-operation with the
I10 interface system.
[21
[31
[4]
[51
[6]
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Vol. PWRS-I, NO.3, August 1986 pp. 195-201. 171 R.Fujiwara, T.Sakaguchi, Y.Kohno and H.Suzuki, "An
Intelligent Load Flow Engine For Power System Planning", IEEE Trans. Vol. PWRS-1, No.3, August 1986, pp. 302-307.
[SI Ivan Bratko, "PROLOG Programming for Artificial Intelligence", Addison-Wesley Publishing Company 1986.
[!I] David Tzouh-Wei Sun and Rayniond R. Shoults, "A Preventive Strategy Method for Voltage and Reactive Power Dispatch', IEEE Vol. PAS-104, No.7, July 1985, pp. 1670- 1676.
[IO] G. Huang, "Reactive and Real Power Control for Computationally Effective Voltage and Thermal Management",
[ l 11 R. Mota-Palomino and V.H. Quintana, "Sparse Reactive Power Scheduling by a Penalty Function-Linear Programming Technique", IEEE Vol. PWRS-1, No.3, August 1986 pp. 31- 39.
IEEE Vol. PAS-104, N0.7, July 1985 pp. 1728-1738.
9. APPENDICES
1. Reactive Power and Voltage Control Reactive power and voltage control plays an important role in
the security of the modern power systems. It is important to provide the customer with a constant voltage level. It is also well known that the system voltage profile must be maintained within a desired bandwidth for power system stability 191, [lo], [ll].
Conventionally, minimization of transmission line losses has been considered to be the main aim in reactive power scheduling. However, the recent trend is towards the elimination of security constraint violations [91, [ 1 1 I.
Proper scheduling of reactive power sources in well planned system leads to the following benefits 11 11. (1) reduction of real power losses in the system (2) increase in system security from augmented reactive power
reserves for emergencies (3) reduction of voltage differences between system nodes for
improved operation. By injecting reactive power into the system, the controllers
adjust both generation and flow of reactive power. In this way, an appropriate node voltage profile can be obtained. The following control measures are commonly used to adjust reactive power and bus voltage of a power system.
Synchronous condenser and capacitor compensation. This measure supplies a certain amount of reactive power to the transmission line and so the voltage drops along the line are controlled. Increasing the compensation capacitor injects reactive power on the bus and increases bus voltage at all loads. Usually the closer the bus to the compensation capacitor electrically, the more the voltage is increased. Transformer tap change. This measure increases or decreases bus voltage by changing the transformer turns ratio. Since buses in a power system are connected via the transmission lines, some bus voltages increase and other bus voltages decrease. Change of the generator terminal voltages. This measure is similar to synchronous condenser compensation. Changing the injected reactive power by changing the generator excitation alters both generator bus and load bus voltages.
When thz above measures are used to control the cower svstem voltage, they are not equally effective. In addition, the amount of control needed from each measure is not unique. For these reasons, some additional criteria are needed in practice. One possible criterion is to minimize the weighted sum of all control actions. This can be mathematically described as follows.
For a given bus voltage violation, find a set of control actions C. I * i = 1 ? . . . , m, where m is the number of the controllers, so
that the voltage violation can be overcome. In addition, this set of controllers will satisfy:
min {W, . Ci} ( i = l , . . . , m )
where: Ci, the irh control measure, is subject to the constraints:
and Wi represents the weighting factor for Ci . As the bus voltage is closely connected to the reactive power
flow, the reactive power dispatch some times can be used to control the bus voltages. This happens when the use of all the above mentioned control measures is not able to overcome the voltage violation problem. Actually, reactive power rearrangement is more or less equal to the measure of reactive power compensation. This is bzcause reducing the reactive power drawn from a certain bus is the same as increasing the reactive power injection at that bus. The difference is that the reactive power compensation measures are pre- installed. They may not be available on each load bus, whereas, the reactive power dispatch is usually available to some extent.
However, as reactive power requirements on the load buses are mainly decided by the user, the reactive power dispatch has to take into account the users' requirements. If those requirements can not be satisfied, it means that additional reactive power compensation measures are needed. This belongs to the system programming problem.
11. Sensitivity Technique Sensitivity technique is widely used to analyze linear systems.
It represents the major relationship between the control actions and their effects. As the power system is actually a non-liner system, the sensitivity factor between a reactive control measure and the bus voltages can not be a constant value. The first order sensitivity function is commonly used for simplicity especially when system nonlinearity is not large. Test results show only a small difference over a wide range of system operating conditions. This implies that the sensitivity technique can be used successfully to analyze the reactive power and voltage control problem.
For an N bus power system with M conaol measures, the relaionship between the bus voltages and the control measures can be represented as shown in Fig.6. It can be seen that for each bus voltage, several control measures can be used. It can also be seen that changes in each control measure result in changes of several bus wlt;i~es. For a certain bus voltage violation, it is possible to calculate by using the sensitivity technique the control action needed to overcome this voltage violation. Two facts limit the control action. First, the control action should not exceed the control constraints. Second, the control action used to overcome the voltage violation should not produce new bus voltage violations.
A similar figure can be used to represent the relationship between the reactive power dispatch and the bus voltages. In that figure, reactive powers drawn from the load buses become the control measures.
The sensitivity technique has long been used to solve the voltage and reactive power control problem. Theoretical analysis and mathematical justification have been done in [6] and [ I l l . All
Yus V o l t a g e
c1 C2 Control1 er
Fig. 6 Representation of the Voltage Control
- CM
these results prove that the stnsitivity technique is an effective way to deal with the power system voltage control problem.
The same technique is used for the reactive power control problem when an extremely large disturbance appears in which the reactive power control is used to recovcf the voltage violation 11 11.
When a reactive power injection is changed for control purposes, it is effective over a limited area, which means only nearby buses or lines show significant sensitivity to such control. This is because reactive power losses are large and because numerous voltage controlled buses absorb the excess injection. This idea is used to simplify the sensitivity tree when developing an expert system for voltage and reactive power control.
III. System Parameters
which * represents the control variable. System parameters in pu are given in thc following table in
, ! ! I I
I
I
I I
1 I 12 12 12 L2 14 16 15 18 19 IO 10 10 10 21 15 22 23 24 25 25 28 27 27 29 8 6 10 19 24
IUS #--BUS #
15
2 3 4 4 5 6 6 7 7 8 9 10 11 10 12 13 14 15 16 15 17 18 19 20 20 17 21 22 22 23 24 24 25 26 27 27 29 x 3c 2e 21 0 0 0 0
R 1.0192 1.0452 1.0570 1.0132 1.0472 1.05 8 1 LO1 19 Lo460 1.0267 1.0120 1.OOO0 l.m l.m 1.oooo l.m 1.OOOO 1.1231 1.0662 1.0945 1.2210 1.0824 1.1070 3.0639 3.0340 3.0936 3.0324 3.0348 0.0727 0.01 16 0. 1000 0.1150 0.1320 0.1885 0.2544 0.1093 O.oo00 0.2198 0.3202 0.2399 0.0636 0.0169 0.0000
0.0000 o.Ooo0
-
o.oooa
-
- X
LO575 1.1852 1.1737 1.0379 1. 1983 1.1763 1.0414 1.1160 1.0820 1.0420 1.2080 1.5560 1.2080 1. 1100 1.2560 3. 1400 1.2559 3.1304 3.1987 3.1997 3.1932 D.2185 0.1292 0.0680 D.2090 0.0845 0.0749 0.1499 0.0236 0.2020 0.1790 0.2700 0.3292 0.3800 0.2087 0.3960 0.4153 0.6027 0.4533
0.0599
0.ooOC 0.000G 0.000c
-
0.2000
o.oooa
-
- B
1.0264 1.0204 1.0184 1.0042 1.0209 5.0187 1.0045 3.0102 3.0085 3.0045 3.oooo 3.0000 D.0000 3.oooo D . m 0.0000 D.0000 D.0000 o.oo00 o.Ooo0 0.0000 0.0000 o.oO0o 0.0000 0.0000 0.0000 O.oo00 O.oo00 O.oo00 O.oo00 0.0000 O.oo00 O.oo00 O.oo00 O.oo00 O.oo00 O.oo00 0.0000 O.oo00 0.0214 0.0065 0.10 * 0.10 * 0.10 * 0.10 * -
rrans. tap. 1.OoOo 1 .m 1.Oooo 1.oooO 1.oo00 1 .oooo 1.oooO 1 .oooo 1.oooO 1.oooO 1.05 * 1.07 * 1.0000 1 .oooo 1.05 * 1.Oooo 1.0000 1.Oooo 1 .OoOo 1.Oooo 1.oooO 1 .oo00 1 .moo 1.0000 1.0000 1 .woo 1 .oooo 1 .m l.m ’ 1.oooO 1.oOoo 1.oooO 1 .oo00 Loo00 1.oo00 1.04 * 1.Oooo 1.oooO 1 .moo 1 .woo 1.oOoo 1.0000 1.0000 1 .oooo 1.oOoo
1455
The control measures are given in the following table. Control # Control measure FFZF 2 3 4 5 6 7 8 9 10 11 12 13
capacitor capacitor capacitor trans. tap trans. tap trans. tap trans. tap gen. voltage gen. voltage gen. voltage gen. voltage gen. voltage
14 I gen. voltage
Control range pu 0.0 - 0.2 0.0 - 0.2 0.0 - 0.16 0.0 - 0.18
’ 0.9 - 1.01 0.9 - 1.1 0.9 - 1.1 0.9 - 1.1 0.9 - 1.1 0.9 - 1.1 0.9 - 1.1 0.9 - 1.1 0.9 - 1.1 0.9 - 1.1
S.J. Cheng (M’87) was born in Hubei, People’s Republic of China, on July 8, 1945. He graduated in electrical engineering from the Xian Jiaotong University, China, in 1967 and obtained the M. Eng. degree in electrical power engineering from the Huazhong University of Science and Technology (HUST), China, in 1981. In 1986 he received the FkD. degree from the University of Calgary, Alberta, Canada.
From 1967 to 1978, he worked with the northwest electrical power plant construction company in China on the aspects of automation and on-line computer control of power plants. From 1981 to 1983, he was a lecturer in the Department of Electrical Poiver Engineering, HUST.
Dr. Cheng is currently working in the university of Calgary, as a post doctorate research fellow. His areas of interest are in Power System System Stability, Reactive Power Dispatch, Optimal Control, Self-tuning Control, Expert Systems and their applications in power systems.
O.P. Malik (M’66 - SM’69 - F‘87) graduated in electrical engineering from Delhi Polytechnic, India, in 1952 and obtained the M.E. degree in electrical machine design from the University of Roorkee, India, in 1962. In 1965 he received the Ph.D. degree from the University of London, London, England, and D.I.C. from the Imperial College of Science and Technology, London.
From 1952 to 1961 he worked with electric utilities in India on various aspew of design, construction, and operation of power systems. For one year he was a Confederation of British Industries scholar in the United Kingdom. In 1965 he worked with the English Electric Company in England. He is now in Canada, where he taught for two years at the University of Windsor and is at present at The University of Calgary.
Dr. Malilc is a fellow of the Institution of Electrical Engineers (London), a member of the Canadian Electrical Association, and the American Society for Engineering Education. He is a registered Professional Engineer in the Provinces of Alberta and Optario, Canada.
G.S. Hope (S’56 - M’67 - SM’72) was born in Edmonton, Alberta, Canada, on September 19, 1931. He received the B.Sc.\degree in electrical engineering from the University of Alberta, Edmonton, Canada; the Ph.D. and D.I.C. degrees in electrical engineering (power systems) from Irn&rial College, University of London, London, England, in 1957 and 1966, respectively.
From 1957 to 1961, he worked with Canadian General Electric Co. Ltd., Civilian Atomic power Department, Peterborough, Ontario. In 1962 and 1963, he was employed as a Consultant to the Petrochemical Industry in Southern Alberta. He joined the staff at The University of Calgary, Department of Electrical Engineering, in 1967; at present, he holds the rank of Professor. Dr. Hope’s current research interests are: Computer interfacing, digital relaying, system identification and power system’s computer application.
