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PV modules used to be expensive, but in recent years, their price has beenslowly dropping, and as they become increasingly economical, they will be used inmore applications. In the U.S. the cost of installing solar had fallen from $55 per peakwatt in 1976 to about $4 per peak watt in 2001 [1]. PV modules output efficiency hasalso increased in recent years. PV cells, having power conversion efficiencies as high as31%, have been developed in a laboratory environment over the last decade [2]. Withthese growths in photovoltaic technology, there is no doubt that PV will have a goodstand in the near future. However in this thesis, the emphasis is on the study of PVsystem control part.1.2.
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AMERICAN UNIVERSITY OF BEIRUT
MAXIMUM POWER POINT TRACKING SYSTEM: AN ADAPTIVE ALGORITHM FOR SOLAR PANELS
by MOHAMMED ALI SERHAN
A thesis submitted in partial fulfillment of the requirements
for the degree of Master of Engineering to the Department of Electrical and Computer Engineering
of the Faculty of Engineering and Architecture at the American University of Beirut
Beirut, Lebanon January 2005
AMERICAN UNIVERSITY OF BEIRUT
MAXIMUM POWER POINT TRACKING SYSTEM: AN ADAPITIVE ALGORITHM FOR SOLAR PANELS
by MOHAMMED ALI SERHAN
Approved by: ______________________________________________________________________ Dr. Sami Karaki, Professor Advisor Electrical and Computer Engineering ______________________________________________________________________ Dr. Fouad Morad, Professor Member of Committee Electrical and Computer Engineering ______________________________________________________________________ Dr. Riad Chedid, Professor Member of Committee Electrical and Computer Engineering Date of thesis defense: January 7, 2005
AMERICAN UNIVERISTY OF BEIRUT
THESIS RELEASE FORM
I, Mohammed Ali Serhan authorize the American University of Beirut to supply copies of my thesis to
libraries or individuals upon request. do not authorize the American University of Beirut to supply copies of my thesis to
libraries or individuals for a period of two years starting with the date of the thesis defense.
____________________ Signature
____________________ Date
v
ACKNOWLEDGMENTS
I would like to thank my advisor Dr. Sami Karaki for the enlightening advice and guidance he provided during the elaboration of this work. Many thanks go to Dr. Fouad Mrad and Dr. Riad Chedid, who were in my committee, for providing a lot of insightful comments during the presentation of this thesis. I'm also very grateful to the dearest Dr. Lana Al Chaar, who proposed the topic in the first place, for her support. All respect and admiration go to Mr. Antoine Al Asal, a true brother, partner and friend. Warm love and support from my parents is the main factor of success throughout all years of study. Lastly, praise goes to Almighty Allah whose help and guidance has given me the strength needed to complete this work.
AN ABSTRACT OF THE THESIS OF
Mohammed Ali Serhan for Master of Engineering Major: Electrical Engineering
Title: Maximum Power Point Tracking System: An Adaptive Control Algorithm for Solar Panels.
Energy is fundamental to the wellbeing of our society—it powers our homes, businesses, and industries. However, energy, obtained from fossil fuels is presenting challenges to many nations; not only these energy resources are depletable but are also major contributors to atmospheric pollution and global warming. ‘Renewable Energy’ is a new trend in clean energy production. This includes power generated from water, wind, solar radiation, biomass and other resources. This development of renewable power sources will save fossil fuel resources, and help improve the quality of our environment. One of the renewable energy sources, Photovoltaic systems have a great potential because it makes use of the most abundant energy on earth that is sunlight.
As the maximum power operating point (MPP) of the PV module changes with atmospheric conditions, e.g. solar radiation and temperature, an important consideration in the design of efficient PV system is to track the MPP correctly. The objective of this thesis is to design and build a Maximum Power Point Tracker (MPPT) to charge a lead acid battery.
The design consists of a PV panel, a 12V battery, H-bridge converter and a control module that uses the PIC16F874 microcontroller. The controller obtains the current and voltage values from the PV array and performs pulse width modulation (PWM) on the converter to charge the battery with maximum available power. Battery’s state of charge is also controlled by the microcontroller to protect the battery from being overcharged. The Perturb and Observe (PAO) method is used as an algorithm to track the maximum power point of the PV array. The performance of the PAO algorithm in tracking maximum power point has been improved by implementing an adaptive perturbation scheme to track correctly the MPP in case of rapidly varying weather conditions and to get high conversion efficiency.
vi
CONTENTS
Page
ACKNOWLEDGEMENTS ...………………………………..………… v ABSTRACT…...……………………………………….……………….….… vi LIST OF ILLUSTRATIONS……………….…………………...……… x LIST OF TABLES......................................................................................... xv Chapter 1. INTRODUCTION…….….…………………………………………... 1 1.1. An Overview ……………………..…………..…….………..... 1 1.2. Brief Background ………….…………………...……………..... 1 1.3. Problem definition and motivation …...……………………..….. 2 1.4. Scope ……………………………………………………………… 3 2. LITERATURE REVIEW …………………………………………. 4 2.1 Maximum Power Point Tracker …..…………....................... 4 2.2. Switched-Mode Converters….……………......................... 5 2.3. Controller ………….………………………………………….... 5 2.3.1 Voltage feedback control …………………………….. 5 2.3.2 Power feedback control ………………………………. 6 2.4. MPPT control Algorithms …………………………………....... 6 2.4.1 Perturb and Observe technique ……………………….. 6 2.4.2 Incremental Conductance technique ………………….. 8 2.4.3 Constant Reference Voltage ………………………….. 10 2.4.4 Other techniques: CMPPT, VMPPT…………………… 11 2.5. Comparative Study………………………………………………. 12 vii
viii
2.6. Contribution of this Thesis………………………………………… 13 3. SYSTEM COMPONENTS MODELING ............…………... 14 3.1. Photovoltaic ………..……………………………………....…….. 14 3.1.1 Solar Cells ………………………………………………. 14 3.1.2 Photovoltaic effect …………… ………………………… 15 3.1.3 Electric Model of the PV cell …………………………… 15 3.3.4 Irradiation and cell Temperature effect ………………. 17 3.3.5 PV models and PV arrays ………………………………. 18 3.2. Battery ……………………………………………………………. 18 3.2.1 Lead Acid battery ………………………………………. 19 3.2.2 Battery Chemistry ……………………………………. 19 3.2.3 Amp-Hour Capacity and Charge Rate ……………….. 20 3.2.4 State of Charge 20 3.2.5 Deep cycles vs. starter batteries ……………………… 21 3.2.6 Lifespan of batteries ……………………………………. 22 3.2.7 Battery hazards …………………………………………. 22 3.3. DC-DC Converters …………………………….………………… 23 3.3.1 Switching converter Topologies ……………………….. 23 3.3.2 Non-Isolated Switching converters …………………….. 24 3.3.2.1 Buck Converter 24 3.3.2.2 Boost Converter 32 3.3.2.3 Buck-Boost Converter 34 3.3.3 Isolated DC-DC Converters ……………………………. 35 3.3.3.1 Flyback Conveter 36 3.3.3.2 Forward Converter 37 3.3.3.3 H-bridge Converter 38 3.4. Zero Voltage Switching ……………………..…………………… 39
4. MPPT SIMULINK MODEL ………………………………… 42 4.1. Introduction……………………………....…….………………….. 42 4.2. Simulink Blocks …………….……………………………………. 42 4.3. What is an S-Function …………………………………………… 43 4.4. Implementation of PV cell using S-Function ………………….… 44
ix
4.5 Converter and Controller Blocks ………………………………… 45 4.6 Battery Block ……………………………………………………. 49 5. MPPT SYSTEM IMPLEMENTATION …………………… 52
5.1. Introduction ……………………………………………………….. 52
5.2. MPPT System ……………………………………………………….. 52 5.2.1 Microcontroller …………………………………………. 53 5.2.2 PV-PIC Interface Circuit ………………………………. 54 5.2.3 Buck-Boost Converter …………………………………. 54 5.2.4 PIC-Converter Interface Circuit …………………….. 54
5.3. Hardware Design ……………..………………………………….. 55
5.3.1 Controller and Converter Design ……………………. 55 5.3.2 Phase Splitter circuit …………………………………. 59 5.3.3 Switch Driver ‘A’ and ‘B’ …………………………… 60 5.3.4 H-Bridge …………………………………………………. 62 5.3.5 Transformer, Rectifier and Filter ………………………. 63
5.4. Software Design …………………………………...……………... 66 5.4.1. Main Program …………………………………………. 66 5.4.2. Charging-Tracking mode ……………………………… 67
6. SYSTEM RESULTS AND DISCUSSION……………….... 74 6.1. Introduction ……………………………..…..….………………... 74 6.2. PV model Validation ……………………..…………………….... 74 6.3. Simulink Simulation Results …………………………….……..… 78 6.4. Hardware Results ………………………………………………… 81 6.5. Comparison of Tracking algorithm ………….………………….. 85 6.5.1 Minor change in the weather conditions ………………. 85 6.5.2 Major change in the weather conditions ………………. 87 6.6. Power Budget ................................................................................. 88 6.6.1. Inductor conduction loss 88 6.6.2. Diode conduction loss 89 6.6.3. MOSFET conduction loss 89 6.6.4. Transformer power loss 90
6.6.5. Other power factor factors 92 7. CONCLUSIONS AND FUTURE WORK …......................... 94 7.1. Summary ………………………………………………………... 94 7.2. Testing Environment ……………………………………………… 94 7.3. Better Tracking Algorithm ……………………………………….. 95 7.4. Simulink Model ………………………………………………….. 96 7.5. Future Work ……………………………………………………… 96 APPENDIX A……..………………………………………………………….. 98 1. Matlab program code ……………………………………………... 98 APPENDIX B…………………………………………………………………. 102 1. PCB circuit design ……………………………………………..... 102 APPENDIX C…………………………………………………………………. 105 1. Assembly program code ………………..………………………..... 105 APPENDIX D……………………………………………………………….. 130 1. Datasheet ………………………………………………………... 130
REFERENCES……..……………………………………………………… 132
x
xi
ILLUSTRATIONS Figure Page 1.1. (a) The I-V characteristic curve, (b) The PV panel Maximum Power
Point.......................................................................................................... 2
2.1. (a) PV panel Insolation characteristics (b) PV panel Temperature characteristics …………………………………………………………. 4
2.2. PAO technique ……………………………............................................ 7
2.3. Deviation of the PAO technique from the MPP ...................................... 8
2.4. The slope ‘conductance’ of the P-V curve …………………………… 8
2.5 Flow chart of ICT algorithm…………………………………………… 9
2.6. MPPT control system with constant voltage reference ........................... 11
2.7. The conventional MPPT controller using open circuit voltage (Voc) ... 12
3.1. The PV cell ……...................................................................................... 14
3.2. Model for a PV cell ................................................................................. 15
3.3. (a) Effect of Varied Irradiation, (b) Effect of Varied Temperature on
the PV cell …………….……………………………………………. 17
3.4. (a) PV Module, (b) PV Array ………………….................................... 18
3.5. Buck Converter …….............................................................................. 24
3.6. Voltage and current changes ………………………………………….. 25
3.7. Inductor current for (a): continuous mode (b): discontinuous mode … 27
3.8. Buck Converter at Boundary ……........................................................... 27
3.9. Buck Converter - Discontinuous Conduction ......................................... 28
3.10. Output Voltage vs Current …….............................................................. 30
3.11. Output voltage ripple in a step-down converter ...................................... 31
3.12. Boost Converter Circuit ……………....................................................... 32
xii
3.13. Voltage and current waveforms (Boost Converter) ……………………. 33 3.14. Schematic for buck-boost converter ........................................................ 34
3.15. Waveforms for buck-boost converter …………………………………. 35
3.16. Flyback converter ………………………….………………................... 36
3.17. Forward Converter ………….................................................................. 37
3.18. H-bridge Converter .................................................................................. 39
3.19 Waveforms …………………………………………………………….. 39
3.20. Power loss associated with high switching frequencies ......................... 40
3.21. ZVS resonant-switch dc-dc converter ………….................................... 41
4.1. PV array 'MPPT' system ……………………..………........................... 43
4.2. S-Function block with three inputs and two outputs …........................... 43
4.3. Model for a PV cell ................................................................................. 44
4.4. PV Cell S-Function block ……............................................................... 45
4.5. Buck converter and Controller blocks ..................................................... 46
4.6. Controller Block Implementation ……………........................................ 46
4.7. MPP tracking algorithm Flow Chart …………....................................... 47
4.8. Different current levels with respect to variable duty cycle ................... 48
4.9. MPPT tracking scheme using a variable step size ……………………. 49
4.10. Battery Model Block ………………………......................................... 50 4.11. PV array 'MPPT' system ………………………………………………. 50 5.1. The PV maximum power point tracking system …………………........ 53 5.2. Converter and Controller ……………………………………………… 55 5.3. (a) 50% duty cycle switching (b) variable duty cycle switching……… 56 5.4. Bridge output due to small and large phase difference ………………. 56
xiii
5.5. Case of zero phase difference between V1 and V2 ……………………. 57 5.6. Case of V1 and V2 being out of phase ……………………………….. 57 5.7. PWM output controls the Bridge output ……………………………… 58 5.8. PWM, Bridge, Rectified and Filtered voltage waveforms …………… 58 5.9. Phase splitter output waveforms …………………………………….. 59 5.10. Phase splitter schematic diagram ……………………………………. 60 5.11. Driver A output waveforms ………………………………………….. 60 5.12. Driver ‘A’ schematic diagram ……………………………………….. 61 5.13. Charging and discharging stages …………………………………….. 62 5.14. Bridge Converter schematic diagram ………………………………… 63 5.15. Transformer, Rectifier and Filter waveforms ……………………….. 64 5.16. Main Program Flow Chart ……………………………………………. 67 5.17. The conventional PAO algorithm Flow Chart ………….………….… 68 5.18 Scanning with small step in case of varying weather conditions …….. 69 5.19 The Adaptive PAO algorithm Flow Chart ……………………………. 70 5.20. Hunting with large step size ∆ ………………………………………. 70 5.21. Hunting with smaller step size ∆/2 ………………………………….. 71 5.22. MPP scanning direction ……………………………………………… 72 5.23. Locking on the MPP with duty-cycle ratio 1/255 …………………… 72 5.24. Scanning in case of varying weather conditions …………………….. 73 6.1. I-V characteristic curves for different Insolation levels ……………… 75 6.2. P-V characteristic curves for different Insolation levels …………….. 75 6.3. I-V characteristic curves for different temperatures …………………. 76 6.4. P-V characteristic curves for different temperatures ………………… 76 6.5. Load circuit schematic diagram ……………………………………… 77
xiv
6.6. PV characteristic curves under different Insolation levels …………. 77 6.7. Characteristic curves of the 'BP 380' PV module using the load circuit 78 6.8. Characteristic curves of the 'BP 380' module using the Simulink model 78 6.9. MPPT Simulink Model ………………………………………………... 79 6.10. P-V characteristic curve of the PV array at 800W/m2, 27oC …………. 79 6.11. Switching Power, Voltage, and Current supplied to the converter …… 80 6.12. Power, Voltage, and Current delivered to the battery ………………… 80 6.13. Characteristic curves: (a) I-V curve, (b) P-V curve ………………….. 81 6.14. VB performance monitor ……………………………………………. 82 6.15 Tracking the MPP in case of varying Insolation level ………………. 84 6.16 Tracking scheme for minor change in the weather conditions ………. 86 6.17 Tracking scheme for major change in the weather conditions ………. 88 6.18 Primary winding current waveform…………………………………… 90 6.19 Waveforms across the terminals of the transformer ………………… 90 6.20. Diodes’ current waveform during different intervals ………………… 91 6.21. Transformer windings contribution to power loss …………………… 92
xv
TABLES Table Page 6.1. MPP readings on a sunny day in October……........................................ 81
6.2. Snapshots of MPP Recorded Data............................................................ 83
6.3. MPP Daily Average Recorded Data 2004…............................................ 83
6.4. Tracking with adaptive incremental step ∆a ………………………..…….. 87
6.5. Scanning with adaptive incremental step ∆a ………………………..…….. 88
6.6. Power Budget……………………........................................................... 93
To My Family …..
AND
To All Palestinians Who Struggle For Freedom!
CHAPTER 1
INTRODUCTION
1.1. An Overview
As green house effects and environmental issues become more of a concern,
renewable energy is one of the options in reducing pollution. Furthermore, fossil fuel
resources used in the production of power are dwindling and becoming more expensive;
‘Renewable Energy’ is the new trend in energy production to reduce emission in the
long run. This includes power generated from water, wind, solar radiation, biomass and
other resources. These resources are considered to be clean and continuously found in
nature.
PV modules used to be expensive, but in recent years, their price has been
slowly dropping, and as they become increasingly economical, they will be used in
more applications. In the U.S. the cost of installing solar had fallen from $55 per peak
watt in 1976 to about $4 per peak watt in 2001 [1]. PV modules output efficiency has
also increased in recent years. PV cells, having power conversion efficiencies as high as
31%, have been developed in a laboratory environment over the last decade [2]. With
these growths in photovoltaic technology, there is no doubt that PV will have a good
stand in the near future. However in this thesis, the emphasis is on the study of PV
system control part.
1.2. Brief Background
The world trend nowadays is to find a non-depletable and clean source of
energy. The most effective and harmless energy source is probably solar energy, which
1
for many applications is so technically straightforward to use. Use of solar energy
instead of fuel combustion, particularly for simple application like low and medium
temperature water heating and for stand alone PV systems in rural areas, can reduce the
load on the environment.
Solar energy for electricity generation can be harvested by the use of
photovoltaic (PV) array, which has an optimum operating point called the maximum
power point (MPP) as shown in Fig. 1.1. This MPP varies depending on cell
temperature and the present insolation level [3]. To get the maximum power from the
PV, a maximum power point tracker (MPPT) must be used.
Fig. 1.1 (a) The I-V characteristic curve, (b) The PV panel Maximum Power Point
1.3. Problem Definition and Motivation
Several maximum power point tracker (MPPT) algorithms are implemented to
track this MPP, yet many research works to implement a low-cost highly efficient
MPPT algorithm are being conducted. This algorithm should respond in a short time to
the change in the atmospheric conditions to avoid energy loss. Moreover it should not
2
be stuck in local power peaks if any; this happens in case of partial shadowing or dust
on the PV panel.
Furthermore, the converter has to be very efficient, in order to transfer more
energy to the load. This is achieved by using a simple soft-switched topology. Much
higher conversion efficiency at lower cost will then result, making the MPPT an
affordable solution for small PV energy systems.
1.4. Scope
The objective of this thesis is to design and build an experimental model,
develop a Simulink model of a stand-alone photovoltaic system with an MPPT
controller, and to analyze its operation.
Chapter 2 reviews the various literature of maximum power point tracking
algorithms. Perturb and Observe, Incremental conductance, Constant reference voltage
and other algorithms are presented in this chapter.
Chapter 3 will highlight the equations that are needed to implement the MPPT
system. PV cells electrical representation and current-voltage relation, Lead acid battery
chemistry and hazards, and dc-dc converters are presented in this chapter.
Chapter 4 and Chapter 5 show the Simulink block and the experimental model
that were implemented. Chapter 6 will discuss the simulated and experimental results.
In this chapter the hardware model data for changing weather conditions are evaluated.
Chapter 7 will conclude the thesis and will look on the future development of
the thesis. References and appendices are attached at the end of this thesis report.
3
4
CHAPTER 2
LITERATURE REVIEW
2.1. Maximum Power Point Tracker
Solar energy can be harvested by the use of a photovoltaic (PV) array, which
has an optimum operating point called the maximum power point (MPP) as shown in
Fig. 1.1(b). The I-V curve will change as the temperature and insolation levels change
as shown in Fig. 2.1, thus the MPP will vary accordingly [4]. So we need to control
either the operating voltage or the current to get maximum power from the PV panel at
the prevailing temperature and insolation conditions using a maximum power point
tracker (MPPT) which should meet the following conditions [5]:
• Operate the PV system as close as possible to the MPP irrespective of the
atmospheric changes.
• Have low cost and high conversion efficiency.
• Provide an output interface compatible with the battery-charging
requirement.
Fig. 2.1 (a) PV panel Insolation characteristics (b) PV panel Temp characteristics [4]
5
The MPPT consists of two basic components: a switched-mode dc-dc converter
and a controller.
2.2. Switched-mode dc-dc converter
The origins of switched-mode converters are linked with the developments in
inverter circuitry. An inverter is a processor for generating AC from DC and is,
therefore, a constituent of some forms of switched-mode power supplies. The DC-DC
converter will change the energy at one potential, stored as magnetic energy in an
inductor, to another potential. Different topologies can be used to construct DC-DC
converters: step down converter (buck converter), step up converter (boost converter),
or a combination of both step up- step down converter (buck-boost converter). The
converter in MPPT will adjust the PV array output voltage to the battery voltage while
driving the PV panel at its MPP.
2.3. Controller
The controller should keep testing if the PV system is operating at the PV
maximum power point; it should force the system to track this MPP. This could be done
by continuously measuring the voltage and current from the PV array, and then
performing either voltage or power feedback control [6].
2.3.1 Voltage feedback control
The control variable here is the PV array terminal voltage. The controller
forces the PV array to operate at its MPP by changing the array terminal voltage.
6
However it has a major drawback where it neglects the variation in the temperature and
insolation level [6, 7].
2.3.2 Power feedback control
The control variable here is the power delivered to the load. To achieve
maximum power the quantity dvdp is forced to zero. This control scheme is not
affected by the characteristics of the PV array, yet it maximizes power to the load and
not power from the PV array [6, 7].
2.4. MPPT controller Algorithms
Several algorithms were proposed to accomplish MPPT controller. Published
MPPT methods include: (1) Perturb and Observe (PAO) [3], (2) Incremental
Conductance Technique (ICT) [3], and (3) Constant Reference Voltage/Current [3, 5].
2.4.1. Perturb and Observe (PAO)
The Perturb and Observe method has a simple feedback structure and few
measured parameters. It operates by periodically perturbing (i.e. incrementing or
decrementing) the duty cycle controlling the array current as shown in Fig. 2.2 and
comparing the PV output power with that of the previous perturbation cycle. If the
perturbation leads to an increase (or decrease) in array power, the subsequent
perturbation is made in the same (or opposite) direction. In this manner, the peak power
tracker continuously seeks the peak power condition. The flow chart for this algorithm
will be discussed in chapters 4 and 5.
7
Fig. 2.2 PAO technique [5]
The PAO technique is easily implemented, costs the least among the other
available techniques, and is considered to be a very efficient scheme in terms of power
being extracted from the PV array [8]. However the PAO technique will be tricked in
catching the MPP under rapid varying solar radiation [3]. If the Insolation level
increases (I2 > I1) then the controller will assume that the incremental step should keep
moving in the same direction toward point when the new MPP is really in the other
direction at point as shown in Fig. 2.3 [3]. So for the PAO algorithm, the power
has increased because the new MPP is toward the right whereas it has already been
passed at point . In the following perturbation the PAO algorithm will increment
the array operating voltage further right, point . In this way the PAO algorithm will
continue to deviate from the actual MPP, with a corresponding power loss, until the
solar radiation change slows or settles down. [3]
8
Fig. 2.3 Deviation of the PAO technique from the MPP [3]
2.4.2. Incremental Conductance Technique (ICT)
The basic idea is that the derivative of the power with respect to the voltage
( dvdp ) vanishes at the MPP since it is the maximum point on the curve as shown in
Fig. 2.4. It is also noticeable from Fig. 2.4 that to the right of the MPP the derivative is
decreasing while to the left of the MPP it is increasing.
Fig. 2.4 The slope ‘conductance’ of the P-V curve [9]
9
Furthermore the derivative dvdp can be written as:
dVdP = dVVId ).( = I + V VddI ; where ∆G = VddI is the incremental
conductance.
Hence: (V1 ) dVdP =
VI + VddI ; where G =
VI is the source conductance.
So at the MPP ( dvdp =0), we get VddI = V
I− i.e. G = - ∆G.
The ICT algorithm checks for MPP by comparing VddI againstV
I− till it
reaches the voltage operating point at which the incremental conductance is equal to the
source conductance [3, 10]. The flow chart for the ICT algorithm is shown in Fig. 2.5.
Fig. 2.5 Flow chart of the ICT algorithm [3]
10
The algorithm starts by obtaining the present values of I and V, then using the
corresponding values stored at the end of the preceding cycle, Ib and Vb, the incremental
changes are approximated as: dI = I – Ib, and dV =V - Vb and according to the result of
this check, the control reference signal Vref will be adjusted in order to move the array
voltage towards the MPP voltage. At the MPP, VddI = V
I− , no control action is
needed, therefore the adjustment stage will be bypassed and the algorithm will update
the stored parameters at the end of the cycle as usual. Another check is included in the
algorithm to detect whether a control action is required when the array was operating at
the previous cycle MPP (dV = 0); in this case the change in weather condition will be
detected using (dI ≠ 0) [3].
This technique offers good performance under varying atmospheric conditions
contrary to the PAO technique. However it requires complete mathematical model for
the topology used and its complex circuitry adds to the cost of the MPPT controller [9].
2.4.3. Constant Reference Voltage
One very common MPPT technique is to compare the PV array voltage (or
current) with a constant reference voltage (or current), which corresponds to the PV
voltage (or current) at the maximum power point, under specific atmospheric conditions
Fig. 2.6. The resulting difference signal (error signal) is used to drive a power
conditioner, which interfaces the PV array to the load. Although the implementation of
this method is simple, the method itself is not very accurate, since it does not take into
account the effects of temperature and irradiation variations [5].
11
Fig. 2.6 MPPT control system with constant voltage reference [5]
2.4.4. Other techniques
Other techniques exist such as current-based maximum power point tracker
‘CMPPT’ and voltage-based maximum power point tracker ‘VMPPT’ [9]. Employed
numerical methods show a linear dependence between the “cell currents corresponding
to maximum power” and the “cell-short circuit currents”. The current IMPP operating at
the MPP is calculated using the following equation:
IMPP = MC ISC (2.1)
where MC is called the ‘current factor’ and differs from one panel to another. This factor
MC differs from one panel to another and is affected by the panel surface conditions,
especially if partial shading covers the panel [11].
Similarly the MPP operating voltage is calculated directly from VOC:
VMPP = MV VOC (2.2)
where MV is the ‘voltage factor’.
The open circuit voltage VOC is sampled by analogue sampler, and then VMPP is
calculated by equation (2.2). This operating VMPP voltage is the reference voltage for the
voltage control loop as shown in Fig. 2.6. This method always, “results in a
12
considerable power error because the output voltage of the PV module only follows the
unchanged reference voltage during one sampling period” [12].
Fig. 2.7 The conventional MPPT controller using open circuit voltage Voc [12]
Others argue that these two techniques are considered to be “fast, practical,
and powerful methods for MPP estimation of PV generators under all insolation and
temperature conditions” [13].
2.5. Comparative Study
A comprehensive experimental comparison between different MPPT
algorithms was prepared at South Dakota State University [14]. After presenting the
advantages and disadvantages of each algorithm, an experiment for the same PV array
setup was run. Results showed that the ICT method has the highest efficiency (98%) in
terms of power extracted from the PV array, next is the PAO technique efficiency
(96.5%), and finally the Constant Voltage method efficiency (88%).
Although the ICT method offers good performance under rapidly changing weather
conditions and seems to provide the highest tracking efficiency, four sensors are
required to perform the measurements for computations and decision making [3]. If the
system requires more conversion time in tracking the MPP, a large amount of power
loss will occur [6]. On the contrary, if the sampling and execution speed of the
13
perturbation and observation method is increased, then the system loss will be reduced.
Moreover, this method only needs two sensors, which results in the reduction of
hardware requirement and cost. Thus, the complexity of the ICT algorithm and the
increased cost of its circuitry, “encourage all to implement the PAO technique” [14].
2.6 Contribution of this Thesis
In this thesis, a hardware MPPT system and a Simulink MPPT model are
designed and tested for different PAO algorithms. The conventional PAO algorithm is
enhanced in a way to overcome the loss in the solar power tracking efficiency
associated with being misled by the scanning direction under rapidly varying weather
conditions. So an adaptive PAO algorithm, which forces the system to respond faster to
any changes in the insolation level irrespective of where the previous operating point
MPP was and without deteriorating the tracking efficiency, is implemented. Chapter 5
discusses the implementation of this algorithm.
14
CHAPTER 3
SYSTEM COMPONENT MODELING
3.1. Photovoltaic
The word photovoltaic is a combination of the Greek word for light and the
name of the Italian physicist Alessandro Volta. It refers to the direct conversion of
sunlight into energy by means of solar cells. The conversion process is based on the
photoelectric effect discovered by Alexander Becquerel in 1839.
3.1.1. Solar Cells
A solar cell is a device that uses the photoelectric effect to generate electricity
from light. Over 95% of all the solar cells produced worldwide are composed of the
semiconductor material Silicon (Si) with efficiency up to about 17% [15]. However
solar cells, having power conversion efficiencies as high as 31%, have been developed
over the last decade in laboratory environment [2]. It consists of a moderately p-doped
base substrate and a thin heavily n-doped top layer. Thin metal contacts on the surface
and a plain metal layer on the back connect this photovoltaic element to the load as
shown in Fig. 3.1.
Fig. 3.1 The PV cell [16]
15
3.1.2. Photovoltaic Effect
The photovoltaic effect is a basic physical process through which a PV cell
converts sunlight into electricity. Sunlight is composed of photon-packets of solar
energy, which contain different amounts of energy that correspond to different
wavelengths of the solar spectrum. When photons strike a PV cell, they may be
reflected or absorbed, or they may pass right through. Absorbed photons, with energy
greater than the band-gap energy of the semiconductor, generate electron-hole pairs.
The created charge carriers in the depletion region are separated by the existing electric
field. This leads to a forward bias of the p-n junction and builds up a voltage potential.
When a load is connected to the cell, this voltage will cause a current to flow through
the load.
3.1.3. Electric Model of the PV cell
A solar cell equivalent electrical circuit can be represented by a current source
in parallel with a diode as shown in Fig. 3.2. This is a simplified PV model where the
shunt resistance Rsh is neglected [17].
Fig. 3.2: Model for a PV cell [17]
16
The model contains a photocurrent source Iph, one diode and a series resistance RS,
which represents the series resistance inside each cell.
Thus the Load current IL is the difference between the photocurrent Iph and the
normal diode current ID.
IL = Iph - ID = Iph – I0 (expmkT
RIVq SL )( +- 1) (3.1)
Iph = Iph(T1) (1 + K0 (T – T1)) (3.2)
Iph(T1) = G * Isc(T1,nom) / G(nom) (3.3)
K0 = (Isc(T2) - Isc(T1)) / (T2 -T1) (3.4)
I0 = I0(T1) * (T/T1)3/n * e-qVg / nk * (1/T – 1/T1) (3.5)
I0(T1) = Isc(T1) / (e-qVoc(T1) / nkT1 – 1) (3.6)
Where m is the ideality factor (ranges between 1 and 2), k is the Boltzmann’s
constant, T is the absolute temperature of the cell, q is the electronic charge and V is the
voltage across the cell. I0 is the dark saturation current and it depends on the
temperature, G is the Insolation level, K0 is the temperature coefficient at Isc, Vg is the
band gap voltage and T1 is a reference temperature supplied by the manufacturer [18].
The most important parameters for PV cells are the short circuit current 'ISC',
the open-circuit voltage 'VOC', and the maximum power point 'MPP'. The short circuit
current (Isc ≈ Iph) is the greatest current value generated by the cell under short circuit
conditions (V=0). The open circuit voltage (VOC), is the voltage across the p-n
junction/diode when IL=0 and when ID = Iph. It represents the voltage of the cell when it
17
is in the dark. The maximum power point (MPP) is the point on the (I-V) characteristic
curve of a PV cell, where power is maximum, as shown earlier in Fig. 1.1.
3.1.4. Irradiation and Cell Temperature Effect on the I-V characteristic curve
Using equation (3.1), we can draw the (I-V) characteristic curves for different
irradiation levels and for different temperature values as shown in Fig. 3.3. It can be
easily interpreted that the open circuit voltage increases logarithmically while the short
circuit current increase linearly as the insolation level increases [18]. Also increasing
the cell’s temperature, decrease the open circuit voltage, thus the cell is less efficient in
terms of power level. The short circuit current increases slightly with cell temperature.
Fig. 3.3 (a) Effect of Varied Irradiation, (b) Effect of Varied Temperature on the PV cell
18
3.1.5. PV Modules and PV Arrays
Single PV cells are combined into PV modules that are usually supplied with
NP parallel branches each with NS solar cells in series as shown in Fig. 3.4 (a). Yet in
photovoltaic energy systems PV modules are connected in arrays. Fig. 3.4 (b) shows an
array of the modules with MP parallel branches each with MS modules in series.
Fig. 3.4 (a) PV Module, (b) PV Array [18]
3.2. Battery
The purpose of a battery is to store chemical energy and to convert this
chemical energy into electrical energy when the need arises. Batteries are divided in two
ways, by application (what they are used for) and construction (how they are built). The
major applications are automotive, marine, and deep-cycle. The major construction
types are flooded (wet), gelled, and AGM (Absorbed Glass Mat). In solar systems it is
19
important to note that nearly all of the batteries commonly used are deep cycle Lead-
Acid batteries [19].
3.2.1. Lead Acid Batteries
A lead-acid battery is an electrical storage device that uses a reversible
chemical reaction to store energy. It uses a combination of lead plates or grids and an
electrolyte consisting of a diluted sulfuric acid to convert electrical energy into potential
chemical energy and back again. A battery consists of a series of cells where each cell
provides about two volts. Connected in series, these cells will provide the desired
battery output voltage.
3.2.2. Battery Chemistry
A voltaic cell develops a potential difference when electrodes of two different
metals are immersed in an electrolyte. One electrode accumulates a positive charge
while the other accumulates negative charge. The potential difference is due to the
difference in charge between the two electrodes [20].
The chemical equation for a lead-acid battery during discharge is:
PbO2 + Pb + 2H2SO4 discharge → 2PbSO4 + 2H2O
The chemical equation for a lead-acid battery during charge is:
PbO2 + Pb + 2H2SO4 charge ← 2PbSO4 + 2H2O
The lead-acid battery uses dilute sulfuric acid for the electrolyte, lead for the
anode, and lead oxide, PbO2, for the cathode. The sulfuric acid dissociates into
hydrogen and sulfate ions. The sulfate ion reacts with the lead anode to form lead
sulfate and releases two electrons through the external circuit. This is the oxidation
20
reaction. At the cathode, the two electrons cause a reaction to create lead sulfate and
water. This is the reduction reaction. The half-cell reactions are:
Pb + SO42-=PbSO4
2- (sol) + 2 e-
PbO2 + 4 H+ + 2 e- + SO42-=PbSO4
2- (sol)
At full discharge, both anode and cathode are covered with lead sulfate, and the
electrolyte is mostly water. Reversing the current flow reverses the reactions, recharging
the battery.
3.2.3. Ampere-Hour Capacity and Charge Rate
The Ampere-hour (Ah) Capacity of a battery tries to quantify the amount of
usable energy it can store at a nominal voltage. All deep cycle batteries are rated in
ampere-hours. An ampere-hour is one ampere for one hour, or 10 A for 1/10 of an hour
and so forth [21]. A good charge rate is approximately 10% of the total capacity (of the
battery) per hour (i.e. 200 amp hour battery charged at 20 amps.) This will reduce
electrolyte loss and damage to the plates. [20]
3.2.4. State of Charge
The State of Charge describes how full a battery is. This can be determined by
one of three ways:
• Voltage measurement, for a battery at 'rest' this method can show the state
of charge by comparing the voltage to a chart showing the percentage of charge relative
to voltage.
21
• Electrolyte density measurement, a sample of the electrolyte is drawn into a
hydrometer, which shows the density of the liquid. The heavier the electrolyte (higher
gravity), the more acid in solution, the higher the state of charge.
• Ampere-hour metering, this method uses an ampere-hour meter, which is set
using the specifications of a new battery at full charge. It measures and records power
going into and coming out of the battery and keeps an electronic balance sheet.
3.2.5. Deep Cycle versus Starter Batteries
Batteries are typically built for specific purposes and they differ in construction
accordingly. Broadly speaking, there are two applications that manufacturers build their
batteries for: Starting and Deep Cycle discharge.
As the name implies, Starter Batteries are meant to get combustion engines
going. They have many thin lead plates, which allow them to discharge a lot of energy
very quickly for a short amount of time. However, they do not tolerate being discharged
deeply, as the thin lead plates needed for starter currents degrade quickly under deep
discharge and re-charging cycles. Most starter batteries will only tolerate being
completely discharged a few times before being irreversibly damaged.
Deep Cycle batteries have thicker lead plates that make them tolerate deep
discharges better (in many cases down to 20% of capacity). They cannot dispense
charge as quickly as a starter battery but can also be used to start combustion engines..
The thicker the lead plates, the longer the life span, all other things being equal. Battery
weight is a simple indicator for the thickness of the lead plates used in a battery. The
heavier a battery for a given group size, the thicker the plates, and the better the battery
will tolerate deep discharges. [20]
22
3.2.6. Lifespan of Batteries
The lifespan of a battery will vary considerably with how it is used, how it is
maintained and charged, temperature, and other factors. Battery manufacturers define
the end-of-life of a battery when it can no longer hold a proper charge (for example, a
cell has shorted) or when the available battery capacity is 80% or less than what the
battery was rated for. The life of Lead Acid batteries is usually limited by several
factors:
Cycle Life is a measure of how many charge and discharge cycles a battery can
take before its lead-plate grids/plates are expected to collapse and short out. Moreover
the greater the average depth-of-discharge, the shorter the cycle life [20].
Age also affects batteries as the chemistry inside them attacks the lead plates.
The healthier the "living conditions" of the batteries, the longer they will serve you.
Lead-Acid batteries like to be kept at a full charge in a cool place.
Sulfation is a constant threat to batteries that are not fully re-charged. A layer
of lead sulfate can form in these cells and inhibit the electro-chemical reaction that
allows you to charge/discharge batteries.
3.2.7. Battery Hazards
Both electrodes dissolve into the electrolyte during the discharge reaction.
When charged the reverse reactions occur. Overcharge will lead to the electrolysis of
water and consequent production of (hazardous) H2 (gas) at the cathode. Precautions
must be routinely practiced to prevent explosions from ignition of the flammable gas
mixture of hydrogen and oxygen formed during overcharge of lead-acid cells.
23
3.3. DC-DC Converters
A DC-to-DC converter is a device that accepts a DC input voltage and
produces a DC output voltage, which is at a different voltage level than the input. DC-
DC converters are widely used in regulated switch-mode dc power supplies and in dc-
motor drive applications. These converters are usually used with an electrical isolation
transformer in the switch mode dc power supply, and without an isolation transformer
in case of dc-motor drive [22].
3.3.1. Switching Converter Topologies
Topology refers to the various configurations of power-switching and energy-
storage elements that can be used to transfer, control and regulate power (voltage) from
an input voltage source. The many different switching-regulator topologies can be
grouped into two basic categories: non-isolated, in which the input source and the
output load share a common current path during operation, and isolated, in which the
energy transfer is achieved by a mutually-coupled magnetic element (a transformer),
and the coupling from the source to the load is achieved by means of a magnetic flux
rather than a common current. One topology is selected over another based upon the
cost goals, performance objectives and input-line/output-load characteristics of the
system in which it is to operate. Any one topology is not “better” than another in all
respects. Each has desirable characteristics and shortcomings, and selection is a matter
of properly applying the correct power converter to the system requirement.
24
3.3.2. Non-Isolated Switching Converters
There are four, non-isolated, switching-regulator topologies applicable to
modular DC/DC converters. They are the buck, or step-down converter, the boost, or
step-up converter, the buck-boost converter, and the Cuk converter.
3.3.2.1. Buck Converter (step-down converter)
As the name implies, a step-down converter produces a lower average output
voltage than the dc input voltage. Its operation is straightforward. When the switch Tr,
in Fig. 3.5, is turned on, the input voltage is applied to inductor L and power is
delivered to the output. This voltage will tend to cause the inductor current to rise.
When the switch Tr is OFF, the current will continue flowing through the inductor L but
now flowing through the diode.
Fig. 3.5 Buck Converter
To analyze the voltages of this circuit let us consider the changes in the
inductor current over one cycle as shown in Fig. 3.6.
25
Fig. 3.6 Voltage and current changes [22]
The voltage across the inductor shown in Fig. 3.5 is given by
dtdiLVV ox =− (3.8)
the change of current satisfies
( )⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
∫ −= dtI
IVoVx
Ldi
2
1
1 (3.9)
For steady state operation the current at the start and end of a period T will not
change. To get a simple relation between voltages we assume no voltage drop across
transistor Tr or diode while ON and a perfect switch change. Thus during the ON time
Vx=Vin and in the OFF period Vx=0. Thus
26
dtoVdtoVinVdiofftont
ont
ont∫ −+−∫==
+
)()(00
(3.10)
which simplifies into
Tont
inVoV
= where T = ton + toff (3.11)
Defining "duty cycle" as
Tont
D = (3.12)
the input-output voltage relationship becomes
Vo=D Vin (3.13)
Since the circuit is lossless and the input and output powers must match on the
average (Vo* Io = Vin* Iin). Thus the average input and output current must satisfy
Iin =D Io (3.14)
These relations are based on the assumption that the inductor current does not
reach zero.
• Discontinuous-Conduction Mode
Thus, the buck is a step-down type, where the output voltage is always lower
than the input (Since D never reaches one). Varying the duty cycle of the switch
provides output voltage regulation. The LC arrangement provides very effective
filtering of the inductor current. Hence, the buck and its derivatives all have very low
output ripple characteristics. The buck is normally always operated in continuous mode
(inductor current never falls to zero) where peak currents are lower as shown in Fig. 3.7,
27
and the smoothing capacitor requirements are smaller. There are no major control
problems with the continuous mode buck.
Fig. 3.7 Inductor current for (a): continuous mode (b): discontinuous mode [22]
• Boundary Between Continuous and Discontinuous Conduction
When the current in the inductor L remains always positive then either the
transistor Tr or the diode D must be conducting. For continuous conduction the voltage
Vx is either Vin or 0. If the inductor current ever goes to zero then the output voltage will
not be forced to either of these conditions. At this transition point the current just
reaches zero as seen in Fig. 3.8.
28
Fig. 3.8 Buck Converter at Boundary
During the ON time Vin-Vo is across the inductor thus
Lt
VVI onOinL peak ).()( −= (3.15)
The average current, which must match the output current, satisfies
)(2
)(2
)()( transition
peakaverage outoin
LL I
LdTVVII =−== (3.16)
If the input voltage is constant the output current at the transition point satisfies
TL
ddVI inout transition2
)1()( −= (3.17)
• Voltage Ratio of Buck Converter (Discontinuous Mode)
As for the continuous conduction analysis, the fact that the integral of voltage
across the inductor is zero over a cycle of switching T is used. The transistor OFF time
is now divided into segments of diode conduction δdT and zero conduction δoT as shown
in Fig. 3.9. [22]
29
Fig. 3.9 Buck Converter - Discontinuous Conduction
The inductor average voltage thus gives:
0)()( =−+− TVDTVV dooin δ (3.18)
Then
din
o
dd
VV
δ+= where 1<+ dd δ (3.19)
To resolve the value of dδ consider the output current which is half the peak
when averaged over the conduction times dd δ+ .
dL
out dI
Ipeak
δ+=2
)( (3.20)
Considering the change of current during the diode conduction time
LTV
I doL peak
)()(
δ= (3.21)
30
Thus from equations (3.20) and (3.21) we can get
LdTV
I ddoout 2
)( δδ += (3.22)
using the relationship in (3.19)
LTdV
I dinout 2
δ= (3.23)
and solving for the diode conduction
dTVLI
in
outd
2=δ (3.24)
The output voltage is thus given as
)2
(2
2
TVLI
d
dVV
in
outin
out
+= (3.25)
defining k = 2L/(Vin T), we can see the effect of discontinuous current on the voltage
ratio of the converter.
31
Fig. 3.10 Output Voltage versus Current [22]
As seen in Fig. 3.10 once the output current is high enough, the voltage ratio
depends only on the duty ratio "d". At low currents the discontinuous operation tends to
increase the output voltage of the converter towards Vin.
• Output Voltage Ripple
For continuous mode of operation the output ripple voltage can be calculated
by considering the waveform in Fig. 3.11. Assuming that the entire ripple component in
iL flows through the capacitor and its average component flows through the load
resistor, the shaded area in Fig. 3.11 represents an additional charge ∆Q. Therefore, the
peak-to-peak voltage ripple ∆Vo can be written as:
∆Vo = 222
11 TICC
Q L ⋅∆
=⋅=∆ (3.26)
32
Fig. 3.11 Output voltage ripple in a step-down converter [22]
From Fig. (7) during toff
TDL
VI L )1(0 −=∆ (3.27)
Then substituting ∆IL from Eq. 20 into previous equation, we get:
TDL
VCTV )1(
80
0 −=∆ (3.28)
222
0
0 )1(2
)1(81
⎟⎟⎠
⎞⎜⎜⎝
⎛−=
−=
∆∴
ff
DLC
DTVV cπ (3.29)
where, f = 1/T is the switching frequency and LC
fc π21
= .
33
3.3.2.2. Boost Converter (step-up converter)
The schematic in Fig. 3.12 shows the basic boost converter. This circuit is used
when the output voltage is required to be higher than the input..
Fig. 3.12 Boost Converter Circuit
While the switch Tr is ON then Vx =Vin, and in the OFF state the inductor
current flows through the diode giving Vx =Vo. For this analysis it is assumed that the
inductor current always remains flowing (continuous conduction). The voltage across
the inductor is shown in Fig. 3.13 and the average must be zero for the average current
to remain in steady state.
Fig. 3.13 Voltage and current waveforms (Boost Converter).
34
Thus
0)( =−+ offtoVinVontinV (3.30)
This can be rearranged as
)1(1
DofftT
inVoV
−== (3.31)
and for a lossless circuit the power balance ensures
)1( DinIoI
−= (3.32)
Since the duty ratio "D" is between 0 and 1 the output voltage must always be
higher than the input voltage in magnitude. The negative sign indicates a reversal of
sense of the output voltage.
3.3.2.3. Buck-Boost Converter
A buck-boost converter can be obtained by cascading the step-down converter
and the step-up converter. The cascade connection can be combined into the topology of
the buck-boost converter using a single switch as shown in Fig. 3.14.
Fig. 3.14 schematic for buck-boost converter
35
With continuous conduction for the Buck-Boost converter Vx =Vin when the
transistor is ON and Vx =Vo when the switch (Tr) is OFF. For zero net current change
over a period the average voltage across the inductor is zero as shown in Fig. 3.15.
Thus:
0=+ offtoVontinV (3.33)
Fig. 3.15 Waveforms for buck-boost converter
Which gives the voltage ratio
DD
VV
in
o
−−=
1 (3.34)
and the corresponding current
DD
II
in
o −−=
1 (3.35)
Since the duty ratio "D" is between 0 and 1 the output voltage can vary
between lower or higher than the input voltage in magnitude. The negative sign
indicates a reversal of sense of the output voltage.
36
3.3.3. Isolated DC-DC Converters
In many DC-DC applications, multiple outputs are required and output
isolation may need to be implemented depending on the application. In addition, input
to output isolation may be required to meet safety standards and / or provide impedance
matching. There are several isolated switching converter topologies; however, three will
be discussed, which are the flyback, forward and H-bridge power converters. For these
circuits, all energy transfer from the input power source to the load is achieved via a
transformer or other flux-coupled magnetic element.
3.3.3.1. Flyback Converter
The flyback switching regulator converts an input voltage into a regulated,
lower or higher-valued output voltage depending on its transformer’s turns ratio. The
flyback converter can be developed as an extension of the Buck-Boost converter Fig.
3.14. A simplified circuit diagram is shown in Fig. 3.16.
Fig. 3.16 Flyback converter
Concerning the input-to-output transfer function, the on-time energy is given by:
Eon = (Vin / N) ton (3.36)
and the off-time energy is given by:
Eoff = (Vo) toff (3.37)
37
Where toff = T – ton and N is the transformer’s turns ratio.
Substituting yields:
(Vin /N) ton = Vo (T – ton) (3.38)
(VIN) ton = N Vo (T – ton) (3.39)
but
Vo = (Vin) ton /(N T – N ton) (3.40)
where
ton /T = D (3.41)
Vo /Vin = D / (N – N D) (3.42)
Vo / Vin = (1 / N) (D / (1 – D)) (3.43)
3.3.3.2. Forward Converter
The forward switching regulator converts an input voltage into a regulated,
lower or higher-valued output voltage depending on its transformer’s turns ratio. A
simplified circuit diagram is shown in Fig. 3.17.
Fig. 3.17 Forward Converter
In determining the input-to-output transfer function, the on-time energy is given by:
38
Eon = (Vin / N – Vo) ton, (3.44)
and the off-time energy is given by:
Eoff = (Vo) toff, (3.45)
where
toff = T – ton and N is the transformer’s turns ratio.
Substituting yields:
(Vin / N – Vo) ton = Vo (T – ton) (3.46)
Vo = (Vin / N)(ton / T) (3.47)
Vo / Vin = (1 / N) D (3.48)
3.3.3.3. H-bridge Converter
The H-bridge inverter changes a dc input voltage into a symmetrical ac output
voltage of desirable magnitude and frequency. The output voltage could be fixed or
variable at a fixed or variable frequency. A variable output voltage can be obtained by
varying the gain of the inverter, which is normally done by pulse-width-modulation
(PWM) control within the inverter. Then the rectifier, and filter circuit is used to extract
the average value (dc) of the voltage and current. A simplified circuit diagram is shown
in Fig. 3.18. When switches S1 and S4 are turned on simultaneously, the input voltage Vs
appears across the terminals (A & B) of the transformer T. If switches S2 and S3 are
turned on at the same time, the voltage VAB is reversed and is - Vs. The waveform for the
output voltage is shown in Fig. 3.19.
The rms output voltage can be found from:
39
Vo = s
T
s VdtVT
=⎟⎟
⎠
⎞
⎜⎜
⎝
⎛∫
2/1
0
2
0
02 (3.49)
Fig. 3.18 H-bridge Converter
Fig. 3.19 Waveforms
This type of converters was shown for the hardware design because it employs
electronic switches that are driven by square wave signals (50% duty cycle). This
40
permits good operation at high frequencies, avoiding problems that may arise when
using simple buck converter topology with variable duty cycle switching. This is
illustrated in Chapter 5, section 5.3.1.
3.4. Zero Voltage Switching
Switching frequencies in the megahertz range are being contemplated to reduce
the size and the weight of transformers and filter components and hence to reduce the
cost as well as the size and the weight of power electronics converters. Realistically, the
switching frequencies can be increased to such high values if the problems of switch
stresses, switching losses, and EMI associated with the switch-mode converters can be
overcome.
Therefore, to realize high switching frequencies in converters, the
aforementioned shortcomings are minimized if each switch in a converter changes its
status (from on to off and vice versa) when the voltage across it ‘Vs’ and/or the current
through it ‘is’ is zero at the switching instant. Otherwise power loss PS in the switch,
being proportional to the switching frequency limits how high the switching frequency
can be pushed, without significantly degrading the system efficiency. The power loss PS
in the switch during turn-off and turn-on is shown in Fig. 3.19.
Fig. 3.20 Power loss associated with high switching frequencies.
41
In these converters, the resonant capacitor Cr produces a zero voltage across
the switch at which instant the switch can be turned on or off. Such a step-down
converter circuit is shown in Fig. 3.20, where a diode Dr is connected in antiparallel
with the switch [22].
Fig. 3.21 ZVS resonant-switch dc-dc converter [22]
After implementing this type of ZVS buck converters in the hardware model,
the power electronics efficiency decreased severely. After all, the implemented system
switching frequency (40khz) is much less than megahertz and the resonant inductor Lr
added more power loss in the form of heat dissipation. So the resonant elements were
removed and an H-bridge converter was built. The H-bridge converter is discussed in
chapter 5.
CHAPTER 4
MPPT SYSTEM SIMULINK MODEL
4.1. Introduction
In this chapter, the mathematical models of the MPPT system implemented in
Simulink will be highlighted.
Simulink is a platform for multi-domain simulation and model-based design of
dynamic systems. It provides an interactive graphical environment and a customizable
set of block libraries that let you accurately design, simulate, implement, and test
control, signal processing, communications, power electronics and other time-varying
systems.
Simulink has an advantage when building hierarchical model system because
of the possibility to test the system at different levels. It also provides the possibility to
build modular models, which means that models can be easily connected to simulate
certain system.
4.2. Simulink Blocks
Simulink possesses a variety of block libraries to represent time varying
systems. However present Simulink libraries don’t include one for PV systems; there is
no solar cell equivalent block. However at one university, a PV toolbox with a PV
module, battery, and battery charge controller had been designed and is being tested
[20]. Fig. 4.1 shows the PV array MPPT system block that includes: PV cell block,
converter block, controller block and the battery load block.
42
In the next few sections, these blocks will be discussed individually. The
sections will investigate how the models are implemented.
Fig. 4.1 PV array 'MPPT' system
4.3. What is An S-Function
An S-Function is a mechanism that allows the user to implement Matlab source
code as a Simulink compatible block. The S-function block is always drawn with one
input port and one output port, regardless of the number of inputs and outputs of the
contained subsystem. To have access to more than one input and output through an s-
function block, a multiplexer and a de-multiplexer are respectively used as shown in
Fig. 4.2.
Fig. 4.2 S-Function block with three inputs and two outputs
43
4.4. Implementation of PV cell using S-Function
One can use the circuit model shown in Fig. 4.3 to represent the solar cell using
the 'SimPower System’ library, or can develop a solar cell block using S-function
Block.
Testing the circuit model during initialization, it was difficult to set Iph and ID
values with respect to varying Insolation and temperature values respectively. Moreover
during simulation, it was also difficult to control these two values while varying the
converter duty cycle using the circuit model.
Fig. 4.3 Model for a PV cell
So using the S-Function approach, a model for the PV cell was developed as
shown in Fig. 4.4. The inputs are the Insolation level (W/m2), the Temperature (oC), and
the current Iin (A) absorbed by the load. The code, implemented in the PV cell block,
defines the set of equation that describes the voltage and current relations as given in
Chapter 3. This code is given in Appendix A.
44
Fig. 4.4 PV Cell S-Function block
4.5. Converter and Controller Blocks
It was decided to use a buck converter as the integrated MPPT's converter. The
buck converter features "low ripple and switching device currents compared to other
converter topologies" [24]. The buck converter model is built using the 'SimPower
System' Simulink library as shown in Fig. 4.5. The power MOSFET is chosen as a
switching device since it has higher switching speed capabilities as compared to BJTs.
It has four pins, where the g pin represents the gate terminal, d the drain, and s the
source. The m pin is used for measurements so it is connected to a terminator box. The
diode model is selected from the Simulink power electronics library. A snubber
resistance (500 ohm), connected in parallel with the diode, is used to reduce the
switching current overshoots. The inductor that maintains current continuity is placed in
parallel with a 10-kΩ resistance to agree with the Simulink environment. The values of
the inductor 200µH and capacitor 220µF are calculated using equations 3.26 and 3.27.
The procedure, used to calculate these values, is present in Chapter 5
45
Fig. 4.5 Buck converter and Controller blocks
To complete the system, a model for the controller, to drive the switching
mechanism of the power MOSFET, was also developed as shown in Fig. 4.6. The PAO
control algorithm varies the duty cycle of the input current, supplied by the PV cell, to
allow the maximum power point (MPP) to be reached. Fig. 4.6 illustrates how the
controller system was built.
Fig. 4.6 Controller Block Implementation
The saw-tooth signal is compared to a controlled constant level with threshold
value k. This level value k will vary according to the algorithm implemented in the S-
function block named threshold level.
46
The PAO algorithm depends on the present value of the current I, and voltage
V, and on the previous value of the threshold value k, and the power Pr supplied by the
PV cell. The voltage V and current I are directly supplied to the 'threshold level' block
while the constant k and the power Pr values are passed first through a delay box,
present in the Simulink library and labeled withz
1, to supply their previous values to
the 'threshold level' block as shown in Fig. 4.6. If this delay box is not inserted, the
present value of the power (I.V) will be compared with itself instead of being compared
to the previous power Pr value.
The flow chart, describing the PAO tracking algorithm implemented in the S-
function block named threshold level, is shown in Fig. 4.7. If the present value of the
power P(n) is greater than the previous value P(n-1), then the threshold value k is
incremented by an incremental step delta; this means that the duty cycle of the
rectangular signal is increased. Otherwise the threshold value k is decremented by delta;
this means that the duty cycle d of the rectangular signal is decreased.
Fig. 4.7 MPP tracking algorithm Flow Chart
47
Moreover as the duty cycle d increases, then the average current Iavg increases and vice
versa. This is illustrated in Fig. 4.8 where the level value k2 is larger than k1, thus the
duty cycle d2 is larger than d3. Therefore the average current Iavg2 is greater than Iavg1.
The algorithm will keep changing the duty cycle until the MPP is reached. The matlab
code for this algorithm is given in Appendix A.
Fig. 4.8 Different current levels with respect to variable duty cycle
To illustrate more on the PAO algorithm, consider the tracking scheme
presented in Fig. 4.9. The algorithm starts hunting for the maximum power point by
changing the duty cycle d in a series of relatively large steps ∆. After each new step, it
measures the voltage Vs and current Is, multiplies their values, and compares the newly
obtained power level Pn with the former value Pn-1. Two cases may arise as a result of
this comparison:
• If the newly obtained power Pn is larger, the algorithm continues changing
the duty cycle d monotonically in the same direction, using the same step size delta (∆).
• If the newly obtained power Pn is lower, the algorithm reverses the direction
of changing the duty cycle d, and divides the step size delta by two )(2∆ .
48
Eventually, the algorithm will reach a stage in its search for the maximum power point,
where it jumps around the maximum power point in very fine steps. The algorithm
should keep scanning, since the MPP is expected to vary due to changes of illumination
and temperature depending on daytime, weather conditions, and shadow effects.
Fig. 4.9. MPPT tracking scheme using a variable step size
4.6. Battery Block
The load, in our case a battery, is approximated by a dc voltage source Vb in
series with a small resistance r. The dc voltage source Vb is set to 12V and the resistance
r is set to 0.01Ω as shown in Fig. 4.10. The battery output voltage Vout will increase as
more current passes through the resistance r.
49
Fig. 4.10 Battery Model Block
Thus the over all, maximum power point tracking (MPPT), system is shown in
Fig. 4.11. The Insolation value (1000 W/m2) and the temperature (22 oC) are introduced
as de-multiplexed inputs to the PV cell block using s-function constant value blocks.
Fig. 4.11 PV array 'MPPT' system
The current Iin is also fed as an input to the PV cell; the load nature will force a
current to flow through, after applying a voltage across the load. The current Iin is
passed first through a delay block to guarantee that the controller algorithm will
compare the present value of the power with that of the previous (delayed) power; else
the system simulation will not converge.
With these three inputs (In, T, Is), the PV cell block will supply the output
voltage Vs. The controller will force the buck converter to draw more current Iin from
50
the PV cell until the MPP is reached. This way the buck converter will charge the
battery with maximum, PV cell, available power.
51
52
CHAPTER 5
MPPT SYSTEM IMPLEMENTATION
5.1. Introduction
In this chapter, the hardware and software design of the MPPT system is
presented and discussed.
The system consists of a PV module, an H-bridge converter, a 12-volts lead
acid battery, and a control circuit that uses the PIC16F874 microcontroller. The
controller obtains the information (current and voltage) from the PV array through the
microcontroller’s analog and digital (A/D) ports. The microcontroller performs the
pulse width modulation (PWM) to the dc-dc converter through its PWM built-in special
register. It then finds the duty cycle at which the converter loads the PV module at the
maximum power point (MPP) when charging the battery. The battery’s state of charge
is also controlled by the microcontroller to protect the battery from being overcharged.
5.2. MPPT System
The complete solar MPPT system is shown in Fig. 5.1. However the most
critical section of the MPPT system is that of the controller and converter. The
controller should keep track and force the system to operate at the maximum power
point of the PV array as the weather conditions change. The dc-dc converter will charge
the battery with maximum power available so any resistance or loss in the converter
will contribute to power loss of the system.
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5.2.1. Microcontroller
PIC16F874 microcontroller is used in the control section. This microcontroller
is responsible for different tasks. The MPP tracking algorithm is implemented in the
microcontroller. So it computes where the MPP of the PV array is and accordingly
control the PWM scheme of the converter. It controls the A/D converter ports to
represent the analog voltage Vs and current Is of the PV array in digital format. It also
monitors the state of charge of the battery to prevent overcharge damage. The
PIC16F874 is a perfect combination of features, performance, and low power
consumption for this application. It has 4K x 14 bits of flash memory, 192 x 8 bytes of
data memory (RAM), two D/A and five A/D channels.
Fig. 5.1 The PV maximum power point tracking system
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5.2.2. PV Array to PIC Interface Circuit
The PV-PIC interface circuit shown in Fig. 5.1 provides the microcontroller
with appropriate voltages that it can endure. The PV output voltage Vs is fed to the
microcontroller using a voltage divider circuit. The current Is is fed to the
microcontroller after passing through a 0.01 ohm resistance rs to get a voltage
representation of the current. These analog voltages are fed to the microcontroller via
two built in A/D channels to represent digitally the voltage Vs and current Is of the PV
array.
5.2.3. H-bridge Converter
The converter transfers energy from the PV array to the battery by regulating its output
voltage to essentially match that of the battery. Since energy will flow in the converter,
resistance heat loss, and switching losses should be minimized. To reduce these loses an
H-bridge converter is used. The H-bridge reduces to and operates as a buck converter
during each half switching cycle [22]. The H-bridge is discussed in the Hardware
Design section.
5.2.4. PIC-Converter Interface Circuit
The PIC-Converter interface circuit is used to control the PWM scheme
needed to drive the dc-dc converter. This board will include a phase splitter and a driver
circuit that will provide the right signals to control the switching scheme of the bridge.
These signals should have the appropriate voltages to turn on or off the bridge switches.
55
5.3. Hardware Design
The schematics design and operation of the MPPT hardware system are
discussed in the following sections. The PCB layouts are given in Appendix B.
5.3.1. Controller and Converter Design
The H-bridge converter that was discussed in Chapter 3 (pp. XX) was
implemented as shown in Fig. 5.2. It employs electronic switches that are driven by
square wave signals (50% duty cycle). This permits good operation at high frequencies,
avoiding problems that may arise when using simple buck converter topology with
variable duty cycle switching; after all the switch may fail to turn off when the off time
Toff is small incase of a variable duty cycle switching as shown in Fig. 5.3 (b). Due to
the ideality of the components, a simple buck converter was used in the Simulink model
because the case where the switch fails to turn off does not exist.
Fig. 5.2 Converter and Controller
56
Fig. 5.3 (a) 50% duty cycle switching (b) variable duty cycle switching
The square wave signals that drive the bridge switches are phase-shifted by an
amount equal to the turn-on time of the PWM microcontroller’s output. The control of
the output voltage (V1 – V2) of this converter depends on controlling the phase
difference between the voltages V1 and V2. This difference (V1 – V2) is the output of the
switch bridge.
Fig. 5.4 shows the impact of phase difference between V1 and V2, on the
output of the bridge for a small and large phase difference. Fig. 5.5 and Fig. 5.6 show
the bridge output when the phase difference is zero and 180o respectively. However in
the software design, the duty cycle has an upper and lower limit as discussed later in the
Software Design section.
Fig. 5.4 Bridge output due to small and large phase difference
57
Fig. 5.5 Case of zero phase difference between V1 and V2
Fig. 5.6 Case of V1 and V2 being out of phase
A phase splitter circuit is designed to generate the phase difference between V1
and V2. This circuit is controlled by the width of the pulses generated by the PWM
output of the microcontroller. V1 changes (inverts) its value with each rising edge of the
PWM output (from 0 volts, to VDD). V2 changes its value to follow that of V1 with each
falling edge of the PWM output (from VDD to 0 volts). This causes the output of the
bridge to become nonzero with the rising edge of the micro-controller’s PWM output,
and zero with the falling edge. Fig. 5.7 below shows the relationship between the PWM
waveform, and the waveforms of V1 and V2.
58
Fig. 5.7 PWM output controls the Bridge output
The output of the bridge is then rectified and filtered to give as a final result, a
DC voltage that is directly proportional to the phase difference between V1 and V2
(subsequently proportional to the pulse width of the micro-controller’s PWM output).
Fig. 5.8 shows the relationships between these signals.
Fig. 5.8 PWM, Bridge, Rectified and Filtered voltage waveforms
59
5.3.2. Phase Splitter Circuit
The phase splitter circuit provides two outputs. The first output (Square wave
output A) changes with each rising edge of the micro-controller’s PWM output. The
second output (Square wave output B) changes with the falling edge of the PWM output
as shown in Fig. 5.9.
Fig. 5.9 Phase splitter output waveforms
To construct this circuit, two type–D edge–triggered flip–flops are used (7474).
One (FF1) is used to toggle with each rising edge of the PWM output, as shown below
in Fig. 5.10. The second (FF2) is forced to follow the change of the first with each
falling edge (rising edge of the inverted PWM wave). Changing the pulse width of the
PWM output changes the phase difference between the output A and the output B.
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Fig. 5.10 Phase splitter schematic diagram
5.3.3. Switch Drivers ‘A’ and ‘B’
The bridge consists of four switches T1, T2, T3, and T4. These switches are, in
fact, MOSFETs having high current handling capability (IRFZ46). To provide these
MOSFETs with the right signals to turn on or off, a driver circuit is designed.
T1 and T2 form a switch pair that controls the voltage V1 and are driven by the
driver circuit ‘A’. T3 and T4 switch pair similarly controls the voltage V2, and are driven
by the driver circuit ‘B’. The operation of the driver circuit A is next explained. The
operation of the driver circuit B will be similar to that of driver circuit A.
Fig. 5.11 Driver A output waveforms
61
Switches T1 and T2 are operated by anti–phase driving signals (when T1 is
closed, T2 is open and vice versa) as shown in Fig. 5.11. Furthermore, the anti – phase
signals should provide a dead – time interval during the transitions to permit the
complete turn OFF of the switch (that was ON), before turning ON the other switch;
this is necessary to avoid the flow of excessive currents in the transition interval, due to
both switches being ON at the same time as shown in Fig. 5.12.
Fig. 5.12 Driver ‘A’ schematic diagram
The driver circuit shown in Fig. 5.12 provides driving pulses to the gates of
transistors T1 and T2, with an amplitude of 12 volts to ensure the complete turn ON of
the switch that should be in the active mode (to have a low ON state resistance), and a
fast turn OFF of the switch that should be deactivated.
The comparators are used to convert the 5 volts logic levels (microcontroller
output) to the 12 volts logic levels used to drive the gates of the MOSFETs. The
MOSFETs are driven with two anti-phase signals. The 1 kΩ and the 1 nF capacitors are
62
used to delay the turn ON of each transistor, for an interval sufficient to make sure that
the other transistor reaches the OFF state, when turned OFF. The clearance interval
(dead time) is labeled by Td in Fig. 5.12. Quick turn OFF is achieved by rapidly
discharging the gate capacitance, and the 1nf capacitor, using a diode (D1 and D2) that
provides low resistance path for discharging current. Fig. 5.13 shows the details of
operation for the gate circuit.
The MOSFET will not turn ON, till the voltage between the gate and source
reaches the threshold value (about 3 volts).
Fig. 5.13 Charging and discharging stages
5.3.4. H-bridge
The standard H-bridge transformer coupled converter is shown in Fig. 5.14.
Switches T1 and T2 are driven by anti – phase signals generated by the driver circuit A.
Similarly switches T3 and T4 are driven by anti – phase signals generated by the driver
circuit B. These switches are n-channel enhanced mode power MOSFETs IRFZ46 that
are characterized with its high speed-switching capabilities [23]. The device is rated at
50V and 50A, which means that the rating is well above maximum operating voltage
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and current which are 20 V and 6 A of the converter. It has a maximum leakage current
of only 100 nA and very low on state resistance of 0.024Ω and hence small conduction
loss that makes it a highly efficient switching device.
Fig. 5.14 Bridge Converter schematic diagram
Although not shown in figure, each transistor is equipped with a built – in fast
– recovery power diode that provides a path for free – wheeling currents that flow
during certain phases of operation.
5.3.5. Transformer, Rectifier, and Filter Circuit
Fig. 5.15 shows the schematics for the transformer, rectifier and filter with the
voltage waveforms present at each stage. The transformer used here has a voltage
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transformation ratio of 1:1.5. Fast recovery diodes are used to rectify the bridge output
by providing a unidirectional voltage. This voltage is then filtered to produce DC output
that is equal to the average value of the pulse train.
Fig. 5.15 Transformer, Rectifier and Filter waveforms
The elements of the rectifier and filter are chosen on the following basis.
• Inductor
Inductor design is almost the hardest among the other elements since there is
no variety of inductor values in the market. The inductor has a certain number of turns
winded around a coil to establish the inductance needed for the converter. However any
additional turn (additional wire length) will add to the coil resistance value. This
additional value will contribute to resistance loss.
The value of inductance is calculated by considering the extreme case; when
the PV array operates at its maximum capacity (70 Watts). Therefore the output current
can be calculated by using the equation Pout = Vo × Io
Hence, Io = Po / Vo = 70 / 12 = 5.8 Amps
65
As discussed in section 3.3.2.1, the amplitude of the inductor current ripple is
selected to be 10% of its dc value. (i.e. LI∆ = Io × 0.1 = 5.8 × 0.1 = 0.58A).
If the converter is assumed to operate at frequency 40 kHz (i.e. Ts = 25 µs),
and the inductor current is assumed to be equal to the output current having 10% current
ripple.
Equation (3.27) gives: sL
TDI
VL )1(0 −
∆=
where D is the duty cycle and is calculated using equation (3.13)
D = Vo/Vd = 12/18 = 0.65
Thus the inductance value is
L = (12 × 0.35 × 25 × 10-6) / (0.58) = 181µH
This is the least inductance value that can endure a current of 5.8 A, so an
inductor of 200µH is chosen for the converter.
• Capacitor
To obtain a desired output voltage ripple, the capacitor value is determined.
Once again, the extreme case is considered. The output current is 4.1A, D = 0.65, Ts =
25µs. Assume that the output voltage ripple is 0.1% of its dc value (i.e. ∆Vo = 0.012V).
Equation (3.26) gives:
C = 222
11 TIVo
L ⋅∆⋅⋅
∆=
Then C = (0.58 × 25 × 10-6) / (8 × 0.012) = 150µF
The minimum capacitance value needed for the converter is 150µF. Hence, a
220µF is chosen for the design smooth more the ripple voltage.
66
• Diode
Diode choice is a trade off between forward bias voltage, and speed. Higher
forward bias voltage will result in more power dissipation and loss. Moreover, a fast
diode that can switch at high frequencies is needed. If the diode is slow to react, the
efficiency of the converter will drop. The best diode combining these features, that
could be found, was the STPS3045CPI from SGS-THOMSON. It has 0.57v of forward
drop at the expected currents of 15A.
5.4. Software Design
The next step in the design is to implement the MPP tracking algorithm on the
microcontroller chip. The PIC16F874 microcontroller is used to carry out the algorithm
function. It operates at speed of 10MHz so each instruction code will be executed at
0.4µs. The program is written in assembly language and is given in Appendix C.
A new strategy in programming the PIC 16F874 chip to track the MPP is adopted. This
new strategy is based on the Perturb and Observe (PAO) technique using an adaptive
incremental step scheme. The maximum power point is quickly hunted using a variable
step size. This adaptive technique reduces the number of iterations needed to catch this
MPP, thus resulting in much faster tracking compared to conventional methods [24].
5.4.1. Main Program
The main program flow chart is shown in Fig. 5.16. The program starts by
initializing the A/D module and the PWM module. Then the battery state of charge is
checked to prevent overcharge damage. The PWM module is turned off at this stage
and the program runs A/D conversion to measure the battery voltage. The measured
67
voltage is then compared to a predefined value (13.8V) to determine the state of charge
of the battery. If the battery voltage is greater than 13.8V (almost fully charged) the
program goes to sleep for 1 second and then goes back to measure the battery voltage
again. If the battery voltage is less than 13.8V the program goes to the Charging-
Tracking mode.
Fig. 5.16 Main Program Flow Chart
5.4.2. Charging-Tracking mode
The microcontroller has a PWM output, having a duty cycle that is controllable
by the microcontroller’s software. The micro-controller provides a duty – cycle ratio
limited to the range [1/255 254/255]. The microcontroller starts hunting for the
maximum power point by changing the duty cycle in a series of relatively large steps.
After each new step, it measures the solar voltage Vs and current Is using the PIC built in
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A/D channels, multiplies their digital representation, and compares the newly obtained
power level with the former value.
The flow chart for the conventional PAO algorithm is shown in Fig. 5.17. If the
newly obtained power Pn is larger than the previous power value Pn-1, the
microcontroller continues changing the duty cycle d monotonically in the same
direction, using the same step size delta (∆). Otherwise the microcontroller reverses the
direction of changing the duty cycle, and divides the step size delta by two (2∆ ). The
microcontroller will finally lock on the MPP with fine step size as shown before in Fig.
4.9.
Fig. 5.17 The conventional PAO algorithm Flow Chart
This algorithm showed good performance for stable weather conditions where
the tracking efficiency ξTr reached 95%. However, this algorithm fails to track the MPP
69
correctly in case of rapidly varying weather conditions where ξTr deteriorated to less
than 85%. This is due to the small incremental step that was reached while tracking the
old MPP. This small incremental step would continue to be used when searching for the
new MPP as shown in Fig. 5.18, which will increase the number of iterations needed to
lock on the new MPP. When frequent weather changes occur, the system will not be
able to track and lock onto the new MPP.
Fig. 5.18 Scanning with small step in case of varying weather conditions
To improve the performance of the conventional PAO algorithm, an adaptive
PAO algorithm is implemented. The flow chart for the adaptive PAO algorithm is
shown in Fig. 5.19. The micro-controller provides a duty–cycle ratio limited to the
range [1/255 254/255]. The microcontroller starts with a duty–cycle ratio of 1/255. It
increments the duty cycle in steps of 32/255 as long as it detects that the power
extracted from the PV module increases with each step (∆). When power drop is
detected, the software starts decrementing the duty cycle. However the new step size
(2∆ ) is half the step size used in the previous stage. The process of reversing the
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scanning direction, while decrementing the duty cycle, continues until the step size
reaches the value 1/255.
Fig. 5.19 The adaptive PAO algorithm flow chart
Three different cases may arise:
• Starting up from zero power conditions
The microcontroller starts with a duty–cycle ratio of 1/255. It increments the
duty cycle in steps of 32/255 as long as it detects that the power extracted from the PV
module increases with each step (∆) as shown in Fig. 5.20.
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Fig. 5.20 Hunting with large step size ∆
However, when a power drop is detected, the software starts decrementing the
duty cycle with a new step size (2∆ ) that is half the step size used in the previous stage.
As long as the power increases, the microcontroller continues to decrement the duty-
cycle ratio as shown in Fig. 5.21.
Fig. 5.21 Hunting with smaller step size
2∆
When another power drop is detected, the software increments its duty-cycle
ratio with a new step size equal to half the previous step size. The process of reversing
the scanning direction, while decrementing the duty cycle, continues until the step size
reaches the value 1/255 as shown in Fig. 5.22. In summary, the algorithm starts by
increasing the duty cycle by a given step size ∆. For each increment, power is calculated
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so that when a power drop is detected the scanning direction is reversed and the duty
cycle is decreased by a new step size ∆/2 equal to half the previous step.
Fig. 5.22 MPP scanning direction
• Hunting around the peak power point
As long as the illumination condition does not change, the microcontroller’s
software keeps hunting around the MPP with increments/decrements of 1/255, as shown
in Fig. 5.23.
Fig. 5.23 Locking on the MPP with duty-cycle ratio 1/255
73
• Changes in the illumination condition
Illumination will vary due to changing weather conditions (presence or absence
of clouds). Hunting for the MPP, the microcontroller detects the power change while
changing the pulse width. If the power increases, as shown in Fig. 5.24(a), the
microcontroller continues to change the pulse width in the same direction causing this
power increase. After four consecutive steps in the same direction, the microcontroller
doubles the step size to speed up the process of tracking the new MPP.
Similarly, if power decreases the microcontroller starts scanning by a small step. After
four consecutive steps in the same direction, it doubles the step size to speed up the
process of tracking the new MPP as shown in Fig. 5.24(b).
Fig. 5.24 Scanning in case of varying weather conditions
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CHAPTER 6
SYSTEM RESULTS AND DISCUSSION
6.1. Introduction
The objective of this thesis is to evaluate the model that represents a stand-
alone PV system charging a lead acid battery through Simulink simulation and present
results of the experimental setup. The Simulink and experimental part consists of the
BP380 solar module (Appendix D), an H-bridge converter, a controller, and a 70Ah
battery that were discussed in Chapters 4 and 5. Results will be presented to assess how
efficient is the algorithm, implemented in the controller, in tracking the MPP; i.e. how
much power is extracted from the PV array. The model will also examine the power
electronics efficiency; i.e. how much power is delivered to the battery.
6.2. PV Model Validation
The PV Simulink model is tested under different atmospheric conditions to
prove its validity. It is first simulated for different insolation levels while keeping the
temperature constant (23oC) as shown in Fig. 6.1 and Fig. 6.2. Then it is tested for
different temperatures while keeping the Insolation constant (1000 W/m2) as shown in
Fig. 6.3 and Fig. 6.4 [9]. To draw the real life characteristic curves, the 'BP 380' PV
module was subjected to a variable load circuit shown in Fig. 6.5. The computer issues
a series of increasing digits that are converted to analog voltages using a D/A converter
(R-2R ladder). These increasing digits will load the PV module with increasing current
value IT (where IT = 4 IC ≈ 4 IE = V* / R ≈ Vin / R). Recording the values of the PV
currents IT and their respective PV voltages VT, the module characteristic curves were
75
drawn as shown in Fig. 6.6, where this model also proved its validity under the
influence of varied insolation levels and different cell temperatures.
Fig. 6.1 I-V characteristic curves for different Insolation levels
Fig. 6.2 P-V characteristic curves for different Insolation levels
76
Fig. 6.3 I-V characteristic curves for different temperatures
Fig. 6.4 P-V characteristic curves for different temperatures
It was observed that the short circuit current Isc of the PV module depends
linearly on the irradiation, while the open-circuit voltage Voc increases logarithmically
77
with irradiation, as shown in Fig. 6.1 [25]. Increasing the cell temperature would
decrease the open circuit voltage Voc. The results relates to the theory that can be found
in chapter 3 [2].
Fig. 6.5 Load circuit schematic diagram
Fig. 6.6 PV characteristic curves under different Insolation levels
To test if the Simulink model and the hardware model match, the characteristic
curves of BP380 solar panel were first drawn using the load circuit as shown in Fig. 6.7,
where the reported radiation flux and temperature were 523.44W/m2 and 16.81oC
respectively on the eleventh of January, 2005 at 2:33 pm. Then these curves were
drawn, for the same data, using the Simulink model as shown in Fig. 6.8. The MPP
78
reading of the hardware model was 40.42W, and that of the Simulink model was
40.76W, which shows that they agree fairly well.
Fig. 6.7 Characteristic curves of the 'BP 380' PV module using the load circuit
Fig. 6.8 Characteristic curves of the 'BP 380' PV module using the Simulink model
6.3. Simulink Simulation Results
The MPPT Simulink model shown in Fig. 6.9 was simulated for different
temperature and insolation level values. After each run the power, extracted by the
MPPT system, was recorded and then compared to the PV module maximum affordable
power.
Fig. 10 shows the P-V characteristic curve of the PV module for an Insolation
level 800W/m2 and temperature 27oC. The graph readings of the MPP, are: Impp =
3.59A, Vmpp= 18V and Pmpp= 64.7W.
79
Fig. 6.9 MPPT Simulink Model
With the adaptive PAO algorithm implemented in the controller, the MPPT
system was simulated for the same input data (T= 27oC and In = 800W/m2). The average
values of the switching current, voltage and power were recoded as follows: Pavg =
62.5W, Iavg = 3.8A and Vavg = 16.4V as shown in Fig. 6.11. These recorded values prove
that the PAO algorithm tracking efficiency is about 96% (ξT = 62.5/ 64.7 = 0.96).
Fig. 6.10 P-V characteristic curve of the PV array at 800W/m2, 27oC
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The power electronics efficiency in the Simulink model is also assessed. The
power delivered to the battery, for the same case, came to be 48W, which means that the
power electronics efficiency is only 80% (ξPE = 50/62.5 = 0.8) as shown in Fig. 6.12.
Fig. 6.11 Switching Power, Voltage, and Current supplied to the converter
Fig. 6.12 Power, Voltage, and Current delivered to the battery
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6.4. Hardware Results
The MPPT hardware system was also examined for different weather
conditions. First the variable load circuit was used to record the MPP data of the PV
module on a clear sunny day at noontime in October as shown in Table 6.1. The MPP
readings came to be: Impp = 4.13A, Vmpp= 13.6V and Pmpp= 56.16W. The characteristic
curves were also plotted as shown in Fig. 6.13.
Fig. 6.13 characteristic curves: (a) I-V curve, (b) P-V curve
Table 6.1 MPP readings on a sunny day in October
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Immediately after recording the MPP data, the MPPT hardware system was set
into action. The visual basic VB program, developed to draw the voltage, current, and
power versus time during tracking action, recorded the following data: Psavg = 53.4W,
Isavg = 4.1A and Vsavg = 13V as shown in Fig. 6.14, where Psavg is the power extracted
form the solar panel. Then the tracking efficiency was calculated as: ξT = Psavg / Pmpp =
53.4 / 56.168 = 0.95. The power electronics efficiency was also measured: ξPE = Pb /
Psavg =43.3/ 53.4 = 0.81, where Pb is the average voltage delivered to the battery.
Fig. 6.14 VB performance monitor
Table 6.2 shows a few selected results taken on various dates and different
daytimes for few minutes of MPPT system operation. It is worth mentioning that as the
solar current Is increases, the power electronics efficiency decreases. This is due to the
fact that the power losses in the hardware design are calculated as the square of the solar
current Is multiplied by the equivalent resistance (Ploss = I2 R), while the input power is
directly proportional to the current and voltage (Pinput=I V). Table 6.3 presents the daily
average reading obtained between 10:00 am and 5:00 pm for the various mentioned
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dates. The average value for the tracking efficiency was recognized at 95% while the
power electronics efficiency at 80% only.
Table 6.2 Snapshots of MPP Recorded Data
Date-Hour Weather condition
Pmmp (W)
Is (A)
Vs (V)
Ps (W)
Pb
(W)
ξT %
ξPE %
29/4/2004 12:50 pm
Sunny day Few clouds
53.4 3.28 15.37 50.42 39.8 94.4 78.9
29/4/2004 3:40 pm
Sunny day Few clouds
50 3.0 15.77 47.32 38 94.6 80.3
30/4/2004 3:30 pm
Sunny day Few clouds
51 3.18 15.12 48.09 38.48 94.3 80
30/4/2004 5:13 pm
Sunny day Few clouds
46.4 2.85 15.51 44.21 36 95.2 81.4
20/10/2004 11:35 am
Hot Sunny day
56 3.4 15.51 52.75 41.8 94.2 79.2
20/10/2004 11:55 am
Hot Sunny day
58 3.3 16.82 55.68 45.34 96 81.4
23/11/2004 10:30 am
Cold Sunny day
49.79 3.06 15.68 48 38.7 96.4 80.6
23/11/2004 10:40 am
Cold Sunny day
50.5
3.06 15.68 48
38.7
95
80.6
Table 6.3 MPP Daily average Recorded Data 2004
Date Weather condition
Pmmp(W) Ps(W) Pb (W) ξT % ξPE %
29/4/2004
Sunny day Few clouds
49.9 47.47 37.97 95 80
30/4/2004
Sunny day Few clouds
49.8 47.2 38.2 94.7 81
20/10/2004
Hot Sunny day
54.7 52.32 42 95.6 80.3
23/10/2004
Hot Sunny day
54.4 51.8 41 95.2 79
23/11/2004
Cold Sunny day
62.7 59.7 48.9 95.2 82
24/11/2004
Cold Sunny day
60.4 57.5 46.2 95.2 80
Average value 95 80
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On a cold sunny day, the average power extracted from the PV module is
greater than that of a hot sunny day. This is due to the fact that Voc increases as
temperature decreases. Consequently the MPP value is raised as shown in Fig. 6.4.
Fig. 6.15 shows how fast is the PAO algorithm, implemented inside the
controller, in tracking the MPP in case of changing weather conditions (varying
insolation level due to the presence of clouds).
Fig. 6.15 Tracking the MPP in case of varying Insolation level
The peaks, present inside the circled region, occur when the MPPT system
starts up and quickly searches for the duty cycle, which loads the PV module at the
MPP. These peaks are issued due to the VB software failure in interpreting the first
input byte by the micrcontroller at startup. These peaks are present for just few
microseconds. Curve (a) represents the PV module varying MPP values due to changing
85
weather conditions while curve (b) represents the power extracted from the PV module.
Still the tracking efficiency ξTr was 95% on average.
6.5. Comparison of Tracking Algorithms
The adaptive PAO algorithm showed better performance than the
conventional PAO described in the literature [14] under varying weather conditions
because it can lock on the new MPP with less time than the conventional PAO can. To
compare between the two algorithms, two cases are considered. The first case compares
between the speeds of the algorithms for a minor change in the weather conditions
while the second compares between the speeds for a major change in the weather
conditions.
6.5.1. Minor change in the weather conditions
The conventional PAO algorithm locks on the MPP with a small incremental
step size ∆c of value 1/255. So if a quick change in the weather conditions occurs, the
conventional PAO algorithms starts searching for the new MPP with this small
incremental step as shown in Fig. 6.16. In the shown case the old MPP readings were
recognized at 50.76W and 2.75A for a 600W/m2 radiation flux and 27oC temperature,
while the new MPP readings at 77.86W and 4.14A for a 900W/m2 radiation flux and
27oC temperature. The current values for the old and new MPP on the 255 scale are 117
and 176. For the conventional PAO method, 60 iterations are needed to lock on the new
MPP (176-117= 59, 59+1=60). In the adaptive PAO method, the incremental step ∆a is
doubled after four consecutive increasing power steps. This way the number of
iterations is reduced to 21 based on the tracking scheme shown in Table 6.4. This table
86
shows how the incremental step is changing as the power is increasing or decreasing.
The initial incremental step ∆a is taken to be 1 assuming that system was locking on a
MPP. So after four consecutive steps the current is 121 (=117 + 1× 4). Since the power
is still increasing the incremental step is doubled (2×1) and after four consecutive steps
the current is 129 (=121+4×2). The scanning method will continue until a power drop is
sensed, where the scanning direction will be reversed, the incremental step is halved and
the increments will be changed into decrements and vice versa. When the value of the
current reaches 177, a power drop is sensed so the direction of scanning is reversed, the
incremental step is halved (4), and the current is decremented. After one iteration the
value of the current reaches 173 (=177 – 1 × 4)) where another power drop is detected,
so again the direction of scanning is reversed, the incremental step is halved (2), but
now the current is incremented. This tracking scheme will continue until the
incremental step ∆a reached the smallest value i.e. one at the MPP. This means that the
adaptive PAO scheme is 2.875 (60/21) times faster than the conventional one. Thus the
tracking efficiency was increased by 10% using this adaptive technique where it was
85% on the best estimate for the conventional algorithm.
Fig. 6.16 Tracking scheme for minor change in the weather conditions
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Table 6.4 Tracking with adaptive incremental step ∆a
∆a value Previous current value
Number of iterations
Number of increments
New current value
Power condition
1 117 4 4 121 increase
2 121 4 8 129 increase
4 129 4 16 145 increase
8 145 4 32 177 drop
4 177 1 - 4 173 drop
2 173 2 4 177 drop
1 177 2 - 2 175 drop
Total number of iterations 21
6.5.1. Major change in the weather conditions
In this case the old MPP readings were recognized at 22.4W and 1.36A for a
300W/m2 radiation flux and 30oC temperature, while the new MPP readings at 82.4W
and 4.56A for a 1000W/m2 radiation flux and 30oC temperature as shown in Fig. 6.17.
The current values for the old and new MPP on the 255 scale are 58 and 194. For the
conventional PAO method, 137 iterations are needed to lock on the new MPP (194-58=
136, 136+1=137). In the adaptive PAO method, the number of iterations is reduced to
33 based on the tracking scheme shown in Table 6.5 where exactly the same procedure
is followed as in the previous case. So the adaptive PAO scheme is 4.1 (=137/ 33) times
faster than the conventional one in this case. Therefore the adaptive PAO algorithm
reacts faster than the conventional one, especially under quickly varying weather
conditions where the conventional technique fails to track the MPP correctly.
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Fig. 6.17 Tracking scheme for major change in the weather conditions
Table 6.5 Scanning with adaptive incremental step ∆a
∆a value Previous current value
Number of iterations
Number of increments
New current value
Power condition
1 58 4 4 62 increase
2 62 4 8 70 increase
4 70 4 16 86 increase
8 86 4 32 118 increase
16 118 4 64 182 increase
32 182 1 32 214 drop
16 214 2 -32 182 drop
8 182 2 16 198 drop
4 198 2 -8 190 drop
2 190 3 6 196 drop
1 196 3 -3 193 drop
Total number of iterations 33
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6.6. Power Budget
The power losses in the whole design system is calculated and summarized in
Table 6.6. The MPPT system was assumed to operate at MPP (70W) and the switching
frequency f of 40 kHz (T = 1/f = 25µs) with the duty cycle D set to 65%. The load
current IL was 5.8A and a battery voltage of 12V.
6.6.1. Inductor conduction loss
The conduction loss in the inductor can be found by considering the load
current and the winding copper resistance. The measured inductor current is equal to
5.8A and the measured inductor resistance is 0.03Ω. Therefore, the power loss due to
the conduction loss in the inductor is: Pind = I2ind . Rind = 1.009W
6.6.2. Diode conduction loss
The diode conduction loss can be calculated using the following equation:
Pd = IL . Vf = 3.306W
where, from data sheet the forward bias of the diode, Vf = 0.57V.
6.6.3. MOSFET conduction loss
Fig. 6.18 shows the waveform for the current Ip that flows in the primary
winding of the transformer T5 shown before in Fig. 5.14. Since the transformer turns
ratio is 1:1.5, then: Ipon = 1.5 IL = 8.7A.
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Fig. 6.18 Primary winding current waveform
The power loss due to the MOSFETs conduction loss is calculated by
considering the switching current waveforms for each pair of switches as shown in Fig.
6.19.
PTr = (Ipon)2. Ron. ton /(2T) = 0.59W
Where, D = ton / T and from data sheet the on resistance of the MOSFET, Ron =
0.024Ω.
Then the power loss PTR for the four MOSFETs is:
PTR = 4.PTr = 2.36W
Fig. 6.19 Waveforms across the terminals of the transformer
91
6.5.4. Transformer power loss
The measured resistance for the primary winding Rpri is 0.0053Ω while that of
the secondary winding Rsec is 0.012Ω.
The waveforms for the current that flows in the secondary winding of the
transformer and the rectifying diodes (D1 and D2) are shown in Fig. 6.20.
Fig. 6.20 Diodes’ current waveform during different intervals
Thus the average power loss in the transformer windings over one cycle can be
divided into two intervals t1 and t2.
During interval t1, only diode D1 of Fig. 5.14 is conducting so the primary
winding and half of the secondary winding contribute to power loss as shown in Fig.
6.21(a). During interval t2, both diodes are conducting so only the secondary winding
contribute to the power losses as shown in Fig. 6.21(b). These two intervals will repeat
but for the next MOSFETs switching period where diode D2 will be conducting as
shown in Fig. 6.21(c).
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Fig. 6.21 Transformer windings contribution to power loss
Thus the energy loss in the transformer during interval t1 can be calculated as:
Et1 = [(Ipon)2 . Rpri + (IL)2 . Rsec ]. ton
During interval t2 the energy loss is calculated as:
Et2 = 2 . [(IL/2)2 . Rsec] . (T-ton)
The average power loss in the transformer Ptrans over one period T is given by:
Ptrans = (Et1 + Et2)/ T = 0.594W
6.5.5. Other power loss factors
Other factors contribute to power loss, among which are the voltage and
current sensing circuit, the microcontroller circuit, the printed copper track resistances
and copper wiring resistance.
A rough estimate calculation was made for the power loss due to these factors
and was found to be 6W.
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Table 6.5 Power Budget
Power Budget Component Input Power Power Loss
BP380 Solar Panel 70W
Inductor 1.009W
Diode 3.306W
MOSFETs 2.36W
Transformer 0.594W
Other Factors 6W
Balance 70W- 13.27W= 56.73W
Power electronics efficiency
ξPE = 56.73/ 70 = 81%
94
CHAPTER 7
CONCLUSION AND FUTURE WORK
7.1. Summary
Photovoltaic power production is gaining more significance as a renewable
energy source due to its many advantages. These advantages include pollution free
energy production scheme, ease of maintenance, no noise and direct sunbeam to
electricity conversion [29]. However the high cost of PV installations still forms an
obstacle for this technology. Moreover the PV array output power fluctuates as the
weather conditions, such as the Insolation level, and cell temperature. In order to make
use of the high initial cost it is very important to extract maximum power from the solar
panels for all weather conditions [30]. Stand-alone PV systems cannot supply enough
energy all day long or when no or little solar irradiation exits. Battery storage
capabilities are required in these systems.
So when the PV array is used as a source of power supply to charge a 12V lead
acid battery, it is necessary to use the MPPT to get maximum power from the PV array.
In this work, the MPPT is implemented by using an H-bridge converter, which is
designed to operate under continuous conduction mode and a microcontroller to control
the PWM signals to the converter and also to monitor the state of charge of the battery.
The Perturb and Observe Algorithm is used as the control algorithm for the MPPT.
7.2. Testing Environment
The solar system consists of an 80W PV module, a converter, a controller and a
70Ah battery. The system was designed, built and tested for a period of ten months and
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for different weather conditions. As the main system component, an H-bridge converter
was constructed for the design. By changing the transformer windings ratio, this bridge
can be easily made to work as either a buck or a boost converter. A turn ratio greater
than one means that the output signal will be amplified resulting in a boosted signal,
whereby a turn ratio smaller than one will result in reducing the output signal amplitude
which is the case of buck converter. Moreover unlike the buck converter, the H-bridge
converter operates with 50% duty cycle driving signals, which reduces the switching
failure associated with the buck converter during the turning on or off transitions for
small or large duty cycle driving signals. However the H-bridge converter has four
switching devices while the buck converter has only one. Having an excellent
combination of features, performance, and low power consumption, the PIC16F874
microcontroller is used in the control section. It has 4K x 14 bits of flash memory, 192 x
8 bytes of data memory (RAM), two D/A and five A/D channels. The tracking
algorithm is implemented in the microcontroller where it senses the present values of
the solar current and voltage and compares resultant power with the previous power and
accordingly controls the PWM scheme of the converter.
7.3. Better Tracking Algorithm
The Perturb and Observe, Incremental Conductance, and other maximum
power point tracking algorithms were reviewed and discussed. Although the ICT
technique offers higher tracking efficiency, the PAO algorithm was chosen to track the
MPP since it has lower cost, easier circuitry and less complicated algorithm. However
the conventional PAO was developed to respond faster for quickly varying weather
conditions. An adaptive incremental step was introduced where the performance of the
96
algorithm was 2.5 to 4 times faster than the conventional one depending on the location
of the new MPP with respect to the old one. Moreover experimental results have shown
that the MPPT using an adaptive PAO has a tracking efficiency of 95% with a converter
efficiency examined and measured to be 80%.
7.4. Simulink Model
The solar system was also designed and simulated using the matlab Simulink
environment. A model that represents the solar module was created using the Simulink
S-function capability. The controller was also implemented with the help of the S-
function block. The converter and battery were modeled using the Simulink power
electronics library. To match the hardware system and the Simulink software
simulation model, both were tested for a specific flux density and temperature. The
MPP reading of both systems showed that they match up as high as 99%.
7.5. Future Work
The MPPT system that was designed and tested can achieve 76% of total
conversion efficiency so it is still possible to improve its efficiency. The component
choice is very important in the design of the MPPT system. Higher power conversion
efficiency can be achieved by using rectifying diodes with less forward bias voltages,
inductors of lower resistive material, transformer with high magnetic flux density, and
MOSFETs with lower on-state resistance. Moreover the size of the MPPT could be
more compact if surface mount devices SMDs are used and if the system is to operate at
higher switching frequencies where the size of the inductor and transformer will be
reduced. This is part of what should be done in the future for a simple stand-alone PV
97
system. However to build a complete system utilizing solar energy for power
generation, a highly efficient dc-ac converter should be implemented. Now instead of
controlling four, six switches should be driven by the control section where it should
keep supplying the correct phase (120o) between the lines. Moreover the transformer-
winding ratio should be carefully chosen to provide 220V on the secondary windings.
APPENDIX A
MATLAB PROGRAM CODE
function k = pulse01(t,x,u) k(1) = u(1); I = u(2); V = u(3); Pr = u(4); delta = u(5); Pn = I * V; if(delta > 0.000000001) if (Pn >= Pr) k(1) = k(1) + delta; if (k(1) < 3) k(1) = 3; end if (k(1) > 24) k(1) = 23; end elseif (Pn < Pr) delta = delta/2; k(1) = k(1) - delta; if (k(1) < 3) k(1) =3; end if (k(1) > 24) k(1) = 23; end end end k(3) = (delta); Pr = Pn;
98
k(2) = Pr; function [sys,x0,str,ts]= pulse01_s(t,x,u,flag) switch flag, case 0 % Initialization s = simsizes; s.NumContStates = 0; s.NumDiscStates = 0; s.NumOutputs = 3; % dynamically sized s.NumInputs = 5; % dynamically sized s.DirFeedthrough = 1; % has direct feedthrough s.NumSampleTimes = 1; sys = simsizes(s); x0 = []; str = []; ts = [-1 0]; % inherited sample time case 3 sys= pulse01(t,x,u); case 1, 2, 4, 9 sys=[]; otherwise error(['Unhandled flag = ',num2str(flag)]); end
99
% this mfile represents the PV module voltage and current relations. % it has three inputs which are the insolation G, the temperature T and the current I function V = PV_Cell(t,x,u) G= u(1); %here is the 1st input G T= u(2); %here is the 2nd input T I= u(3); %here is the 3rd input I Rs=0.1; Rsh=10000; Gnom=1000; k=1.38e-23; q=1.6e-19; A=1.5; Vg=1.12; Ns=36; Voc_T1=22.1/Ns; T1=273+25; T3=273+75; Isc_T1=4.8; Isc_T3=5.04; T0=273+T ; %T k0=(Isc_T3-Isc_T1)/(T3-T1); I0_T1=Isc_T1/(exp((q*Voc_T1)/(A*k*T1))-1); b=(Vg*q)/(A*k); b1=q/(A*k*T0); Iph_T1=Isc_T1*G/Gnom; %G Iph=Iph_T1*(1+k0*(T0-T1)); I0=I0_T1*[(T0/T1)^ (3/A)]*[exp(-b*[(1/T0)-(1/T1)])]; Isc=(k0*(T0-T1)+Isc_T1); % Output Voltage: if (I >= Iph) V=0; else V=(1/b1)*[log(((Iph-I)/I0)+1)]*36; end
100
function [sys,x0,str,ts]= PV_Cell_s(t,x,u,flag) switch flag, case 0 % Initialization ; s = simsizes; s.NumContStates = 0; s.NumDiscStates = 0; s.NumOutputs = 1; % dynamically sized s.NumInputs = 3; % dynamically sized s.DirFeedthrough = 1; % has direct feedthrough s.NumSampleTimes = 1; sys = simsizes(s); x0 = []; str = []; ts = [-1 0]; % inherited sample time case 3 sys= PV_Cell(t,x,u); case 1, 2, 4, 9 sys=[]; otherwise error(['Unhandled flag = ',num2str(flag)]); end
101
APPENDIX B
PCB CIRCUIT DESIGN
Current and voltage sensing circuitry
102
H-Bridge circuit
103
Transformer, Rectifier, Filter circuit
Load circuit
104
APPENDIX C
ASSEMBLY PROGRAM CODE
#INCLUDE<P16F874A.INC> ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;registers LOOP EQU H'20' COUNTER EQU H'21' VACCUH EQU H'22' VACCUL EQU H'23' IACCUH EQU H'24' IACCUL EQU H'25' REFH EQU H'26' REFL EQU H'27' TESTH EQU H'28' TESTL EQU H'29' DIRECTION EQU H'2A' STEP EQU H'2B' SAME EQU H'2C' RESULT EQU H'2D' OUTPUTVALEQU H'2E' SCRATCHH EQU H'2F' SCRATCHL EQU H'30' TEMPO EQU H'31' SHFTCOUNT EQU H'32' ACCUH EQU H'33' ACCUL EQU H'34' SHIFTH EQU H'35' SHIFTL EQU H'36' ROTATERI EQU H'37' FLAG EQU H'38' VAVERAGE EQU H'39' IAVERAGE EQU H'3A' PERIOD EQU H'3B'
105
DEFAULTTIME EQU H'3C' SCRATPER EQU H'3D' SCRAT1PER EQU H'3E' RIPPLEREG EQU H'3F' DELDUMMY EQU H'40' VOREG EQU H'41' PARAMETERTURN EQU H'42' ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;constants VPOINTER EQU H'81' IPOINTER EQU H'89' VOPOINTER EQU H'91' RIPPLEINP EQU H'99' IOINP EQU H'A1' MINIDUTYCYC EQU H'01' MAXDUTYCYC EQU H'FE' ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;startup vector ORG H'0000' GOTO MAIN ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;interrupt vector ORG H'0004' GOTO ISR ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; main ;precautions MOVLW H'00' MOVWF PORTD MOVWF PORTB
106
;preparing variables ;loop register CLRF LOOP ;defaulttime register MOVLW H'04' MOVWF DEFAULTTIME ;same register (no. of passes before incrementing step) MOVLW H'07' MOVWF SAME ;initialization of step register by 32 decimal (H'20') MOVLW H'20' MOVWF STEP ;initialization of direction register CLRF DIRECTION ;initialization of reference register CLRF REFH CLRF REFL ;initialization of result register MOVLW H'30' MOVWF RESULT ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;port configuration BSF STATUS,RP0 ;A - analog input MOVLW H'FF' MOVWF TRISA
107
;B - digital output - duty cycle variable MOVLW H'00' MOVWF TRISB ;C - pin no.1: capture input ;C - pin no.2: pwm output ;C - pin no.6: serial communication with pc (TX)(PROJECTED) ;C - pin no.7: serial communication with pc (RX)(PROJECTED) MOVLW H'B3' MOVWF TRISC ;E - analog input MOVLW H'07' MOVWF TRISE ;D - digital output MOVLW H'00' MOVWF TRISD BCF STATUS,RP0 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;pwm preparation ;setting timer2 period BSF STATUS,RP0 MOVLW H'40' MOVWF PR2 BCF STATUS,RP0 ;setting a dummy pulse width for startup MOVLW H'20' MOVWF CCPR1L ;activate timer 2 with zero prescaling on input and output MOVLW H'04'
108
MOVWF T2CON ;setting pwm mode for module 1 MOVLW H'0F' MOVWF CCP1CON ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;capture preparation ;setting the mode of timer1 MOVLW H'05' MOVWF T1CON ;preparing module 2 to operate as a capture module on rising edge MOVLW H'05' MOVWF CCP2CON ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;timer0 preparation ;initializing the period register (used by TMR0) MOVLW H'C3' MOVWF SCRATPER COMF SCRATPER,F INCF SCRATPER,F ;scratper by now, contains the exact number needed by TMR0 at 50 Hz. MOVF SCRATPER,W MOVWF PERIOD ;initializing TIMER0 BSF STATUS,RP0 MOVLW H'C2' MOVWF OPTION_REG
109
BCF STATUS,RP0 ;presetting timer0 with the default value MOVF PERIOD,W MOVWF TMR0 ;initializing the same register CLRF SAME ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;preparing the a/d conversion module ;configuring analog pins, and output data format in ADRESH, and ADRESL BSF STATUS,RP0 MOVLW H'00' MOVWF ADCON1 BCF STATUS,RP0 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;arranging for interrupts globally ;enabling TIMER0 interrupts BSF INTCON,T0IE ;enabling capture interrupts BSF STATUS,RP0 BSF PIE2,CCP2IE BCF STATUS,RP0 ;enabling peripheral interrupts
110
BSF INTCON,PEIE ;enabling interrupts globally BSF INTCON,GIE ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;serial communications preparation BSF STATUS,RP0 MOVLW H'40' MOVWF SPBRG MOVLW H'26' MOVWF TXSTA BCF STATUS,RP0 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; TRAPLOOP CLRWDT GOTO TRAPLOOP ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;interrupt subroutine root ISR BTFSC INTCON,T0IF ;check whether TMR0 interrupt occured GOTO TMR0SR BTFSC PIR2,CCP2IF ;check whether a capture interrupt occured GOTO CAPTINT RETFIE ;false interrupt indication (normally unreachable) ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
111
;capture interrupt branch CAPTINT CLRF TMR1L CLRF TMR1H BCF PIR2,CCP2IF MOVF CCPR2H,W MOVWF SCRAT1PER COMF SCRAT1PER,F INCF SCRAT1PER,F MOVF SCRAT1PER,W MOVWF PERIOD MOVLW H'04' MOVWF DEFAULTTIME RETFIE ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;timer 0 interrupt branch ;recharge timer with period value TMR0SR MOVF PERIOD,W MOVWF TMR0 ;clear timer0 overflow flag BCF INTCON,T0IF INCF LOOP,F ;check turn of sumup,communication,or normal MOVF LOOP,W SUBLW H'80' BTFSC STATUS,Z GOTO SUMUP BTFSC STATUS,C GOTO NORMAL
112
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;collecting data for i and v averages NORMAL MOVLW VPOINTER MOVWF ADCON0 CALL WAITACQ BSF ADCON0,2 WAIVOL BTFSC ADCON0,2 GOTO WAIVOL ;add the resulting voltage sample to the voltage accumulator (data available in adresh) CALL ADDVACCU MOVLW IPOINTER MOVWF ADCON0 CALL WAITACQ BSF ADCON0,2 WAICURR BTFSC ADCON0,2 GOTO WAICURR CALL ADDCURRACCU GOTO FUNNEL1 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; SUMUP DECFSZ DEFAULTTIME,F GOTO BULK MOVF SCRATPER,W MOVWF PERIOD ;obtaining averages BULK MOVLW H'07'
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MOVWF COUNTER SHIFTV BCF STATUS,C RRF VACCUH,F RRF VACCUL,F DECFSZ COUNTER,F GOTO SHIFTV MOVF VACCUL,W MOVWF VAVERAGE CLRF VACCUL MOVLW H'07' MOVWF COUNTER SHIFTI BCF STATUS,C RRF IACCUH,F RRF IACCUL,F DECFSZ COUNTER,F GOTO SHIFTI MOVF IACCUL,W MOVWF IAVERAGE CLRF IACCUL ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;performing multiplication CALL IVMULTIPL MOVF ACCUH,W MOVWF TESTH MOVF ACCUL,W MOVWF TESTL ;compare the new test value with the refference VALUE MOVF REFH,W SUBWF TESTH,W ;TESTH = REFH?
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BTFSC STATUS,Z GOTO HEQUAL ;TESTH = REFH, continue comparing TESTL and REFL ;testh not equal to REFH. find which is greater. BTFSC STATUS,C GOTO TESTGTREF ;test is greater than refference GOTO REFGTTEST ;refference is greater than test ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; HEQUAL MOVF REFL,W SUBWF TESTL,W ;TESTL = REFL? BTFSC STATUS,Z GOTO TESTGTREF ;behave as if test is greater than refference BTFSC STATUS,C GOTO TESTGTREF ;test is greater than refference GOTO REFGTTEST ;refference is greater than test ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; REFGTTEST INCF DIRECTION,F ;reorient the direction of search ;divide step by 2 BCF STATUS,C RRF STEP,F ;reset the same register CLRF SAME ;goto next stage GOTO FUNNEL2 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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TESTGTREF INCF SAME,F ;check whether the step remained in the same direction for more than 4 times MOVLW H'07' SUBWF SAME,W BTFSS STATUS,C ;not yet GOTO FUNNEL2 ;same greater than or equal to H'07' CLRF SAME ;multiply step by 2 BCF STATUS,C RLF STEP,F ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;check whether step is within boundaries (1<=step<=32) FUNNEL2 MOVLW H'01' SUBWF STEP,W BTFSS STATUS,C ;less than 1 GOTO EQUALIZE1 MOVF STEP,W SUBLW H'20' BTFSS STATUS,C ;greater than h'20'
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GOTO EQUALIZE32 ;within boundaries GOTO CONTINUE ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;load step with h'01' EQUALIZE1 MOVLW H'01' MOVWF STEP GOTO CONTINUE ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;load step with h'20' EQUALIZE32 MOVLW H'20' MOVWF STEP ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;decide whether to increment or decrement CONTINUE BTFSS DIRECTION,0 GOTO ADDSTEP GOTO SUBSTEP ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ADDSTEP MOVF STEP,W ADDWF RESULT,F BTFSS STATUS,C GOTO FUNNEL3 ;result exceeds H'FF' MOVLW H'FF'
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MOVWF RESULT ;change the direction of scanning INCF DIRECTION,F GOTO FUNNEL3 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; SUBSTEP MOVF STEP,W SUBWF RESULT,F BTFSC STATUS,C GOTO FUNNEL3 ;result is less than H'00' CLRF RESULT ;change the direction of scanning INCF DIRECTION,F ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;set recent test values as future refference values FUNNEL3 MOVF TESTH,W MOVWF REFH MOVF TESTL,W MOVWF REFL ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;result correction if output voltage exceeds maximum value FUNNEL1 MOVLW VOPOINTER MOVWF ADCON0
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CALL WAITACQ BSF ADCON0,2 ;wait for A/D process completion WAIVO BTFSC ADCON0,2 GOTO WAIVO MOVF ADRESH,W ;;;;;;;;;;;;;;;; MOVWF VOREG ;;;;;;;;;;;;;;;; SUBLW H'80' BTFSS STATUS,C GOTO VOGTLIMIT GOTO VOLTLIMIT ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;decrement duty cycle VOGTLIMIT MOVLW H'08' SUBWF RESULT,F BTFSC STATUS,C GOTO EXOUT MOVLW H'01' ;set the minimum. subject to change MOVWF RESULT ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; EXOUT MOVF RESULT,W MOVWF OUTPUTVAL GOTO FUNNEL4 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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VOLTLIMIT MOVLW RIPPLEINP MOVWF ADCON0 CALL WAITACQ BSF ADCON0,2 MORETIME BTFSC ADCON0,2 GOTO MORETIME MOVF ADRESH,W MOVWF RIPPLEREG SUBLW H'80' BTFSC STATUS,Z GOTO EQUAL BTFSC STATUS,C GOTO RECLTREQ GOTO REQLTREC ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; EQUAL MOVF RESULT,W MOVWF OUTPUTVAL GOTO FUNNEL4 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; RECLTREQ MOVF RIPPLEREG,W SUBLW H'80' MOVWF OUTPUTVAL MOVF RESULT,W
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ADDWF OUTPUTVAL,F BTFSS STATUS,C GOTO FUNNEL4 MOVLW H'FF' MOVWF OUTPUTVAL GOTO FUNNEL4 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; REQLTREC MOVLW H'80' SUBWF RIPPLEREG,W SUBWF RESULT,W BTFSS STATUS,C GOTO ADJUSTOUT MOVWF OUTPUTVAL GOTO FUNNEL4 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ADJUSTOUT MOVLW H'00' MOVWF OUTPUTVAL GOTO FUNNEL4 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;checkpoint for final values to be outputted FUNNEL4 MOVLW MINIDUTYCYC SUBWF OUTPUTVAL,W BTFSC STATUS,C
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GOTO SECONDTEST MOVLW MINIDUTYCYC MOVWF OUTPUTVAL GOTO EXPORT ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; SECONDTEST MOVF OUTPUTVAL,W SUBLW MAXDUTYCYC BTFSC STATUS,C GOTO EXPORT MOVLW MAXDUTYCYC MOVWF OUTPUTVAL GOTO EXPORT ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; EXPORT MOVF OUTPUTVAL,W ;export the value through the portb MOVWF PORTB ;prepare the number to be exported through the duty cycle register MOVWF SCRATCHH CLRF SCRATCHL ;shift two times BCF STATUS,C RRF SCRATCHH,F RRF SCRATCHL,F BCF STATUS,C RRF SCRATCHH,F
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RRF SCRATCHL,F BCF STATUS,C ;prepare the two least significant bits RRF SCRATCHL,F BCF STATUS,C RRF SCRATCHL,F BCF STATUS,C MOVLW H'30' ANDWF SCRATCHL,F MOVF CCP1CON,W ANDLW H'CF' IORWF SCRATCHL,W MOVWF CCP1CON MOVF SCRATCHH,W ANDLW H'3F' MOVWF CCPR1L MOVF STEP,W MOVWF TEMPO MOVLW H'3F' ANDWF TEMPO,F BTFSS DIRECTION,0 GOTO DISPRES GOTO DISPSET DISPRES BCF TEMPO,6 GOTO STATION2 DISPSET BSF TEMPO,6 STATION2 BSF TEMPO,7 MOVF TEMPO,W
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MOVWF PORTD RETFIE ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;subroutines ;IV multiplication subroutine IVMULTIPL MOVLW H'08' MOVWF SHFTCOUNT CLRF ACCUL CLRF ACCUH CLRF SHIFTH MOVF VAVERAGE,W MOVWF SHIFTL MOVF IAVERAGE,W MOVWF ROTATERI ;;;;;;;;;;;;;;;; BACKAA BCF STATUS,C RRF ROTATERI,F BTFSC STATUS,C CALL ADD_SR CALL SHIFTSR DECF SHFTCOUNT,F BTFSS STATUS,Z GOTO BACKAA RETURN ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ADD_SR CLRF FLAG MOVF SHIFTL,W ADDWF ACCUL,F BTFSC STATUS,C INCF FLAG,F
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MOVF SHIFTH,W ADDWF ACCUH,F BTFSC FLAG,0 INCF ACCUH,F RETURN ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; SHIFTSR BCF STATUS,C RLF SHIFTL,F RLF SHIFTH,F RETURN ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; WAITACQ MOVLW H'0E' MOVWF DELDUMMY DELBACK DECFSZ DELDUMMY,F GOTO DELBACK RETURN ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ADDVACCU MOVF ADRESH,W ADDWF VACCUL,F BTFSC STATUS,C INCF VACCUH,F RETURN ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ADDCURRACCU MOVF ADRESH,W ADDWF IACCUL,F BTFSC STATUS,C INCF IACCUH,F RETURN ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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;communications subroutine COMMUNICAT MOVF LOOP,W ANDLW H'07' SUBLW H'04' BTFSS STATUS,Z GOTO FUNNELEX MOVF LOOP,W MOVWF PARAMETERTURN MOVLW H'78' ANDWF PARAMETERTURN,F BCF STATUS,C RRF PARAMETERTURN,F BCF STATUS,C RRF PARAMETERTURN,F BCF STATUS,C RRF PARAMETERTURN,F BCF STATUS,C MOVLW H'0F' ANDWF PARAMETERTURN,F MOVF PARAMETERTURN,W SUBLW H'00' BTFSC STATUS,Z ;export average input voltage GOTO EXPOVAVERAGE MOVF PARAMETERTURN,W SUBLW H'01' BTFSC STATUS,Z ;export average input current GOTO EXPOIAVERAGE MOVF PARAMETERTURN,W
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SUBLW H'02' BTFSC STATUS,Z ;export lower byte of power output GOTO EXPOPL MOVF PARAMETERTURN,W SUBLW H'03' BTFSC STATUS,Z ;export upper byte of power output GOTO EXPOPH MOVF PARAMETERTURN,W SUBLW H'04' BTFSC STATUS,Z ;export output voltage value GOTO EXPOVO MOVF PARAMETERTURN,W SUBLW H'05' BTFSC STATUS,Z ;export duty cycle GOTO EXPODUTY MOVF PARAMETERTURN,W SUBLW H'06' BTFSC STATUS,Z ;export step GOTO EXPOSTEP MOVF PARAMETERTURN,W SUBLW H'07'
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BTFSC STATUS,Z ;export direction register GOTO EXPODIR MOVF PARAMETERTURN,W SUBLW H'08' BTFSC STATUS,Z ;export output current GOTO EXPOIO MOVF PARAMETERTURN,W SUBLW H'0F' BTFSC STATUS,Z ;export zero flag GOTO EXPOZERO ;export flag (H'FF') GOTO EXPOFLAG ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; EXPOVAVERAGE MOVF VAVERAGE,W MOVWF TXREG GOTO FUNNELEX EXPOIAVERAGE MOVF IAVERAGE,W MOVWF TXREG GOTO FUNNELEX EXPOPL MOVF TESTL,W MOVWF TXREG GOTO FUNNELEX EXPOPH MOVF TESTH,W MOVWF TXREG GOTO FUNNELEX
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EXPOVO MOVF VOREG,W MOVWF TXREG GOTO FUNNELEX ;************************************ EXPOIO MOVLW IOINP MOVWF ADCON0 CALL WAITACQ BSF ADCON0,2 WAK BTFSC ADCON0,2 GOTO WAK MOVF ADRESH,W MOVWF TXREG GOTO FUNNELEX ;************************************ EXPOFLAG MOVLW H'FF' MOVWF TXREG GOTO FUNNELEX EXPOZERO MOVLW H'00' MOVWF TXREG GOTO FUNNELEX EXPODUTY MOVF RESULT,W MOVWF TXREG GOTO FUNNELEX EXPOSTEP MOVF STEP,W MOVWF TXREG GOTO FUNNELEX EXPODIR MOVF DIRECTION,W MOVWF TXREG GOTO FUNNELEX FUNNELEX RETURN ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; END
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APPENDIX D
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