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The University of Queensland Department of Computer Science & Electrical Engineering
SOLAR PANEL MAXIMUM POWER POINT TRACKER
Undergraduate Thesis By Thanh Phu Nguyen 19 October 2001
Abstract “Solar Panel Maximum Power Point Tracker”.
As the name implied, it is a
photovoltaic system that uses the photovoltaic array as a source of electrical power supply and since every photovoltaic (PV) array has an optimum operating point, called the maximum power point, which varies depending on cell temperature, the insolation level and array voltage. A maximum power point tracker (MPPT) is needed to operate the PV array at its maximum power point. The objective of this thesis project is to build two MPPT in parallel to charge a 12-volts lead acid battery by using a field wired 83 Watts PV array.
The design consists of a PV array, a 12-volts lead acid battery, DC_DC Boost converters (also known as step-up converters) and a control section that uses the PIC16F873 microcontroller. The control section obtains the information from the PV array through microcontroller’s Analog and Digital (A/D) ports and hence to perform the pulse width modulation (PWM) to the converter through its D/A ports. Battery’s state of charge is also controlled by the microcontroller to protect the battery from overcharged.
The Incremental Conductance method is used as an algorithm to track the maximum power point of the PV array. The performance of the Incremental Conductance algorithm in tracking maximum power point is better than the Perturbation and Observation algorithm. By using Incremental Conductance algorithm the MPPT is able to track the maximum power point of the PV array quickly under rapidly changing in sun light intensity.
While the Perturbation and Observation algorithm
tends to deviate from the maximum power point under this condition.
Thanh Phu Nguyen 65 Kersley Rd Kenmore QLD 4069 19 October 2001
The Dean School of Engineering University Of Queensland St Lucia, QLD 4072
To the Dean,
In accordance with the requirements of the University of Queensland Bachelor of Electrical and Electronic Engineering degree, I hereby submit my undergraduate thesis entitled “ Solar Panel Maximum Power Point Tracker” for your consideration.
Yours faithfully
Thanh Phu Nguyen
Acknowledgements
I would like to take this opportunity to thank my supervisor, Dr. Geoff Walker for his generous and enthusiastic guidance. Without his assistance, this project would not be possible.
I would also like to thank Mr. Peter Allen for his assistance in providing me the experimental equipment.
Special acknowledgement must also go to my family who has constantly supported me throughout the year.
TABLE OF CONTENT Section
Page
List of Figures………………………………………………………………………….i List of Tables………………………………………………………………………….ii Abbreviation………………………………………………………………………….iii
CHAPTER 1 - INTRODUCTION
1
1.1 BACKGROUND TO THE RESEARCH ......................................................................... 1
CHAPTER 2 – LITERATURE REVIEW
3
2.1 PHOTOVOLTAIC CELLS AND ARRAYS .................................................................... 3 2.2 THE ROLE OF MPPT............................................................................................. 4 2.3 SWITCH MODE CONVERTER ................................................................................. 5 2.4 CONTROL SECTION .............................................................................................. 5 2.4.1 Voltage Feedback Control ................................................................ 5 2.4.2 Power Feedback Control................................................................... 5 2.5 MPPT CONTROL ALGORITHMS ............................................................................ 6 2.5.1 Perturbation and Observation Method............................................... 6 2.5.2 Dynamic Approach Method .............................................................. 6 2.5.3Incremental Conductance Algorithm.................................................. 6 2.6 BATTERY ............................................................................................................. 8 2.6.1 General battery chemistry ................................................................. 8 2.6.2 Starting and Deep-cycle batteries ...................................................... 9 2.6.3 Battery charging ............................................................................... 9 2.6.4 Battery life........................................................................................ 9
CHAPTER 3 - THEORY
11
3.1 DC-DC CONVERTER .......................................................................................... 11 3.2 BOOST CONVERTER ........................................................................................... 12 3.2.1 Continuous Conduction Mode......................................................... 12 3.2.2 Boundary between Continuous and Discontinuous Conduction....... 14 3.2.3 Discontinuous-Conduction Mode.................................................... 15 3.2.4 Effect on Parasitic Elements ........................................................... 17 3.2.5 Voltage and Current Ripple ............................................................ 17 3.2.5.1 Inductor Current Ripple ............................................................... 18 3.2.5.2 Output Voltage Ripple ................................................................. 19 3.2.5.3 Power consumption in the Boost Converter.................................. 19 3.3 DIFFERENTIAL AMPLIFIER .................................................................................. 21
CHAPTER 4 – IMPLEMENTATION
23
4.1 DESIGN OVERVIEW ............................................................................................ 23 4.2 HARDWARE DESIGN ........................................................................................... 25 4.2.1 Inductor .......................................................................................... 25 4.2.2 Output Capacitor ............................................................................ 26 4.2.3 Diode.............................................................................................. 26
4.2.4 Voltage Regulator........................................................................... 27 4.2.5 MOSFET ........................................................................................ 27 4.2.6 MOSFET Driver ............................................................................. 27 4.2.7 Microcontroller............................................................................... 27 4.2.8 Voltage divider network ................................................................. 28 4.2.9 Current-Sensing Circuit .................................................................. 29 4.3 SOFTWARE DESIGN ............................................................................................ 30
CHAPTER 5 – RESULTS AND DISCUSSION
35
5.1 EVALUATION OF THE BOOST CONVERTER ........................................................... 35 5.1.1 Switching Frequency vs. Power Efficiency ..................................... 35 5.1.2 Power Efficiency vs. Duty Cycle Ratio ........................................... 37 5.1.3 Power Budget ................................................................................. 38 5.1.4 Evaluation of the Product................................................................ 42
CHAPTER 6 – CONCLUSION AND FUTURE WORK
43
6.1 CONCLUSION ..................................................................................................... 43 6.2 FUTURE WORK .................................................................................................. 43
APPENDIX A - MPPT SCHEMATIC
44
APPENDIX B - PCB LAYOUT
45
APPENDIX C - C CODES
46
APPENDIX D - PSPICE SIMULATION
51
APPENDIX E - COMPONENT DATA SHEET
53
REFERENCES
54
List of Figure Figure
Title
Page
2.1
Schematic of a typical p-n junction solar cell
3
2.2
The I-V curve of the typical solar panel
4
2.3
The P-V curve
8
3.1
Ideal Switch voltage v, Duty ratio D, and switching period Ts
11
3.2
DC-DC Boost converter
12
3.3
Continuous Conduction mode
13
3.4
Waveforms at the edge of the continuous conduction
14
3.5
Average Output Current at the Boundary of continuous-discontinuous 15
3.6
Converter Waveforms at Discontinuous Conduction
15
3.7
Step-up converter characteristics keeping Vo constant
17
3.8
Effect of parasitic elements on voltage conversion ratio
18
3.9
Ripple Inductor current
19
3.10
Boost converter output voltage ripple
19
3.11
Differential Amplifier
22
4.1
Block Diagram of Maximum Power Point Tracker
25
4.2
Program Flow Chart
33
4.3
Control Flow Chart for S1- Incremental Conductance method
34
4.4
Control Flow Chart for S2- Incremental Conductance method
35
5.1
Switching Frequency vs. Power Efficiency
37
5.2
Power Efficiency vs. Duty Cycle Ratio
39
-i-
List of Table Table
Title
Page
5.1
Switching Frequency vs. Power Efficiency
37
5.2
Power Efficiency vs. Duty Cycle Ration
38
5.3
Power Budget
43
- ii -
Abbreviation
∆Vo
peak to peak output voltage ripple
C
capacitance
D
duty cycle ratio
ID
average diode current
Ids
drain saturation current
Idso
drain source leakage current
IL
average inductor current
ILB
average inductor current at the boundary between continuous and discontinuous mode
IOB
average output current at the boundary continuous and discontinuous conduction mode
IOB MAX
maximum average output current at the boundary between continuous and discontinuous conduction modes
L
inductance
MPP
maximum power point
MPPT
maximum power point tracker
PWM
pulse width modulation
PV
photovoltaic
RL
effective series resistance of the inductor
Rds
drain to source on resistance
tc
conduction time
td
turn on delay time
to
turn off time
toff
off time
ton
on time
tr
turn on rise time
ts
storage time
ts
switching period of the pulse width modulation
Vd
input voltage to the Boost-Converter
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Vdd
MOSFET supply drain voltage
V ds,sat
saturated drain to source voltage
Vf
forward biased diode voltage
VL
average inductor voltage
Vo
output voltage of the Boost-Converter
CMMR
common mode rejection ratio
Vcm
common mode signal
Vdiff
differential signal
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Chapter 1 - Introduction
CHAPTER 1 - INTRODUCTION
1.1 Background to the Research Energy is the most basic and essential of all resources. All the energy we use on Earth comes from fission or fusion of atomic nuclei, or from energy stored in the Earth. The problem with both fission and fusion is that they have dangerous radioactivity and side effect [1]. Therefore, most of the generation of energy in our modern industrialized society is strongly depending on very limited non-renewable resources, particularly fossil fuel. As the world's energy demands rise and resources become scarce, the search for alternative energy resources has become an important issue for our time. Very much exploitation and research for new power has been done not only in the area of nuclear power generation but also in the area of unlimited energy sources such as wind power generation and solar energy transformation.
The most effective and harmless energy source is probably solar energy.
For many
applications it 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, can reduce the load on the environment. Solar energy can be harvested by the use of photovoltaic (PV) array.
PV array has an optimum operating point called the maximum power point (MPP), which varies depending on cell temperature and the present insolation level. To get the maximum power from the PV, a maximum power point tracker (MPPT) is used. The goals of this thesis are: a) Tracking maximum power point with an algorithm suitable for rapidly changing atmospheric condition. Variation in lighting intensity causes these trackers to deviate from the maximum power point. When lighting conditions change, the tracker needs to respond within a short amount of time to the change to avoid energy loss.
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Chapter 1 - Introduction b) Battery charging A 12-Volt lead-acid battery is used as an energy storage unit. An over voltage protection loop is needed to protect the battery from over charged. There are two main groups of MPPTs: those that use analog circuitry and classical feedback control, and others that use a microprocessor to maintain control of the maximum operating point.
Analog systems have the advantage of having low cost components, but are more problematic to control. It is difficult to develop a stable system, which is able to maintain its accuracy even under extreme operating conditions such as the wide temperature variations that occur in an outdoor vehicle.
The digitally controlled MPPT systems have the advantage that a power point tracking algorithm will not be influenced by changes in temperature and therefore will always be very reliable. Additionally, the use of a tracking algorithm allows for additional control modes to cope with certain system states such as a fully charged battery.
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Chapter 2 – Literature Review
CHAPTER 2 – LITERATURE REVIEW
2.1 Photovoltaic Cells and Arrays A solar cell is a semiconductor device that absorbs sunlight and converts it into electrical energy. Today's most common cell is a mass manufactured single p-n junction Silicon (Si) cell with an efficiency up to about 17% [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 (Figure 2.1). If exposed to radiation, electron-hole pairs are created by photons with energy greater than the band-gap energy of the semiconductor. This is called the photovoltaic effect. 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. In photovoltaic energy systems, single cells are combined into solar cell arrays, and hence the name “Photovoltaic Arrays”.
Figure 2.1 Schematic of a typical p-n junction solar cell
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Chapter 2 – Literature Review
2.2 The role of MPPT Photovoltaic (PV) arrays are used to provide energy for many electrical applications. To get the maximum power from the PV array, a maximum power point tracker (MPPT) is used to control the variations in the current-voltage characteristics of the solar cells. Figure 2.2 below shows the typical silicon cell I-V curve, as the output voltage rises, the PV produces significant less current. The I-V curve will change depending on the temperature and illumination. Either the operating voltage or current needs to be carefully controlled, so that the maximum power from the array can be obtained. This maximum power point is seldom located at the same voltage the main system is operating at, and even if the two were equal initially, the power point would quickly move as lighting conditions and temperature change. Hence, a device is needed that finds the maximum power point (MPP) and converts that voltage to a voltage equal to the system voltage.
Figure 2.2 The I-V curve of the typical solar panel.
A MPPT is required to meet the following goals [3]. Make sure that the system operates close to the Maximum Power Point (MPP) when it is subjected to changing in environmental condition. Provide high conversion efficiency. Maintain tracking for a wide range of variation in environmental conditions.
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Chapter 2 – Literature Review Provide an output interface compatible with the battery charging requirement. The MPPT consists of two basic components: a switch mode converter and control section.
2.3 Switch Mode Converter The switch-mode converter is the core of the entire supply. This allows energy at one potential to be drawn, stored as magnetic energy in an inductor, and then released at a different potential. By setting up the switch-mode section in various different topologies, either high-to-low (buck converter) or low-to-high (boost) voltage converters can be constructed. Normally, the goal of a switch-mode power supply is to provide a constant output voltage or current. In power trackers, the goal is to provide a fixed input voltage and/or current, such that the array is held at the maximum power point, while allowing the output to match the battery voltage.
2.4 Control Section The control section is designed to determine if the input is actually at the maximum power point by reading voltage/current back from the switching converter or from the array terminal and adjust the switch-mode section such that it is. Depending on the application, different feedback control parameters are needed to perform maximum power tracking. Most commonly voltage and power feedback controls are employed to control the system and hence to find the MPP of the array. 2.4.1 Voltage Feedback Control The solar array terminal voltage is used as the control variable for the system. The system keeps the array operating close to its maximum power point by regulating the array’s voltage and matches the voltage of the array to a desired voltage. However, this has the following drawbacks [4]: a) The effects of the insolation and temperature of the solar array are neglected. b) It can not be widely applied to battery energy storage systems. Therefore, this control is only suitable for use under constant insolation conditions, such as a satellite system, because it cannot automatically track the maximum power point of the array when variations in insolation and temperature occur. 2.4.2 Power Feedback Control Maximum power control is achieved by forcing the derivative (dP/dV) to be equal to zero under power feedback control. A general approach to power feedback control is to measure and maximize the power at the load terminal. This has an advantage of unnecessarily knowing the solar array characteristics. However, this method maximizes power to the load not power from the solar array. Although a converter with MPPT offers high efficiency over a wide range of operating points, but for a bad converter, the full power may not be delivered to the load due to power loss. Therefore, the design of a high performance converter is a very importance issue [4].
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Chapter 2 – Literature Review
2.5 MPPT Control Algorithms There are many algorithms that are used to control the MPPT. The algorithms that are most commonly used are the perturbation and observation method, dynamic approach method and the incremental conductance algorithm.
2.5.1 Perturbation and Observation Method Perturbation and Observation (P&O) method has a simple feedback structure and fewer measured parameters.
It operates by periodically perturbing (i.e.
incrementing or decreasing) the array terminal voltage and comparing the PV output power with that of the previous perturbation cycle. If the perturbation leads to an increase (decrease) in array power, the subsequent perturbation is made in the same (opposite) direction. In this manner, the peak power tracker continuously seeks the peak power condition [4].
2.5.2 Dynamic Approach Method This method employes the ripple at the array output to maximize the array power by dynamically extrapolate the characteristic of the PV array.
The instantaneous
behavior of array voltage v, current i and power p can be grouped into three cases: current below that for the optimum power, current near the optimum and current above the optimum [5]. The array performance is reflected in both shapes and phase relationships. The product of the derivatives p’ and v’ is negative if the current is below that for optimum power and positive if the current is above the optimum and zero when the maximum power point is being tracked [5]. Since p’ v’ is a chain rule derivative, it is actually equal to dp/dv. This implies that by driving dp/dv to zero, power will be effectively maximized.
2.5.3 Incremental Conductance Algorithm This method uses the source incremental conductance method as its MPP search algorithm. It is more efficient than Perturb and Observe method and independent on device physics. The output voltage and current from the source are monitored upon
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Chapter 2 – Literature Review which the MPPT controller relies to calculate the conductance and incremental conductance, and to make its decision (to increase or decrease duty ratio output).
Mathematical of the Incremental Conductance algorithm is discussed below.
The output power from the source can be expressed as P = V× I----------------------------------------- (2.1) The fact that P = V × I and the chain rule for the derivative of products yields dP/dV = d (V I) / dV = I dV / dV + V dI / dV = I + V dI / dV ∴ (1/V) dP/dV = (I/V) + dI/dV------------------------ (2.2) Let’s define the source conductance: G = I/V ------------------------------------------- (2.3) And the source incremental conductance: ∆ G = dI/dV ------------------------------------- (2.4) In general output voltage from a source is positive. Equation (2.2) explains that the operating voltage is below the voltage at the maximum power point if the conductance is larger than the incremental conductance, and vice versa. The job of this algorithm is therefore to search the voltage operating point at which the conductance is equal to the incremental conductance. These ideas are expressed by equation (2.5), (2.6), (27), and graphically shown in Figure2.2. dP/dV > 0, if G > ∆G --------------------------(2.5) dP/dV = 0, if G = ∆G --------------------------(2.6) dP/dV > 0, if G > ∆G --------------------------(2.7)
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Chapter 2 – Literature Review
Figure 2.3The P-V curve
2.6 Battery A battery is a device capable of storing electrical energy by means of a reversible chemical reaction. There are several different battery types, discerned by size, use and construction. The most common battery is the lead-acid battery, but nickel-cadmium nickel-iron and nickel-hydride are also available, among others. For most solar applications the lead-acid battery is the best choice.
2.6.1 General battery chemistry A lead-acid battery contains sulfuric acid (H2SO4), water (H2O), lead (Pb) and leadoxide (PbO2). The electrolyte is the solution of sulfuric acid in water. A battery consists of a series of cells, connected in series, to provide the desired output voltage. The output of a lead-acid cell is a little over 2 V and also depending on the state of charge. Therefore, for a 12 V lead acid battery there are 6 cells connected in series. A battery stores electrical energy by forcing electrons into positions in which they contain more energy by applying a voltage on the battery connectors. The storage is realized by the following chemical reactions [7]:
On the positive electrode: PbO2 + HSO4- + 3 H+ + 2 e → PbSO4 +H2O On the negative electrode:
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Chapter 2 – Literature Review Pb + HSO4- → PbSO4 + H+ + 2 eOverall reaction: Pb + PbO2 + 2 H+ + 2 HSO4- → 2 PbSO4 + 2 H2O When a load is connected to the battery, the reaction is reversed, and the electrons release the stored energy. The capacity of a battery (how much energy it can store) is measured in AH (Amp Hour).
2.6.2 Starting and Deep-cycle batteries Basically there are two types of batteries, they are namely starting and deep cycle batteries. Different use asks for different battery designs. A starting battery, as used in most cars, is designed to deliver a large current during a short time. A deep cycle batteries that can withstand deep discharges. It has less instant energy but greater long-term energy delivery. The main difference between the two batteries is the plate-thickness. The plates of the deep-cycle batteries are up to 35 times thicker than those of starting batteries. Hence deep cycle batteries can survive a number of discharge cycles and it is suitable for use in application where power supply standby is needed.
2.6.3 Battery charging Batteries are best charged in 3 different steps, bulk charge, absorption charge and float charge. During bulk charge, the highest charge current is sent to the batteries until the battery is 80-90% charged. During absorption charge, current is limited as internal resistance of the battery increases. The applied voltage is a little higher. Absorption charge lasts until the battery is fully charged. During float charge, voltage is reduced. The purpose of float charge is to keep a charged battery from discharging, thus enhancing battery life.
2.6.4 Battery life Since the storage and release of energy in batteries involves solving and dissolving the plates in the electrolyte, batteries do not last forever. Batteries are rated for a certain number of cycles to a certain depth of discharge. When taken care of, batteries can last for decades, while when mistreated, they can die prematurely.
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Chapter 2 – Literature Review Main causes for premature battery death are overcharging, charging with a too high charge current, and sulfating. The first two causes can be prevented by a charge controller. Sulfating is the formation of large lead sulfate on the battery plates, and occurs when the battery is left in a low- or uncharged state for a longer period of time. Sulfating is sometimes (partially) reversible by controlled charging of the battery. In a well-designed system that's being used the way it was designed for, these problems will not occur, and the batteries will provide reliable and convenient energy storage for years or decades, depending on battery quality [7].
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Chapter 3 – Theory
CHAPTER 3 - THEORY
3.1 DC-DC Converter In this section the principles of switching power conversion are introduced and details of the DC-DC boost converter circuits are discussed in steady state. A switching converter consists of capacitors, an inductor, and a switch. All these devices ideally do not consume any power, which is the reason for the high efficiencies of switching converters. The switch is realized with a switched mode semiconductor device, usually a MOSFET. It is switched on and off by the driving square wave signals at the gate. If the semiconductor device is in the off state, its current is zero and hence its power dissipation is zero. If the device is in the on state (i. e. saturated), the voltage drop across it will be close to zero and hence the dissipated power will be very small [8]. During the operation of the converter, the switch will be switched at a constant frequency fs with an on-time of DTs, and an off-time of D’Ts, where Ts is the switching period 1/fs, D is the duty ratio of the switch and D’ is (1 - D) (see Fig 3.1).
The DC-DC converters can have two distinct modes of operation [9]: (1)
continuous current conduction and (2) discontinuous current conduction. In continuous mode, inductor current never falls to zero in one switching cycle, Ts or at least one the switch or diode is conducting. Whereas in discontinuous conduction mode, the inductor current falls to zero before completing one switching cycle, Ts. In practice, a converter may operate in both modes, which have significantly different characteristics.
Figure3.1 Ideal Switch voltage v, Duty ratio D, and switching period Ts - 11 -
Chapter 3 – Theory
3.2 Boost Converter The Boost Converter, as shown in Figure 3.2, is also known as the step-up converter. As the name implies its typical application is to convert low input-voltage to a high output voltage.
Figure3.2 DC-DC Boost converter During the first time interval DTs of the switching period Ts, the closed switch connects the input through the inductor to ground and current starts to flow, the current through the inductor increases and the energy stored in the inductor builds up. The diode is reversed biased so no inductor current flows through the load, thus isolating the output stage. After the switch is opened in the second time interval D’Ts of the switching period, the output stage receives energy from the inductor as well as from the input. In steady state analysis, the output capacitor is assumed to be large to ensure a constant output voltage vo (t) ≅ Vo.
3.2.1 Continuous Conduction Mode Figure 3 [9] below shows the operation of the boost converter in the continuous conduction mode where the inductor current iL (t) > 0. When the switch is closed the source voltage Vd is applied across the inductor and the rate of rise of inductor current is dependent on the source voltage Vd and inductance L. This results in a positive voltage across the inductor in Figure 3.3a. vL = Vd -------------------------------------- (3.1) When the switch is opened in Figure 3b, the inductor voltage becomes vL = Vd – Vo---------------------------------( 3.2)
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Chapter 3 – Theory
Figure 3.3 Continuous Conduction mode: (a) switch on; (b) switch off.
Since in steady state operation the waveform must repeat from one time period, Ts, to the next, the integral of the inductor voltage vL over one time period must be zero [9], where Ts = ton + toff. This implies that the areas A and B in Figure 3.3 must be equal. Therefore, Vd × ton +( Vd – Vo) × toff = 0 ---------------- (3.3)
Dividing both sides by Ts, and rearranging all terms yields Vo / Vd = Ts / toff = 1 / (1-D) ------------------ (3.4) Assuming the circuit is 100% efficiency, i.e. the input power (Pd) and output power (Po) are the same, (Pd = Po). ∴ Vd × Id = Vo × Io Hence, Io / Id = (1 –D) ------------------------------ (3.5)
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Chapter 3 – Theory 3.2.2 Boundary between Continuous and Discontinuous Conduction Figure 3.4 [9] shows the waveforms for vL and iL at the edge of continuous conduction. Being at the boundary between the continuous and the discontinuous mode, by definition, the inductor current iL goes to zero at the end of the off period. The average inductor current at the boundary is ILB = 1 / 2 × i L,peak = 1 / 2 × Vd/L × ton -----------------------(3.6) Substitute equation (3.3) into (4.4), gives ILB = Ts × Vo × D(1 - D) / 2L ----------------(3.7)
Figure 3.4 Waveforms at the edge of the continuous conduction
In steady state the average capacitor current is zero, therefore for the boost converter the inductor current and the input current are the same (id = iL). By using equation (3.3) and (3.5), the average output current at the edge of continuous conduction is IoB = Ts × Vo × D(1 - D)2 / 2L ----------------(3.8)
In most applications, the output voltage Vo is kept constant. Therefore, with Vo constant, IoB are plotted in Figure 3.5 [9] as a function of duty ratio D.
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Chapter 3 – Theory
Figure 3.5 Average Output Current at the Boundary of continuous-discontinuous
From Figure 3.5, at D =0.5 inductor current reaches its maximum value, ILB,max = Ts × Vo / 8L ----------------------------(3.9) Also, maximum output current occurs at D = 1/3 = 0.333: IoB,max = 0.074 × Ts × Vo / L --------------------(3.10)
Figure 3.5 shows that for a given duty cycle, D, with constant Vo, if the average load current drops below IoB and (hence, the average inductor current below ILB), the current conduction will become discontinuous [9].
3.2.3 Discontinuous-Conduction Mode
Figure 3.6 Converter Waveforms at Discontinuous Conduction Figure 3.6 shows the discontinuity of inductor current as the result of the load power decreases. To understand the operation in this mode, the input voltage, Vd, and duty ratio, D, is assumed to be constant (although, in practice, this is not the case, since D would vary in order to keep the output voltage, Vo, constant). - 15 -
Chapter 3 – Theory
Similar to the analysis of continuous conduction mode, the integral of the inductor voltage over one time period is zero, Vd × D × Ts + (Vd – Vo) × ∆1 × Ts = 0 --------------------(3.11) ∴ Vo / Vd = (∆1 + D) / ∆1 --------------------------------------(3.12)
Assume the circuit is 100% efficiency, i.e. the input power, Pd, is equal to the output power, Po, Io / Id = ∆1 / (∆1 + D) ------------------------------------------(3.13)
As mentioned before, the average input current, Id, and the inductor current, IL, of a boost converter are equal. Hence, Id can be obtained by using Figure 6, Id = Vd × D × Ts (D + ∆1) / 2L ------------- -----------------(3.14)
Using the equation (3.11) and (3.12), the average output current can be found: Io = D × ∆1 × Ts × Vd / 2L -----------------------------------(3.15)
In practice, D varies in respond to the variation in Vd while Vo is held constant. It is useful to obtain the required duty ratio D as a function of load current for various values of Vo / Vd [9]. Combining equation (3.8), (3.10) and (3.13) yields: D = [(4 × Vo × Io )(Vo / Vd –1) / (27 × Vd × IoB,max)]1/2 ---- (3.16)
Figure3.7 Step-up converter characteristics keeping Vo constant - 16 -
Chapter 3 – Theory
In Figure 3.7, D is plotted as a function of Io / IoB,max for different values of Vd / Vo. The dashed curve is the boundary between the continuous and discontinuous conduction mode. It can be seen from Figure 3.7 that by vary the duty ratio and the change in the output current will keep the output voltage constant at all time.
3.2.4 Effect on Parasitic Elements The parasitic elements in a boost converter are due to the losses associated with the diode, the inductor, the capacitor and the switch. Figure 3.8 [9] shows the effect of these parasitics on the voltage transfer ratio. In ideal situation, according to equation (3.2) as D approaching unity the ratio between input and output voltage would increase to infinity. However, in practice the ratio between input and output voltage declines as the duty ratio approaches unity. This is due to the fact that very poor switch utilization at high values of duty ratio. The curves in this range are shown in Figure 3.8 as the dashed line.
Figure 3.8 Effect of parasitic elements on voltage conversion ratio
3.2.5 Voltage and Current Ripple While the output voltage ripple amplitude ∆Vo usually ranges within 1% of the dc component Vo, the amplitude of the inductor current ripple ∆IL varies by as much as 10% to 20% of its dc value IL [9]. This is important to know, because the inductor current ripple is determined by the value of the inductance L. If the ripple gets too large, the size of the switching semiconductor device must be increased to handle the high current peaks. Increase in size would result in and increase in weigh and higher cost. - 17 -
Chapter 3 – Theory 3.2.5.1 Inductor Current Ripple By definition, the voltage drops across the inductor is vL = L × diL / dt ------------------------------------(3.17)
Using equation (3.1) and (3.17), the follow expression is obtained: diL / dt = vL / L = Vd / L -------------------------(3.18) Where diL / dt represent the slope of the inductor current during the first time interval DTs of a switching period.
For the second time interval, D’Ts with equation (3.2), the following expression is obtained: diL / dt = vL / L = (Vd - Vo) / L ------------------(3.19) The slopes diL / dt are shown in Figure 3.9 With the linear expression for diL / dt (3.18), the equation for the peak to peak ripple can be derived: ILp-p = 2 ∆iL = Vd × D × Ts / L ----------------(3.20)
Figure 3.9 Ripple Inductor current
Since the converter is assumed to be in steady state and 100 % efficiency, it does not make a difference if DTs or D’Ts is chosen to determine the current ripple amplitude.
- 18 -
Chapter 3 – Theory
Equation (3.20) now can be solved for the inductance L so that desired current ripple amplitude can be achieved: L = (Vd × D × Ts) / (2 × ∆iL) ----------------(3.21) 3.2.5.2 Output Voltage Ripple
Figure 3.10 Boost converter output voltage ripple For a continuous mode of operation, the peak to peak output voltage ripple could be calculated by considering the waveforms shown in Figure 3.10 [9]. It can be assumed that all the ripple current component of the diode current, iD, flows through the capacitor and its average value flows through the load resistor, the shaded area in Figure 3.10 represents the charge ∆Q. Hence, the peak to peak voltage ripple can be determined by [9]: ∆Vo = ∆Q / C = Io × D × Ts / C = (Vo × D × Ts) /(R × C) = (Io × D × Ts) / C --------------------(3.22)
It can be seen in equation (3.22) that for a large value of capacitor, C, the output voltage ripple can be minimized. Hence, the output capacitor acts like a filter.
3.2.5.3 Power consumption in the Boost Converter The components, which cause power loss in the Boost-Converter when operating at high switching frequency, fsw, are the diode conduction loss, inductor conduction loss, MOSFET conduction loss and switching of the MOSFET.
- 19 -
Chapter 3 – Theory
The conductance loss in the diode, Pdiode, is given by [11]: Pdiode = Id × Vf × (1 –D) --------------------(3.23) where the Voltage Vf is the forward bias of the diode, Id is the input current and D is the duty ratio. Since for the Boost-Converter the inductor current, IL, is equal the input current, Id, equation (3.23) can be rewritten as: Pdiode = IL × Vf × (1 –D) --------------------(3.24)
The conduction loss in the inductor, Pinductor, is given by: Pinductor = IL 2 × RL ----------------------------(3.25) where RL is the effective series resistance of the inductor. The conduction loss in the MOSFET, PMOSFET,conduction, is given by: PMOSFET,conduction = IL 2 × Rds × D ------------(3.26) Where Rds is the MOSFET’s drain-to-source on resistance. From equation (3.24), (3.25) and (2.26), the total conduction loss the BoostConverter is: Pconduction loss = IL × Vf × (1 –D) + IL 2 × RL + IL 2 × Rds × D --------(3.27)
The MOSFET switching loss can be found by considered four different switching periods. They are namely the turn-on, conduction, turn-off and off period.
The overlapping of the current and voltage waveforms during the turn-on period accounts for the switching loss and is given by [11]: Pturn-on = (Idso × Vdd × td × f) + f × Ids × tr [ Vdd /2 + (Vds,sat – Vdd) / 3] -(3.28) where f is the switching frequency, Vdd is the drain voltage, td is the turn-on delay time, tr is the turn-on rise time and Vds,sat is the saturated drain-to-source voltage, Idso is the drain-source leakage current of the MOSFET.
- 20 -
Chapter 3 – Theory The overlapping of the current and voltage waveforms during the turn-off period accounts for the switching loss and is given by [11]: Pturn-off = (Ids × ts × Vds,sat × f) + (Vdd × Ids × tf × f / 6) -------------(3.29) where ts is the storage time of the MOSFET.
The average power PCond. during the conduction period is given by [11]: PCond. = Vds,sat × Ids × f × tc ----------------------------------------------(3.30) where tc = D/f - td -tr is the conduction time of the MOSFET.
The average power during the off period is given by [11]: Poff = Vdd × to × f × Idso -----------------------------------------------(3.31) where to is the off time of the MOSFET.
Hence, the total switching loss in a MOSFET, PMOSFETswitching, is: PMOSFETswitching =Pturn-on + Pcond. + Pturn-off + Poff ----------------------------(3.32)
3.3 Differential Amplifier
Figure 3.11 Differential Amplifier
A differential amplifier shown in Fig 3.11 is used as a transducer that converter the current signals into voltage signals. The voltage signals that provide the information about the current therefore can be fed back to the microcontroller for processing.
- 21 -
Chapter 3 – Theory The circuit consists of two input sources V1 and V2. It responds to both the differential signal Vdiff and common-mode signal Vcm. The differential signal is the difference between the input voltages and can be defined as:
Vdiff = (V1 –V2) -------------------------- (3.23) The common mode signal is the average of the input voltages and is given by:
Vcm = 1 / 2 (V1 + V2) ------------------- (3.24) If the gain for the differential signal is denoted as Ad and the gain for the common-mode signal as Acm, then the output voltage of a differential amplifier is given by [10]:
Vo = AdVdiff + AcmVcm----------------- (3.25) For a well-designed differential amplifiers have the differential gain Ad that is much larger than the common-mode gain Acm.
A quantitative specification is the common-mode
rejection ratio (CMRR), which is defined as the ratio of the magnitude of the differential gain to the magnitude of the common-mode gain. The CMRR is defined as [10]:
CMRR = 20 log (|Ad| / |Acm|) --------- (3.26)
From the circuit theory, the output voltage of a differential amplifier is given by the following expression: Vo = (R2 / R1) (V1 –V2) ------------------ (3.27) From equation (3.27) differential amplifier gain, G, is G = (R2 / R1) ------------------------------(3.28)
- 22 -
Chapter 4 – Implementation
CHAPTER 4 – IMPLEMENTATION 4.1 Design Overview The two important things in power tracker design are the switch-mode topology and the control mechanism. The switch-mode topology is usually determined by the input and output voltages desired. The tracker can be designed to either increase (known as a boost topology) or decrease voltage (known as a buck topology) from the array going into the battery. Because a tracker is essentially a specialized switching power supply, the input and output currents are such that the power into and out of the tracker are equal. The research problem states that the PV array is field-wired into two halves and hence two MPPT will have to be built in parallel. Choosing boost converter topology will maximized the efficiency of the PV array in a cloudy day, and since boost converter are technically easier to build and also guarantee continuous current through the array. The control section is involved the design of both analog and digital system. It will take in analog voltages and currents proportional to measured quantities, digitize them, process them in a micro-controller, and then convert a number back to a voltage proportional to what the system believes is the maximum power point voltage of the array and the state of charge of the battery.
The PV array used in this project is the MSX-83.
It is most powerful of Solarex’
Megamodule™ series of photovoltaic modules, a product line which is the industry standard for reliability, and durability. With 36 polycrystalline silicon solar in series, it can generates high current up to 4.85 Amps and a voltage of 17.1 Volts and give rise to a maximum power of 83 Watts. When the PV array is field-wired into two halves, the maximum power of 41.5 Watts can be delivered on each side of the PV array. While the current will stay at the same value of 4.85 Amps and the voltage is reduced by half i.e. 8.55 Volts.
The incremental conductance method is used as a MPPT algorithm. The advantage of using this method to track MPP is because it is more efficient than the P&O method in a way that it is able to correctly locate the operating point of the PV array. There will be a trade off between the power efficiency and reliability of tracking MPP. Since the P&O method will - 23 -
Chapter 4 – Implementation move away from the power operating point under rapidly change in light condition and not be able to go back to the maximum operating point quickly. This will leads to the inefficiency use of the PV array and hence this will effects the whole system performance of tracking MPP. Other advantage of using this method is it does not depend on the device physics. The output voltage and current from the source are monitored upon which the MPPT controller relies to calculate the conductance and incremental conductance, and to make its decision (increase or decrease duty ratio output). By using this method four sensors will be used. Two sensors for each side of the PV array. They are namely: voltage and current sensors.
The battery voltage is measured by using a fifth sensor. The main program will turn off the Boost Converters, then runs a conversion on the battery via the A/D converter.
The
information obtained is then processed and then compared to the predefined values to determine the next stage of charge. Then the main program is then returned to continue tracking MPP.
Figure 4.1 Block Diagram of Maximum Power Point Tracker
The block diagram of the MPPT is shown in Fig. 4.1. It consists of: •
An 83-Watts Photovoltaic Array.
•
Voltage divider network and current sensing circuitry.
- 24 -
Chapter 4 – Implementation •
DC-DC switching converters - The two Boost Converters connected in parallel.
•
Control Section.
•
A12 volt lead acid battery as a load.
4.2 Hardware Design The most critical section of the power tracker is switching converter section. It is this section that operates the PV array at its maximally-efficient point while converting the energy provided up to a voltage that is usable by the rest of the system. It is also in this section that optimal component choice is important. Since this converter has all of the array energy flowing through it, any resistance or loss, no matter how small, will contribute to the power loss of the system. The schematic and the PCB layouts for the MPPT are in Appendix A and B respectively.
4.2.1 Inductor Inductor losses are the hardest to eliminate, because it has a certain number of turns on the coil to maintain the necessary inductance for the converter to function, every additional inch of wire adds milliohms of resistance. However, at this stage, it can be assumed that the converter output voltage is constant at 12 Volts and the converter is 100 % efficiency. i.e. Pin = Pout. And also that the converter is assumed to operates in continuous conduction mode. To find the value of inductance needed for the converter, extreme case has to be considered. That is when the PV array operates at its maximum capacity i.e. 41.5 Watts. Therefore the output current can be calculated by using the equation Pout = Vo × Io: Hence, Io = Po ÷ Vo = 41.5 ÷ 12 ≅ 3.5 Amps As discussed in section 3.2.5, the amplitude of the inductor current ripple can be varying between 10% and 20% of its dc value. If the converter is assumed operating at frequency of 20kHz (i.e. Ts = 10 µs), and the inductor current is assumed to be equal to the output current and its current ripple is 10% (i.e. ∆iL = Io × 0.2 = 3.5 × 0.1 = 0.35A). Equation (3.21) gives: L = (Vd × D × Ts) / (2 × ∆iL) The duty cycle ratio, D, can be calculated by using equation (3.4), - 25 -
Chapter 4 – Implementation Vo / Vd = 1 / (1-D) Knowing that Vd = 8.55 Volts, hence D = 0.2875 The minimum inductance value is L = (8.55 × 0.2875 × 10 × 10-6) / (2 × 0.35) ∴L ≅ 35 µH Since, the inductor must at least be able to handle current of 3.5 Amps. Therefore, an inductor of 220 µH and its rating current of 5.5A with resistance of 63mΩ is chosen for the converter.
4.2.2 Output Capacitor To obtain a desired output voltage ripple, the right value of capacitance is required. Once again, the extreme case is considered. As before, the output current is 3.5A, D = 0.2875, Ts = 10 µs. Assume that the output voltage ripple is 1% of its dc value (i.e. ∆Vo = 0.12V. Equation (3.22) gives: ∆Vo = (Io × D × Ts) / C After rearranging, C = (Io × D × Ts) / ∆Vo C = (3.5 × 0.2875 × 10 × 10-6) / 0.12 ∴C≅ 84 µF The minimum capacitance value needed for the converter is 84 µF. Hence, a 2200 µF is chosen for the design. 4.2.3 Diode Diode choice is a trade off between breakdown voltage, speed, and forward voltage. The higher the forward voltage, the more power that will be dissipated and lost. However, fast diode is needed to act as a switch for the energy in the inductor. If the diode is slow to react, the efficiency of the converter will lower and damaging high voltage transients will develop. In case of these transients and the possibility of large output voltages if the load is suddenly disconnected, the diode also must have a high breakdown voltage. The best combination of these features that could be found was the MBR745 from Fairchild Semiconductor, which has 45 V reverse breakdown, and 0.57 V of forward drop at the expected currents of 7.5A.
- 26 -
Chapter 4 – Implementation 4.2.4 Voltage Regulator Since the microcontroller requires a supply voltage of 5V. A step down voltage regulator LM2936-5.0 is chosen. Its features are: •
Ultra low quiescent current - Low power consumption, hence it allows a better conversion efficiency of the boost converter.
•
40 V operating voltage limit - It is capable of stepping down the voltage from the battery (12V) to 5V.
•
Internal short-circuit current limit - the microcontroller will be protected if there is a short- circuit in the circuitry.
•
Internal thermal shutdown protection – This will protect the regulator from over heat if there is a short-circuit in the circuitry.
4.2.5 MOSFET An n-channel enhancement mode power MOSFET RFP3055LE is used as a high speed-switching device for the Boost-Converter. Since the rating of this device is rated at 60V and 11A, this rating is well above maximum operating voltage and current which are 12 V and 3.5 A of the converter. It has a maximum leakage current of only 100n Amp and very low on state resistance of 0.107Ω and hence small conduction loss that makes it a highly efficient switching device.
4.2.6 MOSFET Driver Since the PWM current signals generated by the microcontroller can only deliver maximum current of 25mA. It is not suitable to drive a large capacitive load such as a MOSFET with high slew rate. In order to achieve high speed switching in power MOSFET, a MOSFET driver MC34152P is used. It has a low output impedance and capable of sourcing and sinking a large gate current for a short duration. And since it is operating at current as low as 10.5mA and is capable of supplying two independent output channels up to 1.5A. This MOSFET driver is a suitable choice since the design required two PWM signals to switch the two power MOSFETs. 4.2.7 Microcontroller PIC16F873 is chosen as a microcontroller for the design. This microcontroller is responsible for all tracker functionality, operating the ADCs and DACs that deal with
- 27 -
Chapter 4 – Implementation
the analog section, computing what the power point of the array is, and monitoring the state of charge of the battery. The PIC16F873 is a perfect combination of features, performance, and low power consumption for this application. It has 8K x 14 bytes of flash memory, 368 x 8 bytes of data memory (RAM) two D/A and five A/D channel. The two D/A converter pins are used to send the analog voltages (PWMs) back out to set the two DC-DC switching converter to the maximum power point voltage of the PV array. For the five A/D converter channels, two are used to monitor the PV array’s currents, two are used to monitor the PV array’s voltages, and the last one is used to monitor the battery voltage.
4.2.8 Voltage divider network Since the PIC16F873 can only process digital information, A/D conversion is required. Analog signals, either the voltage from the voltage divider network or from the differential amplifier must be converted to binary numbers that is digestible by the PIC16F873. Since the A/D reference voltage is the voltage supplied to PIC16F873 from the LM2936-5.0 voltage regulator, hence the maximum voltage that the PIC16F873 is able to sample is 5V. Therefore, to monitor and sample the voltage from the PV array or from the battery, voltage divider network is needed to lower their voltages. The resistors used for the voltage divider network for the PV array voltage are the15kΩ and 12kΩ. This gives the resistance ratio of 12kΩ / (15kΩ + 12kΩ) = 0.44 and therefore gives the maximum input voltage to the A/D conversion channel is 0.44 × 8.55 = 3.76V, which is less than 5V. Since the battery voltage (13.8V at fully charge) is higher than the PV array voltage (8.55V), the resistance ratio need to be smaller. Hence, the resistance values chosen are 22kΩ and 8.2kΩ. This gives the resistance ratio of 8.2kΩ / (22kΩ + 8.2kΩ) = 0.27 and therefore gives the maximum input voltage to the A/D conversion channel is 0.27 × 13.8 = 3.73V.
- 28 -
Chapter 4 – Implementation 4.2.9 Current-Sensing Circuit The current signals from the PV array are monitoring by using the current sensing circuit. The sensing circuit that acts as a transducer that convert the current reading to the voltage signals so that the microcontroller can understand and use the information to process and hence performs the PWMs. By connecting a current resistor at the inputs of the differential amplifier, the current from the PV array passing through the resistor and gives rise to a voltage drop across it. The voltage is then amplified by the differential amplifier. Since the power dissipation in the resistor is P = I2 × R, the power dissipation in the resistor is therefore depending on the resistor value to be used and hence this will contribute to the power loss of the whole system. If the solar panel is assumed operating at its maximum capacity, the maximum output current is 4.85A. And if 0.5W dissipation is allowed for the current sensing resistor, the resistance value can be determined, 0.5 = 4.852 × R ∴ R = 0.5 / 4.852 = 0.0213 Ω A 0.022 Ω surface-mount resistor is chosen for the design, the maximum power loss is estimated to be 0.52 W.
The operation amplifier that is used for the differential amplifier is the LM358N. It has a high common mode rejection ratio of 70dB, therefore the common mode signal at the input will not be amplified in a great extent that affects the design. The resistance value chosen for R1is 15kΩ and R2 is 560kΩ. Hence, the equation (3.28) gives, G = (R2 / R1) = (560k / 15k) ≅ 37 with the maximum current of 4.85A flowing through the 0.022Ω resistor, the maximum voltage drop across it will be 4.85 × 0.022 = 0.1067V.
Hence the
maximum amplified voltage that will be seen at the microcontroller A/D converter channel is Vmax,amp = 0.1067 × 37 = 3.95V
- 29 -
Chapter 4 – Implementation
4.3 Software Design With the hardware circuit design completed, the next step in the design is the on-board software control. The Incremental Conductance method is chosen as a tracking algorithm for the MPPT. The PIC16F873 microcontroller operates at speed of 4MHz is used to carry out the algorithm. At this speed each instruction set will be executed at 1µ second. The program is written in C and then is compiled by a freeware version C compiler “CC5X” from B Knudsen Data.
The program flow chart is shown in Figure 4.1. The program starts by initializing the A/D module and the D/A (PWM) module and sets the duty ratio at 50%, since it is likely that the MPP can be found. The PWM module is turned off at this stage and the program runs A/D conversion on channel RA5 to measure the battery voltage. The measured voltage is then compared to the predefined values to determine the state of charge of the battery. If the battery voltage is greater than the 13.8V 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 high current charging mode. In this mode, the Incremental Conductance algorithm is employed.
First, the program is running the Incremental Conductance algorithm on the first halves of the PV array (S1) and then the second halves of the PV array (S2). The program flow chart for this algorithm is shown in Figure 4.2 for the first halves of the PV array and the program flow chart for the second halves of the PV array is shown in Figure 4.3. Only the first halves of the PV array program flow charge will be discussed, since the other is exactly the same. The operating output current (I(k)_S1) and voltage (V(k)_S1) from S1 are measured by using A/D channels RA0 and RA1. The incremental changes dV_S1 and dI_S1 are approximated by comparing the most recent measured values for (V(k)_S1) and (I(k)_S1) with those measured in the previous cycle (V(k - 1)_S1) and (I(k - 1)_S1). Then G and ∆G are computed. From section 2.5.3 equation (2.6), if dP/dV = 0 (i.e G = ∆ G) is true, then the system operates at the MPP and no change in operating voltage is necessary, thus the adjustment step is bypassed (no adjustment for the duty ratio) and the current cycle ends. The program then runs the Incremental Conductance algorithm on S2. If equation (2.6) is false, equation (2.5) and (2.7)
- 30 -
Chapter 4 – Implementation are used to determine whether the system is operating at a voltage greater or less than the MPP and hence to increase or decrease the duty ratio by 1 accordingly. If the system was operating at the MPP during the previous cycle, the incremental change of the operating voltage will be zero (dV_S1 = 0). This would lead to a division by zero i.e. ∆G_S1 = dI_S1 ÷ dV_S1 = dI_S1 ÷ 0, this is impossible for calculation. To avoid this, the condition (dV_S1 = 0) is checked first and leads to another branch if true in the algorithm with further tests on possible changes of the panel's operating conditions. Since the voltage (dV_S1 = 0) that means it has not changed, now the only useful information about possible changes can be found from the current measurement. If dI_S1 is equal to zero, the operating conditions have not changed and therefore the adjustment of the system voltage is bypassed. If dI_S1 > 0, the duty ratio is increased by 1. If dI < 0, the duty ratio is decreased by 1. The program then returns and starts tracking again until the MPP is reached. The tracking process duration is 1 minute. After 1 minute the program goes back to measure the battery voltage again to determine the state of charge of the battery. The tracking process using Incremental Conductance algorithm is then repeated. For the A/D conversion to work correctly, a delay time of 20 µsec is required at the beginning of each A/D conversion since this allows for the A/D to acquire the data. The maximum duty cycle ratio is set at 90% and the minimum is at 10% to avoid power loss, and hence contributes to the inefficient power transfer of the converter. This will be further discussed in Chapter 5. The actual C codes are included in Appendix C.
- 31 -
Chapter 4 – Implementation Start
Initialize ADC Module
Initialize PWM Module & set duty ratio, duty_S1 = duty_S2 = 50%. PWM Module Off
Measure Battery voltage
Battery Voltage >13.8V ?
No
PWM Module On
Yes
Stop Charging
PWM Module Off
High-Current Charging
High-Current Charging
Tracking MPP for S1 using Incremental Conduction alg.
No Tracking MPP for S2 using Incremental Conduction alg.
Delay 1 minute ?
Figure 4.1 Program Flow Chart Yes Return
- 32 -
Chapter 4 – Implementation Tracking MPP for S1 using Incremental Conductance alg.
Initialize Sense Vin(k) _S1 & Iin(k) _S1 from S1 dV_S1 = Vin(k) _S1 - Vin(k-1)_S1 dI _S1 = Iin (k) _S1 - Iin(k-1) _S1 G_S1 = Vin(k) _S1÷ Iin(k)_S1 ∆G_S1 = dI _S1 ÷ dV_S1
No
Yes
Yes
dV_S1 = 0?
dI_S1= 0?
G_S1=∆G_S1?
No
No dI_S1> 0?
G_S1>∆G_S1?
Yes
No duty_S1 = duty -1
Yes
No
duty_S1 = duty +1
duty_S1 = duty -1
Yes duty_S1 = duty +1
Return
Figure 4.2 Control Flow Chart for S1- Incremental Conductance method
- 33 -
Chapter 4 – Implementation Tracking MPP for S2 using Incremental Conductance
Initialize
Sense Vin(k) _S2 & Iin(k) _S2 from S2
dV_S2 = Vin(k) _S2 - Vin(k-1)_S2 dI S2 = Iin (k) S2 - Iin(k-1) S2
G_S2 = Vin(k) _S2÷ Iin(k)_S2 ∆G S2 = dI S2
No
Yes
÷ dV
S2
Yes
dV_S2 =0 ?
G_S2= ∆G_S2 ?
dI_S2= 0 ?
No
No G_S2> ∆G_S2 ?
No
dI_S2 >0 ?
No
Yes
duty_S2 = duty -1
Yes
duty_S2 = duty +1
duty_S2 = duty -1
Yes duty_S2 = duty +1
Return Figure 4.3 Control Flow Chart for S2- Incremental Conductance method - 34 -
Chapter 5 – Results and Discussion
CHAPTER 5 – RESULTS AND DISCUSSION
5.1 Evaluation of the Boost Converter DC-DC switching Boost-Converter was employed in this thesis project because of its high conversion efficiency. It is capable of delivery most of the input power from the PV array to the load. The following experiments show the behaviour of the Boost-Converter under different switching frequencies and duty cycle ratios that could affect the power efficiency of the Boost-Converter. Since the DC power supply can supply constant voltage and current, therefore it is a suitable device for the experiments that can be use to simulate the PV array. A 12 V lead-acid battery was used as a load at the output of the converter.
5.1.1 Switching Frequency vs. Power Efficiency In this experiment a function generator was used to generate square-wave signals that performed PWM on the designed Boost-Converter. The duty cycle ratio was set and kept constant at 55%. The DC power supply was set at 10V and the current was limited to 3A. The input voltage, input current, output voltage and output current were measured and recorded in Table 5.1 under various PWM switching frequency. The input power (Pin) and output power (Pout) then calculated by using the relationship P = V × I. Hence the power efficiency can be found by using the relation η = Pout / Pin. Switching Frequency vs. Power Efficiency 10V-3A D = 55% Switching Frequency (kHz) 1 3 5 10 15 20 25 30 40 50 60
Input Voltage (V) 3.40 7.42 8.02 8.00 7.98 7.76 7.75 7.73 7.73 7.70 7.68
Input Current (A) 3.000 2.999 3.000 2.999 3.000 3.000 3.000 2.999 2.998 2.998 2.998
- 35 -
Output Voltage (V) 13.44 16.44 16.57 16.58 16.54 16.09 16.08 16.06 16.05 16.03 16.01
Output Current (A) 0.446 1.156 1.296 1.313 1.315 1.315 1.314 1.312 1.311 1.306 1.300
Power Efficiency (%) 58.6980 85.4042 89.2549 90.7367 90.8525 90.8864 90.8779 90.8915 90.7960 90.6889 90.3945
Chapter 5 – Results and Discussion 70 80 90 100 120 140 160
7.65 7.63 7.61 7.58 7.54 7.50 7.45
2.998 2.997 2.997 2.997 2.997 2.997 2.997
16.00 15.98 15.97 15.95 15.92 15.89 15.85
1.295 1.289 1.284 1.278 1.268 1.257 1.246
90.3435 90.0779 89.9080 89.7296 89.3314 88.8610 88.4513
Table 5.1 Switching Frequency vs. Power Efficiency
Figure 5.1 Switching Frequency vs. Power Efficiency
The plot in Figure 5.1 shows the power efficiency reached its maximum value when the switching frequency is around 20kHz. The power efficiency gradually rolled off as the switching frequency increases beyond 20kHz. This is because the switching loss of the MOSFET is proportional to the frequency that driving it. Also, the power efficiency decreased rapidly when the frequency drops below 20kHz. This can be explained by considering that the inductor has reached it saturation. At this state, the inductor is no longer store energy, what it does is drawing the capacitor’s energy and
- 36 -
Chapter 5 – Results and Discussion hence discharging the capacitor. As a result, the current in the inductor at this stage is very high and therefore this gives rise to a very high inductor power loss.
In
conclusion the switching frequency for the Boost-Converter should not be too low or too high.
5.1.2 Power Efficiency vs. Duty Cycle Ratio In this experiment the power supply was set at 10V-3A as in the previous section. However, the switching frequency is kept fixed at 20kHz this time since it is an optimum switching frequency that was found from the section 5.1.1. The input voltage, input current, output voltage and output current were measured and recorded in Table 5.2 under various duty cycle ratio and their relationship is plotted in Figure 5.2.
Power Efficiency vs. Duty Cycle Ratio 10V-3A, f = 20kHz Duty Cycle Ratio, D(%) 10 20 25 30 35 40 45 50 55 60 65 70 75 80
Input Voltage (V) 8.52 10.57 10.51 10.41 10.05 9.33 8.55 7.76 7.16 6.47 5.63 5.13 4.29 3.65
Input Current (A) 0.267 0.407 1.341 2.680 2.991 2.996 2.996 2.996 2.994 2.995 2.996 2.996 2.996 2.996
Output Voltage (V) 10.34 13.05 13.23 13.49 13.53 13.47 13.41 13.35 13.31 13.27 13.22 13.19 13.14 13.09
Output Current (A) 0.205 0.314 0.974 1.785 1.890 1.745 1.589 1.425 1.300 1.156 0.976 0.867 0.689 0.546
Table 5.2 Power Efficiency vs. Duty Cycle Ration
- 37 -
Power Efficiency (%) 93.1802 95.2513 91.4297 86.3107 85.0701 84.0891 83.1849 81.8262 80.7154 79.1640 76.4947 74.4054 70.4394 65.3578
Chapter 5 – Results and Discussion
Figure 5.2 Power Efficiency vs. Duty Cycle Ratio
The plot in Figure 5.2 above shows that the maximum power efficiency occurs at D = 20%. The curve shape is similar to the one in Figure 5.1 and it also shows that the efficiency decreases on either end of the graph, i.e. at low and high duty cycle ratio. At high duty cycle ratio, the Boost Converter experiences poor switching utilization. This is due to the fact that the MOSFET operates in its active region most of the time. At low duty cycle ratio, the power transfer to the load is decreases while the power loss in the MOSFET is staying the same. Therefore the efficiency is lower in this region where D is less than 20%.
5.1.3 Power Budget The power losses in the whole design system is calculated and summarized in the Table 5.3. The MPPT was assumed to operate at MPP and the switching frequency of 20kHz with the duty cycle ratio set to 55%. PSPICE were carried out to simulate the Boost-Converter and is shown in Appendix D.
The
converter’s input voltage and current was set to 8.55V and 4.85A respectively.
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Chapter 5 – Results and Discussion Using the results from PSPICE simulation and the information obtain from component data sheet (see Appendix E), the power losses in the converter can be determined.
Inductor conduction loss The conduction loss in the inductor can be found by using equation (3.25). From PSPICE simulation the RMS inductor current is equal to 4.5604A and from the data sheet the inductor resistance is 0.063Ω.
Therefore, the power loss due to the
conduction loss in the inductor is ∴ Pinductor = 4.5604 2 × 0.063 = 1.31 W
Diode conduction loss Equation (3.24) gives the diode conduction loss, Pdiode = IL × Vf × (1 –D). Where D = 0.55 and from data sheet the forward bias of the diode, Vf = 0.57V. ∴ Pdiode = 4.5604 × 0.57× (1 – 0.55) = 1.17 W
MOSFET conduction loss The power loss due to the MOSFET conduction loss is given by equation (3.26), PMOSFET,conduction = IL 2 × Rds × D = 4.5604 2 × 0.107 × 0.55 = 1.22 W
MOSFET switching loss The MOSFET switching loss can be found by using equations (3.28) - (3.32). The values for Vds,sat, tr, ts, tf, td, to and Idso are obtained from the RFP3055LE data sheet.
Equation (3.28) gives: Pturn-on = (Idso × Vdd × td × f) + f × Ids × tr [ Vdd /2 + (Vds,sat – Vdd) / 3] where the RMS drain current, Ids, is the different between the RMS inductor and diode current. From PSPICE simulation the RMS diode current is equal to
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Chapter 5 – Results and Discussion 3.0580 A. Hence, Ids = 4.5604 -3.0580 = 1.5024 A. MOSFET drain-source voltage waveform Vdd use for PSPICE simulation is equal to 12V. ∴Pturn-on = (100nA ×12V×8ns×20kHz) + 20kHz ×1.5024A × 105ns [12V /2 + (1.25V – 12V) / 3] = 7.62 mW
Equation (3.29) gives: Pturn-off = (Ids × ts × Vds,sat × f) + (Vdd × Ids × tf × f / 6) = (1.5024A × 22ns × 1.25V × 20kHz)+(12V × 1.5024 × 39n × 20kHz / 6) = 3.17 mW
Equation (3.30) gives: PCond. = Vds,sat × Ids × f × tc = Vds,sat × Ids × f × (D / f – tr –td) = 1.25V × 1.5024A × 20kHz × (0.55 / 20khz – 105ns – 8ns) = 1.03 W
Equation (3.31) gives: Poff = 12V × 92ns × 20kHz × 100ns = 2.208 nW The total switching loss in the MOSFET given by equation (3.32) is: PMOSFETswitching = Pturn-on + Pcond. + Pturn-off + Poff = 7.62mW +1.03W + 3.17mW + 2.208 nW = 1.041 W
Current-Sensing Resistor The power dissipated in the current-sensing resistor can be calculated by using the equation Pcurrent-sensing res. = Id2 × R = IL2 × R where Id = IL is the RMS input current obtained from PSPICE simulation. ∴ Pcurrent-sensing res. = 4.5604 2 × 0.022 = 457.54 mW
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Chapter 5 – Results and Discussion Other estimated power loss
Microcontroller From the PIC16F873 data sheet, the maximum current into VDD pin is 250mA. Since the voltage supply to the PIC16F873 is 5V and if the current required by the PIC16F873 is assumed to be 1mA. Then the power consumed by the PIC16F873 can be estimated by using the equation: Pmirco = Vmirco × Imirco = 5V × 1mA = 5 mW
Op-amp LM358 Once again, the voltage supply to the Op-amp is 5V and if the current required by the Op-amp is assumed to be 100 µA. Then the power consumed by the Opamp can be estimated by using the equation: Pop-amp = V op-amp × I op-amp = 5 × 100 µA = 0.5m A
Regulator, LM2936-5.0 Since regulator supplies voltage to the microcontroller and the Op-amp. Hence, the current that drawn from the regulator is sum of the current into the microcontroller and the Op-amp LM358. And since the voltage supplied to the regulator is 12V, the power consumed by the regulator is: Preg = Vreg × Ireg = Vreg × (Imirco + I op-amp) = 12 × (1mA + 0.1mA) = 12 × 1.1mA = 13.2mA
MOSFET Driver MC34152P
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Chapter 5 – Results and Discussion Since the voltage supply to the MOSFET driver is 12V and if the current required by the driver when operating is assumed to be 5mA. Then the estimated power consumed by the driver is: PMosfet-driver = V Mosfet-driver × I Mosfet-driver = 12V × 5mA = 60mA Power Budget Input Power
Components Solar Panel, MSX-83
Power Loss
41.5 W
Inductor Diode Current-Sensing Resistor Microcontroller, PIC16F873 Op-amp, LM358 MOSFET Driver, MC34152P Regulator, LM2936-5.0 MOSFET, FP3055LE
Pinductor = 1.31W Pdiode = 1.17W Pcurrent-sensing res. = 457.54 mW Pmirco = 5 mW Pop-amp = 0.5mA PMosfet-driver = 60mA Preg = 13.2mA PMOSFET,conduction = 1.22W PMOSFETswitching = 1.041W
Balance
41.5 – 5.28 = 36.22
Power efficiency, η
36.22 / 41.5 = 87.28% Table 5.3 Power Budget
5.1.4 Evaluation of the Product The product designed for this thesis project is capable of tracking MPP on two separate PV array panels. From experiment the tracking accuracy of the product was found to be 97.6%, hence the tracking error is 100% - 97.6% = 2.4%. The product is also capable of stop charging the battery when it detects the battery voltage at around 14V. Since the battery voltage at this point is considered as fully charged.
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Chapter 6 – Conclusions and Future Work
CHAPTER 6 – CONCLUSION AND FUTURE WORK
6.1 Conclusion 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 the maximum power point from the PV array. For this thesis project, the MPPT is implemented by using a Boost-Converter, which is designed to operate under continuous conduction mode and a microcontroller to control the PWM signals to the Boost-Converter and also to monitoring the state of charge of the battery. The Incremental Conduction Algorithm is used as the control algorithm for the MPPT. Experimental results have shown that the MMPT has the conversion efficiency of 87.28% and tracking accuracy of 97.6%.
6.2 Future Work Although the product can achieved 87.28% of conversion efficiency. It is still not considered as a high efficiency product. The component choice is very important in the design of the MPPT. Since higher power efficiency can be achieved by carefully selecting the right components. This is what needs to be done in the future. And also since the MPPT can not go into the sleep mode when the PV array not producing significant amount of power due to low insolation level. This is also contributing to the loss of power and needs to be considered in future design of the MPPT.
Since the product can only fast charging the battery by maximizing the current into the battery and stop charging when the battery reaches its full state of charge. In the future, float and absorption charge needs to be considered in the design.
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Appendix
Appendix A - MPPT Schematic
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Appendix
Appendix B - PCB Layout • Top Layer
• Bottom Layer
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Appendix
Appendix C - C Codes #include "16f873.h" #include "math24f.h" #define num1 1012 #define num2 1022 uns8 duty, mcount, ncount; float V_batt, Vin1_S1, Vin2_S1, Iin1_S1, Iin2_S1, G_S1, dI_S1, dV_S1, dG_S1, ero; void int_pwm(void){ TRISC = bin(00110000); PORTC.1 = 0; PIE1.1 = 0; PIE1.2 = 0; CCP1CON = 0; PR2 = 0b.0011.1110; CCP1CON.5 = 0; CCP1CON.4 = 0; duty = 0b.0001.1111; CCPR1L = 0b.0001.1111; T2CON = bin(00000000); TMR2 = 0; CCP1CON = bin(00001100);
// port c2 output (CCP1, PWM1) // disable timer 2 interrupts // disable ccp1 interrupts // CCP1 module off // load period register (62)
// set duty cycle
// prescaler 1:1 // timer 2 off // ccp1 pwm mode, ccp1 module on
} void delay_20us (void){ char count = 0x07; loop: if (-- count == 0){ return;} else goto loop; } void delay_100ms(void){ char mcount = 0x4f;
// M counter = 256
char ncount = 0x4f;
// N counter = 256
loadn: decn: while (-- ncount > 0){ goto decn;} while (-- mcount > 0){ goto loadn;} return; - 46 -
}
void delay_200ms(void){ char mcount = 0xff;
// M counter = 256
char ncount = 0xff;
// N counter = 256
loadn: decn: while (-- ncount > 0){ goto decn;} while (-- mcount > 0){ goto loadn;} return; } void int_adc (void){ TRISA =bin(00011111); ADCON1 = bin(10000000); }
// inputs/outputs // PortA, bit1,0 analog input
void incduty(void){
// Increment the duty ratio by 1
W = 60 - duty; while (STATUS.2 == 1){ return;} duty = duty +1; CCPR1L = duty; return; } void decduty(void){
// decrement the duty ratio by 1
W = 0x2 - duty; while (STATUS.2 == 1){ return;} duty = duty -1; CCPR1L = duty; return; } void start_conv(void){ delay_20us(); ADCON0.2 = 1; test: if ( ADCON0.2 == 1){ finish?
// start conversion // test go/done bit, conversion
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goto test;} delay_100ms(); return; } void get_measure_batt (void){ V_batt.low8 = ADRESL; V_batt.mid8 = ADRESH; result }
// conversion complete get A/D
void get_Vin1_S1 (void){ Vin1_S1.low8 = ADRESL; Vin1_S1.mid8 = ADRESH; result }
// conversion complete get A/D
void get_Iin1_S1 (void){ Iin1_S1.low8 = ADRESL; Iin1_S1.mid8 = ADRESH; result }
// conversion complete get A/D
void get_Vin2_S1 (void){ Vin2_S1.low8 = ADRESL; Vin2_S1.mid8 = ADRESH; result }
// conversion complete get A/D
void get_Iin2_S1 (void){ Iin2_S1.low8 = ADRESL; Iin2_S1.mid8 = ADRESH; result }
// conversion complete get A/D
void test1 (void){ if(Iin2_S1 == Iin1_S1 ){ return;} if (Iin2_S1 > Iin1_S1){ incduty(); return;} if (Iin2_S1 < Iin1_S1){ decduty(); return;} } void test2 (void){ - 48 -
if ( dG_S1 == G_S1 || ero ero){ incduty(); return;}
} void measure_batt(void){ ADCON0 = bin(01101001); on start_conv(); get_measure_batt(); }
// select conversion clock = 8, AN0
void main (void){ int_pwm(); T2CON.2 = 1; InitFpFlags(); int_adc();
// timer 2 on, pwm1 on
measure_batt(); again: if (V_batt >= num1 || V_batt
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