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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

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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

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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.

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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

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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.

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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

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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

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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

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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

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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

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.

Chapter 1 - Introduction

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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.

Chapter 1 - Introduction

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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

Chapter 2 – Literature Review

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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.

Chapter 2 – Literature Review

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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].

Chapter 2 – Literature Review

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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

Chapter 2 – Literature Review

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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)

Chapter 2 – Literature Review

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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 lead-

oxide (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:

Chapter 2 – Literature Review

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Pb + HSO4- → PbSO4 + H+ + 2 e-

Overall 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.

Chapter 2 – Literature Review

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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].

Chapter 2 – Literature Review

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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

Chapter 3 – Theory

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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)

Chapter 3 – Theory

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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)

Chapter 3 – Theory

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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.

Chapter 3 – Theory

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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).

Chapter 3 – Theory

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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

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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.

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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.

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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.

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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 Boost-

Converter 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.

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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.

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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)

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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

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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.

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• 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),

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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.

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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

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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.

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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

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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)

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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.

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Figure 4.1 Program Flow Chart

Chapter 4 – Implementation

Yes

High-Current Charging

Tracking MPP for S1 using Incremental Conduction alg.

Tracking MPP for S2 using Incremental Conduction alg.

No

Delay 1 minute ?

Return

Yes No

Start

Initialize ADC

Module

Initialize PWM Module & set duty ratio, duty_S1 = duty_S2 = 50%.

PWM Module Off

Measure Batteryvoltage

Battery Voltage >13.8V ?

PWM Module On Stop Charging

High-Current Charging PWM Module Off

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Figure 4.2 Control Flow Chart for S1- Incremental Conductance method

Chapter 4 – Implementation

No Yes

No

No

No

Yes Yes

G_S1>∆G_S1?

duty_S1 = duty -1

Yes

dI_S1> 0?

duty_S1 = duty -1 duty_S1 = duty +1 duty_S1 = duty +1

Return

Tracking MPP for S1 using Incremental Conductance alg.

Yes

G_S1 = Vin(k) _S1÷ Iin(k)_S1 ∆G_S1 = dI _S1 ÷ dV_S1

dV_S1 = Vin(k) _S1 - Vin(k-1)_S1 dI _S1 = Iin (k) _S1 - Iin(k-1) _S1

Initialize

Sense Vin(k) _S1 & Iin(k) _S1 from S1

dV_S1 = 0? No

G_S1=∆G_S1? dI_S1= 0?

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G_S2> ∆G_S2

?

dI_S2 > 0 ?

Yes

G_S2 = Vin(k) _S2÷ Iin(k)_S2 ∆G S2 = dI S2 ÷ dV S2

dV_S2 = Vin(k) _S2 - Vin(k-1)_S2 dI S2 = Iin (k) S2 - Iin(k-1) S2

Tracking MPP for S2 using Incremental Conductance

Initialize

Sense Vin(k) _S2 & Iin(k) _S2

from S2

dV_S2 = 0 ?

No

No Yes

Yes G_S2= ∆G_S2

?

No

duty_S2 = duty -1

No Yes

Yes dI_S2= 0 ?

No

duty_S2 = duty -1

duty_S2 = duty +1

duty_S2 = duty +1

Return

Figure 4.3 Control Flow Chart for S2- Incremental Conductance method

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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

ηηηη = Pout / Pin.

Switching Frequency vs. Power Efficiency 10V-3A D = 55%

Switching Frequency

(kHz)

Input Voltage

(V)

Input Current (A)

Output Voltage

(V)

Output Current

(A)

Power Efficiency

(%) 1 3.40 3.000 13.44 0.446 58.6980 3 7.42 2.999 16.44 1.156 85.4042 5 8.02 3.000 16.57 1.296 89.2549

10 8.00 2.999 16.58 1.313 90.7367 15 7.98 3.000 16.54 1.315 90.8525 20 7.76 3.000 16.09 1.315 90.8864 25 7.75 3.000 16.08 1.314 90.8779 30 7.73 2.999 16.06 1.312 90.8915 40 7.73 2.998 16.05 1.311 90.7960 50 7.70 2.998 16.03 1.306 90.6889 60 7.68 2.998 16.01 1.300 90.3945

Chapter 5 – Results and Discussion

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70 7.65 2.998 16.00 1.295 90.3435 80 7.63 2.997 15.98 1.289 90.0779 90 7.61 2.997 15.97 1.284 89.9080 100 7.58 2.997 15.95 1.278 89.7296 120 7.54 2.997 15.92 1.268 89.3314 140 7.50 2.997 15.89 1.257 88.8610 160 7.45 2.997 15.85 1.246 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

Chapter 5 – Results and Discussion

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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(%)

Input Voltage (V)

Input Current (A)

Output Voltage (V)

Output Current (A)

Power Efficiency (%)

10 8.52 0.267 10.34 0.205 93.1802 20 10.57 0.407 13.05 0.314 95.2513 25 10.51 1.341 13.23 0.974 91.4297 30 10.41 2.680 13.49 1.785 86.3107 35 10.05 2.991 13.53 1.890 85.0701 40 9.33 2.996 13.47 1.745 84.0891 45 8.55 2.996 13.41 1.589 83.1849 50 7.76 2.996 13.35 1.425 81.8262 55 7.16 2.994 13.31 1.300 80.7154 60 6.47 2.995 13.27 1.156 79.1640 65 5.63 2.996 13.22 0.976 76.4947 70 5.13 2.996 13.19 0.867 74.4054 75 4.29 2.996 13.14 0.689 70.4394 80 3.65 2.996 13.09 0.546 65.3578

Table 5.2 Power Efficiency vs. Duty Cycle Ration

Chapter 5 – Results and Discussion

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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.

Chapter 5 – Results and Discussion

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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

Chapter 5 – Results and Discussion

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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 = IL

2 × R

where Id = IL is the RMS input current obtained from PSPICE simulation.

∴ Pcurrent-sensing res. = 4.5604 2 × 0.022

= 457.54 mW

Chapter 5 – Results and Discussion

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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 Op-

amp 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

Chapter 5 – Results and Discussion

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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

Components Input Power Power Loss

Solar Panel, MSX-83 41.5 W

Inductor Pinductor = 1.31W Diode Pdiode = 1.17W Current-Sensing Resistor Pcurrent-sensing res. = 457.54 mW Microcontroller, PIC16F873 Pmirco = 5 mW Op-amp, LM358 Pop-amp = 0.5mA MOSFET Driver, MC34152P PMosfet-driver = 60mA Regulator, LM2936-5.0 Preg = 13.2mA

PMOSFET,conduction = 1.22W MOSFET, FP3055LE

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.

Chapter 5 – Results and Discussion

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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.

Chapter 6 – Conclusions and Future Work

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Appendix A - MPPT Schematic

Appendix

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Appendix B - PCB Layout

• Top Layer

• Bottom Layer

Appendix

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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; // port c2 output (CCP1, PWM1) PIE1.1 = 0; // disable timer 2 interrupts PIE1.2 = 0; // disable ccp1 interrupts CCP1CON = 0; // CCP1 module off PR2 = 0b.0011.1110; // load period register (62) CCP1CON.5 = 0; CCP1CON.4 = 0; duty = 0b.0001.1111; // set duty cycle CCPR1L = 0b.0001.1111; T2CON = bin(00000000); // prescaler 1:1 TMR2 = 0; // timer 2 off CCP1CON = bin(00001100); // 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 loadn: char ncount = 0x4f; // N counter = 256 decn: while (-- ncount > 0) goto decn; while (-- mcount > 0) goto loadn; return;

Appendix

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void delay_200ms(void) char mcount = 0xff; // M counter = 256 loadn: char ncount = 0xff; // N counter = 256 decn: while (-- ncount > 0) goto decn; while (-- mcount > 0) goto loadn; return; void int_adc (void) TRISA =bin(00011111); // inputs/outputs ADCON1 = bin(10000000); // 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; // start conversion test: if ( ADCON0.2 == 1) // test go/done bit, conversion finish?

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goto test; delay_100ms(); return; void get_measure_batt (void) V_batt.low8 = ADRESL; V_batt.mid8 = ADRESH; // conversion complete get A/D result void get_Vin1_S1 (void) Vin1_S1.low8 = ADRESL; Vin1_S1.mid8 = ADRESH; // conversion complete get A/D result void get_Iin1_S1 (void) Iin1_S1.low8 = ADRESL; Iin1_S1.mid8 = ADRESH; // conversion complete get A/D result void get_Vin2_S1 (void) Vin2_S1.low8 = ADRESL; Vin2_S1.mid8 = ADRESH; // conversion complete get A/D result void get_Iin2_S1 (void) Iin2_S1.low8 = ADRESL; Iin2_S1.mid8 = ADRESH; // conversion complete get A/D result 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)

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if ( dG_S1 == G_S1 || ero <= 0.01) delay_100ms(); return; if ( dG_S1 < G_S1) decduty(); return; if ( dG_S1 > ero) incduty(); return; void measure_batt(void) ADCON0 = bin(01101001); // select conversion clock = 8, AN0 on start_conv(); get_measure_batt(); void main (void) int_pwm(); T2CON.2 = 1; // timer 2 on, pwm1 on InitFpFlags(); int_adc(); measure_batt(); again: if (V_batt >= num1 || V_batt <= num2) // measuring the battery voltage delay_200ms; goto again; // do nothing PWM module off ADCON0 = bin(01000001); // select conversion clock = 8, AN0 on start_conv(); get_Vin1_S1(); ADCON0 = bin(01001001); // select conversion clock = 8, AN1 on start_conv();

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get_Iin1_S1(); while(1) char n; for (n =0; n <256; n++) // looping for a while ADCON0 = bin(01000001); // select conversion clock = 8, AN0 on start_conv(); get_Vin2_S1(); ADCON0 = bin(01001001); // select conversion clock = 8, AN1 on start_conv(); get_Iin2_S1(); G_S1 = Iin2_S1 / Vin2_S1; dV_S1 = Vin2_S1 - Vin1_S1; dI_S1 = Iin2_S1 - Iin1_S1; dG_S1 = dI_S1 / dV_S1; ero = dG_S1 + G_S1; // error margin if (ero<0) ero = -ero; if (dV_S1 < 0 ) test2(); goto swapIV; if(dV_S1 >= 0) test1(); swapIV: Iin1_S1 = Iin2_S1; Vin1_S1 = Vin2_S1; if (n == 255) // break the while loop and go break; // back to measure battery voltage

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Appendix D - PSPICE Simulation

Appendix

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Appendix

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Appendix E - Component Data Sheet

Appendix

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[6] Shengyi Liu, Maximum Power Point Tracker Models, “ http://vt.engr.se.edu”, January 2001.

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