Type-2 Fuzzy controlled MPPT algorithm for Solar PV ... · TYPE-2 FUZZY LOGIC CONTROLLER BAESD MAXIMUM POWER POINT TRACKING ALGORITHM FOR SOLAR PHOTOVOLTAIC APPLICATION A Thesis Submitted

TYPE-2 FUZZY LOGIC CONTROLLER BAESD MAXIMUM

POWER POINT TRACKING ALGORITHM FOR SOLAR

PHOTOVOLTAIC APPLICATION

A Thesis

Submitted in partial fulfilment of the requirement for the

Degree of

Master of Technology in Intelligent Automation and Robotics

Jadavpur University

May 2014

By

Abhishek Pandit

Registration No: 117000 of 2011-12 Examination Roll No: M6IAR14-14

Under the Guidance of

Prof. Amit Konar

Department of Electronics & Telecommunication Engineering Jadavpur University, Kolkata-700032

India

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FACULTY OF ENGINEERING AND TECHNOLOGY

JADAVPUR UNIVERSITY

CERTIFICATE

This is to certify that the dissertation entitled “Type-2 Fuzzy Controller Based Maximum

Power Point Tracking Algorithm for Solar Photovoltaic Application” has been carried

out by ABHISHEK PANDIT (University Registration No. : 117000 of 2011-12) under my

guidance and supervision and be accepted in partial fulfilment of the requirement for the

degree of Master of Technology in Intelligent Automation and Robotics. The research results

presented in the thesis have not been included in any other paper submitted for the award of

any other University or Institute.

-------------------------------------------------

Prof. Amit Konar Supervisor Dept. of Electronics and Telecommunication Engineering, Jadavpur University -------------------------------------------------

Prof. Iti Saha Misra Head of the Department Dept. of Electronics and Telecommunication Engineering, Jadavpur University

-------------------------------------------------

Prof. Sivaji Bandyopadhaya Dean Faculty of Engineering and Technology Jadavpur University

3

FACULTY OF ENGINEERING AND TECHNOLOGY

JADAVPUR UNIVERSITY

CERTIFICATE OF APPROVAL*

The foregoing thesis is here by approved as a creditable study of an engineering subject and

presented in a manner satisfactory to warrant acceptance as pre-requisite to the degree for

which it has been submitted. It is understood that by this approval the undersigned do not

necessary endorse or approve any statement made, opinion expressed or conclusion drawn

there in but approve the thesis only for which it is submitted.

Committee on final examination

For the evaluation of the Thesis

------------------------------------------

Signature of the Examiner

------------------------------------------

Signature of the Supervisor

* Only in the case the thesis is approved.

4

FACULTY OF ENGINEERING AND TECHNOLOGY

JADAVPUR UNIVERSITY

DECLARATION OF ORIGINALITY AND COMPLIANCE OF ACADEMIC THESIS

I here declare that this thesis titled “Type-2 Fuzzy Controller Based Maximum Power Point Tracking Algorithm for Solar Photovoltaic Application” contains literature survey and original research work by the undersigned candidate, as part of her Degree of Master of Technology in Intelligent Automation and Robotics.

All in information have been obtained and presented in accordance with academic rules and ethical conduct.

I also declare that, as required by these rules and conduct, I have fully cited and reference all materials and results that are not original to this work.

Name: Abhishek Pandit

Examination Roll No: M6IAR14-14

Thesis Title: Type-2 Fuzzy Controlled MPPT Algorithm for Solar Photovoltaic Application

------------------------------------------

Signature of the Candidate

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ACKNOWLEDGEMENTS

This thesis has been conducted at the Intelligent Automation and Robotics unit in the

Department of Electronics and Tele-communication of the Faculty of Engineering and

Technology of Jadavpur University. I would like to acknowledge all the people and institutions

that have contributed directly and indirectly in this work.

First of all, I would like to express my gratitude to my supervisor, Prof. (Dr.) Amit Konar Head

Intelligent Automation and Robotics unit for giving me the opportunity of working under his

supervision. To Mr. Sumantra Chakraborty, instructor of this thesis: it would have not been

possible to complete this work without his invaluable guidance, advice and support. I have

learnt a lot from him during the realization of this thesis.

I am also grateful to Dr. Swati Purakayastha, Managing Director of Optimal Power Synergy

India Pvt. Ltd. and Mr. Ashok Prakash, Chief Technology Officer of Optimal Power Solutions.

Without their active support and encouragement, I could not able to complete my thesis.

Also I would like to express thank to all my fellow colleges in Optimal Power Synergy

India and my University departmental mates.

Finally I would like to dedicate this thesis to my parents and wife, who have encouraged,

motivated and supported me in all odds and to achieve my desired goal in life.

6

ABSTRACT

Solar panels have a nonlinear voltage-current characteristic, with a distinct maximum power

point (MPP), which depends on the environmental factors, such as temperature and

irradiation. In order to continuously harvest maximum power from the solar panels, they have

to operate at their MPP despite the inevitable changes in the environment. This is why the

controllers of all solar power electronic converters employ some method for maximum power

point tracking (MPPT). Over the past decades many MPPT techniques have been published.

The three algorithms that where found most suitable for large and medium size photovoltaic

(PV) applications are perturb and observe (P&O), incremental conductance (InCond) and

fuzzy logic control (FLC) as on today. The first objective of this thesis is to study and analyze

them and later come up with a new type of MPPT technique using Interval Type-2 Fuzzy

control system. These were compared and tested dynamically according a recently issued

standard. This new technique is better in terms of noise reduction over Type-1 Fussy

Controlled MPPT, which overcomes their poor performance when the irradiation changes

continuously.

The dynamic MPPT efficiency tests require long simulations and if detailed models of

the power converter are used they can take a lot of memory and computation time. To

overcome this challenge a simplified model of the PV system was developed. This model was

validated with simulations.

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CONTENTS

CERTIFICATE .................................................................................................................................................... 2

CERTIFICATE OF APPROVAL* ................................................................................................................... 3

DECLARATION OF ORIGINALITY AND COMPLIANCE OF ACADEMIC THESIS ....................... 4

ACKNOWLEDGEMENTS ................................................................................................................................ 5

ABSTRACT .......................................................................................................................................................... 6

CONTENTS .......................................................................................................................................................... 7

TABLE OF FIGURES ........................................................................................................................................10

CHAPTER 1: INTRODUCTION.......................................................................................................................12

MOTIVATION .................................................................................................................................................14

PROBLEM STATEMENT ...............................................................................................................................15

CONTRIBUTIONS ...........................................................................................................................................15

THESIS OUTLINE ...........................................................................................................................................15

CHAPTER 2: SOLAR CELL AND PHOTOVOLTAIC SYSTEM CONFIGURATION ............................16

SOLAR CELL ...................................................................................................................................................16

OPERATING PRINCIPLE ...................................................................................................................................16

EQUIVALENT CIRCUIT OF A SOLAR CELL ..................................................................................................18

OPEN CIRCUIT VOLTAGE, SHORT CIRCUIT CURRENT AND MAXIMUM POWER POINT ..................19

FILL FACTOR ......................................................................................................................................................20

TEMPERATURE AND IRRADIANCE EFFECTS .............................................................................................20

TYPES OF SOLAR CELLS .............................................................................................................................23

MONO-CRYSTALLINE SILICON ......................................................................................................................23

POLYCRYSTALLINE SILICON .........................................................................................................................23

AMORPHOUS AND THIN-FILM SILICON.......................................................................................................24

OTHER CELLS AND MATERIALS ...................................................................................................................24

PHOTOVOLTAIC MODULES ........................................................................................................................26

PHOTOVOLTAIC SYSTEM CONFIGURATION ..........................................................................................27

CENTRAL INVERTER ........................................................................................................................................28

STRING INVERTER ............................................................................................................................................28

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MULTI-STRING INVERTER ..............................................................................................................................29

MODULE INTEGRATED INVERTER ...............................................................................................................29

CHAPTER 3: MAXIMUM POWER POINT TRACKING.............................................................................31

HILL-CLIMBING TECHNIQUES ...................................................................................................................31

PERTURB AND OBSERVE ................................................................................................................................31

INCREMENTAL CONDUCTANCE....................................................................................................................33

FUZZY LOGIC CONTROL .............................................................................................................................37

MAXIMUM POWER POINT TRACKING SUMMARY................................................................................40

CHAPTER 4: DC-DC CONVERTERS .............................................................................................................41

IDENTIFICATION OF SUITABLE CONVERTER FOR MPPT ....................................................................42

BUCK CONVERTER ...........................................................................................................................................43

BOOST CONVERTER .........................................................................................................................................44

BUCK-BOOST CONVERTER .............................................................................................................................44

CONCLUSION .....................................................................................................................................................45

CHAPTER 5: FUNDAMENTAL OF TYPE- 1 FUZZY SETS AND SYSTEMS AND APPLICATION IN MPPT CONTROL ...............................................................................................................................................46

TYPE-1 FUZZY SETS AND MEMBERSHIP FUNCTION ............................................................................47

FUZZY RULES AND INFERENCE ....................................................................................................................48

FUZZY CONTROLLER STRUCTURE ...............................................................................................................48

APPLICATION OF TYPE-1 FUZZY LOGIC IN MPPT CONTROL .................................................................49

DESIGN OF FUZZY LOGIC CONTROLLER PARAMETERS .....................................................................51

CONTROLLER STRUCTURE .............................................................................................................................51

MEMBERSHIP FUNCTIONS ..............................................................................................................................52

SCALING FACTORS ...........................................................................................................................................53

DERIVATION OF CONTROL RULES ...............................................................................................................53

DECISION MAKING ...........................................................................................................................................56

DEFUZZIFICATION ............................................................................................................................................58

SIMULATION OF TYPE-1 FUZZY CONTROL FOR MPPT ............................................................................60

CHAPTER 6: TYPE-2 FUZZY LOGIC AND DESIGN OF CONTROLLER FOR MPPT ALGORITHM ...............................................................................................................................................................................62

TYPE-2 FUZZY SETS ..........................................................................................................................................63

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INTERVAL TYPE-2 FUZZY SETS .....................................................................................................................64

TYPE-2 FUZZY LOGIC SYSTEM BLOCK DIAGRAM ....................................................................................65

TYPE2 FUZZY LOGIC CONTROLLER.........................................................................................................66

FUZZIFICATION AND THE RULES .................................................................................................................68

INFERENCE .........................................................................................................................................................68

TYPE-REDUCER AND DEFUZZIFICATION....................................................................................................69

SIMULATION OF TYPE-2 MPPT FUZZY CONTROLLER ..............................................................................71

CHAPTER7: CONCLUSION AND FUTURE WORK ...................................................................................73

CONCLUSION .....................................................................................................................................................73

FUTURE WORK ..................................................................................................................................................74

REFERENCE ......................................................................................................................................................75

APPENDICES ......................................................................................................................................................77

A-1 MATLAB CODE FOR TYPE-1 FUZZY MPPT SYSTEMS ........................................................................77

A-2 MATLAB CODE FOR TYPE-2 FUZZY MPPT SYSTEMS ........................................................................84

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TABLE OF FIGURES

Figure 1-Structure of Solar Cell ............................................................................................................ 17

Figure 2-Equivalent Circuit of Solar Cell ............................................................................................. 18

Figure 3-P-V-I Curve of Solar Cell ....................................................................................................... 19

Figure 4-V-I and V-P curves at constant temperature (25°C) and three different insolation values .... 21

Figure 5-V-I and V-P curves at constant irradiation (1 kW/m2) and three different temperatures ...... 22

Figure 6-Typical construction of PV Module ....................................................................................... 26

Figure 7-MPPT Block Diagram ............................................................................................................ 27

Figure 8-Arrangement for Central Inverter ........................................................................................... 28

Figure 9-Arrangement for String Inverter ............................................................................................. 29

Figure 10-Arrangement for Multi String Inverter ................................................................................. 29

Figure 11-Arrangement for Module Inverter ........................................................................................ 30

Figure 12-V-I-P of Solar Array ............................................................................................................. 32

Figure 13-Flow Chart of P&O algorithm .............................................................................................. 33

Figure 14-Flow Chart of InCond Algorithm ......................................................................................... 34

Figure 15-MPP at different radiation level ........................................................................................... 35

Figure 16-Membership function for MPPT .......................................................................................... 38

Figure 17-Flow Chart of FLC based MPPT algorithm ......................................................................... 39

Figure 18-Block Diagram of DC-DC converter ................................................................................... 41

Figure 19-Duty Ration of DC-DC converter ........................................................................................ 42

Figure 20-Behavioural curve of MPP for different converter operation ............................................... 43

Figure 21-Circuit of a buck-boost converter ......................................................................................... 45

Figure 22-A Gaussian type-1 fuzzy membership function ................................................................... 48

Figure 23-Basic configuration of a fuzzy logic controller .................................................................... 49

Figure 24-Fuzzy control scheme for a maximum power point tracker ................................................. 51

Figure 25-Functional block of the fuzzy controller .............................................................................. 52

Figure 26-Membership functions for (a) change in power (b) change in duty cycle ............................ 53

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Figure 27-Quantization effect during maximum power search ............................................................ 56

Figure 28-Fuzzy inference and defuzzification using Mamdani method .............................................. 59

Figure 29-Fuzzy Membership function for Power ................................................................................ 60

Figure 30-Fuzzy Membership function of output ................................................................................. 60

Figure 31- Final output of Duty Cycle Signal ....................................................................................... 61

Figure 32-A Gaussian type-2 fuzzy membership function (FOU) ........................................................ 64

Figure 33-T2FLS block diagram........................................................................................................... 66

Figure 34-Structure of a type2 FLC ...................................................................................................... 67

Figure 35-Membership function of input .............................................................................................. 67

Figure 36-Membership function of output ............................................................................................ 68

Figure 37- Fuzzy Membership function of Power ................................................................................ 71

Figure 38-Fuzzy Membership function of Voltage ............................................................................... 71

Figure 39-Fuzzy Membership function of Duty cycle .......................................................................... 72

Figure 40-Final output of Duty Cycle Signal in Type-2 Fuzzy Controller ........................................... 72

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CHAPTER 1: INTRODUCTION

Energy has been one of the most important driving forces in our fast growing world. Nations

are in an endless search for new energy sources. This search passed through many

revolutions, from the use of fire and coal to the discovery of fossil fuels such as oil and

natural gas. However, this search was faced by many challenges, since many of these

resources are expensive, destructive to the environment, or ceasing to exist in the near future.

Significant progress has been made over the last few years in the research and development of

renewable energy systems such as wind, sea wave and solar energy systems. Among these

resources, solar energy is considered nowadays as one of the most reliable, daily available,

and environment friendly renewable energy source.

The amount of energy in the sunlight reaching the earth’s surface is equivalent to around

10,000 times the world’s energy requirements. Consequently, only 0.01 percent of the energy

in sunlight would need to be harnessed to cover mankind total energy needs. Given that the

sun shines on this part of the globe nearly the entire year, many new projects are intended to

make use of solar energy as a backup source to the existing power system.

Another incentive of the spread of such projects is the fact that the cost trend of photovoltaic

(PV) systems is descending, while the fuel price is ascending. The reason behind this trend is

the growing mass production and market of PV systems. The advancement in solar systems is

based on the new technological advances in the industries of photovoltaic cells, power

electronics switches, microcontrollers, and computer-based simulation packages. Solar

systems not only can serve as a backup to existing energy systems, but they can also be easily

integrated with large grid systems, or can be used as standalone systems serving as

independent energy sources.

India is a country that has tremendous solar energy potential. As the nation is facing an

increasing demand - supply gap in energy, it is important to tap the solar potential to meet the

energy needs. This article analyzes the Indian Solar industry, its major growth drivers, the

challenges it faces and the various policy initiatives taken by the government. The article also

tries to identify the various actions required to promote the growth and development of the

industry, enabling India to meet the rising energy demands of the future.

India is in a state of perennial energy shortage with a demand-supply gap of almost 12% of

the total energy demand. This trend is significant in the electricity segment that is heavily

13

dependent on coal and other non-renewable sources of energy. Renewable energy (RE)

sources contribute only 7.7% of the total installed power capacity of 167,077 MW in India.

Among the RE sources, wind power is the dominating component while solar energy

currently contributes to less than 0.1% (on-grid+ off-grid) of the total installed capacity.

The solar energy potential in India is immense due to its convenient location near the

Equator. India receives nearly 3000 hours of sunshine every year, which is equivalent to 5000

trillion kWh of energy. India can generate over 1,900 billion units of solar power annually,

which is enough to service the entire annual power demand even in 2030 (estimates).

Rajasthan and Gujarat are the regions with maximum solar energy potential. This, coupled

with the availability of barren land, increases the feasibility of solar energy systems in these

regions. Considering India’s solar potential, the government has rolled out various policies

and subsidy schemes to encourage growth of the Solar Industry, which is expected to

experience exponential growth in the coming years.

There are three government bodies established to promote solar energy in India. The first is

the Ministry of New and Renewable Energy (MNRE), which is the nodal unit for all matters

relating to RE. The second, India Renewable Energy Development Agency (IREDA), is a

public limited company established in 1987 to promote, develop and extend financial

assistance for RE and energy efficiency/conservation projects. Finally, Solar Energy Centre

(SEC) is a dedicated unit of the MNRE and the Government for the development of solar

energy technologies and promotion of its applications through product development. Besides

this, government has also rolled out various policies and subsidies to promote this sector.

India’s National Action Plan on climate change (NAPCC) identifies eight critical missions to

promote climate mitigation and adaptation. National Solar Mission, which has the specific

goal of increasing the usage of solar thermal technologies in urban areas, industry, and

commercial establishments, is one of the core components of this policy. The government

also offers capital subsidies to semiconductor manufacturing plants in Special Economic

Zone (SEZs) and outside SEZs through semiconductor policy launched in 2007. In 2009,

MNRE launched “Jawaharlal Nehru National Solar Mission (JNNSM)” with the ambitious

goal of making India a global leader in solar energy. JNNSM plans a three-phase approach

with specific targets for each phase. The other targets of this mission include achieving grid

parity (same production cost as current electricity source) by 2022 and parity with coal based

power generation in 2030.

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One of the recent applications of such intelligent controllers is the efficiency optimization of

photovoltaic energy systems. These techniques are used to maximize the power output of solar

systems as well as improve their robustness against external disturbances.

MOTIVATION

If the parameters of a system can be obtained precisely, then its control would be a relatively

straightforward problem and model-based approaches such as PID and pole placement could

be used. However, in real-time industrial systems, it is often the case that there exist

considerable difficulties in obtaining an accurate model. Even when the model is sufficiently

accurate, there are many other uncertainties for example due to the precision of the sensors,

noise produced by the sensors, environmental conditions of the sensors, and nonlinear

characteristics of the actuators. Then, not only does the performance of the model-based

approaches drastically decrease, but the complexity of the controller design also increases. In

such cases, model-free approaches are generally preferred both for modelling and control

purposes. The most common model-free approaches are the use of fuzzy logic systems

(FLSs).

The concept of a type-2 fuzzy set was introduced by Zadeh as an extension of the concept of

an ordinary fuzzy set (henceforth called a type-1 fuzzy set). Such sets are fuzzy sets whose

membership grades themselves are type-1 fuzzy sets; they are very useful in circumstances

where it is difficult to determine an exact membership function for a fuzzy set; hence, they

are useful for incorporating linguistic uncertainties, e.g., the words that are used in linguistic

knowledge can mean different things to different people. A fuzzy relation of higher type (e.g.,

type-2) has been regarded as one way to increase the fuzziness of a relation, and, according to

Hisdal, “increased fuzziness in a description means increased ability to handle inexact

information in a logically correct manner. According to John, “Type-2 fuzzy sets allow for

Linguistic grades of membership, thus assisting in knowledge representation, and they also

offer improvement on inference with type-1 sets.

Type-2 sets can be used to convey the uncertainties in membership functions of type-1 sets, due to

the dependence of the membership functions on available linguistic and numerical information.

Linguistic information (e.g., rules from experts), in general, does not give any information about

the shapes of the membership functions. When membership functions are determined or tuned

based on numerical data, the uncertainty in the numerical data, e.g., noise, translates into

uncertainty in the membership functions.

15

Out the many MPPT algorithm Type-1 Fuzzy one of the proven algorithm and there are many

papers have been published. But it will be the first approach to apply Type-2 Fuzzy logic in MPPT

algorithm. Here we will the Interval Type-2 Fuzzy controller to design the MPPT.

PROBLEM STATEMENT

In line with the global initiative toward the design and development of PV systems as alternative

energy sources, this work will investigate the potential of using solar energy systems in the India.

One of the drawbacks of PV systems is their low efficiencies compared to their cost. In order to

overcome these drawbacks, maximum power should be extracted from these systems. The aim is

to develop an efficient standalone photovoltaic system. This system employs a new digital control

scheme using fuzzy-logic and a dual maximum power point tracking (MPPT) controller. The

MPPT algorithm controls the power converter between the PV panel and the load and implements

a new Type-2 fuzzy-logic (FLC) based MPPT control scheme to keep the system power operating

point at its maximum. Such systems are exceedingly demanded in remote areas where it is difficult

to connect to the grid system.

CONTRIBUTIONS

This work will explore the effectiveness of intelligent and digital control techniques for PV system

efficiency optimization. These techniques combine both physical as well as Type-2 fuzzy-based

MPPT tracking techniques. Furthermore, this work will offer a stability analysis for the

Type-2 FLC based MPPT controller. Though literature is rich with PV systems implementations,

no work was based on actual outdoor testing in this part of the world. This work will use

experimental data to investigate the potential of solar energy in India and the effects of the harsh

environment on PV systems efficiencies.

THESIS OUTLINE

In this thesis, a detailed literature review about tracking techniques will be presented in Chapter 3.

Chapter 2 will focus on PV systems modelling and simulation featuring a MATLAB/Simulink full

simulation of the overall standalone PV system. Chapter 5 will discuss the design and

implementation of type-1 fuzzy logic controller systems. The proposed Type-2 FLC controller

will be fully investigated in chapter 6 highlighting a simulation comparison between the

proposed controller and the conventional ones. Chapter 6 will verify the proposed technique

effectiveness through presenting the PV system hardware implementation and trial results. Finally,

chapter 7 will conclude the work discussing the work limitations along with the future work.

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CHAPTER 2: SOLAR CELL AND PHOTOVOLTAIC SYSTEM

CONFIGURATION

SOLAR CELL

OPERATING PRINCIPLE

Solar cells are the basic components of photovoltaic panels. Most are made from silicon even

though other materials are also used.

Solar cells take advantage of the photoelectric effect: the ability of some

semiconductors to convert electromagnetic radiation directly into electrical current. The

charged particles generated by the incident radiation are separated conveniently to

create an electrical current by an appropriate design of the structure of the solar cell, as

will be explained in brief below.

A solar cell is basically a p-n junction which is made from two different layers of

silicon doped with a small quantity of impurity atoms: in the case of the n-layer, atoms

with one more valence electron, called donors, and in the case of the p-layer, with one

less valence electron, known as acceptors. When the two layers are joined together, near

the interface the free electrons of the n-layer are diffused in the p-side, leaving behind

an area positively charged by the donors. Similarly, the free holes in the p-layer are

diffused in the n-side, leaving behind a region negatively charged by the acceptors. This

creates an electrical field between the two sides that is a potential barrier to further flow.

The equilibrium is reached in the junction when the electrons and holes cannot surpass

that potential barrier and consequently they cannot move. This electric field pulls the

electrons and holes in opposite directions so the current can flow in one way only:

electrons can move from the p-side to the n-side and the holes in the opposite direction.

A diagram of the p-n junction showing the effect of the mentioned electric field is

illustrated in Figure 1.

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Figure 1-Structure of Solar Cell

Metallic contacts are added at both sides to collect the electrons and holes so the current

can flow. In the case of the n-layer, which is facing the solar irradiance, the contacts are

several metallic strips, as they must allow the light to pass to the solar cell, called

fingers.

The structure of the solar cell has been described so far and the operating principle is

next. The photons of the solar radiation shine on the cell. Three different cases can

happen: some of the photons are reflected from the top surface of the cell and metal

fingers. Those that are not reflected penetrate in the substrate. Some of them, usually the

ones with less energy, pass through the cell without causing any effect. Only those with

energy level above the band gap of the silicon can create an electron-hole pair. These

pairs are generated at both sides of the p-n junction. The minority charges (electrons in

the p-side, holes in the n-side) are diffused to the junction and swept away in opposite

directions (electrons towards the n-side, holes towards the p-side) by the electric field,

generating a current in the cell, which is collected by the metal contacts at both sides.

This can be seen in the figure above, Figure-1. This is the light-generated current which

depends directly on the irradiation: if it is higher, then it contains more photons with enough

energy to create more electron-hole pairs and consequently more current is generated by

the solar cell.

18

EQUIVALENT CIRCUIT OF A SOLAR CELL

The solar cell can be represented by the electrical model shown in Figure-2. Its current-

voltage characteristic is expressed by the following equation (1):

(1)

where I and V are the solar cell output current and voltage respectively, I0 is the dark

saturation current, q is the charge of an electron, A is the diode quality factor, k is the

Boltzmann constant, T is the absolute temperature and RS and RSH are the series and shunt

resistances of the solar cell. RS is the resistance offered by the contacts and the bulk

semiconductor material of the solar cell. The origin of the shunt resistance RSH is more

difficult to explain. It is related to the non ideal nature of the p-n junction and the presence of

impurities near the edges of the cell that provide a short-circuit path around the junction. In

an ideal case RS would be zero and RSH infinite. However, this ideal scenario is not possible

and manufacturers try to minimize the effect of both resistances to improve their products.

Figure 2-Equivalent Circuit of Solar Cell

Sometimes, to simplify the model, the effect of the shunt resistance is not considered, i.e.

RSH is infinite, so the last term is neglected.

A PV panel is composed of many solar cells, which are connected in series and parallel

so the output current and voltage of the PV panel are high enough to the requirements of

the grid or equipment. Taking into account the simplification mentioned above, the

output current-voltage characteristic of a PV panel is expressed by equation (2), where

np and ns are the number of solar cells in parallel and series respectively.

19

(2)

OPEN CIRCUIT VOLTAGE, SHORT CIRCUIT CURRENT AND MAXIMUM POWER

POINT

Two important points of the current-voltage characteristic must be pointed out: the open

circuit voltage VOC and the short circuit current ISC. At both points the power generated

is zero. VOC can be approximated from (1) when the output current of the cell is zero, i.e. I=0

and the shunt resistance RSH is neglected. It is represented by equation (3). The short circuit

current ISC is the current at V = 0 and is approximately equal to the light generated current IL

as shown in equation (4).

(3)

(4)

The maximum power is generated by the solar cell at a point of the current-voltage

characteristic where the product of VI is Maximum. This point is known as the MPP and is

unique, as can be seen in Figure 3, where the previous points are represented.

Figure 3-P-V-I Curve of Solar Cell

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FILL FACTOR

Using the MPP current and voltage, IMPP and VMPP, the open circuit voltage (VOC) and the

short circuit current (ISC), the fill factor (FF) can be defined as:

(5)

It is a widely used measure of the solar cell overall quality [4]. It is the ratio of the

actual maximum power (IMPPVMPP) to the theoretical one (ISCVOC), which is actually not

obtainable. The reason for that is that the MPP voltage and current are always below the

open circuit voltage and the short circuit current respectively, because of the series and

shunt resistances and the diode depicted in Figure 2. The typical fill factor for commercial solar

cells is usually over 0.70.

TEMPERATURE AND IRRADIANCE EFFECTS

Two important factors that have to be taken into account are the irradiation and the

temperature. They strongly affect the characteristics of solar modules. As a result, the MPP

varies during the day and that is the main reason why the MPP must constantly be tracked and

ensure that the maximum available power is obtained from the panel. The effect of the

irradiance on the voltage-current (V-I) and voltage-power (V-P) characteristics is depicted in

Figure 4, where the curves are shown in per unit, i.e. the voltage and current are normalized

using the VOC and the ISC respectively, in order to illustrate better the effects of the

irradiance on the V-I and V-P curves. As was previously mentioned, the photo-generated

current is directly proportional to the irradiance level, so an increment in the irradiation leads

to a higher photo-generated current. Moreover, the short circuit current is directly

proportional to the photo-generated current; therefore it is directly proportional to the

irradiance. When the operating point is not the short circuit, in which no power is generated,

the photo-generated current is also the main factor in the PV current, as is expressed by

equations (1) and (2). For this reason the voltage-current characteristic varies with the

irradiation. In contrast, the effect in the open circuit voltage is relatively small, as the

dependence of the light generated current is logarithmic, as is shown in equation (4).

21

Figure 4-V-I and V-P curves at constant temperature (25°C) and three different insolation values

Figure-4 shows that the change in the current is greater than in the voltage. In practice,

the voltage dependency on the irradiation is often neglected. As the effect on both the current

and voltage is positive, i.e. both increase when the irradiation rises, the effect on the

power is also positive: the more irradiation, the more power is generated.

The temperature, on the other hand, affects mostly the voltage. The open circuit voltage is

linearly dependent on the temperature, as shown in the following equation:

(6)

According to (6), the effect of the temperature on VOC is negative, because Kv is

negative, i.e. when the temperature raises, the voltage decreases. The current increases with

the temperature but very little and it does not compensate the decrease in the voltage

caused by a given temperature rise. That is why the power also decreases. PV panel

22

manufacturers provide in their data sheets the temperature coefficients, which are the parameters

that specify how the open circuit voltage, the short circuit current and the maximum power vary

when the temperature changes. As the effect of the temperature on the current is really small,

it is usually neglected. Figure 5 shows how the voltage-current and the voltage-power

characteristics change with temperature. The curves are again in per unit, as in the previous

case.

As was mentioned before, the temperature and the irradiation depend on the

atmospheric conditions, which are not constant during the year and not even during a single

day; they can vary rapidly due to fast changing conditions such as clouds. This causes the

MPP to move constantly, depending on the irradiation and temperature conditions. If the

operating point is not close to the MPP, great power losses occur. Hence it is essential to

track the MPP in any conditions to assure that the maximum available power is obtained

from the PV panel. In a modern solar power converter, this task is entrusted to the MPPT

algorithms.

Figure 5-V-I and V-P curves at constant irradiation (1 kW/m2) and three different temperatures

23

TYPES OF SOLAR CELLS

Over the past decades, silicon has been almost the only material used for manufacturing solar

cells. Although other materials and techniques have been developed, silicon is used in more than

the 80% of the production. Silicon is so popular because it is one of the most abundant materials

in the Earth’s crust, in the form of silicon dioxide, and it is not toxic. Mono-crystalline and

polycrystalline silicon solar cells are the two major types of silicon solar cells. There is a third

type, amorphous silicon, but the efficiency is worse than with the previous types so it is less

used. Other new solar cells are made of copper indium gallium (di)selenide (CIGS) or cadmium

telluride (CdTe). Much research and development (R&D) effort is being made to develop new

materials, but nowadays there are no commercial substitutes to the above types of solar cells. In

this section these different solar cells are reviewed.

One of the most important characteristics of solar cells is the efficiency, which is the percentage

of solar radiation that is transformed into electricity. It is measured under Standard Test

Conditions (STC), irradiance of 1000 W/m², air mass coefficient (it characterizes the solar

spectrum after the solar radiation has travelled through the atmosphere) A.M 1.5, and a cell

junction temperature of 25°C. The higher efficiency, the smaller surface is needed for a given

power. This is important because in some applications the space is limited and other costs and

parameters of the installation depend on the installed PV surface.

MONO-CRYSTALLINE SILICON

Mono-crystalline silicon solar cells are the most efficient ones. They are made from wafers (very

thin slices) of single crystals obtained from pure molten silicon. These single crystal wafers have

uniform and predictable properties as the structure of the crystal is highly ordered. However the

manufacturing process must be really careful and occurs at high temperatures, which is

expensive. The efficiency of these cells is around 15-18% and the surface needed to get 1 kW in

STC is about 7 m2.

POLYCRYSTALLINE SILICON

These cells are also made from wafers of pure molten silicon. However, the crystal structure is

random: as the silicon cools, it crystallizes simultaneously in many different points producing an

irregular structure: crystals of random sizes, shapes and orientation. These structures are not as

ideal as in the mono-crystalline cells so the efficiency is lower, around 11-15%. However the

manufacturing process is less expensive, so the lower efficiency is compensated in some way.

24

The surface needed to obtain 1 kW in STC is about 8m2.

AMORPHOUS AND THIN-FILM SILICON

Amorphous silicon is the non-crystalline form of the silicon and it can be deposited as thin-films

onto different substrates. The deposition can be made at low temperatures. The manufacturing

process is simpler, easier and cheaper than in the crystalline cells. The weak point of these cells

is their lower efficiency, around 6-8%. This efficiency is measured under STC. However, the

performance under weaker or diffuse irradiation, such as that in cloudy days, can be higher than

in crystalline cells and their temperature coefficient is smaller. Amorphous silicon is also a

better light absorber than crystalline, so despite having low efficiency, the thin film is a

competitive and promising technology. The first solar cells were of thin-film technology. They

have been used since the 1980s in consumer electronics applications, such as calculators. In

recent years it has also begun to be used in high power applications due to the characteristics

mentioned above. One common use nowadays is as building cladding, for example in facades, as

its price is competitive compared with other high quality cladding materials and it offer the

advantage of electricity generation. The main advantages of thin film technologies are the ease of

manufacturing at low temperatures using inexpensive substrates and continuous production

methods, avoiding the need for mounting individual wafers and the potential for lightweight and

flexible solar cells. These advantages are common to most of the thin-film solar cells, not only

the ones made from amorphous silicon.

Over recent years, one more type of silicon has been developed, microcrystalline silicon. It can

also be deposited as thin-films onto different substrates, minimizing the quantities of crystalline

silicon needed and improving the efficiency of amorphous silicon. However, the light absorption

of micro-crystalline silicon compared to amorphous silicon is poor. The solution can be an

effective light trapping to keep the incident light within the film. This type of silicon is not a

commercial technology yet and more R&D is needed.

OTHER CELLS AND MATERIALS

As was mention in the introduction of this chapter, there are other materials apart from silicon

that can be used for manufacturing solar cells. These compounds are also thin-film deposited, so

they have the same advantages as the silicon thin film solar cells but with a better efficiency.

Among these compounds, two are already used in commercial solar cells. They are CIGS and

CdTe. The efficiency is around 10-13% [3] and it will rise in the following years as the

technologies are improved. It is commonly said that thin film technology is the way to achieve

25

the grid parity, i.e. the point at which the cost of generating electricity is equal, or cheaper than

grid power.

The main disadvantages of these technologies are the toxicity of some of the compounds

and the shortage of some of the elements used. In the case of the CIGS, indium is used. This

element is not as abundant as silicon in the Earth’s crust and it is in high demand for other

electronics products such as liquid-crystal display (LCD) monitors, which has generated a

shortage and consequently a high price rise in the recent years. Moreover, to create the p-n

junction, CIGS is interfaced with cadmium sulphide (CdS), another semiconductor. The problem

is that cadmium is a heavy metal which is cumulatively poisonous. In the case of CdTe, the other

compound used in commercial thin film solar cells, it is not as toxic as its individual

components, but some precautions must be taken during the manufacturing process. Gallium

Arsenide (GaAs) has been used for space applications mainly for two reasons: firstly, it is less

susceptible to suffer damage from the space radiation than silicon, and secondly, due to its direct

bandgap of 1.42 eV, it can take advantage of a greater part of the solar spectrum. Despite being a

more expensive material, space projects can afford it as cost is not the most important factor to

decide the components. Nowadays it is being investigated to be used in terrestrial PV

applications using light concentrators (mirror or lenses) to focus the light onto small cells,

reducing the price as less material is required.

Triple junction GaAs cells have already passed 40% efficiency in the laboratory using light

concentrators. The main handicap at present for this technology is that concentration systems are

expensive as they have to track the Sun along the day. One other technology that is being

actively researched is dye-sensitized cells. These cells are made from artificial organic materials

and are seen as part of the “third generation” of solar cells. The efficiency of these cells is above

that of amorphous silicon and within the thin-film ones. The main advantage is that they work

well under low and diffuse light and their temperature coefficients are lower. The materials used

are non-toxic and abundant and their manufacturing processes are relatively simple. Flexible

modules can easily be made using flexible substrates and they can be used for building integrated

PV: roofs, windows, as they can be manufactured in many shapes, sizes and design criteria.

These last two paragraphs illustrate technologies that are being currently investigated. They are

non commercial technologies yet, but it is expected that in the following years they will become

competitive and will be also used, increasing the possibilities of PV power generation. The

silicon and thin film solar cells described before are currently the technologies used in

commercial PV applications.

26

Nevertheless, what is important for this work is that all the different solar cells presented

above have similar non-linear voltage-current characteristics and are affected by irradiation and

temperature in a similar way. The only difference is that different type of cells have different

levels of sensitivity, nevertheless the same algorithms can be used to track the MPP.

PHOTOVOLTAIC MODULES

PV modules are made from solar cells connected in series and parallel to obtain the desired

current and voltage levels. Solar cells are encapsulated as they have to be weatherproofed and

electric connections also have to be robust and corrosion free. The typical construction of a PV

module can be seen in Figure-6.

Figure 6-Typical construction of PV Module

As the cells are brittle, they are encapsulated in an airtight layer of ethylene vinyl acetate

(EVA), a polymer, so the cells are cushioned and in that way are protected during transport

and handling. The top cover is a tempered glass treated with an anti-reflection coating so the

maximum light is transmitted to the cell. The underneath is a sheet of polyvinyl fluoride

(PVF), also known as Tedlar, a synthetic polymer (CH2CHF)n that constitutes a barrier

to moisture and prevents the cell from chemical attack. An aluminium frame is used to

simplify mounting and handling and to give extra protection. Frameless modules are

sometimes used in facades for aesthetic reasons. This typical construction is used because the

PV module has to “survive” outdoors for at least 20-25 years under different weather

conditions, sometimes extreme. This construction assures at least the lifetime of the PV

27

modules. In fact, PV panel manufacturers provide a guarantee of at least 20 years, for

example BP Solar assures 85 % of minimum warranted power output after 25 years of

service, 93 % of the minimum warranted power output at 12 years and a five-year warranty

of materials and workmanship. Such a long guarantee is extremely long compared to most

products and is due to the exceptional construction of PV modules.

PHOTOVOLTAIC SYSTEM CONFIGURATION

PV modules generate DC current and voltage. However, to feed the electricity to the

grid, AC current and voltage are needed. Inverters are the equipment used to convert

DC to AC. In addition, they can be in charge of keeping the operating point of the PV

array at the MPP. This is usually done with computational MPP tracking algorithms.

There are different inverter configurations depending on how the PV modules are

connected to the inverter. The main types are described in this chapter. The decision

on what configuration should be used has to be made for each case depending on the

environmental and financial requirements. If the modules are not identical or do not

work under the same conditions, the MPP is different in each panel and the resulting

voltage-power characteristic has multiple maxima, which constitutes a problem, because

most MPPT algorithms converge to a local maximum depending on the starting point. If

the operating point is not the MPP, not all the possible power is being fed to the grid.

For these reasons each case has to be carefully studied to optimize the plant and obtain

the maximum performance.

The below image describes the typical arrangement of the Solar PV with MPPT controller with

DC-DC converter Buck, Boost or Cuk converter.

Figure 7-MPPT Block Diagram

28

The different configurations are described shortly in this chapter because they are not the

focus of this thesis.

CENTRAL INVERTER

It is the simpler configuration: PV strings, consisting of series connected PV panels, are

connected in parallel to obtain the desired output power. The resulting PV array is

connected to a single inverter, as is shown in Figure 7. In this configuration all PV

strings operate at the same voltage, which may not be the MPP voltage for all of them.

The problem of this configuration is the possible mismatches among the different PV

modules. If they are receiving different irradiation (shading or other problems), the true MPP

is difficult to find and consequently there are power losses and the PV modules are

underutilized.

Figure 8-Arrangement for Central Inverter

STRING INVERTER

In this configuration, every string of PV panels connected in series is connected to a

different inverter, as can be seen in Figure-8. This can improve the MPP tracking in case of

29

mismatches or shading, because each string can operate at a different MPP, if

necessary, whereas in the central inverter there is only one operating point which may not be

the MPP for each string, thus leading to power losses. On the other hand, the number of

components of the system increases as well as the installation cost, as an inverter is used for

each string.

Figure 9-Arrangement for String Inverter

MULTI-STRING INVERTER

In this case each string is connected to a different DC-DC converter, which is in charge

of the MPP tracking of the string, and the converters are connected to a single inverter,

as depicted in Figure 9. The advantages related to MPP tracking are the same as in the

string configuration; each string can have a different MPP. The disadvantages, an

increase in the price compared to the central inverter, as a converter is used for each

string.

Figure 10-Arrangement for Multi String Inverter

MODULE INTEGRATED INVERTER

In this configuration, as shown in Figure-10, each PV module is connected to a different

inverter and consequently the maximum power is obtained from each panel as the individual

30

MPP is tracked by each inverter. This configuration can be used when the differences in the

operating point of the different modules are large. However, it is more expensive because each

panel has its own inverter.

Figure 11-Arrangement for Module Inverter

31

CHAPTER 3: MAXIMUM POWER POINT TRACKING

As was previously explained, MPPT algorithms are necessary in PV applications because the

MPP of a solar panel varies with the irradiation and temperature, so the use of MPPT

algorithms is required in order to obtain the maximum power from a solar array.

Over the past decades many methods to find the MPP have been developed and

published. These techniques differ in many aspects such as required sensors,

complexity, cost, range of effectiveness, convergence speed, correct tracking when

irradiation and/or temperature change, hardware needed for the implementation or

popularity, among others.

Among these techniques, the P&O and the InCond algorithms are the most common. These

techniques have the advantage of an easy implementation but they also have drawbacks,

as will be shown later. Other techniques based on different principles are fuzzy logic

control, neural network, fractional open circuit voltage or short circuit current, current

sweep, etc. Most of these methods yield a local maximum and some, like the fractional

open circuit voltage or short circuit current, give an approximated MPP, not the exact one.

In normal conditions the V-P curve has only one maximum, so it is not a problem. However,

if the PV array is partially shaded, there are multiple maxima in these curves. In order to

relieve this problem, some algorithms have been implemented. There are many methods

for MPPT, in the next section three most popular MPPT techniques are discussed.

HILL-CLIMBING TECHNIQUES

Both P&O and InCond algorithms are based on the “hill-climbing” principle, which consists of

moving the operation point of the PV array in the direction in which power increases. Hill-

climbing techniques are the most popular MPPT methods due to their ease of implementation

and good performance when the irradiation is constant. The advantages of both methods are the

simplicity and low computational power they need. The shortcomings are also well-known:

oscillations around the MPP and they can get lost and track the MPP in the wrong direction

during rapidly changing atmospheric conditions.

PERTURB AND OBSERVE

The P&O algorithm is also called “hill-climbing”, but both names refer to the same algorithm

depending on how it is implemented. Hill-climbing involves a perturbation on the duty cycle of

32

the power converter and P&O a perturbation in the operating voltage of the DC link between

the PV array and the power converter. In the case of the Hill-climbing, perturbing the duty cycle

of the power converter implies modifying the voltage of the DC link between the PV array and

the power converter, so both names refer to the same technique.

In this method, the sign of the last perturbation and the sign of the last increment in the power

are used to decide what the next perturbation should be. As can be seen in Figure 11, on the left

of the MPP incrementing the voltage increases the power whereas on the right decrementing the

voltage increases the power.

Figure 12-V-I-P of Solar Array

If there is an increment in the power, the perturbation should be kept in the same

direction and if the power decreases, then the next perturbation should be in the opposite

direction. Based on these facts, the algorithm is implemented. The process is repeated until the

MPP is reached. Then the operating point oscillates around the MPP. This problem is common

also to the InCond method, as was mention earlier. A scheme of the algorithm is shown in

Figure 13.

33

Figure 13-Flow Chart of P&O algorithm

INCREMENTAL CONDUCTANCE

The incremental conductance algorithm is based on the fact that the slope of the curve power vs.

voltage (current) of the PV module is zero at the MPP, positive (negative) on the left of it and

negative (positive) on the right, as can be seen in Figure 11:

• ∆V/∆P = 0 ( ∆I/∆P = 0 ) at the MPP

• ∆V/∆P > 0 ( ∆I/∆P < 0 ) on the Left

• ∆V/∆P < 0 ( ∆I/∆P > 0 ) at the Right

By comparing the increment of the power vs. the increment of the voltage (current)

between two consecutives samples, the change in the MPP voltage can be determined. A

scheme of the algorithm is shown in Figure 13.

34

Figure 14-Flow Chart of InCond Algorithm

In both P&O and InCond schemes, how fast the MPP is reached depends on the size of the

increment of the reference voltage.

The drawbacks of these techniques are mainly two. The first and main one is that they can

easily lose track of the MPP if the irradiation changes rapidly. In case of step changes they

track the MPP very well, because the change is instantaneous and the curve does not keep on

changing. However, when the irradiation changes following a slope, the curve in which the

algorithms are based changes continuously with the irradiation, as can be seen in Figure 14,

so the changes in the voltage and current are not only due to the perturbation of the voltage. As

a consequence it is not possible for the algorithms to determine whether the change in the

power is due to its own voltage increment or due to the change in the irradiation.

35

Figure 15-MPP at different radiation level

The other handicap of both methods is the oscillations of the voltage and current around the

MPP in the steady state. This is due to the fact that the control is discrete and the voltage and

current are not constantly at the MPP but oscillating around it. The size of the oscillations

depends on the size of the rate of change of the reference voltage. The greater it is, the higher

is the amplitude of the oscillations. However, how fast the MPP is reached also depends on this

rate of change and this dependence is inversely proportional to the size of the voltage

increments. The traditional solution is a trade off: if the increment is small so that the

oscillations decrease, then the MPP is reached slowly and vice versa, so a compromise solution

has to be found.

To overcome these drawbacks some solutions have been published in recent years. Regarding

the rapid change of the irradiation conditions, Sera et al. published in an improved P&O

method, called “dP-P&O”, in which an additional measurement is performed without

perturbation in the voltage and current. In this way, every three consecutive samples the effect

of the perturbation in the voltage (current) and the effect of the change in the atmospheric

conditions can be evaluated so that the increment in the power used in the algorithm only

36

contains the effect caused purely by the MPPT algorithm. Then the correct decision about the

direction of the next perturbation can be taken. The efficiency of the tracking is improved.

Although the method was tested using irradiation slopes, they were not the ones proposed in

the new European Standard EN 50530.

A different solution is suggested, which considers the traditional P&O algorithm, in which the

perturbation amplitude is tuned constantly taking into account the previous changes in the

power. It also includes a stage in which the latest increment in the power is compared with the

latest perturbation amplitude to determine if the power increment was due to a change in the

irradiation. If this is the case, then the voltage perturbation is set to the same direction as the

change in the power condition. The steady state error and the tracking speed are improved, but

the algorithm has only been tested with irradiation step changes and not with the irradiation

slopes proposed.

In relationship with the oscillations around the MPP in steady state, Zhang et al. proposed a

variable perturbation step for the P&O algorithm to reduce the oscillation around it. This

modified P&O method determines also if the operating point is near to or far from the MPP

and adjusts the size of the perturbation according to that: if the operating point is near to the

MPP, the perturbation size is reduced and if the point is far, then it is increased. This technique

improves the convergence speed and reduces

the oscillation around the MPP. A similar technique is found: a variation of the traditional

P&O algorithm in which the amplitude of the voltage perturbation is adapted to the actual

operating conditions: large perturbation amplitudes are chosen far from the maximum whereas

small ones are used near the MPP. The proposed algorithm requires initial panel identification

and has to be tuned for each plant. With this technique the dynamic response and the steady

state stability are improved. Unfortunately, the last

two algorithms do not improve the tracking under changing irradiance conditions. Although

the authors claim the performance is better, the algorithms have only been tested with

irradiation step changes but not with irradiation ramps as proposed in the European Standard

mentioned above.

Many papers have been published about optimizing the parameters of these algorithms for

different hardware configurations. The sample frequency for P&O is optimized and it is shown

how the P&O MPPT parameters must be customized to the dynamic behaviour of the specific

converter adopted. It has been traditionally said that the performance of InCond algorithm is

37

better than the P&O. However, according to the performance is similar if the parameters of the

P&O method are optimized. In any case, both algorithms are based on the same principle and

have the same problem so they have been analyzed together.

The amount of literature presenting slight modifications of the existing methods or adapting

them to different hardware configurations is so extensive that it is not possible to present it in

this thesis.

In any case, none of the solutions reviewed before solves the problems satisfactorily and none

has been tested under the slopes proposed to test the dynamic efficiency of the MPPT

algorithms. These profiles simulate rapid environmental changes such as clouds. It is very

important to track the MPP during these situations to obtain the maximum power from the PV

module. As will be shown in the next chapter, this thesis proposes some modification to both

P&O and InCond methods so that the tracking under irradiation profiles containing slopes is

very good.

FUZZY LOGIC CONTROL

The use of fuzzy logic control has become popular over the last decade because it can deal

with imprecise inputs, does not need an accurate mathematical model and can handle

nonlinearity. Microcontrollers have also helped in the popularization of fuzzy logic control.

The fuzzy logic consists of three stages: fuzzification, inference system and defuzzification.

Fuzzification comprises the process of transforming numerical crisp inputs into linguistic

variables based on the degree of membership to certain sets.

Membership functions, like the ones in Figure 16, are used to associate a grade to each

linguistic term. The number of membership functions used depends on the accuracy of the

controller, but it usually varies. In Figure 16 seven fuzzy levels are used: NB (Negative Big),

NM (Negative Medium), NS (Negative Small), ZE (Zero), PS (Positive Small), PM

(Positive Medium) and PB (Positive Big). The values a, b and c are based on the range values

of the numerical variable. In some cases the membership functions are chosen less

symmetric or even optimized for the application for better accuracy.

38

Figure 16-Membership function for MPPT

The inputs of the fuzzy controller are usually an error, E, and the change in the error, ∆∆∆∆E.

The error can be chosen by the designer, but usually it is chosen as ∆∆∆∆P/∆∆∆∆V because it is zero

at the MPP. Then E and ∆∆∆∆E are defined as follows:

(7)

(8)

In other cases ∆P/∆I is used as error or other inputs are considered, where ∆V and ∆P are

used. The output of the fuzzy logic converter is usually a change in the duty ratio of the

power converter, ∆D, or a change in the reference voltage of the DC-link, ∆V. The rule base,

also known as rule base lookup table or fuzzy rule algorithm, associates the fuzzy output to

the fuzzy inputs based on the power converter used and on the knowledge of the user. Table I

shows the rules for a three phase inverter, where the inputs are E and ∆E, as defined in (7)

and (8), and the output is a change in the DC-link voltage, ∆V. For example, if the operating

point is far to the right of the MPP, E is NB, and ∆E is zero, then to reach the MPP the

reference voltage should decrease, so ∆V should be NB (Negative) to move the operating

point towards the MPP.

39

Table 3-1 Fuzzy controller rule base for MPPT

The last stage of the fuzzy logic control is the defuzzification. In this stage the output is

converted from a linguistic variable to a numerical crisp one again using membership

functions as those in Figure 15. There are different methods to transform the linguistic

variables into crisp values. It can be said that the most popular is the centre of gravity

method. However the analysis of these methods is beyond the scope of this thesis.

Figure 17-Flow Chart of FLC based MPPT algorithm

40

The advantages of these controllers, besides dealing with imprecise inputs, not needing

an accurate mathematical model and handling nonlinearity, are fast convergence and

minimal oscillations around the MPP. Furthermore, they have been shown to perform

well under step changes in the irradiation. However, no evidence was found that they

perform well under irradiation ramps. Therefore, their performance under the conditions

specified in for testing the dynamic MPPT efficiency is unknown. Another

disadvantage is that their effectiveness depends a lot on the skills of the designer; not

only on choosing the right error computation, but also in coming up with an appropriate

rule base.

MAXIMUM POWER POINT TRACKING SUMMARY

Most of the MPPT algorithms developed over the past years have been reviewed in the

previous sections. Some of them are very similar and use the same principle but expressed in

different ways, like the last three algorithms listed in the hill-climbing techniques. The most

popular MPPT algorithms according to the number of publications are P&O, InCond and

Fuzzy Logic. It makes sense because they are the simplest algorithms capable of finding the

real MPP. However, they have some disadvantages, as discussed earlier. In the following

chapter, the performance of these three algorithms is analyzed. They were selected because of

their simplicity and popularity. In the case of P&O and InCond some modifications are

proposed, which overcome the limitations of the original methods in tracking the MPP under

irradiation slopes. The FLC is designed according to the references and its dynamic efficiency

is tested and compared to the hill-climbing MPPT methods.

41

CHAPTER 4: DC-DC CONVERTERS

In this chapter the characteristics of the basic dc-dc converter topologies; buck, boost, and

buck-boost, are analyzed to determine the best topology for performing PV module maximum

power point tracking. A model of the identified topology is then formulated. The model is

used to carry out simulations to determine the effect of component non-idealises on converter

efficiency and output voltage. The simulation results are used as the basis for developing

control strategies and selecting converter components. The converter model forms the main

part in the complete MPPT model used for tuning the fuzzy logic controller.

The schematic diagram of a dc-dc converter is shown in Figure 18. It converts a dc input

voltage Vg (t), to a dc output voltage VO (t), at a different voltage level from the input. It is

desirable that the conversion be made with low losses in the converter. Therefore, the

transistor is operated as a switch using the control signal δ (t), which is held high for a time

ton, and low for a time toff as shown in Figure 19.

Figure 18-Block Diagram of DC-DC converter

While the transistor is on, the voltage across it is low which means that the power loss in the

transistor is low. While the transistor is off, the current through it is low and the power loss is

also low. The average output voltage is controlled by changing the width of the pulses while

the switching period Ts is held constant. The duty cycle, d (t) is a real value in the interval 0 to

1 and it is equal to the ratio of the width of a pulse to the switching period i.e. d(t)= ton/Ts.

42

Figure 19-Duty Ration of DC-DC converter

To obtain low losses, resistors are avoided in dc-dc converters. Capacitors and inductors are

used instead since ideally they have no losses. The electrical components can be combined

and connected to each other in different ways, called topologies, each one having different

properties. The buck, boost, and buck-boost converters are three basic converter topologies.

The buck converter has an output voltage that is lower than the input voltage; the boost

converter has an output voltage that is higher than the input voltage, and the buck-boost

converter is able to produce an output voltage magnitude that is higher or lower than the input

voltage magnitude.

IDENTIFICATION OF SUITABLE CONVERTER FOR MPPT

The different converter topologies are analyzed in this section in order to ascertain their

performance and identify the most suitable topology for maximum power point tracking.

The power produced from a photovoltaic module depends strongly on the operating voltage

of the load to which it is connected, as well as to the solar radiation level and cell

temperature. If a variable load resistance R is connected across the module’s terminals, the

operating point is determined by the intersection of module I-V curve and the load I-V

characteristic. Figure 20 illustrates the operating characteristic of a PV module. It consists of

two regions:

Zone I is the current source region, and Zone II is the voltage source region. In Zone I, the

internal impedance of the module is high, while in Zone II the internal impedance is low. The

maximum power point Pmp, is located at the knee of the power curve. Increase in solar

radiation at constant temperature causes a decrease in internal impedance as it causes an

increase in short-circuit current. An increase in temperature at constant solar radiation causes

a decrease in internal impedance since it causes a decrease in open circuit voltage.

43

According to the maximum power transfer theory, the power delivered to the load is

Maximum when the source internal impedance matches the load impedance. The load

characteristic is a straight line with a slope of I /V = 1/ R. If R is small, the module operates in

the region AB only and behaves like a constant current source at a value close to Isc. If R is

large, the module operates in the region CD behaving like a constant voltage source, at a

value almost equal to Voc.

Figure 20-Behavioural curve of MPP for different converter operation

BUCK CONVERTER

For an ideal buck converter, averaged input voltage Vg , output voltage Vo , input current Ig ,

and output current Io are related as follows:

VO = Vg D (9)

Io = Ig / D (10)

Where, D is the equilibrium duty cycle of the converter. The dc load R connected to the

converter can be expressed using Ohm’s law as:

R = VO / Io (11)

44

The load resistance ' R referred to the input terminals of the converter can be derived from Equations (9) and (10) as:

R’ = RL / D2 (12)

Since 0 < D <1, varying D can only increase the load seen by the source. A buck converter is

therefore, only able to extract maximum power if the original load draws a higher current

than the maximum power point current Imp of the PV module (Zone-1 in Figure-).

BOOST CONVERTER

For an ideal boost converter, the averaged input and output values of current and voltage are

related as follows:

VO =Vg / (1 - D) (13)

Io =Ig (1 – D) (14)

The load resistance R’ referred to the input side is given by:

R’ = R (1 – D) 2 (15)

Since 0 < D <1, varying D can only decrease the load seen by the source. It is therefore noted

that a tracker based on the boost converter is only able to extract maximum power if the

original load draws lower current than maximum power point current Imp, of the PV module

(Zone-II in Figure-).

BUCK-BOOST CONVERTER

For an ideal buck-boost converter, the averaged input and output values of current and

voltage are related as follows:

VO =Vg (D / 1 - D) (16)

Io =Ig (1 – D / D) (17)

The load resistance R’ referred to the input side is given by:

R’ = R (D / 1 – D) 2 (18)

Since 0 < D <1, varying D can increase or decrease the load seen by the source. The buck-

boost converter is therefore able to operate in both Zone-I and Zone-II in Figure-.

45

Figure 21-Circuit of a buck-boost converter

CONCLUSION

It is noted from the analysis carried out in the preceding sub-sections that the buck-boost

converter has the best performance since it is able to perform maximum power tracking in

both zones I and II of Figure-20.

46

CHAPTER 5: FUNDAMENTAL OF TYPE- 1 FUZZY SETS AND

SYSTEMS AND APPLICATION IN MPPT CONTROL

The fuzzy theory was first introduced into the scientific literature in 1965 by Professor Lotfi

A. Zadeh at the University of California at Berkeley who proposed a set theory that operated

over the range [0; 1]. While Boolean logic results are restricted to 0 and 1, fuzzy logic results

are between 0 and 1. In other words, fuzzy logic defines some intermediate values between

sharp evaluations like absolute true and absolute false. This means that fuzzy sets can handle

some concepts that we commonly meet in daily life, like ”very old”, ”old”, ”young”, ”very

young”. Fuzzy logic is more like human thinking because it is based on degrees of truth and

uses linguistic variables.

Fuzzy logic was not an acceptable theory for the scientists at that time because it contained

vagueness in the engineering field. However, since 1970s, this approach to set theory has

been widely applied to control systems. The principles of fuzzy logic were used to control a

steam engine by Ebraham Mamdani of University of London in 1974. It was a milestone for

fuzzy logic. The first industrial application was a cement kiln built in Denmark in 1975. In

the 1980s, Fuji Electric applied fuzzy logic theory to the control of a water purification

process. As a challenging engineering project, in 1987, Sendai Railway system that had

automatic train operation control was built with fuzzy logic principles in Japan. Fuzzy

control techniques were used in all the critical operations in the control of the train, such as

accelerating, breaking, and stopping operations. In 1987, Takeshi Yamakawa used fuzzy

control in an inverted pendulum experiment which is a classical control problem. After these

successful applications, not only the engineers but also the social scientists applied fuzzy

logic into different areas. In today’s technology, many companies use fuzzy logic in their

engineering projects like for example air conditioners, video cameras, televisions, washing

machines, bus time tables, medical diagnoses, antilock braking system, etc.

Classical control theory, typically PID controller, uses a mathematical model to define the

relationship between the inputs and the outputs of a system. The most serious disadvantage

of these controllers is that they usually assume the system to be linear or at least that it

behaves as a linear system in some range. If an accurate mathematical model of a system is

available, a conventional PID controller can make the performance of the system quite

acceptable. However, in real life, an accurate mathematical model of a control process is not

generally available, even it may not exist. The real world is nonlinear, uncertain and contains

47

always incomplete data. If the mathematical model is not known by the designer, there is no

way to come up with a proper PID controller design. Even in those cases, when the

mathematical model is known to be relatively accurate, the parameters of the system are

likely to change by some external factors, like heat or pressure, etc. In such cases, a model-

free approach is preferable. Fortunately, fuzzy logic controllers (FLCs) have the ability to

control a system using some limited expert knowledge. In most cases, the design procedure of

a FLC tries to imitate an expert or a skilled human operator. Besides, FLCs are low-cost

implementations based on cheap sensors.

In general, fuzzy logic is a nonlinear mapping of an input data vector into a scalar output. The

main approaches to design of a Type-1 FLC in literature those Type-1 fuzzy sets:

Membership functions are totally certain.

TYPE-1 FUZZY SETS AND MEMBERSHIP FUNCTION

A type-1 fuzzy set, A, which is in terms of a single variable, x ∈ X, may be represented as:

A = {(x, µA(x))| ∀∀∀∀x ∈∈∈∈ X} (19)

A can also be defined as:

(20)

Where ∫∫∫∫ denotes union over all admissible x.

As can be seen from Figure 2.1, a type-1 Gaussian membership function, µA(x), is

constrained to be between 0 and 1 for all x ∈ X, and is a two-dimensional function. This type

of membership function does not contain any uncertainty. In the other word, there is a clear

membership value for every input data point.

48

Figure 22-A Gaussian type-1 fuzzy membership function

FUZZY RULES AND INFERENCE

The use of fuzzy sets allows the characterization of the system behaviour through fuzzy rules

between linguistic variables. A fuzzy rule is a conditional statement Ri based on expert

knowledge expressed in the form:

Ri : IF x is small THEN y is large (21)

Where x and y are fuzzy variables and small and large are labels of the fuzzy sets. If there are

n rules, the rule set is represented by the union of these rules i.e.

R = R1 else R2 else ….. Rn . (22)

A fuzzy controller is based on a collection R, of control rules. The execution of these rules is

governed by the compositional rule of inference.

FUZZY CONTROLLER STRUCTURE

The general structure of a fuzzy logic controller is presented in Figure- and comprises of four

principal components:

• Fuzzification interface: - It converts input data into suitable linguistic values using a

membership function.

49

• Knowledge base: - Consists of a database with the necessary linguistic definitions

and the control rule set.

• Inference engine: - It simulates a human decision making process in order to infer the

fuzzy control action from the knowledge of the control rules and the linguistic

variable definitions.

• Defuzzification interface: - Converts an inferred fuzzy controller output into a non-

fuzzy control action.

Figure 23-Basic configuration of a fuzzy logic controller

APPLICATION OF TYPE-1 FUZZY LOGIC IN MPPT CONTROL

DC-DC converter systems are becoming strong candidates for modern fuzzy control

techniques due to their complex, nonlinear behaviour, particularly for large load and line

variations. The highly nonlinear behaviour of these power circuits is caused by the presence

of a switch, which can be any electronic switch such as a transistor, a Mosfet, or any other

switching device. Depending on the state of the switch (ON/OFF) the plant structure exhibits

very different functioning modes, resulting in a severe nonlinearity. PV modules also have

nonlinear current-voltage (I-V) characteristics that are dependent on solar radiation,

temperature, and degradation due to environmental effects. Therefore, their operating point

that corresponds to the maximum output power varies with the environmental and load

conditions.

MPPT control is therefore an intriguing subject from the control point of view, due to the

intrinsic nonlinearity of dc-dc converters and PV modules. This is because an accurate model

of the plant and the controller is necessary while formulating the control algorithm. There are

50

two possible ways of overcoming this. One method is to develop more accurate nonlinear

models for controllers, but the discouraging fact about taking this route is that complex

mathematical derivations are involved. Even when developed, the complicated control

algorithms may not be suitable for practical implementations. The other method is to employ

heuristic reasoning based on human experience of the plant. Such experience is usually

collected in the form of linguistic statements and rules. In this case, no modeling is required,

and the whole business of controller design reduces to the "conversion" of a set of linguistic

rules into an automatic control algorithm. Here, fuzzy logic comes into play as it provides the

essential machinery for performing the said conversion. Such a completely different approach

is offered by fuzzy logic, which does not require a precise mathematical modeling of the

system nor complex computations. This control technique relies on the human capability to

understand the system's behaviour and is based on qualitative control rules. Thus, controller

design is simple, since it is only based on linguistic rules of the type: “IF the change in output

power is positive AND the change in duty cycle is negative THEN reduce slightly the duty

cycle" and so on.

Fuzzy logic control relies on basic physical properties of the system, and it is potentially able

to extend control capability even to those operating conditions where linear control

techniques fail, i.e., large signal dynamics and large parameter variations. As fuzzy logic

control is based on heuristic rules, application of nonlinear control laws to overcome the

nonlinear nature of dc-dc converters is easy. Fuzzy logic offers several unique features that

make it a particularly good choice for these types of control problems because:

• It is inherently robust as it does not require precise, noise-free inputs. The output

control is a smooth control function despite a wide range of input variations.

• It can be easily modified to improve system performance by generating appropriate governing rules.

• Any sensor data that provides some indication of a system's actions and reactions is

sufficient. This allows the sensors to be inexpensive and imprecise thus keeping the

overall system cost and complexity low.

• Its rule-based operation enables any reasonable number of inputs to be processed and

numerous outputs generated. The control system can be broken into smaller units that

51

use several smaller fuzzy logic controllers distributed on the system, each with more

limited responsibilities.

DESIGN OF FUZZY LOGIC CONTROLLER PARAMETERS

CONTROLLER STRUCTURE

The basic scheme of a fuzzy logic based maximum power point tracker is shown in Figure-.

The dc-dc converter is represented by a “black box” from which only the terminals

corresponding to input voltage Vm, input current Im from the PV module, and the controlled

switch S are extracted. As observed, only two state variables are sensed; the input voltage and

input current. The two values are used to calculate the input power. From these

measurements, the fuzzy logic controller provides a signal proportional to the converter duty

cycle which is then applied to the converter through a pulse width modulator. The modulator

uses the value of D to perform Pulse Width Modulation (PWM), which generates the control

signals for the converter switch. The fuzzy logic controller scheme is a closed loop system.

Figure 24-Fuzzy control scheme for a maximum power point tracker

A functional block diagram representation of the fuzzy controller is shown in Figure-. The

inputs to the controller are the scaled change of power, kp∆∆∆∆Pk and the previous change of

duty, ∆∆∆∆Dk-1, where kp is a power scale factor, and k is the sampling instant. The output of the

fuzzy controller is the duty cycle Dk at the k -th sampling instant, and is defined as

52

Dk = Dk-1 + kd ∆∆∆∆Dk (23)

Where ∆∆∆∆Dk is the inferred change of duty cycle by the fuzzy controller at the k-th sampling

instant and kd is a duty-cycle scale factor. The block containing the term 1 Z − in Figure-

indicates a unit time delay.

Figure 25-Functional block of the fuzzy controller

MEMBERSHIP FUNCTIONS

Fuzzy sets for each input and output variable are defined as shown in Figure-. Five fuzzy

subsets Negative Big (NB), Negative Small (NS), Zero (ZE), Positive Small (PS), and

Positive Big (PB) are chosen for the input variable ∆∆∆∆Pk, eleven subsets are used for the input

and output variable ∆∆∆∆Dk-1. The subsets are NB, Negative Medium (NM), Negative Medium

Medium (NMM), NS, Negative Small Small (NSS), ZE, Positive Small Small (PSS), PS,

Positive Medium Medium (PMM), Positive Medium (PM), and PB. Eleven fuzzy subsets

were chosen for ∆∆∆∆Dk-1 in order to smooth the control action. As shown in Figure-, triangular

and trapezoidal shapes have been adopted for the membership functions; the value of each

input and output variable is normalized. The same membership function is used for the output

value ∆∆∆∆Dk and the input value ∆∆∆∆Dk-1.

53

Figure 26-Membership functions for (a) change in power (b) change in duty cycle

The membership functions for ∆∆∆∆Pk and ∆∆∆∆Dk-1 are made denser at the centre in order to

provide more sensitivity as the variation of power approaches zero. The duty cycle is

internally limited to a maximum value of 90% to prevent operation at low efficiencies. It is

also limited to a minimum value of 10% to ensure that the converter switching process does

not stop as operation at D = 0 will indicate a false maximum power point.

SCALING FACTORS

For simplicity, the universe of discourse for each fuzzy variable was normalized to be in the

range [-1 1]; this procedure involves scale mapping for the input and output data. The choice

of the scale factors kp and kd greatly affects the bandwidth and the overall performance of the

controller. The factor kp determines the sensitivity of the controller to changes in power, and

kd determines the sensitivity to change in duty cycle. Suitable values of kp and kd were

chosen based on simulation results.

DERIVATION OF CONTROL RULES

Fuzzy control rules are obtained from the analysis of the system behaviour. The different

operating conditions are considered in order to improve tracking performance in terms of

dynamic response and robustness. The algorithm can be explained as follows: the tracking

process is started with an initial duty cycle, D0. The converter input current Im, and voltage

Vm, are then measured and used to compute the module power Pk. Then, the duty cycle is

increased by the controller based on the initial changes in power and duty cycle. At stage two,

m I and m V are measured and used to compute Pk+1. After gathering the past and present

information of the module power, the controller makes a decision on whether to increase or

decrease the duty cycle. This tracking process repeats itself continuously until the peak power

point is reached. The control rules are divided into four categories.

54

Category I

These rules are used to guide the controller under constant operating conditions i.e. when

there are no variations in solar radiation, temperature, or load. Operation is based on the

meta-rule:

“IF the last change in the duty cycle has caused the power to increase, keep moving the duty

cycle in the same direction; otherwise if it has caused power to decrease, move it in the

opposite direction.”

The duty cycle is changed in adaptive steps which depend on the change in power to ensure

the maximum power point is approached at a fast speed and to prevent oscillations around it.

There are forty rules in this category and they are shown in Table 5-1 with a degree of

support of 1. These rules are given the strongest degree of support since the task they

represent describes the normal system operation. The rules are read as,

• IF ∆∆∆∆Pk is NB AND ∆∆∆∆Dk- 1 is NB THEN ∆∆∆∆Dk is PM

• IF ∆∆∆∆Pk is NB AND ∆∆∆∆Dk- 1 is NM THEN ∆∆∆∆Dk is PMM

• IF ∆∆∆∆Pk is NB AND ∆∆∆∆Dk- 1 is NS THEN ∆∆∆∆Dk k is PSS

• …………………………………………………………..

• IF ∆∆∆∆Pk is PB AND ∆∆∆∆Dk- 1 is PB THEN ∆∆∆∆Dk is PM.

Table 5-1 Fuzzy controller rule base

55

Category II

The rules in this category guide the controller when there are sudden changes in solar

radiation, temperature, or load leading to an overall shift in the optimum point. There are four

rules in this collection and are found in the vertical column of Table 5-1 corresponding to

∆∆∆∆Dk-1 = 0, and a degree of support of 0.5. This condition is rare and the rules are used to

return the system to normal operation where category I rules are activated to search for the

new optimum operating point.

Category III

The rules in this group are used to ensure that the maximum power transfer search only stops

when the true maxima has been reached. Several false maxima are introduced due to the

quantization effect shown in Figure 27. Since the input signals are digitized, the continuous

curve is broken into a series of plateaus (points with constant power). It is observed from

Figure 27 that the steeper the curve, the shorter the plateau. Since the optimum point satisfies

the condition δP / δD = 0, the controller might recognize any large plateau as a maximum

power point and stop. There are ten rules in this category and are found in the horizontal

column of Table 5-1 corresponding to ∆∆∆∆Pk = 0. The rules are given a degree of support of 0.5

since the condition is rare.

Category IV

There is only one rule in this category. The rule is activated when the system reaches the

optimum point and it is used to stabilize operation at the maximum power point. It is given a

weight of 0.25 as shown in Table 5-1. The rule is read as,

• IF ∆∆∆∆Pk is E AND ∆∆∆∆Dk-1 is ZE THEN ∆∆∆∆Dk is ZE

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Figure 27-Quantization effect during maximum power search

DECISION MAKING

From the membership functions in Figure 26, it is observed that every input and output

belongs to at most two fuzzy sets. A maximum of four rules are therefore activated at any

sampling instant during which the input signals ∆∆∆∆Pk and ∆∆∆∆Dk-1 are processed. For instance, let

∆∆∆∆Pk = 0.2 and ∆∆∆∆Dk-1= -0.35. Change in power belongs ∆ ∆ ∆ ∆Pk to the fuzzy set PS and PB with a

degree of membership µPS(∆∆∆∆Pk) = 0.33, and µPB(∆∆∆∆Pk) = 0.71. Change in duty cycle ∆∆∆∆Dk-1

belongs to the fuzzy set NMM and NM with µNMM(∆∆∆∆Dk-1) = 0.5, and µNM(∆∆∆∆Dk-1) = 0.25. The

degree of membership for the other membership functions is zero. Therefore, the following

four rules are activated,

• Rule 1: IF ∆∆∆∆Pk is PS AND ∆∆∆∆Dk-1 is NM THEN ∆∆∆∆Dk is NMM.

• Rule 2: IF ∆∆∆∆Pk is PS AND ∆∆∆∆Dk-1 is NMM THEN ∆∆∆∆Dk is NS

• Rule 3: IF ∆∆∆∆Pk is PB AND ∆∆∆∆Dk-1 is NM THEN ∆∆∆∆Dk is NMM

• Rule 4: IF ∆∆∆∆Pk is PB AND ∆∆∆∆Dk-1 is NMM THEN ∆∆∆∆Dk is NS

57

The inference result of each rule consists of two parts, the degree of fulfilment, DOFi of the

individual rule, and the weighting factor wi, according to the rule. The degree of fulfilment

(DOF) is obtained by means of Mamdani’s min-fuzzy implication and wi is retrieved from the

control rule table. The degree of fulfilment of each rule using Mamdani’s min fuzzy

implication is given by,

DOFi = min { µ∆∆∆∆P (∆∆∆∆Pk), µ∆∆∆∆D k-1(∆∆∆∆Dk-1) } (24)

And the output of the each rule is given by,

zi = (DOFi) wi (25)

Where, zi denotes the fuzzy representation of change in duty cycle inferred from the i-th rule.

Since the inferred output is fuzzy, the defuzzification operation is performed to obtain a crisp

output.

The fuzzy inference system with the Mamdani’s min fuzzy implication method for inputs ∆∆∆∆Pk

= 0.2 and ∆∆∆∆Dk-1= -0.35, is illustrated in Figure 4-6. The degree of fulfilment of Rule 1 is given

by:

DOF1= µPS (∆Pk) ∧ µNM (∆Dk-1) = 0.33 ∧ 0.25 (26)

Where Ù = minimum (AND) operator. The rule output z1, is given by the truncated

membership function NMM. Similarly, degrees of fulfilment for Rules 2, 3 and 4 are

evaluated using Equation (27) to give:

DOF1 = 0.33 (27)

DOF2 = 0.25 (28)

DOF3 = 0.5 (29)

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The corresponding outputs for Rules 2, 3 and 4 are the truncated membership functions NS’,

NMM’ and NS’ respectively, as shown in Figure 28. The total fuzzy output is the union of all

the component membership functions and is given by,

µPS ( Ζ ) = µNMM’ ( Ζ ) ∨∨∨∨ µNS’ ( Ζ ) ∨∨∨∨ µNMM’ ( Ζ ) ∨∨∨∨ µNS’ ( Ζ ) (30)

Where Ú = maximum (OR) operator. The fuzzy output ( ) out µ Z is shown in Figure 28.

DEFUZZIFICATION

The output of an inference process is a fuzzy set specifying a distribution space of fuzzy

control actions defined over an output universe of discourse. Defuzzification is the conversion

of this fuzzy output to crisp output suitable for a control action. A defuzzification strategy is

aimed at producing a non-fuzzy control action that best represents the possibility distribution

of an inferred fuzzy control action. Unfortunately, there is no systematic procedure for

choosing a defuzzification strategy. This process involves the operation:

Z0 = defuzzifier (Z) (31)

The term Z0 in Equation (31) is the non-fuzzy control output and defuzzifier is the

defuzzification operator. There are various defuzzification methods which include, centre of

area (COA), bisector, mean of maxima, sum of maxima, etc. The COA method commonly

known as centre of gravity is used in this work. The method is computationally intensive but

more accurate than other methods. In this method, the crisp output Z0of the Z variable is taken

to be the geometric centre of the output fuzzy value µout ( Z ), where µout ( Z ) is formed by

taking the union of all the contributions of rules whose DOF > 0 as shown in Figure 4-6. The

general expression for the COA method in the case of a discretized universe of discourse is

given by,

(32)

59

Figure 28-Fuzzy inference and defuzzification using Mamdani method

A crisp value for the change in duty cycle is calculated by applying Equation (32) to the

output fuzzy value µout ( Z ) in Figure 28.

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SIMULATION OF TYPE-1 FUZZY CONTROL FOR MPPT

Using matlab program and feeding the data manually in the program we got the simulation

result for the duty cycle signal.

Figure 29-Fuzzy Membership function for Power

Figure 30-Fuzzy Membership function of output

61

Figure 31- Final output of Duty Cycle Signal

62

CHAPTER 6: TYPE-2 FUZZY LOGIC AND DESIGN OF

CONTROLLER FOR MPPT ALGORITHM

Type-2 fuzzy sets were introduced by Zadeh in 1975 as an extension of type-1 fuzzy sets.

Mendel and Karnik have developed the theory of type-2 fuzzy sets further. The theoretical

background of interval type-2 fuzzy system and its design principles are described. T2FLSs

appear to be a more promising method than their type-1 counterparts for handling

uncertainties such as noisy data and changing environments. The effects of the measurement

noise in type-1 and type-2 FLCs (T2FLCs) and identifiers are simulated to perform a

comparative analysis. It is concluded that the use of T2FLCs in real world applications which

exhibit measurement noise and modeling uncertainties can be a better option than type-1

FLCs (T1FLCs).

When a system has large amount of uncertainties, T1FLSs may not be able to achieve the

desired level of performance with a reasonable complexity of the structure. In such cases, the

use of T2FLSs is suggested as the preferable approach in the literature in many areas, such as

forecasting of time-series, controlling of mobile robots, and the truck backing-up control

problem are discussed. It is shown that when the parameters are tuned properly, T2FLSs can

result in a better ability to predict as compared to T1FLSs. T2FLS is applied to real time

mobile robots for indoor and outdoor environments. The real time implementation studies

show that a traditional T1FLC cannot handle the uncertainties in the system effectively and a

T2FLC using type-2 fuzzy sets results in a better performance. Moreover, with the latter

approach the number of rules to be determined may be reduced (it should be noted that this

may not mean a corresponding decrease in the parameters to be updated).

Type-2 FLSs use type-2 fuzzy sets which are described by membership functions which

themselves are fuzzy. This allows Type-2 FLSs to model and handle the uncertainty of

measurement and any rule uncertainty. Examples are the variability of expert opinion on a

fuzzy set, and their self-referencing variability over time; opinions do change. Noise of the

system and errors of measurement also have an effect.

According to a nonlinear current-voltage characteristic Photovoltaic for exploitation of this

optimization we need to track maximum output instantly. The aim of this paper is to search

maximum power point (MPP) Based on the Type2 Fuzzy logic controller (T2FLC) which is a

novel method in maximum power point tracking (MPPT). Solar cells’ MPP varies with solar

insolation and ambient temperature. With the improved efficiencies of power electronics

63

converters, it is now possible to operate photovoltaic (PV) power systems at its MPP in order

to improve the overall system efficiency. The results of simulation show that the T2FLC

significantly improves the robustness of controller’s PV during the tracking phase as

compared to a conventional type1 fuzzy logic control (T1FLC) in present of noise in

photovoltaic power systems. This noise maybe insert to system when voltage and current are

measured. We show that the results obtained with T2FLC are better than the ones obtained

with the T1FLC method.

TYPE-2 FUZZY SETS

A type-2 fuzzy set, Ã may be represented as,

à = {((x, u), µÃ (x, u))| ∀x ∈ X ∀u ∈ Jx ⊆ [0, 1]} (33)

Where, µÃ (x, u) is the type-2 fuzzy membership function in which 0 ≤ µÃ (x, u) ≤ 1. à can

also be defined as

(34)

Where, ∫ ∫ denotes union over all admissible x and u.

Jx is called primary membership of x. There is a secondary membership value corresponding

to each primary membership value that defines the possibility for primary memberships.

Whereas the secondary membership functions can take values in the interval of [0, 1] in

generalized T2FLSs, they are uniform functions that only take on values of 1 in interval

T2FLSs. Since the general T2FLSs are computationally very demanding, the use of interval

T2FLSs is more commonly seen in the literature, due to the fact that the computations are

more manageable.

If the circumstances are so fuzzy, the places of the membership functions may not be

determined precisely. In such cases, the membership grade cannot be determined as a crisp

number in [0, 1], then the use of type-2 fuzzy sets might be a preferable option.

In Figure 29, the membership function does not have a single value for a specific value of x.

The values that the vertical line intersects the membership functions do not need all is

weighted same. Moreover, an amplitude distribution can be assigned to all of those points.

Hence, a three-dimensional membership function-a type-2 membership function- that

64

characterizes a type-2 fuzzy set is created if the amplitude distribution operation is done for

all x ∈ X.

The footprint of uncertainty (FOU), the union of all primary memberships, is said to be the

bounded region that represents the uncertainty in the primary memberships of a type-2 fuzzy

set (Figure 29). An upper membership function and a lower membership function are two

type-1 membership functions that are the bounds for the FOU of a type-2 fuzzy set.

Figure 32-A Gaussian type-2 fuzzy membership function (FOU)

INTERVAL TYPE-2 FUZZY SETS

When all µÃ (x, u) are equal to 1, then à is an interval T2FLS. The special case of Equation

(35) might be defined for the interval T2FLSs:

(35)

As general T2FLS has huge computational burden. So, interval T2FLSs is commonly used in

literature. Both the general and interval type-2 fuzzy membership functions are three-

dimensional. As can be seen from Figure 33, the only difference between them is that the

secondary membership value of the interval type-2 membership function is always equal to 1.

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TYPE-2 FUZZY LOGIC SYSTEM BLOCK DIAGRAM

The type-2 FLSs are shown in Figure 30. As can see from Figure 30, an additional block

(type reduction) is needed in type-2 FLS design. Although the structure in Figure 30 brings

some advantages when dealing with uncertainties, it also increases the computational burden.

The followings are the basic blocks of a T2FLS:

Fuzzifier: The fuzzifier maps crisp inputs into type-2 fuzzy sets which activates the inference

engine.

Rule base: The rules in T2FLS remains the same as in T1FLS, but antecedents and

consequents are represented by interval type-2 fuzzy sets.

Inference: Inference block assigns fuzzy inputs to fuzzy outputs using the rules in the rule

base and the operators such as union and intersection. In type-2 fuzzy sets, join (⊔) and meet

operators (⊓), which are new concepts in fuzzy logic theory, are used instead of union and

intersection operators. These two new operators are used in secondary membership functions.

Type-reduction: The type-2 fuzzy outputs of the inference engine are transformed into type-

1 fuzzy sets that are called the type-reduced sets. There are two common methods for the

type-reduction operation in the interval T2FLSs: One is the Karnik- Mendel iteration

algorithm, and the other is Wu-Mendel uncertainty bounds method. These two methods are

based on the calculation of the centroid.

Defuzzification: The outputs of the type reduction block are given to defuzzification block.

The type-reduced sets are determined by their left end point and right end point, the

defuzzified value is calculated the average of these points.

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Figure 33-T2FLS block diagram

TYPE2 FUZZY LOGIC CONTROLLER

A T2FLC composed of four basic elements: the type1 fuzzyfier, the fuzzy rule-base, the

inference engine, and the type1 defuzzifier. The fuzzy rule-base is a collection of rules, which

are combined in the inference engine, to produce a fuzzy output. Table1 shows these rule

bases with Lower Standard Deviation (LSD) and Upper Standard Deviation (USD) which are

one of important characteristics of T2FLC, which these shows in Fig. 4. The type1 fuzzifier

maps the crisp input into type1 fuzzy sets, which are subsequently used as inputs to the

inference engine, whereas the type1 defuzzifier maps the type1 fuzzy sets produced by the

inference engine into crisp numbers. A T1FLCs are unable to handle rule uncertainties

directly, because they use type1 fuzzy sets that are certain. On the other hand, T2FLCs are

very useful in circumstances where it is difficult to determine an exact, and measurement

uncertainties. It is known that type 2 fuzzy set let us to model and to minimize the effects of

uncertainties in rule base FLC. Unfortunately, type2 fuzzy sets are more difficult to use and

understand than type1 fuzzy sets; hence, their use is not widespread yet. A T2FLC Ã is

characterized by the membership function:

à = {((x, u), µÃ (x, u))| ∀x ∈ X ∀u ∈ Jx ⊆ [0, 1]} (36)

(37)

67

Figure 34-Structure of a type2 FLC

Hence, a type2 membership grade can be any subset in [0, 1], the primary membership, and

corresponding to each primary membership, there is a secondary membership (which can also

be in [0, 1]) that defines the possibilities for the primary membership. This uncertainty is

represented by a region called footprint of uncertainty (FOU) which can be described in terms

of an upper membership function (UMF) and a lower membership function (LMF) as shown

in Fig. 32.

Figure 35-Membership function of input

68

Figure 36-Membership function of output

FUZZIFICATION AND THE RULES

The fuzzifier maps a crisp point x=(x1,..........,xp)T

∈ X1 × X2 ×........ × XP ≡ X into a type2

fuzzy set ÃX in X. As a type2 singleton fuzzifier in a singleton fuzzification with the input

fuzzy set having only a single point on nonzero membership is used, we have:

(38) The structure of rules in a T1FLC and a T2FLC is the same. However, in the latter the

antecedents and the consequents will be represented by T2FLCs. Suppose a T2FLC has p

inputs x1, x2, x3,...........,xp an output y, and a multiple input single output (MISO). It is

assumed that there are M rules and the lth rule in the type2 FLC can be written as follows:

(39)

INFERENCE

In T2FLC, the inference engine combines rules and gives a mapping from input T2FLCs to

output T2FLCs. It is necessary to compute the join Џ (unions), the meet Π (intersections), and

the extended sup-star composition (sup-star compositions) of type2 relations.

(40)

69

Rl Rule is described by the membership function µRl (x, y) =4 µR

l(x1,........, xp, y) where:

(41)

In general, the p-dimensional input to Rl is given by the type2 fuzzy set Ãx whose membership function is:

(42) Where, Xt= (i=1; . . . ; p) are the labels of the fuzzy sets describing the inputs. Each rule Rl

determines a type2 fuzzy set Bl = Ax ◦Rl such that:

(43) This equation is the input / output relationship between the T2FSLC that activates one rule in

the inference engine and the T2FLC at the output of that engine as described in Fig. 3. In the

FLC we used interval T2FLCs and meet under product t-norm, so the result of the input and

antecedent operations, which are contained in the firing Set = ∏P i=1 µFi(xi’), is an interval

T1FLC set :

(44)

Where

(45)

Note * is the product operation.

TYPE-REDUCER AND DEFUZZIFICATION

The type-reducer generates a T1FLC output which is then converted into a crisp output

through the defuzzifier. This T1FLC is also an interval set. For the case of our FLC we used

center of sets (cos) type reduction, Ycos which is given by:

70

Ycos = [yl, yr] =

(46)

This interval set is determined by its two end points, yl and yr, which correspond to the

centroid of the type2 interval consequent set Gi expressed as:

(47)

Before the computation of Ycos (X), we must evaluate (47), and its two end points, yl and yr.

Let the values of fi and yi that are associated with yl are denoted by fil and yi

l, respectively, and

the values of fi and yi that are associated with yr are denoted by frl and yr

l, respectively, then

from (46), we have:

(48)

(49)

From the type-reducer we obtain an interval set Ycos (X), to defuzzify it we use the average of

yl and yr, so the defuzzified output of an interval singleton T2FLS is:

(50)

71

SIMULATION OF TYPE-2 MPPT FUZZY CONTROLLER

Using matlab program and feeding the data manually in the program we got the simulation

result for the duty cycle signal.

Figure 37- Fuzzy Membership function of Power

Figure 38-Fuzzy Membership function of Voltage

72

Figure 39-Fuzzy Membership function of Duty cycle

Figure 40-Final output of Duty Cycle Signal in Type-2 Fuzzy Controller

73

CHAPTER7: CONCLUSION AND FUTURE WORK

CONCLUSION

The aim of this thesis was to develop a method to optimize the energy extraction in a

photovoltaic power system. The concept of PV module maximum power point tracking has

been presented and various methods of addressing existing challenges are explored. A fuzzy

logic based algorithm for tracking the maximum power is proposed in this work. In order to

formulate and implement the algorithm, a system model is needed. The various components

and subsystems are analyzed, modeled, validated, and combined together to produce a

complete maximum power point tracker model. A hardware implementation was then carried

out to determine the performance of the algorithm in a practical setup.

Analysis of different dc-dc converter topologies showed that the buck-boost topology is the

most suitable for a maximum power tracker. The PV module and the buck-boost converter

were modeled and validated in Simulink while the fuzzy logic algorithm was formulated

using the Fuzzy Logic Toolbox in Matlab. The complete Maximum Power Point Tracker

model was formed by combining the PV module and the converter model with the fuzzy logic

controller. The MPPT model was used to tune the fuzzy logic controller rules and

membership functions. The PV module model was found to be sufficiently accurate and can

model any solar panel using information supplied in manufacturer data sheets. Simulation

results show that the proposed fuzzy logic algorithm has an average efficiency of 98% under

rapidly varying conditions and in the presence of measurement noise. The results show that

compared to other MPPT techniques, it provides improved performance in terms of

scillations about the maximum power point, speed and sensitivity to parameter variation. This

is possible since fuzzy logic controller rules can be assigned separately for the various regions

of operation resulting in effective small-signal and large-signal operation.

A hardware design and implementation of the MPPT was then carried out in order to test the

performance of the proposed algorithm. The design was broken down into several smaller

components, which are described in turn. For each subcircuit, a thorough description of the

relevant design issues and decisions was provided. Experimental results show that the

proposed algorithm is able to transfer peak power from a PV module to the load. The results

indicate that a significant amount of additional energy can be extracted from a photovoltaic

module by using a fuzzy logic based maximum power point tracker. This results in improved

74

efficiency for the operation of a photovoltaic power system since batteries can be sufficiently

charged and used during periods of low solar radiation. The improved efficiency is expected

to lead to significant cost savings in the long run.

FUTURE WORK

The overall control goal in a photovoltaic power system is not to deliver the maximum

amount of possible power to the load or batteries, but only as much as is needed at any given

time; this can be referred to as power matching. Usable power that is not extracted from a

particular solar panel (because it is not operating at its current maximum power point) is

dissipated as heat through its surface. In a practical pplication like a water pump in a remote

village, the MPPT circuit must include a way to determine how much power is needed at any

given time and perform maximum power tracking only to a level where power requirements

are met. The MPPT should also include a second voltage regulation stage that maintains a

steady output regardless of variations in the load demand. These improvements will greatly

boost the functionality of the system in a practical setup.

As part of future work, ways of implementing a fuzzy logic algorithm in a dedicated single-

chip microcontroller needs to be addressed. The control algorithm is fairly complex and

modifications need to be made in order to meet the limited memory space and speed of

microcontrollers. The microcontroller must also incorporate timers, PWM input and output,

A/D and D/A interfaces, and interrupts for timing control and communications. The overall

circuit also needs to be modified to include ways of supplying power to the control circuit

using batteries charged by the MPPT. The redesigned circuit should be implemented in a

printed circuit board.

On the whole, it is concluded that the overall objective of formulating and implementing a

fuzzy logic based maximum power point tracker for a photovoltaic power system has been

met. Although there is a large amount of work that can and should still be done, the work in

this thesis has created a solid foundation to allow that work to continue.

75

REFERENCE

1. Ocran, T.A. et al, Artificial Neural Network Maximum Power Point Tracker for Solar

Electric Vehicle, Tsinghua Science & Technology, Vol. 10, No. 2, pp. 204-208, 2005.

2. Hua C., Lin J., A modified tracking algorithm for maximum power tracking of solar

array, Energy Conversion and Management 45 (2004) 911-925, Elsevier Ltd. 2003.

3. Salas V., et al, New algorithm using only one variable measurement applied to a

maximum power point tracker, Solar Energy Materials &Solar Cells 87 (2005) 675-

684, Elsevier B.V. 2004.

4. C. Hua and C. Shen, Comparative study of peak power tracking techniques for solar

storage systems, in Proc. IEEE Appl. Power Electron. Conf. and Expo., Feb. 1998,

vol. 2, pp. 676–683.

5. Koutroulis E., Kalaitzakis K., Voulgaris N.C., Development of a Microcontroller

Based Photovoltaic Maximum Power Point Tracking Control System, IEEE

Transactions on Power Electronics, Vol. 16, No. 1, 2001.

6. J. H. R. Enslin, D. B. Snyman, Simplified feed-forward control of the maximum power

point tracker for photovoltaic applications, Proc. Int.Conf. IEEE Power Electron.

Motion Control, 1992, vol. 1, pp. 548–553.

7. M. Bodur and M. Ermis, Maximum power point tracking for low power photovoltaic

solar panels, in Proc. IEEE Electro Tech. Conf., 1992, vol. 2, pp. 758–761.

8. C. R. Sullivan and M. J. Powers, A high-efficiency maximum power point trackers for

photovoltaic array in a solar-powered race vehicle, in Proc.IEEE PESC, 1993, pp.

574–580.

76

9. M. Veerachary, T. Senjyu, and K. Uezato, Feed-forwardmaximum powerpoint

tracking of PV systems using fuzzy controller, IEEE Trans. Aerosp. Electron. Syst.,

vol. 38, no. 3, pp. 969–981, Jul. 2002.

10. Ocran, T.A. et al, Artificial Neural Network Maximum Power Point Tracker for Solar

Electric Vehicle, Tsinghua Science & Technology, Vol. 10, No. 2, pp. 204-208, 2005.

11. Bidyadhar Subudhi, and Raseswari Pradhan, A Comparative Study on Maximum

Power Point Tracking Techniques for Photovoltaic Power Systems, IEEE

TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 4, NO. 1, JANUARY 2013

12. Qilian Liang and Jerry M. Mendel, Interval Type-2 Fuzzy Logic System: Theory and

Design, IEEE TRANSACTIONS ON FUZZY SYSTEMS, VOL. 8, NO. 5,

OCTOBER 2000

13. Chian-Song Chiu, T-S Fuzzy Maximum Power Point Tracking Control of Solar

Power Generation Systems, IEEE TRANSACTIONS ON ENERGY CONVERSION,

VOL. 25, NO. 4, DECEMBER 2010

14. Pongsakor Takun, Somyot Kaitwanidvilai and Chaiyan Jettanasen, Maximum Power

Point Tracking using Fuzzy Logic Control for Photovoltaic Systems, Proceeding of the

International MultiConference of Engineers and Computer Scientists 2011 Vol II,

IMECS 2011, March 16-18, 2011, Hong Kong

77

APPENDICES

A-1 MATLAB CODE FOR TYPE-1 FUZZY MPPT SYSTEMS

clear all;

clc;

seed(1,:)=[-1.41872966171615,-1.50937336396472,1.35940535370735,0.552050153997157,-3.56300846530129,-3.92921289153443,3.59350530002252,2.91377613583114,-4.06830134654488,-9.38315840253697,5.33163240608823,2.55427454937803];

x=-5:0.01:5;

m11=seed(1,1);

nmf_1=1.*(x>=-5 & x<=-2)+((m11-x)/(m11+2)).*(x>-2 & x<=m11)+0.*(x>m11);

m12=seed(1,2);

m13=seed(1,3);

mmf_1=0.*(x>=-5 & x<m12)+((m12-x)/m12).*(x>=m12 & x<=0)+((m13-x)/m13).*(x>0 & x<=m13)+0.*(x>m13);

m14=seed(1,4);

pmf_1=0.*(x>=-5 & x<=m14)+((m14-x)/(m14-2)).*(x>m14 & x<=2)+1.*(x>2);

plot(x,nmf_1,x,mmf_1,x,pmf_1);

m21=seed(1,5);

nmf_2=1.*(x>=-5 & x<=-4)+((m21-x)/(m21+4)).*(x>-4 & x<=m21)+0.*(x>m21);

m22=seed(1,6);

m23=seed(1,7);

mmf_2=0.*(x>=-5 & x<m22)+((m22-x)/m22).*(x>=m22 & x<=0)+((m23-x)/m23).*(x>0 & x<=m23)+0.*(x>m23);

m24=seed(1,8);

pmf_2=0.*(x>=-5 & x<=m24)+((m24-x)/(m24-4)).*(x>m24 & x<=4)+1.*(x>4);

figure,plot(x,nmf_2,x,mmf_2,x,pmf_2);

x1=-10:0.01:10;

78

m31=seed(1,9);

nmf_3=((m31-x1)/(m31+10)).*(x1>=-10 & x1<=m31)+0.*(x1>m31);

m32=seed(1,10);

m33=seed(1,11);

mmf_3=0.*(x1>=-10 & x1<m32)+((m32-x1)/m32).*(x1>=m32 & x1<=0)+((m33-x1)/m33).*(x1>0 & x1<=m33)+0.*(x1>m33);

m34=seed(1,12);

pmf_3=0.*(x1>=-10 & x1<=m34)+((m34-x1)/(m34-10)).*(x1>m34 & x1<=10);

figure,plot(x1,nmf_3,x1,mmf_3,x1,pmf_3);

N=[1.38482138927092,0.331695099753793,-0.240571581094563,2.20154050244822,-0.985997992943328,0.797006278255187,2.54603755463328,-0.520374576999944,0.798959298794457,0.402293283259269,-0.438415331019449,-0.00447452677584946,0.777744982882119,2.93138207608262,1.11594667083867,-0.307285420662612,-2.48401344836948,0.313548106522630,0.328551210929899,-0.996415148210786,1.27067528727686,0.492079604011546,0.738863773478882,-0.612072816570621,-0.860921659303211,-0.588452929194514,-1.39813810236020,-0.657840044896512,0.915040345406705,-2.83931333524345,-2.23078107238103,0.0334746917300934,0.413548212695413,-1.19450604408623,0.675340681022256,1.58501469306781,0.860781214720267,-1.96819725194340,-0.919725180931747,-1.07488393366207,-0.426464469193661,-0.845097270811198,-1.05953001399227,2.40443850189278,-0.419183396909719,-0.191893646091304,0.360508723751472,-2.18073828376819,-1.43723087054719,0.591524735185831,0.442373364363211,-1.46163551257501,1.41711950219533,-0.0840194870036627,0.178377958396273,0.137579969481291,-0.692374305594608,-2.30544630152871,-0.164764290116440,-1.97018180362483,-0.207303081972442,0.261033736690033,0.249219702822809,-1.74521294286126,0.461522032143667,-1.52388653756162,0.316836855719714,0.759385473279033,2.01227378752132,-2.58180950742198,1.04397922994940,-0.204141190654463,-0.0948098401765951,-0.708024898446485,0.294783332926228,-0.325581450216494,-0.778977027986079,-0.678064431097863,0.775853002347159,0.618921803752649,1.38559834740879,0.456920211723040,-0.183669740772424,-1.43312498597510,0.396289483615839,-0.385967739623539,0.278871258925728,1.10103051869061,-0.620458179923327,-0.607129928473020,-0.326305208067380,0.267642873780794,2.56435187859992,-1.09890948557486,1.68686800418637,-0.271213340121641,1.13038441475108,0.0751663592513872,-0.672532835522489,-

79

0.326313069554429,1.20715091109962,1.59478856853022,1.20985451794234,-0.709733517885276,-1.62253316166248,0.504662521251894,0.664687758803999,-3.16311397468132,0.0305049438818347,2.63815385047041,-0.237227564710709,-0.810989836660408,-1.26870294985077,-2.27986325737011,-0.616168452531363,0.379476424687043,-1.23866577748961,0.319095006076758,0.991993482703499,-0.746915320515773,0.619647796416560,0.711903023399526,-0.0538889834616139,2.46302275482213,-1.60160766888651,0.346287672168541,-1.16670174165339,-0.908644284160093,0.555153221342472,1.37587269088625,0.214147065107326,1.64270854545363,-1.17096593249108,0.425715806624958,-0.668355859092558,-0.953455700447712,-3.31293774445661,0.957012593902646,2.36029663518581,0.629010196960602,1.73268806468481,0.0742519574849388,-1.54900649455698,-1.09837682340403,-1.01049651017435,1.38780936079022,-0.604739218714607,0.115119018704842,-1.67833464939734,-0.230465085880884,-2.04684504233435,-0.884298841604003,0.956144095483507,2.15232623483605,0.611134208728999,0.122415697272733,1.35115572576624,0.916522195581153,-3.08294560475902,-2.25544875236212,-1.04913259864545,-1.09980791326250,-2.01457100885465,-0.853870757405701,-1.17228176747221,1.38509687958932,-0.767913447832517,-1.60640927798435,-0.524048117771788,-0.862322890137972,0.330040567392754,-0.291171495747007,-1.87015498579144,0.730583582771480,-0.458187629546408,-0.755392975482703,-1.07234780120883,0.999445753113964,-0.137134537773299,-1.95487580833494,2.73286818905448,-0.430169976298140,0.341241619992428,0.446700891720196,-1.64481849451659,1.53732736004414,0.316138108925763,0.180849151231216,1.70035504065231,0.200288920770145,-2.16822816746923,-0.0202180624284108,1.46915766449766,1.52661429361812,0.333207355174898,-2.13195674555119,1.38033890677280,-0.0722427447820588,0.241578668250488,1.61302629291383,0.507040819164125,-4.68598632713944,-2.09451999908524,-1.04240098247441,-1.62564163023764,0.193199883541485,0.191305877638837,-0.872577808736155,1.47225988375540,-0.992137065435284,-0.435075815807036,-0.840179042254998,-1.12858042648021,0.0687588334093583,-1.75513853204869,-0.393026027672157,1.04531647679078,1.02448855076122,-2.44996562819912,0.512029121886063,-0.576567692922137,0.567191547821422,0.216684387745333,-0.397921416741962,-0.0167642343395225,0.765303717680543,0.914010981885747,-0.943802840946499,-1.67103885400230,-0.527555626199160,1.28410055389022,0.431575334880573,0.496015609411085,-0.557116242203661,-0.963908547825090,2.61482895891171,-0.132394911920200,-0.0418560718158022,-0.344563907114072,0.0877658996804111,-0.402238830184576,-1.31459134111788,0.620578141078599,1.81258652177899,0.232736050551499,-0.936828193582948,0.0710388883600386,1.28448596066744,2.24484441868597,-

80

1.76909706539437,0.143530009393017,-0.545472219995132,0.685612789422788,0.212653221227279,-0.741039005791648,-2.27511514718797,-1.52855613527878,-0.763412876820536,-0.344570600821842,1.48017292741012,-0.748521835886504,0.468362944669008,1.14036432368427,0.291646396072781,0.106754322079998,-0.768633679355067,1.05915862292141,2.05030769543055,0.598666879262569,0.386885662668656,0.296313001682898,1.30177733034342,-0.416575211880557,-0.644812776504438,0.669576876548693,-0.385837054714682,1.12273950769089,-1.84290166633205,1.66979591137321,-0.919794957209801,0.300315920938156,-0.589025122794665,0.898332180141968,-1.78452205387631,-1.34364320022215,2.05504428231793,-1.22794200952554,-0.879185134153416,0.0784525833047537,-1.00550998703650,0.184692752840272,1.48040320478173,0.0864680037024968,2.17313990076000,-1.82511473183257,-0.358344231145863,-1.10035312328395,0.463914261232699,-1.58834651728004,-2.21519823700076,-0.495428858200163,-2.28499688781302,-1.13064733767543,-0.689012644380276,-2.10289906069769,0.709932431204590,0.384743166507179,-0.789533445080592,-1.75285118036256,-0.346576661696050,-0.211310789339244,-2.73557842264944,1.64594116804254,0.548299403368277,-2.20758347930695,2.49025451547024,-0.193303674254264,-1.85488901966005,-1.16582117315815,0.330728774934612,-1.81259403855072,-0.596157138402061,-0.127788291412250,-0.535004691627498,0.256401389690463,-0.896371835959952,-0.315381261983667,0.240111530182619,-2.79492386598159,-2.41487958140448,-1.34337210024082,0.100530022799672,0.255303364958176,-0.920427480834600,1.65225589947731,1.42636788706646,-0.222963825631180,4.18660155874998,-0.459898019136465,1.23801784891321,-0.0793394582787517,-2.17145983927161,2.36657126583045,-1.33893204834467,0.0928219928919509,2.41816270189124,0.809150578909097,0.467057143698821,-0.183072725021343,0.308690901185450,2.37958051500274,-0.580314306138870,-0.278901121813475,-0.573538914351919,-0.518739490720163,-0.217141466533065,0.779116367510426,0.111049139965645,-0.957689937883396,2.07969626585448,-1.09472340320257,-0.415995060539202,0.100836660136994,-2.11777085160188,-1.27035859514546,-1.62862378691149,-3.35415115093708,2.68528791471479,-0.919460493323576,1.05757222390175,0.0216460661706082,-1.25154600732988,-0.0508477475736162,0.509543225470446,-1.43871703485559,1.50832413484387,1.50673068429782,-0.122589722632457,0.773417560248220,-1.53412783839406,0.719946448584196,-0.161532745972635,2.02500412701583,-1.20488369102054,2.53234006762520,0.0252853577291452,0.560861055158647,1.82484927445748,1.38853221483562,-1.10264690252973,-1.15221817338068,-1.15169268362569,1.35303045937092,-0.170833770910056,-0.559857820407075,0.103882776922012,1.30395483367127,-

81

0.200030250311312,0.389363198677451,-2.91492212093074,-0.840438292722718,-1.34275121118885,-0.804649766806675,-0.959260445230660,-0.531399691881970,-0.618545443970905,0.828052290457057,1.80792141618184,-1.93249207041947,2.20670052420605,1.61526532213254,0.117888821361295,1.98922656795367,0.308164390102684,-1.28442413489953,1.41986729480852,2.81051157936995,-0.974719340939937,-1.26076002675356,1.43306796735528,-0.0301532636828884,-1.71696313429771,1.55642986030246,-0.193969365712743,-1.00110577936122,-0.732156504386608,-0.626521851553325,1.18015193829293,-1.45497459431202,0.590717841827051,1.26447899039292,-1.08247772869104,0.420967691671818,-2.08159440885561,0.877318207824867,-1.41277796500988,1.01515124514750,0.545826078532877,-0.517921878218660,-1.86304365511266,1.67636849360081,0.192241494966741,2.11159460969132,0.0107828131199507,-2.23885434740051,2.12766776895631,-0.366836682891734,1.16375091168049,-0.909246647359768,0.770254099390070,1.05118819463518,1.27539984142651,0.628265367935514,-0.0513779150639639,0.181886703562448,0.380629795439442,-0.929668244170861,0.692941793154290,-1.34009389481400,-2.39872855038055,0.209693824619781,0.248929633576670,0.277890539078031,2.23187821257961,1.55210707722581,2.34637631838160,0.277405016835427,1.14390426417808,-0.744239213853409,-0.290786408320864,-2.20031142724091,0.0879135419050389,1.16699980796735,-1.33216471111545,-0.280091458826250,-0.911564512656003,-1.01772574216173,1.13604608478516,0.0846842332222333,0.931092727553606,0.499510520214393,1.17809172900377,-2.84165143411804,-1.28677646228305,-0.216390149826244,0.437995425035824,1.44579088690221,-0.805238556680096,-0.761583686530278,-0.358988895162106,0.875230733052720,0.133993444040174,1.41717441814692,-0.971804688293527,0.517586590556182,0.487441365598103,-2.06968315539206,0.373131409047017,2.19014455836489,-1.50792224073924];

N=.001*N;

y1(1)=-1.5;

y2(1)=-3;

t=1:500;

n=length(t);

u(1)=0;

for k=2:n

p1=y1(k-1);

82

p2=y2(k-1);

if(p1>2)

p1=2;

end

if(p1<-2)

p1=-2;

end

if(p2>4)

p2=4;

end

if(p2<-4)

p2=-4;

end

n12=nmf_1(uint16(100*p1+501));

z12=mmf_1(uint16(100*p1+501));

p12=pmf_1(uint16(100*p1+501));

n22=nmf_2(uint16(100*p2+501));

z22=mmf_2(uint16(100*p2+501));

p22=pmf_2(uint16(100*p2+501));

p=max(max(min(p12,p22),min(p12,z22)),min(z12,p22));

z=max(max(min(n12,p22),min(z12,z22)),min(p12,n22));

n=max(max(min(n12,z22),min(z12,n22)),min(n12,n22));

mf=max(min(n,nmf_3),max((min(p,pmf_3)),(min(z,mmf_3))));

83

num=0.0;

den=0.0;

for k1=1:2001

num=num+x1(k1)*mf(k1);

den=den+mf(k1);

end

u(k)=num/den;

y1(k)=y1(k-1)+0.05*y2(k-1)+N(k);

y2(k)=0.05*(y1(k-1)+N(k))+y2(k-1)-u(k);

end

sum=0;

for k=1:500

sum=sum+(y1(k)*y1(k));

end

RMS=sqrt(sum);

subplot(311),plot(t,y1)

title('Signal response')

subplot(312),plot(t,y2)

title('Error-dot response')

subplot(313),plot(t,u),xlabel('Time(s)')

title('Control signal')

84

A-2 MATLAB CODE FOR TYPE-2 FUZZY MPPT SYSTEMS

clear all;

clc;

seed(1,:)=[-1.44486191714372,-1.33296143708818,-0.0637895310191314,0,0,0.0338396663311227,0.264521471975207,0.318430228036970,-4,-3.51852513113980,-1.21733109857411,-0.655547464226103,1.54298297536309,1.73450196171244,2.06437212068236,2.38667974339272,-10,-9.29849944705924,-8.46461202642989,-7.51611612278146,0,1.66721382815816,3.92216833878827,4.06015421266160];

x=-5:0.01:5;

m11=seed(1,4);

numf_1=1.*(x>=-5 & x<=-2)+((m11-x)/(m11+2)).*(x>-2 & x<=m11)+0.*(x>m11);

m12=seed(1,1);

m13=seed(1,8);

mumf_1=0.*(x>=-5 & x<m12)+((m12-x)/m12).*(x>=m12 & x<=0)+((m13-x)/m13).*(x>0 & x<=m13)+0.*(x>m13);

m14=seed(1,5);

pumf_1=0.*(x>=-5 & x<=m14)+((m14-x)/(m14-2)).*(x>m14 & x<=2)+1.*(x>2);

m21=seed(1,12);

numf_2=1.*(x>=-5 & x<=-4)+((m21-x)/(m21+4)).*(x>-4 & x<=m21)+0.*(x>m21);

m22=seed(1,9);

m23=seed(1,16);

mumf_2=0.*(x>=-5 & x<m22)+((m22-x)/m22).*(x>=m22 & x<=0)+((m23-x)/m23).*(x>0 & x<=m23)+0.*(x>m23);

m24=seed(1,13);

pumf_2=0.*(x>=-5 & x<=m24)+((m24-x)/(m24-4)).*(x>m24 & x<=4)+1.*(x>4);

85

x1=-10:0.01:10;

m31=seed(1,20);

numf_3=((m31-x1)/(m31+10)).*(x1>=-10 & x1<=m31)+0.*(x1>m31);

m32=seed(1,17);

m33=seed(1,24);

mumf_3=0.*(x1>=-10 & x1<m32)+((m32-x1)/m32).*(x1>=m32 & x1<=0)+((m33-x1)/m33).*(x1>0 & x1<=m33)+0.*(x1>m33);

m34=seed(1,21);

pumf_3=0.*(x1>=-10 & x1<=m34)+((m34-x1)/(m34-10)).*(x1>m34 & x1<=10);

m11=seed(1,3);

nlmf_1=1.*(x>=-5 & x<=-2)+((m11-x)/(m11+2)).*(x>-2 & x<=m11)+0.*(x>m11);

m12=seed(1,2);

m13=seed(1,7);

mlmf_1=0.*(x>=-5 & x<m12)+((m12-x)/m12).*(x>=m12 & x<=0)+((m13-x)/m13).*(x>0 & x<=m13)+0.*(x>m13);

m14=seed(1,6);

plmf_1=0.*(x>=-5 & x<=m14)+((m14-x)/(m14-2)).*(x>m14 & x<=2)+1.*(x>2);

plot(x,numf_1,x,mumf_1,x,pumf_1,x,nlmf_1,x,mlmf_1,x,plmf_1);

m21=seed(1,11);

nlmf_2=1.*(x>=-5 & x<=-4)+((m21-x)/(m21+4)).*(x>-4 & x<=m21)+0.*(x>m21);

m22=seed(1,10);

m23=seed(1,15);

mlmf_2=0.*(x>=-5 & x<m22)+((m22-x)/m22).*(x>=m22 & x<=0)+((m23-x)/m23).*(x>0 & x<=m23)+0.*(x>m23);

m24=seed(1,14);

plmf_2=0.*(x>=-5 & x<=m24)+((m24-x)/(m24-4)).*(x>m24 & x<=4)+1.*(x>4);

86

figure,plot(x,numf_2,x,mumf_2,x,pumf_2,x,nlmf_2,x,mlmf_2,x,plmf_2);

m31=seed(1,19);

nlmf_3=((m31-x1)/(m31+10)).*(x1>=-10 & x1<=m31)+0.*(x1>m31);

m32=seed(1,18);

m33=seed(1,23);

mlmf_3=0.*(x1>=-10 & x1<m32)+((m32-x1)/m32).*(x1>=m32 & x1<=0)+((m33-x1)/m33).*(x1>0 & x1<=m33)+0.*(x1>m33);

m34=seed(1,22);

plmf_3=0.*(x1>=-10 & x1<=m34)+((m34-x1)/(m34-10)).*(x1>m34 & x1<=10);

figure,plot(x1,numf_3,x1,mumf_3,x1,pumf_3,x1,nlmf_3,x1,mlmf_3,x1,plmf_3);

N=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.3,0,0.5,0.1,0,0,0,0,0.1,-0.4,0,-0.2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0];

y1(1)=-1.5;

y2(1)=-3;

t=1:length(N);

n=length(t);

u(1)=0;

for k=2:n

p1=y1(k-1);

p2=y2(k-1);

if(p1>2)

p1=2;

end

if(p1<-2)

87

p1=-2;

end

if(p2>4)

p2=4;

end

if(p2<-4)

p2=-4;

end

n11=numf_1(uint16(100*p1+501));

z11=mumf_1(uint16(100*p1+501));

p11=pumf_1(uint16(100*p1+501));

n12=numf_2(uint16(100*p2+501));

z12=mumf_2(uint16(100*p2+501));

p12=pumf_2(uint16(100*p2+501));

n21=nlmf_1(uint16(100*p1+501));

z21=mlmf_1(uint16(100*p1+501));

p21=plmf_1(uint16(100*p1+501));

n22=nlmf_2(uint16(100*p2+501));

z22=mlmf_2(uint16(100*p2+501));

p22=plmf_2(uint16(100*p2+501));

p_1=max(max(min(p12,p11),min(p11,z12)),min(z11,p12));

z_1=max(max(min(n11,p12),min(z11,z12)),min(p11,n12));

n_1=max(max(min(n11,z12),min(z11,n12)),min(n11,n12));

p_2=max(max(min(p22,p21),min(p21,z22)),min(z21,p22));

88

z_2=max(max(min(n21,p22),min(z21,z22)),min(p21,n22));

n_2=max(max(min(n21,z22),min(z21,n22)),min(n21,n22));

umf=max(min(n_1,numf_3),max((min(p_1,pumf_3)),(min(z_1,mumf_3))));

lmf=max(min(n_2,nlmf_3),max((min(p_2,plmf_3)),(min(z_2,mlmf_3))));

%figure,plot(x1,umf,x1,lmf)

upperx=0;

upper=0;

for m=1:2001

upperx=upperx+umf(m)*x1(m);

upper=upper+umf(m);

end

cl=(upperx)/(upper);

cr=cl;

a=uint16(100*cl+1001);

lowleft=0;

lowleftx=0;

for m=1:a-2

lowleftx=lowleftx+lmf(m)*x1(m);

lowleft=lowleft+lmf(m);

end

lowright=0;

lowrightx=0;

for m=a+2:2001

89

lowrightx=lowrightx+lmf(m)*x1(m);

lowright=lowright+lmf(m);

end

b=uint16(100*cl+1001);

while(b>1)

upperx=0;

upper=0;

lowerx=0;

lower=0;

for m=1:b

upperx=upperx+umf(m)*x1(m);

upper=upper+umf(m);

end

for m=b+1:a+1

lowerx=lowerx+lmf(m)*x1(m);

lower=lower+lmf(m);

end

c=(upperx+lowerx+lowrightx)/(upper+lower+lowright);

if (c<cl)

cl=c;

b=uint16(100*cl+1001);

else

break;

end

end

90

b=uint16(100*cr+1001);

while(b<2001)

upperx=0;

upper=0;

lowerx=0;

lower=0;

for m=b:2001

upperx=upperx+umf(m)*x1(m);

upper=upper+umf(m);

end

for m=a-1:b-1

lowerx=lowerx+lmf(m)*x1(m);

lower=lower+lmf(m);

end

c=(upperx+lowerx+lowleftx)/(upper+lower+lowleft);

if (c>cr)

cr=c;

b=uint16(100*cr+1001);

else

break;

end

end

cl1(k)=cl;

cr1(k)=cr;

u(k)=(cl+cr)/2;

91

y1(k)=y1(k-1)+0.08*y2(k-1)+N(k);

y2(k)=0.08*(y1(k-1)+N(k))+y2(k-1)-u(k);

end

sum=0;

for k=1:length(N)

sum=sum+(y1(k)*y1(k));

end

RMS=sqrt(sum);

figure,

subplot(311),plot(t,y1)

title('Signal response')

subplot(312),plot(t,y2)

title('Error-dot response')

subplot(313),plot(t,u),xlabel('Time(s)')

title('Control signal')