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CHAPTER 2

POWER CONVERTERS IN PV SYSTEM

2.1 INTRODUCTION

Photovoltaic system is gaining increased importance as a renewable

source because of its advantages such as the absence of fuel cost, little

maintenance and no noise and wear due to the absence of moving parts. But

there are still two principal barriers to the use of photovoltaic systems: the

high installation cost and the low energy conversion efficiency.

A PV panel is a non-linear power source, i.e., its output current and

voltage (power) depend on the terminal operating point. The maximum power

generated by the PV panel changes with the intensity of the solar radiation

and the operating temperature. To increase the ratio of output power/cost of

the installation, the PV panel should operate in the maximum output power

point.

The main focus of this research is to identify the proper DC-DC

converter which uses the adaptive perturbs and observe MPPT algorithm to

maximize energy extraction from the solar PV module and to increase the

conversion efficiency of MPPT system

2.2 CHARACTERISTICS OF SOLAR PV MODULE

Solar cells consist of a p-n junction fabricated in a thin layer of

semiconductor. The semiconductor electron can be located in either the

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valence band or conduction band. Initially, all the electrons in the

semiconductor fill up the valence band but when sunlight hits the

semiconductor, some electrons acquire enough energy to move from the

valence band to the conduction band. The electrons in the conduction band,

then, begin to move freely creating electricity. The electron leaving the

valence band leaves a positively charged hole behind and now the valence

band is no longer full; it aids the current flow. Most solar cells are doped to

reduce the energy required for the electron to move from the valence band to

the conduction band.

The amount of energy from sunlight that is absorbed by a solar cell

determines its efficiency. This energy is called photon and it can be reflected,

absorbed or it can pass through a semiconductor. Since only the photons that

are absorbed contribute to the electrical energy, it is important to reduce the

percentage of photons that pass through and are reflected. An anti-reflective

coating is usually applied to the surface of the solar cell to decrease the

number of photons that are reflected. This reduces the percentage of photons

reflected but some photons are still able to pass right through the

semiconductor material.

There are several approaches to manufacturing solar cells,

including the kind of semiconductor used and the crystal structure employed,

with each different factor affecting the efficiency and cost of the cell. Other

external factors such as the ambient weather conditions like temperature,

illumination, shading, etc., also affect the solar panels output. The aim is to

design a system that will extract the most possible power regardless of

ambient weather conditions or solar cell efficiency.

Irradiance is a characteristic related to the amount of sun energy

reaching the ground, and under ideal conditions it is measured as 1000 W/m2

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at the equator. The sun energy around the earth is highest around the equator

when the sun is directly overhead. Some important magnitudes related to

irradiance include the spectral irradiance, irradiance, and radiation. Spectral

irradiance is the power received by a unit surface area at a particular

wavelength, while irradiance is the integral of the spectral irradiance extended

to all wavelengths of interest. Radiation is the time integral of the irradiance

extended over a given period of time.

In designing PV systems, the main concern is the radiation received

from the sun at a particular location at a given inclination angle and

orientation and for long periods of time. Since solar radiation is the energy

resource of the solar panel, the output of the panel is significantly affected by

changing irradiance. The I-V characteristic of a solar cell including the effects

of irradiance is shown in Figure 2.1.

Figure 2.1 I-V Characteristics of a solar PV module for change in

irradiation

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The irradiance at any location is strongly dependent on the

orientation and inclination angles of the solar panel. Orientation is usually

measured relative to the south in northern latitudes while it is measured

relative to the north in southern latitudes. On the other hand, the inclination

angle is measured relative to the horizontal. Using these two parameters, the

irradiation at any location can be determined.

The output power is directly proportional to the irradiance. As such,

a smaller irradiance will result in reduced power output from the solar panel.

However, it is also observed that only the output current is affected by the

irradiance.

Although irradiance is an important factor in determining the I-V

characteristic of a solar panel, it is not the only factor. Temperature also plays

an important role in predicting the I-V characteristic, and the effects of both

factors have to be considered when designing a PV system. Whereas the

irradiance mainly affects the output current, the temperature mainly affects

the terminal voltage. A plot of I-V characteristic with varying temperature is

shown in Figure 2.2.

Figure 2.2 Effects of temperature on I-V curve

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It is observed from Figure 2.2 that the terminal voltage increases

with decreasing temperature. This is somewhat surprising as one would

typically expect the solar panel to operate more efficiently as temperature

increases. However, one of the reasons the solar panel operates more

efficiently with decreasing temperature is due to the electron and hole

mobility of the semiconductor material. As temperature increases, the electron

and hole mobility in the semiconductor material decrease significantly. The

electron mobility for Silicon at 25 C is about 1700cm2/Volt-sec and will

decrease to about a fourth of this value as temperature increases to 225 C,

and likewise the hole mobility decreases from about 600cm2/Volt-sec at 25 C

to 200cm2/Volt-sec as temperature increases to 225 C. While the higher

reference temperatures are not realistic operating conditions for a solar panel,

it does show that electron and hole mobility decrease with increasing

temperature.

It should be noted here that irradiance and temperature represent

only two of the most significant external factors that affect the efficiency of a

solar cell; inclination, location, and time of the year are also factors that affect

the efficiency of solar cells. Additional parameters of a solar cell can be discussed

by an illustration of the maximum power point as shown in Figure.2.3

Figure 2.3 Illustration of maximum power point

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The cells short circuit current intersects the Y-axis at point B and

the open circuit voltage intersects the X-axis at point C. To achieve maximum

energy transfer, systems powered by solar cells should be designed to transfer

energy to the load at point A on the I-V curve. No energy should be delivered

at points B and C, and most of the energy should be delivered as the operating

point approaches point A. In a solar panel array, it is even more important that

load impedance and source impedance are well matched. Once the cells are

matched by their I-V characteristics, they can be grouped into individual

arrays and each array is then made to operate at its maximum energy transfer

point. Majority of solar cells have high capacitance associated with their

forward biased p-n junctions because the charged carriers are much closer

together. The unwanted capacitance increases as the size of the solar cell and

junction area increases. The I-V curve of the solar cell can be determined by

taking fast I-V measurements which is done by applying a constant voltage

and measuring the resulting current for the device being tested. However, the

high capacitance makes it difficult to get fast I-V measurements.

2.2.1 Modelling of Solar PV Module

A simplified equivalent circuit of a solar cell consists of a diode

and a current source which are switched in parallel. The photocurrent

generated when the sunlight hits the solar panels can be represented with a

current source and the p-n transition area of the solar cell can be represented

with a diode. The voltage and current relationship of the simplified solar cell

can be derived from Kirchhoffs current law. This simplified equivalent

circuit, however, does not give an accurate representation of the electrical

process at the solar cell. On real solar cells, voltage losses occur at the

boundary and external contacts and leakage currents occur throughout the

cell; these losses can be represented with a series resistance Rs

and a parallel

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resistance Rp, respectively. The equivalent circuit of the solar cell showing the

series and parallel resistance is shown in Figure 2.4.

Figure 2.4 Equivalent circuit of a solar PV module

For Figure.2.4, the current Equation is given by

Isc = ID +Ipv + (VD / R p) (2.1)

Vpv=VD - (Ipv*Rs) (2.2)

where diode current is, ID = Io + ( e (VD / VT) - 1), Isc is the short circuit current,

Vt = NsKT / q is the thermal voltage with Ns cells connected in a series (K is

the Boltzmann constant, q is the electron charge and T is the temperature of

the PV cells). The short circuit current is directly proportional to the

irradiation and slightly proportional to the level of the cell temperature.

Using Equations 2.1 and 2.2, the solar PV module is modeled in

MATLAB/Simulink as shown in Figure 2.6 and used to enhance the

understanding and predict the I-V and P-V characteristics and to analyze the

effect of temperature and irradiation variation. If irradiance increases, the

fluctuation of the open-circuit voltage is very small. But the short circuit

current has sharp fluctuations with respect to irradiance. However, for a rising

operating temperature, the open-circuit voltage is decreased in a non-linear

fashion.

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The P-V and I-V characteristics are validated in MATLAB

software for the L1235-37Wp (Watt peak) solar module. Table 2.1 shows the

technical specification of L1235-37Wp solar panel under test which is shown

in Figure 2.5. The I-V characteristic is obtained based on experimental results

under irradiation =1000 W/m2, temperature =25 C

Figure 2.5 L1235-37Wp solar module under test

The simulated I-V and P-V characteristics of solar module L1235-37Wp are

shown in Figure 2.7 and 2.8.

Table 2.1 Specification of a solar PV module under test

Parameter Values Open circuit voltage (Voc) 21V Short circuit current (Isc) 2.5A Voltage at MPP (Vmax) 16.4VCurrent at MPP (Imax) 2.25APower rating (Pmax) 37WMaximum system voltage 600V Module efficiency (%) 10.82%Size (mm) 645*530*16Weight (kg) 4

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Figure 2.6 MATLAB model for PV module

Figure 2.7 I-V Characteristics of solar PV module

Figure 2.8 P-V Characteristics of solar PV module

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2.3 MPPT METHODS

The efficiency of energy conversion depends mainly on the

efficiency of the PV panels that generate the power. Weather conditions also

influence the efficiency, which depends non-linearly on the irradiation level

and temperature. When a PV array is directly connected to a load, the

systems operating point will be at the intersection of the IV curves of the

PV panel and load. The non-linear variations in the output voltage and

current, which depend on solar-radiation levels, operating temperature and

load current, can cause a low electrical efficiency. To solve these problems

with the utilization of solar arrays for electrical power, the MPP of the PV

system (at given conditions) is tracked using offline or online algorithms,

where the system operating point is forced towards optimal conditions. The

PV array has an optimum operating point called the MPP, which is never

constant over time and varies depending on cell temperature and the present

irradiation level.

To obtain the maximum power from a PV array, an MPPT is

applied. The location of the MPP in the IV plane is not known in prior. It

can be calculated using a model of the PV array and measurements of

irradiance and array temperature, but making such measurements is usually

too expensive for this application, and often the required parameters for the

PV array model are not known adequately. Thus, the MPPT must

continuously search for the MPP of the solar PV module. Many techniques

for MPPT of solar PV have been proposed to track maximum power from

solar PV module. Some important useful techniques such as as hill climbing

/ Perturb And Observe (PAO), Incremental Conductance (IncCond), fractional

open-circuit voltage, fractional short-circuit current, fuzzy logic control,

neural network, and Ripple Correlation Control (RCC) are discussed briefly

in the following section.

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2.3.1 Hill Climping / PAO

Hill climbing involves a perturbation in the duty ratio of the power

converter, and PAO involves a perturbation in the operating voltage of the PV

array. In the case of a PV array connected to a power converter, perturbing the

duty ratio of power converter perturbs the PV array current and consequently

perturbs the PV array voltage. Hill climbing and PAO methods are different

ways to envision the same fundamental method.

Incrementing (or decrementing) the voltage increases (or decreases)

the power when operating on the left of the MPP and decreases (or increases)

the power when on the right of the MPP. Therefore, if there is an increase in

power, the subsequent perturbation should be kept the same to reach the MPP

and if there is a decrease in power, the perturbation should be reversed.

The process is repeated periodically until the MPP is reached. The

system then oscillates about the MPP. The oscillation can be minimized by

reducing the perturbation step size. However, a smaller perturbation size

slows down the MPPT. Hill climbing and PAO methods can fail under rapidly

changing atmospheric conditions. Two sensors are usually required to

measure the PV array voltage and current from which power is computed.

Two sensors are usually required to measure the PV array voltage and current

from which power is computed.

2.3.2 Incremental Conductance

The incremental conductance MPPT method implemented based on

the fact that the slope of the PV array power curve is zero at the MPP,

positive on the left of the MPP, and negative on the right.

= 0 at MPP (2.3)

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> 0 left of MPP (2.4)

< 0 right of MPP (2.5)

Also the change in current to change in voltage is related to track

maximum power.

I/ V = I/V, at MPP (2.6)

I/ V > I/V, left of MPP (2.7)

I/ V < I/V, right of MPP (2.8)

The maximum power is extracted from the solar PV module by

comparing the instantaneous conductance (I/V) to the incremental

conductance ( I/ V). Vref is the reference voltage at which the PV array is

forced to operate. At the MPP, Vref equals VMPP. Once the MPP is reached,

the operation of the PV array is maintained at this point unless a change in I

is noted, indicating a change in atmospheric conditions and the MPP. The

algorithm decrements or increments Vref to track the new MPP. The increment

size determines how fast the MPP is tracked. Fast tracking can be achieved

with bigger increments but the system might not operate exactly at the MPP.

By proper control of the power converter, the initial operating point is set to

match a load resistance proportional to the ratio of the open-circuit voltage

(VOC) to the short-circuit current (ISC) of the PV array.

In order to implement incremental conductance algorithm,

measurements of the instantaneous PV array voltage and current require two

sensors. IncCond method lends itself well to DSP and microcontroller control,

which can easily keep track of previous values of voltage and current and

make all the decisions.

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2.3.3 Fractional Open-Circuit Voltage

The near linear relationship between Vm and VOC of the PV array,

under varying irradiance and temperature levels, has given rise to the

fractional VOC method.

Vm R1VOC ` (2.9)

Where R1 is a constant of proportionality. Since R1 is dependent on

the characteristics of the PV array being used, it usually has to be computed

beforehand by empirically determining Vm and VOC for the specific PV array

at different irradiance and temperature levels. The factor R1 has been reported

to be between 0.71 and 0.78. Once R1 is known, Vm can be computed with

VOC measured periodically by momentarily shutting down the power

converter. However, this incurs some disadvantages, including temporary loss

of power. Once Vm has been approximated, a closed-loop control on the array

power converter can be used to asymptotically reach this desired voltage. The

PV array technically never operates at the MPP. Depending on the application

of the PV system, this can sometimes be adequate. Even if fractional VOC is

not a true MPPT technique, it is very easy and cheap to implement as it does

not necessarily require DSP or micro-controller control. The selection of the

value of R1 is no more valid if the solar module is partial shading (which

causes multiple local maxima) which proposes sweeping the PV array voltage

to update R1. This obviously adds to the implementation complexity and

incurs more power loss.

2.3.4 Fractional Short-Circuit Current

Fractional is used to track maximum power from solar PV module.

Under varying atmospheric conditions, Im is approximately linearly related to

the ISC of the PV array

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Im R2Isc (2.10)

where R2 is proportionality constant. Just like in the fractional VOC technique,

R2 has to be determined according to the PV array in use. The constant R2 is

generally found to be between 0.78 and 0.92.

Measuring ISC during operation is problematic. An additional

switch usually has to be added to the power converter to periodically short the

PV array so that ISC can be measured using a current sensor. This increases

the number of components and cost. Power output is not only reduced when

finding ISC but also because the MPP is never perfectly matched. To track

maximum power using this MPPT in the presence of multiple local maxima,

periodically sweeps the PV array voltage from open-circuit to short-circuit

which is required to update R2.

2.3.5 Ripple Correlation Control

Ripple Correlation Control (RCC) makes use of ripple to perform

MPPT. RCC correlates the time derivative of the time-varying PV array

power (p) with the time derivative of the time-varying PV array current or voltage v to drive the power gradient to zero, thus reaching the MPP.

if v or i is increasing (v > 0 or > 0) and p is increasing (P > 0), then the operating point is below the MPP (V Vm or I > Im). Combining these observations, we

see that P v or P are positive to the left of the MPP, negative to right of the MPP, and zero at the MPP. Simple and inexpensive analog circuits can be

used to implement RCC.

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Another advantage of RCC is that it does not require any prior

information about the PV array characteristics.

The derivatives are usually undesirable, but AC-coupled

measurements of the PV array current and voltage can be used instead since

they contain the necessary phase information. The derivatives can also be

approximated by high-pass filters with cutoff frequency higher than the ripple

frequency. A different and easy way of obtaining the current derivative is to

sense the inductor voltage, which is proportional to the current derivative

2.3.6 Fuzzy Logic Control

Fuzzy logic control has the advantages of working with imprecise

inputs, not needing an accurate mathematical model, and handling nonlinearity.

Fuzzy logic control generally consists of three stages: fuzzification, rule base table

lookup, and defuzzification. During fuzzification, numerical input variables are

converted into linguistic variables based on a membership function.

In this case, five fuzzy levels are used: NB (negative big), NS

(negative small), ZE (zero), PS (positive small), and PB (positive big). Seven

fuzzy levels are used, probably for more accuracy. The inputs to an MPPT

fuzzy logic controller are usually an error E and a change in error E. The

user has the flexibility of choosing how to compute E and E.

E(n) = ( ) ( )( ) ( ) (2.11) E(n) = E(n) E(n 1) (2.12)

Once E and E are calculated and converted to the linguistic

variables, the fuzzy logic controller output, which is typically a change in

duty ratio D of the power converter, can be looked up in a rule base table.

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In the defuzzification stage, the fuzzy logic controller output is

converted from a linguistic variable to a numerical variable still using a

membership function. MPPT fuzzy logic controllers have been shown to

perform well under varying atmospheric conditions to track maximum power.

2.3.7 Neural Network

The maximum power is tracked from the solar PV module using

neural network. Neural networks commonly have three layers: input, hidden,

and output layers. The number of nodes in each layer varies and they are user-

dependent. The input variables can be PV array parameters like Voc and Isc,

atmospheric data like irradiance and temperature, or any combination of

these. The output is usually one or several reference signal(s) like a duty cycle

signal used to drive the power converter to operate at or close to the MPP.

How close the operating point gets to the MPP depends on the algorithms

used by the hidden layer and how well the neural network has been trained.

The links between the nodes are all weighted. Also the PV arrays have

different characteristics. A neural network has to be specifically trained for

the PV array with which it will be used. The characteristics of a PV array also

change with time, implying that the neural network has to be periodically

trained to guarantee accurate MPPT.

2.4 APPLICATION-BASED SELECTION OF MPPT

ALGORITHM

An MPPT method that has quick response characteristics and is

able to make good use of the electrical power generated under any weather

condition is needed to optimize the system management. Many MPPT control

methods have been proposed that search for the maximum operating

conditions from the output power and voltage characteristics of solar arrays

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using differential techniques, like the hill-climbing method or fuzzy rules. The

main aspects for selection of the MPPT techniques are essentially:

The ease of implementation is an important factor in deciding

which MPPT technique to use. Some techniques require

analogue circuitry and others digital circuitry, even if that may

require the use of software and programming

The number of sensors required to implement MPPT also

affects the selection process. It is easier and more reliable to

measure voltage than current. Moreover, current sensors are

usually expensive and bulky. It is also uncommon to find

sensors that measure irradiance levels, as needed in the linear

current controls and the maximum power point current

(IMPP) and maximum power point voltage (VMPP)

computation methods

The occurrence of multiple local maxima due to partial

shading of the PV array can be a real hindrance to the proper

functioning of an MPP tracker. Considerable power loss can

be incurred if a local maximum is tracked instead of the real

MPP;

It is hard to mention the monetary costs of every single MPPT

technique unless it is built and implemented. A good cost

comparison can be made by knowing whether the technique is

analogue or digital, whether it requires software and

programming, and the number of sensors. Analogue

implementation is generally cheaper than digital, which

normally involves a microcontroller that needs to be

programmed;

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Different MPPT techniques will suit different applications. For

example, in space satellites and orbital stations that involve a large amount of

money, the costs and complexity of the MPP tracker are not as important as

its performance and reliability. The tracker should be able to continuously

track the true MPP in minimum amount of time and should not require

periodic tuning. In this case, hill climbing/PAO, IncCond, and RCC are

appropriate. Solar vehicles would mostly require fast convergence to the

MPP. Fuzzy logic control, neural network, and RCC are good options in this

case. Since the load in solar vehicles consists mainly of batteries, load current

or voltage maximization should also be considered. The goal, when using PV

arrays in residential areas, is to minimize the payback time and to do so, it is

essential to constantly and quickly track the MPP. Since partial shading (from

trees and other buildings) can be an issue, the MPPT should be capable of

bypassing multiple local maxima. Therefore, the two-stage IncCond and the

current sweep methods are suitable. Since a residential system might also

include an inverter, the open circuit voltage MPPT can also be used. PV

systems used for street lighting only consist of charging up batteries during

the day. They do not necessarily need tight constraints; easy and cheap

implementation might be more important, making fractional VOC or ISC viable.

The method considered in this research work is a PAO method.

This method is widely diffused because of its low-cost and ease of

implementation. When atmospheric conditions are constant or change slowly,

the PAO method oscillates close to MPP. However, when these change

rapidly, this method fails to track MPP and gives rise to a waste of part of the

available energy.

The main limitation of this kind of algorithm is connected with the

opposite exigencies required by the fast dynamic response and the steady-

state stability. Indeed, to improve the dynamic performance it is necessary to

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use a large perturbation value, whereas a smaller value is necessary to ensure

good stability. During cloudy days, the solar irradiation can vary many times

and quickly. Because of this, so as not to lose great quantities of energy, it is

necessary to achieve a good dynamic response for the system. The basic

principle of the algorithm proposed is to adapt the perturbation amplitude to

the actual operating conditions. In particular, far from the MPP, large

perturbation amplitudes are chosen, whereas small ones are used in proximity

to the maximum. It is therefore necessary to have knowledge of the maximum

position. However, a perfect knowledge is not required because working at

the real maximum is ensured by the PAO technique. An adaptive PAO

method is discussed and implemented in this research. It has faster dynamics

and improved stability compared to the traditional PAO.

2.5 ADAPTIVE PERTURB AND OBSERVER MPPT

In the PAO algorithm, the operating voltage of the PV array is perturbed by a small increment, and the resulting change in power, P, is measured. If P is positive, the perturbation of the operating voltage moves the PV arrays operating point closer to the MPP. Thus, further voltage perturbations in the same direction (that is, with the same algebraic sign) should move the operating point towards the MPP. If P is negative, the system operating point moves from the MPP, and the algebraic sign of the perturbation should be reversed towards the MPP. Though PAO algorithm is simple and easy to implement, it fails when the atmospheric conditions change rapidly. To overcome this problem, the adaptive PAO algorithm improves the dynamic response without affecting stability. In this algorithm, high perturbation is selected when the operating point is far away from MPP and low perturbation is selected when the operating point is closer to MPP. The adaptive PAO algorithm has been implemented in ATMEGA16 micro-controller to generate gate pulse which can be given to the switches of DC-DC converter.

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The flow chart of the adaptive perturbs and observer MPPT algorithm is illustrated in Figure 2.9. The parameter K is the step given to the PWM signal. This parameter can vary depending on the working point of th e DC-DC converter. To get a faster convergence, high value of K is selected to avoid big oscillations near to the MPPT. The PAO MPPT control algorithm is implemented in a micro-controller (ATMEGA16) that has ten 10-bits analogue-to-digital converter (ADC) and two fast PWM mode signals with 10-bits of resolution. The control circuit compares the PV output power before and after a change in the duty-cycle of the DC-DC converter control signal and acts in conformity. The PWM_old is the sample of the PWM signal in the previous iteration of the algorithm and PPV is the variation of the delivered power to the load.

Figure 2.9 Flow chart of Adaptive perturb and observer algorithm

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2.6 DIRECT CONTROL METHOD

Conventional MPPT systems have two independent control loops to

control MPPT. The first control loop contains the MPPT algorithm and the

second one is usually a Proportional Integral (PI) controller. Perturb and

observer algorithm is used to generate an error signal which is zero at MPP;

however, it is not zero at most of the operating points under rapid change in

atmospheric conditions. The main purpose of the second control loop is to

make the error from the MPPs near to zero. Simplicity of operation, ease of

design, inexpensive maintenance and low cost made PI controllers very

popular in most linear systems. However, MPPT system of standalone

photovoltaic in space applications is a non-linear control problem due to the

non-linearity nature of PV and unpredictable environmental conditions and,

hence, PI controllers do not generally work well.

The research work discusses direct control adaptive perturb and

observer algorithm. The PI control loop is eliminated and duty cycle is

adjusted directly in the algorithm using ATMEGA16 micro-controller. The

control loop is simplified and the computational time for tuning controller

gains is eliminated. To compensate for the lack of PI controller in the

proposed system, a small marginal error of 0.002 was allowed. The objective

of this work is to eliminate the second control loop and to show that

sophisticated MPPT methods do not necessarily obtain the best results but

employing them in a simple manner for complicated electronic subjects is

considered necessary. Feasibility of the proposed system is investigated with

a DC-DC Cuk converter which is configured as the MPPT.

2.7 DC-DC CONVERTERS IN A SOLAR PV SYSTEM

PV interfacing is a challenging task and there is a need for

clarification of the existing DC-DC converter topologies used in the PV

41

applications. DC-DC converter shown in Figure 2.10 is an essential element

in the MPPT process and this process can be performed either by controlling

the input current or voltage of the interfacing converter. Also it is known that

DC-DC converters increase or decrease the magnitude of the DC-voltage

and/or invert its polarity. This is accomplished by the pulse width modulation

technique, usually to a constant frequency. The duty cycle (d) is the ratio of

the time of conduction (TON) to the switching period (Ts). The three basic

configurations of converters (buck, boost and buckboost derived) are similar

to a DC transformer, both in continuous conduction mode (CCM) and

discontinuous conduction mode (DCM). In a DC transformer, the relationship

of transformation can be controlled electronically by changing the duty cycle

of the converter from the range 0 to 1.

The power electronics interface is connected between a solar panel

and a load or battery bus is a pulse width modulated DC-DC converter or their

derived circuits operating in Discontinuous Inductor Current Mode (DICM) or

Discontinuous Capacitor Voltage Mode (DCVM) is used to extract maximum

power from solar PV panel. The DCDC converter has the input resistance

characteristics being proportional or inversely proportional to the switching

frequency. Hence, by adjusting the nominal duty cycle of the main switch of DC-

DC converter, the input resistance can be made equal to the equivalent output

resistance of the solar PV panel and ensures the maximum power transfer.

Figure 2.10 MPPT process using DC-DC converter

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The input voltage and the equivalent input resistance of the DC-DC

converter are V and R , respectively. As the input power Pi to the converter is equal to the output power Po of the solar panel,

Pi =Po = (2.13)

The rate of change Pi with respect to V and R can be shown p = V - R (2.14)

At the MPP, the rate of change of Pi equals zero and R = Reqp =0, hence = (2.15)

The Equation gives the required dynamic resistance characteristics

of the tracker at MPP.

Resistor emulation techniques have been used previously, most

commonly in Power Factor Correction (PFC) applications. Some approaches

for PFC are based on converters with natural resistor emulation at the input

port (without current feedback), including boost type converters in critical

conduction mode and buckboost-type converters in DCM. At higher current

levels, most PFC circuits operate in CCM with more advanced current and

voltage feedback control.

The natural emulation techniques and approximations to them are

used in this work to achieve resistor emulation and characterize current

voltage curves of PV modules using open loop control circuitry. The

relationships among the input resistance (Ri, the emulated resistance at the

output terminals of the PV module), equivalent inductance (Leq), and load (R)

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connected to the converter for CCM and DCM are to be analyzed for all the

conventional DC-DC converters. These relationships have been obtained by

assuming converters without losses and with small switching ripple compared

with their respective DC components. In each case, the dimensionless

parameter K is a measure of the tendency of a converter to operate in DCM.

Large values of K lead to CCM, whereas small values lead to DCM. The

critical value of K at the boundary between modes (Kcrit) is a function of the

duty cycle. If K is greater than one, then the converter operates in CCM for all

duty cycles. Usually, the mode boundary is given in terms of the load

resistance R rather than the dimensionless parameter K. The various

conventional DC-DC converters are discussed and their suitability to solar PV

power conditioning process is analyzed in the below section.

2.7.1 Buck Converter

The basic circuit configuration used in the buck converter is shown

in Figure 2.11. There are only four main components: switching power

MOSFET S, flywheel diode, inductor L, and output filter capacitor C. When S

is turned on, current begins flowing from the input source through S and L,

and then into C and the load R. The magnetic field in L, therefore, builds up,

storing energy in the inductor,with the voltage drop across L opposing or

bucking part of the input voltage. Then when S is turned off, the inductor

opposes any drop in current by suddenly reversing its Electromotive Force

(EMF), and now supplies current to the load itself via D. Without going too

deeply into its operation, the DC output voltage which appears across the load

is a fraction of the input voltage, and this fraction turns out to be equal to the

duty cycle.

= d (2.16)

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where d is the duty cycle, and equal to Ton/Ts. So by varying the switching

duty cycle, the buck converter output voltage can be varied as a fraction of the

input voltage.

Figure 2.11 Buck converter

For the buck converter, the input resistance Ri (Continuous

conduction mode) must have a value in the interval Ri (CCM) [R, )] and Riis equal to R/d2 and the input resistance Ri (Discontinuous conduction mode)

must have a value in the range

Ri = ( ( R/4)*(1+ (1 + 4 K ) )^2 , ) (2.17)where R is the load resistance and K = 2 L / R Ts

According to this expression, a buck converter cannot emulate

smaller impedances than the load impedance, and therefore, it does not reach

values near the short-circuit current of the PV module when it is used to

obtain I-V curves. Hence, it is concluded that buck converter is not useful in

MPP tracking process of a solar PV powered system.

2.7.2 Boost Converter

The basic circuit configuration used in the boost converter is shown

in Figure.2.12. When S is switched on, current flows from the input source

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through L and S, and energy is stored in the inductors magnetic field. There

is no current through diode D, and the load current is supplied by the charge

in C. Then when S is turned off, L opposes any drop in current by

immediately reversing its EMF. So that the inductor voltage adds to the

source voltage and current due to this boosted voltage now flows from the

source through L, D and the load, recharging C as well. The output voltage is,

therefore, higher than the input voltage, and it turns out that the voltage step-

up ratio is equal to:

= (2.18)

Figure2.12 Boost converter

The input resistance Ri (CCM) of the boost converter is equal to

R*(1-d) 2 and Ri (DCM) is equal to ( )^ . This expression indicates that a boost converter cannot emulate impedances greater than the impedance

of load, and, therefore, it does not reach values near the open circuit voltage

of the PV module. Hence, it is observed that boost converter may not be

useful for PV applications.

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2.7.3 Buck- Boost Converter (Single Inductor)

The basic circuit configuration used in the buck-boost converter is

shown in Figure 2.13. When MOSFET S is turned on, inductor L is connected

directly across the source voltage and current flows through it, storing energy

in the magnetic field. No current can flow through the load since during the

on- time of the switch S, the diode is connected and it is reverse biased.

Capacitor C must supply the load current in this Ton time of the switch. But

when S is turned off, L is disconnected from the source. The inductor L

opposes any tendency for the current to drop, and instantly reverses its EMF.

This generates a voltage which forward biases D, and current flows into the

load and to recharge C. The ratio between the output and input voltages is

given by

= (2.19)

The output voltage is always reversed in polarity with respect to the

input. So the buck-boost converter is also a voltage inverter.

Figure 2.13 Buck-Boost converter

The input resistance Ri during the continuous conduction mode is

given by

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R i (CCM) [0, ]

Ri (CCM) = ( )

(2.20)

The input resistance Ri during the discontinuous conduction mode

is given by

Ri (DCM) = (2.21)

Therefore, the buck-boost converter is capable of sweeping the

whole I-V curve of a PV module in CCM from open circuit voltage (Voc) to

short circuit current (Isc) condition. The buck-boost converter has the

advantage of true resistance emulation. As a result, the I-V characteristic

curve of solar PV module can be covered and measured quickly (in ms) to

have a reliable real-time measure of their evolution. But the buck-boost

converter has discontinuous input current characteristics because the switch S

is placed in a series with the panel causing high harmonic distortion in

current and hence high input ripples and noise were present. So the buck

boost converter with single inductor may not be a suitable converter in MPP

tracking processes.

2.7.4 SEPIC Converter

In a Single Ended Primary Inductor Converter (SEPIC) converter,

the output voltage can be higher or lower than the input voltage. Unlike the

buck-boost, the output is not inverted. The SEPIC converter shown in

Figure 2.14 uses two inductors, L1 and L2. The capacitor C1 isolates the input

from the output and provides protection against a shorted load when the

switch S is turned on. The first inductor, L1, is charged from the input voltage

source during this time. The second inductor takes energy from the first

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capacitor, and the output capacitor is left to provide the load current. The fact

is that both L1 and L2 are disconnected from the load when the switch is on.

When the power switch is turned off, the first inductor charges the capacitor

C1 and also provides current to the load. The second inductor is also

connected to the load during this time. The output capacitor sees a pulse of

current during the off time, making it inherently noisier than a buck converter.

The relation between input and output currents and voltage is given

by

= ( ) (2.22) = ( ) (2.23)

The input current is non-pulsating. In SEPIC converter, link-

capacitor (C1) voltage must follow the input voltage, and this means that the

capacitor size can be smaller. So the SEPIC converter is suitable in MPP

tracking process.

Figure 2.14 SEPIC converter

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2.7.5 Cuk Converter

The basic circuit configuration used in Cuk converter is shown in

Figure 2.15. Cuk converter has two modes of operation. The first mode of

operation is when the switch (MOSFET) is closed (ON) and it is conducting

as a short circuit as shown in Figure 2.16. In this mode, the current through

inductor L1 rises. At the same time, the voltage of capacitor C1 reverse biases

the diode D and turns it off. The capacitor (C1) releases its stored energy to

the load. The second operating mode is when the switch (S) is open (OFF),

diode (D) is forward biased and conducting energy to the output as shown in

Figure 2.17. Capacitor C1 is charging from input supply and the energy stored

in the inductor L2 is transferred to the load. The diode D and switch (S)

provide a synchronous switching action

The relation between input and output currents and voltage is

given by

( ) (2.24) ( ) (2.25)

Figure 2.15 Cuk converter

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Figure 2.16 Mode 1: Switch S is ON

Figure2.17 Mode 2: switch S is OFF

The input resistance of Cuk converter Ri during the continuous

conduction mode is given by

R i (CCM) [0, ]

Ri (CCM) = (2.26)

where Leq = L1 // L2 and fs switching frequency

The input resistance Ri during the discontinuous conduction mode

is given by

Ri (DCM) = (2.27)

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Therefore, the Cuk converter is capable of sweeping the whole I-V

curve of a solar PV module in CCM from open circuit voltage (Voc) to short

circuit current (Isc) condition.

Due to the input and output inductor in Cuk converter, the input

current is non-pulsating. Therefore, the sweep of the I-V curve is carried out

in a more reliable and less noisy way. So Cuk converter is more suitable in

MPP tracking circuits. The Cuk converter is preferred in power conditioning

process of solar PV system since Cuk converter works based on the energy

transfer of the capacitor and hence less EMI

2.8 CONCLUSION

This chapter explained the operating characteristics of solar PV

module, modelling of solar PV in MATLAB/Simulink and provided an

overview of various MPP algorithms used for maximum power tracking. This

study dealt with general ways to select MPP algorithms based on the solar PV

application. This chapter also explained the detailed analysis of MPP tracking

process using various DC-DC converters used for PV application and

concluded that DC-DC Cuk converter is a good choice to be used in MPP

tracking process in solar PV powered system.