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CHAPTER 3

CUK CONVERTER BASED MPPT SYSTEM USING

ADAPTIVE PAO ALGORITHM

3.1 INTRODUCTION

The power electronics interface, connected between a solar panel

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

to extract maximum power from solar PV panel. The I-V characteristic curve

of photovoltaic generator is validated based on various DC-DC converters.

The nominal duty cycle of the main switch in the DC-DC converter is

adjusted to a value, so that the input resistance of the converter is equal to the

equivalent output resistance of the solar panel at the MPP. This approach

ensures maximum power transfer under all atmospheric conditions. Buck

converter cannot emulate smaller impedance than the load impedance, and

therefore, it does not reach values near the short circuit current of the PV

module. The input resistance of buck converter is given by R i = R / d2. Boost

converter cannot emulate greater impedances than the impedance of load, and

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

module. The value of input resistance is given by Ri = R (1-d) 2. Buck-Boost

derived converters are capable of sweeping the whole I-V curve of a module

in CCM, from open circuit voltage (Voc) to short-circuit current (Isc). The

input resistance of Buck-Boost converter is given by Ri = R (1-d) 2/ d2. But it

has discontinuous input current which creates greater harmonic distortion

factor in current. Hence, it is also not useful in practice. But Cuk converter is

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capable of sweeping the whole I-V curve of a module in CCM, from open

circuit voltage (Voc) to short-circuit current (Isc). Hence, it is inferred that Cuk

converter is a good choice to track maximum power from solar PV module.

3.2 DESIGN CONSIDERATION OF CUK CONVERTER

The relation between input and output currents and voltage is given

in Equations 2.24 and 2.25.

The duty cycle of the Cuk converter under continuous conduction

mode is given by

d = (3.1)

V is the forward voltage drop across the diode (D). The maximum

duty cycle is given by Equation (3.2).

dmax =( )

(3.2)

The value of the inductor is selected based on the following

Equation

L1 = L2 = L = ( ) (3.3)

I is the peak-to-peak ripple current at the minimum input voltage

and fs-switching frequency. The value of C1 depends on RMS current which

is given by

Ic1(rms) = Iout *( )

(3.4)

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The voltage rating of capacitor C1 must be greater than the input

voltage. The ripple voltage on C1 is given by

Vc1 =( ) (3.5)

The parameters governing the selection of the MOSFET are the

minimum threshold voltage Vth(min), the on-resistance RDS (ON), gate-drain

charge QGD, and the maximum drain to source voltage, VDS(max). The peak

switch voltage is equal to Vin + Vout. The peak switch current is given by

IQ1(Peak) = IL1(PEAK) + IL2(PEAK) (3.6)

The RMS current is given by

I Q1(rms) = I out v + v ( )( )

( 3.7)

The total power dissipation for MOSFET includes conduction loss

(as shown in the first term of the above equation) and switching loss as shown

in the second term. IG is the gate drive current. The RDS(ON) value should be

selected at maximum operating junction temperature and is typically given in

the MOSFET datasheet.

Pswitch = (IQ1(rms)*RDS (ON) *dmax) + (Vin (min)+Vout) * I Q1(Peak * (QGD * fS )/ IG

(3.8)

The output diode must be selected to handle the peak current and

the reverse voltage. In a Cuk converter, the diode peak current is the same as

the switch peak current IQ1(peak). The minimum peak reverse voltage that the

diode must withstand is

VRD = Vin(max) + Vout (max) (3.9)

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Similar to the boost converter, the average diode current is equal to

the output current. The power dissipation of the diode is equal to the output

current multiplied by the forward voltage drop of the diode. Schottky diodes

are recommended in order to minimize the efficiency loss.

Table 3.1 shows the components used in simulation and hardware

setup for the power circuit.

Table 3.1 Specification of Cuk converter

Input inductor L1 500e-6 H

Filter inductor L2 500e-6H

Capacitor C1 220e-6F

Filter capacitor C2 220e-6F

Resistive load R

Switching frequency 25kHz

Switch : MOSFET IRF510

Optocoupler MCT2E

Diode MUR450

3.3 CUK CONVERTER-BASED MPPT FOR SOLAR PV

SYSTEM

Figure 3.1 shows a Cuk converter-based MPPT system consisting

of solar PV module, Cuk converter (DC-DC) and load. Cuk converter is

capable of sweeping the I-V curve of solar PV module in CCM from open

circuit voltage to short-circuit current condition and, hence, Cuk converter is

suitable to be employed in designing the MPPT circuits.

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Figure 3.1 Cuk converter-based MPPT system

The closed loop control is obtained by implementing the MPPT

algorithm using micro-controller. 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 array’s 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. To improve the dynamic

response without affecting stability the Adaptive Perturb and Observer

algorithm (APAO) is used. In APAO 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.

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3.4 SIMULATION RESULTS

The closed loop diagram was simulated in MATLAB /Simulink

which is given in Figure 3.2 that includes the solar PV module electric circuit

subsystem (MATLAB model), DC-DC Cuk converter, and adaptive PAO

algorithm. Figures 3.3, 3.4 and 3.5 show the MATLAB models for solar PV

subsystem, power sampling and PWM pulse generation using MPPT

algorithm.

PV module is modeled based on the electrical Equations (2.1) and

(2.2) to provide voltage and current to the Cuk converter and the micro

controller simultaneously. Using the adaptive PAO algorithm, the duty cycle

is adjusted. 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. When the obtained tracked power is equal or nearby actual

maximum, the variation in the duty cycle is minimum in such a way that the

memory increment value is selected.

Figure 3.2 Cuk converter based MPPT system model in MATLAB

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Figure 3.3 Solar PV module sub-system in MATLAB

Figure 3.4 Power sampling circuit model in MATLAB

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Figure 3.5 Pulse generation scheme using APAO MPPT algorithm

Using APAO algorithm, the output is obtained in terms of pulses

which may be used to trigger MOSFET. Also the changing irradiation is

modeled to study the MPPT algorithm performances. The temperature is

constant at 25°C and the illumination level is varying between two levels.

Initial irradiation is set as 1000 W/m2. After 0.02 sec, the irradiation (G) is

suddenly changed to 500 W/m2.

The relationship between the duty cycle and tracked solar PV

power is shown in Figures. 3.6 and 3.7 They show that the output power at

G=1000 W/m2 and 500 W/m2 are 36.74 W and 17 W, respectively.

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Figure 3.6 Change in duty cycle for various irradiation levels

The duty cycle of the main switch of Cuk converter-based MPP

tracking is 35.3%. The voltage and current through the main switch of Cuk

converter is shown in Figure 3.8.

Figure 3.7 Change in power for various irradiation levels

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Figure 3.8 Voltage and current through the switch S of Cuk converter

3.4.1 Study of Effects of Partial Shading

A shadow falling on a group of three cells will reduce the total

tracked power by two mechanisms: 1) by reducing the energy input to the

cell, and 2) by increasing energy losses in the shaded cells. Problems become

more serious when shaded cells get reverse-biased. A group of cells under

full illumination is connected in series with another group of cells under

shaded illumination. Figure 3.9 shows the MATLAB-based equivalent circuit

of solar module under partial shaded condition. The photon current of fully

illuminated cells Isci is high compared with that of the shaded illuminated cells

Iscs. If the module current I < Iscs, diode Ds is forward-biased and there is no

risk for the shaded cells. But if I > Iscs, then the diode current IDs = Iscs -I

flows through the diode in the reverse direction. Reverse-biased diode Ds

offers high resistance which will consume power and significantly reduce the

load current (I) itself. The point B will assume negative potential. If the

difference in illumination levels is high, Ds may get damaged due to

overheating.

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Figure 3.9 MATLAB-based equivalent circuit when three cells are

partially shaded

3.4.2 Parameters Affecting the Performance of Solar PV Module

under Partial Shading

The photo current generated by the shaded illuminated cell is FIL

(or Iscs), where F is the ratio of photo current generated by the shaded cell to

that of the fully illuminated cell. F=0 means, fully shaded and F=1 means

fully illuminated. When a solar cell in a series array is under shadow, its

current output is given by

Is = F I L - Io exp 1 - (3.10)

where V = Vs + Rss I and

v - Voltage across the diode in shaded cell.

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Similarly, the current through the illuminated cell is given by

Ii = I L - Io exp 1 - (3.11)

where V = Vs + Rsi Ii and

V - Voltage across diode in illuminated solar cell

As the shaded and illuminated cells are connected in a series, the

same current is forced to flow through both. Hence Is and Ii are replaced by

the same current I. Therefore,

I = F IL - Io exp 1 - (3.12)

I = IL - Io exp 1 - (3.13)

As the value of F (illumination) decreases from 1 to 0, exp

tends to reach zero. Hence, the equation can be simplified as

I = F I L - Io - (3.14)

The voltage across the shaded cell Vs is given by

Vs = (F IL – I ) RShs – I Rss (3.15)

In the above equation, Io Rshs is neglected in comparison with larger

terms. The total module output voltage is the sum of voltages across each cell

operating at the same current I. So the module consists of 36 identical series

connected cells, the output voltage can be expressed

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V = V + V (3.16)

The power dissipated by the shaded cell is obtained by

P= I * Vs = I * (F IL – I ) Rshs – I Rss (3.17)

Power dissipation in the shaded cell may be substantial leading to

increase in its temperature. Due to increased temperature, the cell current gets

concentrated in an increasingly small region of the cell, producing the hot

spot. The power extracted from the solar cell is reduced when the cells are

shaded.

The effectiveness of APAO MPPT algorithm to track the maximum

power under partial shaded condition is simulated in MATLAB/Simulink

Under partially shaded conditions. In APAO MPPT algorithm, large step size

is selected when the maximum power point is faraway and small step size is

preferred when the operating point is near to MPP. So the APAO MPPT

tracks true maximum power. The effectiveness of MPPT algorithm is shown

in Figure 3.10

Figure 3.10 Effectiveness of APAO MPPT under partial shaded condition

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The APAO MPPT tracks maximum power of 37 W under unshaded

condition with a voltage of 16.4 V. The tracked power from the solar PV

module is lowered when solar cells are shaded. The voltage corresponding to

maximum power under shaded condition is 15.6 V with the true maximum

power of 33 W. The implemented MPPT algorithm effectively tracks

maximum power from solar PV module under shaded and unshaded

conditions.

3.5 STEADY STATE PERFORMANCE

Figure 3.11 show the duty cycle of the main switch of Cuk

converter against different load resistance at the constant irradiation (G) of

1000 W/m2. Figure 3.12 shows that, for the load range of 1 RL 7 , the

obtained tracked power for the computer simulation.

Figure 3.11 Variation in Duty cycle for the changes in load resistance

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Figure 3.12 Variation in Tracked power for the changes in load

resistance

In Figures 3.13 and 3.14, the simulated tracked power from solar

PV module by implementing the adaptive PAO algorithm on Cuk converter is

illustrated. The obtained results are compared with the traditional PAO

algorithm. It shows the effectiveness of the proposed algorithm, resulting in

an improvement in the transient response. The settling time is reduced as

0.002sec.

Figure 3.13 Tracked power using PAO algorithm

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The tracking efficiency is 99.3% without considering the efficiency

of the solar PV module and converter. The Cuk converter conversion

efficiency is 86.266%. This is a good advantage during cloudy days when the

working conditions change rapidly.

Figure 3.14 Tracked power using Adaptive PAO algorithm

3.6 CONCLUSION

The Adaptive Perturb and Observe algorithm with direct control

was simulated using Cuk converter in MATLAB Simulink. The PI control

loop was eliminated in MPPT system. This is the main advantage of the

proposed tracking system when compared to direct control MPPT method

which uses two control loops. The adaptive PAO algorithm improves steady

state stability, dynamic response and tracks the maximum power of

36.74Watts with tracking efficiency of 99.3% in computer simulation without

considering the efficiency of solar PV module / converter. The duty cycle of

the main switch of the Cuk converter is 35.3%. The effectiveness of Adaptive

Perturb and Observer algorithm is under shaded condition.