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CHAPTER 4

DESIGN OF CUK CONVERTER-BASED MPPT SYSTEM

WITH VARIOUS CONTROL METHODS

4.1 INTRODUCTION

The main objective of this research work is to implement and

compare four control methods, i.e., PWM with periodic carrier, Zero voltage

switching, Zero Current switching, chaotic PWM with chaotic carrier in

terms of their performance in suppressing ripples, reducing peaky

electromagnetic inference and increasing converter conversion efficiency in

MPPT circuits of the solar PV powered Cuk converter system.

This research work proposed to design chaotic PWM-based MPP

tracking using Cuk converter in order to improve electromagnetic

compatibility, converter conversion efficiency and this method is compared

with soft switching Cuk converter based MPP tracking. Due to continuous

power spectrum feature in chaotic PWM, the power density peak in output

voltage and hence the electromagnetic inference is reduced to great extent.

The proposed MPP tracking is achieved by connecting a chaotic PWM based

Cuk converter between a solar panel and a load (Rheostat).

4.2 CUK CONVERTER WITH PERIODIC CARRIER

Cuk converter shown in Figure 4.1 provides an output voltage

which is less than or greater than the input voltage. It works based on the

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capacitor energy transfer. It has low switching losses and highest efficiency

among all non-isolated DC-DC converters. It exhibits non-pulsating input

current characteristic due to the inductor in the input stage. Also Cuk

converter is capable of sweeping the V-I curve of solar PV module in CCM

from open circuit voltage to short circuit current condition and hence Cuk

converter is a suitable converter to be employed in designing the MPPT

circuits. Cuk converter is used as the power stage interface between PV

module and the load. Cuk converter has two modes of operation. First mode

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

conducting as a short circuit. In this mode, the current through inductor L1

rises. At the same time, the voltage of capacitor C1 reverse biases diode D and

turns it off. The capacitor (C1) releases its stored energy to the load

.

Figures 4.1 Cuk converter as the solar PV power stage interface

Figure 4.2 shows the generation scheme of PWM pulse using

periodic carrier to trigger main switch (MOSFET) of Cuk converter. The

periodic carrier and PWM pulse are shown in Figures 4.3.and 4.4.

Figure 4.2 MATLAB model to generate PWM pulse

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Figure 4.3 PWM pulse using periodic carrier

Figure 4.4 Periodic carrier

Figures 3.6 and 3.7 show the relation between tracked power from

the solar PV module and duty cycle for the change in irradiations using

periodic carrier. The percentage duty cycle of the main switch of the Cuk

converter is 35.3. The converter conversion efficiency of the Cuk converter is

86.26%.

4.3 ZVS-PWM CUK CONVERTER

The converter that connects to the solar panel and load is a ZVS-

Cuk shown in Figure 4.5. By connecting ZVS-PWM Cuk converter between

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solar PV module and load, the APAO MPPT algorithm has been

implemented. The ZVS is facilitated in order to reduce the EMI during

switching transitions, high efficiency with high voltage inputs, no power loss

due to the discharge of output capacitance of MOSFET, zero power ‘lossless’

switching transition. To track maximum power from PV module, the duty

cycle of the main switch is adjusted by using ATMEGA16 micro-controller

such that the input resistance of the ZVS-PWM Cuk converter is equal to the

output resistance of the solar PV module.

The output power of solar module is equal to the input power of the

converter which ensures maximum power transfer. To compare the adaptive

MPPT algorithm with a traditional PAO method, the same converter is being

used. The switching frequency of the converter is 25 kHz.

The Active-Clamp ZVS-PWM Cuk converter is shown in

Figure 4.5 featuring PWM, and soft switching (ZVS) in all three active

switches, resulting in high efficiency at high-frequency operation without

significant increase in voltage and current stresses on switches. It consists of

an input inductor Li, power switch S1, S2, S3, energy transfer capacitor Ca,

output inductor Lo, filter capacitor Co and resonant capacitors Cr and resonant

inductor Lr. The ZVS-Cuk converter will not have any switching losses across

all three power devices. The function of this converter is to transfer electrical

energy from the input voltage supply Vs to the output load Ro at a voltage

level that can be higher or lower than the input supply through the energy

transfer capacitor. As in any power application, high efficiency is essential

and, hence, the increasing of frequency can be problematic because of the

direct dependence of switching losses on frequency.

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Figure 4.5 Active Clamp ZVS-Cuk converter

The input filter inductance is assumed to be a current source in the

proposed circuit. The capacitors Cc and Ca are chosen to have large

capacitances so that the voltages Vc and Vca are considered as constants. The

six topological stages and key waveforms of the proposed modified Active

Clamp ZVS-PWM Cuk converter, to one switching cycle, are shown in

Figure 4.6 (a) to (f), respectively. The two switches S1 and S3 are triggered in

a complementary way and soft switching is employed for all three switches.

The main switch S1 is switched off at t = to, when the switching cycle starts.

Prior to t= to, the main switch S1 is turned on, the auxiliary switch S2 is turned

off, and S3 is also off. When S1 is turned off, at t= to, the first stage has started,

as shown in Figure 4.6(a). The capacitor is charged under constant current.

When Vcr (t) reaches V0+VS, the diode of switch S3 starts conducting, at this

instant, S3 also triggers. Thus switching losses across the diode is eliminated.

At the second stage, current through Lr and voltage across Cr rings

in a resonant way. Voltage Vcr(t) increases until it reaches (Vs+V0+Vc) when

Vcr(t) = Vs+Vo+Vc, the antiparallel diode of S2 starts conducting.

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At the third stage, Lr current ramps down, because it is considered

as a constant voltage source, until it reaches zero, when it changes its

direction and rises again and voltage across is clamped at Vs+Vo+Vc. When

the antiparallel diode of S2 is conducting, the auxiliary switch S2 is switched

on to achieve a lossless turn-on. This stage ends when S2 is turned off at t = t4.

At the fourth stage, the voltage across Cr falls due to the resonance

between Lr and Cr, until it reaches zero at t = t4. This stage ends when Vcr(t)

becomes null and the antiparallel diode of S1 and S3 begins conducting.

Hence lossless turn-on is achieved for the switch S3.

(a) (b)

(C) (d)

(e) (f )

Figure 4.6 Operational modes of the Active clamp ZVS-Cuk converter

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At the fifth stage, S1 is turned on without switching losses, in a

ZVS way, because Vcr(t) becomes zero. The current through Lr changes its

polarity and ramps up to reach Is at t = t5. Then, the diode of switch

S3becomes reversibly biased and turns off, and, at the sixth stage, S1 conducts

a current equal to Is+I0 and the auxiliary switch S2 is off. The S3 is off and the

stage ends when S3 is turned off at the end of the period. The theoretical

waveform during the one switching cycle is shown in Figure 4.7.

Figure 4.7 Theoretical waveform of modified Active clamp ZVS-

PWM Cuk converter

Due to the capacitance Cr, S1, S2 and S3 are turned off with no

losses, in an ZVS way. However, S1, S2 and S3 will turn on with no losses,

only if there is enough energy stored in Lr to achieve soft commutation. At,

t = t1, it is necessary to charge Cr from V0 +Vs to V0+Vs+Vc. At t = t3, it is

necessary to discharge Cr from V0+Vs+Vc to zero. The latter is very tedious

because it needs more energy. Thus, if enough energy is guaranteed to

achieve soft commutation for S1, then S2 and S3 will also achieve soft

commutation. From the energy relationship in Lr and Cr, at t = t3, we have

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½ Lr.(Is+Io)2 ½ Cr .(Vc+Vo+Vs)2 (4.1)

T= fs / fo and 0 = 1 / (LrCr) ½ (4.2)

fs-switching frequenc, fo-resonant frequency.

The voltage gain is given by,

= (4.3)

where d is duty cycle. L - normalized load current which is given by

L = (4.4)

The normalized clamping voltage is given by

=( )

*( )

(4.5)

The output voltages for various values of duty cycle are shown in

Figure 4.8. The input voltage is 16.4 V, swithing frequency (fs) =25kHz,

Figure 4.8 Duty cycle versus output voltage

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The input resistance Ri of the Active clamp ZVS-PWM Cuk

converter is given by

= ( ) (4.6)

where L =Li // Lo, f -switching frequency, D- is the duty cycle of the main

switch S1. Under discontinuous inductor current mode of operation, the

voltage across Ca is given by Vca = Vs + Vo. Where the Vs is the converter

input voltage and Vo is the converter output voltage. The maximum voltage

stress on the main switch S1,VS1stress, occurs in the time interval from to to t4

when S1 is off and S3 is on. Maximum voltage stress on S3, s3stress occurs in

the interval t4 to t6when S1 is on and S3 is off.

VS1stres= Vs3stress =Vca = Vs+Vo (4.7)

The specifications of ZVS-PWM Cuk converter are given in

Table 4.1.

Table 4.1 Specification of ZVS-PWM Cuk converter

Maximum power 37watts Switching frequency 25kHzConverter Output voltage 8V Input voltage 16.4VMain inductor L1 500e-6HResonant inductor Lr 5e-6HResonant capacitor Cr 50e-9FCapacitor Ca 220e-6FCapacitor Cc 20e-6FCapacitor Co 220e-6FESR (Element Series Resistance)

0.5

Load resistance R 2Step size 1e-7MOSFET IRF510

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4.4 ZCS-CUK CONVERTER

To achieve ZCS, the resonant inductor Lr, is in a series with a

switch as shown in Figure 4.9. If zero current resonant switching operates in

half-wave mode, the switch current can flow unidirectionally and is permitted

to resonate only in the positive half cycle. To avoid overvoltage across the

switch S, and parasitic oscillation, a unidirectional current switch is

implemented.

IGBT S1 and series-wound diode D form the principal

unidirectional current switch, Lr, and Cr, form the resonant circuit, C2 is the

output filter capacitor and R, represents the load. The equivalent circuit of

ZCS-Cuk converter is shown in Figure 4.10

Five modes of operation in the ZCS-Cuk converter have been

identified during one switching cycle.

Figure 4.9 ZCS-Cuk converter

Figure 4.10 Equivalent circuit of ZCS-Cuk converter

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MODE 1: Linear stage (to - t1)

Mode1 starts a switching cycle at time t0, IGBT ( S1), is turned on

at zero current condition with a positive gating signal due to the resonant

inductor Lr, which limits the di/dt of the IGBT S1 current. Output diode D

remains on. The IGBT current, is1, rises linearly and the current through Lr,

will decrease linearly at the same rate. The voltage across Cr is equal to input

voltage of the converter. This mode ends at time t1, when the switch current,

is1,, is equal to is. The equivalent circuit for mode 1 is shown in Figure 4.11.

Figure 4.11 Mode 1: Linear stage

MODE 2: Resonant stage (t1- t2)

At t= t1, the output diode D is off and resonant mode starts. The

equivalent circuit of mode 2 is shown in Figure 4.12. The IGBT current is1

increases in a sinusoidal fashion and the voltage across C1 decreases in a

linear fashion at the same time. The resonant capacitor Cr, is discharged and

its voltage becomes negative. The resonant inductor current ir starts to

decrease in a resonant mode, becomes negative, and increases again. At time

t2, the resonant capacitor voltage reaches the minimum negative peak voltage

and the switch current is equal to (is + io).

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Figure 4.12 Mode 2: Resonant stage

MODE 3: Resonant Stage (t2- t3)

After time t2, the current is1, is less than the input current is, and it

decreases until zero. The resonant capacitor voltage is negative, and increases

again. This mode ends at time t3, the switch current is, is equal to zero. The

resonant inductor current iLr reaches the maximum positive peak current. At

this moment, the voltage of capacitor C1 will reach a minimum positive

voltage, and increase linearly again. The equivalent circuit of mode 3 is

shown in Figure 4.13.

Figure 4.13 Mode 3: Resonant stage

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MODE 4: Linear stage (t3- t4)

At time t3, IGBT S is turned off and the resonant capacitor Cr and

the capacitor C1, respectively are charged linearly by the input current is. The

resonant inductor current iLr, is reduced to zero. This mode ends when the

resonant capacitor voltage Vcr is more than the capacitor voltage Vc1. At time

t4, D, will turn on. The equivalent circuit for mode 4 is shown in Figure 4.14.

Figure 4.14 Mode 4: Linear stage

MODE 5: Power Transfer Stage (t4- t5)

At time t4, the resonant capacitor voltage is clamped by D. This

mode ends when the resonant capacitor voltage Vcr,, is equal to Vs. The

equivalent circuit for mode 5 is shown in Figure 4.15.

Figure 4.15 Mode 5: Power transfer stage

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The voltage and current across the IGBT is shown in Figure 4.16.

Figure 4.16 Voltage and current waveforms across IGBT under ZCS

Table 4.2 shows the designed values for ZCS-Cuk converter-based

MPP tracking. The power rating is 37 W. The duty cycle is around 20 %. The

operating frequency is 25 kHz.

Table 4.2 Specifications of ZCS-Cuk converter

Maximum power 37wattsSwitching frequency 25kHz Input voltage 16.4VMain inductor L1 500e-6HResonant inductor Lr 5e-6HResonant capacitor Cr 2.2e-6FCapacitor Ca 220e-6FESR(Element Series Resistance) 0.5Load resistance 2Step size 1e-7IGBT G15N60Diode BY129

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4.5 CHAOTIC PWM-CUK CONVERTER

The output waveform of the Cuk converter-based MPPT solar PV

system, controlled by the traditional PWM, consists of many harmonic

components. The distribution of harmonics is influenced by the periodic

carrier. The carrier frequency and carrier amplitude are invariant under

traditional PWM. Thus, the spectrum has biggish peaks close to the carrier

frequency or its multiples. This makes the Cuk converter difficult to satisfy

the international standards of Electro Magnetic compatibility (EMC).

Conventionally, filters are used to reduce EMI of Cuk converter-based MPPT

system. Moreover, each filter can only restrain EMI in a certain frequency

band. The existence of a number of biggish peaks of the spectrum with

traditional PWM makes it difficult to design filters for the Cuk converter.

It is desirable for DC-DC Cuk converter used in MPPT system to

eliminate EMI without using filters. The distribution of harmonics is

influenced by the carrier and the chaotic behavior of DC-DC Cuk converter

can be used to reduce EMI. So, chaotic frequency or chaotic amplitude can be

used to distribute the harmonics continuously and evenly over a wide

frequency range. Although the total energy is not changed, the peaks of the

harmonics are reduced, thereby restraining the EMI.

Chaotic phenomena are useful in suppressing electromagnetic

interference by adjusting the parameters of the Cuk converter and making it

operate in chaos, a chaos-based pulse width modulation is proposed to

distribute the harmonics of the DC-DC converters continuously and evenly

over a wide frequency range, thereby reducing the EMI. The output waves

and spectral properties of the EMI are simulated and analyzed.

In order to improve the electromagnetic compatibility of solar PV-

powered system, direct control chaotic pulse width modulated Cuk converter

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as shown in Figure 4.17 is proposed to track maximum power from the solar

PV module.

Therefore, in order to get chaotic frequency f or chaotic amplitude

A , chaotic PWM, as shown in Figure 4.17, is proposed and analyzed. The

analogue chaotic PWM has its advantages over the digital one in its low cost

and easy design, making it suitable for high-frequency operation.

Figure 4.17 Chaotic PWM-Cuk converter

The analogue chaotic PWM generation circuit consists of 555 timer

circuit (triangular or saw toothed waveform circuit) in combination with

Chua’s diode in order to generate chaotic pulse width modulation which is

used to trigger the main switch of Cuk converter, and used for reducing EMI

in tracked converter voltage.

The CPWM adopts sawtooth to modulate, but its carrier period

T changes according to the equation 4.8.

T =( )

* T (4.8)

where T is invariant period, x , i= 1,2,….N, a chaotic sequence,

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x=(x 1,x2…xN ), and Mean(x),average of the sequence, defined as

Mean(x) = Lim |Xi|N (4.9)

Similarly, the CPWM also adopts sawtooth to modulate, but its

carrier amplitude A changes according to

A = {1+ k ( )

} A (4.10)

where A is the invariant amplitude, X , i= 1,2,….N, a chaotic sequence,

x = (x1,x2…xN ), and Mean(x), average of the sequence, and K is the

modulation factor of the amplitude. The value of K is selected as low so that

the ripple in the output voltage of the Cuk converter is low. Also the ripple in

the output voltage controlled by chaotic PWM is low when compared with

soft-switching Cuk converter-based MPPT system.

4.6 SIMULATION RESULTS

The closed loop diagram was simulated in MATLAB /Simulink

which is given in Figure 4.22 that includes a PV module electric circuit sub-

system (MATLAB model), a DC-DC converter and an adaptive PAO

algorithm. Four different control methods, i.e., traditional PWM with periodic

carrier, ZVS-soft switching, ZCS-soft switching and PWM with chaotic

carrier are simulated and compared in terms of their performance in suppressing

ripples, reducing EMI and increasing converter conversion efficiency.

The soft-switching ZVS-PWM active clamp Cuk converter has

been simulated with the solar PV module rating of 37Wp in MATLAB/

Simulink as shown in Figure 4.22. The maximum power tracking efficiency at

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the input of the converter from the solar PV module is 98.9%. The ZVS-PWM

converter conversion (output power to the input power) efficiency is 91.3%.

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.

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

shown in Figure 4.18. The method of generation of 3 pulses which can be

given to the switches of a ZVS-Cuk converter.

Figure 4.18 PWM-Pulse generation scheme for three switches

4.6.1 Generation of Chaotic PWM in MATLAB

The chaotic PWM is generated in MATLAB using the following

circuit model shown in Figure 4.19. The generated chaotic carrier and chaotic

PWM are shown in Figures 4.20 and 4.21.

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Figure 4.19 MATLAB model to generate Chaotic PWM

Figure 4.20 Generation of chaotic PWM in MATLAB

Figure 4.21 Generation of chaotic carrier in MATLAB

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The adaptive PAO MPPT algorithm is coded in embedded file and

the maximum power is tracked using ZVS-Cuk converter which is shown in

Figure 4.22.

Figure 4.22 ZVS-PWM Cuk converter-based MPP tracking

The changing irradiation is modeled to study the system operation.

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 0.01sec, the

irradiation (G) is suddenly changed to 500 W/m2.

The relationship between the duty cycle and solar PV power are

shown in Figures 4.23 and 4.24. They show that the output power at

G =1000 W/m2 and 500 W/m2 is 36.74 W and 17 W, respectively, for ZVS-

Cuk converter-based MPP tracking. The percentage duty cycle of the main

switch S1 is 43%. The ZVS-Cuk converter conversion efficiency is 91.26%.

The voltage across and current through the main switch of ZVS-Cuk

converter is shown in Figure 4.25.

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Figure 4.23 Change in duty cycle for various irradiation levels for ZVS

Cuk converter-based tracking

Figure 4.24 Change in power for various irradiation levels for ZVS-Cuk

converter-based tracking

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Figure 4.25 Voltage and current waveform across main switch S of ZVS-

Cuk converter

Similarly, the ZCS-Cuk converter is used to track maximum power

from the solar PV module which is shown in Figure 4.26.

Figure 4.26 ZCS-Cuk converter-based MPP tracking

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

(G) is suddenly changed to 500 W/m2. The relationship between the duty

cycle and solar PV power is shown in Figures 4.27 and 4.28. They show that

the output power at G=1000 W/m2 and 500 W/m2 is 36.74 W and 17 W,

respectively, for ZCS-Cuk converter-based MPP tracking. The percentage

duty cycle of the main switch is 18.5%. The ZCS-Cuk converter conversion

efficiency is 91.12%. The voltage across and current through the main switch

is ZCS-Cuk converter as shown in Figure 4.29.

Figure 4.27 Change in duty cycle for various irradiation levels in ZCS-

Cuk coneverter- based tracking

Figure 4.28 Change in power for various irradiation levels in ZCS-Cuk

converter-based tracking

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Figure 4.29 Voltage and current waveform across main switch S of ZCS-

Cuk converter

Chaotic PWM-Cuk converter shown in Figure 4.30 is used to track

maximum power from the solar PV module. The chaotic PWM shown in

Figure 4.19 is used to trigger the main switch of the Cuk converter.

The initial irradiation is set as 1000 W/m2. After tracking of

maximum power at 0.1sec, the irradiation (G) is suddenly changed to

500W/m2. The percentage duty cycle of the main switch S is 26%. The

tracked solar PV power using chaotic PWM-Cuk converter is shown in

Figure 4.31. The voltage across and current through the main switch of

CPWM-Cuk converter is shown in Figure 4.32.

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Figure 4.30 Chaotic PWM Cuk converter based MPP tracking

Figure 4.31 Change in power for various irradiation levels in CPWM-

Cuk converter-based tracking

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Figure 4.32 Voltage across and current through main switch of CPWM

– Cuk converter

The maximum power tracking efficiency is 99.3% without

considering the efficiency of solar PV module and converter. The converter

conversion efficiency is improved to 93.1% when chaotic PWM Cuk

converter is used for MPPT purposes.

4.7 CONCLUSION

Cuk converter-based tracking with conventional PWM, and zero

voltage switching for all the three switches, zero current switching and

chaotic PWM were proposed to overcome the limitations of the conventional

Cuk converter-based MPPT. The zero voltage switching reduces the EMI

during switching transitions. The converter conversion efficiency is improved

to 93.1% when chaotic PWM Cuk converter is used to track maximum power

from solar PV module.