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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 ZVSCuk 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 V c 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 = t o, 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 V cr(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 = t 4. 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)
(e)
(d)
(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 ZVSPWM 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 C r 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
T= fs / fo and
0
½ Cr .(Vc+Vo+Vs)2
(4.1)
= 1 / (LrCr) ½
(4.2)
fs-switching frequenc, f o-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 (f s) =25kHz,
Figure 4.8 Duty cycle versus output voltage
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The input resistance R i 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 t o 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
Switching frequency
Converter Output voltage
Input voltage
Main inductor L1
Resonant inductor Lr
Resonant capacitor Cr
Capacitor Ca
Capacitor Cc
Capacitor Co
ESR (Element Series
Resistance)
Load resistance R
Step size
MOSFET
37watts
25kHz
8V
16.4V
500e-6H
5e-6H
50e-9 F
220e-6 F
20e-6 F
220e-6 F
0.5
2
1e-7
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 t 0, 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 i s1
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 i Lr 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 C r and
the capacitor C1, respectively are charged linearly by the input current i s. The
resonant inductor current iLr, is reduced to zero. This mode ends when the
resonant capacitor voltage V cr is more than the capacitor voltage V c1. 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
37watts
Switching frequency
25kHz
Input voltage
16.4V
Main inductor L1
500e-6H
Resonant inductor Lr
5e-6H
Resonant capacitor Cr
2.2e-6F
Capacitor Ca
220e-6F
ESR(Element Series Resistance)
0.5
Load resistance
2
Step size
1e-7
IGBT
G15N60
Diode
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 PVpowered system, direct control chaotic pulse width modulated Cuk converter
83
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
where T is invariant period, x , i= 1,2,….N, a chaotic sequence,
(4.8)
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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
A
changes according to
= {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 subsystem (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 microcontroller 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 ZVSCuk 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 ZVSCuk 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 ZCSCuk 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 ZCSCuk 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 CPWMCuk 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.