Table of Contents
ISRN Renewable Energy
VolumeΒ 2012Β (2012), Article IDΒ 317982, 9 pages
Research Article

MATLAB-Based Investigation of Multiphase Interleaved Buck-Boost Converter for PV System

1Department of Electrical Engineering, Sarvajanik College of Engineering & Technology, Dr. R. K. Desai Marg, Athwalines, Surat 395001, India
2Department of Electronics Engineering, Rajasthan Technical University, Kota 324022, India
3Department of Electrical Engineering, S. V. National Institute of Technology, Ichchhanath, Surat 395 007, India

Received 30 September 2011; Accepted 9 November 2011

Academic Editor: S.Β Dai

Copyright Β© 2012 Hardik P. Desai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A photovoltaic (PV) generator exhibits nonlinear voltage-current characteristics and its maximum power point varies with solar radiation. Analytical investigations of the new family of switching converters based on a parallel connection of 𝑁(=4) identical buck-boost converters employed in PV system are presented. The interleaving strategy ensures that all the converters operate at the same switching frequency. Mathematical models developed using the state-space average technique are presented in this paper. Various steady-state performance expressions are also derived. The present converter system has the advantages of reduced size of the converter, and ripple in the total inductor current. The effectiveness of the four-phase interleaved dc-dc converter combined with PV system is demonstrated through simulations carried out in MATLAB environment.

1. Introduction

Generation of electrical energy from renewable sources has growing interest globally. As Photovoltaic (PV) power generator has advantages of no supply limitations, no pollution, and no noise, it can become the biggest contributor to electricity generation among all renewable energy sources. PV source is nonlinear power generator. Different techniques to maximise PV power transfer to various loads have been reported in the literature [1], some techniques only approximate the maximum power transfer of PV energy because they are associated with specific atmospheric and load conditions. In order to draw its maximum power, it is possible to insert dc-dc power converters between the PV and load. Power converters are required for many functions. A dc-dc converter converts a dc input voltage into a desired regulated dc output voltage [2, 3]. The dc input may be an unregulated or regulated voltage. dc/dc converters are widely used in photovoltaic generating systems as an interface between the photovoltaic panel and the load, allowing the follow-up of the maximum power point (MPP). These converters are known as maximum power point trackers (MPPTs). A maximum power point tracker should provide a maximum power to the load, even if irradiation, load, and temperature vary [4–8]. The dc-dc conversion process implies in turn an associated effect of impedance transformation, that is, the input impedance shows a dependence on a number of parameters such as load resistance, and duty cycle. Development of parallel connected converters with interleaving control strategies is coming up to increase the power processing capability and to improve the reliability of the power electronic system. In this paper, mathematical models are developed using state-space average technique for four-phase dc-dc converter employed with PV. Also various steady-state performance expressions are derived. Simulations carried out in MATLAB environment finds effectiveness of the four-phase interleaved dc-dc converter combined with PV system.

2. Multiphase Interleaved Buck-Boost Converter

Figure 1 shows the new family of switching converters based on a parallel connection of 𝑁(=4) identical interleaved buck-boost converters employed in PV system which is considered for an analytical investigations.

Figure 1: 4-phase interleaved buck boost converter with PV generator.

A PV module consists of a combination of many small PV cells that are connected in series and parallel configurations to provide the desired voltage and current quantities. It is known that a PV cell module shows a nonlinear characteristic between voltage and current quantities, which is dependent on the insolation and temperature. The equation [9] which describe the I-V characteristics of the cell, is𝐼PV=𝐼PHOTOβˆ’πΌ0𝑒(π‘ž(𝑉PV+𝐼PV𝑅𝑆)/𝑛𝐾𝑇)ξ€Έβˆ’1,(1) where 𝐼PHOTOis the cell photo current, 𝑅𝑆 is the series resistance of PV cell, 𝐾 is Boltzmann’s constant, π‘ž is charge on an electron, 𝑛 is the diode quality factor, 𝑇 is the cell temperature, and 𝑉PV is the output voltage of PV cell. Reorganization of the equation provides the output voltage of the PV generator as𝑉PV=ξ‚΅π‘›πΎπ‘‡π‘žξ‚Άξ€·πΌln0+𝐼PHOTOβˆ’πΌPV𝐼0βˆ’πΌPV𝑅𝑆,(2) With 𝑁 identical cells connected in series and 𝑀 number of series combinations connected in parallel, the resultant voltage would be𝑉PVξ‚΅=π‘π‘›πΎπ‘‡π‘žξ‚Άξ€·πΌln0+𝐼PHOTOβˆ’πΌPV𝐼0βˆ’π‘πΌPV𝑅𝑆𝑀.(3)

To extract maximum power from the PV generator, MPP tracker is employed by connecting a dc-dc converter between the PV generator and load. Protection circuits like string combiners, blocking diodes, bypass diodes; and fuses can also be used in the circuit. String combiners are the physical point at which the leads from the PV generator circuits are joined in parallel to create the main array output. Each converter consists of a power MOSFET used as a controllable switch, an inductor 𝐿, a diode, a filter capacitor 𝐢, and a load resistor 𝑅𝐿.

With the interleaving PWM method, pulses are applied to the semiconductor switches such that SW1, SW2, SW3, and SW4 are on and off in interleaving fashion as shown in Figure 2. Here, conduction period for the switches may be the same depending on the duty cycle of PWM pulses and 𝑑1+𝑑2+𝑑3+𝑑4+𝑑5+𝑑6+𝑑7+𝑑8=𝑇, where 𝑇 is the total time period for switching with the on duty ratio 𝑑=𝑑on/𝑇, where 𝑑on is the time interval when the switch is on.

Figure 2: (a)–(d) PWM pulses applied to switches SW1–SW4, (e) current through inductor.

Different modes of operation are as follows.

(i) Mode 1 (0≀𝑑≀𝑑1)
In this mode, SW1, and 𝐷4 are on and SW2, SW3, SW4, D1, D2, and D3 are off.
The state space equations for Figure 3 are ̇𝑖𝐿1=𝑉PV𝐿1βˆ’π‘ŸπΏ1𝐿1𝑖𝐿1,̇𝑖𝐿2̇𝑖=0,𝐿3̇𝑖=0,𝐿4=𝑉𝐿𝐿4βˆ’π‘ŸπΏ4𝐿4𝑖𝐿4,̇𝑉𝐿𝑖=βˆ’πΏ4πΆβˆ’π‘‰πΏπ‘…πΏπΆ.(4)

Figure 3: Mode 1.

(ii) Mode 2 (𝑑1<𝑑≀𝑑2)
In this mode; SW1 is on and SW2, SW3, SW4, D1, D2, D3, D4 are off.
The state space equations for Figure 4 are ̇𝑖𝐿1=𝑉PV𝐿1βˆ’π‘ŸπΏ1𝐿1𝑖𝐿1,̇𝑖𝐿2̇𝑖=0,𝐿3̇𝑖=0,𝐿4̇𝑉=0,𝐿𝑉=βˆ’πΏπ‘…πΏπΆ.(5)

Figure 4: Mode 2.

(iii) Mode 3 (𝑑2<𝑑≀𝑑3)
In this mode, SW2, and D1 are on and SW1, SW3, SW4, D2, D3, and D4 are off.
The state space equations for Figure 5 are ̇𝑖𝐿1=𝑉𝐿𝐿1βˆ’π‘ŸπΏ1𝐿1𝑖𝐿1,̇𝑖𝐿2=𝑉PV𝐿2βˆ’π‘ŸπΏ2𝐿2𝑖𝐿2,̇𝑖𝐿3̇𝑖=0,𝐿4̇𝑉=0,𝐿𝑖=βˆ’πΏ1πΆβˆ’π‘‰πΏπ‘…πΏπΆ.(6)

Figure 5: Mode 3.

(iv) Mode 4 (𝑑3<𝑑≀𝑑4)
In this mode, SW2 is on and SW1, SW3, SW4, D1, D2, D3, and D4 are off.
The state space equations for Figure 6 are ̇𝑖𝐿1̇𝑖=0𝐿2=𝑉PV𝐿2βˆ’π‘ŸπΏ2𝐿2𝑖𝐿2̇𝑖𝐿3̇𝑖=0𝐿4̇𝑉=0𝐿𝑉=βˆ’πΏπ‘…πΏπΆ.(7)

Figure 6: Mode 4.

(v) Mode 5 (𝑑4<𝑑≀𝑑5)
In this mode, SW3 and D2 are on and SW1, SW2, SW4, D1, D3, and D4 are off.
The state space equations for Figure 7 are ̇𝑖𝐿1̇𝑖=0,𝐿2=𝑉𝐿𝐿2βˆ’π‘ŸπΏ2𝐿2𝑖𝐿2,̇𝑖𝐿3=𝑉PV𝐿3βˆ’π‘ŸπΏ3𝐿3𝑖𝐿3,̇𝑖𝐿4̇𝑉=0,𝐿𝑖=βˆ’πΏ2πΆβˆ’π‘‰πΏπ‘…πΏπΆ.(8)

Figure 7: Mode 5.

(vi) Mode 6 (𝑑5<𝑑≀𝑑6)
In this mode, SW3 is on and SW1, SW2, SW4, D1, D2, D3, and D4 are off.
The state space equations for Figure 8 are ̇𝑖𝐿1̇𝑖=0,𝐿2̇𝑖=0,𝐿3=𝑉PV𝐿3βˆ’π‘ŸπΏ3𝐿3𝑖𝐿3,̇𝑖𝐿4̇𝑉=0,𝐿𝑉=βˆ’πΏπ‘…πΏπΆ.(9)

Figure 8: Mode 6.

(vii) Mode 7 (𝑑6<𝑑≀𝑑7)
In this mode, SW4 and D3 are on and SW1, SW2, SW3, D1, D2, and D4 are off.
The state-space equations for Figure 9 are ̇𝑖𝐿1Μ‡i=0,𝐿2̇𝑖=0,𝐿3=𝑉𝐿𝐿3βˆ’π‘ŸπΏ3𝐿3𝑖𝐿3,̇𝑖𝐿4=𝑉PV𝐿4βˆ’π‘ŸπΏ4𝐿4𝑖𝐿4,̇𝑉𝐿𝑖=βˆ’πΏ3πΆβˆ’π‘‰πΏπ‘…πΏπΆ.(10)

Figure 9: Mode 7.

(viii) Mode 8 (𝑑7<𝑑≀𝑑8)
In this mode, SW4 is on and SW1, SW2, SW3, D1, D2, D3, and D4 are off.
The state-space equations for Figure 10 are ̇𝑖𝐿1̇𝑖=0,𝐿2̇𝑖=0,𝐿3̇𝑖=0,𝐿4=𝑉PV𝐿4βˆ’π‘ŸπΏ4𝐿4𝑖𝐿4,̇𝑉𝐿𝑉=βˆ’πΏπ‘…πΏπΆ.(11)

Figure 10: Mode 8.

From, the above equations,̇𝑖𝐿1=𝑑1+𝑑2𝑉PV𝐿1βˆ’ξ€·π‘‘1+𝑑2+𝑑3ξ€Έπ‘ŸπΏ1𝐿1𝑖𝐿1+𝑑3𝑉𝐿𝐿1,̇𝑖𝐿2=𝑑3+𝑑4𝑉PV𝐿2βˆ’ξ€·π‘‘3+𝑑4+𝑑5ξ€Έπ‘ŸπΏ2𝐿2𝑖𝐿2+𝑑5𝑉𝐿𝐿2,̇𝑖𝐿3=𝑑5+𝑑6𝑉PV𝐿3βˆ’ξ€·π‘‘5+𝑑6+𝑑7ξ€Έπ‘ŸπΏ3𝐿3𝑖𝐿3+𝑑7𝑉𝐿𝐿3,̇𝑖𝐿4=𝑑1𝑉𝐿𝐿4+𝑑7+𝑑8𝑉PV𝐿4βˆ’ξ€·π‘‘1+𝑑7+𝑑8ξ€Έπ‘ŸπΏ4𝐿4𝑖𝐿4,̇𝑉L𝑖=βˆ’πΏ1𝑑3+𝑖𝐿2𝑑5+𝑖𝐿3𝑑7+𝑖𝐿4𝑑1πΆβˆ’π‘‘π‘‰πΏπ‘…πΏπΆ,(12) where 𝑑=𝑑1+𝑑2+𝑑3+𝑑4+𝑑5+𝑑6+𝑑7+𝑑8.

Further simplifying the above equations,βŽ‘βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ£Μ‡π‘–πΏ1̇𝑖𝐿2̇𝑖𝐿3̇𝑖𝐿4Μ‡π‘‰πΏβŽ€βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯⎦=βŽ‘βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ£βˆ’ξ€·π‘‘1+𝑑2+𝑑3ξ€Έπ‘ŸπΏ1𝐿1𝑑0003𝐿1𝑑0βˆ’3+𝑑4+𝑑5ξ€Έπ‘ŸπΏ2𝐿2𝑑005𝐿2𝑑00βˆ’5+𝑑6+𝑑7ξ€Έπ‘ŸπΏ3𝐿30𝑑7𝐿3𝑑000βˆ’1+𝑑7+𝑑8ξ€Έπ‘ŸπΏ4𝐿4𝑑1𝐿4βˆ’π‘‘3πΆβˆ’π‘‘5πΆβˆ’π‘‘7πΆβˆ’π‘‘1πΆβˆ’π‘‘π‘…πΏπΆβŽ€βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ¦βŽ‘βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ£π‘–πΏ1𝑖𝐿2𝑖𝐿3𝑖𝐿4π‘‰πΏβŽ€βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯⎦+𝑉PVβŽ‘βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ£ξ€·π‘‘1+𝑑2𝐿1𝑑3+𝑑4𝐿2𝑑5+𝑑6𝐿3𝑑7+𝑑8𝐿40⎀βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯⎦,(13)where, 𝑖𝐿𝑛: is the inductor current of 𝑛th phase converter, 𝐿𝑛: is the inductance of phase 𝑛.

Considering the operation of converter 1, 𝑑1+𝑑2=𝑑 and 𝑑3=π‘‘ξ…ž, converter 2, 𝑑3+𝑑4=𝑑 and 𝑑5=π‘‘ξ…ž, and so on, π‘Ÿ1=π‘Ÿ2=π‘Ÿ3=π‘Ÿ4=π‘Ÿ and 𝐿1=𝐿2=𝐿3=𝐿4=𝐿, output voltage is given by𝑉𝐿=βˆ’π‘‘π‘‰PVπ‘‘ξ…ž,(14) where π‘‘ξ…ž is the duty cycle when the converter is supplied to load and after that inductor current becomes zero.

The previous equation describes the output voltage function of dc-dc converter. Input voltage of the converter (𝑉PV) can be adjusted to maximum power point by adjusting the duty cycle. The maximum switch and diode peak currents are given by𝐼𝑆𝑁𝑀=𝐼𝐷𝑁𝑀=𝑉PV𝑇𝑑𝑁+𝑑𝑁+1ξ€Έ2𝐿𝑁ξƒͺ,(15) Where 𝑀 tends for maximum values.

For multiphase interleaved dc-dc converter, losses occur in MOSFETs, diodes, inductor, output capacitor, and so forth. =Lossesthatoccurredinswitches𝑁𝑖=1π‘Ÿswi𝐼2swiπ‘Ÿ+𝑓𝐢swi𝑉PV+𝑉𝐿2,(16) where 𝐼swiπ‘Ÿ=Ξ”π‘–πΏβˆš(𝑑𝑖+𝑑𝑖+1)/3.=Lossesthatoccuredindiodes𝑁𝑖=1π‘Ÿdi𝐼2diπ‘Ÿ+𝑉𝐹𝑖𝐼di,(17) where 𝐼diπ‘Ÿ=Ξ”π‘–πΏβˆš(𝑑𝑖+𝑑𝑖+1)/3.=Inductorconductionlosses𝑁𝑖=1π‘ŸπΏπ‘–πΌ2πΏπ‘Ÿπ‘–,(18) where πΌπΏπ‘Ÿπ‘–=Ξ”π‘–πΏβˆš(𝑑2π‘–βˆ’1+𝑑2𝑖+𝑑2𝑖+2)/3.Lossesthatoccurredinoutputcapacitor=π‘Ÿπ‘πΌ2π‘Ÿπ‘,(19)=Totallosses𝑁𝑖=1[π‘Ÿswi𝐼2π‘Ÿswi+𝑓𝐢swi𝑉PV+𝑉𝐿2+π‘Ÿdi𝐼2π‘Ÿdi+𝑉𝐹𝑖𝐼di+π‘ŸπΏπ‘–πΌ2πΏπ‘Ÿπ‘–]+π‘Ÿπ‘πΌ2π‘Ÿπ‘,(20) where π‘Ÿswi and π‘Ÿdi are switch resistance diode resistance, respectively; 𝑉𝐹 is the forward voltage of diode, and suffix π‘Ÿ tends to rms value. Thus, the converter efficiency is given by, π‘ƒπœ‚=𝐿𝑃𝐿+TotalLosses.(21)

3. Simulation Results

The following parameters are used for simulation. PV generator parameters [10]: open circuit voltage: 21.8 V; short circuit current: 4.7 A; power at MPP = 75 W; converter parameters: switching frequency = 25 kHz; π‘ŸπΏ1=π‘ŸπΏ2=π‘ŸπΏ3=π‘ŸπΏ4=0.01 Ω, 𝐿1=𝐿2=𝐿3=𝐿4=20 μH, 𝐢 = 1000 μF, 𝑉𝐹 = 0.1 V; π‘ŸπΆ = 0.06 Ω.

It was found that maximum power is extracted from PV generator with 4-phase interleaved dc-dc converter as shown in Figure 11 in which PV power (a) voltage (b) and current (c) at MPP is shown. At MPP, power of 74.3 W is extracted with voltage of 18.1 V and current of 4.1 A from PV. Figure 12 shows the current through inductors 𝐿1 to 𝐿4. Current through inductors for time duration of 0.3 to 0.3002 s are shown in Figure 13.

Figure 11: PV output (a) power, (b) voltage, and (c) current at MPP.
Figure 12: Current through inductors (a) 𝐿1, (b) 𝐿2, (c) 𝐿3, and (d) 𝐿4.
Figure 13: Current through inductors (a) 𝐿1, (b) 𝐿2, (c) 𝐿3, and (d) 𝐿4.

Figure 14 shows the pulse pattern applied to SW1 to SW4. It can be seen that one out of four converters is in operation with PV at a time. As shown in Figure 15, which shows total inductor current continuous in nature, the ripple current reduced significantly. Figure 16 shows the converter output power (a), voltage (b), and current (c) for the given MPP condition. At MPP, power of 65.1 W with voltage of 8.07 V and current of 8.07 A is available at load.

Figure 14: PWM pulses applied to (a) SW1, (b) SW2, (c) SW3, and (d) SW4.
Figure 15: Total inductor current.
Figure 16: Converter output (a) power, (b) voltage and (c) current at MPP.

4. Conclusion

By using the state-space averaging technique, mathematical models are developed for parallel connected 4 identical buck-boost converters employed in PV system. The interleaving strategy employed for PWM pulses ensures that all the converters operate at the same switching frequency. Various steady-state performance expressions were derived. The present converter system has the advantages of reduced size of the converter as inductor size is reduced; total inductor current is continuous although individual inductor current is discontinuous. The maximum power tracking effectiveness of the four-phase interleaved dc-dc converter combined with PV system is demonstrated through simulations carried out in MATLAB environment.


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