Abstract

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 (=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 (=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, is where is the cell photo current, is the series resistance of PV cell, is Boltzmann’s constant, is charge on an electron, is the diode quality factor, is the cell temperature, and is the output voltage of PV cell. Reorganization of the equation provides the output voltage of the PV generator as With identical cells connected in series and number of series combinations connected in parallel, the resultant voltage would be

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 , a diode, a filter capacitor , and a load resistor .

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 , where is the total time period for switching with the on duty ratio , where is the time interval when the switch is on.

(a) PWM pulses applied to SW1

(b) PWM pulses applied to SW2

(c) PWM pulses applied to SW3

(d) PWM pulses applied to SW4

(e) Inductor current

(a) PWM pulses applied to SW1
(b) PWM pulses applied to SW2
(c) PWM pulses applied to SW3
(d) PWM pulses applied to SW4
(e) Inductor current

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 ()
In this mode, SW₁, and are on and SW₂, SW₃, SW₄, D₁, D₂, and D₃ are off.
The state space equations for Figure 3 are

Figure 3 

Mode 1.

(ii) Mode 2 ()
In this mode; SW₁ is on and SW₂, SW₃, SW₄, D₁, D₂, D₃, D₄ are off.
The state space equations for Figure 4 are

Figure 4 

Mode 2.

(iii) Mode 3 ()
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

Figure 5 

Mode 3.

(iv) Mode 4 ()
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

Figure 6 

Mode 4.

(v) Mode 5 ()
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

Figure 7 

Mode 5.

(vi) Mode 6 ()
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

Figure 8 

Mode 6.

(vii) Mode 7 ()
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

Figure 9 

Mode 7.

(viii) Mode 8 ()
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

Figure 10 

Mode 8.

From, the above equations, where .

Further simplifying the above equations,where, : is the inductor current of th phase converter, : is the inductance of phase .

Considering the operation of converter 1, and , converter 2, and , and so on, and , output voltage is given by where 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 () can be adjusted to maximum power point by adjusting the duty cycle. The maximum switch and diode peak currents are given by Where tends for maximum values.

For multiphase interleaved dc-dc converter, losses occur in MOSFETs, diodes, inductor, output capacitor, and so forth. where . where . where . where and are switch resistance diode resistance, respectively; is the forward voltage of diode, and suffix tends to rms value. Thus, the converter efficiency is given by,

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;  Ω,  μH, = 1000 μF, = 0.1 V; = 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 to . Current through inductors for time duration of 0.3 to 0.3002 s are shown in Figure 13.

(a)

(b)

(c)

(a)
(b)
(c)

Figure 11 

PV output (a) power, (b) voltage, and (c) current at MPP.

(a)

(b)

(c)

(d)

(a)
(b)
(c)
(d)

Figure 12 

Current through inductors (a) , (b) , (c) , and (d) .

(a)

(b)

(c)

(d)

(a)
(b)
(c)
(d)

Figure 13 

Current through inductors (a) , (b) , (c) , and (d) .

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.

(a)

(b)

(c)

(d)

(a)
(b)
(c)
(d)

Figure 14 

PWM pulses applied to (a) SW1, (b) SW2, (c) SW3, and (d) SW4.

Figure 15 

Total inductor current.

(a)

(b)

(c)

(a)
(b)
(c)

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.