# Application of Circuit Model for Photovoltaic Energy Conversion System

Authors: Natarajan Pandiarajan; Ramabadran Ramaprabha; Ranganath Muthu
Journal: International Journal of Photoenergy
 (2012)

---

## Abstract

Circuit model of photovoltaic (PV) module is presented in this paper that can be used as a common platform by material scientists and power electronic circuit designers to develop better PV power plant. Detailed modeling procedure for the circuit model with numerical dimensions is presented using power system blockset of MATLAB/Simulink. The developed model is integrated with DC-DC boost converter with closed-loop control of maximum power point tracking (MPPT) algorithm. Simulation results are validated with the experimental setup.


---

## Body

## 1. Introduction

The field of photovoltaics (PV) has experienced a remarkable growth for past two decades in its widespread use from standalone to utility interactive PV systems. The best way to utilize the electric energy produced by the PV array is to deliver it to the AC mains directly, without using battery banks [1].A recent study in Germany, of 21 PV systems in operation for 10 years, revealed that inverters contributed for 63% of failures, modules 15%, and other components 23%, with a failure occurring, on an average, every 4.5 years [2]. To reduce the failure rate of PV systems, it is necessary to reduce the failure rate of inverters and components also called the PV balance of systems (BOSs) that would result in their economic viability.At present, PV BOS research uses mathematical functional models for the performance analysis of newly developed systems. These developed systems could not be readily adopted by the field professionals and hence the above failure rate. Hence the need for simplified Simulink modeling of PV module has been long felt.Simple circuit-based PV models have been proposed in the literature [3–12]. Some authors have proposed indirect methods to adjust the I-V curve through artificial intelligence [13, 14]. Although interesting, such methods are impractical, complicated and require high computational effort. In all the above, modeling was limited to simulation of PV module characteristics.In this paper, the design of PV system using simple circuit model with detailed circuit modeling of PV module is presented. In Section2, the physical equations governing the PV module (also applicable to PV cell) are presented. Simulink model for each equation is presented with numerical results for different values of irradiation and temperature. The tabulation of the above numerical results gives the relationship of module parameters with characteristics curves of PV module, which are the indicators of circuit performance. In Section 3, complete circuit model is evolved after due experimental verification. In Section 4, modeling of MPPT using perturb and observe (P&O) algorithm is carried out using Simulink. The operation of developed circuit model with DC to DC boost converter for closed-loop MPPT control is verified with simulation. Section 5 presents the experimental verification of simulation results. In Section 6 result and discussions are presented.


## 2. Modeling of PV Module

### 2.1. Equivalent Circuit

A PV module consists of a number of solar cells connected in series and parallel to obtain the desired voltage and current output levels. Each solar cell is basically a p-n diode. As sunlight strikes a solar cell, the incident energy is converted directly into electrical energy without any mechanical effort.Transmitted light is absorbed within the semiconductor, by using this light energy to excite free electrons from a low energy status to an unoccupied higher energy level. When a solar cell is illuminated, excess electron-hole pairs are generated throughout the material, hence the p-n junction is electrically shorted and current flows.For simplicity, the single-diode model of Figure1 is used in this paper [15]. This model offers a good compromise between simplicity and accuracy with the basic structure consisting of a current source and a parallel diode. In Figure 1, Iph represents the cell photocurrent while Rsh and Rs are, respectively, the intrinsic shunt and series resistances of the cell.Figure 1
PV cell modeled as diode circuit.


### 2.2. Equations of PV Module

PV cells are grouped in larger units called PV modules, which are further interconnected in a series-parallel configuration to form PV arrays.The following are the basic equations from the theory of semiconductors and photovoltaics     [15] that mathematically describe the I-V characteristic of the photovoltaic cell and module.


### 2.3. Photocurrent

In Figure1, the module photocurrent Iph of the photovoltaic module depends linearly on the solar irradiation and is also influenced by the temperature according to the following equation:
(1)Iph=[ISCr+Ki(Tk-Tref)]*λ1000,
where Iph [A] is the light-generated current at the nominal condition (25°C and 1000 W/m2), Ki   is the short-circuit current/temperature coefficient (0.0017A/K), Tk and Tref are, respectively, the actual and reference temperatures in K, λ is the irradiation on the device surface (W/m2), and the nominal irradiation is 1000 W/m2.Detailed Simulink model of (1) of photocurrent Iph is shown in Figure 2. The value of module short-circuit current  is ISCr taken from the datasheet of the reference model as given in Section 2.4.Figure 2
Photocurrent.Iph for different values of insolation and temperature is shown in Table 1.Table 1
Iph for various insolations and temperatures.
S. no.Insol W/m2Value ofIph (A)25°C30°C40°C50°C90°C110002.552.5592.5752.5922.6627001.7851.7911.8031.8151.86235001.2751.2791.2881.2961.3342500.63750.63960.64890.64810.665151000.2550.25590.25760.25920.2661


### 2.4. Reference Model

Solkar make 36 W PV module is taken as the reference module for simulation and the datasheet details are given in Table2Table 2
Electrical characteristic data of solkar 36 W PV module.
DescriptionRatingRated power37.08 WpVoltage at maximum power (Vmp)16.56 VCurrent at maximum power (Imp)2.25 AOpen circuit voltage (VOC)21.24 VShort circuit current (ISCr)2.55 ATotal number of cells in series (Ns)36Total number of cells in parallel (Np)1Note. The electrical specifications are under standard test conditions (STCs) which means an irradiation of 1000 W/m2 with an AM1.5 spectrum at 25°C.


### 2.5. Module Reverse Saturation Current

Module reverse saturation current,Irs,is given by (2) as follows. 								(2)Irs=ISCr[exp⁡(qVOC/NSkAT)-1],
where q is the electron charge (1.6 × 10-19C),Voc is the Solkar module open-circuit voltage (21.24 V), Ns is the number of cells connected in series (36), k is the Boltzmann constant (1.3805 × 10−23 J/K), and A is the ideality factor (1.6).Detailed Simulink model of (2) is shown in Figure 3.Figure 3
Module reverse saturation current.Module reverse saturation current varies with temperature as shown in Table3.Table 3
Irs for various temperatures.
S. no.Temperature °CModule reverse saturation current (A)1251.182* 10(−006)2301.503* 10(−006)3402.377* 10(−006)4503.654* 10(−006)5901.609* 10(−005)


### 2.6. Module Saturation CurrentI0

The module saturation currentI0 varies with the cell temperature and is given by
(3)I0=Irs[TTr]3exp⁡[q*Eg0Ak{1Tr-1T}],
where Eg0 is the bandgap energy of the semiconductor (Eg0≈ 1.1 eV for the polycrystalline Si at 25°C).This equation is simulated and shown in Figure4. The module operating temperature, reference temperature, and module reverse saturation current are taken as inputs.Figure 4
Module saturation current.The module saturation currentI0 is calculated for various temperatures and is given in Table 4.Table 4
I0 for various temperatures.
S. no.Temperature °CModule saturation current (A)1251.182* 10(−006)2302.456* 10(−006)3409.92* 10(−006)4503.686* 10(−005)5900.003491


### 2.7. Module Output CurrentIPV

The basic equation that describes the current output of PV moduleIPV of the single-diode model presented in Figure 1 is given by
(4)IPV=NP*Iph-NP*I0[exp⁡{q*(VPV+IPVRs)NSAkT}-1]-VPV+(IPVRS)/RSh,
where Np and NS are, respectively, the number of parallel and series connections of cells in the given photovoltaic module (Np = 1 and Ns = 36), VPV=Voc=21.24V, Rs is the equivalent series resistance of the module, and Rshis the equivalent parallel resistance.The current leakages, the tunnel effect, breakdown by micro plasmas, leaks along surface channels, and so forth, are modeled as a parallel resistance. The parallel resistance has its greatest effect when the voltage is lowest, that is, when the current passing through the diode of the equivalent circuit is very small. The effect of parallel resistance, when it is sufficiently small, is to reduce the open-circuit voltage and the fill factor [16]. The short-circuit current is not affected by it.The graph between the relative efficiency of PV modules and isolation for various valuesRsh is shown in Figure 6 [17]. In the graph, it can be seen that for large values Rsh, the module efficiency at low values of isolation decreases by 3 to 5 percent.WhenRsh is very large, we can neglect the same. In such case simulation values would be higher than the actual values by 3 to 5 percent at low values of isolation only. However there would not be any appreciable variation at normal/higher values of isolation.The use of simplified circuit model in this paper makes this model suitable for power electronics designers who are looking for an easy and effective model for simulation of photovoltaic devices with power converters. The value of parallel resistanceRsh is generally high and hence neglected to simplify the model as given in (5).The series resistanceRs (0.1 Ω) is the sum of several structural resistances of the PV module and its influence is stronger especially near the maximum power point region.Equation (4) for the current output of PV module can be modified as
(5)IPV=NP*Iph-NP*I0[exp⁡{q*(VPV+IPVRs)NSAkT}-1].
The solution for (5) involves iteration and requires solving of algebraic loop in Simulink. To avoid this problem, the functional models are used in PV research for modeling of PV module.


### 2.8. Algebraic Loop Problem

Solving algebraic loop is an iterative process. A successful solution results only if the algebraic loop solver converges to a definite answer. Proper care is to be taken of the feedback loop to get quicker convergence. In this paper simplification of equation is done by excludingRsh.The iterative MATLAB/Simulink model of output currentIpv is shown in Figure 5.Figure 5
Module output currentIpv..Figure 6
Relative efficiency versus irradiation.


### 2.9. Simulink Model ofIPV

All the above four blocks are interconnected to get Simulink model ofIPV for the PV module. This model takes insolation, temperature, and VPV as inputs and calculates IPV. VPV is varied from 0 to 21.5 V. Simulink model of IPV is simulated with the setup shown in Figure 7.Figure 7
Simulation ofIpv Simulink model.Detailed discussion of simulation steps ofIpvmodel for obtaining I-V and P-V characteristics under varying irradiation with constant temperature and constant irradiation with varying temperature is available in [18].


### 2.10. Experimental Validation

The hardware for validating the results obtained in developed Simulink model is given in Figure9.The description of experimental circuit given in Figure8 is as follows.(i)
The Op-Amp, the MOSFET, and the resistorRsense are connected so that the current of the solar panel is proportional to the voltage applied to the noninverting port of the Op-Amp.(ii)
A linear MOSFET (IRF 150/IRF 460) is used. Gate-Source port of the MOSFET is driven by a low-frequency triangular wave signal.(iii)
DSO has been used and therefore repetitive trigger signal is not required and only a slow changing ramp signal is required to change the current from zero to the short-circuit value.(iv)
The experimental characteristics smoothened by curve fitting along with characteristics of Simulink model are shown in Figures10 and 11.Figure 8
Circuit for obtaining the experimental characteristics of PV module.Figure 9
Hardware setup of an electronic load with sample snapshot of DSO screen forV-I plot.Figure 10
Simulation and experimentalV-I characteristics.Figure 11
Simulation and experimentalP-V characteristics.It can be seen from Figure10 that the simulated value of current at λ=1000 W/m2 and  T=25 °C is 2.55 A while the experimental value of current is 2.49 A, giving a percentage error of 2.35.The simulated values of current using the developed model are higher than the experimental values of current by about 2% at higher values of insolation and hence the circuit model has reasonable accuracy.The above graph also shows that useful voltage output varies from 12 V to 19 V. The maximum power point for all these temperatures lies between these voltages.


## 2.1. Equivalent Circuit

A PV module consists of a number of solar cells connected in series and parallel to obtain the desired voltage and current output levels. Each solar cell is basically a p-n diode. As sunlight strikes a solar cell, the incident energy is converted directly into electrical energy without any mechanical effort.Transmitted light is absorbed within the semiconductor, by using this light energy to excite free electrons from a low energy status to an unoccupied higher energy level. When a solar cell is illuminated, excess electron-hole pairs are generated throughout the material, hence the p-n junction is electrically shorted and current flows.For simplicity, the single-diode model of Figure1 is used in this paper [15]. This model offers a good compromise between simplicity and accuracy with the basic structure consisting of a current source and a parallel diode. In Figure 1, Iph represents the cell photocurrent while Rsh and Rs are, respectively, the intrinsic shunt and series resistances of the cell.Figure 1
PV cell modeled as diode circuit.


## 2.2. Equations of PV Module

PV cells are grouped in larger units called PV modules, which are further interconnected in a series-parallel configuration to form PV arrays.The following are the basic equations from the theory of semiconductors and photovoltaics     [15] that mathematically describe the I-V characteristic of the photovoltaic cell and module.


## 2.3. Photocurrent

In Figure1, the module photocurrent Iph of the photovoltaic module depends linearly on the solar irradiation and is also influenced by the temperature according to the following equation:
(1)Iph=[ISCr+Ki(Tk-Tref)]*λ1000,
where Iph [A] is the light-generated current at the nominal condition (25°C and 1000 W/m2), Ki   is the short-circuit current/temperature coefficient (0.0017A/K), Tk and Tref are, respectively, the actual and reference temperatures in K, λ is the irradiation on the device surface (W/m2), and the nominal irradiation is 1000 W/m2.Detailed Simulink model of (1) of photocurrent Iph is shown in Figure 2. The value of module short-circuit current  is ISCr taken from the datasheet of the reference model as given in Section 2.4.Figure 2
Photocurrent.Iph for different values of insolation and temperature is shown in Table 1.Table 1
Iph for various insolations and temperatures.
S. no.Insol W/m2Value ofIph (A)25°C30°C40°C50°C90°C110002.552.5592.5752.5922.6627001.7851.7911.8031.8151.86235001.2751.2791.2881.2961.3342500.63750.63960.64890.64810.665151000.2550.25590.25760.25920.2661


## 2.4. Reference Model

Solkar make 36 W PV module is taken as the reference module for simulation and the datasheet details are given in Table2Table 2
Electrical characteristic data of solkar 36 W PV module.
DescriptionRatingRated power37.08 WpVoltage at maximum power (Vmp)16.56 VCurrent at maximum power (Imp)2.25 AOpen circuit voltage (VOC)21.24 VShort circuit current (ISCr)2.55 ATotal number of cells in series (Ns)36Total number of cells in parallel (Np)1Note. The electrical specifications are under standard test conditions (STCs) which means an irradiation of 1000 W/m2 with an AM1.5 spectrum at 25°C.


## 2.5. Module Reverse Saturation Current

Module reverse saturation current,Irs,is given by (2) as follows. 								(2)Irs=ISCr[exp⁡(qVOC/NSkAT)-1],
where q is the electron charge (1.6 × 10-19C),Voc is the Solkar module open-circuit voltage (21.24 V), Ns is the number of cells connected in series (36), k is the Boltzmann constant (1.3805 × 10−23 J/K), and A is the ideality factor (1.6).Detailed Simulink model of (2) is shown in Figure 3.Figure 3
Module reverse saturation current.Module reverse saturation current varies with temperature as shown in Table3.Table 3
Irs for various temperatures.
S. no.Temperature °CModule reverse saturation current (A)1251.182* 10(−006)2301.503* 10(−006)3402.377* 10(−006)4503.654* 10(−006)5901.609* 10(−005)


## 2.6. Module Saturation CurrentI0

The module saturation currentI0 varies with the cell temperature and is given by
(3)I0=Irs[TTr]3exp⁡[q*Eg0Ak{1Tr-1T}],
where Eg0 is the bandgap energy of the semiconductor (Eg0≈ 1.1 eV for the polycrystalline Si at 25°C).This equation is simulated and shown in Figure4. The module operating temperature, reference temperature, and module reverse saturation current are taken as inputs.Figure 4
Module saturation current.The module saturation currentI0 is calculated for various temperatures and is given in Table 4.Table 4
I0 for various temperatures.
S. no.Temperature °CModule saturation current (A)1251.182* 10(−006)2302.456* 10(−006)3409.92* 10(−006)4503.686* 10(−005)5900.003491


## 2.7. Module Output CurrentIPV

The basic equation that describes the current output of PV moduleIPV of the single-diode model presented in Figure 1 is given by
(4)IPV=NP*Iph-NP*I0[exp⁡{q*(VPV+IPVRs)NSAkT}-1]-VPV+(IPVRS)/RSh,
where Np and NS are, respectively, the number of parallel and series connections of cells in the given photovoltaic module (Np = 1 and Ns = 36), VPV=Voc=21.24V, Rs is the equivalent series resistance of the module, and Rshis the equivalent parallel resistance.The current leakages, the tunnel effect, breakdown by micro plasmas, leaks along surface channels, and so forth, are modeled as a parallel resistance. The parallel resistance has its greatest effect when the voltage is lowest, that is, when the current passing through the diode of the equivalent circuit is very small. The effect of parallel resistance, when it is sufficiently small, is to reduce the open-circuit voltage and the fill factor [16]. The short-circuit current is not affected by it.The graph between the relative efficiency of PV modules and isolation for various valuesRsh is shown in Figure 6 [17]. In the graph, it can be seen that for large values Rsh, the module efficiency at low values of isolation decreases by 3 to 5 percent.WhenRsh is very large, we can neglect the same. In such case simulation values would be higher than the actual values by 3 to 5 percent at low values of isolation only. However there would not be any appreciable variation at normal/higher values of isolation.The use of simplified circuit model in this paper makes this model suitable for power electronics designers who are looking for an easy and effective model for simulation of photovoltaic devices with power converters. The value of parallel resistanceRsh is generally high and hence neglected to simplify the model as given in (5).The series resistanceRs (0.1 Ω) is the sum of several structural resistances of the PV module and its influence is stronger especially near the maximum power point region.Equation (4) for the current output of PV module can be modified as
(5)IPV=NP*Iph-NP*I0[exp⁡{q*(VPV+IPVRs)NSAkT}-1].
The solution for (5) involves iteration and requires solving of algebraic loop in Simulink. To avoid this problem, the functional models are used in PV research for modeling of PV module.


## 2.8. Algebraic Loop Problem

Solving algebraic loop is an iterative process. A successful solution results only if the algebraic loop solver converges to a definite answer. Proper care is to be taken of the feedback loop to get quicker convergence. In this paper simplification of equation is done by excludingRsh.The iterative MATLAB/Simulink model of output currentIpv is shown in Figure 5.Figure 5
Module output currentIpv..Figure 6
Relative efficiency versus irradiation.


## 2.9. Simulink Model ofIPV

All the above four blocks are interconnected to get Simulink model ofIPV for the PV module. This model takes insolation, temperature, and VPV as inputs and calculates IPV. VPV is varied from 0 to 21.5 V. Simulink model of IPV is simulated with the setup shown in Figure 7.Figure 7
Simulation ofIpv Simulink model.Detailed discussion of simulation steps ofIpvmodel for obtaining I-V and P-V characteristics under varying irradiation with constant temperature and constant irradiation with varying temperature is available in [18].


## 2.10. Experimental Validation

The hardware for validating the results obtained in developed Simulink model is given in Figure9.The description of experimental circuit given in Figure8 is as follows.(i)
The Op-Amp, the MOSFET, and the resistorRsense are connected so that the current of the solar panel is proportional to the voltage applied to the noninverting port of the Op-Amp.(ii)
A linear MOSFET (IRF 150/IRF 460) is used. Gate-Source port of the MOSFET is driven by a low-frequency triangular wave signal.(iii)
DSO has been used and therefore repetitive trigger signal is not required and only a slow changing ramp signal is required to change the current from zero to the short-circuit value.(iv)
The experimental characteristics smoothened by curve fitting along with characteristics of Simulink model are shown in Figures10 and 11.Figure 8
Circuit for obtaining the experimental characteristics of PV module.Figure 9
Hardware setup of an electronic load with sample snapshot of DSO screen forV-I plot.Figure 10
Simulation and experimentalV-I characteristics.Figure 11
Simulation and experimentalP-V characteristics.It can be seen from Figure10 that the simulated value of current at λ=1000 W/m2 and  T=25 °C is 2.55 A while the experimental value of current is 2.49 A, giving a percentage error of 2.35.The simulated values of current using the developed model are higher than the experimental values of current by about 2% at higher values of insolation and hence the circuit model has reasonable accuracy.The above graph also shows that useful voltage output varies from 12 V to 19 V. The maximum power point for all these temperatures lies between these voltages.


## 3. Circut-Oriented Model of PV Module

In the equivalent circuit of a PV cell, as shown in Figure1, the voltage available across the PV cell is nothing but the PN junction forward bias voltage of 0.6 V. The open-circuit voltage of the PV module is 21.24 V/36 cells = 0.594 V ≈ 0.6 V.Simulink model ofIPV, developed in Section 2, provides the module current IPV. This PV current is calculated from irradiation and temperature and is the input to be used directly in the circuit model.The voltage at the output terminal of the model is fed back as the voltage inputVin for Simulink model of IPV [10]. A small resistance of 0.01 Ω is added to the circuit to aid the charging of capacitor normally used with the current source.The detailed circuit model of PV module is shown in Figure12. The circuit model block of PV module is given in Figure 13.Figure 12
Detailed circuit model of PV module.Figure 13
Circuit model block of PV module.Further, the forward bias voltage of the diode shown in Figure12 is taken as 19 V (as it represents the series connection of 36 PV cells) which is the higher value of useful voltage level.Here, a voltage value is chosen initially and the iteration of power equation is carried out as done in normal functional PV model as it involves the algebraic loop problem.


## 4. Design of PV Maximum Power Extraction System

With the variation of irradiation and temperature, the power output of PV module varies continuously. The maximum power point tracking (MPPT) algorithm is used for extracting the maximum power from the solar PV module and transferring that power to the load [15]. A DC-DC converter (step up/step down), as shown in Figure 14, serves the purpose of transferring maximum power from the PV module to the load and acts as an interface between the load and the module.Figure 14
DC-DC converter for operation at the MPP.By changing the duty cycle of the PWM control signal, the load impedance as seen by the source varies and matches the point of the peak power of the source so as to transfer the maximum power.


### 4.1. Power Electronic Circuit

The PV modules are always used with DC-to-DC converters to obtain the maximum power point operation. The types of converters used are buck, boost, and buck-boost. For battery charging applications buck-boost configuration is preferred where as boost converters are used for grid-connected applications. DC-DC boost converters are used often in PV systems to step up the low module voltage to higher load voltages. Hence, DC-DC boost converter is used for the design of MPPT controller.


### 4.2. Design of DC-DC Boost Converter

The boost converter configuration, as shown in Figure15, consists of a DC input voltage source Vs, boost inductor L, controlled switchS, diode D, filter capacitor C, and load resistance R.Figure 15
Configuration of DC to DC boost converter.If the switch operates with a duty ratioD, the DC voltage gain of the boost converter is given by
(6)Mv=VoVs=11-D,
where Vsis input voltage,Vo is output voltage, and D is the duty cycle of the pulse width modulation (PWM) signal used to control the MOSFET ON and OFF states.The boost converter operates in the continuous conduction mode for value of inductanceL>Lb where,(7)Lb=(1-D2)DR2f,
where Lb is the minimum value of inductance for continuous conduction.The current supplied to the output RC circuit is discontinuous. Thus, a larger filter capacitor is required to limit the output voltage ripple. The minimum value of filter capacitor that provides the output DC current to the load when the diodeD is off is given by Cmin. The minimum value of the filter capacitance, that results in the ripple voltage Vc, is given by
(8)Cmin⁡=DVoVrRF.Designed component values of  DC-to-DC boost converter used for simulation are given in Table5.Table 5
Component values of DC-to-DC boost converter.
DescriptionRatingInductor120μHMOSFETIRF P460Power diode1N5408Capacitor330μFResistive load50 Ω, 50 WSwitching frequency20 kHz


### 4.3. Design of MPPT

The DC-DC converter (with configuration given in Figure15 and component values in Table 5) is simulated with battery supply as shown in Figure 16.Figure 16
Boost converter circuit with DC supply.With DC supply, the converter voltage boost ratio is directly proportional to the duty cycle.The battery supply in circuit shown in Figure16 is replaced by the developed circuit model in Section 3 and simulated as shown in Figure 17.Figure 17
Boost converter circuit with PV input.The detailed experimental verification with circuit response of this developed circuit model is available in [19].For the design of MPPT, the data is collected through simulation with the developed circuit model and results are tabulated in Table6.Table 6
Duty cycle variation.
Duty cycleInput voltage (V)Input current (A)Input power (WP)Output voltage (V)Output current (A)Output power (W)Irradiation—1000 W/m2 Temp—25°C0.417.822.05936.6940.080.810632.130.4116.72.30338.4640.450.808932.720.515.052.4436.7239.060.781230.52Irradiation—700 W/m2 Temp—25°C0.317.61.37524.2132.460.649221.08Irradiation—500 W/m2Temp—25°C0.217.640.866115.2825.760.51513.27From Table6, it can be seen that for lower values of irradiation and constant load, the duty cycle has to be reduced from 0.41 for irradiation of 1000 W/m2 to 0.2 for irradiation of 500 W/m2. This variation coincides with the graph shown in Figure 18, as found in [20], where the duty cycle variation with respect to irradiation is reported.Figure 18
Duty cycle variation with respect to irradiation.


### 4.4. MPPT Control Algorithm

Many MPPT techniques have been proposed in the literature; examples are the Perturb and Observe (P&O), Incremental Conductance (IC), Fuzzy Logic, and so forth. The P&O algorithm is very popular and simple. So it is used in this paper. The power graph for P&O algorithm is shown in Figure19.Figure 19
Power graph for P and O algorithm.In P&O algorithm, a slight perturbation (ΔD=0.01) is introduced in the system. This perturbation causes the power of the solar module to change. If the power increases due to the perturbation, then the perturbation is continued (D+ΔD) in that direction. After the peak power is reached, the power at the next instant decreases and after that the perturbation reverses (D-ΔD). The flow chart of MPPT algorithm is shown in Figure 20.Figure 20
Flow chart of  P&O MPPT algorithm.The Simulink model for P & O MPPT algorithm is shown in Figure21. Vin and Iin are taken as input to the MPPT unit and duty cycle is obtained as the output.Figure 21
Simulink model for P&O MPPT algorithm.The above MPPT unit is placed as closed-loop control in the simulation circuit, as shown in Figure17 and the detailed Simulink model for closed-loop control of developed circuit model of PV module with MPPT control unit is shown in Figure 22.Figure 22
MPPT control circuit.


## 4.1. Power Electronic Circuit

The PV modules are always used with DC-to-DC converters to obtain the maximum power point operation. The types of converters used are buck, boost, and buck-boost. For battery charging applications buck-boost configuration is preferred where as boost converters are used for grid-connected applications. DC-DC boost converters are used often in PV systems to step up the low module voltage to higher load voltages. Hence, DC-DC boost converter is used for the design of MPPT controller.


## 4.2. Design of DC-DC Boost Converter

The boost converter configuration, as shown in Figure15, consists of a DC input voltage source Vs, boost inductor L, controlled switchS, diode D, filter capacitor C, and load resistance R.Figure 15
Configuration of DC to DC boost converter.If the switch operates with a duty ratioD, the DC voltage gain of the boost converter is given by
(6)Mv=VoVs=11-D,
where Vsis input voltage,Vo is output voltage, and D is the duty cycle of the pulse width modulation (PWM) signal used to control the MOSFET ON and OFF states.The boost converter operates in the continuous conduction mode for value of inductanceL>Lb where,(7)Lb=(1-D2)DR2f,
where Lb is the minimum value of inductance for continuous conduction.The current supplied to the output RC circuit is discontinuous. Thus, a larger filter capacitor is required to limit the output voltage ripple. The minimum value of filter capacitor that provides the output DC current to the load when the diodeD is off is given by Cmin. The minimum value of the filter capacitance, that results in the ripple voltage Vc, is given by
(8)Cmin⁡=DVoVrRF.Designed component values of  DC-to-DC boost converter used for simulation are given in Table5.Table 5
Component values of DC-to-DC boost converter.
DescriptionRatingInductor120μHMOSFETIRF P460Power diode1N5408Capacitor330μFResistive load50 Ω, 50 WSwitching frequency20 kHz


## 4.3. Design of MPPT

The DC-DC converter (with configuration given in Figure15 and component values in Table 5) is simulated with battery supply as shown in Figure 16.Figure 16
Boost converter circuit with DC supply.With DC supply, the converter voltage boost ratio is directly proportional to the duty cycle.The battery supply in circuit shown in Figure16 is replaced by the developed circuit model in Section 3 and simulated as shown in Figure 17.Figure 17
Boost converter circuit with PV input.The detailed experimental verification with circuit response of this developed circuit model is available in [19].For the design of MPPT, the data is collected through simulation with the developed circuit model and results are tabulated in Table6.Table 6
Duty cycle variation.
Duty cycleInput voltage (V)Input current (A)Input power (WP)Output voltage (V)Output current (A)Output power (W)Irradiation—1000 W/m2 Temp—25°C0.417.822.05936.6940.080.810632.130.4116.72.30338.4640.450.808932.720.515.052.4436.7239.060.781230.52Irradiation—700 W/m2 Temp—25°C0.317.61.37524.2132.460.649221.08Irradiation—500 W/m2Temp—25°C0.217.640.866115.2825.760.51513.27From Table6, it can be seen that for lower values of irradiation and constant load, the duty cycle has to be reduced from 0.41 for irradiation of 1000 W/m2 to 0.2 for irradiation of 500 W/m2. This variation coincides with the graph shown in Figure 18, as found in [20], where the duty cycle variation with respect to irradiation is reported.Figure 18
Duty cycle variation with respect to irradiation.


## 4.4. MPPT Control Algorithm

Many MPPT techniques have been proposed in the literature; examples are the Perturb and Observe (P&O), Incremental Conductance (IC), Fuzzy Logic, and so forth. The P&O algorithm is very popular and simple. So it is used in this paper. The power graph for P&O algorithm is shown in Figure19.Figure 19
Power graph for P and O algorithm.In P&O algorithm, a slight perturbation (ΔD=0.01) is introduced in the system. This perturbation causes the power of the solar module to change. If the power increases due to the perturbation, then the perturbation is continued (D+ΔD) in that direction. After the peak power is reached, the power at the next instant decreases and after that the perturbation reverses (D-ΔD). The flow chart of MPPT algorithm is shown in Figure 20.Figure 20
Flow chart of  P&O MPPT algorithm.The Simulink model for P & O MPPT algorithm is shown in Figure21. Vin and Iin are taken as input to the MPPT unit and duty cycle is obtained as the output.Figure 21
Simulink model for P&O MPPT algorithm.The above MPPT unit is placed as closed-loop control in the simulation circuit, as shown in Figure17 and the detailed Simulink model for closed-loop control of developed circuit model of PV module with MPPT control unit is shown in Figure 22.Figure 22
MPPT control circuit.


## 5. Hardware Implementation

The schematic diagram of the proposed hardware system is shown in Figure23.(i)
The DC-DC boost converter acts as an interface between the PV module and the load.(ii)
The voltage and current output are sensed and an error signal in digital is generated by the software.(iii)
The error signal in digital form is given to the DAC (0808) which converts it to the corresponding analog signal.(iii)
This signal is then compared with a high-frequency triangular wave of 20 kHz. The pulse generated given is to the gate of the power semiconductor device (MOSFET), thereby changing the duty cycle of the converter.(iv)
This generated pulse must be able to trigger the power circuit of the MOSFET.(v)
Thus the source impedance is matched with the load impedance and maximum power is transferred.Figure 23
Proposed hardware system.The hardware setup of the proposed system is shown in Figure24. The microcontroller programming should be fed with the required range of duty cycle as given in Table 6 for quicker response.Figure 24
Hardware of MPPT.The experiment is carried out for 1000 W/m2 at 25°C. The experimental values of PV module power and current are lower by about 2 to 5 percent compared to the simulation values, as shown in Figure 25.Figure 25
Variation of current, power for variable irradiation with experimental results.Thus the performance of the developed circuit model, in closed-loop control, follows the simulation values with reasonable accuracy.


## 6. Results and Discussion

In Section2, in (1) and Figure 1, it can be seen that the PV current Iph is a function of the solar irradiation and is the only energy conversion process in which light energy is converted to electrical energy.The next two equations, (2) and (3), indicate that the PV voltage is a function of the junction voltage of diode, which is the material property of the semiconductors, susceptible to failure at higher temperatures. The physical equations governing the PV module (also applicable to PV cell) is elaborately presented with numerical values of module saturation current at various temperatures. Hence, this circuit model presents the relationship between module parameters and circuit performance.In Section3, voltage level of the PV module is selected as 19 V. However, for functional PV models used in other papers, the voltage level for the iterative process is chosen as per the convenience of end-circuit requirements and affect the circuit performance considerably. This has an effect on the temperature performance of the circuit. So the selection of this voltage level which is very important has to be selected appropriately.


## 7. Conclusion

Circuit model of photovoltaic (PV) module is presented in this paper, which can be used as a common platform by material scientists as well as power electronic circuit designers to develop the better PV power plant.



---

*Source: 410401-2012-03-28.xml*