application of circuit model for photovoltaic energy conversion

Hindawi Publishing CorporationInternational Journal of PhotoenergyVolume 2012, Article ID 410401, 14 pagesdoi:10.1155/2012/410401

Research Article

Application of Circuit Model for PhotovoltaicEnergy Conversion System

Natarajan Pandiarajan, Ramabadran Ramaprabha, and Ranganath Muthu

Department of Electrical & Electronics Engineering, SSN College of Engineering, Kalavakkam 603110, India

Correspondence should be addressed to Natarajan Pandiarajan, [email protected]

Received 15 August 2011; Revised 11 November 2011; Accepted 15 November 2011

Academic Editor: Songyuan Dai

Copyright © 2012 Natarajan Pandiarajan et al. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

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

1. Introduction

The field of photovoltaics (PV) has experienced a remarkablegrowth for past two decades in its widespread use fromstandalone to utility interactive PV systems. The best wayto utilize the electric energy produced by the PV array isto deliver it to the AC mains directly, without using batterybanks [1].

A recent study in Germany, of 21 PV systems in operationfor 10 years, revealed that inverters contributed for 63% offailures, modules 15%, and other components 23%, witha failure occurring, on an average, every 4.5 years [2]. Toreduce the failure rate of PV systems, it is necessary to reducethe failure rate of inverters and components also called thePV balance of systems (BOSs) that would result in theireconomic viability.

At present, PV BOS research uses mathematical func-tional models for the performance analysis of newly devel-oped systems. These developed systems could not be readilyadopted by the field professionals and hence the above failurerate. Hence the need for simplified Simulink modeling of PVmodule has been long felt.

Simple circuit-based PV models have been proposedin the literature [3–12]. Some authors have proposedindirect methods to adjust the I-V curve through artificialintelligence [13, 14]. Although interesting, such methods

are impractical, complicated and require high computationaleffort. In all the above, modeling was limited to simulation ofPV module characteristics.

In this paper, the design of PV system using simplecircuit model with detailed circuit modeling of PV moduleis presented. In Section 2, the physical equations governingthe PV module (also applicable to PV cell) are presented.Simulink model for each equation is presented with numer-ical results for different values of irradiation and temper-ature. The tabulation of the above numerical results givesthe relationship of module parameters with characteristicscurves of PV module, which are the indicators of circuitperformance. In Section 3, complete circuit model is evolvedafter due experimental verification. In Section 4, modelingof MPPT using perturb and observe (P&O) algorithm iscarried out using Simulink. The operation of developedcircuit model with DC to DC boost converter for closed-loop MPPT control is verified with simulation. Section 5presents 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 numberof solar cells connected in series and parallel to obtain the

2 International Journal of Photoenergy

Ideal PV cell

Practical PV device

I

VIPh ↓

→

I0 Rp

Rs

Figure 1: PV cell modeled as diode circuit.

2.25

Product

1

25

25

2.55

273

Product

Temp

++

Insolation

0.0017

Temp coeff Ki

×

×

++

++

++

Tk

ISC

Iph

Tref

Figure 2: Photocurrent.

desired voltage and current output levels. Each solar cell isbasically a p-n diode. As sunlight strikes a solar cell, theincident energy is converted directly into electrical energywithout any mechanical effort.

Transmitted light is absorbed within the semiconductor,by using this light energy to excite free electrons from alow energy status to an unoccupied higher energy level.When a solar cell is illuminated, excess electron-hole pairs aregenerated throughout the material, hence the p-n junction iselectrically shorted and current flows.

For simplicity, the single-diode model of Figure 1 is usedin this paper [15]. This model offers a good compromisebetween simplicity and accuracy with the basic structureconsisting of a current source and a parallel diode. InFigure 1, Iph represents the cell photocurrent while Rsh andRs are, respectively, the intrinsic shunt and series resistancesof the cell.

2.2. Equations of PV Module. PV cells are grouped in largerunits called PV modules, which are further interconnected ina series-parallel configuration to form PV arrays.

The following are the basic equations from the theory ofsemiconductors and photovoltaics [15] that mathematically

describe the I-V characteristic of the photovoltaic cell andmodule.

2.3. Photocurrent. In Figure 1, the module photocurrentIph of the photovoltaic module depends linearly on thesolar irradiation and is also influenced by the temperatureaccording to the following equation:

Iph = [ISCr + Ki(Tk − Tref)] ∗ λ

1000, (1)

where Iph [A] is the light-generated current at the nominalcondition (25◦C and 1000 W/m2), Ki is the short-circuitcurrent/temperature coefficient (0.0017A/K), Tk and Tref are,respectively, the actual and reference temperatures in K , λis the irradiation on the device surface (W/m2), and thenominal irradiation is 1000 W/m2.

Detailed Simulink model of (1) of photocurrent Iph isshown in Figure 2. The value of module short-circuit currentis ISCr taken from the datasheet of the reference model asgiven in Section 2.4.

Iph for different values of insolation and temperature isshown in Table 1.

International Journal of Photoenergy 3

2.55

1

Constant

363

Fcn

A

T

36

1.6 Product

21.24

Isc

Irs

÷÷

÷

÷

1.609e − 005(u(1))/(exp(u(2))− u(1))

1.3805∗10(−23)

1.6∗10(−19)

Voc

Ns

k

q ××

Figure 3: Module reverse saturation current.

x

0. 003491

Mod sat current

Fcn 1

Product5

Constant

Fcn

Product4

Product1

Product3

Product2

Eg

296

363

1

1.1

1.6

A

1.3805∗10(−23)

k

q

1.6∗10(−19)

×÷

×÷

×÷

×

××

÷

÷

Irs

Tak

Trk

-C-

(u(1))3

exp(u(1))

+−

Figure 4: Module saturation current.

Table 1: Iph for various insolations and temperatures.

S. no. Insol W/m2 Value of Iph (A)

25◦C 30◦C 40◦C 50◦C 90◦C

1 1000 2.55 2.559 2.575 2.592 2.66

2 700 1.785 1.791 1.803 1.815 1.862

3 500 1.275 1.279 1.288 1.296 1.33

4 250 0.6375 0.6396 0.6489 0.6481 0.6651

5 100 0.255 0.2559 0.2576 0.2592 0.2661

2.4. Reference Model. Solkar make 36 W PV module is takenas the reference module for simulation and the datasheetdetails are given in Table 2

2.5. Module Reverse Saturation Current. Module reversesaturation current, Irs, is given by (2) as follows.

Irs = ISCr[exp(qVOC/NSkAT

) − 1] , (2)

where q is the electron charge (1.6 × 10−19 C), Voc is theSolkar module open-circuit voltage (21.24 V), Ns is the


1

0.1

1

3

2

4

1.6∗10(−19)

q

Is − u(4)

Iph − u(3)

Vpv − u(1)

NsAkT

Ipv

Rs

u(3)− u(4)x(exp((u(2)x(u(1) + u(6)))/(u(5)))− 1)

Figure 5: Module output current Ipv..

100

95

0 400 600200 800 1000

90

85

80

75

Irradiation (W/m2)

Rsh = 5–10 ohmRsh = 20–30 ohm

Rsh = 10–20 ohm

Rsh < 50 ohmRsh > 30 ohm

Rel

. mod

ule

effi

cien

cy (

%)

Figure 6: Relative efficiency versus irradiation.

Table 2: Electrical characteristic data of solkar 36 W PV module.

Description Rating

Rated power 37.08 Wp

Voltage at maximum power (Vmp) 16.56 V

Current at maximum power (Imp) 2.25 A

Open circuit voltage (VOC) 21.24 V

Short circuit current (ISCr) 2.55 A

Total number of cells in series (Ns) 36

Total number of cells in parallel (Np) 1

Note. 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.

number of cells connected in series (36), k is the Boltzmannconstant (1.3805 × 10−23 J/K), and A is the ideality factor(1.6).

Table 3: Irs for various temperatures.

S. no. Temperature ◦C Module reverse saturation current (A)

1 25 1.182 ∗ 10(−006)

2 30 1.503 ∗ 10(−006)

3 40 2.377 ∗ 10(−006)

4 50 3.654 ∗ 10(−006)

5 90 1.609 ∗ 10(−005)

Table 4: I0 for various temperatures.

S. no. Temperature ◦C Module saturation current (A)

1 25 1.182 ∗ 10(−006)

2 30 2.456 ∗ 10(−006)

3 40 9.92 ∗ 10(−006)

4 50 3.686 ∗ 10(−005)

5 90 0.003491

Detailed Simulink model of (2) is shown in Figure 3.Module reverse saturation current varies with tempera-

ture as shown in Table 3.

2.6. Module Saturation Current I0. The module saturationcurrent I0 varies with the cell temperature and is given by

I0 = Irs

[T

Tr

]3

exp

[q ∗ Eg0

Ak

{1Tr− 1

T

}]

, (3)

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 Figure 4. Themodule operating temperature, reference temperature, andmodule reverse saturation current are taken as inputs.

The module saturation current I0 is calculated for varioustemperatures and is given in Table 4.


PV module: Simulink modelPV current

Temp

25

Insolation

Product

PV power

PV power

Irradiation

Ppv

i -V ch

×VoutVin

Inso

Temp Ipv

Ipv

Ppv

Workspace Ppv

Workspace Ipv

Workspace Vpv

Vpv

Vpv

Ipv

Vpv

Figure 7: Simulation of Ipv Simulink model.

CRO

or

IRF150

RPS

uA 741

PV Module

+(−

−

)

−(+

+

)

Yn

Xn

Vtraiangular

Vramp

∼Rsense

VPS

Figure 8: Circuit for obtaining the experimental characteristics of PV module.

μA 741 Op-amp

-Waveform

generator ICICL8038

MOSFETIRF 460

From PV

module

resistor

Currentsensing

Figure 9: Hardware setup of an electronic load with sample snapshot of DSO screen for V-I plot.


Voltage (V)

Cu

rren

t (A

)

0.5

0 15 20105

1

1.5

2.5

SimulationExperimental

2

0 15105

Figure 10: Simulation and experimental V-I characteristics.

Voltage (V)

Pow

er (

Wp)

00 15 20105

10

20

30

SimulationExperimental

Figure 11: Simulation and experimental P-V characteristics.

2.7. Module Output Current IPV. The basic equation thatdescribes the current output of PV module IPV of the single-diode model presented in Figure 1 is given by

IPV = NP ∗ Iph −NP ∗ I0

[

exp

{q ∗ (VPV + IPVRs)

NSAkT

}

− 1

]

−VPV + (IPVRS)/RSh,(4)

where Np and NS are, respectively, the number of parallel andseries connections of cells in the given photovoltaic module(Np = 1 and Ns = 36), VPV = Voc = 21.24V , Rs is theequivalent series resistance of the module, and Rsh is theequivalent parallel resistance.

The current leakages, the tunnel effect, breakdown bymicro plasmas, leaks along surface channels, and so forth, aremodeled as a parallel resistance. The parallel resistance hasits greatest effect when the voltage is lowest, that is, when thecurrent passing through the diode of the equivalent circuitis very small. The effect of parallel resistance, when it issufficiently small, is to reduce the open-circuit voltage andthe fill factor [16]. The short-circuit current is not affectedby it.

The graph between the relative efficiency of PV modulesand isolation for various values Rsh is shown in Figure 6 [17].In the graph, it can be seen that for large values Rsh, themodule efficiency at low values of isolation decreases by 3to 5 percent.

When Rsh is very large, we can neglect the same. Insuch case simulation values would be higher than the actualvalues by 3 to 5 percent at low values of isolation only.However there would not be any appreciable variation atnormal/higher values of isolation.

The use of simplified circuit model in this paper makesthis model suitable for power electronics designers who arelooking for an easy and effective model for simulation ofphotovoltaic devices with power converters. The value ofparallel resistance Rsh is generally high and hence neglectedto simplify the model as given in (5).

The series resistance Rs (0.1Ω) is the sum of severalstructural resistances of the PV module and its influence isstronger especially near the maximum power point region.

Equation (4) for the current output of PV module can bemodified as

IPV = NP ∗ Iph −NP ∗ I0

[

exp

{q ∗ (VPV + IPVRs)

NSAkT

}

− 1

]

.

(5)

The solution for (5) involves iteration and requires solvingof algebraic loop in Simulink. To avoid this problem, thefunctional models are used in PV research for modeling ofPV module.

2.8. Algebraic Loop Problem. Solving algebraic loop is aniterative process. A successful solution results only if thealgebraic loop solver converges to a definite answer. Propercare is to be taken of the feedback loop to get quickerconvergence. In this paper simplification of equation is doneby excluding Rsh.

The iterative MATLAB/Simulink model of output cur-rent Ipv is shown in Figure 5.

2.9. Simulink Model of IPV. All the above four blocks areinterconnected to get Simulink model of IPV for the PVmodule. 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 inFigure 7.

Detailed discussion of simulation steps of Ipv model forobtaining I-V and P-V characteristics under varying irradia-tion with constant temperature and constant irradiation withvarying temperature is available in [18].

2.10. Experimental Validation. The hardware for validatingthe results obtained in developed Simulink model is given inFigure 9.

The description of experimental circuit given in Figure 8is as follows.

(i) The Op-Amp, the MOSFET, and the resistor Rsense

are connected so that the current of the solar


s

Diode Voltage measurement

PV Current

2

1

Continuous

Powergui

2

1

Insolation

Temp

Inso

Temp

PV module: Simulink model

Vin

Ipv

Rs

+V

−V

−0.01

Figure 12: Detailed circuit model of PV module.

+V

−VTemp

Insolation

Figure 13: Circuit model block of PV module.

panel is proportional to the voltage applied to thenoninverting 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 triggersignal is not required and only a slow changing rampsignal is required to change the current from zero tothe short-circuit value.

(iv) The experimental characteristics smoothened bycurve fitting along with characteristics of Simulinkmodel are shown in Figures 10 and 11.

It can be seen from Figure 10 that the simulated value ofcurrent at λ = 1000 W/m2 and T = 25 ◦C is 2.55 A while theexperimental value of current is 2.49 A, giving a percentageerror of 2.35.

The simulated values of current using the developedmodel are higher than the experimental values of current byabout 2% at higher values of insolation and hence the circuitmodel has reasonable accuracy.

The above graph also shows that useful voltage outputvaries from 12 V to 19 V. The maximum power point for allthese temperatures lies between these voltages.

3. Circut-Oriented Model of PV Module

In the equivalent circuit of a PV cell, as shown in Figure 1,the voltage available across the PV cell is nothing but thePN junction forward bias voltage of 0.6 V. The open-circuitvoltage of the PV module is 21.24 V/36 cells = 0.594 V ≈0.6 V.

Simulink model of IPV, developed in Section 2, providesthe module current IPV. This PV current is calculated fromirradiation and temperature and is the input to be useddirectly in the circuit model.

The voltage at the output terminal of the model is fedback as the voltage input Vin for Simulink model of IPV [10].A small resistance of 0.01Ω is added to the circuit to aid thecharging of capacitor normally used with the current source.

The detailed circuit model of PV module is shown inFigure 12. The circuit model block of PV module is given inFigure 13.

Further, the forward bias voltage of the diode shownin Figure 12 is taken as 19 V (as it represents the seriesconnection of 36 PV cells) which is the higher value of usefulvoltage level.

Here, a voltage value is chosen initially and the iterationof power equation is carried out as done in normal functionalPV model as it involves the algebraic loop problem.

4. Design of PV Maximum PowerExtraction System

With the variation of irradiation and temperature, thepower output of PV module varies continuously. The max-imum power point tracking (MPPT) algorithm is used forextracting the maximum power from the solar PV moduleand transferring that power to the load [15]. A DC-DCconverter (step up/step down), as shown in Figure 14, servesthe purpose of transferring maximum power from the PVmodule to the load and acts as an interface between the loadand the module.


MPPT

PWM control signal

PV current and voltage sensing

PV moduleDC/DCconverter

Load

PV power calculation andPWM duty-cycle

adjustment

Figure 14: DC-DC converter for operation at the MPP.

D

SC

++

+VS

VL

iS iC

−

−

−

L

Vo

IoIL

Figure 15: Configuration of DC to DC boost converter.

By changing the duty cycle of the PWM control signal,the load impedance as seen by the source varies and matchesthe point of the peak power of the source so as to transfer themaximum power.

4.1. Power Electronic Circuit. The PV modules are alwaysused with DC-to-DC converters to obtain the maximumpower point operation. The types of converters used arebuck, boost, and buck-boost. For battery charging applica-tions buck-boost configuration is preferred where as boostconverters are used for grid-connected applications. DC-DCboost converters are used often in PV systems to step up thelow module voltage to higher load voltages. Hence, DC-DCboost converter is used for the design of MPPT controller.

4.2. Design of DC-DC Boost Converter. The boost converterconfiguration, as shown in Figure 15, consists of a DC inputvoltage source Vs, boost inductor L, controlled switch S,diode D, filter capacitor C, and load resistance R.

If the switch operates with a duty ratio D, the DC voltagegain of the boost converter is given by

Mv = Vo

Vs= 1

1−D, (6)

where Vs is input voltage, Vo is output voltage, and D is theduty cycle of the pulse width modulation (PWM) signal usedto control the MOSFET ON and OFF states.

Table 5: Component values of DC-to-DC boost converter.

Description Rating

Inductor 120 μH

MOSFET IRF P460

Power diode 1N5408

Capacitor 330 μF

Resistive load 50Ω, 50 W

Switching frequency 20 kHz

The boost converter operates in the continuous conduc-tion mode for value of inductance L > Lb where,

Lb =(1−D2

)DR

2 f, (7)

where Lb is the minimum value of inductance for continuousconduction.

The current supplied to the output RC circuit is discon-tinuous. Thus, a larger filter capacitor is required to limit theoutput voltage ripple. The minimum value of filter capacitorthat provides the output DC current to the load when thediode D is off is given by C min. The minimum value of thefilter capacitance, that results in the ripple voltage Vc, is givenby

Cmin = DVo

VrRF. (8)

Designed component values of DC-to-DC boost con-verter used for simulation are given in Table 5.

4.3. Design of MPPT. The DC-DC converter (with configu-ration given in Figure 15 and component values in Table 5)is simulated with battery supply as shown in Figure 16.

With DC supply, the converter voltage boost ratio isdirectly proportional to the duty cycle.

The battery supply in circuit shown in Figure 16 isreplaced by the developed circuit model in Section 3 andsimulated as shown in Figure 17.

The detailed experimental verification with circuitresponse of this developed circuit model is available in [19].

For the design of MPPT, the data is collected throughsimulation with the developed circuit model and results aretabulated in Table 6.


Output load voltage

Input voltage Voltage measurement in

PWM

0.5 Cd

Continuous

Powergui

19.7

53.01

Terminator 1

.

66.0213.62

0.69131.06

Current measurement 2

Diode IN 5408 Voltage measurement out

Input power

Input current

Product in Product out

Output current

MosfetIRF P 460

i

+

Current measurement L

i

= 120 uH

19.7 V

+

+

+

+−

−

−

−

−

g D

SE

C = 330 μF R = 50 ohm v

v

Mod index

Boost-output

× ×

Figure 16: Boost converter circuit with DC supply.

1

Temp

Irradiation

30

Current measurement

Circuit model of PV module

PV output current

PV output power

Terminator 1

Diode IN 5408

Current measurement1

Voltage measurement in

Voltage measurement

Output load current

Output load power

MosfetIRF P 460

Continuous

Powergui

Insolation

Temp

v 14.91

2.418

36.05

0.5

PWM

i

39.35

30.97

0.787

Output load voltage

i

L = 120 uH

+ −

+−

v+

+

−

−

g D

Cd

SE

C = 250 μF

R = 50 ohm

Boost-output

×

×

−V+V

Input voltage

Duty cyC = 330 μF

Figure 17: Boost converter circuit with PV input.

From Table 6, it can be seen that for lower values ofirradiation and constant load, the duty cycle has to bereduced from 0.41 for irradiation of 1000 W/m2 to 0.2 forirradiation of 500 W/m2. This variation coincides with thegraph shown in Figure 18, as found in [20], where the dutycycle variation with respect to irradiation is reported.

4.4. MPPT Control Algorithm. Many MPPT techniques havebeen proposed in the literature; examples are the Perturband Observe (P&O), Incremental Conductance (IC), FuzzyLogic, and so forth. The P&O algorithm is very popular andsimple. So it is used in this paper. The power graph for P&Oalgorithm is shown in Figure 19.


Table 6: Duty cycle variation.

Duty cycle Input voltage (V) Input current (A)Input power(WP)

Output voltage(V)

Output current(A)

Output power(W)

Irradiation—1000 W/m2 Temp—25◦C

0.4 17.82 2.059 36.69 40.08 0.8106 32.13

0.41 16.7 2.303 38.46 40.45 0.8089 32.72

0.5 15.05 2.44 36.72 39.06 0.7812 30.52

Irradiation—700 W/m2 Temp—25◦C

0.3 17.6 1.375 24.21 32.46 0.6492 21.08

Irradiation—500 W/m2Temp—25◦C

0.2 17.64 0.8661 15.28 25.76 0.515 13.27

0.310

20

30

40

20 40 60 80 100

0.7

0.6

0.5

0.4

PW

M d

uty

rat

io

Opt

imu

m im

peda

nce

(oh

ms)

Optimum impedance 56◦ C

56◦ C

Optimum impedance 28◦ C

28◦ C

Solar radiation (%)

R min

Duty ratio for 4.7 ohm load

Figure 18: Duty cycle variation with respect to irradiation.

Voltage (V)

2 4 6 8 10 12 14 160

10

20

30

40

Pow

e (W

p)

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 thepower of the solar module to change. If the power increasesdue 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 theperturbation reverses (D − ΔD). The flow chart of MPPTalgorithm is shown in Figure 20.

The Simulink model for P & O MPPT algorithm is shownin Figure 21. Vin and Iin are taken as input to the MPPT unitand duty cycle is obtained as the output.

The above MPPT unit is placed as closed-loop control inthe simulation circuit, as shown in Figure 17 and the detailedSimulink model for closed-loop control of developed circuitmodel of PV module with MPPT control unit is shown inFigure 22.

5. Hardware Implementation

The schematic diagram of the proposed hardware system isshown in Figure 23.

(i) The DC-DC boost converter acts as an interfacebetween the PV module and the load.

(ii) The voltage and current output are sensed and anerror 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 analogsignal.

(iii) This signal is then compared with a high-frequencytriangular wave of 20 kHz. The pulse generated givenis to the gate of the power semiconductor device(MOSFET), thereby changing the duty cycle of theconverter.

(iv) This generated pulse must be able to trigger thepower circuit of the MOSFET.

(v) Thus the source impedance is matched with the loadimpedance and maximum power is transferred.

The hardware setup of the proposed system is shown inFigure 24. The microcontroller programming should be fedwith the required range of duty cycle as given in Table 6 forquicker response.

The experiment is carried out for 1000 W/m2 at 25◦C.The experimental values of PV module power and currentare lower by about 2 to 5 percent compared to the simulationvalues, as shown in Figure 25.

Thus the performance of the developed circuit model,in closed-loop control, follows the simulation values withreasonable accuracy.


To switch

Start

Read V(k) and I(k) frompanel and calculatep(k) = V(k)∗I(k)

D = D − ΔD D = D − ΔDD = D + ΔD D = D + ΔD

Δp > 0

V < 0ΔV < 0

instant P(k − 1), V(k − 1)

Δp− p(k)− p(k − 1)ΔV = V(k)−V(k − 1)

Delay p(k) and V(k) by k − 1

Figure 20: Flow chart of P&O MPPT algorithm.

Product

Saturation

1

2

Switch

Switch1

0.01

Switch2

0.29

Display1

1

d

0.31

Display20.29

Display

Memory

D + ΔD

Iin

ΔV > 0

Vin

Memory 2

Memory2

D − ΔD

Δp > 0

ΔP < 0

ΔV < 0

−

−

++

+

+

+

−

×

Figure 21: Simulink model for P&O MPPT algorithm.

6. Results and Discussion

In Section 2, in (1) and Figure 1, it can be seen that thePV current Iph is a function of the solar irradiation and isthe only energy conversion process in which light energy isconverted to electrical energy.

The next two equations, (2) and (3), indicate that thePV 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 physicalequations governing the PV module (also applicable toPV cell) is elaborately presented with numerical values ofmodule saturation current at various temperatures. Hence,this circuit model presents the relationship between moduleparameters and circuit performance.

In Section 3, voltage level of the PV module is selectedas 19 V. However, for functional PV models used in otherpapers, the voltage level for the iterative process is chosen as


36.93

1.215

Irradiation

Insolation

Continuous

Powergui

Temp

30

Current measurement

+ v 16.41

2.36

PV output current

38.73

PV output power

PWM

d C

Terminator 1

E S

g D

Diode IN 5408

Current measurement 1

Voltage measurement in

30.39

Circuit model of PV module

PO MPPT

d

MosfetIRF P 460

Product

Product 10.29

d

Scope

Voltage measurement

Output load current

Output load power

Insolation

Temp

Output load voltage

i+ −

−

i+ −

v+−C = 250 μF

R = 50 ohm

×

−V+V

Input voltage

C = 330 μF

Vin

Iin

×

L = 120 uH

Boost-output

Figure 22: MPPT control circuit.

IRF150

Opto coupler IC

R1

R2

PIC microcontroller

ADC

MPPT algorithm

Calculation of phref

Calculation of error

DAC

ICL 8038

LMT10

C

DL

VpvIpv

R current sense

R Load

PV module

Figure 23: Proposed hardware system.


MPPTOptocoupler

DACPIC

controller

Power inputfor controller

PV panel board

Figure 24: Hardware of MPPT.

0

Input current

Input powerInput voltageOutput voltage

5

40

35

30

25

20

15

10

0 0.040.005 0.01 0.015 0.02 0.025 0.03 0.035

Ex. PV currentEx. PV powerEx. PV and con. voltage

Time (s)

Cu

rren

t (A

), v

olta

ge (

V),

pow

er (

W)

Figure 25: Variation of current, power for variable irradiation withexperimental results.

per the convenience of end-circuit requirements and affectthe circuit performance considerably. This has an effect onthe temperature performance of the circuit. So the selectionof this voltage level which is very important has to be selectedappropriately.

7. Conclusion

Circuit model of photovoltaic (PV) module is presentedin this paper, which can be used as a common platformby material scientists as well as power electronic circuitdesigners to develop the better PV power plant.

Acknowledgment

The authors wish to thank the management of SSN Collegeof Engineering, Chennai for providing experimental andcomputational facilities to carry out this work at SSNCE EEEDepartment Solar Photovoltaic Research Laboratory.

References

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