Photovoltaic Cell Mathematical Modelling

Photovoltaic Cell Mathematical Modelling

Boussada Zina , Ben Hamed Mouna, Sbita Lassaad

#Photovoltaic Wind and Geothermal Systems (SPEG), Gabes University

6029 zrig Gabes street Tunisia

Abstract The photovoltaic cells description is usually defined

TABLE I

by a coupled nonlinear equation, difficult to solve using analytical methods. This paper presents a mathematical model using Matlab/ simulink, able to demonstrate the cell's output features in terms of irradiance and temperature environment changes.

Keywords Photovoltaic cell, Matlab/Simulink, Model

1. INTRODUCTION

   In recent years, photovoltaic energy is increasingly used because of its important benefits. In fact, this type of energy ensures an electricity production without green house gases emission. Besides, photovoltaic energy is totally flexible and can meet a wide range of needs [1-2], [4], [8] and [11]. PV cell is the basic unit of power conversion system of a photovoltaic generator [3]. Solar cells convert sunlight directly into electricity. Solar cells are widely used in terrestrial and space applications. They are made of semiconducting materials similar to those used in computer chips. A photovoltaic cell converts the solar energy into the electrical energy by the photovoltaic effect. When sunlight is absorbed by these materials, the solar energy knocks electrons loose from their atoms, allowing the electrons to flow through the material to produce electricity [9]. This process of converting light (photons) to electricity (voltage) is called the photovoltaic (PV) effect. In this paper, we present three models for a photovoltaic cell [10]. These models are characterized by the use of a single diode.

2. PV CELL MODELS

   1. Nomenclature

      PV CELL PARAMETRS

      Parameters	Value
      Vocs	0.6
      Iccs	3.45
      Rsh	11592
      Rs	0.018
      voc	-0.0022
      Gs	1000
      Ts	298
      A	1.2
      K	1.3806.10-23
      icc	0.00095
      Q	1.60217733.10-19

   2. Three-parameter model

      It is considered as an ideal equivalent circuit for a photovoltaic cell and it is the simplest model [5] and [10].

      Fig. 1: three-parameter model The three parameters are A1, Id and Iph.

      V: cell output voltage (V).

      Voc: open circuit voltage (V). Ipv: cell output current (A).

      Iph: solar cell photocurrent (current generated by the incident light and it is directly proportional to the sun irradiation) (A).

      IPV I ph Id

      g

      ph s

      I iccs g (1 icc(T T ))

      s

      (1)

      (2)

      Isat: reverse saturation or leakage current of the diode (A). Id: diode current (A).

      Ts: solar cell absolute reference temperature at STC = 298 K. T: solar cell absolute operating temperature (K).

      Id Isat

      v TAk

      (e q

      I

      1)

      (3)

      A: diode ideality factor.

      K: Boltzmann constant = 1.3806.10-23 J/K. q: Electron charge = 1. 60217733 10-19 C. Rs: cell intrinsic series resistance.

      Rsh: cell intrinsic shunt or parallel resistance.

      g: total solar radiation absorbed at the plane of array (POA), W/m2.

      gs: total solar reference radiation at STC, 1000 W/m2 .

      ph

      I

      sat Voc

      TAk

      e q 1

      Voc Vocs voc(Ts T )

      (4)

      (5)

   3. Four-parameter model The five parameters are Rs, Rsh , A, Id and Iph.

   This model takes into account resistors various contacts and connections represented by a series resistor Rs [1-3] and [5]

   IPV I ph Id Ish (1) (11)

   g

   and [10].

   I ph iccs (1 icc(Ts T ))

   g

   s

   (12)

   I ph

   • Voc

   R

   Voc

   Isat sh

   TAk

   (13)

   e q 1

   v IRs TAk

   q

   Id Isat (e

   1)

   (14)

   Fig. 2: four-parameter model

   Voc Vocs voc(Ts T )

   (15)

   The four parameters are Rs, A, ID

   IPV I ph Id

   and I

   ph.

   (6)

   Ish

   v I.Rs

   Rsh

   (16)

   g

   ph

   I iccs g

   s

   (1 icc(Ts T ))

   (7)

   E. Simulation results

   The simulation results obtained from these models are made under standard conditions (reference temperature: 25° (298 K)

   Id Isat

   v IRs

   TAk

   (e q

   1)

   (8)

   and reference illumination: 1000 W/m2). The comparison between the two models: the four-parameter model and the five-parameter model show that the effect of the shunt

   Isat

   I ph

   Voc TAk

   (9)

   resistance Rsh is negligible. Besides, the series resistance Rs removing (four-parameter model and three-parameter model) creates a large difference between the test results and those

   e

   V V

   q 1

   • voc(T

   T )

   (10)

   presented by this model (Fig. 4 and Fig. 5). The five parameters model is the most simpler and accurate.

   oc ocs s

   D. Five-parameter model

   This model is the best known in the literature. It is composed of a current source which models the conversion of the light flux into electrical energy, a shunt resistor Rsh is the consequence of the state along the periphery of the surface of the cell, a series resistor Rs representing resistors various contacts and connections, and a diode which models the PN junction [4-5] and [10].

   The different developed PV cell models characteristics are estimated as follows. I-V and P-V characteristics under two conditions: under varying irradiation with constant temperature (Fig. 6 and Fig. 7) and under varying temperature with constant irradiation (Fig. 8 and Fig. 9). The simulation results show that when the irradiation increases at a constant temperature, the output current increases and the output voltage also increases. This results in increase in power output with increase in irradiation at constant temperature. Similarly a temperature increase at a constant irradiation, the output current increases but the output voltage decreases. This results in reduction in power output with rise temperature.

   Fig. 3: five-parameter model (single-diode)

   4

   3.5

   3

   2.5

   I(A)

   2

   1.5

   1

   0.5

   0

   I (V) characteristic of single diode model

   5PM 4PM 3PM

   0 0.1 0.2 0.3 0.4 0.5 0.6

   V (Volt)

   Fig. 4: I (V) characteristics (five-parameter model, four-parameter model and three-parameter model).

   1.8

   1.6

   1.4

   1.2

   P (W)

   1

   0.8

   P(V) characteristic of sinle diode model 5PM 4PM 3PM

   5

   4.5

   4

   3.5

   3

   I (A)

   2.5

   2

   —– M3P

   – – – M4P

   —– M5P (single diode) temperature variation

   0.6

   0.4

   0.2

   0

   0 0.1 0.2 0.3 0.4 0.5 0.6

   1.5

   1

   0.5

   0

   0 0.1 0.2 0.3 0.4 0.5 0.6

   V (volt)

   V(Volt)

   Fig. 5: P (V) characteristics (five-parameter model, four-parameter model and three-parameter model).

   Fig. 8: The I (V) output characteristics of the different modelswith varying temperature.

   5

   4.5

   4

   3.5

   3

   I (A)

   2.5

   2

   1.5

   1

   —– M3P

   – – – M4P

   —– M5P (single diode)

   1000 W/m²

   600 W/m²

   200 W/m²

   1.8

   1.6

   1.4

   1.2

   P (W)

   1

   0.8

   0.6

   0.4

   0.2

   —– M3P

   – – – M4P

   —– M5P (single diode)

   temperature variation

   0.5

   0

   0

   0 0.1 0.2 0.3 0.4 0.5 0.6

   V (Volt)

   0 0.1 0.2 0.3 0.4 0.5 0.6

   V (volt)

   Fig. 6: The I (V) output characteristics of the different models with varying irradiation.

   1.8

   Fig. 9: P (V) output characteristics of the different models with varying temperature.

3. CONCLUSIONS

Photovoltaic modeling cells is important to describe their behavior under all conditions and ensure a closer

1.6

1.4

1.2

P (W)

1

0.8

0.6

0.4

0.2

—– M3P

– – – M4P

—– M5P (single diode)

1000 W/m²

600 W/m²

200 W/m²

understanding of I-V and P-V characteristics of a PV cell. The photovoltaic cells must be operated at their maximum power point. The maximum power point varies with illumination, temperature, radiation dose and other ageing effects.

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   0

   0 0.1 0.2 0.3 0.4 0.5 0.6

   V (volt)

   Fig. 7: The P (V) output characteristics of the different models with varying irradiation.

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