978-1-4799-3602-1/14/$31.00 ©2014 IEEE

Modeling, Simulation and Parameters Estimation for Photovoltaic Module

Badr Aldwane Electrical Engineering Department - Polytechnic Institute -Sukna

Aljufra-Libya Badr_engineer2012@Yahoo.com

Abstract - Integration and application of Solar Panels as clean energy resources in electricity production and distribution is gaining wide spread implementation in market, to implement these resources successfully and to operate them in efficient way. It is so important to model solar cell and analyze its behavior and dynamics in proper method. In this paper, Photovoltaic module is analyzed, modeled and simulated in Simulink /Matlab environment using basic circuit equations, one - diode model is implemented. Pure Analytical approach is introduced to estimate unknown Parameters of PV module; performance of circuit is evaluated with different environmental conditions and compared with real results as presented by datasheets supplied by manufacturer

Keywords: Photo-Effect, Solar cell, simulation, Explicit Method, Parameter Estimation, Photovoltaic, irradiance

I. INTRODUCTION

The Photovoltaic systems (PV) have been under continuous development and study works for many years by many research projects worldwide, the main objectives of these researches were to develop, improve, and design reliable, efficient and cost effective energy resources alternatives for fossil fuel based resources as Petroleum, coal and natural gas. As the demand for clean and sustainable energy resources are sharply increasing worldwide and become public concern in many countries; solar energy represents very promising clean energy for mankind. Every day, the earth receives extremely huge amount of solar energy that can be utilized for electricity production. Up to now, although still PV systems are operating with low efficiency, less than 18% [1] under uncontrolled environment conditions, and they still require high initial investment cost, but on other hand, utilization of PV systems brings many benefits: they are clean energy provider, where no emissions produced during operation, PV systems Require minimal maintenance, because there is no need to lubrication, or heat transfer equipments, no parts to be replaced due of wearing or damage since they do not use any heat engine or rotating equipment in process of electricity production, they are almost silent during working , no noise is caused, PV systems have very low

operation cost since no fuel to consume, PV systems are easy to transport and easy to install, Furthermore ,PV systems are flexible, Photovoltaic systems can be built in virtually any size, these systems are flexible as more panels can be easily added to increase output to meet continuously growing loads. Currently there are many electrical Applications powered by PV systems include communications, remote monitoring, lighting, water pumping, and battery charging.

Modeling of Photovoltaic system is very crucial to achieve integration and optimization of PV based power system as renewable energy resources. Building accurate model of PV Array helps in understanding its dynamics and the influence of external factors and parameters changes on the overall performance. Many models for PV cells, modules and arrays were developed and presented; [2] presented generalized photovoltaic model that was developed in Matlab/Simulink platform; the results of simulation were validated with commercial PV modules. This model is based on one-diode model; [3] proposed two-diode model implemented on Matlab Simulink environment for PV systems. This model provides better accuracy especially in the case of low irradiance levels. Based on work of [4] PV model is developed in Mat-lab/Simulink by using basic circuit equations, the effect of solar insolation and temperature variations were included, the model response is tested for both DC loads and AC loads. Matlab/Simulink model for PV array is presented [5]; this model is based on power system block offered in Simulink, the model is integrated with DC-DC boost convertor and results of simulations are verified by lab setup. [6] Introduced general model which can be implemented on simulation platforms such as PSPICE or SABER. Many research efforts have been made to calculate unknown parameters of PV cell, including numerical based methods, analytical approaches and curve fitting techniques, [6] proposed curve fitting technique for estimating parameters for PV model, this technique requires I-V measurements which in not quit convenient, as outlined by [7] iterative algorithm introduced to compute the five unknown parameters of one -diode model presuming a value of diode ideality factor. [8] Presented technique to

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extract parameters of one-diode model by solving a system of simultaneous non-linear equations. [9] And [10] proposed neglecting the shunt resistance, resulting in one-diode four based model for PV array. This enables analytical calculation of parameters, this assumption considers that slope of I-V curve is flat at the short circuit conditions. This model predicts reliably the performance of both mono-crystalline and polycrystalline PV systems. Pure analytical methods were used to calculate parameters for Solar cell for both single and double-diode PV models [11].

II. PV CELL

Photovoltaic (PV) modules are solid-state devices that convert sunlight directly into electricity, this is due to photo-effect phenomena [12]; A PV cell is basic unit of PV module, it basically consists of two or more thin layers of semiconducting material, most commonly silicon. When the solar cell is exposed to sun light, pairs of hole and electrons are generated; these charges are swept apart by internal electric field in P-n junction, if the cell is connected to external circuit, these charges can be conducted as form of direct current. The electrical output from a single PV cell is extremely small, so multiple cells are connected in series and parallel, packed into modules that produce a specific voltage and current. A typical PV generator consists of PV panel, Battery, charge controller, dc-dc converter and ac inverter, this inverter is used to transfer dc power into ac power, Fig. 1 shows typical PV generator.

Fig. 1 Typical PV generator system

III. PV CELL MODELING

A PV cell is modeled basically as current source in parallel with a diode; To account for losses occurs inside solar cell, Rs ( series resistance) and Rsh (parallel resistance) are included in this model as shown in fig. 2; Rs is very low in value usually < 1 Ω. Rsh is usually high as compared to Rs, i.e. Rsh >> Rs; Rsh represents leakage current to ground in cell [2].

Fig. 2 Equivalent Circuit of Solar Cell

The current source generates photocurrent Iph, which is directly proportional to solar irradiance and the working temperature of cell. By referring to fig. 2 applying Kirchhoff current Law to circuit: (1)

Fig. 3 Equivalent Circuit of PV array

Where I: Cell's output current measured in Ampere (A); IPH is photocurrent generated in cell measured in (A); ID is a diode current and Ish is current flows in parallel resistance. As this paper concerns the modeling of PV array, not a single solar cell, Fig. 3 represents equivalent circuit of PV array composed of series and parallel connected solar cells, by using Shockley equation for diode current, (1) becomes:

( ) 1 (2)

IS: Dark saturation current dependant on temperature; q is a charge of electron, 1.6x10-19 coulomb (C); V is Cells output voltage, measured in volts; Rs represents interstice losses of PV cell; Rsh represents earth leakage current to ground. K is Boltzmann's gas constant, 1.381 x 10-23 Joule/Kelvin (J/K); Ns is number of cells in series and Np are number of cells in parallel, A is Ideality factor of cell, depends on type of material and manufacturing technology, its value ranges [1-5]; T is absolute Temperature of the cell, measured in Kelvin (K); I is function of cells' voltage V. In modeling; V is considered as input, I as output, Iph is related mathematically to insolation (G) and temperature T as follows:

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(3)

Diode dark saturation current depends strongly on temperature of solar cell [3] [4], this is expressed as:

(4)

Where Ego is band-energy gap of semiconductor =1.12eV. It is clear that (2) is implicit nonlinear equation, so there is no analytical solution. In order to solve it, numerical iterative method must be used. But firstly we need to calculate the values of parameters (Iph, Is, Rs, Rsh and A ); these parameters determine overall performance of solar cell, unfortunately these parameters are not listed in photovoltaic panels data-sheet as supplied by manufacturer, so it is necessary to esti-mate parameters of the circuit to achieve the simulation, Data sheets for PV panels provide some important operating spe-cifications of solar panel, including short circuit current Isc, open circuit voltage and maximum power point, these infor-mation can be used to estimate the unknown parameters for solar cell and solar array as explained in section IV.

Fig. 4 illustrates voltage current characteristics (I-V) for solar panel of Polycrystalline type, under standard test conditions (STC); i.e. solar irradiance of 1000 W / m2, T =25C0, and Air mass =1.5.

Fig. 4 current vs. voltage curve for typical PV module

The curve shows nonlinear behavior of solar module for fixed Sun irradiance, fixed temperature. With reference to fig. 5 three remarkable points can be identified on V- I curve shown as red circuits; these point are: short circuit point (0, Isc) where current is maximum and cell voltage = 0; Open voltage point (Voc, 0) where voltage of cell is maximum and cell current = 0; maximum power Point MPP (Vmpp, Impp); PV cell works as current source near the short circuit point area, while it works as almost voltage source near the point Voc, on

other hand ; it behaves as combination of both sources near MPP.

Fig. 5 three Key operating points of PV module as specified in Data Sheet

Fig. 6 display the Voltage - Power characteristic curve of PV panel under STC, Note that there is only one maximum power point corresponding to maximum power that can PV panel produce; to optimize the working of PV cell in practice, it must be operated as near as possible to MPP, to achieve this, maximum power point tracking algorithm techniques are used to control dc-dc converter controlling the outputs of PV panel

Fig. 6 Power vs. voltage curve for typical PV module

IV. ESTIMATION OF PARAMETERS OF SOLAR CELL

Analytical solution for parameters calculation can be adopted by introducing some simplification and approximation in (2); it is confirmed in [9] and [10], that Rsh is very large, assuming it as open circuit Rsh=∞; assuming Np=1, (2) becomes:

( ) 1 (5)

The exponential term in (5) very big compared to 1

exp [q (V + RsI) / KAT] >> 1, so omitting term 1 from (5);

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( ) (6)

Is is very low as compared to Iph value, usually Is in range of μA ( 10-10 to 10-5) [1]:

Iph >> Is exp [q ( v + RsI )/ NsKAT]

Photocurrent approximately becomes: Isc ≈ Iph (7) Employing (7) and the knowledge of point (Voc, 0), substituting it in (6), we get: 0 ( ) (8)

Rearranging (7) to:

( ) (9)

Now solving (8) for saturation current Is

( ) (10)

(1) Becomes: 1 ( ) (11)

Now we need third equation to find third parameter Rs, using the point (Vmpp, Impp) in (12):

1 (12)

Solving this equation to find Rs

(13)

To find A, forth equation must be introduced. It is ma-thematically clear that the derivative of Power curve at maxi-mum power point is zero. Since the power is P =VI: so

0

Now differentiating (5) in term of V

0 1 ( (14)

At MPP:

1 ( (15)

Using equation (10) & (13) for Is and Rs respectively.

( ) 1 (16)

Where: 1 (17)

( (18)

Solving (17) for A, pure analytical formula to calculate A: 2 1 (19)

V. MAKING OF SIMULINK/MATLAB MODEL

The equations (3), (4), (5) and (10) are modeled in Simulink simulation environment as subsystems blocks, connected together to form overall system as shown in fig. 7. The inputs for subsystem are: Voltage, solar irradiation and temperature, while the output is current. Function block parameters box are used to access the PV panel specifications. The Unknown parameters are calculated during model's initialization by associated M File - code Script. Since the environmental conditions are not controlled, testing the proposed Model for different levels of solar intensity G and Temperature variations is very crucial for PV module efficiency, Simulation results are verified by comparing them against experimental results provided in PV data sheets, mono-crystalline based PV system and Polycrystalline based PV system were used for comparison .

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Fig. 7 Simulink-Based Subsystem Model of PV module

Fig. 8 Under-Mask view of block diagrams of subsystems making PV module

Fig. 9 Simulink Block model representing Photocurrent dependency on the solar insolation and temperature

Fig. 10 Simulink model representing formula for PV's output current

Fig. 11 Function block Parameters dialog box to access PV's Parameters

Fig. 12 Simulink Block model representing equation of temperature dependency of Saturation Current

VI. RESULTS AND CONCLUSIONS

Fig. 13 shows the influence of solar irradiance G on the I-V Characteristics of PV Module, the Current of PV module is

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Fig. 13 Effect of Solar radiation variation on output current of PV module

directly proportional to the solar irradiance G; while voltage V is slightly increasing with irradiance; points out that Irradiance has little effect on the voltage of PV module.

Fig. 14 Effect of Solar radiation variation on generated power of PV module

Fig. 14 depict the significant change in power generated in PV module as result of varying the solar irradiance levels. As the sun irradiance decreases, power generated in photovoltaic cell drops.

Fig. 15 Effect of module working temperature variation on output current and voltage of PV module

Fig. 16 Effect of module working temperature variation on generated power of PV module

The influence of temperature fluctuation on PV's output voltage is remarkable as indicated in fig. 15; voltage drops considerably with increasing of temperature, while current is not sensitive to temperature changes, as result power P generated by solar panel experiences sever drop as T rises as shown in Fig. 16

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