Simulation of Current-voltage (i-v) and Power-voltage (p-v) Characteristics

Abstract: This paper simulates the mathematical model of the PV (photovoltaic) module based on the MATLAB script file with all the parameters are involved. Modeling this device environmental factors such as irradiation and temperature needs as input variables. The output of the PV module varies depending on the environmental factors. Any changes in the entries immediately implies changes in output. Physical parameters (series and shunt resistance, ideality factor, temperature coefficient of current and voltage, etc.) are significant effects on the operating curves of solar PV module. The chosen model is the single-diode model with both series and shunt resistances for precise output and investigates all parameters influence on solar PV module operation and focuses on a program developed in MATLAB/M-file of 50W PV module. When compared the two results of the program simulation results and manufacturer’ data sheets are found the two are identical.

Keywords: Solar energy, PV module, I-V and P-V characteristics, Irradiance, Temperature

Introduction

Valuable energy can extract from our surroundings by several ways. These include energy extraction from sunlight, wind, biomass, sea levels, etc. All these ways are renewable in nature. The energy source itself renews, which can provide energy forever. Among all renewable energy strategies, photovoltaic system has own several fundamental advantages compare to others. By using semiconductor devices, solar energy has identified as a static, movement-free and quiet alternative energy which can result to a long-term and low maintenance cost renewable system.

Solar cells can convert sun light into electricity directly. That produces DC voltage and DC electricity. A PV module is comprised many solar cells that are connected in series or parallel depends on the desired amount of voltage or current. A typical PV cell can produces 0.5V (2-3W). The PV module is the fundamental conversion unit of a PV generator system. So, it is necessary to model the PV module for the design and simulation of maximum power point tracking (MPPT) for PV system applications since PV module has non-linear characteristics. For a given environmental conditions, there is Maximum Power Point (MPP), an optimal point on the V-I curve, where maximum power output is achieved. So, at the MPP the efficiency will be optimized. The performance of the PV module is specified under Standard Test Condition (STC), where the irradiance is 1000W/m2, module temperature is 25°C and air mass is 1.5. This paper presents the modeling method and simulation of photovoltaic (PV) module. The parameters for the PV module are based on the manufacturers’ data sheets values.

A solar cell is a basic unit of a solar module. A PV module is comprised many solar cells in series and parallel. For consider only a single solar cell, it can be modeled by utilizing a current source, a diode and two resistors. This model represents a single diode model of a solar cell.

A diode is connected in anti-parallel with the photocurrent in Figure 2 and the output current is obtained by Kirchhoff’s law;

Where, is the photocurrent, is the current in the shunt resistor, and is the diode saturation current and is given by the equation;

Where, V is the voltage imposed on the diode. is the saturation current of the diode, is the thermal voltage of its exclusive dependence of temperature. is the number of PV cells connected in series. A is the ideal factor of the diode and it depends on the PV cell technology. [2]

Where, is the actual cell temperature (K), k is Boltzmann’s constant (1.3805x10-23 J/K) and q is Electron charge (1.6021x10-19 C).So, the output current is

The power produced by a single PV cell is less and not enough for almost any applications. So, the cells may be configured in series and parallel features to increase the capability of overall PV systems. The Equation (4) can be expressed as;

Where, as the number of cells connected in parallel, and are the series and shunt resistance of the solar cell.

Modeling the PV devices, if the number of unknown parameters increases the results are away from being the ideal form. Most of the manufacturer’s datasheets do not provide enough information about the parameters which depends on weather conditions. There are five parameters ( , , A, , ) are considered depends on the irradiation and cell temperature. Ideality factor (A) is chosen 1.3 for silicon.[2]

The output of the PV module is unstable when weather conditions changes. So the proper nonlinear methods such as Simple fixed point method, Newton-Raphson method, and Secant method should be used for this unstable conditions. In this proposed model Newton-Raphson method is chosen.

In which is the actual amount of the function, is the derivation of the function, is the current amount and is the next amount. Newton-Raphson method needs one iteration loop which continues its operation, until the stopping point condition is met.

Depends on the saturation, the stopping condition by two different ways is:

(1) Once the pre-specified numbers of iteration is done

(2) Once the present error which can be obtained by Equation (21) is less than the pre-specified error. [5]

Parameters Values

Maximum Power (Pmax) 50W

Power Tolerance ±3%

Maximum Power Voltage (Vmp) 17.9V

Maximum Power Current (Imp) 2.79A

Open Circuit Voltage (Voc) 22.1V

Short Circuit Current (Isc) 2.97A

Maximum System Voltage 1000VDC

Operating Temperature -40˚C to + 85˚C

Product Application Class A

Weight 4.5KG

Dimension 760x510x30mm

All technical data at standard test conditions: AM = 1.5,

G=1000W/m², T=25˚C.

Matlab Script File For PV Module

%%Information from the RL-6P050/18 solar module datasheet %%

clear; clc;

Vocn = 22.1; %Nominal open-circuit voltage (V)

Iscn = 2.97; %Nominal short-circuit current (A)

Vmp = 17.9; %Maximum voltage (V)

Imp = 2.79; %Maximum current (A)

Eg = 1.12; % Band gap energy (eV)

Np = 1; % Number of parallel cells

Ns = 36; % Number of series cells

Pmax_e = Vmp*Imp; %Module maximum output power (W)

Ki = 0.0013; % Temperature coefficient of current (A/K)

Kv = -0.0079;%Temperature coefficient of voltage (V/K)

Gn = 1000; % Nominal irradiance (W/m²)

Tn = 298; %Nominal operating temperature (K)

Tc = Ta+273; % Cell temperature (K)

%% Constants %%

k = 1.3805*10^(-23); % Boltzmann constant (J/K)

q = 1.6021*10^(-19); % Electron charge (C)

A = 1.3; % Diode ideality factor

Vtn = (k*Tn)/q; % Thermal junction voltage (nominal)

Vt = (k*T)/q; %Thermal junction voltage (current temperature)

G = input ('G:'); % Actual irradiance (W/m²)

Ta = input ('Ta:'); % Actual temperature (K)

%% Reference values of Rs and Rp %%

Rs_max = (Vocn-Vmp)/Imp;

Rp_min = Vmp/(Iscn-Imp)-Rs_max;

Rs = 0; %Initial value of Rs

Iph = (Iscn+Ki*(T-Tn))*G/Gn; %Nominal photocurrent (A)

Ion = Iscn/ (exp(Vocn/(A*Ns*Vt))-1); %Nominal diode saturation current (A)

Io = Ion*(Tc/Tn)^(3)*exp((q*Eg)/(k*A)*(1/Tn-1/Tc));

% Diode reverse saturation current (A)

error = Inf; %dummy value

%% Iterative process for Rs and Rp until Pmax = Pmax,ex %%

while (error>0.001)

Rs = Rs+0.01; %Increment Rs

Rp= (Vmp+(Imp*Rs))/(Iscn-(Iscn*exp((Vmp+(Imp*Rs)-(Vocn)/(A*Ns*Vt)))+(Iscn*exp(-Vocn/(A*Ns*Vt)))-(Pmax_e/Vmp); % Shunt resistance

V = 0:0.1:50; % Voltage vector

I = zeros (1,size(V,2)); % Current vector

%% Solve with Newton-Raphson method %%

for j = 1:size(V,2)

g(j)=Np*Iph-I(j)-Np*Io*exp((V(j)+(I(j)*Rs))/(A*Ns*Vt) -1)-((Np/Ns*V(j))+(I(j)*Rs))/Rp;

while (abs(g(j))>0.001)

g(j)=Np*Iph-I(j)-Np*Io*exp((V(j)+(I(j)*Rs))/(A*Ns*Vt) -1) - ((Np/Ns*V(j))+(I(j)*Rs))/Rp;

f(j) = -1-(Np*Io*Rs)/(A*Ns*Vt)* exp((V(j)+(I(j)*Rs))/(A*Ns*Vt));

I_(j) = I(j) - g(j)/f(j);

I(j) = I_(j);

end

end

P = (Np*Iph-Io*(exp((V+I.*Rs)/(A*Ns*Vt))-1)-(V+I.*Rs)/Rp).*V; % Calculate power

Pmax_m = max(P);

error = Pmax_m-Pmax_e;

end

The temperature increase around the solar cell has a negative impact on the power generation capability. When increasing the temperature (25˚C to 100˚C) I-V and P-V curves of PV module shifts towards the left and voltage drop drastically although the current is staying constant. This leads to net reduction in power output with increase in temperature. So, the maximum power also decreases with increase in temperature.

The effect of irradiance on the current-voltage (I-V) and power-voltage (P-V) characteristics can be seen in Figure.6 and Figure.7. When varying the irradiance (200W/m² to 1000W/m²) the current of the PV module increases sharply and the voltage also increase slightly. So, the photo generated current is directly proportional to the irradiance. As the effect on both the current and voltage is positive and the effect on the power is also positive. Therefore, the more irradiation on the solar cell, the more power is generated.

Conclusion

The presented paper is the simulation of PV cell and module implemented under MATLAB/M-file. In this paper seen that the PV module output parameters can be varied depending on their cell temperature and irradiation. Also the simulation results are matched with the manufacturer’ data sheets. It is importance to compute and because the experimental maximum output power does not match with the computed one in most case. So the iteration process and appropriate iteration method should be used for matching. is iteratively increased until the match condition. In the proposed model show ( = 0.22Ω, and = 621.7Ω) and the result ( = 49.933Ω) is great accuracy with the datasheet ( = x = 49.941Ω). Therefore, this model can be used to study all types of commercial PV modules and determine all necessary parameters under new conditions of irradiance and temperature and then, obtain the I-V and P-V characteristics.

Acknowledgments

The author would like to thanks my supervisor Dr. Nay Win Zaw, Head of the Department of Electronic Engineering, and all of teachers from West Yangon Technological University who gave advices, fully guidance and supports to complete this paper.