The working principle of PV cells is the same as the working principle of p-n junction diodes. The output I-V characteristic curve of PV cells in the dark are very similar to the characteristic curve of the diode. The single diode equivalent mode of PV cells consists of photocurrent produced by PV cell, series, a parallel resistor and diode. PV modules are obtained by connecting the produced cells to each other with solders, panels by connecting the modules to each other, and photovoltaic arrays are obtained by connecting the panels to each other.

The PV cell equivalent circuit is nonlineardue to the diode current and additional losses occur in the PV cell. The PV system is very sensitive to changes irradiation intensity and temperature. Solar irradiation and temperature affect some parameters in the PV cell equivalent circuit and change the PV modul characteristic.

In addition, I0 and Isc currents, which are seen as constant in the PV cell equıvalent circuit, vary depending on irradiation and temperature. In practice, the five-variable equivalent circuit model for PV cells is extensively used. The equivalent circuit of the PV cell is shown in Fig. 2.

The parameters in this equivalent circuit model are dependent on radiation and temperature. The series resistance (Rs) in the equivalent circuit is a significant parameter that affects the performance of a PV cell. The increase in the short-circuit current density of the PV cell causes an increase in resistance loss.

The case the solar cell is active, Rs acts as the voltage source of the solar cell and Rsh serves as the current source of the cell [21, 22]. Parallel resistance (Rsh), which expresses the leakage currents in the PV cell, is among the parameters affecting the performance of the PV cell [23–25]. The mathematical expressions found as a result of the circuit analysis of the PV cells are given in the equations below.

$${I}_{ph}-{I}_{d}-{I}_{sh}=0$$

1

The diode current can be expressed as:

$${I}_{d}={I}_{0}({e}^{\frac{{q}_{{V}_{D}}}{mkT}}-1)$$

2

Resistance of parallel current is defined in Eq. (3).

$${I}_{sh}=\frac{V+I{R}_{s}}{{R}_{sh}}$$

3

The load current of PV cell as defined by Eq. (4).

$$I={I}_{ph}-{I}_{0}\left({e}^{\frac{q(V+I{R}_{s})}{m{N}_{s}kT>}}-1\right)-\frac{V+I{R}_{s}}{{R}_{sh}}$$

4

Here, Iph denotes the photocurrent, Io denotes the reverse saturation diode current, q denotes electron charge, V denotes the PV cell output voltage, I denotes the output of the PV cell current, k denotes the Boltzmann constant, and T indicates the junction temperature. Another parameter used in the modeling of the solar PV cell is m as the ideality factor.

This factor varies depending on the material used in the production of solar cells. It ranges from 1,2 to 6 according to the technology. For example; m = 1,2 for silicon monocrystal and m = 1,5 for Cadmium Tellurium. Ns is the number of cells connected in series, Rs is the series internal resistance, Rsh is the parallel leakage current resistance, I0 is the reverse saturation diode current [24–26]. The short circuit current of the PV cell is found from the equation given below.

$${I}_{sc}={I}_{ph}-{I}_{0}\left({e}^{\frac{{I}_{sc}{R}_{s}}{{N}_{s}{V}_{t}}}-1\right)-\frac{{I}_{sc}{R}_{s}}{{R}_{sh}}$$

5

Vt is defined thermal voltage and given in Eq. 6.

$${V}_{t}=\frac{mkT}{q}$$

6

The maximum current of PV cell can be expressed using Eq. (4), (at I = Imp) as,

$${I}_{mp}={I}_{ph}-{I}_{0}\left({e}^{\frac{{V}_{mp}+{I}_{mp}{R}_{s})}{{N}_{s}{V}_{t}}}-1\right)-\frac{{V}_{mp}+{I}_{mp}{R}_{s}}{{R}_{sh}}$$

7

The open circuit voltage of PV cell can be expressed using Eq. (4), (at I = 0) as

$${V}_{oc}={V}_{t}Ln(\frac{{I}_{ph}}{{I}_{0}}+1)$$

8

The single diode PV cell equivalent circuit model is simple as it only contains an exponential expression in the diode current. Therefore, this model is used extensively in photovoltaic applications. Performance parameters of a PV module are as follows; It consists of maximum output power (PMP), short circuit current (Isc), open circuit voltage (Voc), efficiency (η), filling multiplier (FF) and performance ratio (PR).

In order to calculate the performance of the PV cell at a given irradiance value and cell temperature, the characteristic of the I-V curve of the solar cell must be known [27, 28]. I-V and P-V characteristic curves of the PV cell can be drawn using the PV cell equivalent circuit parameters. The photocurrent produced by the PV cell is as expressed in the equation given below.

$${I}_{ph}=[{I}_{sc}+{K}_{i}\left(T-{T}_{ref}\right)]\frac{G}{{G}_{ref}}$$

9

If we use the Ki and Tref values in Eq. (9), the Photocurrent equation is found as follows.

$${I}_{ph}=[{I}_{sc}+0.0017\left(T-298\right)]\frac{G}{1000}$$

10

The Ki coefficient is a coefficient used to express the change of light flux with temperature. This coefficient takes a different value for each model and it is obtained as a result of experiments carried out in the laboratory environment. The diode saturation current can be determined using Eq. (11) given below:

$${I}_{0}\left(T\right)={I}_{0\left({T}_{ref}\right)}({\frac{T}{{T}_{ref}})}^{2}\text{e}\text{x}\text{p}[\frac{{E}_{q}}{{V}_{t}}(\frac{T}{{T}_{ref}}-1)$$

11

Here, I0 is the reverse saturation diode current, Eq is the band gap energy of the semiconductor material, Tref is the nominal reference temperature and Vt denotes the thermal voltage. Five unknown parameters were found using the single diode equivalent circuit of the PV cell [29, 30]. The simulation circuit diagram given in Fig. 3 is used to obtain the I-V curve and the P-V curve of the PV cell.

Environmental factors like cell temperature, solar irradiation, clouding and partial shadowing can negatively affect both output power and overall system efficiency. Modeling of single diode equivalent circuit model was simulated by using Matlab/Simulink. The I-V and P-V characteristic curves obtained from the simulation model are as shown in Fig. 4.

In this study, the single diode equivalent circuit parameters of the photovoltaic cell were found with the developed software program. After finding the equivalent circuit parameters of the solar cell, the V-I and V-P characteristic curves of the Suntech STP 27520/Wfw module are plotted.

## 2.1. Simulation of the PV Cell Model

Simulink is used for the analysis and modeling of linear and nonlinear systems. It reduces the need for prototypes. Modeled in continuous time, discrete time, or a combination of both. As is known, PV modules consist of solar cells and are generated by connecting the solar cells in a series. Arrays are obtained when modules come together in a series or parallel. The boundary diagram related to the PV solar cell is shown in Fig. 5.

The most common models used to simulate I-V curves of modules; Single and double diode are equivalent circuit models. The dual diode equivalent circuit model gives better results in shading and low radiation. However, the single diode equivalent circuit model is still the most widely used model due to its accuracy and ease of calculation. In this study, a single diode equivalent circuit model was used to simulate I-V curves at a given irradiance and module temperature and to find equivalent circuit parameters.

The aim of this study is to model a PV cell close to reality, to obtain characteristic curves and to estimate the necessary parameters for analysis. The I-V characteristic curve for the PV cell is as given in Fig. 6.

The output characteristics of the I-V and P-V curves of the PV cell depend on weather conditions. As the weather condition is constantly changing, the properties of I-V and P-V curves of the PV cell are also altered. The Suntech STP275-20/Wfw module was used to find the equivalent circuit parameters of the PV cell. The change of the I-V curve of this PV module is nonlinear. The I-V characteristic of Suntech STP275-20/Wfw module is given in Fig. 7.

The parameters values of diode idality factor m, parallel resistor Rsh, series resistor Rs, diode saturation current Io and photocurrent Iph, which are not included in the PV panel manufacturer catalog data, were found using the Newton-Raphson method. This method is simple and requires less computation time. At the end of the iteration, reasonable results are obtained. The software program for this method is given in appendix-A in the article. It is impossible to obtain the equivalent circuit without knowing these parameters. Therefore, simulation of PV cells and panels will not be possible. In this study, five points were determined on the I-V characteristic curve of the PV module. The differential equations of the PV cell were found using Eq. (4).