# Effect of various model parameters on solar photovoltaic cell simulation: a SPICE analysis

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## Abstract

In this paper, all the models of PV cell, namely ideal single-diode model, single-diode \(R_{\rm s}\) model, single-diode \(R_{\rm p}\) model, the two-diode model, and the three-diode model, have been discussed. SPICE simulation is done to evaluate the impact of model parameters on the operation of PV cell. The effects of the parameters are discussed. The photocurrent, \(I_{\rm L},\) is proportional to irradiance, and the series resistance, \(R_{\rm s},\) reduces the short-circuit current and fill factor. The parallel resistance, \(R_{\rm p},\) reduces the open-circuit voltage, and both the diffusion diode and recombination diode reduce the open-circuit voltage value and fill factor. Finally, it is shown that an increase in cell operating temperature reduces the open-circuit voltage and fill factor and thus degrades the performance significantly.

## Keywords

Photovoltaic modeling SPICE simulation of PV cell Single-diode model Two-diode model Solar cell modeling## Background

A photovoltaic (PV) cell generates electricity when it is illuminated by the sun or some other light sources. Small PV cells can be grouped to form panels, and panels can be grouped to form arrays. The tremendous growth of PV industry and the increased number of installed PV systems all over the world raised the need for supervision and simulation tools for PV systems. To understand the PV system in a better way, modeling the PV system in various operating and weather conditions is necessary (Soto et al. 2006; Carrero et al. 2007). The simulation is also useful for various purposes like: (1) to analyze and study the behavior of power converters when they are attached with the PV system (Camps et al. 2015; Eccher et al. 2015), (2) to simulate the behavior of maximum power point tracker (MPPT) (Bendib et al. 2015; Ishaque et al. 2014), and (3) to estimate the efficiency of the PV system (Khazaei et al. 2015; Sivakumar et al. 2015). In addition to these, the simulation can also be used to analyze various operational conditions like: partial shading, change in irradiance, and fault conditions (Brano et al. 2010, 2012).

On the other hand, manufacturers of the PV modules provide electrical parameters only at standard test conditions (STC) which are \({\rm irradiance} = 1000\;{\rm{W/m^2}}\), 1.5 air mass (AM), and cell temperature of *T* _{cell} = 25 °C (Soto et al. 2006). Manufacturers datasheet only provides the short-circuit current \(I_{\rm{{SC}}}\), open-circuit voltage \(V_{\rm{{OC}}}\), the voltage at maximum power point \(V_{\rm{{MP}}}\), the current at maximum power point \(I_{\rm{MP}},\) and the temperature coefficients at open-circuit voltage and short-circuit current (Sera et al. 2007). However, the operating range of the PV panel is large and operating and weather conditions also vary. Therefore, performance models are built to predict the performance of the PV system at any operating and weather condition. The model predicts the I–V characteristic of a PV system as a function of irradiance, angle of incidence of solar radiation, the spectrum of sunlight, and temperature (Chatterjee et al. 2011). For the last few years, substantial amount of work has been done to develop simulation models and extraction of model parameters of photovoltaic systems (Chouder et al. 2012; Ma et al. 2014; Villalva et al. 2009; Castaner and Silvestre 2002; Bal et al. 2012; Xie et al. 2014). Specially, Ma et al. (2014b) have developed a model to simulate the performance characteristics of crystalline silicon photovoltaic modules/strings/arrays. Zeroual et al. (1998) designed and constructed a closed loop sun-tracker with microprocessor management. Chin et al. (2011) have done a design, modeling, and testing of standalone single axis active solar tracker using MATLAB/Simulink. Chin (2012) has also done model-based simulation of an intelligent microprocessor-based standalone solar tracking system. Models for numerical device simulations of crystalline silicon solar cells were also reviewed by Altermatt (2011). De Blas et al. (2002) found suitable models for characterizing photovoltaic devices. Celik and Acikgoz (2007) have done the modeling and experimental verification of the operating current of monocrystalline photovoltaic modules using four- and five-parameter models. Chatterjee et al. (2011) have identified suitable photovoltaic source models. However, the effects of individual model parameters were not clearly reviewed in the present literature.

The objective of this work is to analyze the effects of model parameters on the simulation of PV cell. PSPICE is used to analyze and simulate the effects of parameters on photovoltaic cell performance.

## How a photovoltaic cell works?

*n*is the diode ideality factor (dimensionless), and \(k = 1.38065 \times 10^{23}\;{\rm{J/K}}\) is the Boltzmann constant. The reciprocal term of \((q/nkT_{\rm{cell}})\) is called the thermal voltage of the diode. Therefore, thermal voltage of the diode is:

## Different parameter models of solar cell

Electrical and thermal parameters available from manufacturer datasheet

Parameters | Symbol (Unit) |
---|---|

| |

Maximum power rating | \(P_{max}\, (W_{\text{p}})\) |

Rated current | \(I_{MPP}\) (A) |

Rated voltage | \(V_{MPP}\) (V) |

Short-circuit current | \(I_{sc}\) (A) |

Open-circuit voltage | \(V_{oc}\) (V) |

| |

Normal operating cell temperature | NOCT (°C) |

Temperature coefficient: short-circuit current | (A/°C) |

Temperature coefficient: open-circuit voltage | V (°C) |

| |

Air mass | \(AM = 1.5\) |

Irradiance | \(G = 1000\;{\rm{W/m^2}}\) |

Cell temperature | |

### Ideal cell model

*n*indicates how closely the diode follows the ideal diode equation (Archer and Hill 2001). The value of

*n*greater than 1 represents non-ideal condition, whereas \(n=1\) represents ideal behavior of the diode.

Model parameters of different models

Models | No. of parameters | Parameters | Parameter meanings |
---|---|---|---|

Ideal single-diode model | 3 | \(I_{\rm L}\), \(I_{01}\), \(n_1\) | \(I_{\rm L}\), the photocurrent |

Single-diode \(R_{\rm s}\) model | 4 | \(I_{\rm L}\), \(I_{01}\), \(n_1\), \(R_{\rm s}\) | \(I_{01}\), the reverse saturation current of the first diode |

Single-diode Rp model | 5 | \(I_{\rm L}\), \(I_{01}\), \(n_1\), \(R_{\rm s}\), \(R_{\rm p}\) | \(I_{02}\), the reverse saturation current of the second diode |

Two-diode model | 7 | \(I_{\rm L}\), \(I_{01}\), \(I_{02}\), \(n_1,n_2\), \(R_{\rm s}\), \(R_{\rm p}\) | \(I_{03}\), the reverse saturation current of the third diode |

Three-diode model | 9 | \(I_{\rm L}\), \(I_{01}\), \(I_{02}\), \(I_{03}\), \(n_1\), \(n_2,n_3\), \(R_{\rm s}\), \(R_{\rm p}\) | \(n_1\), the first diode ideality factor |

\(n_2\), the second diode ideality factor | |||

\(n_3\), the third diode ideality factor | |||

\(R_{\rm s}\), lumped series resistance | |||

\(R_{\rm p}\), shunt resistance |

### Single-diode \(R_{\rm s}\) model

In fact, the current generated in the photovoltaic cell travels through semiconductor material which are not heavily doped and thus show resistivity (Duffie and Beckman 2006; Ma et al. 2014a). Besides this, the resistance of the metal grid, contacts, and current-collecting wires also contribute to the total series resistive losses. Usually, a lumped resistor, \(R_{\rm s},\) is added in series with the ideal circuit model to represent these series losses as shown in Fig. 3b (Ma et al. 2014a). This model is called single-diode \(R_{\rm s}\) model.

From Eq. (4), it can be seen that there are now four unknown parameters: photocurrent \(I_{\rm L}\), reverse saturation current \(I_{\rm{0}}\), diode ideality factor A, and the newly added lumped series resistor \(R_{\rm s}\). This model is therefore named as 4-p model. However, in recent research it is shown that the 4-p model which ignores the shunt resistance effect does not perfectly fit the experimental I–V and P–V data (Dongue et al. 2012).

### Single-diode \(R_{\rm p}\) model

*n*layer of the p–n junction PV cell. Localized short circuit or short circuiting of the cell border are the most common form of shunt losses (Castaner and Silvestre 2002). This is represented generally by a lumped resistor, \(R_{\rm{sh}}\), in parallel with the ideal device. The single-diode \(R_{\rm p}\) model which has both the series resistance \(R_{\rm s}\) and shunt resistance \(R_{\rm p}\) is shown in Fig. 3c. As there are five unknown parameters in this model, it is called the 5-p model. Table 2 illustrates the models along with their parameters. The current through the parallel resistor, \(I_{\rm{P}},\) can be given as:

This single-diode \(R_{\rm p}\) model or 5-p model is the most widely used and accepted model found in the literature (Chatterjee et al. 2011; Chenni et al. 2007; Chin et al. 2015; Ciulla et al. 2014; Mahmoud et al. 2012; Patel and Agarwal 2008; Brano et al. 2010, 2012). Most of the research has been done on the improved 5-p model and its parameter \((I_{\rm L},I_0,V_T,R_{\rm s},R_{\rm p})\) extraction procedure (Soto et al. 2006; Brano et al. 2010, 2012; Sera et al. 2007; Chatterjee et al. 2011; Villalva et al. 2009; Ishaque et al. 2011).

### Two-diode model

Even though the commonly used 5-p model can achieve acceptable level of accuracy, the saturation current of the photovoltaic cell is the linear superposition of charge diffusion and recombination in the space-charge layer (Luque and Hegedus 2011) and therefore the more accurate electrical representation of the PV cell can be done by two Shockley diodes in parallel with a current source and associated series and shunt resistances (Castaner and Silvestre 2002). This model is more relevant at low-voltage bias, i.e., at low irradiance level operation of the PV cell (Luque and Hegedus 2011). Figure 3d illustrates the circuit of this model.

We can see form Table 2 that the number of parameters is increased to seven in two-diode model. To reduce the number of unknowns, the ideality factor of the first diode is usually taken as 1 and the second diode ideality factor is taken as 2. This assumption is done based on the approximation of Shockley–Read–Hall recombination in the space-charge layer of the photodiode (Chih-Tang et al. 1957). Unfortunately, this assumption does not always hold true (McIntosh et al. 2000).

### Three-diode model

To take the influence of grain boundaries and leakage current through the peripheries into consideration, another diode can be added in parallel with the two other diodes of the two-diode model (Nishioka et al. 2007). This model has nine parameters (see Table 2) and a really cumbersome solution process. Most of the time, ignoring few parameters is done to reduce the number of equations of this model. Figure 3e shows the circuit diagram of this model.

## Experimental setup

Electrical and thermal parameters of SM50 module

Electrical parameters | ||
---|---|---|

Maximum power rating, \(P_{\rm{{max}}}\) | (Wp) | 50 |

Rated current \(I_{\rm{{MPP}}}\) | (A) | 3.05 |

Rated voltage \(V_{\rm{{MPP}}}\) | (V) | 16.6 |

Short-circuit current \(I_{\rm{SC}}\) | (A) | 3.4 |

Open-circuit voltage \(V_{\rm{OC}}\) | (V) | 21.4 |

| ||

NOCT | (°C) | \(45\pm 2\) |

Temp. coefficient: short-circuit current | 1.2 mA/°C | |

Temp. coefficient: open-circuit voltage | −0.077 V/°C |

## Results and discussion

### Effect of photocurrent, \(I_{\rm L}\)

### Effects of the series resistance, \(R_{\rm s}\)

### Effects of the shunt resistance, \(R_{\rm p}\)

### Effects of the diffusion and recombination diode, \(D_1\) and \(D_2\)

### Temperature effects, \(T_{\rm{cell}}\)

### Experimental results

## Conclusion

The development of PV system raised the need of simulation of PV system. In this paper, all the modeling methods have been discussed and SPICE simulation is done to evaluate the impact of model parameters on the operation of PV cell. The models discussed here are ideal single-diode model, single-diode \(R_{\rm s}\) model, single-diode \(R_{\rm p}\) model, the two-diode model, and the three-diode model. All the model parameters are enlisted in Table 2. The effect of the parameters are discussed with PSPICE simulation. The photocurrent, \(I_{\rm L},\) is proportional to irradiance, and the series resistance, \(R_{\rm s},\) reduces the short-circuit current and fill factor. The parallel resistance, \(R_{\rm p},\) reduces the open-circuit voltage, and both the diffusion diode and recombination diode reduce the open-circuit voltage value. Finally, the increase in cell operating temperature reduces the open-circuit voltage and fill factor and thus degrades the performance significantly.

## Notes

### Competing interests

The author declare that he has no competing interests.

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