# Parameter Estimation of the Bishop Photovoltaic Model Using a Genetic Algorithm
## 1 Introduction  
Photovoltaic (PV) cells are devices that convert solar irradiance into electricity. This type of energy source has three main advantages: (1) it has an estimated lifespan of 25 years, (2) it does not require short-term maintenance and (3) its raw material is renewable [1, 2]. However, the energy production of a PV system depends on the weather conditions of the place where the system is installed, which can quickly change. The behavior of the PV cell under particular environmental conditions is often described by using the current-voltage (I-V) curve, because it provides relevant information about the transformed energy and it can be used to calculate the maximum power that can be delivered to a load [3]. The cell behavior for different irradiance and temperature conditions can be modeled using an equivalent electrical circuit, which is designed to represent the electrical phenomena associated with the energy transformation process [4, 5, 6, 7]. The most commonly studied circuital models are the single-diode model (SDM) [8, 9, 10, 11] and the double-diode model (DDM) [12, 13, 14, 15]. Both have been used to model commercial PV cells, modules and panels made of monocrystalline silicon (mc-SI) or polycrystalline silicon (pc-SI). However, when a PV panel is under partial shading, the shaded PV cells might not generate energy; on the contrary, they might consume the energy produced by the other cells of the panel. In this phenomenon, known as reverse bias, the cell exhibits a negative voltage at its terminals; therefore, it operates in the second quadrant (negative voltage and positive current). It is worth noting that neither SDM or DDM can accurately represent this phenomenon at the cell level. The previous condition has been addressed by using the avalanche mechanism to represent the reverse bias at the cell level. This is the case of the Bishop model [16; 17], which introduces a variation to the SDM that affects the shunt resistance current (\(R_{sh}\)) by means of an ohmic term and a non-linear multiplication factor. Such a model, proposed in [18], was implemented to analyze the \(ESTI\) database, which contains the I-V profiles of mc-SI cells. In particular, the parameters proposed in [18] correspond to the average value of the parameters obtained for each cell in the database; unfortunately, that study does not include a detailed description of the procedure used to estimate the model parameters. Other authors have used this [PERSON] model to analyze PV systems [19; 20; 21] because it estimates the cell behavior under partial shading conditions at the cell level. In general, the parameters suggested by [PERSON] are adopted when the second quadrant is analyzed [18]. A simulation method was developed in [19] to diagnose PV systems, where the PV current of the shaded region is calculated as a relationship between the current under standard operating conditions, the irradiance value and the applied shadow. Although that work does not emphasize the estimation of the parameters related to the first quadrant, the parameters associated with the second quadrant are selected equal to the values reported by [PERSON] in [18]. A more general approach was proposed in [21], where a method for modeling PV arrays and modules was based on calculating the I-V relationship regardless of whether the arrays or modules have different electrical connections. The general equations system was obtained by applying [PERSON]'s laws and the damped Newton method was used for calculating the system solution. The PV system in that work was built in layers; the first one from cell to module and the second one from module to array. Nevertheless, that study does not specify the method adopted to estimate the model parameters. The [PERSON] model has also been used to develop tools (such as PVSIM) to evaluate the performance of PV cells, modules, arrays and large-scale PV systems [20]; for example, PVSIM also includes elements such as bypass diodes and blocking diodes.