# Online Identification of Photovoltaic Source Parameters by Using a Genetic Algorithm
## 1 Introduction  
The photovoltaic (PV) single-diode model (SDM), shown in Figure 1, is widely used for describing the electrical behavior of a photovoltaic source because it is a good trade-off between model complexity and precision. Such a model is mainly adopted to reproduce the electrical I-V curve of the PV source, and in general, it operates offline with respect to the system under investigation. The SDM is also useful in online applications such as model-based maximum power point tracking (MPPT) and monitoring/diagnosis operation [1; 2; 3; 4]. The five parameters (\(I_{ph}\), \(I_{s}\), \(\eta\), \(R_{s}\), \(R_{h}\)) appearing in (1), which is the equation underlying the SDM, are usually calculated by using datasheet information, or experimental data, or a combination of them. Due to the strong nonlinearity and the involved implicit relationships, the calculation of the SDM  
Figure 1: Equivalent circuit of the single-diode model. parameters is a challenging task. In particular, this calculation involves the use of iterative algorithms that have some drawbacks: they are slow and do not guarantee the convergence to the exact solution if a good initial estimate (guess solution) is not available. Therefore, iterative methods for the SDM parameter identification are not suitable to be applied on-line, for example to support MPPT [5]. Some papers highlighted how the variation of the SDM parameters is strictly related to some degradation phenomena occurring inside the PV panel. Such degradation phenomena should be properly monitored and eventually removed to avoid significant losses in the energy production [6; 7]. In this scenario, the adoption of online parameter identification procedures, working during the normal operation of the PV source, is very attractive. By comparing the identified values with the ones assumed as the reference and related to the proper operation of the source, the state of health of the PV panels can be detected. Besides the aging issues, there are some common circumstances where the state of health of the PV panels changes suddenly as for hot-spot phenomena. In these cases, a prompt identification of the SDM parameters' variations can avoid destroying the PV panels and prevent dangerous situations like triggering a fire. In mismatched PV fields, hot-spot phenomena appear frequently, so that an on-line monitoring of the state of health is highly recommended. For all the above reasons, several technical contributions have been proposed to perform the online parameter identification of the PV SDM. For example, in [8], a four-parameter formulation of the SDM is used to estimate the I-V curve and the maximum power point (MPP) in real time by using six pairs of voltage-current experimental points close to the MPP, whereas in [2], a software running on a personal computer (PC), which is connected to a testbed system, is used to validate the real-time implementation of such a technique. In [9], the calculation of the SDM parameter is proposed based on explicit formulas. Specifically, the number of parameters of the SDM is reduced to four (one of the two resistances is neglected) on the basis of a suitable classification of PV panels according to their series to parallel ratio (SPR). In [10], a method that allows identifying the set of five SDM parameters by explicit formulas is given; it always keeps the fifth-order model, but in extreme conditions, it can result in unrealistic negative values of one of these two resistances. Moreover, in [11], suitable parameter translation equations, used to evaluate the SDM parameters under any environmental condition, are tested for several identification methods based on explicit formulas, and the accuracy of the translation procedure is quantitatively assessed for different case studies. Most of the procedures described in the literature to calculate the SDM parameters require the knowledge of the short circuit current (\(I_{sc}\)) and the open circuit voltage (\(V_{oc}\)) in the actual environmental conditions.