Use of Wiener- Hammerstein (WH) Model Optimized with Genetic ‎Algorithm in Identification of Photovoltaic System

<span style="font-size: 11pt; line-height: 125%; font-family: Calibri, sans-serif;">System identification is a method of identification or measuring a mathematical model of a system by measuring the inputs and outputs of the system. In this paper we apply the Genetic Algorithm (GA) approach to model a photovoltaic (PV) </span><strong><span lang="AR-SA" style="font-size: 10pt; line-height: 125%; font-family: Calibri, sans-serif;">&lrm;</span></strong><span style="font-size: 11pt; line-height: 125%; font-family: Calibri, sans-serif;">systems with a Wiener-Hammerstein structure. Non-linear dynamic systems have both </span><strong><span lang="AR-SA" style="font-size: 10pt; line-height: 125%; font-family: Calibri, sans-serif;">&lrm;</span></strong><span style="font-size: 11pt; line-height: 125%; font-family: Calibri, sans-serif;">dynamic elements (energy storage elements) and in these types of systems there are non-linear </span><strong><span lang="AR-SA" style="font-size: 10pt; line-height: 125%; font-family: Calibri, sans-serif;">&lrm;</span></strong><span style="font-size: 11pt; line-height: 125%; font-family: Calibri, sans-serif;">relationships between some variables. If in such systems it can be assumed that dynamic parts </span><strong><span lang="AR-SA" style="font-size: 10pt; line-height: 125%; font-family: Calibri, sans-serif;">&lrm;</span></strong><span style="font-size: 11pt; line-height: 125%; font-family: Calibri, sans-serif;">and non-linear parts are separable, they can be modeled with the structures of block-oriented </span><strong><span lang="AR-SA" style="font-size: 10pt; line-height: 125%; font-family: Calibri, sans-serif;">&lrm;</span></strong><span style="font-size: 11pt; line-height: 125%; font-family: Calibri, sans-serif;">models. These types of models are composed of a combination of linear dynamic block(s) and </span><strong><span lang="AR-SA" style="font-size: 10pt; line-height: 125%; font-family: Calibri, sans-serif;">&lrm;</span></strong><span style="font-size: 11pt; line-height: 125%; font-family: Calibri, sans-serif;">static nonlinear block(s). This approach is concerned with the </span><strong><span lang="AR-SA" style="font-size: 10pt; line-height: 125%; font-family: Calibri, sans-serif;">&lrm;</span></strong><span style="font-size: 11pt; line-height: 125%; font-family: Calibri, sans-serif;">estimation of a photovoltaic </span><strong><span lang="AR-SA" style="font-size: 10pt; line-height: 125%; font-family: Calibri, sans-serif;">&lrm;&lrm;</span></strong><span style="font-size: 11pt; line-height: 125%; font-family: Calibri, sans-serif;">(PV) system based on observed data. The nonlinear input and output </span><strong><span lang="AR-SA" style="font-size: 10pt; line-height: 125%; font-family: Calibri, sans-serif;">&lrm;</span></strong><span style="font-size: 11pt; line-height: 125%; font-family: Calibri, sans-serif;">are taken from the </span><strong><span lang="AR-SA" style="font-size: 10pt; line-height: 125%; font-family: Calibri, sans-serif;">&lrm;</span></strong><span style="font-size: 11pt; line-height: 125%; font-family: Calibri, sans-serif;">irradiance and DC output current data of the real system, respectively. The </span><strong><span lang="AR-SA" style="font-size: 10pt; line-height: 125%; font-family: Calibri, sans-serif;">&lrm;</span></strong><span style="font-size: 11pt; line-height: 125%; font-family: Calibri, sans-serif;">simulation results </span><strong><span lang="AR-SA" style="font-size: 10pt; line-height: 125%; font-family: Calibri, sans-serif;">&lrm;</span></strong><span style="font-size: 11pt; line-height: 125%; font-family: Calibri, sans-serif;">revealed the effectiveness and robustness of the proposed </span><strong><span lang="AR-SA" style="font-size: 10pt; line-height: 125%; font-family: Calibri, sans-serif;">&lrm;</span></strong><span style="font-size: 11pt; line-height: 125%; font-family: Calibri, sans-serif;">model using a genetic algorithm. </span><strong><span lang="AR-SA" style="font-size: 10pt; line-height: 125%; font-family: Calibri, sans-serif;">&lrm;</span></strong><span style="font-size: 11pt; line-height: 125%; font-family: Calibri, sans-serif;">The simulation results show an MSE value of </span><strong><span lang="AR-SA" style="font-size: 10pt; line-height: 125%; font-family: Calibri, sans-serif;">&lrm;</span></strong><span style="font-size: 11pt; line-height: 125%; font-family: Calibri, sans-serif;">0.000774</span><strong><span lang="AR-SA" style="font-size: 10pt; line-height: 125%; font-family: Calibri, sans-serif;">&lrm;</span></strong><span style="font-size: 11pt; line-height: 125%; font-family: Calibri, sans-serif;"> for </span><strong><span lang="AR-SA" style="font-size: 10pt; line-height: 125%; font-family: Calibri, sans-serif;">&lrm;</span></strong><span style="font-size: 11pt; line-height: 125%; font-family: Calibri, sans-serif;">normal operation of the PV </span><strong><span lang="AR-SA" style="font-size: 10pt; line-height: 125%; font-family: Calibri, sans-serif;">&lrm;</span></strong><span style="font-size: 11pt; line-height: 125%; font-family: Calibri, sans-serif;">system</span><strong><span lang="AR-SA" style="font-size: 10pt; line-height: 125%; font-family: Calibri, sans-serif;">&lrm;</span></strong><span style="font-size: 11pt; line-height: 125%; font-family: Calibri, sans-serif;"> and </span><strong><span lang="AR-SA" style="font-size: 10pt; line-height: 125%; font-family: Calibri, sans-serif;">&lrm;</span></strong><span style="font-size: 11pt; line-height: 125%; font-family: Calibri, sans-serif;">0.009863</span><strong><span lang="AR-SA" style="font-size: 10pt; line-height: 125%; font-family: Calibri, sans-serif;">&lrm;</span></strong><span style="font-size: 11pt; line-height: 125%; font-family: Calibri, sans-serif;"> for the shading effect</span><strong><span lang="AR-SA" style="font-size: 10pt; line-height: 125%; font-family: Calibri, sans-serif;">&lrm;</span></strong><span style="font-size: 11pt; line-height: 125%; font-family: Calibri, sans-serif;"> between the estimated </span><strong><span lang="AR-SA" style="font-size: 10pt; line-height: 125%; font-family: Calibri, sans-serif;">&lrm;</span></strong><span style="font-size: 11pt; line-height: 125%; font-family: Calibri, sans-serif;">and reference information </span><strong><span lang="AR-SA" style="font-size: 10pt; line-height: 125%; font-family: Calibri, sans-serif;">&lrm;</span></strong><span style="font-size: 11pt; line-height: 125%; font-family: Calibri, sans-serif;">rates.&nbsp;</span>