Estimation of the voltage value at the maximum power point using the Levenberg-Marquardt algorithm

In order to meet the desired power requirement in photovoltaic (PV) systems, PV panels can have a series, parallel or series-parallel connection structure. Especially for the series PV panel connection structure, the irradiance difference between the panels directly affects the generated current value. The current generated by each panel varies with the irradiance value. Bypass diodes prevent possible negativities by disabling the PV panel with low irradiance value. However, bypass diodes cause the formation of maximum power points (MPPs) in the power-voltage ($\mathrm{P}-\mathrm{V}$) characteristics of PV systems. In order to obtain maximum power from PV systems, Maximum Power Point Tracking (MPPT) algorithms are used to keep the system’s operating point at the most efficient point. These algorithms can instantly determine the highest power that the PV panel can produce, depending on changes in environmental conditions such as solar irradiance and temperature. Thus, the efficiency of the system is increased. In this regard, the two most critical parameters that directly affect the voltage value at the operating point, irradiance and temperature, were randomly selected and initial conditions for modeling were created. The temperature values were used as the same value for the panels. A total of 2001 data were used for a panel in the study. 70% of this data was separated as train, 15% as test and 15% as validation. The Levenberg-Marquardt algorithm and the Scaled Conjugate Gradient algorithm were compared in terms of mean square error (MSE) and coefficient of determination $\left(\mathbf{R}^{\mathbf{2}}\right)$ performance criteria. It was observed that the coefficient of determination for the training phase was 0.9993,0.999 and 0.9989 for train, test and validation, respectively. From the obtained results, it was observed that the Levenberg-Marquardt algorithm made 3.09%, 3.4% and 3.08% more accurate predictions in train, test and validation values than the Scaled Conjugate Gradient algorithm. In addition, the effectiveness of the proposed model for three different scenarios was tested with the Matlab/Simulink simulation program.