Development of Nottingham Arc Model for DC Series Arc Modeling in Photovoltaic Panels

DC series arc faults are known as a great threat to photovoltaic (PV) systems. Due to component aging and the high level of dc voltage, the occurrence of dc series arc fault is a serious concern in PV generation units. This article deals with driving effective dc series arc models from the original Nottingham arc model using the recorded practical data in a PV system. The original Nottingham arc model has three constant parameters and suffers significant inaccuracy for modeling the series arc faults. To avoid the inaccuracy in the modeling, at first, a Nottingham model is developed that is relevant to voltage and current of the fault with three parameters including one constant model order for exponents of the current and two time-series coefficients. Also, to further improvement in the model's accuracy, a two-fold Nottingham model is proposed that is relevant to voltage and current of the fault with five parameters including two constant model orders for exponents of the current and three time-series coefficients. Finally, a full-time-variant Nottingham model is proposed that mathematically contains three time-series parameters including one time-variant model order of the current exponent. In the full-time-variant Nottingham model, the optimal parameters corresponding to each sliding window of data are utilized. In all the proposed models, the arc coefficients are estimated using a new formulation using the least-squares error technique. Verifying the effectiveness of the proposed models through actual data, the accuracy of the proposed models is compared with the original Nottingham model.