Transient and Steady-State Response of a Fractional-Order Dynamic PV Model Under Different Loads

In this paper, a fractional-order dynamic model of the photovoltaic (PV) solar module is introduced. Dynamic modeling of PV solar modules is useful when used in switching circuits and grid-connected situations. The dynamic elements of the proposed model are a fractional-order inductor and capacitor of two independent orders which allow for two extra degrees of freedom over the conventional dynamic model. The step response and transfer function of the load current are investigated for different orders under resistive and supercapacitor loading conditions. Closed-form expressions for the time response of the load current at equal orders of capacitor and inductor are derived. Stability analysis of the load current transfer function is carried out for different orders and loading conditions. The regions for pure real and pure imaginary input admittance scenarios are calculated numerically for both resistive and supercapacitor load cases. It is found that the order of the inductor has a dominant effect on the responses. As a proof of concept, the model is fitted to experimental data to show its flexibility in regenerating the actual response. The fitted fractional-order model response is compared to optimized integer-order ones from literature showing noticeable improvement.