Proportional-Integral and Nonlinear Cubic Control to Enhance Small-Signal and Transient Stability of EV Charging Station and DC Microgrid

Abstract

A proportional-integral (PI) controller in parallel with a nonlinear cubic controller is proposed in order to achieve the objective of addressing both the issues of small-signal and large-signal stability, with the latter also being referred to as transient stability. Within the scope of application and of practical relevance is the enhancement of the region of attraction for which equilibrium states are found for an electric vehicle (EV) charging station while considering constraints. As a main contribution, a methodology for the design of the cubic controller to expand the constrained region of attraction (CROA) through sum-of-squares (SOS) programming is formulated, implemented, and validated. The developed SOS program incorporates the construction of Lyapunov functions, which are employed to estimate the CROA. The optimal coefficient of the cubic controller is obtained by estimating the largest CROA. The integration of the cubic controller enhances the robustness of the EV charging station against large disturbances, while the performance under minor disturbances is dealt with by the accompanying PI controller. As a result, the proposed PI-cubic voltage controller enhances the stability across wide operating ranges including fast charging and in the presence of constant power loads. In general, application also includes DC microgrid stability. Time-domain simulations conducted in Matlab validate the made claims. During the considered outage of local power generation on the DC side of the charging station and microgrid, transient stability was only maintained with the proposed controller, and an overcurrent situation was avoided. The PI-cubic controller is shown to be effective in enhancing robustness.