Analytical Factorized Model for Stability Analysis and Optimization of Shunt RC Damped LCL Filter for Grid-Connected Voltage Source Inverters

In this article, an optimal design procedure of shunt RC damped LCL filter is discussed. The proposed design procedure finds the minimum damping resistance to guarantee the stability of the grid-current controller without affecting the effectiveness of the filter. This minimum value is derived using the factorized filter input admittance and filter forward transadmittance. The proposed factorization procedure allows us to have an analytical expression of system poles and zeros. Moreover, the minimum damping resistor is determined upon the desired crossover frequency and the desired phase margin of the grid-current controller. After that, an objective function is assumed, and an optimization problem is formulated to minimize the physical size of the filter by minimizing the total capacitance and inductance and by minimizing the filter ripple content as well. Accordingly, the proposed objective function minimizes the filter physical size and filter power losses and, hence, enhances filter's efficiency. A prototype demonstrates and validates the proposed filter design and analysis experimentally.