On MATLAB-based Stability Analysis of Discrete Differential Capacitor Voltage Feedback for Active Damping of LCL Filters

Active damping of LCL filter with capacitor voltage feedback poses design and implementation challenge since a pure differentiator cannot be replicated exactly in the digital domain. Different approximations are used for implementing the discrete differentiator, whose behaviour (particularly phase contribution) often deviates from its continuous domain counterpart. Hence the performance guaranteed by the control system, designed in continuous domain, won't be delivered by the digital implementation. The paper proposes a virtual-impedance model for two of the discretization methods - (i) backward Euler approximation, and (ii) backward Euler approximation with lead compensator, to aid in the design and stability analysis of the converter control system in continuous domain. With the equivalent virtual impedance model, the feedback gain for active damping can be designed appropriately in continuous domain itself, and the designed value can be implemented in the discrete domain, without compromising the system performance. Simulation studies, done in MATLAB/Simulink based on the proposed approach are provided to substantiate the efficacy of the method.