Design of Virtual Impedance Control Loop using the Complex Frequency Approach

In this paper the dynamic response of the virtual impedance control loop for power electronic converters is studied using the recently proposed concept of complex frequency. This quantity captures bus frequency variations due to changes in both the phase angle and the amplitude of the voltage and current. The paper analytically derives the link between complex power and complex frequency, allowing the incorporation of the virtual impedance control equations. First, the impact of the virtual impedance control on the complex frequency is considered independently of other control loops by simplifying the overall control structure. Then, the equations are generalised to include the interaction between the virtual impedance and the proportional-integral voltage controller. The paper shows that the proposed theoretical formulation allows identifying the dynamic effect of the virtual impedance and simplifies its design. These features are demonstrated by using simulations based on a modified version of the WSCC 9-bus system.