Application of State Feedback Controller to Ensure Robust D-Stable Operation of Virtual Synchronous Generators
Mehdi Pourmohammad, Mohammadreza Toulabi, Ali Mohammad Ranjbar
Abstract
This article presents a comprehensive small signal model for a virtual synchronous generator (VSG) integrated into a microgrid. In the developed state-space, active and reactive power control loops of the VSG as well as resistances, and reactances of the lines are considered. Based on this model, the robust D-stable region in terms of different values of inertia constant <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(M)$</tex-math></inline-formula> , and damping coefficient <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(D)$</tex-math></inline-formula> values of the VSG is obtained. To enhance both transient performance as well as guarantee the robust D-stable operation of VSG, an optimization problem is also proposed. Moreover, a new control method is suggested to damp frequency oscillations of the microgrid. The proposed controller is a state feedback which uses the pole placement method and can be used in both of the grid-connected, and isolating modes of operation. In this controller, poles can be placed in the desired locations in order for the microgrid to achieve the desired transient response. In order to access all state variables, a state observer is used to avoid measurement of state variables. Accordingly, one of the features of the proposed method is its ability to move poles without requiring additional sensors. The performance of the proposed method is evaluated in MATLAB/SIMULINK, which shows enhanced dynamic behavior of the microgrid.