Controlling Time-Variant Virtual Inertia from Storage by Dynamic Programming and PROPT

The integration of renewables gradually replaces the traditional power plants, and this makes that the rotational inertia provided by the power plants is decreasing with time. Virtual inertia emulated by power electronic devices is becoming a promising way to stabilize the frequency of power system when a disturbance happens. And how to control virtual inertia to achieve desired performance is an important question to be answered. In this work, authors formulate an optimal control problem to describe the behaviour of controlling the time-variant inertia from storage, and structure preserving model is utilized to describe the dynamics of system, where frequencies of all buses are preserved. Also, practical constraints such as frequency contraints for buses, power/energy constraints for storage are incorporated in the optimal control problem. To solve this optimal control problem, dynamic programming (DP) and PROPT MATLAB Optimal Control Software are employed to obtain global optimal solution (virtual inertia trajectory). The simulation results show the correctness and effectiveness of our problem formulation and solving method.