  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.
