The renewable power systems have become more susceptible to the system insecure than traditional power systems due to the reducing inertia and damping properties. In the meantime, inevitable time delays commonly exist in different procedures of the energy systems, such as computational delay, which may lead to poor performance, or even instability. Therefore, the time-delay impacts should be properly taken into account. However, the time-delay system belongs to the class of functional differential equations mathematically. With a transcendental characteristic equation, infinite dimension will increase transformation complexity and computation pressure. To rapidly describe the time-delay impact for multiarea power systems with time delays, a dimension reduction method based on the solution operator discretization is proposed in this paper. The quantitative relationship between time delays and system damping ratio is revealed for the first time. It starts with a state space equation for the entire frequency regulation system, the spectrum of time delayed systems is transferred into the spectrum of infinite-dimensional operators, followed by discretizing the solution operator. After that, a simple approximate matrix of finite dimensions is established, which sufficiently reflects the effect of time delays. The proposed method can not only ensure low computational burden efficiency via dimension reduction, but also extract the nonlinear coupling between the time delay and the damping deterioration.
Keywords renewable energy resources, dimension reduction, time delays, solution operator discretization