Small‐signal stability analysis and control of stochastic time‐variant power system through differential inclusion theory

Abstract

Here, small-signal stability issue associated with multi-scale uncertainty excitation is investigated by using differential inclusion theory. Specifically, a polytopic linear differential inclusion (PLDI) model for large-scale uncertainty system is developed, in which a modified non-sequence Monte Carlo method is introduced to identify a series of time-variant operation states. Additionally, a simplified small-signal model of renewable energy resources (RES) is proposed, the outputs of RES are modelled as time-varying elements in PLDI model to reflect the uncertainty in the linearised matrix. The stability criterion for the stochastic time-varying system is mathematically deduced based on convex hull Lyapunov function (CHLF). The criterion is then utilised to design robust stabilisers for stochastic system. Simulation, utilising two-area four-machine system and New England 39-bus test system, demonstrates the benefits of the proposed model in describing system stochastic characteristics, designing additional controllers and reducing computational burden.