Stochastic-Robust Optimal Power Flow With Small-Signal Stability Guarantee Under Renewable Uncertainties

Abstract

The diversification of power system operation modes raises the necessity of incorporating dynamic characteristics into steady-state operation. Small-signal stability is a representative issue. Though, existing frameworks either ignore the uncertainties of renewables, or only focus on the worst case. In this regard, this paper establishes a small-signal stability constrained stochastic-robust optimal power flow (OPF) model, which aims to optimize the expected cost of scheduling results with respect to the probability distributions of uncertainties while ensuring the small-signal stability requirement even in extreme scenarios. However, the synergy of uncertainties and the complicated small-signal stability mechanism significantly increase the solving difficulty. This paper proposes a comprehensive framework to overcome this challenge. First, we solve the stochastic OPF without small-signal stability constraints. For those results that do not meet the stability requirements, we use them as initial points to locate the effective boundary of the OPF feasible region where the robust small-signal stability requirement is satisfied. The effective boundary location is realized in an iterative manner. Then, in the neighborhood of this effective boundary, we construct a linear surrogate expression to represent the original robust small-signal stability constraint with Markov-chain Monte Carlo (MCMC) sampling and sample weighted support vector machine (swSVM). Finally, we solve the OPF model with the surrogate constraint. Moreover, we further propose a constraint correction strategy to guarantee the stability requirement. Case studies verify that the proposed method can acquire economical operation schemes and meet the robust small-signal stability requirement at the same time.