Risk assessment of critical time to renewable operation with steady-state security region

Uncertain and variable characteristics of renewable energy resources introduce challenges to power system operation. A normal operating point might be drifted towards an unreliable operating point due to stochastic outputs od renewables. This paper proposes a novel method for estimating critical time to unreliable operating point with steady-state constraints. In this work, a stochastic differential equation is employed to describe the distribution of renewables with predictable tendency and stochastic errors of prediction; meanwhile, the DC power flow based steady-state security region is used to restrict the injected space. To find the critical time that uncontrollable renewables leave the security region, according the flexibility requirements defined by NERC, the uncontrollable region is identified with the Fourier-Motzkin elimination first. And then, by solving the Chebychev center problem, the critical distance for variable renewable outputs is obtained. Finally, an analytical solution of expected exit-time for renewable outputs leaving the security region is given with the Martingale stopping theorem. The proposed method can be used to construct the condition-driven risk indicators. An illustrative example is employed to demonstrate and validate the proposed method.