Estimating the Probability of Infeasible Real-Time Dispatch Without Exact Distributions of Stochastic Wind Generations

This paper proposes a data-driven and convex optimization based method to quantify the probability of infeasible real-time dispatch (RTD) of power systems with volatile wind energy integrations. The required information about wind power is a finite sequence of moments, instead of the exact probability distribution function (PDF). The candidate PDFs are restricted in a functional set subject to moment constraints. By assuming the dispatchable region of nodal wind power injection is available, we propose a semi-definite programming (SDP) based method and a linear programming (LP) based method to estimate the probability of infeasibility in the worst wind power distribution. We also suggest two alternative methods based on the emerging generalized Chebyshev inequality (GCI) and generalized Gauss inequality (GGI), which only utilize the first and second order moments, and boil down to solving SDPs. We compare the performances of all the discussed methods on the moderately sized IEEE 118-bus system. Experimental results demonstrate that our method can offer monotonically better estimation when higher order moments are provided and is competitive with GCI and GGI.