Data-Driven Chance-Constrained Optimal Gas-Power Flow Calculation: A Bayesian Nonparametric Approach

This paper proposes a data-driven chance-constrained optimal gas-power flow (OGPF) calculation method without any prior assumption on the distribution of uncertainties of wind power generation. The Gaussian mixture model is employed to fit the uncertainty distribution, where the Bayesian nonparametric Dirichlet process is adopted to tune the component number. To facilitate the online application of the proposed methods, an online-offline double-track distribution construction approach is established, where the frequency of training the relatively time-consuming Dirichlet process Gaussian mixture model can be reduced. On account of the quadratic gas consumption expression of gas-fired generators as well as the linear decision rule based uncertainty mitigation mechanism, the chance constraints would become quadratic ones with quadratic terms of uncertainties, which makes the proposed model more intractable. An equivalent linear separable counterpart is then provided for the quadratic chance constraints, after which the intractable chance constraints could be converted into traditional linear ones. The convex-concave procedure is used to crack the nonconvex Weymouth equation in the gas network and the auxiliary quadratic equalities. Simulation results on two test systems validate the effectiveness of the proposed methods.