Long-Term Voltage Stability-Constrained Coordinated Scheduling for Gas and Power Grids With Uncertain Wind Power

Considering the increased trend that power systems are closer to the operating bounds because of the increased demand and new challenges in consideration of gas systems and wind power, this paper investigates long-term voltage stability-constrained integrated electric and gas system optimal scheduling in consideration of wind energy integration. A sufficient condition, which is represented as an explicit function of voltage and injected power, is used to constrain power system long-term voltage stability. Due to bilinear terms in this condition, tightening piecewise McCormick envelope relaxation is used to convert it into convex constraints. The second-order cone programming (SOCP) formulation is employed to represent the operational constraints of the integrated electric and gas system. The loss of wind power probability, representing wind power uncertainties, is established by a chance-constrained programming model, which is transformed into a deterministic optimization model by means of the star-inequality-based extended formulation of sample average approximation. Two test systems, the 9-bus electric system with the 6-node gas system and the IEEE 118-bus electric system with the 40-node gas system, are used to validate the proposed model.