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.

中文翻译：

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具有不确定风电的燃气和电网的长期电压稳定约束协调调度

考虑到由于需求增加和考虑燃气系统和风电的新挑战，电力系统更接近运行边界的增加趋势，本文研究了长期电压稳定约束的综合电力和燃气系统优化调度。风能整合。充分条件表示为电压和注入功率的显式函数，用于约束电力系统的长期电压稳定性。由于此条件下的双线性项，使用收紧分段 McCormick 包络松弛将其转换为凸约束。二阶锥规划 (SOCP) 公式用于表示集成的电力和天然气系统的操作约束。风电损失概率，表示风电不确定性，是通过机会约束规划模型建立的，该模型通过基于星形不等式的样本平均近似扩展公式转化为确定性优化模型。两个测试系统，带有 6 节点燃气系统的 9 总线电气系统和带有 40 节点燃气系统的 IEEE 118 总线电气系统，用于验证所提出的模型。