Chance-constrained program (CCP) is a popular stochastic optimization method in power system planning, and operation problems. Conditional Value-at-Risk (CVaR) provides a convex approximation for chance constraints which are nonconvex. Although CCP assumes an exact empirical distribution, and the optimum of a stochastic programming model is thought to be sensitive in the designated probability distribution, this letter discloses that CVaR reformulation of a chance constraint is intrinsically robust. A pair of indices are proposed to quantify the maximum tolerable perturbation of the probability distribution, and can be computed from a computationally-cheap dichotomy search. An example on the coordinated capacity optimization of energy storage, and transmission line for a remote wind farm validates the main claims. The above results demonstrate that stochastic optimization methods are not necessarily vulnerable to distributional uncertainty, and justify the positive effect of the conservatism brought by the CVaR reformulation.

中文翻译：

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分析和量化机会约束随机程序的 CVaR 重构的内在分布稳健性

机会约束规划 (CCP) 是电力系统规划和运行问题中流行的随机优化方法。条件风险价值 (CVaR) 为非凸的机会约束提供凸近似。尽管 CCP 假设了一个精确的经验分布，并且随机规划模型的最优值被认为在指定的概率分布中很敏感，但这封信揭示了机会约束的 CVaR 重新制定本质上是稳健的。提出了一对指标来量化概率分布的最大可容忍扰动，并且可以通过计算成本低廉的二分法搜索来计算。远程风电场的储能和输电线路的协调容量优化示例验证了主要主张。