Distributionally Robust Chance Constrained Optimal Power Flow Assuming Log-Concave Distributions
Distributionally Robust Chance Constrained Optimal Power Flow Assuming Log-Concave Distributions
复制标题
假设对数凹分布的分布鲁棒机会约束最优潮流
DOI：
10.23919/pscc.2018.8442927
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Ruiwei Jiang
中科院分区：
文献类型：
--
作者：
Bowen Li;J. Mathieu;Ruiwei Jiang
在各种不确定性（如可再生能源生产和负荷消耗）下，已经广泛提出了具有机会约束的优化公式来操作电力系统。像系统的物理限制的约束，需要在高置信水平得到满足。传统的求解方法要么对潜在的不确定性分布做出假设，要么给出过于保守的结果。我们开发了一个新的分布鲁棒（DR）的机会约束最优潮流公式，其中的机会约束满足一个家庭的分布与已知的一阶矩，椭球支持，并假设概率分布是对数凹的。由于大多数实际的不确定性具有对数凹概率分布，因此与传统的DR方法相比，在不牺牲可靠性的情况下，在公式中包括该假设降低了目标成本。我们推导出二阶锥近似的DR机会约束，从而在一个易于处理的制定，可以解决与商业求解器。我们评估我们的方法使用修改后的IEEE 9节点系统与不确定的风力发电生产的性能，并将其与标准方法进行比较。我们发现，我们的方法产生的解决方案是足够可靠的，成本低于传统的DR方法。
Optimization formulations with chance constraints have been widely proposed to operate the power system under various uncertainties, such as renewable production and load consumption. Constraints like the system's physical limits are required to be satisfied at high confidence levels. Conventional solving methodologies either make assumptions on the underlying uncertainty distributions or give overly-conservative results. We develop a new distributionally robust (DR) chance constrained optimal power flow formulation in which the chance constraints are satisfied over a family of distributions with known first-order moments, ellipsoidal support, and an assumption that the probability distributions are log-concave. Since most practical uncertainties have log-concave probability distributions, including this assumption in the formulation reduces the objective costs as compared to traditional DR approaches without sacrificing reliability. We derive second-order cone approximations of the DR chance constraints, resulting in a tractable formulation that can be solved with commercial solvers. We evaluate the performance of our approach using a modified IEEE 9-bus system with uncertain wind power production and compare it to standard approaches. We find that our approach produces solutions that are sufficiently reliable and less costly than traditional DR approaches.