Smoothing Property of Load Variation Promotes Finding Global Solutions of Time-Varying Optimal Power Flow
Smoothing Property of Load Variation Promotes Finding Global Solutions of Time-Varying Optimal Power Flow
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DOI：
10.1109/tcns.2021.3084039
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发表时间：
2021-09
影响因子：
4.2
通讯作者：
Julie Mulvaney-Kemp;S. Fattahi;J. Lavaei
中科院分区：
文献类型：
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作者：
Julie Mulvaney-Kemp;S. Fattahi;J. Lavaei
本文分析了时变负荷下最优潮流的求解轨迹。尽管它是非线性的，但时变的最优潮流通常每隔5-15分钟使用局部搜索算法来求解。如果不能获得电力优化问题的全局最优解，将危及电网的可靠性，并造成经济和环境问题。本文的目的是通过了解最优潮流解轨迹的最优性行为来解决这个问题。对加州数据的实证研究表明，在数据变化足够大的情况下，即使问题存在许多局部极小值，局部搜索方法也能将最优潮流解到全局最优。为了解释这一现象，我们引入了一个反向映射，它将时变最优潮流在给定时刻的全局解与一组期望的初始点联系起来。我们证明了这种映射可以作为隐式凸化的最优潮流的随机梯度上升算法，证明了随着时间的推移，劣解的逃逸是合理的。这项工作首次从数学上解释了时态数据变化如何影响解决电力运营问题的复杂性。
This article analyzes solution trajectories for optimal power flow (OPF) with time-varying load. Despite its nonlinearity, time-varying OPF is commonly solved every 5–15 min using local-search algorithms. Failing to obtain the globally optimal solution of power optimization problems jeopardizes the grid's reliability and causes financial and environmental issues. The objective of this article is to address this problem by understanding the optimality behavior of OPF solution trajectories. An empirical study on California data shows that, with enough variation in the data, local search methods can solve OPF to global optimality, even if the problem has many local minima. To explain this phenomenon, we introduce a backward mapping that relates the time-varying OPF's global solution at a given time to a set of desirable initial points. We show that this mapping could act as a stochastic gradient ascent algorithm on an implicitly convexified formulation of OPF, justifying the escape of poor solutions over time. This work is the first to mathematically explain how temporal data variation affects the complexity of solving power operational problems.