Load Variation Enables Escaping Poor Solutions of Time-Varying Optimal Power Flow
Load Variation Enables Escaping Poor Solutions of Time-Varying Optimal Power Flow
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DOI：
10.1109/pesgm41954.2020.9281807
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发表时间：
2020-08
期刊：
影响因子：
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通讯作者：
Julie Mulvaney-Kemp;S. Fattahi;J. Lavaei
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文献类型：
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作者：
Julie Mulvaney-Kemp;S. Fattahi;J. Lavaei
分析了时变负荷下最优潮流的解轨迹。尽管它的非凸性，它是常见的解决随时间顺序使用简单的局部搜索算法随时间变化的最优潮流。我们的目标是了解这些局部解轨迹的局部和全局最优性行为。对加州数据的实证研究表明，在不同点初始化的局部解轨迹可能收敛到数据驱动的OPF的时变全局解，即使问题在整个时间内有多个局部解。也就是说，这些轨迹可以避免糟糕的解决方案。为了解释这一现象，我们引入了一个向后映射，该映射将时变OPF全局解的邻域与一组理想的初始点联系起来。我们表明，这个建议向后映射可以作为一个随机梯度上升算法上的隐式convexified制定的OPF，这证明了逃逸的差的解决方案随着时间的推移。
This paper analyzes solution trajectories for optimal power flow (OPF) with time-varying load. Despite its nonconvexity, it is common to solve time-varying OPF sequentially over time using simple local-search algorithms. We aim to understand the local and global optimality behavior of these local solution trajectories. An empirical study on California data shows that local solution trajectories initialized at different points may converge to the time-varying global solution of the data-driven OPF, even if the problem has multiple local solutions throughout time. That is, these trajectories can avoid poor solutions. To explain this phenomenon, we introduce a backward mapping that relates a neighborhood of the time-varying OPF’s global solution at a given time to a set of desirable initial points. We show that this proposed backward mapping could act as a stochastic gradient ascent algorithm on an implicitly convexified formulation of OPF, which justifies the escaping of poor solutions over time.