用强化学习找电力网络中更多稳定解的配置。
Reinforcement Learning for Power-Flow Network Analysis
- 设计概率奖励函数逼近电力方程解的数量。
- 发现解数远超平均基线的网络参数组合。
- 适用于电力系统设计与非线性代数问题研究者。
电力潮流方程是非线性多变量方程，描述了电网中节点功率注入与母线电压之间的关系。给定网络拓扑，我们关注的是寻找具有多个平衡点的网络参数，即电力潮流方程具有多个实数解的情形。当前计算代数领域的最先进算法无法处理变量较多的网络。为此，我们设计了一个概率奖励函数，近似估算方程的实根数量，并构建模仿潮流方程空间的状态空间。我们推导了高斯模型下的平均根数作为基线，强化学习代理在此基础上发现了远超平均值的解数实例。这展示了强化学习在电力潮流网络设计与分析中的潜力，也表明其可为复杂非线性代数或几何问题提供实质性贡献。
原文摘要 · Abstract (English)
The power flow equations are non-linear multivariate equations that describe the relationship between power injections and bus voltages of electric power networks. Given a network topology, we are interested in finding network parameters with many equilibrium points. This corresponds to finding instances of the power flow equations with many real solutions. Current state-of-the art algorithms in computational algebra are not capable of answering this question for networks involving more than a small number of variables. To remedy this, we design a probabilistic reward function that gives a good approximation to this root count, and a state-space that mimics the space of power flow equations. We derive the average root count for a Gaussian model, and use this as a baseline for our RL agents. The agents discover instances of the power flow equations with many more solutions than the average baseline. This demonstrates the potential of RL for power-flow network design and analysis as well as the potential for RL to contribute meaningfully to problems that involve complex non-linear algebra or geometry. \footnote{Author order alphabetic, all authors contributed equally.
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