Reinforcement Learning for Power-Flow Network Analysis
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| Format: | Preprint |
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2026
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| _version_ | 1866908868777345024 |
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| author | Ergur, Alperen Lindberg, Julia Miller, Vinny |
| author_facet | Ergur, Alperen Lindberg, Julia Miller, Vinny |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_05673 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Reinforcement Learning for Power-Flow Network Analysis Ergur, Alperen Lindberg, Julia Miller, Vinny Machine Learning Symbolic Computation Algebraic Geometry 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. |
| title | Reinforcement Learning for Power-Flow Network Analysis |
| topic | Machine Learning Symbolic Computation Algebraic Geometry |
| url | https://arxiv.org/abs/2603.05673 |