Paper
Evaluating Power Flow Manifold from Local Data around a Single Operating Point via Geodesics
Authors
Qirui Zheng, Dan Wu, Franz-Erich Wolter, Sijia Geng
Abstract
The widespread adoption of renewable energy poses a challenge in maintaining a feasible operating point in highly variable scenarios. This paper demonstrates that, within a feasible region of a power system that meets practical stability requirements, the power flow equations define a smooth bijection between nodal voltage phasors (angle and magnitude) and nodal active/reactive power injections. Based on this theoretical foundation, this paper proposes a data-based power flow evaluation method that can imply the associated power flow manifold from a limited number of data points around a single operating point. Using techniques from differential geometry and analytic functions, we represent geodesic curves in the associated power flow manifold as analytic functions at the initial point. Then, a special algebraic structure of the power flow problem is revealed and applied to reduce the computation of all higher-order partial derivatives to that of the first-order ones. Integrating these techniques yields the proposed data-based evaluation method, suggesting that a small number of local measurements around a single operating point is sufficient to imply the entire associated power flow manifold. Numerical cases with arbitrary directional variations are tested, certifying the efficacy of the proposed method.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.21514v1</id>\n <title>Evaluating Power Flow Manifold from Local Data around a Single Operating Point via Geodesics</title>\n <updated>2026-03-23T03:12:04Z</updated>\n <link href='https://arxiv.org/abs/2603.21514v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.21514v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>The widespread adoption of renewable energy poses a challenge in maintaining a feasible operating point in highly variable scenarios. This paper demonstrates that, within a feasible region of a power system that meets practical stability requirements, the power flow equations define a smooth bijection between nodal voltage phasors (angle and magnitude) and nodal active/reactive power injections. Based on this theoretical foundation, this paper proposes a data-based power flow evaluation method that can imply the associated power flow manifold from a limited number of data points around a single operating point. Using techniques from differential geometry and analytic functions, we represent geodesic curves in the associated power flow manifold as analytic functions at the initial point. Then, a special algebraic structure of the power flow problem is revealed and applied to reduce the computation of all higher-order partial derivatives to that of the first-order ones. Integrating these techniques yields the proposed data-based evaluation method, suggesting that a small number of local measurements around a single operating point is sufficient to imply the entire associated power flow manifold. Numerical cases with arbitrary directional variations are tested, certifying the efficacy of the proposed method.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='eess.SY'/>\n <published>2026-03-23T03:12:04Z</published>\n <arxiv:comment>10 pages,11 figures, submitted to IEEE Transactions on Power Systems</arxiv:comment>\n <arxiv:primary_category term='eess.SY'/>\n <author>\n <name>Qirui Zheng</name>\n </author>\n <author>\n <name>Dan Wu</name>\n </author>\n <author>\n <name>Franz-Erich Wolter</name>\n </author>\n <author>\n <name>Sijia Geng</name>\n </author>\n </entry>"
}