Evaluating Power Flow Manifold from Local Data around a Single Operating Point via Geodesics
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914413785645056 |
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| author | Zheng, Qirui Wu, Dan Wolter, Franz-Erich Geng, Sijia |
| author_facet | Zheng, Qirui Wu, Dan Wolter, Franz-Erich Geng, Sijia |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21514 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Evaluating Power Flow Manifold from Local Data around a Single Operating Point via Geodesics Zheng, Qirui Wu, Dan Wolter, Franz-Erich Geng, Sijia Systems and Control 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. |
| title | Evaluating Power Flow Manifold from Local Data around a Single Operating Point via Geodesics |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2603.21514 |