Evaluating Power Flow Manifold from Local Data around a Single Operating Point via Geodesics
This work addresses power system stability for grid operators by enabling efficient manifold inference from limited data, though it appears incremental as it builds on existing differential geometry techniques.
The paper tackles the challenge of maintaining feasible power system operation with renewable energy variability by proposing a data-based method to evaluate the power flow manifold from local measurements around a single operating point, demonstrating efficacy through numerical tests with arbitrary directional variations.
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.