Evaluating Power Flow Manifold from Local Data around a Single Operating Point via Geodesics

TL;DR

This paper introduces a novel data-driven method to evaluate the power flow manifold in power systems using local measurements and differential geometry, enabling efficient analysis of system behavior around a single operating point.

Contribution

It presents a theoretical foundation and a practical algorithm that reconstructs the power flow manifold from limited local data using geodesics and algebraic simplifications.

Findings

Accurately reconstructs power flow manifold from few local measurements.

Reduces computational complexity by leveraging algebraic structure.

Validated with numerical tests demonstrating effectiveness.

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.