Data-Driven Optimal Power Flow: A Behavioral Systems Approach

The increasing decentralization of power systems driven by a large number of renewable energy sources poses challenges in power flow optimization. Partially unknown power line properties can render model-based approaches unsuitable. With increasing deployment of sensors, data-driven methods rise as a promising alternative. They offer the flexibility to adapt to varying grid structures and unknown line properties. In this paper, we propose a novel data-driven representation of nonlinear power flow equations for radial grids based on Willems' Fundamental Lemma. The approach allows for direct integration of input/output data into power flow optimisation, enabling cost minimization and constraint enforcement without requiring explicit knowledge of the electrical properties or the topology of the grid. Moreover, we formulate a convex relaxation to ensure compatibility with state-of-the-art solvers. In a numerical case study, we demonstrate that the novel approach performs similar to state-of-the-art methods, without the need for an explicit system identification step.