Data-Driven Active Power Flow Modeling: 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 the increasing deployment of sensors, data-driven methods rise as a promising alternative, offering flexibility to adapt changes and deal with unknown properties. In this paper, we propose a novel data-driven representation of nonlinear active power flow equations for radial grids based on Willems' Fundamental Lemma. Our approach allows for direct integration of input/output data into active power flow optimization, enabling cost minimization and constraint enforcement without requiring explicit knowledge of the electrical properties of the grid. Moreover, we derive a computationally tractable convex relaxation and show in a numerical case study that our approaches yield results that are identical to optimal active power flow formulations with known parameters.