Equivalent Reduced DC Network Models With Nonlinear Load Functions: A Data-Driven Approach

Nonconvex AC power flow models feature a heavy computational burden and lack optimality guarantees to be considered in industry expansion and operational planning activities. Additionally, the consideration of full network models, in general, leads to undesirable levels of computational burden, even under standard DC approximations. Notwithstanding, current reduction methods fail to accurately reproduce actual system behavior for a wide range of operating points. In this context, we propose a novel data-driven network reduction method to generate equivalent reduced DC power flow models with nonlinear load functions. Our method aims at providing a high-quality representation of the internal system by minimizing the mismatch between the response of the equivalent DC model and the complete AC power flow (or real measurements) under multiple operating-point data. Thus, the approach can be interpreted as a physics-informed machine-learning method as it trains (or estimates) some parameters of the reduced DC power-flow model to fit pre-calculated data. The method determines: 1) a reduced external equivalent network model (topology and parameters), 2) the optimal allocation of external power injections to the boundary buses, and 3) the coefficients determining artificial nonlinear load functions of the operating-point data. Out-of-sample evaluation tests corroborate the performance of our model against modified Ward reduction benchmark models.