Modeling the AC Power Flow Equations with Optimally Compact Neural Networks: Application to Unit Commitment
This addresses a computational bottleneck for power system operators by providing a more efficient method for embedding power flow constraints in optimization, though it is incremental as it builds on existing neural network approaches.
The paper tackles the computational intractability of nonlinear AC power flow equations in power system optimization by developing an 'optimally compact' neural network that maintains high accuracy with a tractable number of binary variables, showing it outperforms DC and linearized approximations in AC unit commitment problems.
Nonlinear power flow constraints render a variety of power system optimization problems computationally intractable. Emerging research shows, however, that the nonlinear AC power flow equations can be successfully modeled using Neural Networks (NNs). These NNs can be exactly transformed into Mixed Integer Linear Programs (MILPs) and embedded inside challenging optimization problems, thus replacing nonlinearities that are intractable for many applications with tractable piecewise linear approximations. Such approaches, though, suffer from an explosion of the number of binary variables needed to represent the NN. Accordingly, this paper develops a technique for training an "optimally compact" NN, i.e., one that can represent the power flow equations with a sufficiently high degree of accuracy while still maintaining a tractable number of binary variables. We show that the resulting NN model is more expressive than both the DC and linearized power flow approximations when embedded inside of a challenging optimization problem (i.e., the AC unit commitment problem).