  Effective power flow modeling critically affects the ability to efficiently
solve large-scale grid optimization problems, especially those with
topology-related decision variables. In this work, we put forth a generative
modeling approach to obtain a piecewise linear (PWL) approximation of AC power
flow by training a simple neural network model from actual data samples. By
using the ReLU activation, the NN models can produce a PWL mapping from the
input voltage magnitudes and angles to the output power flow and injection. Our
proposed generative PWL model uniquely accounts for the nonlinear and
topology-related couplings of power flow models, and thus it can greatly
improve the accuracy and consistency of output power variables. Most
importantly, it enables to reformulate the nonlinear power flow and line
status-related constraints into mixed-integer linear ones, such that one can
efficiently solve grid topology optimization tasks like the AC optimal
transmission switching (OTS) problem. Numerical tests using the IEEE 14- and
118-bus test systems have demonstrated the modeling accuracy of the proposed
PWL approximation using a generative approach, as well as its ability in
enabling competitive OTS solutions at very low computation order.

Systems and Control;Systems and Control