DeepOPF-FT: One Deep Neural Network for Multiple AC-OPF Problems With Flexible Topology

Abstract

We propose <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ \mathsf{DeepOPF} $</tex-math></inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ \mathsf{FT}$</tex-math></inline-formula> as an embedded training approach to design <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">one</i> deep neural network (DNN) for solving multiple AC-OPF problems with flexible topology and line admittances, addressing a critical limitation of learning-based OPF schemes. The idea is to embed the discrete topology representation into the continuous admittance space and train a DNN to learn the mapping from (load, admittance) to the corresponding OPF solution. We then employ the trained DNN to solve AC-OPF problems over any power network with the same bus, generation, and line capacity configurations but different topology and/or line admittances. Simulation results over IEEE 9-/57- bus and a synthetic 2000-bus test cases demonstrate the effectiveness of our design and highlight the training efficiency improvement of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ \mathsf{DeepOPF} $</tex-math></inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ \mathsf{FT}$</tex-math></inline-formula> over training one DNN for every combination of power network topology and line admittances.