Deep learning-based approach for solving optimal power flow problems with flexible topology

A method for solving multiple OPF equations of an AC electrical power system with plural topologies and admittances is provided. The method includes determining a continuous admittance space to embed the plural topologies, determining a plurality of voltage magnitudes and a plurality of voltage phase angles of the plurality of buses by a deep neural network, and reconstructing an active power generation and a reactive power generation using power flow equations according to the plurality of voltage magnitudes, the plurality of voltage phase angles, and the load inputs. The continuous admittance space is an admittance matrix of a plurality of line admittances each having a default admittance computed using a conductance and a susceptance of the plurality of branches. The deep neural network receives the load inputs and the plurality of line admittances as inputs.