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

A computer-implemented method for solving multiple optimal power flow (OPF) equations of an alternating-current (AC) electrical power system under a plurality of constraints with plural topologies and admittances, the AC electrical power system being modeled with a plurality of branches interconnecting a plurality of buses and generators each having a pre-determined line capacity, the plurality of buses being assigned with load inputs of a plurality of active loads

• p
• i
• d
• and a plurality of reactive loads
• q
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• d
• such that an individual bus is arranged to satisfy a respective active load and a respective reactive load, the method comprising:
• determining a continuous admittance space Y to embed the plural topologies, wherein the continuous admittance space Y is an admittance matrix of a plurality of line admittances Yi,j each having a default admittance computed using a conductance bij and a susceptance gij of the plurality of branches;
• determining a plurality of voltage magnitudes v and a plurality of voltage phase angles θ of the plurality of buses such that a complex-valued voltage observed at the individual bus is predicted, wherein the plurality of voltage magnitudes v and the plurality of voltage phase angles θ are computed by a deep neural network (DNN), and wherein the DNN receives the load inputs and the plurality of line admittances Yi,j as inputs;
• reconstructing an active power generation pg and a reactive power generation qg using power flow equations according to the plurality of voltage magnitudes v, the plurality of voltage phase angles θ, and the load inputs, whereby a plurality of required active power generations and a plurality of required reactive power generations for the plurality of buses are obtained;
• and
• training the DNN with a training dataset before using the DNN to compute the plurality of voltage magnitudes v and the plurality of voltage phase angles θ, wherein the training dataset includes a plurality of training admittances used as the plurality of line admittances in training the DNN, an individual training admittance being associated with a corresponding line admittance, the individual training admittance being randomly and uniformly sampled from a region of −2% to 120% of the default admittance of the corresponding line admittance such that the individual training admittance covers both on and off statuses of the corresponding line admittance to thereby enable the DNN to be used for solving the multiple OPF equations under the plurality of constraints with the plural topologies and admittances without a need to retrain the DNN.