ADMM-based algorithm for solving DC-OPF in a large electricity network considering transmission losses

The authors address the problem of solving DC-optimal power flow (OPF) considering transmission losses in a large electricity network. The loss in a line is considered in the power balance equation and is taken as proportional to the absolute value of the flow through the line. Many standard solvers fail to converge to an optimal solution of the DC-OPF for comparatively large bus systems, even with a quadratic cost of generation. The authors use a decomposition algorithm such as alternating directions method of multipliers (ADMM) to address this problem. However, the ADMM algorithm cannot be directly applied to this problem because of the sparsity of the coefficient matrices of the objective function and the presence of inequality constraints. Thus, the authors introduce two relaxations to the DC-OPF problem, namely the regularisation and the modified penalisation. The authors provide a novel ADMM algorithm for the regularised and the modified penalised problem which converges to an optimal solution even for large bus systems. The authors show that the ADMM algorithm converges near to the optimal solution of the DC-OPF problem if the regularisation and modified penalisation parameters are chosen carefully. Numerical simulations illustrate the effectiveness of the algorithm.