A parallel method for solving the DC security constrained optimal power flow with demand uncertainties

The security constrained optimal power flow (SCOPF) is a fundamental tool to analyze the security and economy of a power system. To ensure the safe and economic operation of a system considering demand uncertainties and to acquire economic and reliable solutions, in this paper, a parallel method for solving the interval DC SCOPF with demand uncertainties is presented. By using the interval optimization method, the uncertain nodal load can be expressed as interval variables and integrated into the DC SCOPF model, which is then formed as a large scale nonlinear interval optimization formulation. According to the theory of interval matching and selection of the extreme value intervals, the interval DC SCOPF problem can be transformed into two deterministic nonlinear programming problems and solved by alternating direction method of multipliers (ADMM) to obtain the range information of interval formulation variables. Using ADMM, the above two deterministic problems, which are large in scale because of the large number of preconceived contingencies, all can be split into independent sub-problems corresponding to pre-contingency status and each individual post-contingency cases. These small-scale sub-problems can be solved in parallel to improve the computing speed. Compared with the Monte Carlo (MC) method, the simulation results of the IEEE 30-, 57- and 118-bus systems validate the effectiveness of the proposed method.