Active/Reactive Power Decomposition Approaches To The AC Optimal Power Flow Problem

This paper revisits active and reactive power decomposition techniques as applied to the optimal power flow problem. The full nonlinear AC optimal power flow problem is decoupled into two lower dimensional nonlinear subproblems (active and reactive), seeking to characterize and exploit the well recognized property of the power flow Jacobian matrix: that the off-diagonal submatrix blocks are in some sense "small," reflecting the fact that network flow of active power is relatively weakly dependent on bus voltage magnitudes, while reactive power flow is relatively weakly dependent on bus voltage phase angles. We further exploit the fact that the standard objective function of the optimal power flow depends directly on active powers (of generators) only, and different, loss-related objective functions may be used for the reactive subproblem. These formulations are examined in a number of numerical examples, evaluating speed of convergence, and how close decoupled P-Q OPF solution is to that of the full AC OPF. While the improvements in computation time are modest, use of decoupled solutions as initial guesses to a full AC OPF is shown to be promising. In addition to the solution algorithms themselves, a method to characterize the magnitude of off-diagonal coupling terms in the power flow Jacobian is examined.