Lagrangian relaxation based optimal power flow

Optimal Power Flow (OPF) using Modified Lagrangian Relaxation (MLR) method is presented. Classical Lagrangian Relaxation (LR) method is modified using multiplier prediction. The algorithm is improved by decoupling the active and reactive power sub-problems and using approximate Hessian matrices. A practical OPF problem definition is used without any approximations.;A generalized and practical OPF problem definition including linear, piece-wise linear, and non-linear and heuristic functions is used. The problem is solved using primal-dual iteration. To overcome the notoriously slow convergence of traditional gradient search multiplier update, multiplier prediction is used. At each dual iteration Lagrange multipliers are predicted using sensitivity matrices. The sensitivity matrices provide a relationship between multipliers and constraint violations. To reduce the problem size, active and reactive power sub-problems are decoupled. Throughout the solution approximate Hessian matrices are used. To reduce computational time, these approximate matrices are formed only when necessary.;The method is implemented on a HP9000/720 workstation using C++ language. It is tested using 17-bus, 57-bus and 1059-bus systems. Generation cost, transmission loss, amount of control movement and number of control actions are minimized. Results obtained using minimum loss and minimum number of control actions are presented. The optimality of the MLR method is tested against traditional LR method. The run-time is obtained in terms of the number of LU factorizations necessary, and compared with Newton's OPF method. The run-time is also obtained as a multiple of that of fast decoupled loadflow method.;Test results show a considerable improvement in run-time compared to Newton's method with the same accuracy. The run time is approximately equivalent to linear programming methods, but more accurate results are indicated since no linear programming approximations are used.;The MLR method is approximately 20 to 30 times faster than Newton's method. The run-time is 3 to 5 times that of fast decoupled loadflow and hence close to that of linear programming methods.