Short-term generating scheduling with transmission and environmental constraints using an augmented Lagrangean-relaxation

This paper proposes a new approach based on augmented Lagrangean relaxation for short term generation scheduling problem with transmission and environmental constraints. In this method, the system constraints, e.g. load demand, spinning reserve, transmission capacity and environmental constraints, are relaxed by using Lagrangean multipliers, and quadratic penalty terms associated with system load demand balance are added to the Lagrangean objective function. Then the decomposition and coordination technique is used, and non-separable quadratic penalty terms are replaced by linearization around the solution obtained from the previous iteration. In order to improve the convergence property, the exactly convex quadratic terms of decision variables are added to the objective function as strongly convex, differentiable and separable auxiliary functions. The overall problem is decomposed into N subproblems, multipliers and penalty coefficients are updated in the dual problem and system constraints are satisfied iteratively. The corresponding unit commitment subproblems are solved by dynamic programming, and the economic dispatch with transmission and environmental constraints is solved by an efficient network flow programming algorithm. The augmented Lagrangean relaxation method enhanced by decomposition and coordination technique avoids oscillations associated with piece-wise linear cost functions. Numerical results indicate that the proposed approach is fastand efficient in dealing with numerous system constraints.