Short-term generation scheduling with transmission and environmental constraints using an augmented Lagrangian relaxation

This paper proposes a new approach based on augmented Lagrangian relaxation for short term generation scheduling problems with transmission and environmental constraints. In this method, the power system constraints, e.g. load demand, spinning reserve, transmission capacity and environmental constraints, are relaxed by using Lagrangian multipliers, and quadratic penalty terms associated with power system load demand balance are added to the Lagrangian objective function. Then, the decomposition and coordination technique is used, and nonseparable 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 power 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 Lagrangian relaxation method enhanced by the decomposition and coordination techniques avoids oscillations associated with piece-wise linear cost functions. Numerical results indicate that the proposed approach is fast and efficient in dealing with numerous power system constraints