A new Lagrangian relaxation based method for power system scheduling with identical units

When the Lagrangian relaxation based methods are used to solve power system scheduling problems, severe solution oscillation may be caused by homogeneous subproblems with identical solutions. In this case the dual solution may be far away from the optimal schedule and, as a result, the quality of the feasible schedule obtained may be very unsatisfactory. This problem has long been recognized as an inherent disadvantage of the price based methods but few effective methods are developed to resolve this issue. In this paper, a new method is presented, combing the concepts of the augmented Lagrangian relaxation and surrogate subgradient method to produce a good search direction. The piece-wise linear penalty associated with the system constraints is added to the Larangian and subproblems are solved sequentially so that no approximation as in the augmented Lagrangian relaxation method is needed to maintain the decomposability. As a result, the better dual solution structure and better feasible schedules are obtained comparing with the standard Lagrangian relaxation method, and solution oscillation can be avoided or greatly reduced. Numerical testing shows the new methods are efficient and the quality of the feasible schedule is greatly improved.