Power system scheduling with fuzzy reserve requirements

The modeling of constraints is an important issue in power system scheduling. Constraints can be generally classified into two categories: (1) physical limits; and (2) operating limits. A schedule violating a physical limit or constraint would not be acceptable. An operating limit, however, is often imposed to enhance power system security but does not represent a physical bound. This kind of "soft limit" can be temporarily violated "a little bit" if necessary, but not "too much". These constraints are therefore "fuzzy" in nature, and crisp treatment of them may lead to over-conservative solutions. In this paper, a fuzzy optimization-based method is developed to solve the power system scheduling problem with fuzzy reserve requirements. The problem is first converted to a crisp and separable optimization problem. Lagrange multipliers are then used to relax system-wide constraints and decompose the problem into a number of unit-wise subproblems and a membership subproblem. These subproblems can be efficiently solved, and the multipliers are updated by using a subgradient method. Heuristics are then used to construct a feasible schedule based on subproblem solutions. Numerical testing results show that near optimal schedules are obtained, and the method can provide a good balance between reducing costs and satisfying reserve requirement.