Solution of Grey Chance Constrained Programming and Convexity of its Feasible Set

If there are grey variables in the constraint conditions in uncertain programming, the programming is called grey chance constrained programming. In this paper we provide the concept of grey chance constrained programming. When the whitenization weight functions of grey variables are known and the distribution functions are constructed, we studied the certainty equivalence solution of grey chance constrained programming. In different situations, the solution of grey chance constrained programming is given. Further, convexity of the feasible set is study. Then an optimization algorithm based on genetic algorithm is suggested to solve this model. Comparing with traditional power transmission system planning, there are more uncertain factors to be processed during power transmission system planning under electricity market environment. In view of the grey properties of installed capacity of generators and the load increasing, we build up a model of power transmission system planning based on grey chance constrained programming. The objective function is solved by genetic algorithm with grey simulation, and optimal power transmission system planning schemes on different confidence levels are obtained.