Study on guaranteed output constraints in the long term joint optimal scheduling for the hydropower station group

Long-term joint scheduling of hydropower station group (LJSHSG) is a constrained optimization problem, which suffers from a variety of complex and time-state coupling constraints. It is beset with difficulties to solve LJSHSG problem owing to these equality constraints, rigid constraints and flexible constraints of hydropower station group (HSG). The new hybrid constraint handling method combining e-constraint (EC) and penalty functions (PF) (named EC-PF) is proposed to deal with these constraints in this paper. In the proposed EC-PF, all equality constraints are forced to satisfy according to the equation; EC handle all rigid constraints with minimizing the value of constraint violation and constraint relaxation rule; and the unique flexible constraint, guaranteed output constraint, is processed by PF. Then the proposed EC-PF is compared with the superiority of feasible solutions (SF), stochastic ranking (SR), PF, EC and lexicographic method (LM) in the application to LJSHSG problems; the experimental results verify the superiority of the proposed method. Moreover, the conclusions that it is necessary to deal with rigid constraints from flexible constraints differently in LJSHSG problem are obtained. On this basis, in view of the defect that guaranteed output constraints are difficult to satisfy in LJSHSG, the LJSHSG with the cooperative mode to handle guaranteed output constraints (named LJSHSG-cm) is puts forward. The comparative experimental results of LJSHSG and LJSHSG-cm show that LJSHSG-cm can increase the power generation by 0.3% while increasing the satisfaction rate of guaranteed output constraints by 78.56% compared with LJSHSG for long sequence calculation from 1959 to 2014. These are fully illustrated that the hybrid constraint handling method EC-PF and LJSHSG-cm with the cooperative mode to handle guaranteed output constraints are valid and reliable practical tools in solving LJSHSG.