Two-phase mixed integer programming for non-convex economic dispatch problem with spinning reserve constraints

This paper proposes a deterministic two-phase mixed integer programming (TPMIP) approach to solve the non-convex economic dispatch (ED) problem considering ramp rate constraints, valve-point effect (VPE), prohibited operating zones (POZs), transmission loss, and spinning reserve constraints. In the first phase, the non-smooth cost function induced by VPE is piecewise linearized and the POZs constraints are formulated as a set of mathematical formulas via a mixed integer encoding technique. Then, the non-convex ED problem is converted to a mixed integer programming (MIP) problem and can be solved by commercial optimization solvers. In the second phase, based on the solution obtained in the first phase, the range of the power output of each unit is compressed and then solve the MIP problem again to make a further exploitation for an optimal solution in the subspace of the whole solution domain. To demonstrate the effectiveness of TPMIP, it is applied to eight test systems and the simulation results are compared with those obtained by the existing methods cited in this paper. Numerical simulations have verified that the proposed method provides a comprehensive framework in solving the non-convex ED problem.