### Mathematical Biosciences and Engineering

2022, Issue 7: 6455-6468. doi: 10.3934/mbe.2022303
Research article

# Solution to dynamic economic dispatch with prohibited operating zones via MILP

• Received: 08 March 2022 Revised: 05 April 2022 Accepted: 13 April 2022 Published: 24 April 2022
• Dynamic economic dispatch (DED) problem considering prohibited operating zones (POZ), ramp rate constraints, transmission losses and spinning reserve constraints is a complicated non-linear problem which is difficult to solve efficiently. In this paper, a mixed integer linear programming (MILP) method is proposed to solve such a DED problem. Firstly, a novel MILP formulation for DED problem without considering the transmission losses, denoted by MILP-1, is presented by using perspective cut reformulation technique. When the transmission losses are considered, the quadratic terms in the transmission losses are replaced by their first order Taylor expansions, and then an MILP formulation for DED considering the transmission losses, denoted by MILP-2, is obtained. Based on MILP-1 and MILP-2, an MILP-iteration algorithm is proposed to solve the complicated DED problem. The effectiveness of the MILP formulation and MILP iteration algorithm are assessed by several cases and the simulation results show that both of them can solve to competitive solutions in a short time.

Citation: Shanshan Pan, Jinbao Jian, Linfeng Yang. Solution to dynamic economic dispatch with prohibited operating zones via MILP[J]. Mathematical Biosciences and Engineering, 2022, 19(7): 6455-6468. doi: 10.3934/mbe.2022303

### Related Papers:

• Dynamic economic dispatch (DED) problem considering prohibited operating zones (POZ), ramp rate constraints, transmission losses and spinning reserve constraints is a complicated non-linear problem which is difficult to solve efficiently. In this paper, a mixed integer linear programming (MILP) method is proposed to solve such a DED problem. Firstly, a novel MILP formulation for DED problem without considering the transmission losses, denoted by MILP-1, is presented by using perspective cut reformulation technique. When the transmission losses are considered, the quadratic terms in the transmission losses are replaced by their first order Taylor expansions, and then an MILP formulation for DED considering the transmission losses, denoted by MILP-2, is obtained. Based on MILP-1 and MILP-2, an MILP-iteration algorithm is proposed to solve the complicated DED problem. The effectiveness of the MILP formulation and MILP iteration algorithm are assessed by several cases and the simulation results show that both of them can solve to competitive solutions in a short time.

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沈阳化工大学材料科学与工程学院 沈阳 110142

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