Multiobjective Optimal Power Flow Using a Semidefinite Programming-Based Model

Elnaz Davoodi

doi:10.1109/JSYST.2020.2971838

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Multiobjective Optimal Power Flow Using a Semidefinite Programming-Based Model

2021-03-01

Elnaz Davoodi

Ebrahim Babaei

Behnam Mohammadi‐Ivatloo *

Miadreza Shafie‐khah

João P. S. Catalào

DOI：10.1109/JSYST.2020.2971838

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Abstract

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In spite of the significant advance achieved in the development of optimal power flow (OPF) programs, most of the solution methods reported in the literature have considerable difficulties in dealing with different-nature objective functions simultaneously. By leveraging recent progress on the semidefinite programming (SDP) relaxations of OPF, in the present article, attention is focused on modeling a new SDP-based multiobjective OPF (MO-OPF) problem. The proposed OPF model incorporates the classical epsilon-constraint approach through a parameterization strategy to handle the multiple objective functions and produce Pareto front. This article emphasizes the extension of the SDP-based model for MO-OPF problems to generate globally nondominated Pareto optimal solutions with uniform distribution. Numerical results on IEEE 30-, 57-, 118-bus, and Indian utility 62-bus test systems with all security and operating constraints show that the proposed convex model can produce the nondominated solutions with no duality gap in polynomial time, generate efficient Pareto set, and outperform the well-known heuristic methods generally used for the solution of MO-OPF. For instance, in comparison with the obtained results of NSGA-II for the 57-bus test system, the best compromise solution obtained by SDP has 1.55% and 7.42% less fuel cost and transmission losses, respectively.

Keywords:

Linear programming

Fuels

Propagation losses

Power systems

Pareto optimization

Minimization

Convexification

multiobjective OPF (MO-OPF)

optimal power flow (OPF)

semidefinite programming (SDP)

ϵ -constraint method