Multi-objective optimization using MISOCP model for service restoration in electrical distribution grids in the presence of distributed generation and voltage-dependent loads

Nang-Van Pham; Trong-Sang Vo; Trung-Hai Nguyen; Dinh-Phu Vu; Nang-Van Pham; Trong-Sang Vo; Trung-Hai Nguyen; Dinh-Phu Vu

doi:10.3934/energy.2025038

AIMS Energy

2025, Volume 13, Issue 5: 1012-1051. doi: 10.3934/energy.2025038

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Research article

Multi-objective optimization using MISOCP model for service restoration in electrical distribution grids in the presence of distributed generation and voltage-dependent loads

School of Electrical and Electronic Engineering, Hanoi University of Science and Technology, Hanoi, Vietnam

Received: 25 June 2025 Revised: 28 August 2025 Accepted: 02 September 2025 Published: 08 September 2025

In this study, we present a multi-objective optimization framework formulated as mixed-integer second-order cone programming (MISOCP) to restore electricity distribution systems following fault clearance. The proposed model incorporated two objective functions: Minimizing the total unserved load while considering load prioritization and reducing the frequency of switching actions of sectionalizing devices. The model's constraints included preserving the radial configuration of the reconfigured distribution grid, power flow equations, PV models of distributed energy resources, voltage-dependent load models, node voltage limits, and branch power flow limits. The presented optimization framework was converted from the optimization model formulated as mixed-integer nonlinear programming (MINLP), achieved through the reformulation of nodal power balance equations as second-order cone constraints and the approximate formulation of the voltage-dependent load models for conic solvers. Pareto optimal solutions were then achieved through a heuristic approach. The proposed optimization framework was validated on the enhanced IEEE 33-node test feeder and a Vietnamese real 190-bus distribution grid, utilizing the CPLEX solver under the GAMS programming language. We also explored various fault location scenarios across the distribution grid and evaluated the influence of the different objective functions, as well as two load models, on the optimization outcomes.
Citation: Nang-Van Pham, Trong-Sang Vo, Trung-Hai Nguyen, Dinh-Phu Vu. Multi-objective optimization using MISOCP model for service restoration in electrical distribution grids in the presence of distributed generation and voltage-dependent loads[J]. AIMS Energy, 2025, 13(5): 1012-1051. doi: 10.3934/energy.2025038

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Abstract

In this study, we present a multi-objective optimization framework formulated as mixed-integer second-order cone programming (MISOCP) to restore electricity distribution systems following fault clearance. The proposed model incorporated two objective functions: Minimizing the total unserved load while considering load prioritization and reducing the frequency of switching actions of sectionalizing devices. The model's constraints included preserving the radial configuration of the reconfigured distribution grid, power flow equations, PV models of distributed energy resources, voltage-dependent load models, node voltage limits, and branch power flow limits. The presented optimization framework was converted from the optimization model formulated as mixed-integer nonlinear programming (MINLP), achieved through the reformulation of nodal power balance equations as second-order cone constraints and the approximate formulation of the voltage-dependent load models for conic solvers. Pareto optimal solutions were then achieved through a heuristic approach. The proposed optimization framework was validated on the enhanced IEEE 33-node test feeder and a Vietnamese real 190-bus distribution grid, utilizing the CPLEX solver under the GAMS programming language. We also explored various fault location scenarios across the distribution grid and evaluated the influence of the different objective functions, as well as two load models, on the optimization outcomes.

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