A survey on conic relaxations of optimal power flow problem

Zohrizadeh, Fariba; Josz, Cédric; Jin, Ming; Madani, Ramtin; Lavaei, Javad; Sojoudi, Somayeh

doi:10.1016/j.ejor.2020.01.034

Cited by 66 publications

(24 citation statements)

References 152 publications

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“…A very extensive overview on relaxations and approximations of AC Power flow equations can be found in the book [5], while a particular focus on conic relaxations is given in [6]. We focus here on results on the conic relaxations of AC OPF problems for single phase radial networks.…”

Section: Optimal Power Flow Problemmentioning

confidence: 99%

Multi-stage Stochastic Alternating Current Optimal Power Flow with Storage: Bounding the Relaxation Gap

Grangereau

Ackooij

Gaubert

2022

Electric Power Systems Research

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We propose a generic multistage stochastic model for the Alternating Current Optimal Power Flow (AC OPF) problem for radial distribution networks, to account for the random electricity production of renewable energy sources and dynamic constraints of storage systems. We consider single-phase radial networks. Radial three-phase balanced networks (medium-voltage distribution networks typically have this structure) reduce to the former case. This induces a large scale optimization problem, which, given the non-convex nature of the AC OPF, is generally challenging to solve to global optimality.We derive a priori conditions guaranteeing a vanishing relaxation gap for the multi-stage AC OPF problem, which can thus be solved using convex optimization algorithms. We also give an a posteriori upper bound on the relaxation gap. In particular, we show that a null or low relaxation gap may be expected for applications with light reverse power flows or if sufficient storage capacities with low cost are available. Then, we discuss the validity of our results when incorporating voltage regulation devices. Finally, we illustrate our results on problems of planning of a realistic distribution feeder with distributed solar production and storage systems. Scenario trees for solar production

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Section: Optimal Power Flow Problemmentioning

confidence: 99%

Multi-stage Stochastic Alternating Current Optimal Power Flow with Storage: Bounding the Relaxation Gap

Grangereau

Ackooij

Gaubert

2022

Electric Power Systems Research

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“…In 2019, Fariba Zohrizadeh et al [4], reviews the most recent research to show the achievement of conic optimization while used to power systems. The most important focal point was on how linear programming, second-order cone programming, and semi definite programming were exploited to addresses a central problem called the OPF problem.…”

Section: Literature Reviewmentioning

confidence: 99%

“…The generally exploited objective function is the reduction cost function of fuel, active power loss, emission, and deviation of bus voltage. Whereas the control variables of a power system, such as generators bus voltage magnitudes, real power outputs, and shunt capacitor outputs and so on, are operated to attain an optimal network setting [3] [4]. Because of the detail in which there are numerous control variables, and not all, are incessant, such as the shunt capacitor outputs, OPF problem is believed as a multi-modal, non-convex, large-scale, and non-linear constrained optimization problem [13] [14] [15].…”

mentioning

confidence: 99%

Hybrid Genetic Algorithm and Particle Swarm Optimization Algorithm for Optimal Power Flow in Power System

K.S¹

2019

JCMPS

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In power systems, the Optimal Power Flow (OPF) problem is considered as the majority extensively nonlinear optimization problems. This work presents a new hybrid optimization approach that integrates the advantages of the Genetic Algorithm (GA) with the Particle Swarm Optimization (PSO) approach to solve the OPF problem. The developed hybrid algorithm is considered to achieve environmental, technical, and economic, advantages. The proposed technique is used to single and multi-objective optimization problems using diverse objective models like minimization of generation cost, reduction of emission, minimization of transmission power loss, maximization of voltage profile, and maximization of voltage stability. To show the ability of developed hybrid optimization method, single-objective cases are used and verified on three standard bus systems. The developed PSO-GA technique attains considerably the efficiency, and the robustness of OPF outcomes for the cases, are represented. The experimentation outcomes show that the developed technique tends to better levels of techno-economic-environmental advantages evaluated. Additionally, the sensitivity analysis study verifies that the proposed hybrid algorithm constructs robust outcomes over parameter variations.

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“…Convex relaxation models have been proposed in the literature for the AC-OPF problem as summarized in [7], where classic formulations and recent advances are shown. Convex relaxations based on second-order cone programming (SOCP) have been proposed in [8] for reconfiguration problems, or in [9], where authors expose the conditions for obtaining an exact equivalent model in balanced distribution networks.…”

Section: Introductionmentioning

confidence: 99%