Optimal power flow based on successive linear approximation of power flow equations

Yang, Zhifang; Zhong, Haiwang; Xia, Qing; Bose, Anjan; Chen, Kang

doi:10.1049/iet-gtd.2016.0547

Cited by 108 publications

(65 citation statements)

References 22 publications

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“…(2) The controlled variable parameters: the bounds which are shown as (7), and the steps of T and C Q . The considering controlled variable are listed as follow:…”

Section: Procedures Of Many-objective Optimizationmentioning

confidence: 99%

“…Optimal power flow (OPF) plays a major part role in guaranteeing the safe and economical operation of power systems [1,2], and it has been receiving the wide-spread attention of professionals and researchers from academia and industry [3,4], especially in the case of large-scale integrations of renewable energy resources [5,6]. The key idea of OPF is to find the optimal operating point with the lowest generation/operating costs under the premise of constraints [7][8][9], which contain a series of equality and inequality equations [10,11]. However, the conventional mono-objective OPF, which generally seeks optimum economy [12,13], such as active power losses or generation costs, becomes unable to meet the diversified needs of electricity consumers.…”

Section: Introductionmentioning

confidence: 99%

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Two-Step Many-Objective Optimal Power Flow Based on Knee Point-Driven Evolutionary Algorithm

2018

Processes

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To coordinate the economy, security and environment protection in the power system operation, a two-step many-objective optimal power flow (MaOPF) solution method is proposed. In step 1, it is the first time that knee point-driven evolutionary algorithm (KnEA) is introduced to address the MaOPF problem, and thereby the Pareto-optimal solutions can be obtained. In step 2, an integrated decision analysis technique is utilized to provide decision makers with decision supports by combining fuzzy c-means (FCM) clustering and grey relational projection (GRP) method together. In this way, the best compromise solutions (BCSs) that represent decision makers' different, even conflicting, preferences can be automatically determined from the set of Paretooptimal solutions. The primary contribution of the proposal is the innovative application of manyobjective optimization together with decision analysis for addressing MaOPF problems. Through examining the two-step method via the IEEE 118-bus system and the real-world Hebei provincial power system, it is verified that our approach is suitable for addressing the MaOPF problem of power systems.Keywords: optimal power flow; optimal operation; power systems; multi-objective optimization; knee point-driven evolutionary algorithm; decision analysis; best compromise solutions Recent research suggests that multi-objective evolutionary algorithms (MOEAs) are promising tools for addressing various challenging optimization tasks in engineering fields [29][30][31][32]. In order to optimal distributed generation planning, a MOEA is employed in [29]. Reference [30] reviews the most representative MOEAs that have been reported, and MOEA has developed as an effective method to solve such an optimization problem. In [31], MOEA is employed for planning overtime of software engineers. The layout of wind farms is optimized via MOEA in [32]. In particular, MOEAs can be also applied to solve the OPF issue [23][24][25][26][27][28]. Unfortunately, the MOPF can only cope with the optimization issue with two to three objectives, which, to a certain extent, limits the practicality of this type of methods. In addition, many-objective optimization problems (MaOPs), considering four or more objective functions in the OPF problem [33][34][35][36], are commonly existed phenomenon in the practice of real-world power system operation [33]. In [34], a specially tailored MOEA is presented for tackling the current large-scale MaOPs. Another MOEA based on adaptive search strategy is presented for coping with MaOPs in [35]. In [36], six different evolutionary algorithms (EAs) are tested, and the results prove that MOEAs exhibit their own capabilities in dealing with different MaOPs. For this reason, MaOPs have recently gained a great deal of attention as most existing MOEAs are inadequate for solving OPF problems with four or more objectives, and it has become a hotspot to enhance the ability of MOEAs for addressing MaOPs issues [37][38][39]. However, manyobjective OPF (MaOPF) is quite challenging for solving sinc...

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“…(2) The controlled variable parameters: the bounds which are shown as (7), and the steps of T and C Q . The considering controlled variable are listed as follow:…”

Section: Procedures Of Many-objective Optimizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Two-Step Many-Objective Optimal Power Flow Based on Knee Point-Driven Evolutionary Algorithm

2018

Processes

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“…Myriad algorithms for solving OPF have been proposed in recent years. Linearized power flow equations have been used extensively in practice, often called DC OPF, see [5][6][7][8]. It approximates the AC power flow in a mathematical format resembling DC power flow.…”

Section: Introductionmentioning

confidence: 99%

SOCP Relaxations of Optimal Power Flow Problem Considering Current Margins in Radial Networks

Chen

Xiang

2018

Energies

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Optimal power flow (OPF) is a non-linear and non-convex problem that seeks the optimization of a power system operation point to minimize the total generation costs or transmission losses. This study proposes an OPF model considering current margins in radial networks. The objective function of this OPF model has an additional term of current margins of the line besides the traditional transmission losses and generations costs, which contributes to thermal stability margins of power systems. The model is a reformulated bus injection model with clear physical meanings. Second order cone program (SOCP) relaxations for the proposed OPF are made, followed by the over-satisfaction condition guaranteeing the exactness of the SOCP relaxations. A simple 6-node case and several IEEE benchmark systems are studied to illustrate the efficiency of the developed results.

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“…Although the aforementioned models are not capable of solving practical-constrained models (either complex ED or OPF problems), they have brought new insights into this area of research by showing the importance of solverbased models. Even in some existing linear models for ACOPF problems, [24] and [25], due to the complexity of linearization that highly depends on the approximation techniques, the logical constraints have been neglected. Therefore, the main motivations of proposing the solver-based MINLP models that may fill the existing gap in this area of research can be summarized as (a) the popularity and efficient outcomes of solver-based models in other areas, and (b) the lack of an efficient solver-based model for LCOPF-based problems.…”

Section: Introductionmentioning

confidence: 99%

Logically constrained optimal power flow: Solver-based mixed-integer nonlinear programming model

Pourakbari‐Kasmaei

Mantovani

2018

International Journal of Electrical Power & Energy Systems

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There is increasing evidence of the shortage of solver-based models for solving logically-constrained AC optimal power flow problem (LCOPF). Although in the literature the heuristic-based models have been widely used to handle the LCOPF problems with logical terms such as conditional statements, logical-and, logical-or, etc., their requirement of several trials and adjustments plagues finding a trustworthy solution. On the other hand, a welldefined solver-based model is of much interest in practice, due to rapidity and precision in finding an optimal solution. To remedy this shortcoming, in this paper we provide a solver-friendly procedure to recast the logical constraints to solver-based mixed-integer nonlinear programming (MINLP) terms. We specifically investigate the recasting of logical constraints into the terms of the objective function, so it facilitates the pre-solving and probing techniques of commercial solvers and consequently results in a higher computational efficiency. By applying this recast method to the problem, two sub-power-and sub-function-based MINLP models, namely SP-MINLP and SF-MINLP, respectively, are proposed. Results not only show the superiority of the proposed models in finding a better optimal solution, compared to the existing approaches in the literature, but also the effectiveness and computational tractability in solving large-scale power systems under different configurations.

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Optimal power flow based on successive linear approximation of power flow equations

Cited by 108 publications

References 22 publications

Two-Step Many-Objective Optimal Power Flow Based on Knee Point-Driven Evolutionary Algorithm

Two-Step Many-Objective Optimal Power Flow Based on Knee Point-Driven Evolutionary Algorithm

SOCP Relaxations of Optimal Power Flow Problem Considering Current Margins in Radial Networks

Logically constrained optimal power flow: Solver-based mixed-integer nonlinear programming model

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