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A Modified Benders Decomposition Algorithm to Solve Second-Order Cone AC Optimal Power Flow
KTH, School of Electrical Engineering and Computer Science (EECS), Electric Power and Energy Systems.ORCID iD: 0000-0003-0471-9066
(English)In: IEEE Transactions on Smart Grid, ISSN 1949-3053, E-ISSN 1949-3061Article in journal (Refereed) In press
Abstract [en]

This paper proposes to speed up solving large-scale second-order cone AC optimal power flow (SOC-ACOPF) problem by decomposition and parallelization. Firstly, we use spectral factorization to partition large power network to multiple subnetworks connected by tie-lines. Then a modified Benders decomposition algorithm (M-BDA) is proposed to solve the SOC-ACOPF problem iteratively. Taking the total power output of each subnetwork as the complicating variable, we formulate the SOC-ACOPF problem of tie-lines as the master problem and the SOC-ACOPF problems of the subnetworks as the subproblems in the proposed M-BDA. The feasibility and optimality (preserving the original optimal solution of the SOC-ACOPF model) of the proposed M-BDA are analytically and numerically proved. A GAMS grid computing framework is designed to compute the formulated subproblems of M-BDA in parallel. The numerical results show that the proposed M-BDA can solve large-scale SOC-ACOPF problem efficiently. Accelerated M-BDA by parallel computing converges within few iterations. The computational efficiency (reducing computation CPU time and computer RAM requirement) can be improved by increasing the number of partitioned subnetworks.

Keywords [en]
Optimal power flow, Network partitioning, Modified Benders decomposition, Feasibility and optimality proof, Parallel computing.
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electrical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-227042OAI: oai:DiVA.org:kth-227042DiVA, id: diva2:1202969
Note

QC 20180607

Available from: 2018-05-02 Created: 2018-05-02 Last updated: 2018-06-07Bibliographically approved
In thesis
1. Convex Optimal Power Flow Based on Second-Order Cone Programming: Models, Algorithms and Applications
Open this publication in new window or tab >>Convex Optimal Power Flow Based on Second-Order Cone Programming: Models, Algorithms and Applications
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Optimal power flow (OPF) is the fundamental mathematical model to optimally operate the power system. Improving the solution quality of OPF can help the power industry save billions of dollars annually. Past decades have witnessed enormous research efforts on OPF since J. Carpentier proposed the fully formulated alternating current OPF (ACOPF) model which is nonconvex. This thesis proposes three convex OPF models (SOC-ACOPF) based on second-order cone programming (SOCP) and McCormick envelope. The underlying idea of the proposed SOC-ACOPF models is to drop assumptions of the original SOC-ACOPF model by convex relaxation and approximation methods. A heuristic algorithm to recover feasible OPF solution from the relaxed solution of the proposed SOC-ACOPF models is developed. The quality of solutions with respect to global optimum is evaluated using MATPOWER and LINDOGLOBAL. A computational comparison with other SOC-ACOPF models in the literature is also conducted. The numerical results show robust performance of the proposed SOC-ACOPF models and the feasible solution recovery algorithm. We then propose to speed up solving large-scale SOC-ACOPF problem by decomposition and parallelization. We use spectral factorization to partition large power network to multiple subnetworks connected by tie-lines. A modified Benders decomposition algorithm (M-BDA) is proposed to solve the SOC-ACOPF problem iteratively. Taking the total power output of each subnetwork as the complicating variable, we formulate the SOC-ACOPF problem of tie-lines as the master problem and the SOC-ACOPF problems of the subnetworks as the subproblems in the proposed M-BDA. The feasibility of the proposed M-BDA is analytically proved. A GAMS grid computing framework is designed to compute the formulated subproblems in parallel. The numerical results show that the proposed M-BDA can solve large-scale SOC-ACOPF problem efficiently. Accelerated M-BDA by parallel computing converges within few iterations.Finally, various applications of our SOC-ACOPF models and M-BDA including distribution locational marginal pricing (DLMP), wind power integration and ultra-large-scale power network or super grid operation are demonstrated.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2018. p. 212
Keywords
Optimal Power Flow, Second-Order Cone Programming, Distribution Locational Marginal Pricing, Wind Power, Super Grid
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electrical Engineering
Identifiers
urn:nbn:se:kth:diva-227044 (URN)9789177296782 (ISBN)
Public defence
2018-05-29, Kollegiesalen, Brinellvägen 8, Stockholm, 09:00 (English)
Opponent
Supervisors
Note

QC 20180507

Available from: 2018-05-07 Created: 2018-05-02 Last updated: 2018-05-17Bibliographically approved

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