Fast SDP Relaxation of the Optimal Power Flow Using the Line-Wise Model for Representing Meshed Transmission Networks

In this paper, we propose a novel Semidefinite Programming (SDP) relaxation of the Optimal Power Flow (OPF) problem. The proposed formulation utilizes the Line-Wise Model (LWM) to represent meshed transmission networks. This allows the constraints of the proposed formulation to mostly depend on diag...

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Bibliographic Details
Published in:IEEE transactions on power systems Vol. 38; no. 4; pp. 3814 - 3827
Main Authors: Aldik, Abdel Rahman, Venkatesh, Bala
Format: Journal Article
Language:English
Published: New York IEEE 01.07.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Computational efficiency
Computing time
Constraint modelling
Convex relaxations
Generators
Load flow
Mathematical models
Matrix decomposition
optimal power flow
Optimization
Power flow
Reactive power
semi- definite programming
Semidefinite programming
Solvers
ISSN:0885-8950, 1558-0679
Online Access:Get full text
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Summary:In this paper, we propose a novel Semidefinite Programming (SDP) relaxation of the Optimal Power Flow (OPF) problem. The proposed formulation utilizes the Line-Wise Model (LWM) to represent meshed transmission networks. This allows the constraints of the proposed formulation to mostly depend on diagonal elements of the voltages' Hermitian <inline-formula><tex-math notation="LaTeX">{\boldsymbol{W}}</tex-math></inline-formula> matrix in contrast to the Bus Injection Model (BIM) where constraints heavily utilize its off-diagonal elements. Test cases with bus sizes of 3 to 9241 were considered and chordal sparsity was exploited for them. Obtained results show that the proposed SDP-LW OPF formulation manages to provide solutions of similar or better quality for most test cases that belong to the Typical and Congested (TYP and API) Operating conditions. Furthermore, the proposed SDP-LW OPF formulation manages to reduce the solver's computational time for most of large-scale test cases with reductions up to 80.298%. Results analysis shows that reductions in the solver's computational time upon using the proposed SDP-LW OPF formulation are affected by its ability to significantly reduce constraints with off-diagonal elements of the <inline-formula><tex-math notation="LaTeX">{\boldsymbol{W}}</tex-math></inline-formula> matrix without drastically increasing constraints with diagonal elements of the <inline-formula><tex-math notation="LaTeX">{\boldsymbol{W}}</tex-math></inline-formula> matrix. Furthermore, the percentage of large sized cliques is found to affect the obtained reductions through its influence over the number of needed linking constraints for relating the elements of the <inline-formula><tex-math notation="LaTeX">{\boldsymbol{W}}</tex-math></inline-formula> matrices of decomposed cliques.
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ISSN:0885-8950
1558-0679
DOI:10.1109/TPWRS.2022.3200970