Tightening QC Relaxations of AC Optimal Power Flow Problems Via Complex Per Unit Normalization
Abstract
Optimal power flow (OPF) is a key problem in power system operations. OPF problems that use the nonlinear AC power flow equations to accurately model the network physics have inherent challenges associated with non-convexity. To address these challenges, recent research has applied various convex relaxation approaches to OPF problems. The QC relaxation is a promising approach that convexifies the trigonometric and product terms in the OPF problem by enclosing these terms in convex envelopes. The accuracy of the QC relaxation strongly depends on the tightness of these envelopes. This paper presents two improvements to these envelopes. The first improvement leverages a polar representation of the branch admittances in addition to the rectangular representation used previously. The second improvement is based on a coordinate transformation via a complex per unit base power normalization that rotates the power flow equations. The trigonometric envelopes resulting from this rotation can be tighter than the corresponding envelopes in previous QC relaxation formulations. Using an empirical analysis with a variety of test cases, this paper suggests an appropriate value for the angle of the complex base power. Comparing the results with a state-of-the-art QC formulation reveals the advantages of the proposed improvements.
Recommended Citation
M. R. Narimani et al., "Tightening QC Relaxations of AC Optimal Power Flow Problems Via Complex Per Unit Normalization," IEEE Transactions on Power Systems, vol. 36, no. 1, pp. 281 - 291, article no. 9123567, Institute of Electrical and Electronics Engineers (IEEE), Jan 2021.
The definitive version is available at https://doi.org/10.1109/TPWRS.2020.3004289
Department(s)
Electrical and Computer Engineering
Keywords and Phrases
Convex Relaxation; Optimal Power Flow
International Standard Serial Number (ISSN)
1558-0679; 0885-8950
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2021 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.
Publication Date
01 Jan 2021