Foundations and Trends® in Electric Energy Systems > Vol 4 > Issue 1-2

A Survey of Relaxations and Approximations of the Power Flow Equations

Daniel K. Molzahn, Georgia Institute of Technology, USA, molzahn@gatech.edu Ian A. Hiskens, University of Michigan, USA, hiskens@umich.edu
 
Suggested Citation
Daniel K. Molzahn and Ian A. Hiskens (2019), "A Survey of Relaxations and Approximations of the Power Flow Equations", Foundations and TrendsĀ® in Electric Energy Systems: Vol. 4: No. 1-2, pp 1-221. http://dx.doi.org/10.1561/3100000012

Published: 04 Feb 2019
© 2019 D. K. Molzahn and I. A. Hiskens
 
Subjects
Advances in power dispatch,  Design and optimization of electric services,  Power system analysis and computing
 

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In this article:
1. Introduction
2. Overview of the Power Flow Equations
3. Optimization Tools
4. Convex Relaxations of the Power Flow Equations
5. Power Flow Approximations
6. Obtaining a Feasible Point
7. Conclusion
Acknowledgements
References

Abstract

The power flow equations relate the power injections and voltages in an electric power system and are therefore key to many power system optimization and control problems. Research efforts have developed a wide variety of relaxations and approximations of the power flow equations with a range of capabilities and characteristics. This monograph surveys relaxations and approximations of the power flow equations, with a particular emphasis on recently proposed formulations.

DOI:10.1561/3100000012
ISBN: 978-1-68083-540-3
234 pp. $99.00
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ISBN: 978-1-68083-541-0
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Table of contents:
1. Introduction
2. Overview of the Power Flow Equations
3. Optimization Tools
4. Convex Relaxations of the Power Flow Equations
5. Power Flow Approximations
6. Obtaining a Feasible Point
7. Conclusion
Acknowledgements
References

A Survey of Relaxations and Approximations of the Power Flow Equations

The power flow equations model the relationship between voltage phasors and power injections at nodes (buses) in an electric power system and are fundamental in their analysis and operation. A wealth of literature exists on these equations, many providing different representations of them. This monograph provides the first comprehensive survey of representations in the context of optimization. To achieve this the power flow representations surveyed are categorized as either relaxations or approximations.

The techniques described in here form the basis of running an optimally efficient modern day power system. Survey of Relaxations and Approximations of the Power Flow Equations is a must-read for all students and researchers working on the cutting edge of electric power systems.

 
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