Convex Relaxation of Optimal Power Flow—Part I: Formulations and Equivalence

By Steven H. Low. IEEE Transactions on Control of Network Systems, 2014

987 citations recorded by the source corpus.

This tutorial summarizes recent advances in the convex relaxation of the optimal power flow (OPF) problem, focusing on structural properties rather than algorithms. Part I presents two power flow models, formulates OPF and their relaxations in each model, and proves equivalence relationships among them. Part II presents sufficient conditions under which the convex relaxations are exact.

Subfields: Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/e064fbf15b96ea5f6ce53e83a18bf571bcca8f75

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In Electrical and Electronic Engineering

1. Steven H. Low
2. Daniel D. Molzahn
3. Xu Andy Sun
4. Santanu S. Dey
5. Burak Kocuk
6. Rajit Gadh
7. Wenbo Shi
8. Chi-Cheng Peter Chu

Citations in the corpus

• Inexactness of SDP Relaxation and Valid Inequalities for Optimal Power Flow (2014, background): “A recent, comprehensive survey can be found in [4] and [5].”
• A Survey of Distributed Optimization and Control Algorithms for Electric Power Systems (2017, background): “, given any OPF instance, its SOCP relaxation is exact if and only if its SDP relaxation is exact [16], [17].”
• BlackIoT: IoT Botnet of High Wattage Devices Can Disrupt the Power Grid (2018, background): “In a comprehensive work [28], Fernandes et al.”
• A survey of distributed optimization (2019, background): “…the readers to the recent survey Molzahn et al. (2017) , which provides a comprehensive review for these problems, Lam, Zhang, and Tse (2012) ; Low (2014) and Madani, Sojoudi, and Lavaei (2015) for the semidefinite program (SDP) relaxation of OPF, Zheng, Wu, Zhang, Sun, and Liu (2016) and Peng…”
• Distributed Optimal Energy Management in Microgrids (2015, methodology): “For the deferable load, the start time is chosen randomly from [10, 13] and the deadline is chosen randomly from [20, 23].”
• Real-Time Energy Management in Microgrids (2017, methodology): “OPF is NP-hard to solve in general due to the quadratic power flow constraints [27].”
• A Sufficient Condition on Convex Relaxation of AC Optimal Power Flow in Distribution Networks (2017, background): “The details of the convex relaxation for the AC OPF can be found in [17], [18].”
• Distributed and Decentralized Voltage Control of Smart Distribution Networks: Models, Methods, and Future Research (2017, methodology): “Classic AC power flow equations are used to formulate the bus injection model (BIM) of the distribution system operation [19].”
• Fully Decentralized Policies for Multi-Agent Systems: An Information Theoretic Approach (2017, background): “2 to the optimal power flow (OPF) problem [Low, 2014], as initially proposed by Sondermeijer et al.”
• Solving Multiperiod OPF Problems Using an AC-QP Algorithm Initialized With an SOCP Relaxation (2017, background): “In contrast, the SOCP relaxation in [13] can be quickly solved for large networks to obtain a lower bound on the globally optimal objective value and an initialization for the AC-QP algorithm.”
• Review of Challenges and Research Opportunities for Voltage Control in Smart Grids (2019, background): “The OPF-based formulations lead to solving challenging non-linear, nonconvex problems that require the use of convex relaxation techniques [16], [17].”