Convex relaxations and linear approximation for optimal power flow in multiphase radial networks

By Lingwen Gan, Steven H. Low. Power Systems Computation Conference, 2014

415 citations recorded by the source corpus.

Distribution networks are usually multiphase and radial. To facilitate power flow computation and optimization, two semidefinite programming (SDP) relaxations of the optimal power flow problem and a linear approximation of the power flow are proposed. We prove that the first SDP relaxation is exact if and only if the second one is exact. Case studies show that the second SDP relaxation is numerically exact and that the linear approximation obtains voltages within 0.0016 per unit of their true values for the IEEE 13, 34, 37, 123-bus networks and a real-world 2065-bus network.

Subfields: Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/2a8337c1e5dfeecf8bf8bba495c8164972f51640

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In Electrical and Electronic Engineering

Citations in the corpus

A Survey of Distributed Optimization and Control Algorithms for Electric Power Systems (2017, methodology): “By considering its single-phase equivalent circuit, the SDP relaxation is extended in [32] and [33] to this generalized model.”
Optimal Reactive Power Dispatch for Voltage Regulation in Unbalanced Distribution Systems (2016, methodology): “The angle relaxation is exact for balanced radial and mesh networks, but the SOCP is not suited for the unbalanced three-phase case.”
Solving Multiperiod OPF Problems Using an AC-QP Algorithm Initialized With an SOCP Relaxation (2017, methodology): “The first is to explore initializing multiperiod OPF problems using other recently developed linear and SOCP relaxations and approximations of the power flow equations, such as those in [19], [20], [35], [48], [49].”
Robust Dynamic Operating Envelopes for DER Integration in Unbalanced Distribution Networks (2022, background): “…since linear UTOPF is an approximation commonly obtained by linearising around an operating point [24], [25], [26] or by neglecting power losses [27], model errors become more signiﬁcant when the true operating point deviates from the operating point used in the linearisation, or when dealing…”
Distributed Optimal Energy Management in Microgrids (2015, background): “As can be seen from the figure, the load is shifted from the time when the energy price is high (t ∈ [14, 17]) to when the price is low (t ∈ [19, 21]).”