Optimal Power Flow With Step-Voltage Regulators in Multi-Phase Distribution Networks
Power transmission lines, Voltage control, Regulators, Admittance, Load flow, Power distribution
College of Natual Science and Mathematics, Mathematics
This paper develops a branch-flow-based optimal power flow (OPF) problem for multi-phase distribution networks that allows for tap selection of wye, closed delta, and open delta step-voltage regulators (SVRs). SVRs are assumed ideal and their taps are represented by continuous decision variables. To tackle the non-linearity, the branch-flow semidefinite programming framework of traditional OPF is expanded to accommodate SVR edges. Three types of non-convexity are addressed: (a) rank-1 constraints on non-SVR edges, (b) nonlinear equality constraints on SVR power flows and taps, and (c) trilinear equalities on SVR voltages and taps. Leveraging a practical phase-separation assumption on the SVR secondary voltage, novel McCormick relaxations are provided for (c) and certain rank-1 constraints of (a), while dropping the rest. A linear relaxation based on conservation of power is used in place of (b). Numerical simulations on standard distribution test feeders corroborate the merits of the proposed convex formulation.
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Bazrafshan, Mohammadhafez, et al. “Optimal Power Flow With Step-Voltage Regulators in Multi-Phase Distribution Networks.” IEEE Transactions on Power Systems, vol. 34, no. 6, 2019, pp. 4228–4239. doi: 10.1109/tpwrs.2019.2915795.