Optimal Power Flow With Step-Voltage Regulators in Multi-Phase Distribution Networks

Abstract

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.

Applications of optimization models for electricity distribution networks

“…The following devices are often included in distribution network control problems: OLTC : An OLTC can change the tap ratio of a transformer while it is energized, in discrete steps. A key distinction is whether the OLTC is gang‐operated or not, that is, whether it uses the same setpoint for the tap ratio across phases (Gutierrez‐Lagos & Ochoa, 2019; Y. Liu et al, 2019b) or controls them individually (Bazrafshan et al, 2019; Jha et al, 2019; Nguyen et al, 2019; Sharma et al, 2015). Secondly, transformers come in a wide variety of configurations.…”

“…Three‐phase transformers are often modeled as Wye–Wye connected (Y. Liu et al, 2019b; Nguyen et al, 2019; Sharma et al, 2015) or delta‐Wye connected (Gutierrez‐Lagos & Ochoa, 2019), where it is usually assumed that the Wye‐connected windings are solidly grounded. More exotic configurations exist, such as open‐delta windings (Bazrafshan et al, 2019). The generic ABCD model can cover a wide range of these options (Sharma et al, 2015).…”

“…Modeling these explicitly through integer variables leads to a mixed‐integer problem, which together with a nonlinear network model is considered to be insufficiently scalable. Several approaches exist to deal with this: some authors relax the integer variables as continuous ones (Bazrafshan et al, 2019; Sharma et al, 2015), with additional penalty terms for deviations from the discrete values (Nguyen et al, 2019) or a heuristic for mapping to a higher or lower discrete value (Gutierrez‐Lagos & Ochoa, 2019). Other authors approximate or relax the network model and solve the mixed‐integer problem directly (Jha et al, 2019; Vanin et al, 2020).…”

Voltage-Dependent Load Models in Unbalanced Optimal Power Flow Using Power Cones

“…Recently, several authors have extended this work further by incorporating other network elements. Liu et al include gangoperated on-load tap changers [18] and Bazhrafshan et al model voltage regulators (autotransformers) [19]. Zhao et al first considered delta-connected constant-power loads [20].…”

An Average Voltage Approach to Control Energy Storage Device and Tap Changing Transformers Under High Distributed Generation

“…Therefore, in such long feeders, SVRs are installed along the feeders to help boost voltage magnitudes. The philosophy of operation of an SVR is similar to that of an OLTC, it keeps the voltage magnitude of interest at a predetermined and fixed voltage magnitude [11][12]. This voltage magnitude of interest can be the voltage where it is located, or the voltage at a remote location that is estimated through the line drop compensation (LDC) technique [12].…”