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

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.

[1]  J. Le Boudec,et al.  Load Flow in Multiphase Distribution Networks: Existence, Uniqueness, Non-Singularity and Linear Models , 2017, IEEE Transactions on Power Systems.

[2]  Jaydev Sharma,et al.  Coordination Between OLTC and SVC for Voltage Regulation in Unbalanced Distribution System Distributed Generation , 2014, IEEE Transactions on Power Systems.

[3]  Jie Li,et al.  Chordal Relaxation Based ACOPF for Unbalanced Distribution Systems With DERs and Voltage Regulation Devices , 2018, IEEE Transactions on Power Systems.

[4]  Kankar Bhattacharya,et al.  Optimal Operation of Distribution Feeders in Smart Grids , 2011, IEEE Transactions on Industrial Electronics.

[5]  Lorenz T. Biegler,et al.  On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming , 2006, Math. Program..

[6]  Daniel S. Kirschen,et al.  Accurate Semidefinite Programming Models for Optimal Power Flow in Distribution Systems , 2017, 1711.07853.

[7]  Steven H. Low,et al.  Chordal relaxation of OPF for multiphase radial networks , 2014, 2014 IEEE International Symposium on Circuits and Systems (ISCAS).

[8]  Santanu S. Dey,et al.  Matrix minor reformulation and SOCP-based spatial branch-and-cut method for the AC optimal power flow problem , 2017, Math. Program. Comput..

[9]  Lei Wu,et al.  Coordinated Optimal Network Reconfiguration and Voltage Regulator/DER Control for Unbalanced Distribution Systems , 2019, IEEE Transactions on Smart Grid.

[10]  Bikash C. Pal,et al.  Stochastic Distribution System Operation Considering Voltage Regulation Risks in the Presence of PV Generation , 2015, IEEE Transactions on Sustainable Energy.

[11]  Bikash C. Pal,et al.  Distribution voltage control considering the impact of PV generation on tap changers and autonomous regulators , 2014, 2014 IEEE PES General Meeting | Conference & Exposition.

[12]  Song Gao,et al.  A VAR optimization model in distribution networks with precise linear modelling for OLTC of transformer , 2017, 2017 IEEE Conference on Energy Internet and Energy System Integration (EI2).

[13]  Nikolaos Gatsis,et al.  Comprehensive Modeling of Three-Phase Distribution Systems via the Bus Admittance Matrix , 2017, IEEE Transactions on Power Systems.

[14]  Nikos D. Hatziargyriou,et al.  Distributed and Decentralized Voltage Control of Smart Distribution Networks: Models, Methods, and Future Research , 2017, IEEE Transactions on Smart Grid.

[15]  William Kersting,et al.  Distribution System Modeling and Analysis , 2001, Electric Power Generation, Transmission, and Distribution: The Electric Power Engineering Handbook.

[16]  Stephen P. Boyd,et al.  Graph Implementations for Nonsmooth Convex Programs , 2008, Recent Advances in Learning and Control.

[17]  Jonathan Currie,et al.  Opti: Lowering the Barrier Between Open Source Optimizers and the Industrial MATLAB User , 2012 .

[18]  Nikolaos Gatsis,et al.  Convergence of the Z-Bus Method for Three-Phase Distribution Load-Flow with ZIP Loads , 2016, IEEE Transactions on Power Systems.

[19]  T. Inoue,et al.  Three-phase cogenerator and transformer models for distribution system analysis , 1991 .

[20]  Elaine Sison-Lebrilla,et al.  Studies on the Effects of High Renewable Penetrations on Driving Point Impedance and Voltage Regulator Performance: National Renewable Energy Laboratory/Sacramento Municipal Utility District Load Tap Changer Driving Point Impedance Project , 2018 .

[21]  Georgios B. Giannakis,et al.  Distributed Optimal Power Flow for Smart Microgrids , 2012, IEEE Transactions on Smart Grid.

[22]  Steven H. Low,et al.  Convex relaxations and linear approximation for optimal power flow in multiphase radial networks , 2014, 2014 Power Systems Computation Conference.

[23]  Johan Löfberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004 .

[24]  Melvin Z. Thomas,et al.  Enhanced Utilization of Voltage Control Resources with Distributed Generation , 2016 .

[25]  Nikolaos Gatsis,et al.  Optimal Tap Selection of Step-Voltage Regulators in Multi-Phase Distribution Networks , 2018, 2018 Power Systems Computation Conference (PSCC).

[26]  Ahmed S. Zamzam,et al.  Beyond Relaxation and Newton–Raphson: Solving AC OPF for Multi-Phase Systems With Renewables , 2016, IEEE Transactions on Smart Grid.

[27]  Brett Robbins,et al.  Optimal Tap Setting of Voltage Regulation Transformers in Unbalanced Distribution Systems , 2016, IEEE Transactions on Power Systems.

[28]  Boming Zhang,et al.  An Exact Linearization Method for OLTC of Transformer in Branch Flow Model , 2016, IEEE Transactions on Power Systems.