Comprehensive Modeling of Three-Phase Distribution Systems via the Bus Admittance Matrix

The theme of this paper is three-phase distribution system modeling suitable for the Z-Bus load-flow. Detailed models of wye and delta constant-power, constant-current, and constant-impedance loads are presented. Models of transmission lines, step-voltage regulators, and transformers that build the bus admittance matrix (Y-Bus) are laid out. The Z-Bus load-flow is then reviewed and the singularity of the Y-Bus in case of certain transformer connections is rigorously discussed. Based on realistic assumptions and conventional modifications, the invertibility of the Y-Bus is proved. Last but not least, MATLAB scripts that model the components of the IEEE 37-bus, the IEEE 123-bus, the 8500-node feeders, and the European 906-bus low-voltage feeder are provided.

[1]  T. Overbye.  A power flow measure for unsolvable cases , 1994 .

[2]  Tsai-Hsiang Chen,et al.  Open wye-open delta and open delta-open delta transformer models for rigorous distribution system analysis , 1992 .

[3]  Om P. Malik,et al.  Electric Distribution Systems , 2012 .

[4]  S. Carneiro,et al.  A Three-Phase Optimal Power-Flow Algorithm to Mitigate Voltage Unbalance , 2013, IEEE Transactions on Power Delivery.

[5]  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.

[6]  Bruce F. Wollenberg,et al.  Solving for three phase conductively isolated busbar voltages using phase component analysis , 1995 .

[7]  Dan Jiang,et al.  Optimal electric distribution system switch reconfiguration and capacitor control , 1996 .

[8]  S. Zampieri,et al.  On the Existence and Linear Approximation of the Power Flow Solution in Power Distribution Networks , 2014, IEEE Transactions on Power Systems.

[9]  Andrew Keane,et al.  Open and Closed-Loop Residential Load Models for Assessment of Conservation Voltage Reduction , 2017, IEEE Transactions on Power Systems.

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

[11]  Ross Baldick,et al.  Voltage regulation algorithms for multiphase power distribution grids , 2015, 2016 IEEE Power and Energy Society General Meeting (PESGM).

[12]  Rabih A. Jabr,et al.  Transformer Modeling for Three-Phase Distribution Network Analysis , 2015, IEEE Transactions on Power Systems.

[13]  S. S. Moorthy,et al.  A New Phase-Coordinate Transformer Model for y Bus Analysis , 2002 .

[14]  N. Martins,et al.  Three-phase power flow calculations using the current injection method , 2000 .

[15]  A.H. El-Abiad,et al.  Three phase load flow program , 1976, IEEE Transactions on Power Apparatus and Systems.

[16]  Mo-Shing Chen,et al.  Power system modeling , 1974 .

[17]  J. Le Boudec,et al.  Existence and Uniqueness of Load-Flow Solutions in Three-Phase Distribution Networks , 2017, IEEE Transactions on Power Systems.

[18]  D. Hoadley,et al.  A New Phase-Coordinate Transformer Model for y Bus Analysis , 2002, IEEE Power Engineering Review.

[19]  Florian Dörfler,et al.  Fast power system analysis via implicit linearization of the power flow manifold , 2015, 2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[20]  Tsai-Hsiang Chen,et al.  Distribution system power flow analysis-a rigid approach , 1991 .

[21]  Konstantin S. Turitsyn,et al.  Simple certificate of solvability of power flow equations for distribution systems , 2015, 2015 IEEE Power & Energy Society General Meeting.

[22]  T. Fernandes,et al.  A three-phase optimal power flow applied to the planning of unbalanced distribution networks , 2016 .

[23]  S. Kumagai,et al.  Steady-State Security Regions of Power Systems , 1982 .

[24]  Alejandro Garces,et al.  A Linear Three-Phase Load Flow for Power Distribution Systems , 2016, IEEE Transactions on Power Systems.

[25]  Andrey Bernstein,et al.  Explicit Conditions on Existence and Uniqueness of Load-Flow Solutions in Distribution Networks , 2016, IEEE Transactions on Smart Grid.

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

[27]  Peng Xiao,et al.  A unified three-phase transformer model for distribution load flow calculations , 2006, IEEE Transactions on Power Systems.

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

[29]  Alexandra von Meier,et al.  UC Berkeley Sustainable Infrastructures Title A Linear Power Flow Formulation for Three-Phase Distribution Systems Permalink , 2016 .

[30]  W. H. Phillips,et al.  A new approach to modeling three-phase transformer connections , 1998, 1998 Rural Electric Power Conference Presented at 42nd Annual Conference.

[31]  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.

[32]  R. C. Dugan,et al.  The IEEE 8500-node test feeder , 2010, IEEE PES T&D 2010.

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