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

Abstract

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 constantimpedance 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 lowvoltage feeder are provided.

ExaGridPF: A parallel power flow solver for transmission and unbalanced distribution systems

“…The mutual admittance of each branch is represented by a 3×3 matrix, taking into account the impact of phases over each other. The details of line models can be found in [1], [11]. For three-phase systems, we use the current injection method to formulate the power flow problem based on the admittance matrix construction methods (CIM) [18] discussed in [1], [11].…”

“…The objective of solving power flow is to determine the voltage profile, the current flow, and power loss, etc., across the power grid topology. Previous research has focused on modeling approaches [1], [2] in different systems and convergence properties of different algorithms, using multi-core processors or graphics processing units (GPU) [3]. As smart grid technologies advance, the power system is becoming more observable, enabling modeling and planning over larger networks with more details.…”

“…This paper investigates some parallelization strategies of solving power flow problems in both transmission and unbalanced distribution systems. This paper serves to 1) introduce the open-source implementation of ExaGridPF, which is a large-scale power flow solver designed for use on HPC platforms, 2) explore the parallelization strategies to speed/scale up the iterative power flow algorithms using multiple threads on multi-core computers, 3) present the experimental results and performance improvement over standard IEEE test cases and synthesized larger ones. This paper is organized as follows: Section II summarizes the formulations the power flow algorithms for transmission and distribution systems, respectively; Section III discusses the parallelization strategies of iterative algorithms using existing computing architectures; Section IV presents the experimental results and discussions; And Section V concludes the paper with future work.…”

On the Properties of the Compound Nodal Admittance Matrix of Polyphase Power Systems

“…E-mail: forename.surname@epfl.ch. a subblock of the nodal admittance matrix, which is obtained by removing the rows and columns associated with one single node (i.e., the slack node), has full rank in practice [21], [22]. However, this finding cannot be generalized straightforwardly (i.e., for generic polyphase grids, or removal of several nodes).…”

Estimating the Frequency Coupling Matrix From Network Measurements

“…Several approaches have been proposed to compute the line admittance matrix of a network. In [21], the admittance matrix is determined experimentally from known subnetwork models such as transmission lines, transformers and step-voltage regulators. In [22], the fundamental frequency admittance matrix is estimated using least squares.…”