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

Most techniques for power system analysis model the grid by exact electrical circuits. For instance, in power flow study, state estimation, and voltage stability assessment, the use of admittance parameters (i.e., the nodal admittance matrix) and hybrid parameters is common. Moreover, network reduction techniques (e.g., Kron reduction) are often applied to decrease the size of large grid models (i.e., with hundreds or thousands of state variables), thereby alleviating the computational burden. However, researchers normally disregard the fact that the applicability of these methods is not generally guaranteed. In reality, the nodal admittance must satisfy certain properties in order for hybrid parameters to exist and Kron reduction to be feasible. Recently, this problem was solved for the particular cases of monophase and balanced triphase grids. This paper investigates the general case of unbalanced polyphase grids. Firstly, conditions determining the rank of the so-called compound nodal admittance matrix and its diagonal subblocks are deduced from the characteristics of the electrical components and the network graph. Secondly, the implications of these findings concerning the feasibility of Kron reduction and the existence of hybrid parameters are discussed. In this regard, this paper provides a rigorous theoretical foundation for various applications in power system analysi

Efficient Load Flow Techniques Based on Holomorphic Embedding for Distribution Networks

The Holomorphic Embedding Load flow Method (HELM) employs complex analysis to solve the load flow problem. It guarantees finding the correct solution when it exists, and identifying when a solution does not exist. The method, however, is usually computationally less efficient than the traditional Newton-Raphson algorithm, which is generally considered to be a slow method in distribution networks. In this paper, we present two HELM modifications that exploit the radial and weakly meshed topology of distribution networks and significantly reduce computation time relative to the original HELM implementation. We also present comparisons with several popular load flow algorithms applied to various test distribution networks.Comment: Accepted for publication in the Proceedings of 2019 IEEE PES General Meeting, 5 Page

Transmission loss allocation through a modified Ybus

A methodology to allocate the active power transmission loss among agents of a power pool is proposed. The approach is based on the inclusion of the admittances equivalent to bus power injections in the bus admittance matrix. For a given power-flow solution, the relationship between the branch currents and the load/generator current injections is determined using a modified bus admittance matrix, which allows the power loss of each transmission line to be expressed in terms of bus current injections. The proposed technique is simple to implement and flexible enough to allow the assignment of loss parcels to a preselected set of buses. An example, with a six-bus system illustrates the main steps of the proposed allocation strategy, and numerical results obtained with the IEEE 57-bus system are used to assess the quality of the loss allocation