Accelerated Computation of Multiphase Short Circuit Summary for Unbalanced Distribution Systems Using the Concept of Selected Inversion

Abstract

In this paper, an ultra-fast algorithm for the computation of multiphase short-circuit currents at all buses is proposed by addressing the concept of selected inversion. The short circuit summary is achieved through the computation of multiphase Thevenin equivalent at each bus by using the augmented nodal matrix. This typically requires the sequential solution of linear system of equations, i.e., direct inversion which can be demanding in terms of CPU time. In this paper, it is shown that dramatic gains in computational time can be obtained when the selected inversion (SelInv) technique is performed where only a subset of entries of the inverse of augmented nodal matrix is computed. These entries include the phase domain Thevenin impedances seen from network buses which are used in the computation of short-circuit currents with the predefined boundary conditions specific to the fault type. The performance of the method is demonstrated with very large scale and realistic distribution systems.Index Terms-Distribution systems, power system analysis, short circuit, sparse matrix methods, unbalanced networks.

Online Thévenin Equivalent Determination Considering System Side Changes and Measurement Errors

“…TE has been, and is being, used for a wide variety of applications including, but not limited to: short circuit current calculation in both distribution [1], [2] and transmission systems [3]; fault location [4], [5]; parameter identification for instability detection [6] and for electromagnetic transient studies [7]; harmonic detection and analysis in distribution systems [8], [9]; under voltage load shedding [10]; online estimation of maximum power transfer limits [11]; and voltage stability monitoring [12]- [20].…”

“…Methods for determining the TE parameters, depending on the application, have many different bases. The TE in an unbalanced three-phase system is obtained by measurements of the root mean square (RMS) values of terminal voltages and currents [20], inverting the 3-phase [3], or determining the multiphase matrix either by load insertion [2] or current injection [1] at each phase one at a time. For harmonic detection, is determined and compared with the critical impedance [8], while in [9], the harmonic source is characterized by a Norton equivalent determined by making a change in the system side, changing the transformer tap.…”

A common modeling platform for the multiphase analysis and simulation of modern distribution systems in offline and distribution management system applications

“…On the other hand, by using a selected inversion algorithm developed for symmetric matrices [15], the full inversion of A can be avoided given that matrix A is symmetric, and remarkable gains in computational efficiency can be observed [16].…”

Analysis of faulted power system during simultaneous open conductor and ground fault

“…Also, the computational burden increases when accommodating multiple faults at multiple locations in the network in the bus impedance matrix. Lacroix and Kocar [8] proposed the concept of selected inversion wherein fault points can be added in modular form but an inversion of a large augmented matrix containing a full admittance matrix is required. A major limitation of this method is that it is suitable for shunt faults only.…”