Reduction and Equivalencing of Equations of Electrical Network based on Matrix Annihilators

  • Magomed Gadzhiev Institute of Electrical Power Engineering, National research university MPEI, Moscow, Russia
  • Misrikhan Misrikhanov Institute of Electrical Power Engineering, National research university MPEI, Moscow, Russia
  • Vladimir Ryabchenko Institute of Electrical Power Engineering, National research university MPEI, Moscow, Russia
  • Yuriy Sharov Institute of Electrical Power Engineering, National research university MPEI, Moscow, Russia
Keywords: electrical network, nodal stress equations, reduction, matrix annihilator, equivalencing, conditionality, large and very large matrices

Abstract

This paper proposes an original method for the reduction of node voltage equations, aimed at equivalencing electrical network. The method is based on equivalent matrix transformations using matrix annihilators. The offered method, in comparison with the traditional one, makes it possible to improve the conditionality of the solved equations by an order of magnitude or more. This has a positive effect on the numerical stability of the resulting electrical network equivalents. The results of reduction of a small, large, and very large system of node voltage equations are presented

Author Biographies

Magomed Gadzhiev, Institute of Electrical Power Engineering, National research university MPEI, Moscow, Russia

Magomed Gadzhiev graduated from the Electric Power Department (EPD) of the Moscow Power Engineering Institute (MPEI) in 2006. In 2012 he defended his PhD thesis "Improving the accuracy of accounting for power losses to the crown during the operational optimization of the EPS regime" in MPEI. Presently he is the head of the Research Laboratory of the Department of electric power systems MPEI.

Misrikhan Misrikhanov, Institute of Electrical Power Engineering, National research university MPEI, Moscow, Russia

Misrikhan Misrikhanov graduated from the Electric Power Department (EPD) of the Moscow Power Engineering Institute (MPEI) in 1974. In 2010 he defended his doctoral dissertation «Fundamentals of the theory of invariant control and its application to the creation of technical systems». Professor Ivanovo State University

Vladimir Ryabchenko, Institute of Electrical Power Engineering, National research university MPEI, Moscow, Russia

Vladimir Ryabchenko graduated from the Irkutsk High Military Aviation Engineering School in 1983 on speciality «Aeronautical Instrument and Electrical Equipment». In 2002 he defended his doctoral dissertation in Air Force Academy named after Professor N.E. Zhukovsky. Leading researcher of the Research Laboratory «Automation of Electrical Distribution Networks» National Research University MPEI.

Yuriy Sharov, Institute of Electrical Power Engineering, National research university MPEI, Moscow, Russia

Yuriy Sharov graduated from the EEF MPEI in 1986. In 1994 he defended his PhD thesis "Development of methods and tools for assessing the effectiveness of the management of electric power systems under large disturbances of the regime" in MPEI. Presently he is the head of the Department of electric power systems MPEI.

Published
2018-04-26