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Improved algorithm for periodic steady-state analysis in nonlinear electromagnetic devices

Sobczyk T. J., Radzik M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2019

Vol. 67, nr 5

863--869

This paper presents the improved methodology for the direct calculation of steady-state periodic solutions for electromagnetic devices, as described by nonlinear differential equations, in the time domain. A novel differential operator is developed for periodic functions and the iterative algorithm determining periodic steady-state solutions in a selected set of time instants is identified. Its application to steady-state analysis is verified by an elementary example. The modified algorithm reduces the complexity of steady-state analysis, particularly for electromagnetic devices described by high-dimensional nonlinear differential equations.

Application of novel discrete differential operator of periodic function to study electromechanical interactions

Sobczyk T. J., Radzik M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2018

Vol. 66, nr 5

645--653

This paper investigates an algorithm for finding steady-states in electromechanical systems for the cases of their periodic nature. The algorithm enables to specify the steady-state solution identified directly in time domain. The basis for such an algorithm is a discrete differential operator that specifies the values of the first derivative of the periodic function in the selected set of points on the basis of the values of that function in the same set of points. It creates algebraic equations describing the steady-state solution for the nonlinear differential equations describing electromechanical systems. In this paper, the direct time-domain approach is tested for the simple converter considering. The algorithm used in this paper is competitive with respect to the one known in literature an approach based on the harmonic balance method operated in frequency domain.

Algorithm for determining two-periodic steady-states in AC machines directly in time domain

Sobczyk T.J.

Archives of Electrical Engineering

2016

Vol. 65, nr 3

575--583

This paper describes an algorithm for finding steady states in AC machines for the cases of their two-periodic nature. The algorithm enables to specify the steady-state solution identified directly in time domain despite of the fact that two-periodic waveforms are not repeated in any finite time interval. The basis for such an algorithm is a discrete differential operator that specifies the temporary values of the derivative of the twoperiodic function in the selected set of points on the basis of the values of that function in the same set of points. It allows to develop algebraic equations defining the steady state solution reached in a chosen point set for the nonlinear differential equations describing the AC machines when electrical and mechanical equations should be solved together. That set of those values allows determining the steady state solution at any time instant up to infinity. The algorithm described in this paper is competitive with respect to the one known in literature an approach based on the harmonic balance method operated in frequency domain.