Direct Determination of Two‐periodic Solutions for Nonlinear Dynamic Systems

Sobczyk, Tadeusz

doi:10.1108/eb010132

Cited by 14 publications

(20 citation statements)

References 2 publications

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“…Such infinite set of non-linear algebraic equations can be solved only numerically by using an iterative procedure [1]. In this paper the Newton-Raphson algorithm has been applied.…”

Section: Harmonic Balance Equations Accouting For the Motion Equmentioning

confidence: 99%

“…The problem of creation the Jacobian matrix for such cases has been has been solved in [1]. In order to determine the Jacobian matrix it is enough to calculate the matrices …”

Section: Newton-raphson Algorithm Of Finding Steady-state Solutionsmentioning

confidence: 99%

“…An iterative procedure of determining the X vector for the non-linear equations by the Newton-Raphson algorithm is described in [1] MATLAB has been used to implement the Newton-Raphson algorithm described in this section. Numerical tests, which are not presented here, confirm its convergence.…”

Section: Newton-raphson Algorithm Of Finding Steady-state Solutionsmentioning

confidence: 99%

See 2 more Smart Citations

Direct determination of currents spectra of synchronous machines at load perturbations

Sobczyk

Radzik

2009

2009 IEEE International Symposium on Diagnostics for Electric Machines, Power Electronics and Drives

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“…Such infinite set of non-linear algebraic equations can be solved only numerically by using an iterative procedure [1]. In this paper the Newton-Raphson algorithm has been applied.…”

Section: Harmonic Balance Equations Accouting For the Motion Equmentioning

confidence: 99%

“…The problem of creation the Jacobian matrix for such cases has been has been solved in [1]. In order to determine the Jacobian matrix it is enough to calculate the matrices …”

Section: Newton-raphson Algorithm Of Finding Steady-state Solutionsmentioning

confidence: 99%

See 1 more Smart Citation

Direct determination of currents spectra of synchronous machines at load perturbations

Sobczyk

Radzik

2009

2009 IEEE International Symposium on Diagnostics for Electric Machines, Power Electronics and Drives

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“…The Harmonic Balance Method (HBM) [26][27][28][29][30][31][32][33] gives the possibility of analyzing solutions of mathematic model equations of electrical machines in case of periodic variation of their coefficients; it is a simple extension of the symbolic method and leads to algebraization of the machine description in steady states. This approach is competitive with FEM analysis and allows to combine the electromagnetic phenomena occurring in the process of energy conversion in electrical machines.…”

Section: Introductionmentioning

confidence: 99%

Application of the Harmonic Balance Method for Spatial Harmonic Interactions Analysis in Axial Flux PM Generators

2021

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In this paper, an application of the Harmonic Balance Method (HBM) for analysis of Axial Flux Permanent Magnet Generator (AFPMG) is carried out. Particular attention was paid to development of mathematical model equations allowing to estimate the machine properties, without having to use quantitative solutions. The methodology used here allowed for precise determination of Fourier spectra with respect to winding currents and electromagnetic torque (both quantitatively and qualitatively) in steady state operation. Analyses of space harmonic interaction in steady states were presented for the three-phase AFPMG. Satisfactory convergence was between the results of calculations and measurements which confirmed the initial assumption that the developed circuit models of AFPMG are sufficiently accurate and can be useful in the diagnostic analyses, tests and the final stages of the design process.

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“…In [5] this algorithm is extended to a nonlinear magnetic circuit example. In [6] an algorithm is described to determine a steady-state solution for a symmetrical synchronous machine, described by "classical" equations (i.e.…”

Section: Introductionmentioning

confidence: 99%

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

Sobczyk¹

2016

Archives of Electrical Engineering

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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.

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Direct Determination of Two‐periodic Solutions for Nonlinear Dynamic Systems

Cited by 14 publications

References 2 publications

Direct determination of currents spectra of synchronous machines at load perturbations

Direct determination of currents spectra of synchronous machines at load perturbations

Application of the Harmonic Balance Method for Spatial Harmonic Interactions Analysis in Axial Flux PM Generators

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

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