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Abstract

The paper presents abilities and advantages following from the use of the harmonicbalance method for analysis of steady state of a multiphase system with switching devices on example of a matrix converter. Switching elements are modelled as resistances with step-wise variable parameters, what allows to describe the converter by a linear infinite set of equations. The analysis in frequency domain is presented on example of the one-periodic control strategy. External systems were also added using the Thevenin method approach. The numerical calculation results of a linear equations set were verified by the variable structure method in a time domain and the numerical convergence was confirmed. Furthermore, the exemplary complex system was analysed using the cascade method and current waveforms were obtained.

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Authors and Affiliations

Dariusz Borkowski
Tadeusz J. Sobczyk
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Abstract

The paper investigates a significant influence of transients on steady states in a matrix converter with the one-periodic control strategy. Proposed controller can be used as an interconnection device within a power system for a power flow control. However, the presence of inductances in external systems has the significant influence on steady state of a matrix converter operation. The special current injection method has been developed to ensure a proper operation of a matrix converter. Presented analysis of steady states is carried out in a frequency domain using the harmonic balance method. Obtained numerical results, which are confirmed by a time domain analysis, prove the effectiveness of the proposed method.
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Authors and Affiliations

Dariusz Borkowski
Tadeusz Sobczyk
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Abstract

In this paper we present a mixed shooting – harmonic balance method for large linear mechanical systems on which local nonlinearities are imposed. The standard harmonic balance method (HBM), which approximates the periodic solution in frequency domain, is very popular as it is well suited for large systems with many degrees of freedom. However, it suffers from the fact that local nonlinearities cannot be evaluated directly in the frequency domain. The standard HBM performs an inverse Fourier transform, then calculates the nonlinear force in time domain and subsequently the Fourier coefficients of the nonlinear force. The disadvantage of the HBM is that strong nonlinearities are poorly represented by a truncated Fourier series. In contrast, the shooting method operates in time-domain and relies on numerical time-simulation. Set-valued force laws such as dry friction or other strong nonlinearities can be dealt with if an appropriate numerical integrator is available. The shooting method, however, becomes infeasible if the system has many states. The proposed mixed shooting-HBM approach combines the best of both worlds.

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Authors and Affiliations

Frederic Schreyer
Remco I. Leine
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Abstract

This study presents a method to directly calculate the stator current Fourier spectra in double-cage induction motors to diagnose faults in rotor cages. A circuit model is developed for this purpose, allowing the modelling of any asymmetry in the outer and inner rotor cages. The model extends the conventional model of a cage motor by considering the higher space harmonics generated by the stator windings. The asymmetry of the cages is modelled by growing the resistance of any of the rotor bars. This results in various model equations, to be solved by looking for diagnostic signals. Motor current signature analysis is typically used to diagnose cage motors based on the Fourier spectra of the stator currents during steady-state operation. This study determines these spectra for double cage motors using the harmonic balance method, omitting the transient calculations. The calculation results confirmed the sensitivity of the stator current Fourier spectra as a diagnostic signal to distinguish faults in the outer and inner cages.
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Authors and Affiliations

Jarosław Tulicki
1
ORCID: ORCID
Tadeusz Jan Sobczyk
1
ORCID: ORCID
Maciej Sułowicz
1
ORCID: ORCID

  1. Department of Electrical Engineering, Faculty of Electrical and Computer Engineering, Cracow University of Technology, 24 Warszawska str., 31-155 Kraków, Poland

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