Lumped-circuit models for nonlinear inductors exhibiting hysteresis loops

Chua, Leon O.; Stromsmoe, K.A.

doi:10.1109/tct.1970.1083192

Cited by 131 publications

(41 citation statements)

References 17 publications

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“…It can be seen that the dependency of these losses on the frequency and the flux linkage corresponds to the eddy-current losses according to (1).…”

Section: B Constant Core-loss Resistormentioning

confidence: 98%

“…A general framework for modelling of hysteresis utilizing a dissipating function and a restoring function was presented in [1], [2], but no explicit function was given. In [3] a polynomial function was used to model the hysteresis loop assuming sinusoidal voltage excitation.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, the core losses are modelled according to the principles in [1], [2]. The dissipating function is derived based on the desired steady-state core-loss profile.…”

Section: Introductionmentioning

confidence: 99%

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Inclusion of hysteresis and eddy current losses in nonlinear time-domain inductance models

Ranta

Hinkkanen

Belahcen

et al. 2011

IECON 2011 - 37th Annual Conference of the IEEE Industrial Electronics Society

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Abstract-A time-domain model including the core losses of a nonlinear inductor is proposed. The model can be seen as a parallel combination of a nonlinear inductance modelling the saturation and a nonlinear resistance modelling the core losses. The desired steady-state core-loss profile is used to determine the resistance function. The model is easy to implement and can be used in many different applications. The hysteresis loop of an electrical steel sample is measured at several frequencies in order to experimentally verify the model. It is shown that the model is able to predict both major and minor hysteresis loops very well. I. INTRODUCTIONModelling of nonlinear hysteretic inductances has challenged researchers for many years. A good accuracy can indeed be achieved by a physical in-depth analysis, but the resulting differential equations are very complicated. In, for instance, design and real-time control of electric drives and power electronic devices, dynamic time-domain models that are easy to implement and tune are desirable. The increasing demand for energy efficiency makes the need for accurate models of losses even larger in the future.The core losses can be divided into three parts: hysteresis losses, classical eddy current losses and excess losses. The hysteresis losses are proportional to the frequency, while the classical eddy current losses and the excess losses are proportional to the frequency raised to the second and 1.5th power, respectively.A generally used and very simple model of the core losses of an inductance is a constant resistance in parallel to the inductance. In the case of a sinusoidal waveform, the power dissipated in a constant resistor is proportional to the square of the frequency. This frequency dependency corresponds to the classical eddy current losses. Particularly at lower frequencies, the hysteresis losses constitute a significant part of the total core losses, and the losses predicted by a constant resistance deviate remarkably from the actual losses.Several methods have been developed to achieve more accurate models. A general framework for modelling of hysteresis utilizing a dissipating function and a restoring function was presented in [1], [2], but no explicit function was given. In [3] a polynomial function was used to model the hysteresis loop assuming sinusoidal voltage excitation. A polynomial model for the B-H relation using the concept of a hysteresis related field intensity was proposed in [4]. In [5], a system of differential equations was developed based on the idea of separating the magnetic field into two parts, where one part

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“…It can be seen that the dependency of these losses on the frequency and the flux linkage corresponds to the eddy-current losses according to (1).…”

Section: B Constant Core-loss Resistormentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Inclusion of hysteresis and eddy current losses in nonlinear time-domain inductance models

Ranta

Hinkkanen

Belahcen

et al. 2011

IECON 2011 - 37th Annual Conference of the IEEE Industrial Electronics Society

View full text Add to dashboard Cite

show abstract

“…A general framework for hysteresis modeling was presented in [4], [5] while no explicit functions were given. Here, an explicit function for the iron-loss resistance is proposed based on the desired steady-state iron-loss profile.…”

Section: Preliminaries: Nonlinear Inductormentioning

confidence: 99%

“…In this paper, the idea of a dynamic hysteresis model [4], [5] is used in the modeling of the iron losses. An explicit resistance function that includes the rotation and pulsation of the flux vector in the circuit model is proposed.…”

Section: Introductionmentioning

confidence: 99%