# Direct Consideration of Eddy Current Losses in Laminated Magnetic Cores in Finite Element Method (FEM) Calculations Using the Laplace Transform

The following article presents a computation procedure that enables us to simulate the dynamic states of electric machines with a laminated magnetic core, with direct consideration of the eddy current losses. The presented approach enables a significant reduction of the simulation process computatio...

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Main Authors: , , , Article English 2020-03-01 Energies https://www.mdpi.com/1996-1073/13/5/1174
id doaj-713337d6b08c4e00bf0085e22781f0f7 Article doaj-713337d6b08c4e00bf0085e22781f0f72020-11-25T02:40:34ZengMDPI AGEnergies1996-10732020-03-01135117410.3390/en13051174en13051174Direct Consideration of Eddy Current Losses in Laminated Magnetic Cores in Finite Element Method (FEM) Calculations Using the Laplace TransformMarek Gołębiowski0Lesław Gołębiowski1Andrzej Smoleń2Damian Mazur3Department of Electrical and Computer Engineering, Rzeszow University of Technology, 35-959 Rzeszów, PolandDepartment of Electrical and Computer Engineering, Rzeszow University of Technology, 35-959 Rzeszów, PolandDepartment of Electrical and Computer Engineering, Rzeszow University of Technology, 35-959 Rzeszów, PolandDepartment of Electrical and Computer Engineering, Rzeszow University of Technology, 35-959 Rzeszów, PolandThe following article presents a computation procedure that enables us to simulate the dynamic states of electric machines with a laminated magnetic core, with direct consideration of the eddy current losses. The presented approach enables a significant reduction of the simulation process computational complexity. The verification of the obtained data correctness is based on a detailed balance of energy and power in the investigated system. The correctness of the obtained results was also confirmed by comparing them with the results included in norms that describe the losses in laminated sheets. The presented approach is based on expressing the equivalent permeability of transformer metal sheets by using RC or RL circuits. The impedances of these circuits are treated as the transmittance of Infinite Impulse Response filters (IIR) of the Laplace s variable. In this form they are implemented in direct calculations of the dynamics of electric machines based on field-circuital models, using the Finite Element Method (FEM). In this way, we present the method of including eddy current losses in laminated metal circuits of chokes or transformers, during calculations using the finite element method, with the IIR filter in the domain of the variable s of the Laplace transform. Eddy current losses are directly included in the calculation process. Therefore, they have a direct impact on the transient state waveforms. However, the use of the Laplace variable s caused an excessive increase in the number of state variables, and the overall computational efficiency of the presented method is sufficiently low so as to be used in the simulation process of electrical machine dynamic states with a relatively large number of elements in the FE Model.https://www.mdpi.com/1996-1073/13/5/1174laminated transformer sheeteddy current lossesfem methodchokelaplace’s transformation DOAJ English Article DOAJ Marek Gołębiowski Lesław Gołębiowski Andrzej Smoleń Damian Mazur Marek Gołębiowski Lesław Gołębiowski Andrzej Smoleń Damian Mazur Direct Consideration of Eddy Current Losses in Laminated Magnetic Cores in Finite Element Method (FEM) Calculations Using the Laplace Transform Energies laminated transformer sheet eddy current losses fem method choke laplace’s transformation Marek Gołębiowski Lesław Gołębiowski Andrzej Smoleń Damian Mazur Marek Gołębiowski Direct Consideration of Eddy Current Losses in Laminated Magnetic Cores in Finite Element Method (FEM) Calculations Using the Laplace Transform Direct Consideration of Eddy Current Losses in Laminated Magnetic Cores in Finite Element Method (FEM) Calculations Using the Laplace Transform Direct Consideration of Eddy Current Losses in Laminated Magnetic Cores in Finite Element Method (FEM) Calculations Using the Laplace Transform Direct Consideration of Eddy Current Losses in Laminated Magnetic Cores in Finite Element Method (FEM) Calculations Using the Laplace Transform Direct Consideration of Eddy Current Losses in Laminated Magnetic Cores in Finite Element Method (FEM) Calculations Using the Laplace Transform direct consideration of eddy current losses in laminated magnetic cores in finite element method (fem) calculations using the laplace transform MDPI AG Energies 1996-1073 2020-03-01 The following article presents a computation procedure that enables us to simulate the dynamic states of electric machines with a laminated magnetic core, with direct consideration of the eddy current losses. The presented approach enables a significant reduction of the simulation process computational complexity. The verification of the obtained data correctness is based on a detailed balance of energy and power in the investigated system. The correctness of the obtained results was also confirmed by comparing them with the results included in norms that describe the losses in laminated sheets. The presented approach is based on expressing the equivalent permeability of transformer metal sheets by using RC or RL circuits. The impedances of these circuits are treated as the transmittance of Infinite Impulse Response filters (IIR) of the Laplace s variable. In this form they are implemented in direct calculations of the dynamics of electric machines based on field-circuital models, using the Finite Element Method (FEM). In this way, we present the method of including eddy current losses in laminated metal circuits of chokes or transformers, during calculations using the finite element method, with the IIR filter in the domain of the variable s of the Laplace transform. Eddy current losses are directly included in the calculation process. Therefore, they have a direct impact on the transient state waveforms. However, the use of the Laplace variable s caused an excessive increase in the number of state variables, and the overall computational efficiency of the presented method is sufficiently low so as to be used in the simulation process of electrical machine dynamic states with a relatively large number of elements in the FE Model. laminated transformer sheet eddy current losses fem method choke laplace’s transformation https://www.mdpi.com/1996-1073/13/5/1174 AT marekgołebiowski directconsiderationofeddycurrentlossesinlaminatedmagneticcoresinfiniteelementmethodfemcalculationsusingthelaplacetransform AT lesławgołebiowski directconsiderationofeddycurrentlossesinlaminatedmagneticcoresinfiniteelementmethodfemcalculationsusingthelaplacetransform AT andrzejsmolen directconsiderationofeddycurrentlossesinlaminatedmagneticcoresinfiniteelementmethodfemcalculationsusingthelaplacetransform AT damianmazur directconsiderationofeddycurrentlossesinlaminatedmagneticcoresinfiniteelementmethodfemcalculationsusingthelaplacetransform 1724780772247732224