NDLI: Instantaneous Power Balance in Finite-Element Simulation of Electrical Machines

Content Provider	IEEE Xplore Digital Library
Author	Rasilo, P. Perkkiö, L. Hannukainen, A. Silwal, B. Eirola, T. Arkkio, A.
Copyright Year	1965
Abstract	Conservation of power in time-stepping finite-element (FE) simulation of electrical machines is studied. We propose a method for accurately obtaining the instantaneous time derivative of the FE solution, from which the instantaneous eddy-current losses and the rate-of-change of the magnetic field energy are calculated. The method is shown to be consistent with different time-integration schemes, unlike the typically used backward-difference (BWD) approximation, which is only accurate if the BWD method is also used for the time integration. We first formulate the FE equations for a locked-rotor induction machine as a differential-algebraic equation (DAE) system. An approach called the collocation method is then used to derive the BWD, trapezoidal (TR), and implicit midpoint integration rules in order to show how these methods approximate the solution in time. We then differentiate the constraint equations of the DAE to form a system from which the time derivative of the solution can be solved. The obtained derivative is shown to satisfy the power balance exactly in the collocation points. In case of the TR rule, the losses calculated with the proposed method are shown to be less sensitive to the time-step length than ones obtained with the BWD approximation for the time derivatives. The collocation approach also allows studying the power balance continuously during the time step.
Sponsorship	IEEE Magnetics Society
Starting Page	1
Ending Page	7
Page Count	7
File Size	1778962
File Format	PDF
ISSN	00189464
Volume Number	50
Issue Number	5
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Equations Mathematical model Iron Approximation methods Stator windings Rotors power balance Collocation method eddy currents electrical machines field energy finite element methods finite element (FE) methods
Content Type	Text
Resource Type	Article
Subject	Electronic, Optical and Magnetic Materials Electrical and Electronic Engineering

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