Bishal Silwal

Computation of torque of an electrical machine with different types of finite element mesh in the air gap

In the numerical analysis of electrical machines, accurate computation of the electromagnetic torque is desired. Maxwell stress tensor method and Coulombs method are the most commonly used methods for computing torque numerically. However, several other methods have also been developed and are being used. These methods are observed to have several accuracy issues related to the finite element discretization used in the air gap of the machine. In this paper, the effect of various finite element meshes in the air gap of the machine and the effect of the shape of the elements used to compute the torque are studied and discussed. This paper carefully compares the torques obtained from a direct method and a method based on the power balance of the machine.

Evaluation and comparison of different numerical computation methods for the electromagnetic torque in electrical machines

In the numerical analysis of electrical machines, there exist various methods for the computation of electromagnetic torque. Maxwell stress tensor method is the most commonly used for computing torque numerically. However, several other methods have been developed and are being used. In this paper, different numerical methods for torque computation in an electrical machine are reviewed and compared. A complementary method of torque computation, based on the power balance of the electrical machine is studied and used as a reference to assess the accuracy of other torque computation methods.

Numerical Analysis of the Power Balance of an Electrical Machine With Rotor Eccentricity

The power balance in the numerical simulation of a cage induction machine with eccentric rotor has been studied. The asymmetrical air-gap flux density distribution caused by the non-uniform air gap due to eccentricity produced forces that play an important role in the rotor dynamic stability. These forces act both in the radial and the tangential directions. The tangential force together with the whirling motion produces additional power in the shaft. If the power balance of the simulation satisfies, the power due to the whirling can be calculated from the power balance. This could also give a new approach to compute the forces due to eccentricity or verify the existing force computation methods. The error in the power balance of an eccentric machine has been calculated and the sources of the errors have been illustrated and discussed.

Instantaneous Power Balance in Finite-Element Simulation of Electrical Machines

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.

Power balance approach to study electromagnetic damping in rotor dynamics

The electromagnetic damping of mechanical vibrations in a cage induction machine with an eccentric rotor is studied. The method used in the study is based on the numerical power balance of the machine. Time-stepping finite element method is used to compute the powers. The damping power calculated from the power balance is used in the mechanical rotor model and the response of the system is observed.

Energy-Preserving Methods and Torque Computation From Energy Balance in Electrical Machine Simulations

The finite-element analysis for the simulation of magnetic fields in electrical machines leads to an index-1 differential-algebraic equation (DAE) (as opposed to a conventional ordinary differential equation), because the electrical conductivity can be zero in certain regions. First, we construct a DAE-compatible time integration scheme which is energy-balanced, meaning that in a linear system, the input stored and lost powers sum exactly to zero. Second, we use a method based on the energy balance to compute torque. We show that the energy balance method approaches the virtual work principle applied at remeshing layer, as the time step is refined. A similar result also holds if the rotation of the rotor is implemented by Nitsches method, which is an instance of the so-called mortar methods.

Measurement of torque harmonics of a cage induction machine under rotor eccentricity

Eccentricity creates an unbalanced magnetic pull in the rotor of the cage induction machine which plays a vital role in the rotor dynamic stability. In this case, it is desirable to know how different quantities of the machine behave, for example torque. Numerical analysis shows an increase in the average torque of the machine with eccentricity. The amplitudes of some of the harmonic components of the torque are also affected. In such case, the measurement of the torque waveform could give a good insight to the behavior of the torque and its harmonics. Here, a novel measurement rig is presented.