# Investigating the Complex Characteristics of an Hybrid Electric Vehicle Motor

Motors and generators with MotorSolveBrushless DC machines, particularly those of the interior permanent magnet (IPM) type are gaining favour for hybrid and electric vehicle applications.

These machines are characterized by high power density, high output torque over a wide range of operational speed due to a highly salient rotor and a strong reluctance torque component. Field weakening and operation in the constant-power speed range (CPSR) is key to operating at a wide range of vehicle speeds without the need for excessive gearing.

Field weakening is accomplished by increasing the advance angle as speed increases to reduce the back EMF so it does not exceed the available supply voltage.

MotorSolve is able to provide useful results to investigate these complex characteristics. The FEA engine that powers MotorSolve can consider non-linear materials, PWM drive circuitry and set up complicated geometries with only a few simple instructions.

### METHODS and RESULTS

## 8-pole, 48 slot IPM machine

The 8-pole, 48 slot three phase IPM machine, while complicated in appearance, is specified in minutes using the MotorSolve geometry editor. The stator poles take advantage of strong neodymium iron boron (NdFeB) magnets as well as a highly salient rotor design that gives a large reluctance torque component for extended speed range operation.

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## SATURATION in the ROTOR BRIDGE

The interior permanent magnet machine relies on rotor core saturation to operate, requiring consideration of non-linear material characteristics. The flux plot (100 A current) shows the saturation in the rotor bridge areas and allows the designer to optimize the geometric parameters.

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## CONSTANT POWER SPEED RANGE (CPSR) of the IPM

Determining the torque-speed curve for a machine like this is not a trivial task, requiring an optimization of advance angle for each speed. MotorSolve allows a quick setup of multiple runs for several speeds and advance angles to show the torque available. The envelope of these curves provides the torque speed curve and the corresponding optimal advance angle as a function of the desired performance. The wide CPSR (constant power speed range) of the IPM is shown.

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## PEAK TORQUE and FIELD WEAKENING

This plot extracts the peak torque at each speed at the optimal advance angle. The advantage of field weakening becomes apparent as the machine exceeds the constant-torque region around 875 rpm.

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## Ld AND Lq as a FUNCTION of CURRENT

The IPM's wide speed range results from its high saliency ratio (the d-axis inductance relative to the q-axis inductance). The non-linear behaviour of this inductance due to magnetic saturation can be accurately depicted by MotorSolve. This graph shows Ld and Lq as a function of current.

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## ROTOR HYSTERESIS and EDDY CURRENT LOSSES

Core losses can be a significant fraction of total losses in motors and MotorSolve's advanced loss calculation capabilities allow the user to not only estimate the induced core losses in each component, but more specifically to determine the distribution of these losses into their hysteresis and eddy current contributions. The figure on the left shows the rotor's hysteresis and eddy current losses as a function of rotor speed (or equivalently, the frequency). The eddy current trend shows a parabolic behavior while the hysteresis loss follows a power law behavior as expected.

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