Simulating the Toyota Prius electric motor using Opera-2d

This application note shows how to create and analyze the 2004 version of the Toyota PRIUS electric motor using the 2D Machine Environment (ME2D). The experimental characterization of the motor and of the drive system has been done by the Oak Ridge National Laboratory (ORNL) which presented its findings in a series of papers [1]-[5].

The steps needed to customize the geometry of the stator and rotor of the default embedded magnet synchronous model in order to recreate the precise geometry of the PRIUS motor are detailed.

A combination of the DC_ST, AC_ST and AC_RM analysis available for the PMSM are used in order to model the electromagnetic effects produced in the machine. The analyses are validated against the measured data provided by ORNL.

A more detailed version of this application note is available on request. The full version includes the complete material and geometric definition of the motor. Supported customers can also request the machines environment data files that can be used to reproduce the results contained herin.


Motor characteristics


Geometric outline of the PRIUS motor

Figure 2: Geometric outline of the PRIUS motor

The external diameter of the stator is 269.24 mm and the stack length is 83.56 mm. Other key dimensions for the stator and rotor are described in references [1} – [5]. The resulting airgap for the PRIUS PMSM is 0.75 mm.

The 2004 Toyota PRIUS Hybrid Vehicle uses a three phase, 48 slots, embedded permanent magnet motor with 8 poles. The windings are distributed, single layered with 9 turns per slot and connected in series.


Geometric dimensions


The V-shaped magnets are housed in specially designed rotor slots that aim to increase the quadrature-axis reactance in order to improve the motor’s performance. The air regions at the top of the magnet cutaway are designed to narrow the flux bridge in order to further increase Xq.


Magnetic characteristics


The material used for the stator and rotor cores definition is M19 laminated steel based on the magnetic data provided by the manufacturer. The permanent magnets are characterised in the Oakridge paper [1] and the BH curve used in the modelling is obtained by interpolating the measured points. Hence as the measured data for the magnets is limited, the magnetic properties of the magnetic material used in these simulations do not necessarily match the materials used in the real motor. This is also true for the steel used in the rotor and stator as no bh data is supplied for this within the ORNL papers. Instead a generic bh curve for M19 laminated steel has been used. These two factors more than likely account for some of the differences observed between measured and simulated data.


Measured data


The tests published by the Oak Ridge National Laboratory cover a wide range of mechanical, electromagnetic, thermal and energy efficiency characteristics. The purpose of this application note is to compare the electromagnetic characteristics of the ME2D model against the ones produced by the real motor. Therefore, only the electromagnetic tests of the traction motor are considered in the following comparisons.


ME2D model


Setting up the model


The 2D Machines Environment is an automated toolbox that aid in the design of electrical machines within Opera FEM software. For more information about the Machines Environment and how to set it up, please see the ME2D User Guide. The steps needed to set-up the model for the Prius electric motor are outlined in the following.

Start the environment by running StartEnvironment.comi from the tool button added to the 2D Pre/Post-Processor window.

Start the 2d Machiens Environment

Figure 3: Start the 2d Machiens Environment

Next, the type of electrical machine needs to be selected from the list. In this case, the Permanent Magnet Embedded machine is selected.

Motor type selection

Figure 4: Motor type selection

In the Permanent Magnet Embedded dialog select Default Values and then select rotor Type 2, as this type of rotor offers the V-shaped magnets needed for the PRIUS motor.

Rotor type selection

Figure 5: Rotor type selection

Next, the rotor dimensions need to be inserted. The position of the magnets in the rotor is defined by the distance from the center of the shaft to the intersection of the two magnets (variable C).

Rotor dimensions dialog

Figure 6: Rotor dimensions dialog

The air region at the top of the magnets has a triangular shape in the default rotor definition. Further adjustment to the geometry of this region needs to be done in order to precisely model the real geometry and the optimized bridges near the airgap. For information regarding how to set up these modifications, see the section “Model customising”.

The default indents in the Permanent Magnet Embedded model are symetrical and situated between the two V-shaped magnets. In the case of the PRIUS motor the indents are situated in a different position and are asymetrical, thus they need to be set using a customised rotor file (see “Model customising” on page 8.) At this step, the default indents will be neglected by setting their depth and angle to zero.

Next, the stator dimensions are specified. As the geometry of the stator defined in the default machine model offers a square slot bottom, the stator will also undergo a further customising.

Stator dimensions dialog

Figure 7: Stator dimensions dialog

The winding used for the PRIUS model is distributed, single layer.

Winding type selection

Figure 8: Winding type selection

Winding layer selection (distributed)

Figure 9: Winding layer selection (distributed)

Finally, depending on the type of analysis performed, specific information is required. The specific parameters for the DC_ST and the AC_ST analysis will be discussed separately as well as the meshing options (see the “Analysis” section).


Model customising


In addition to the pre-defined stator and rotor geometries provided by the 2D Machines Environment the user has the possibility of using a custom built geometry, both for the stator and/or for the rotor or to modify the geometry provided by the environment.

After building the initial section of the machine, the environment will look for certain files in the working directory and if it finds them will proceed to modify the geometry accordingly. The modifications made on a section of the machine (in the case when the machine has a periodicity condition) will be automatically replicated on all of the motor sections without the need for further intervention from the user.

When the modifications have been completed, the environment will proceed to the meshing of the model and will present the user with the meshed geometry. The user will then have the option to continue with the analysis or to temporarily step out of the automated process and manually make further adjustments. After these have been made, the user needs to re-mesh the model and continue the analysis using the toolbutton.

For the PRIUS model, both the rotor and the stator need minor alterations in order to match the complex geometry of the real motor. The files containing these modifications need to have a specific filename: customRotor.comi and customStator.comi, respectively.

The geometrical modifications of the rotor deal with the shape of the air regions at the top of the magnets and with the custom indents.

Rotor before customization

a) before

Rotor after customization

b) after

Figure 10: Rotor customization


The stator geometry also needs to be altered, in order to modify the bottom of the stator slots to give them a rounded shape.

Stator before customization

a) before

Stator after customization

b) after

Figure 11: Stator customization





The evaluation of the PRIUS model is done based on the electromagnetic characteristics provided by the Oak Ridge National Laboratory (ORNL). The cogging torque, static torque over a range of currents, and continuous torque are compared. For this, two types of analysis are used : DC_ST analysis and AC_ST analysis. For details about using these two analysis in a correlated way, refer to the ME2D User Guide (see Appendix – Combining Permanent Magnet Machines Analyses).

The first analysis to be run is a DC_ST analysis, over 15 degrees with a fine step, in order to obtain the cogging torque in the motor.

The parameters used for this analysis can be seen in Figure 10. Note that, as the cogging torque is obtained from a non-exited case, there is no need for a current to be given at this step.

Analysis data for the DC_ST analysis of the cogging torque

Figure 12: Analysis data for the DC_ST analysis of the cogging torque

The next analysis is also a DC_ST, which looks at the static torque vs. angle for a range of currents. The simulation step can be coarser in this case and the analysis is done over 90 degrees. Note that the values of the excitation currents to be used in this analysis are the AC peak values multiplied by sqrt(3)/2 (see Appendix – Combining Permanent Magnet Machines Analyses in the ME2D User Guide for further details).

Changes to the DC_ST analysis for static torque computation

Figure 13: Changes to the DC_ST analysis for static torque computation

The Advanced Options dialog in the Meshing Parameters section gives the user the possibility to modify the default values of the scalling coefficients for all the regions of the machine. For the PRIUS model the default values of the parameters are used The resulting meshed model is shown in Figure 15.

Advanced mesh properties

Figure 14: Advanced mesh properties

Meshed PRIUS model (1/8 of the periodic model)

Figure 15: Meshed PRIUS model (1/8 of the periodic model)

The second analysis that is run is an AC_ST which allows to obtain the nominal torque ripple of the machine for a given current (in this case 250A).

Model data for the AC_ST analysis

Figure 16: Model data for the AC_ST analysis

Finally, a RM analysis is run in order to obtain the transients of the PRIUS motor and to verify the back-EMF results obtained from the previous analysis. The rotating machine analysis ramps the voltage for two cycles in order to overcome startup transients. The torque vs. speed characteristic for a given excitation can also be calculated using the RM analysis.




The cogging torque produced by the motor’s geometry, over two stator poles, is presented in Figure 17.

Cogging torque over two stator slots

Figure 17: Cogging torque over two stator slots

The static DC torque has been computed for currents ranging from 50A to 250A. The measured data from the ORNL for these currents are overlayed on top of the FEM results. As it can be seen in Figure 16, the simulation results are within the expected range, with a slight error between the two peak values, which can probably be accounted for by the approximations made in the material definition, both of the laminations and of magnets.

DC static torque for different currents

Figure 18: DC static torque for different currents

A second analysis is conducted at rated speed and 250A using the AC_ST solver. The starting angle is 22.5 degrees which is the peak torque position obtained from the DC_ST analysis. The steady state torque is presented in Figure 19.

AC torque results

Figure 19: AC torque results

The dynamic torque for a given speed of 1000 rpm, obtained from the RM analysis is presented in Figure 20. The applied voltage is 280V in order to overcome back EMF at this speed and still achieve the 400+ Nm of torque.

Dynamic torque

Figure 20: Dynamic torque

The back-EMF results obtained for this machine are shown in Figure 21 and a comparison with the measured results is presented in Figure 22. The RMS values for the back EMF are calculated from the integral of the back EMF waveform.

Line to line back EMF

Figure 21: Line to line back EMF

Simulation vs. measured back-EMF

Figure 22: Simulation vs. measured back-EMF




[1] Hsu, J.S.; Ayers,C.W.; Coomer, C.L.; Report on Toyota/Prius motor design and manufacturing assessment, Oak Ridge National Laboratory, July 2004, ORNL/TM-2004/137

[2] Hsu, J.S.; Ayers, C.W.; Coomer, C.L.; Wiles, R.H.; Campbell, S.L.; Lowe, K.T.; Michelhaugh, R.T.; Report on Toyota/Prius motor torque capability, torque property, no-load back emf and mechanical losses, Oak Ridge National Laboratory, September 2004, ORNL/TM-2004/185

[3] Ayers, C.W.; Hsu, J.S.; Marlino, L.D.; Miller, C.W.; Ott, G.W.; Oland, C.B.; Evaluation of 2004 Toyota Prius hybrid electric drive system interim report, Oak Ridge National Laboratory, November 2004, ORNL/TM-2004/247

[4] Hsu, J.S.; Nelson, S.C.; Jallouk, P.A.; Ayers, C.W.; Campbell, S.L.; Coomer, C.L.; Lowe, K.T.; Burress, T.A.; Report on Toyota Prius motor thermal management, Oak Ridge National Laboratory, February 2005, ORNL/TM-2005/33

[5] Staunton, R.H.; Ayers, C.W.; Marlino, L.D.; Chiasson, J.N.; Burress, T.A., Evaluation of 2004 Toyota Prius hybrid electric drive system, Oak Ridge National Laboratory, May 2006, ORNL/TM-2006/423

[6] Opera ME2D User Guide