Efficiency Map Simulations for an Interior PM Motor with Experimental Comparison and Investigation of

Magnet Size Reduction

Emad Dlala, Mark Solveson, Scott Stanton, Zed Tang and Mark Christini

ANSYS, Inc. 225 West Station Square Drive Pittsburgh, PA 15219, USA

Email: emad.dlala@ansys.com

Raymond Ong and Brian Peaslee Magna Electronics, 1955 Enterprise Drive

Rochester Hills, MI 48309, USA Email: raymond.ong@magna.com

Abstract— Reduction of permanent magnet materials in electric machines is of interest to many machine manufacturers and designers as cost of rare-earth materials is of increasing concern. The impact of changing a machine design parameter, such as the shape of the magnets, may have consequences such as a reduction in efficiency, or introduce a change in torque quality. In this paper, an efficiency map computation is compared with measurements for a permanent magnet synchronous machine, including the complete torque-speed operating region. The validated simulation model led to an investigation of reducing the permanent magnet size where 20% of magnet size reduction was achieved. The impact of the magnet size reduction on the efficiency and machine performance was quantified, and design changes were simulated which maintained the desired efficiency over the operating range.

Keywords—Permanent magnet; PM motor; efficiency; MTPA control; simulation; finite element

I. INTRODUCTION

The prediction of efficiency maps in the design stage of the traction motor is a crucial development for the optimal operation of Hybrid Electric Vehicles (HEV/EV). The motor designer must ensure that the motor produces optimal efficiency in the speed range and road-load profiles during the drive cycles [1-2].

Studies of different machine topologies have been characterized by their efficiency [3], as electric machines used for traction applications are often characterized by the efficiency that exists throughout the torque-speed curve range [4].

This paper focuses on introducing a method for computation of the efficiency map in a permanent magnet synchronous machine using a customized script to control commercially available finite-element (FEA) software. Using optimization routines, the optimal operating condition is found for the entire torque-speed curve and the efficiency is calculated from transient 2-D FEA simulations. The time-domain FEA approach allows for greater simulation accuracy and is able to capture time and spatial harmonics as well as small geometric details of the

machine very accurately, although there is a tradeoff in simulation time as compared to methods that characterize the machine performance from static solutions [5]. Thus, implementation of the efficiency computation described in this paper is distributed on multiple CPUs which allows for a significant decrease in the total simulation time [6, 7]. The simulated efficiency results are presented for a machine and are compared with an experimentally obtained efficiency map. Reduction of permanent magnet material is often a goal for machine designers. Here, changes are made in the magnet design, comparisons of the resulting efficiency map are observed, and suggested modifications are studied to achieve performance of the original design.

II. METHOD OF EFFICNECINY MAP COMPUTATION

A phasor diagram illustrating the operation of a PM machine based on the d-q axis theory is shown Fig. 1.

Fig. 1. Phasor diagram illustrating the operation of a PM machine based on the d-q axis theory where is the current (control) angle, is the torque angle, is the power factor angle, is the induced voltage, and is the operating fundamental frequency.

At a given operating condition of torque, speed, and DC bus voltage, the trajectory of the current is crucial for the optimal efficiency operation of PM machines. Other important factors include the PWM method and switching frequency. In theory, by varying the input voltage supplied to the machine, there can be an infinite number of and combinations that can produce the required torque at a given speed. Therefore, the control strategy needs to be carefully implemented to minimize the losses in the motor and thus increase the efficiency [2].

The control of PM machines is typically established using the Maximum-Torque Per Ampere unit (MTPA) strategy below base speed while maximizing output power ( ) in the flux weakening region and maintaining voltage and current limits [8-11]:

max (1)

max (2)

Applying the MTPA control allows the PM machine to accelerate with constant torque ( ) until the speed reaches a value at which the terminal voltage reaches the voltage limit max. In this work, the MTPA strategy is implemented

numerically where the algorithm searches for the optimal and that provide maximum torque as shown in Fig. 2. The d-q

currents are defined from the stator current and current angle as follows:

sin (3)

cos (4)

Fig. 2. Concept of the MTPA illustrated in the torque vs. current angle and magnitude. The MTPA control algorithm finds the optimal current angle that gives the minimum current at a given torque. An evolutionary algorithm based on Nondominated Sorting Genetic Algorithm (NSGA-II) with (Pareto) dominate solution and combined with spline interpolation technique is used for the optimization.

This strategy results in minimizing the stator current and thus maximizing the efficiency below base speed applying the assumption that the winding loss is dominant [2]. In the flux-weakening region, the algorithm makes use of the available voltage and the optimal control angle is found to maximize power. In this paper, the MTPA control strategy is implemented in the experimental and simulation work to obtain the efficiency maps for interior PM machines. The simulation is conducted with a time-domain 2D FEA model. The machine is assumed to be current controlled and thus sinusoidal currents are used in the FEA simulations. The method of computation of the efficiency map consists of the following steps:

1. Simulate a parametric sweep of transient simulations for different current magnitudes and angles, , at a constant speed to obtain a family of voltage and torque curves that are tabulated and used in spline interpolation.

2. Apply the MTPA algorithm using multi-objective optimization to calculate the operation points ( and ) for the torque-speed range in motoring, generating, or both modes. An evolutionary computation, Nondominated Sorting Genetic Algorithm (NSGA-II) with (Pareto) dominate solution, is used [12].

3. Run the final simulations using the calculated operation points found using the MTPA. These operation points are simulated at the whole torque-speed range in order to compute the core loss and eddy-current magnet loss at different supply frequencies.

4. Compute the efficiency from the output power and total losses that include winding loss, core loss, eddy current loss in the magnets, and mechanical loss.

The method offers the following advantages:

1. Requires only the voltage and current limits as inputs and it automatically applies the MTPA algorithm and computes the optimal control angle at the whole torque-speed range accordingly.

2. Requires only running a parametric sweep of the current and current angle at a single speed. The torque is assumed to be independent of the speed in current-fed machines. The voltage is assumed to satisfy constant volts per hertz relation. These are considered to be valid assumptions in synchronous machines where the losses, including core loss and eddy-current loss, have minimal influence on the torque and back emf production.

3. Integrates various vital effects such as skewing, DC/AC winding resistance at rated temperature, end-turn winding inductance, frequency-dependent core loss coefficients, and mechanical loss.

Fig. 3. Script interface for efficiency map computation used in the ANSYS-Maxwell software. The script requires the maximum current and voltage limit to compute the efficiency map and it integrates various vital effects.

The power core loss per unit volume is computed based on the following frequency-dependent core-loss model:

. (5)

where is the peak of flux density, is the frequency and , , represent the coefficients of hysteresis, classical eddy-

current and excess losses. The accurate prediction of core loss is complicated and requires advanced models due to various effects such as skin effect in the laminations, minor hysteresis loops, and vector hysteresis [13]. Therefore, in this paper, the loss coefficients are assumed to be dependent on the fundamental frequency of the supply [14]. Eq. (5) is implemented in the time-domain and the core-loss formula is modified to be time-dependent [15] where higher harmonics in the flux density are accounted for. The total core loss is computed by integrating over the volume of the machine.

The effects of the DC resistance of the stator winding Rs and the inductance of the end-windings Le are important for the calculation of the terminal voltage:

dt

td

dt

tdiLtiRtv s

esss

)()()()(

(6)

where )(tis and )(t are the instantaneous values of the stator

current and flux linkages respectively.

Fig. 4. Cross-section of a pole of the interior PM motor designed by Magna Electronics for an HEV drive.

Fig. 5. Experimental setup for measuring the efficiency map in the interior PM motor at Magna Electronics.

For the convenience of the user, a customized script with interface, shown in Fig. 3, has been developed in the course of this work to compute and display the losses and efficiency maps. The script executes the method described above completely and automatically. It computes and displays the torque speed curves and efficiency maps for an arbitrary PM synchronous machine, in motoring mode or generating mode, or both. A list of output quantities are automatically produced such as efficiency, electromagnetic losses, power factor, , , etc. The script is also capable of leveraging multiple CPUs to solve the parametric sweep and reduce simulation time significantly.

III. COMPARISON OF EFFICICNECY MAP COMPUTATION WITH

MEASURMENTS

Experimental results of a 3-phase, 8-pole, 40-kW, interior PM machine without rotor skew were used to validate the FEA results. The motor, designed by Magna Electronics, is used in an HEV drive. A cross-section of one pole of the motor is shown in Fig. 4.

The motor is operated at maximum RMS current of 298 Amps and produces maximum torque of 90 N·m. The measured base speed was approximately 4100 rpm with a DC bus voltage

maintained fixed at 220 V. The measured maximum speed was 9000 rpm. As with most of HEV/EV motor suppliers, Magna Electronics applied an experimental calibration procedure to find the optimal control angle for the MTPA scheme of the PM motor. The experimental lab setup is shown in Fig. 5.

The motor was simulated using the same conditions used in the measurements, specifically, the same maximum current and voltage limit. However, in the simulation, the MTPA control scheme is realized via the numerical procedure as described in Section II. The currents used in the simulations over the torque-speed range are shown in Fig. 6. Each of these operation points was then simulated in a time-domain FEA model to obtain the efficiency map, where the core loss coefficients , and were allowed to be frequency-dependent. The coefficients were identified in advance from experimental data provided by the manufacturer of the steel laminations.

Fig. 6. Stator currents calculated at different constant-torque levels by the proposed method using FEA combined with evolutionary computation optimization algorithm.

In addition, the mechanical loss was measured and is also included in the efficiency calculation. The DC resistance was measured at the state-steady temperature. The stator end-winding inductance was calculated using ANSYS-RMxprt based on an analytical approach.

The experimental and simulation results of the efficiency map are shown in Figs. 7 and 8 respectively, and are in good agreement in both magnitude and contour. The simulated results of the efficiency are slightly higher and this can be due to an underestimation of the core loss that is in reality affected by the manufacturing process of the steel sheets [16]. Separating the loss calculations allows for a number of observations. The simulated total loss map (including winding loss, core loss, eddy current loss in the magnets, and mechanical loss) is shown in Fig. 9, and as expected, higher losses are concentrated at the high torque and high speed regions. In the high-torque region, the winding loss is high due to high currents, as shown in Fig. 10.

Fig. 7. Experimental results of efficiency map in the interior PM motor measured by Magna Electronics.

Fig. 8. Simulated results of efficiency map in the interior PM motor.

Fig. 9. Simulated results of total loss map in the interior PM motor including winding loss, core loss, eddy current loss in the magnets, and mechanical loss.

0 1000 2000 3000 4000 5000 6000 7000 8000 90000

50

100

150

200

250

300

Speed, rpm

stat

or c

urre

nt, A

Fig. 10. Simulated results of winding loss map in the interior PM motor.

Fig. 11. Simulated results of core loss map in the interior PM motor.

Fig. 12. Instantaneous flux densities at a point in a tooth tip of the stator simulated at 42 A, 56 A, 8500 rpm. Higher harmonics cause an increase in losses with an increase of speed.

On the other hand, in the field-weakening, high-speed region, the core loss, shown in Fig. 11, is high due to the increase in the fundamental frequency and also due to an increase in the high harmonic content as the motor starts to operate at higher control angles [2]. This can also be seen in the x- and y-components of

flux densities calculated at a point in the stator tooth tip versus time as shown in Fig 12, where the higher fundamental frequency along with the higher order harmonics are observed.

IV. STUDY OF MAGNET SIZE REDUCTION

The validation of the FEA simulation now allows the model to be used for further study of design changes to the interior PM motor shown in Fig. 4. This section studies the reduction of magnet size and aims to maintain the original characteristics of the machine performance including torque and efficiency throughout the full operating range. First, a parametric study was conducted to reduce the magnet length (direction aligned with magnetization). A time-domain FEA simulation of the reduced magnet length was evaluated as a function of control angle , where the time averaged torque was calculated. First, as expected, the reduction of the magnet length resulted in a reduction of torque. To compensate for this drop in torque, the “V-angle” between the magnets was then varied in the parametric analysis to reestablish the desired maximum torque. The final modified design shown in Fig. 13 shows a 20% reduction of magnet length and decreased “V-angle.” An explanation for the obtained increase in simulated torque production can be explained in the well-known torque equation defined in terms of the d-q inductances and currents from which the synchronous and reluctance torque can be separated:

ψ (7)

where ψ is the magnet flux on the d-axis at no load and is the number pole pairs.

Fig. 13. The modified design and the original design provided by Magna Electronics. The modification included the reduction of the magnet length and decrease of “V-angle” of the magnets. The color scale of the flux distribution varies linearly from 0 to 2 Tesla.

In the final modified design, shows a decrease, and shows a slight increase versus Iq current as shown in the FEA results in Fig. 14. This increase in the saliency ratio accounts for the added reluctance torque that compensates for the reduction in

the torque initially produced by the design with smaller magnets (see Fig. 15). Although the maximum torque was maintained, the torque ripple slightly increased but was approximately less than 15% of rated torque. Fig. 16 shows the difference in the torque ripple between the original and modified designs for the entire operating range. The result shows that the there is a maximum 8.5 N·m increase in the torque ripple in the modified design as compared to the original design.

The FEA results show that the efficiency was maintained approximately the same as evidenced in Fig. 17 where the difference in the simulated efficiency maps between the original design and modified design is plotted for the whole torque-speed range. The plot shows that the efficiency has improved below the base speed and slightly decreased at higher speeds.

Fig. 14. FEA results of and of the original and modified designs of the interior PM motor. The increase in the saliency of the modified design is illustrated by the slight increase of , and the decrease of which is due to the magnet reduction.

Fig. 15. FEA results of the average torque prodcued by the interior PM motor with the original and modified designs. The increase of the saliency in the modified design is illustrated in the maxmimun torque which occurs at a higher current angle than that of the original design.

Fig. 16. The absolute difference in the torque ripple in N·m between the modified and original designs. The result shows that the there is a maximum 8.5 N·m increase in the torque ripple in the modified design as compared to the original design.

Fig. 17. The percentage difference of efficiency between the original and modified designs of the interior PM motor simulated. The positive scale means that an increase of the efficiency is gained in the modified design.

V. DISCUSSION AND CONCLUSION

A robust method for calculating an efficiency map from a time-domain 2D FEA model that is validated with experimental results is presented. The approach provides valuable information from which design studies show the impact on the efficiency for the full torque-speed operating range. A reduction in the magnet size can allow for a significant cost reduction of rare-earth material, but can affect the performance of the machine. In this paper, a design with 20% reduced magnet size was presented which meets the original performance throughout the operating range and the model shows exactly where efficiency is enhanced or diminished. Although the efficiency map for the modified design was effectively maintained in this study, it does not necessarily imply that by simply adjusting the “V-angle” to achieve desired torque, the efficiency throughout the entire torque speed profile will also be met. Thus, the importance of being able to quickly and accurately simulate the efficiency map is significant. It is also noted that additional studies naturally

follow such as how the magnet reduction may affect demagnetization from short-circuit or high temperatures.

Furthermore, other considerations such as torque quality may need further investigation, as was shown by changes in the torque ripple [17]. The methods presented also lay the ground work for further design and optimization studies that consider the efficiency for electric machines. The accuracy shown by the FEA results gives us confidence in applying the FEA data of the MTPA control in an inverter control algorithm. The data can be provided as a look-up table and used in the online vector control as a potential replacement for analytical formulae and experimental calibration methods [10, 18].

In this work, the study of magnet reduction was done by varying two variables, magnet length and “V-angle”, while there are several other geometry variables that can be varied to obtain optimal design performance. Such studies may require tens of thousands of parametric variations where the use of parallel computations becomes vital to speed up the design process. The efficiency calculation of the Magna PM motor with 400 operating points took approximately 3 hours using 4 cores on a Dell Laptop machine. In other similar work conducted, an interior PM motor software was optimized using ANSYS-Maxwell where a parametric study of 10,000 variations was simulated on a computer cluster. The simulations times with different core configurations are shown in Table I. For example, the total simulation time of the parametric analysis was reduced from two weeks using 1 core to around 4 hours using 96 cores. This great scalability can help optimize a PM motor with thousands of design points.

Table I. Simulation times and speed-up factors for a parametric study of 10,000 variations done for the optimization of an interior PM motor using ANSYS-Maxwell software.

Number of cores

Simulation time (hours)

Speed-up factor

Cores utilization %

1 368.3 1 100%24 16.2 22.8 94%48 8.0 46.1 96%96 4.2 90.0 94%

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