Concentrated Winding IPM Synchronous Motor Design for Wide Field Weakening Applications

Mohammad Sedigh Toulabi, John Salmon

Department of Electrical and Computer Engineering University of Alberta Edmonton, Canada toulabi@ualberta.ca

Andrew M Knight Department of Electrical and Computer Engineering

University of Calgary Calgary, Canada

andyknight@ieee.org

Abstract—A series of 12-slot 8-pole concentrated winding IPM synchronous motors (IPMSMs) are analyzed to understand the impact that certain design changes may have on performance over a wide speed range. Basic theory of operation is used to describe desirable characteristics; investigations are carried out to show how these characteristics may be realized through rotor design changes. Simulations are conducted using finite element analysis, leading to a final prototype design. The prototype is constructed and preliminary test results are presented.

Keywords— IPM Synchronous Motor, Constant Power Speed Region (CPSR), Concentrated Winding

I. INTRODUCTION In recent decades IPMSMs have been broadly utilized in

many applications due to their high power density, efficiency and brushless structure. With scientific progresses in developing the rare earth magnets, IPMSM optimization for high power density in wide speed ranges has been one of the objectives of many studies. [1]-[8].

Simple analysis of the well-known two-axis equations for IPMSM shows that torque, speed range, and power density of an IPMSM are directly affected by the winding flux linkage and the inductance of machine. High flux and saliency ratio result in larger high density and wide CPSR. The question of how to achieve these characteristics from any given rotor design is of considerable interest. Influences of rotor geometry to maximize the power density of this kind of machines are discussed in [9]-[13], with the influence of magnet strength and shape specifically discussed in [13]-[15].

This paper attempts to provide understanding of the complex interactions between physical design choices, equivalent circuit parameters and final motor performance. The basic equations of IPMSM operation are reviewed and presented in a form that allows the impact on wide speed range operation to be easily understood. The relationship between circuit parameters is discussed and related to the physical rotor lamination layout. Defining some basic characteristics of a simple V-type IPMSM, a range of case study analysis is conducted using commercial finite element analysis (FEA). Based on the understanding from the simulation results, a final design is developed and a prototype is constructed. Preliminary test results are presented and discussed.

II. THEORY The two-axis voltage and torque equations of an IPMSM

are:

(1) (2) (3) In steady state, the voltage and current limits on operation are given by. (4) . (5)

In (1)-(5), vd, vq, id, iq , Ld and Lq are d- and q- axes voltages, currents and inductances respectively, p is the pole number, λpm is the permanent magnet flux linkage, Te is the electromagnetic torque of machine, Rs is phase resistance, and ωe is electrical frequency. vmax, imax are the maximum permitted (peak) voltage and current from the main bridge converter, mmax is the maximum amplitude modulation depth and VDC the supply DC link voltage At a given operating point, at maximum voltage, (1) and (2) may be plotted as a vector diagram as shown in Fig. 1. For a given terminal voltage, it is also possible to plot the loci of possible current combinations as functions of electrical frequency, as shown in 0. 0 indicates that as electrical frequency increases, the loci converge on the central point at id=-λpm/Ld , iq=0. As a principle purpose of this paper, the machine design aims to place the center of the loci as close as possible to the rated current circle, thus maximizing speed range.

Fig. 1. Vector Diagram for IPMSM in d/q frame

978-1-4673-7151-3/15/$31.00 ©2015 IEEE 3865

Fig. 2. Current loci (ellipses) as functions of speed, maximum current circle and Maximum Torque Per Amp (MTPA) locus for an IPMSM

III. DESIGN PROCESS An initial design is developed using conventional processes,

based on assumptions about magnetic loading and electric loading. As a starting point, after review of concentrated winding factors, MMF harmonics and designs suitable for wide speed range [2], [3], a 12 slot/8 pole double layer concentrated winding V shaped magnet IPMSM is selected as a suitable candidate in high torque density performance. The initial design requirements are presented in Table I.

TABLE I. INITIAL MACHINE SPECIFICATIONS

Parameter Value

Power (W) 1000

Rated Speed (rpm) 900

Slot 12

Pole 8

Maximum current (A) 5

Power factor 0.9

Stack length (mm) 50

DC link voltage (V) 300 When considering how to realize the required performance

from a physical design, the rotor and stator variables are defined as shown in Fig 3. Considering what is known from the two-axis theory, for high torque density it is desirable to have high saliency (Ld-Lq), and high λpm. For a wide speed range, high Ld and low λpm are desirable. Inevitably, a compromise is likely to be required and the physical parameters influence a number of the electrical circuit parameters. As an additional complication, the physical parameters are not independent variables. A change to the angle between the magnets, with fixed magnet pitch, requires changes to either the magnet height (as shown in Fig 3) or the clearance between the magnets (OA in Fig 3). In order to maintain required λpm and induced voltage, the number of stator turns or magnet remenant flux density may need to be adjusted. In this study, where possible the number of physical layout changes has been limited, with small changes to the turns used to maintain voltage. All simulations are carried out using JMAG Designer.

(a) (b)

Fig. 3. a) Rotor and b) Stator physical layout variables

A: Magnet Clearance

Conventionally, in a V-shaped IPMSM, the clearance between magnets is minimized, so as to reduce leakage flux from the magnets. The impact of this choice is to significantly reduce Ld. If speed range is not a concern, this is a beneficial step, increasing saliency and providing additional torque capability. However, it is clear from Fig. 2 that low Ld limits speed range. In this section the impact of opening the clearance between the magnets is investigated.

Fig. 4. Ld and Lq evaluation in wide and minimum clearance between two pieces of magnets in three different V-shaped magnet IPMSM

Initially, there magnet pitch is set at 100% of the pole for the machine. Fig. 4 presents the variation of the inductances as functions of the angle between magnets for two clearances, minimum and maximum. The minimum clearance is set to 1mm for all three V angles, and maximum clearances are 7.5 mm, 5mm, and 4.3 mm for 60 , 75 , and 90 V angles respectively. It is clear that increasing the clearance increases the d-axis inductance at the expense of saliency, especially at wider angles between the magnets. However, this figure does not tell the full story. In order to maintain λpm in each case, the magnet strength has to be increased by 0.2T and the number of turns has to be increased from 135 turns in minimum clearances to 145 turns in maximum clearances. With inductance proportional to turns squared, it is clear that the change in Lq seen in Fig. 4 is due to more than just the change in the number of turns.

20 40 60 75 900

0.02

0.04

0.06

0.08

V angle (deg)

Indu

ctan

ce (H

)

Ld(Min clearance)Lq(Min clearance)Ld(Wide clearance)Lq(Wide clearance)

3866

B: Magnet Pitch As a second design variable, the magnet pitch is considered.

From inspection of Fig. 3 one can expect that reducing the magnet pitch will have two positive impacts: (a) the harmonic content of the airgap field will be reduced, improving voltage THD (b) the q-axis flux path will have lower reluctance, resulting in higher Lq and saliency ration

Fig. 5, plot the variations of Ld and Lq for three different magnet V-angles. 45º, 60º, and 75º with the magnet pitch at 100% and 85% magnet pitches. Based on the results of the previous investigation, the clearance between the two pieces of magnets is set to the widest possible range.

Fig. 5. Ld and Lq variations in 100% and 85% magnet pitch for three different v-angle IPMSMs

Fourier analysis of the airgap flux density shows that the harmonic content of the airgap field (and hence induced voltage) can be reduced by adjusting the pitch of the magnets. Reducing the magnet pitch eliminates some unwanted harmonics, while also causing an increase in winding inductance (increased turns offset the slight reduction in fundamental flux).

Fig, 6 shows the harmonic spectra of the Back-EMF waveform for cases with a 75-degree angle between the magnets. As expected, the amplitude of fifth and thirteenth harmonics in machine with 85% magnet pitch is less than machine with 100% magnet pitch. Again, there is a negative to reducing the magnet pitch. Reducing the pitch reduces the fundamental flux density, and again requires compensation with increased turns and/ or magnet strength.

(a)

(b)

Fig, 6, Back-EMF harmonic spectrum for a) 100% pitch, b) 85% pitch

C: Magnet Strength The analysis of Fig 2 indicates that speed range is a

function of magnet strength and d-axis inductance. Reducing the strength of the magnet may aid performance in a number of ways : increased speed range, increased reluctance torque (low flux must be offset by increased turns to maintain flux linkage) and reduced iron losses at high speeds. It can be seen in Fig. 7 that with a lower magnet strength, the angle has significant impact on the inductances. A design with a magnet angle of 75 degrees offers relatively high d-axis inductance and saliency. Comparing the two plots, it should be noted that, the weaker magnets are offset by requiring higher number of stator turns, resulting in increased reluctance torque and Ld.

(a)

(b)

Fig. 7. Inductances as functions of magnet angles (a) Br=1.4,T (b) ) Br=1.

20 45 60 75 800.04

0.06

0.08

0.1

0.12

V angle (deg)

Indu

ctan

ce (H

)

Ld(100%)Lq(100%)Ld(85%)Lq(85%)

0 500 1000 1500 20000

50

100

150

Electrical Frequency (Hz)

Am

plitu

de (V

)

X = 60Y = 138

0 500 1000 1500 20000

50

100

150

Electrical Frequency (Hz)

Am

plitu

de (V

)

X = 60Y = 133

45 60 75 900.04

0.05

0.06

0.07

0.08

V angle (deg)

Indu

ctan

ce (H

)

LdLq

45 60 75 900.05

0.06

0.07

0.08

0.09

V angle (deg)

Indu

ctan

ce (H

)

LdLq

3867

The CPSR for these 5 designs is calculated and plotted in Fig. 8.

Fig. 8. CPSR evaluation for five different IPMSMs with different v angles and B (r) of 1.2 T

IV. FINAL DESIGN SIMULATIONS Based on the analysis in the previous section, it appears that

a wide speed range may be obtained by compromising magnet leakage and magnet strength in order to gain desirable inductance values. A final physical design with magnet pitch of 85%, 75 degree angle between magnets and a wide leakage path between the magnets is developed. Detailed simulations are carried out using as-built design with the materials available at the time of construction of the prototype. The prototype is constructed using 29 gauge M19 steel (from AK steel), and NEOMAX-35EH magnets. The final structure for the finally optimized machine is seen in Fig, 9.

Fig. 9. Final design structure

The harmonic spectrum of Back-EMF in rated speed is plotted in Fig. 10 along with inductance variation as a function of current angle and magnitude. Using the field weakening control method, the final design has shown a wide CPSR region (pointed out as region A in Fig, 2). Predictions indicate that the machine should be capable of operation up to eight

times base speed (7200 rpm) at rated power. Torque and power versus speed and an efficiency map prediction carried out using JMAG-RT analysis are illustrated in Fig. 11.

(a)

(b)

(c)

Fig. 10. a) Back-EMF harmonic spectrum in rated speed, b) Ld variation versus current’s angle and magnitude, c) Lq variation versus current’s angle and magnitude for the final model.

20 30 45 60 75 902

3

45

6

78

9

V angle (deg)

CPS

R

0 500 1000 1500 20000

50

100

150

Electrical Frequency (Hz)

Am

plitu

de (V

)

0 20 40 60 80 1000.05

0.055

0.06

0.065

0.07

0.075

0.08

0.085

Current's Angle (degree)

Ld

(H)

3.9 A4.1 A4.3 A4.5 A4.75 A5 A

0 20 40 60 80 1000.085

0.09

0.095

0.1

0.105

0.11

0.115

Current's Angle (degree)

Lq (H

)

3.9 A4.1 A4.3 A4.5 A4.75 A5 A

3868

(a)

(b)

Fig. 11. a) Torque and power variation versus speed, b) Efficiency analysis

V. EXPERIMENTAL RESULTS To verify the expectations carried out by Finite Element

Method, the final model has been built and tested in lab. The laminations are laser-cut 29 Gauge M19 Stress Relief Annealed (SRA) supplied by Proto Laminations Inc. NEOMAX -35EH magnet is used for the magnets and each coil has 135 turns of AWG 20 copper wire. Fig, 12 shows the different views and parts of the built machine.

A: Test Facility To control and monitor the machine performance, two

independent DSC control based schemes are used for motor side and load side. Each DSC is a TI28335 and is part of a PowerCon controller which handles all signals conditioning between the hardware and DSC. Control is implemented in C using TI code composer and is monitored in real time via JTAG emulator connection to a PC. The load is a 1KW 12 slot, 10 poles IPMSM and it is used to tune the load applied to the built v-shaped magnet IPMSM. A Semikron IGBT Inverter is used to control the load side and a Semiteach IGBT Inverter is used for controlling the motor side. The DC links of the two converters are linked, enabling power circulation at the DC level, with the AC supply providing losses through at rectifier. The test bench is shown in Fig, 13.

(a)

(b)

(c)

B: Test results The open circuit voltage of the built machine and its

harmonic spectrum at 900 rpm are shown in Fig 14. The THD of the open circuit voltage in simulation was 3% while in experiment it is 6%. In addition the peak of fundamental component of voltage in simulation is 144 V, while it is 114V in real time tests. The permanent magnet flux linkage in simulation was 0.38Wb, while in reality it is 0.31 Wb. The smaller size and volume of the magnet used to be inserted into the rotor tolerances can be pointed out as the main reason of these discrepancies.

0 900 2000 4000 6000 72000

200

400

600

800

1000

1200

Speed (rpm)

Pow

er (W

) and

Tor

que

(N.m

)

Power100*Torque

3869

(a)

(b)

Fig. 13. Test facility a) complete bench, b) close-up of motor stand

Stand-still inductance test are been used to calculate the static values of Ld and Lq. The d- and q-axes inductances are calculated by Equations (7) and (8) and from the measurements of the reactive power Q, RMS current I and supply electrical frequency fe, with a rotor locked in the d- and q-axes position respectively [17].

(7)

(8)

Fig. 15 plots the measured and simulated inductances. There is good agreement for Lq over the range to 4A, but the d-axis inductance shows little variation, unlike the simulation.

At this time, load testing has been limited by problems with the load-side converter therefore only preliminary results are available. At rated speed, the load machine was unable to develop the required torque, and at high speeds became susceptible to noise. Table II shows the machine maximum power performance from base speed to three times base speed. The profile of developed torque in base speed is shown in Fig. 16.

(a)

(b)

Fig. 14. a) Open circuit voltage in 900 rpm, b) Harmonic spectrum

(a)

(b)

Fig. 15. a) d/q axes inductance evaluation, b) simulated value

0 0.005 0.01 0.015-150

-100

-50

0

50

100

150

Time (s)

Back

-EM

F (V

)

0 500 1000 1500 20000

20

40

60

80

100

120

Electrical Frequency (Hz)A

mpl

itude

(V)

X = 60Y = 114

7th Harmonic

11th Harmonic

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.050.060.070.080.090.1

0.110.120.130.14

Current-rms (A)

Indu

ctan

ce (H

)

LdLq

0 0.5 1 1.5 2 2.5 3 3.5 4

0.08

0.09

0.1

0.11

0.12

Current-rms (A)

Indu

ctan

ces (

H)

LdLq

3870

TABLE II, CONTROLLING CURRENTS, DEVELOPED TORQUE, COPPER LOSS VERSUS SPEED IN EXPECTED CONSTANT POWER

REGION

Speed (rpm)

Developed Torque (N.m)

Iq (A)

Id (A)

Power (W)

Copper Loss (W)

900 9.3 4.1 -3.5 880 171

1800 5.3 2.3 -3.7 1000 111

2700 3.5 1.5 -3.8 1000 98

In base speed, the built machine can support 9.3 N.m developed torque which causes 880W as the output of machine.

Fig. 16. Torque profile in base speed

VI. CONCLUSIONS In this paper, it is shown that compromise between

inductance and permanent flux linkage (and magnet leakage flux) enables the designer to extend the constant power speed range of IMPSM. Application of discrete physical changes to the V shaped magnet IPMSMs enables investigation and understanding of their effects on the inductances, flux linkage and ultimate performance. Based on the lessons learned, a final design is developed and constructed as a prototype motor. Preliminary test results indicate good agreement with some of the simulation findings, but difficulties with the test load limit the test range to date; additional testing is ongoing and will be presented in the future.

REFERENCES [1]. Katteden Kamiev, Juho Montonen, Mahendarkar Prabhakaran

Ragavendra, et al, “ Design Principles of Permanent Magnet Synchronous Machines for Parallel Hybrid or Traction Applications” IEEE Trans on Industrial Electronics, Vol: 60, No: 11, Pp: 4881-4890, 2013

[2]. F. Magnussen, C. Sadarangani, “Winding Factors and Joule Losses of Permanent Magnet Machines With Concentrated Windings” Int Conf on Electric Machines and Drives Conference (IEMDC), Pp:333-339, 2003

[3]. EL-Refaie, A. M, and Jahns, T. M, “Comparison of Synchronous PM Machine Types for Wide Constant Power Speed Operation: Converter Performance” IET, Electric Power Applications, Vol: 1, Issue : 2, Pp: 217-222, 2007

[4]. Massimo Barcaro, Nicola Bianchi, and Freddy Magnussen, “Rotor Flux Barrier Geometry Design to Reduce Stator Iron Losses in Synchronous IPM Motors Under FW Operations” IEEE Trans on Industry Applications, Vol: 46, No: 5, Pp: 1950-1958, 2010

[5]. Peter Sergeant, Alex P.M Van den Bossche, “Influence of the Amount of Permanent Magnet Material in Fractional Slot Permanent Magnet Synchronous Machines” IEEE Trans on Industrial Electronics, Vol: 61, No: 9, Pp: 4979-4989, 2014

[6]. Rukmi Dutta, Lester Chong, and M. F. Rahman, “Design and Experimental Verification of an 18 Slot/14 pole Fractional Slot Concentrated Winding Interior Permanent Magnet Machine” IEEE Trans on Energy Conversion, Vol: 28, No: 1, Pp:181-190, 2013

[7]. Patel B. Reddy, Kum-Kang Huh, Ayman M. EL-Refaie, “Generalized Approach of Stator Shifting in Interior Permanent Magnet Machines Equipped with Fractional Slot Concentrated Windings” IEEE Trans on Industrial Electronics, Vol: 61, No: 9, Pp: 5035-5046, 2014

[8]. Seok-Hee Han, Thomas M. Jahns, and Z. Q. Zhu, “Analysis of Rotor Core Eddy Current Losses in Interior Permanent Magnet Synchronous Machines” IEEE Trans on Industry Applications, Vol: 46, No: 1, Pp: 196-205, 2010

[9]. Sung-Li Kim, Young Kyoun Kim, Geun Ko Lee, and Jung Pyo Hong, “ A Novel Rotor Configuration and Experimental Verification of Interior PM Synchronous Motor for High-Speed Applications” IEEE Trans on Magnetics, Vol: 48, No: 2, Pp: 843-846, 2012

[10]. Piergiogio Alotto, Massimo Barcaro, Nicola Bianchi, and Massimo Guarnieri, “Optimization of Interior PM Motors with Machaon Rotor Flux Barriers” IEEE Trans on Magnetics, Vol: 47, No: 5, Pp: 958-961, 2011

[11]. Massimo Barcaro, and Nicola Bianchi, “Interior PM Machines Using Ferrite to Replace Rare-Earth Surface PM Machines” IEEE Trans on Industry Applications, Vol: 50, No: 2, Pp: 979-985, 2014

[12]. L. Chong, and M. F. Rahman, “Saliency Ratio Derivation and Optimization for an Interior Permanent Magnet Machine with Concentrated Windings using Finite Element Analysis” IET Electric Power Applications, Vol: 4, Issue: 4, Pp: 249-258, 2009

[13]. Sorgdrager, A. J, Grobler, A. J, “Influence of Magnet Size and Rotor Topology on the Air Gap Flux Density of a Radial Flux PMSM” IEEE International Conference on Industrial Technology (ICIT), Pp: 337-343, 2013

[14]. Mi-Jung Kim, Su-Yeon Cho, Ki-Doek Lee, et al, “ Torque Density Elevation in Concentrated Winding Interior PM Synchronous Motor with Minimized Magnet Volume” IEEE Trans on Magnetics, Vol: 49, No: 7, Pp: 3334-3337, 2013

[15]. Rahman, S. A, Vaseghi, B. Knight, A. M, “Influence of Rotor Magnet Variations in Concentrated Winding IPMSM” IEEE XXth International Conference on Electrical Machines (ICEM), Pp: 315-320, 2012

[16]. Lester Chong, “Design of an Interior Permanent Magnet Machine with Concentrated Windings for Field Weakening Applications” PhD Thesis, University of new South Wales, 2011

[17]. Florence Meier, “Permanent Magnet Synchronous Machine with Non-Overlapping Concentrated Windings for Low Speed Direct Drive Applications” PhD Thesis, Royal Institute of Technology, 2008

-0.05 0 0.050123456789

1011

Time (s)

Torq

ue (N

.m)

Developed Torque in Base Speed

3871

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