Influence of Inverter Output Voltage Harmonic on Surface ...€¦ · Influence of Inverter Output...

Draft

Influence of Inverter Output Voltage Harmonic on Surface Mounted Permanent Magnet Synchronous Motor

Performance

Journal: Transactions of the Canadian Society for Mechanical Engineering

Manuscript ID TCSME-2018-0121.R2

Manuscript Type: Article

Date Submitted by the Author: 12-Dec-2018

Complete List of Authors: Qiu, Hongbo; Zhengzhou University of Light Industry, College of electric and information engineeringZhang, Yong; Zhengzhou University of Light Industry, College of electric and information engineeringYang, Cunxiang; Zhengzhou University of Light Industry, College of electric and information engineeringYI, Ran; Zhengzhou University of Light Industry, College of electric and information engineering

Keywords: SMPMSM, harmonic voltage, air-gap magnetic density, torque ripple, loss

Is the invited manuscript for consideration in a Special

Issue? :Not applicable (regular submission)

https://mc06.manuscriptcentral.com/tcsme-pubs

Transactions of the Canadian Society for Mechanical Engineering

Draft

1

Influence of Inverter Output Voltage Harmonic on

Surface Mounted Permanent Magnet Synchronous

Motor Performance

Hongbo Qiu , Yong Zhang , Cunxiang Yang and Ran Yi

Zhengzhou University of Light Industry

Hongbo Qiu He received the B.E.E. degree from the Harbin University of Science and Technology, Harbin, China, and the

Ph.D. degree in electrical engineering from the same university in 2014. He has been with the Zhengzhou University of Light

Industry, Zhengzhou, China, since 2014. His research interests include electromagnetic and thermal analysis on electrical

machine, especially in permanent magnetic machines.

Yong Zhang He is working toward the M.S. degree in electrical machines at Zhengzhou University of Light Industry,

Zhengzhou, China. His current research interests include electromagnetic and thermal analysis on electrical machines,

particularly on permanent magnetic machines.

Cunxiang Yang He received the B.E.E. degree from the Zhengzhou University of Light Industry, Zhengzhou, China, and

the Ph.D. degree from the College of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan,

China in 2009. He has been with the Zhengzhou University of Light Industry, Zhengzhou, China, since 1988. His research

interests include intelligent control and electrical fault diagnosis technology.

Ran Yi She received the M.S. degree from the Harbin University of Science and Technology, Harbin, China, in 2012. She

has been with the Zhengzhou University of Light Industry, Zhengzhou, China, since 2014. Her research interests include research

on electromagnetic and thermal analysis on electrical machine, particularly in superconducting machines.

Corresponding Author: Yong Zhang

Telephone numbers：+8615603915641

E-mail：[email protected]

Address：Zhengzhou University of Light Industry, No.5 Dongfeng road , Zhengzhou , 450000, China

Page 1 of 29



Draft

2

Influence of Inverter Output Voltage Harmonic on

Surface Mounted Permanent Magnet Synchronous

Motor Performance

Hongbo Qiu * , Yong Zhang**, Cunxiang Yang*** and Ran Yi †

* Zhengzhou University of Light Industry

Abstract

The application of inverter is becoming more and more widespread in surface mounted permanent magnet synchronous motor

(SMPMSM). A large number of voltage harmonics can be generated by the inverter. The electromagnetic torque, loss and air-gap

magnetic density of SMPMSM are affected by voltage harmonic. In order to analyze its influence, taking a 3kW 1500r/min

SMPMSM as an example, a 2-D transient electromagnetic field model is established. The correctness of the model is verified by

comparing the experimental data with the calculated data. Firstly, the finite element method is used to calculate the electromagnetic

field of the SMPMSM, and the performance parameters of SMPMSM are obtained. Based on these parameters, the influence of

voltage harmonic on motor performance is analyzed quantitatively. Secondly, the influence of the voltage harmonic on the air-gap

magnetic field is analyzed, and the influence degree of the time harmonic on the air-gap magnetic field is determined. At the same

time, torque ripple, average torque and loss are studied, when the different harmonics orders, amplitudes, and phase angles are

contained in voltage, and the variation is obtained. Finally, the variation mechanism of eddy current loss is revealed. The conclusion

of this paper provides reliable theoretical guidance for improving motor performance.

Key words: SMPMSM; harmonic voltage; air-gap magnetic density; torque ripple; loss

I. INTRODUCTION

Because of the advantages of simple structure, high efficiency and high power factor, the SMPMSM has been widely used in

electronic information, mining, communication technology, aerospace, transportation and other fields (Chen et al. 2017; Lee and Ha

2012). In order to better start and control the SMPMSM, it is very necessary to combine the PWM frequency-converting techniques

Page 2 of 29



Draft

3

with the SMPMSM. However, it has an adverse effect on the performance of the SMPMSM because the output voltage contains

massive harmonic components. Compared with the fundamental voltage, the existence of harmonic makes the skin effect more

obvious, which will increase the losses and torque ripple (Xia et al. 2017). Meanwhile, when the different frequency, amplitude and

phase angle are contained in voltage harmonics, the influence of voltage harmonics on the SMPMSM performance will be obviously

different (Tawadros et al. 2013). Therefore, it is of great theoretical research significance and engineering practical value to study the

influence of inverter output voltage harmonics on motor performance.

In recent years, many scholars have carried out some research on the influence of harmonics on the SMPMSM. In reference

(Khomsi et al. 2014), the harmonic content and distortion of the voltage and the current of the pulse width modulation voltage source

inverter motor are analyzed. It is innovative that the static power converter can better control the motor. In reference (Duarte and

Kagan 2010), a new power-quality (PQ) index is proposed to combine the effects of voltage unbalance and harmonic distortions. It

will be used to determine how the asymmetric voltage is raised by the motor temperature. In reference (Kang et al. 2017), an

improved switching selection method was presented for the direct torque control (DTC) of five-phase induction motors (IMs). It can

be obtained from the torque ripple is reduced in the steady state, and the performance of the torque response speed is improved. In

reference (Feng et al. 2017), the torque ripple minimization for PMSM is investigated in this paper, and a novel analytical solution of

optimal stator current design for torque ripple minimization is proposed. The proposed design is theoretically proven to be able to

minimize the torque ripple with minimal machine losses. However, many researches are limited to the analysis of the performance

for the algorithm, and they analyze the effect of harmonic on motor performance without considering the motor noumenon.

In this paper, taking a 3kW, 1500r/min SMPMSM as an example, the two-dimensional finite element electromagnetic field

model is established. Using the finite element method, the air-gap magnetic field, torque and loss are calculated when the SMPMSM

is operated at different conditions. Through analysis of the air-gap magnetic field, torque ripple and loss, the variation laws are

obtained. When the SMPMSM is running at rated load, the distribution of the eddy current density is studied, and the change

mechanism of the eddy current loss is revealed. Through the above analysis, some useful conclusions are obtained, which could

provide the theoretical basis for further research on the SMPMSM.

II. PARAMETERS AND MODEL OF SMPMSM

A. Parameters and Model

In this paper, a 3kW and 1500r/min SMPMSM is taken as an example to study the effect of voltage harmonic on the motor

performance. Based on the actual structure and parameters of the prototype, the finite element model of the SMPMSM is

established, as shown in Fig. 1. The basic parameters of the SMPMSM are shown in Table I.

Page 3 of 29



Draft

4

In the SMPMSM electromagnetic field analysis process, in order to simplify the calculation, the following assumptions are

made (Xia and Li 2015):

(1) When the electromagnetic field is analyzed, the end effect of the motor can be ignored. It is assumed that the axial

magnetic field of the motor is constant.

(2) The influences of temperature on the material conductivity and permeability are negligible.

(3) The outward flux leakage with the SMPMSM stator core in radial direction should be ignored.

Based on the above assumptions, when the electromagnetic field is analyzed, the influence of the displacement current and

the parallel plane field of perpendicular on the motor shaft are not considered. The vector magnetic potential A only has

z-component.

B. Experimental testing and data comparison

In order to verify the correctness of the finite element model, the SMPMSM prototype is tested. The test system consists of

a Magtrol dynamometer machine, HIOKI PW6001 power analyzer, industrial condensing unit, DSP data acquisition system,

permanent magnet motor and other forms of equipment. The correctness of the calculated result is verified. The experimental

platform of the prototype is shown in Fig. 2.

Through the above experimental platform, the SMPMSM is tested, and the experimental data are compared with the

calculated results. Table II and Table Ⅲ are the experimental value and the calculated value of SMPMSM current, torque,

no-load back EMF losses and efficiency at different loads.

Based on the comparison of the above data, it is concluded that there is little difference between the experimental value and

calculated value of the prototype under different loads, and the errors are within 5%. The experimental data are in good

agreement with the calculated data, which verify the accuracy of the model.

III. THE INVERTER OUTPUT VOLTAGE HARMONIC ANALYSIS

When the SMPMSM is driven by the inverter, the voltage is not the standard sine wave. In order to analyze the harmonic

distribution of inverter output voltage, the Bessel functions and Fourier transforms are used. The three-phase bridge PWM

inverter circuit has a common carrier signal. In the output line voltage, the angular frequency of the component is (Endo et al.

2015):

（1）cn k

ωc is the carrier angular frequency and ωr is the modulated carrier frequency.

In the formula,

Page 4 of 29



Draft

5

1,3,5, 3 2 1 1, 1,2,3,

6 1 0,1,2,4,6,

6 1 1,2,

n k m m

m mn k

m m

L

LL

The following conclusions can be obtained from the formula (1): The output harmonic frequency of the inverter is related to

the carrier frequency and mainly distributes in the around integer multiples of the carrier frequency.

In order to verify the correctness of the above conclusions, power analyzer is used to decompose the output voltage of the

inverter, and the harmonic amplitude of each voltage is obtained as shown in Fig. 3.

In this prototype, besides the fundamental voltage, the largest harmonic order appears at 96th, 98th, 102th and 104th,

namely, 9.6 kHz, 9.8 kHz, 10.2 kHz and 10.4 kHz. They are 10.3%, 13.1%, 14.8%, and 12.3% of the fundamental voltage,

respectively. The inverter fc is 100Hz, and fr is 10kKz (fc is the carrier frequency and fr is the frequency of modulated signals).

The voltage harmonic distribution law and the amplitude of higher voltage harmonic amplitude are shown in Fig. 3 and Table Ⅳ,

and the correctness of the above analysis is verified.

It can be seen from Table Ⅳ that the inverter can output the zero-sequence voltage harmonic components with large

amplitude. However, the SMPMSM is star-type connection in three-phase three-wire symmetrical system, and there is no zero

sequence voltage harmonic current conduction circuit, so the 96th and 102th zero-sequence voltage harmonics have no effect on

SMPMSM. In order to verify the correctness of the above analysis, when zero-sequence harmonic components are contained in

the motor windings, the several performances are observed. The torque ripple is taken as an example to make specific analysis,

and the data is shown in Table V.

From Table V, it can be seen that the increase of the harmonic voltage amplitude has little influence on the torque ripple,

which proves the correctness of the above analysis. Combined with Table IV and Table V, it can be concluded that the inverter

can output zero-sequence voltage harmonic, but it has no effect on SMPMSM operation.

Based on above analysis, the influences of the 98th and 104th voltage harmonics on the motor performance will be

emphatically analyzed.

IV. THE EFFECT OF VOLTAGE HARMONICS ON THE AIR-GAP MAGNETIC DENSITY

The air-gap magnetic density is an important parameter in the SMPMSM. The air-gap magnetic density affects the power

density of the motor, which directly determines the ability of the motor to drag the load. There are many factors that influence the

air-gap magnetic density. For example, the change of the air-gap length, the choice of the rotating shaft material and the change

of the pole logarithm will have different influence on the motor (Dalal, Kumar 2015). In this section, the finite element method is

used to study the influence of the inverter output voltage harmonics on the air-gap magnetic density.

Page 5 of 29



Draft

6

A. Analysis of magnetic field under rated load of SMPMSM.

When the motor is running at rated load, the complex magnetic field is generated by coupling the magnetic field of the

permanent magnet and the armature magnetic field. This section mainly analyzes the air-gap magnetic field at the rated load

operation.

As can be seen from Fig. 4, the magnetic density is mainly distributed around the stator teeth. The maximum magnetic flux

density is about 1.7T. The silicon steel sheet of the prototype is DW465-50. The maximum magnetic flux density is the silicon steel

sheet saturation point, which shows that the motor has good output performance and the loss is relatively low. The SMPMSM has

the cogging effect, and the rotating magnetic field of air-gap will be affected by the cogging, producing space harmonics. When the

SMPMSM is controlled by the inverter, a large amount of time harmonics are generated. It will also have a certain influence on the

SMPMSM. The influence of voltage harmonic on the air-gap magnetic density is studied in detail.

B. Influence of voltage harmonic on air-gap magnetic density

The finite element method is used to calculate the air-gap magnetic density when the SMPMSM is operated at different

working conditions, and a series of air-gap magnetic density distribution curves are obtained, as shown in Fig. 5. In this paper,

taking the 98th voltage harmonic as an example, the influence of the voltage harmonic on the air-gap magnetic density is

analyzed.

When only the fundamental voltage is contained in the windings, the air-gap magnetic field is not a standard sine wave.

Because of the influences of the slots and windings, the spatial harmonics are formed. So the air-gap magnetic field is distorted,

as can be seen from Fig. 5.

When the harmonic is contained in the winding, the distribution of the air-gap magnetic density at a certain time has not

been great variation. It can be seen that when a small amount of time harmonics are contained in the windings, the variation of

the air-gap magnetic density is not very obvious. Although the variation of air-gap magnetic density is very small, it can cause

large torque ripple.

In order to eliminate the influence of the fundamental voltage, the air-gap magnetic density is analyzed when only the 98th

voltage harmonic is contained in the windings.

When the fundamental voltage is ignored and only 98th voltage harmonic is contained, there is a slight change in air-gap

magnetic density. Although the change of the air gap magnetic density is very small, it can still cause large torque ripple and loss.

In this paper, the influence degree of the voltage harmonic on the torque and loss are studied in the next chapter.

V. INFLUENCE OF VOLTAGE HARMONICS ON MOTOR TORQUE

The average torque and torque ripple of SMPMSM are an important index to measure the performance of the motor. The

average torque directly affects the output of SMPMSM, and the torque ripple is related to the vibration and noise of the motor

Page 6 of 29



Draft

7

running (Tripathi and Narayanan 2016).

In these factors, the higher harmonics are the main factors. The fundamental voltage and higher voltage harmonics generates

respective rotating magnetic fields in the armature windings. The electromagnetic torque is generated by the interaction of two

magnetic fields and it is unstable, so it has a pulsating property and the torque ripple is formed. Torque ripple can affect the

stability of the motor, cause motor vibration, shorten motor life, and increase electromagnetic loss (Zhu et al. 2017).

Based on the above analysis, it can be seen that the existence of voltage harmonic will have a significant effect on the torque

ripple. The variations of torque ripple and average torque are analyzed when the different harmonic orders, amplitude and phase

angles are contained in the windings.

A. The influence of the harmonic amplitude on the torque

a. Influence of harmonic voltage amplitude on motor torque ripple

Based on the finite element method, the torque ripple is calculated when only the fundamental voltage, additional 98th

harmonic voltage and additional 104th harmonic voltage with different amplitudes are contained in the armature windings,

respectively. The change of torque ripple is obtained, as shown in Fig. 6.

This paper uses the formula（2）to measure the torque ripple

（2）max minrippleT T T

Tmax is the maximum torque in one cycle. Tmin is the minimum torque in one cycle.

It is shown from Fig. 6 that the torque ripple of SMPMSM is 1.73 N•m when only the fundamental voltage is contained.

This torque ripple is caused by spatial harmonics. When the amplitudes of 98th and 104th voltage harmonics are 20V, that is,

10% of the fundamental voltage, the increase of the torque ripple is 0.31 N•m and 0.37 N•m respectively. The torque ripple

increased by 18% and 21%, respectively. It can be seen that the torque ripple obviously increases when harmonic is contained in

the windings. The torque ripple increases with the increase of harmonic voltage amplitude. The torque ripple shows a linearly

increasing trend with the increase of the voltage harmonic amplitude. Taking the 98th harmonic as an example, the amplitude of

the harmonic voltage increases by 15%, 20%, and 25% of the fundamental voltage amplitude, and the torque ripple increases by

nearly 2 times.

It can be seen that the influence of voltage harmonic on torque ripple cannot be ignored. Therefore, in practical applications,

in order to reduce the torque ripples and improve the operating stability of motor, the effective technology is used to suppress the

voltage harmonic content.

b. Influence of harmonic voltage amplitude on motor average torque

Voltage harmonic with different amplitudes are contained in the stator armature winding of SMPMSM. The influence of

voltage harmonic on the average torque is analyzed by the finite element method, and the specific data are shown in Table VI.

Page 7 of 29



Draft

8

It can be seen from Table VI that the maximum change of the average torque is 0.25N•m and 0.34N•m, respectively, when

the 98th voltage harmonic and 104th voltage harmonic are contained in the armature windings. The ripple range of the average

torque is less than 2%. With the increase of voltage harmonic amplitude, the average torque of SMPMSM is not significantly

affected.

B. Influence of harmonic phase angle on torque

The influence of the harmonic voltage amplitude on the torque is studied, and the phase angle of the harmonic voltage will

also affect the torque. The influences of the torque ripple and the average torque on the SMPMSM will be analyzed at the

different phase angle. Quantitative analysis method is used to analyze the influence of voltage harmonic phase angle on the

torque. The phase angle of the voltage harmonic increases 30 degrees each time. The specific data is shown in Table Ⅶ.

It can be seen from Table Ⅶ that with the increase of the voltage harmonic phase angle, the torque ripple also

corresponding changes. When the 98th voltage harmonic and 104th voltage harmonic are contained, the maximum variation of

torque ripple is 0.06 N•m and 0.04 N•m, and the ripple range is less than 3%.

Table Ⅶ also gives the change of the average torque when the voltage harmonic phase angle is different. By analyzing the

data, it can be concluded that the average torque has little effect when the phase angle is different, and the variation range of the

average torque is within 2%.

To sum up, the change of the voltage harmonic phase angle has little effect on the average torque and torque ripple of the

SMPMSM.

VI. INFLUENCE OF HARMONIC VOLTAGE ON MOTOR LOSS

Loss is one of the important indicators of measure the efficiency of the motor. When the inverter is used to control the

SMPMSM, the output voltage contains a large number of higher harmonics. These higher harmonics changes the magnetomotive

force and generates additional harmonic losses (Shin et al. 2018). Therefore, it is very valuable to study the loss of SMPMSM.

A. Calculation of motor core loss based on harmonic analysis method

In the core loss calculation model, the Steinmetz model and iron loss separation model are more commonly used. The core

loss consists of three parts, such as hysteresis loss, classical eddy current loss and excessive loss. The calculation formula of

motor core loss is (YouGuang et al. 2003):

（3）2 2 1.5 1.5Fe h c e h c eP P P P K fB K f B K f B

In the formula, PFe—core loss，Ph—hysteresis loss，Pc—classical eddy current loss，Pe—excessive loss, Kh Kc Ke —loss factor.

Page 8 of 29



Draft

9

It can be seen from the above formula that the core loss of the motor is related to the frequency and the magnetic amplitude.

In the sinusoidal wave voltage, the core loss calculation formula is:

(4) 1 1 2, ,Fe ts fs ts js fs jsP G K P B f G K P B f

In the formula, Gts—Core quality of stator tooth，Gjs—Core quality of stator yoke，Bts—Magnetic density amplitude of stator

teeth，Bjs—Magnetic density amplitude of stator yoke，K1—Correction coefficient of stator tooth core loss，K2—Correction

coefficient of stator yoke core loss.

The inverter output voltage contains higher harmonic components. These higher voltage harmonics will generate harmonic

magnetic field, which will increase the core loss of the stator and rotor. When higher harmonic components are contained in the

voltage source, the core loss calculation formula is:

(5)

1 22 ' '

1 2

, ,

, ,ts fs tsk k ts fs jsk k

Fektr fs trk k jr fs jrk k

G K P B f G K P B fP

G K P B f G K P B f

In the formula, Gtr—Core quality of rotor tooth, Gjr—Core quality of rotor yoke, Bjr—Magnetic density amplitude of rotor teeth，

Btr—Magnetic density amplitude of rotor yoke, K’1—Correction coefficient of rotor tooth core loss, K’

2—Correction coefficient of

rotor yoke core loss.

In summary, the approximate calculation formula for the total core loss can be obtained:

(6)1Fe Fe FekP P P

In this paper, harmonic analysis method and finite element method are combined to analyze the core loss of SMPMSM.

B Influence of voltage harmonic on the core loss

Core loss of stator is one of the major losses of SMPMSM. It is caused by the variation of the main magnetic field, which

produces hysteresis loss and eddy current loss in the stator and rotor. The core loss leads to the decrease of the efficiency and

increase temperature of the SMPMSM, which limits the output performance of SMPMSM (Evstatiev et al.2017).

By using the finite element analysis method, the voltage harmonics with different amplitudes are analyzed and calculated.

The stator core loss of the SMPMSM is obtained, as shown in Table Ⅷ.

From Table Ⅷ, it can be seen that with the amplitudes of 98th voltage harmonic and 104th voltage harmonic increasing, the

stator core loss of SMPMSM gradually increases. But there is no big change, and the maximum variation range is within 3.4%.

C Influence of voltage harmonics on eddy current loss

When the SMPMSM is controlled by inverter, the harmonic contents are large. And it can cause the larger eddy current loss

(Jung et al.2017.).

Page 9 of 29



Draft

10

Compared with the stator core loss, the eddy current loss of the rotor is relatively small, but it can increase the eddy current

density. In addition, the size of the motor is small and the heat dissipation of the rotor is poor. These reasons are not conducive to

the safety and reliability of motor operation. The study of the eddy current loss has become one of the most important

technologies in the field of SMPMSM (Dai et al. 2017).

When the different voltage harmonic orders and voltage harmonic amplitudes are contained in the armature winding, the

variation of the eddy current loss will be analyzed. The variation of the eddy current loss is shown as shown in Fig. 7.

From Fig. 7, it can be seen that the eddy current loss of the SMPMSM increases obviously when the harmonic voltage is

contained in the armature winding, and the eddy current loss increases exponentially. When the amplitudes of the 98th harmonic

voltage and 104th harmonic voltage increase by 10% of the fundamental voltage amplitude, that is, 20V, the increases of eddy

current loss are 0.93W and 0.68W, respectively, increasing by 40% and 29% respectively. When the amplitudes of the 98th

harmonic voltage and 104th harmonic voltage increase by 15% of the fundamental voltage amplitude, that is, 30V, the increases

of eddy current loss of SMPMSM are 2.1W and 1.88W, respectively, increasing by 90% and 80% respectively. It can be seen

that the existence of voltage harmonic has a great influence on the eddy current loss of the SMPMSM. The influence of 98th

voltage harmonic on the eddy current loss is relatively large.

In order to reveal the influence mechanism of the eddy current loss, voltage harmonic of 30V is taken as an example. The

eddy current density distribution of the SMPMSM is analyzed when the fundamental voltage and additional 98th harmonic

voltage are contained in armature windings.

Based on the finite element method, the eddy current density distribution can be obtained, as shown in Fig. 8. Fig. 8 (a)

shows the eddy current density distribution of the fundamental voltage, and Fig. 8(b) shows the eddy current density distribution

when the 98th voltage harmonic amplitude is 30V. In order to facilitate the analysis and comparison, the same scale is adopted.

The eddy current loss can be calculated by the formula (7) (Li et al. 2010).

(7)2 1

1

1

e

k

e e e r tiTe

P J l dtT

Where Pe is the eddy current losses, Je is the current density in each element, Δe is the element area, lt is the rotor axial

length, σr is the conductivity of the eddy current zone, and Te is the cycle of time.

According to the above formula, the eddy current losses are influenced by: (a) the current density in the eddy current zone;

(b) The region of eddy current distribution; (c) The conductivity of the zone where the eddy current losses appear.

From the above analysis, it is found that the eddy current density of the additional 98th voltage harmonic increases by 1.04

times compared with the eddy current density with the fundamental voltage. And the area of eddy current distribution also

increases obviously. These two factors make the eddy current loss increase obviously. Combined with Fig. 7, it can be seen that

the eddy current loss is 2.34 W when only the fundamental voltage is contained, and the eddy current loss is 4.43 W when the

Page 10 of 29



Draft

11

voltage harmonic with 30 V is contained, increasing by nearly 2 times.

It can be concluded that the eddy current density of SMPMSM is mainly concentrated on the permanent magnet. With the

increase of harmonic voltage amplitude, the maximum value of the eddy current density will also increase correspondingly, and

the region of the eddy current density distribution becomes larger. The change of the eddy current density corresponds to the

variation of the eddy current loss, and the change mechanism of the eddy current loss is revealed.

VII. CONCLUSIONS

In this paper, a 1500r/min 3kW SMPMSM is taken as an example. The finite element method is used to analyze and

calculate the air-gap magnetic density, torque and loss. The influence of voltage harmonic on the air-gap magnetic density,

torque and loss is studied and the mechanism of eddy current loss is revealed. The following conclusions could be obtained:

1) When only the fundamental voltage is contained in the stator windings of the SMPMSM, the eddy current loss is 2.34W.

However, the eddy current loss increased by 30%-40%, when the amplitude of the 98th voltage harmonic increased by10%. The

eddy current loss increased by 80%-90%, when the amplitude of the 98th voltage harmonic increased by15%. This rule also can

be applied to other higher harmonics. The eddy current loss shows an increasing exponential trend with the increase of the

voltage harmonic amplitude.

2) The eddy current loss caused by 98th voltage harmonic is greater than the eddy current loss of 104th voltage harmonic.

With the increase of voltage harmonic amplitude, the disparity between them gradually becomes larger. The difference between

the maximum core loss and the minimum core loss is 3.4%. The voltage harmonics amplitude has little effect on the core loss.

3) The torque ripple is 1.7N•m when only the fundamental voltage is contained. However, the torque ripple increased by

20%, when the amplitude of the 104th voltage harmonic increased by10%. The torque ripple shows a linearly increasing trend

with the increase of the voltage harmonic amplitude.

4) When the different amplitudes of voltage harmonic are contained in the stator windings, the average torque of the

SMPMSM has little effect. The average torque also has little effect when the phase angles are different. Their variation ranges

are within 2%. Therefore, it is not necessary to consider the phase angle too much in the motor control system.

5) By analyzing the air-gap magnetic density, the influence of harmonic on motor performance cannot be well displayed.

Because the main magnetic field intensity is very large, the influence of the voltage harmonic on the air-gap magnetic density is

not obvious. The variation of air-gap magnetic density is very small, but it can cause the large torque ripple and loss.

Page 11 of 29



Draft

12

ACKNOWLEDGEMENTS

This work was supported in part by the National Natural Science Foundation of China under Grant 51507156, in part by the

University Key Scientific Research Programs of Henan province under Grant 17A470005, in part by the Key R & D and

Promotion Projects of Henan Province under Grant 182102310033, in part by the Doctoral Program of Zhengzhou University of

Light Industry under Grant 2014BSJJ042, and in part by the Foundation for Key Teacher of Zhengzhou University of Light

Industry.

REFERENCES

Chen, W., Zhao, Y., Zhou, Z., Yan, Y., and Xia, C. 2017. Torque ripple reduction in three-level inverter-fed permanent magnet

synchronous motor drives by duty-cycle direct torque control using an evaluation table. J Power Electron. 17(2): 368-379.

doi:10.6113/JPE.2017.17.2.368.

Duarte, S.X., and Kagan, N. 2010. A power-quality index to assess the impact of voltage harmonic distortions and unbalance to

three-phase induction motors. IEEE T Power Deliver. 25(3): 1846-1854. doi:10.1109/TPWRD.2010.2044665.

Dalal, A., and Kumar, P. 2015. Analytical model for permanent magnet motor with slotting effect, armature reaction, and

ferromagnetic material property. IEEE T Magn 51(12). doi:10.1109/TMAG.2015.2459036.

Dai, R., Zhang, F., Liu, G., and Hao, Y. 2017. Eddy Current Loss Analysis of High Speed Permanent Magnet Motor with Partial

Shielding. IEEE 12th International Conference on Power Electronics and Drive Systems (PEDS), Honolulu, HI, USA. 12-15 Dec. 2017.

pp. 758-760.

Endo, S., Kanazawa, Y., and Yamamoto, M. 2015. Analytical calculation of the voltage ripple on the input capacitor of the

voltage-PWM inverter for high frequency operation. IEEE International Telecommunications Energy Conference (INTELEC), Osaka,

18-22 Oct 2015. IEEE Power Elect Soc. Osaka. pp. 1-4.

Evstatiev, B. I., Kiriakov, D. V., and Beloev, I. H. 2017. A different approach for measurement of hysteresis losses in magnetic

cores. IEEE 23rd International Symposium for Design and Technology in Electronic Packaging (SIITME). Constanta,Romania 26-29

Oct. 2017. pp. 138-140.

Feng, G., Lai, C., and Kar, N.C. 2017. An analytical solution to optimal stator current design for PMSM torque ripple minimization

with minimal machine losses. IEEE T Ind Electron. 64(10): 7655-7665. doi:10.1109/TIE.2017.2694354.

Jung, J. W., Lee, B. H., Kim, K. S., and Hong, J. P. 2017. Design of IPMSM for reduction of eddy current loss in permanent

magnets to prevent irreversible demagnetization. IEEE International Electric Machines and Drives Conference (IEMDC), Miami, FL,

21-24 May 2017. pp. 1-6.

Khomsi, C., Bouzid, M., and Jelassi, K. 2014. Investigation of the harmonic content and its impact on the performance of

induction motor. International Conference on Electrical Sciences and Technologies in Maghreb (CISTEM) Tunis, Tunisia. 03-06, Dec

2014. IEEE Tunis, Tunisia.pp. 1-9.

Page 12 of 29



Draft

13

Kang, S., Shin, H.U., Park, S., and Lee, K. 2017. Optimal voltage vector selection method for torque ripple reduction in the direct

torque control of five-phase induction motors. J Power Electron. 17(5): 1203-1210. doi:10.6113/JPE.2017.17.5.1203.

Li, W. L., Wang, J., Zhang, X. C., and Kou, B. Q., 2010. Loss calculation and thermal simulation analysis of high-speed PM

synchronous generators with rotor topology. International Conference on Computer Application and System Modeling (ICCASM 2010),

Taiyuan, China, 22-24 Oct. 2010. pp. 612-616.

Lee, K., and Ha, J. 2012. Evaluation of back-emf estimators for sensorless control of permanent magnet synchronous motors. J

Power Electron. 12(4): 604-614. doi:10.6113/JPE.2012.12.4.604.

Shin, K., Hong, K., Cho, H., and Choi, J. 2018. Core loss calculation of permanent magnet machines using analytical method.

IEEE T Appl Supercon 28(3). doi:10.1109/TASC.2018.2800706.

Tawadros, M., Rizk, J., and Nagrial, M. 2011. Estimation of commutation instances using back emf mapping for sensorless control

of brushless permanent magnet motors. IET Electr Power App. 7(4): 270-277. doi:10.1049/iet-epa.2011.0382.

Tripathi, A., and Narayanan, G. 2016. Influence of three-phase symmetry on pulsating torque in induction motor drives. 7th India

International Conference on Power Electronics (IICPE), Patiala, India. 17-19 Nov. 2016. IEEE, Patiala, India. pp. 1-6.

Xia, K., Li, Z., Lu, J., Dong, B., and Bi, C. 2017. Acoustic noise of brushless dc motors induced by electromagnetic torque ripple.

J Power Electron. 17(4): 963-971. doi:10.6113/JPE.2017.17.4.963.

Xia, C., and Li, X. 2014. Z-Source inverter-based approach to the zero-crossing point detection of back emf for sensorless

brushless dc motor. IEEE T Power Electr. 30(3): 1488-1498. doi:10.1109/TPEL.2014.2317708.

YouGuang, G., Jian, G.Z., Jin, J.Z., and Wei, W. 2003. Core losses in claw pole permanent magnet machines with soft magnetic

composite stators. IEEE T Magn. 39(5): 3199-3201. doi:10.1109/TMAG.2003.816057.

Zhu, C., Zeng, Z., and Zhao, R. 2017. Torque ripple elimination based on inverter voltage drop compensation for a three-phase

four-switch inverter-fed PMSM drive under low speeds. IET Power Electron. 10(12): 1430-1437. doi:10.1049/iet-pel.2016.0936.

Fig .1. Finite element model of prototypeFig.2. Prototype test platformFig. 3. Harmonic voltage distribution spectrogramFig. 4. The distribution of the magnetic density and the magnetic force lineFig. 5. The air gap magnetic density distribution curveFig. 6. The variation curve of torque ripple with the harmonic voltage amplitudeFig. 7. Eddy current loss and growth trend（The curve 1 and the curve 2 represent the growth curve of the eddy current loss when

the amplitude of the 98th and 104th harmonic voltages increases.）

Fig. 8. Eddy current density distribution of the PMSMTable I Basic parameters of the PMSM prototypeTable II Comparison of the test data and calculated resultsTable Ⅲ.Comparison of the test data and calculated results of loss and efficiencyTable IV Accounts for the percentage of higher harmonic Table V Change of torque rippleTable VI Average torque at different voltage harmonic amplitudeTable Ⅶ The data torque ripple and average torqueTable Ⅷ The core loss of PMSM

Page 13 of 29



DraftFig .1. Finite element model of prototype

Page 14 of 29



DraftFig.2. Prototype test platform

Page 15 of 29



Draft

198

Vol

tage

(V)

Harmonic order

20.4

2629.4

24.3

198

Fig. 3. Harmonic voltage distribution spectrogram

Page 16 of 29



DraftFig. 4. The distribution of the magnetic density and the magnetic force line

Page 17 of 29



Draft

Only first harmonicAdd 98th harmonicOnly 98th harmonic

Right Y-axial

Left Y-axial

Fig. 5. The air gap magnetic density distribution curve

Page 18 of 29



DraftFig 6. The variation curve of torque ripple with the harmonic voltage amplitude

Page 19 of 29



DraftFig. 7. Eddy current loss and growth trend（The curve 1 and the curve 2 represent the growth curve of the eddy

current loss when the amplitude of the 98th and 104th harmonic voltages increases.）

Page 20 of 29



Draft

8.24

6.454.672.88

1.09-0.25-2.48-4.26-6.05-7.84

5 2(10 / )J A m

(a) The eddy current density distribution under the fundamental voltage

(b) The eddy current density distribution under the 98th voltage harmonic

Fig. 8. Eddy current density distribution of the PMSM

Page 21 of 29



Draft

Table I

Basic parameters of the PMSM prototypeParameters Value

Rated power 3 kWRated speed 1500 r/min

Pole number 8

Axial length 72.5 mmRotor magnetic circuit structure Surface-mounted type

Stator outer diameter 168 mm

Stator inner diameter 107 mm

Slot number 36Number of parallel branches 1

Winding connection type Y

Page 22 of 29



Draft

Table II

Comparison of the test data and calculated resultsPower 2 kW 3 kW 3.5 kW

Average torque 12.6(N•m) 19.2(N•m) 22.1(N•m)Armature current 5.9(A) 8.9(A) 10.1(A)Calculated results

No-load back EMF 151 (V)

Average torque 12.7(N•m) 19.1(N•m) 22.3(N•m)

Armature current 5.8(A) 8.7(A) 10.09(A)Test data

No-load back EMF 150 (V)

Average torque 1.7% 2.3% 0.1%

Armature current 0.8% 0.5% 0.9%Change rate

No-load back EMF 0.7%

Page 23 of 29



Draft

TableⅢ.Comparison of the test data and calculated results of loss and efficiencyPower 2 kW 3 kW 3.5 kW

Copper loss 43.5(W) 95.2(W) 128.6(W)Core loss and mechanical loss 91(W) 110.5(W) 121.3(W)

Total losses 134.5 (W) 205.7(W) 249.9(W)Calculated results

Efficiency 93.69% 93.58% 93.34%Copper loss 41(W) 90(W) 122.7(W)

Core loss and mechanical loss 87(W) 106(W) 125.3(W)Total losses 128 (W) 196(W) 248(W)

Test data

Efficiency 93.98% 93.87% 93.38%Copper loss 6.1% 5.8% 4.8%

Core loss and mechanical loss 3.7% 4.2% 3.2%Total losses 5.1% 4.9% 0.8%

Change rate

Efficiency 0.31% 0.3% 0.04%

Page 24 of 29



Draft

Table IV Accounts for the percentage of higher harmonic

Inverter parameters

Frequency（Hz）

Harmonic order

Percentage（%）

100 Hz 1 100.0

9600 Hz 96 10.39800 Hz 98 13.110200 Hz 102 14.8

fc=10kHz

fr=100Hz

10400 Hz 104 12.3

Page 25 of 29



Draft

Table V Change of torque ripple

Torque ripple under different harmonic orders( N·m)Harmonic voltage amplitude

3th 60th 90th 96th 102th Maximum error0% 1.73 1.73 1.73 1.73 1.73 0%

25% 1.78 1.78 1.75 1.73 1.75 2.8%

50% 1.75 1.75 1.82 1.72 1.73 5%

75% 1.81 1.82 1.81 1.80 1.81 1.1%

100% 1.81 1.79 1.73 1.75 1.75 4.4%Maximum error 4.4% 5% 4.6% 4% 4.4%

Page 26 of 29



Draft

Table VIAverage torque at different voltage harmonic amplitude

average torque（N•m）Amplitude of harmonic voltage（V） 98th 104th

0 19.20 19.20

20 19.12 19.11

25 19.03 19.03

30 19.12 18.94

35 19.12 19.03

40 18.95 19.20

45 19.12 18.94

50 19.03 18.86

Page 27 of 29



Draft

Table Ⅶ The data torque ripple and average torqueTorque ripple（N•m） Average torque（N•m）Phase angle

98th 104th 98th 104th0° 2.12 2.13 19.20 19.0330° 2.13 2.10 19.12 19.2060° 2.13 2.10 19.03 19.1190° 2.11 2.08 19.12 19.29120° 2.15 2.12 19.12 19.03150° 2.12 2.11 19.03 18.94180° 2.10 2.11 19.20 19.03210° 2.11 2.13 19.21 19.12240° 2.16 2.15 18.86 19.03270° 2.13 2.14 19.12 18.95300° 2.14 2.11 19.12 19.12330° 2.13 2.13 19.03 19.13

Page 28 of 29



Draft

Table ⅧThe core loss of PMSM

Core loss（W）Voltage amplitude（V） 98th 104th

0 39.54 39.54

20 39.81 39.81

25 39.91 39.90

30 40.00 40.08

35 40.29 40.23

40 40.40 40.38

45 40.65 40.66

50 40.85 40.86

Page 29 of 29



Influence of Inverter Output Voltage Harmonic on Surface ...€¦ · Influence of Inverter Output...

Documents

Transcript of Influence of Inverter Output Voltage Harmonic on Surface ...€¦ · Influence of Inverter Output...