Influence of inverter voltage harmonics on the torque ripple of surface permanent magnet synchronous motor

Abstract

The application of surface permanent magnet synchronous motor (SPMSM) driven by inverter is becoming more and more extensive. However, the voltage harmonics generated by the inverter will have a severe impact on the motor torque ripple. In order to analyze its impact, a 1500 r/min 3 kW SPMSM is taken as an example. Firstly, the two-dimensional finite element model is established, and the accuracy of the model is verified by the experiment. Secondly, the torque ripple is calculated and analyzed. The influences of voltage harmonic amplitude and voltage harmonic initial phase angle on torque ripple are mainly studied, and the variation law is obtained. At the same time, in order to distinguish the influence of higher harmonics on torque ripple, the voltage harmonics is decoupled to get the variation law of torque ripple. Finally, based on the analysis of the current ripple and air gap magnetic density, the influence mechanism of voltage harmonics on torque ripple is revealed. The conclusion is helpful to optimize motor design and improve motor performance.

Keywords

Air-gap flux density finite element method SPMSM torque ripple voltage harmonic

1. Introduction

Because of the advantages of simple structure, large torque and high power density, high efficiency and so on, PMSM has been widely used in communication technology, aerospace, industrial drive and other occasions [1–5]. In order to better start and control the PMSM, it is very necessary to combine the PWM frequency conversion technology with the PMSM. But it will also have some negative impacts on the performance of the PMSM, because the output voltage of the inverter contains a large number of harmonic components. With the increase of the harmonic, the air gap magnetic field is distorted, which leads to the increase of the torque ripple [6–8]. Therefore, it is more and more important to study the influence of the output voltage harmonics on the torque ripple. The influence of different voltage harmonics amplitude and initial phase angles on torque ripple will be different. It is of great theoretical significance and practical value to study the torque ripple under different harmonics amplitudes and harmonics initial phase angles.

At the present stage, studying and analyzing the influence of voltage harmonic on the motor torque ripple not only improve the overall performance of the motor, but also expand the application field [9]. In recent years, many scholars have carried out some comprehensive and in-depth study on the torque ripple. In reference [10], the influence of concentrated winding configurations and stator core structures on torque performance of fractional-slot PM machines is investigated. It can be found that the alternate teeth wound machines have larger torque ripple compared to all teeth wound machines with the same dimensions. In reference [11], a robust ILC strategy via adaptive SMC is presented, for the purpose of torque ripple minimization as well as improvement of the anti-disturbance ability of the PMSM speed control system. In reference [12], it represents different techniques for reduction of ripples for BLDC drives. Minimizations of ripples have strategies related to motor side control which is hardware based and some of algorithm based. In reference [13], based on analysis of noise sources of switched reluctance motor (SRM), the paper puts forward methods to reduce noise in terms of torque ripple and phase change from the point of control view. The proposed methods of reducing noise do not require any hardware, which can be achieved through software. However, many studies only focus on the algorithm analysis of motor, and studying on the influence of higher voltage harmonics and different amplitudes on motor performance are few. From power electronics technology, it can be contained that the order of the output voltage harmonics is related to the carrier frequency. In actual application, we should choose different carrier frequency inverter according to the motor power. If the carrier frequency is different, the harmonics frequency which mainly influences the motor torque ripple will be different. Therefore, it is very necessary to study the effect of higher voltage harmonics on motor torque ripple.

In this paper, taking a 3 kW, 1500 r/min SPMSM as the research object, the two-dimensional finite element electromagnetic field model is established. At the same time, the experimental platform is built, and the motor was tested through the platform. Using two-dimensional finite element method, the voltage harmonic amplitude and harmonic initial phase angle under different harmonic orders are analyzed and calculated. By analyzing the torque ripple, the influence law of voltage harmonic and harmonic initial phase angle on the torque ripple is obtained.

2. Prototype parameters and inverter output voltage harmonic analysis

2.1. Prototype parameters

In this paper, a 3 kW and 1500 r/min SPMSM is taken as an example to study the influence of the inverter output voltage harmonics on the motor torque ripple. According to the structure and parameters of the prototype, the finite element motor model was established. The basic parameters of the SPMSM are shown in Table 1. The prototype finite element model is shown in Fig. 1. In the finite element model, the total number of mesh elements is 10500, which can satisfy the solution accuracy [14].

2.2. Experimental study

In order to verify the influence of voltage harmonics on the motor torque ripple, a SPMSM experimental test platform is established to test parameters of the motor. The test system consists of a Magtrol dynamometer machine, YOKOGAWA power analyzer, industrial condensing unit, DSP data acquisition system, SPMSM and other forms of equipment. The correctness of the simulation result is verified by the experimental results. The experimental platform of the prototype is shown in Fig. 2.

Table 1
Prototype parameters

Parameters Value

Rated power 3 kW

Rated speed 1500 r/min

Pole number 8

Axial length 72.52 mm

Rotor magnetic circuit structure Surface-mounted type

Stator outer diameter 168.42 mm

Stator inner diameter 107.26 mm

Slot number 36

Number of parallel branches 1

Winding connection type Y

Parameters	Value
Rated power	3 kW
Rated speed	1500 r/min
Pole number	8
Axial length	72.52 mm
Rotor magnetic circuit structure	Surface-mounted type
Stator outer diameter	168.42 mm
Stator inner diameter	107.26 mm
Slot number	36
Number of parallel branches	1
Winding connection type	Y

Fig. 1.

Finite element model of prototype.

Through the above experimental platform, the SPMSM is tested, and the experimental data and simulation results are compared. Under different power, the prototype test data and simulation data are shown in Table 2.

Table 2

Test data and calculation results of SPMSM with different loads

Power		2 kW	3 kW	3.5 kW
Calculated results	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
	No-load back EMF	150 V
Test data	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
	No-load back EMF	150 V
Change rate	Average torque	1.7%	2.3%	0.1%
	Armature current	0.8%	0.5%	0.9%
	No-load back EMF	0%

Fig. 2.

Test platform of the prototype.

It can be concluded that from the above data under different power, the error of the experimental data and simulation values are controlled within 2.3%. Experimental data and model calculations are in good agreement, which verifies the accuracy of the model.

2.3. Inverter output voltage harmonics analysis

The PWM technology is used to control the SPMSM. The voltage of the input motor is not a standard sine wave. In order to analyze the higher harmonic components of the inverter output voltage, the Bessel functions and Fourier transforms are used. The three-phase bridge PWM inverter circuit has a carrier signal. In the output line voltage, the harmonic angular frequency is: $\begin{eqnarray}\displaystyle n{\omega}_{c}\pm k{\omega}_{r} & & \displaystyle\end{eqnarray}$ (1) ω_c is the carrier angular frequency and ω_r is the modulated carrier frequency.

In the Eq. (1), $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle n=1,3,5\quad k=3(2m-1)\pm 1,\quad m=1,2,3\ldots \nonumber\\ \displaystyle \text{} & \text{} & \displaystyle n=2,4,6\quad k=\left\{\begin{array}{@{}l@{}}6m+1\quad m=0,1\ldots \\ 6m-1\quad m=1,2\ldots \end{array}\right.\nonumber\end{eqnarray}$

The power analyzer is used to get the amplitude of every voltage harmonic. The harmonic spectrum diagram is shown in Fig. 3.

Fig. 3.

Harmonic voltage spectrogram.

In this prototype, except for the fundamental voltage, the maximum harmonic frequencies appear at 96th, 98th, 102th, and 104th respectively. They are 10.3%, 12.95%, 10.3%, and 12.95% of the fundamental voltage respectively. In the test, the inverter f _r is 100 Hz and f _c is 10 kHz. f _c is the carrier frequency and f _r is the frequency of modulated signals. The amplitude of the voltage harmonic is large near the carrier frequency or the carrier frequency. The amplitude of each harmonic voltage is clearly showed in Fig. 3, which provides strong support for the law of voltage harmonic distribution.

2.4. The motor model with PWM control

In order to facilitate the analysis of torque ripple, the following assumptions are made [20]:

(1) The motor windings is evenly and symmetrical.

(2) Ignore the end effect of motor.

When the input voltage contains harmonics, the three phase voltage relationship is shown as Eq. (2). $\begin{eqnarray}\displaystyle \begin{array}{@{}c@{}}U_{an}=\sqrt{2}U\sin ({\omega}t)+\sqrt{2}U_{n}\sin (n{\omega}t+{\varphi}_{n})\\[6.0pt] U_{bn}=\sqrt{2}U\sin ({\omega}t-{\displaystyle \frac{2{\pi}}{3}})+\sqrt{2}U_{n}\sin \left(n{\omega}t-{\displaystyle \frac{2n{\pi}}{3}}+{\varphi}_{n}\right)\\[6.0pt] U_{cn}=\sqrt{2}U\sin \left({\omega}t+{\displaystyle \frac{2{\pi}}{3}}\right)+\sqrt{2}U_{n}\sin \left(n{\omega}t+{\displaystyle \frac{2n{\pi}}{3}}+{\varphi}_{n}\right)\end{array} & & \displaystyle\end{eqnarray}$ (2)

U _an U _bn U _cn respectively represents the excitation sources of the three windings of the motor. U is fundamental phase voltage. U _n is n-th harmonic voltage. 𝜑_n is the n-th initial phase of the harmonic. ω is frequency.

The SPMSM is star type connection in three-phase three-wire symmetrical system. Although the inverter can output zero sequence voltage harmonic components, there is no harmonic current conduction circuit in the winding. Therefore, the 96th and 102th zero sequence harmonics do not play a role in the winding.

Based on the above analysis, the influence of 98th voltage harmonic, 104th voltage harmonic on motor torque ripple is analyzed.

3. Effect of voltage harmonic on torque ripple

3.1. Effect of voltage harmonic amplitude on torque ripple

Torque ripple is an important parameter to measure the operating stability of a motor. When the input voltage contains the harmonic, it will cause the change of the torque ripple and affects the stability of the motor [15]. Therefore, it is of great value to study the influence of the voltage harmonic amplitude on the torque ripple.

According to the experimental results, the fundamental voltage amplitude is 198V. When the 98th voltage harmonic amplitude accounts for 10%, 13% 15%, 18%, 20%, 23% and 25% of the fundamental voltage, the variation of torque ripple will be analyzed. The torque ripple with 104th voltage harmonic is analyzed in the same method.

The torque ripple is measured by the Eq. (3) [16]. $\begin{eqnarray}\displaystyle T_{ripple}=T_{\max }-T_{\min }. & & \displaystyle\end{eqnarray}$ (3) T _max is the maximum torque in one cycle. T _min is the minimum torque in one cycle.

Fig. 4.

The curve of the torque ripple with the voltage harmonic.

The curve of the torque ripple with the voltage harmonic is shown in Fig. 4. It can be obtained that the torque ripple is 1.73 N ⋅ m when it only contains the fundamental voltage. Under the 98th voltage harmonic, when the voltage harmonic amplitude increases by 10%, 20%, 25% of the fundamental voltage respectively, the torque ripple is 2.04 N ⋅ m, 2.4 N ⋅ m and 2.54 N ⋅ m, respectively. Compared with the torque ripple when only the fundamental voltage is contained, the torque ripples increases by 18%, 38%, 47% respectively.

When the 104th voltage harmonic amplitude increases by 10%, 20%, 25% of the fundamental voltage, respectively, the torque ripple is 2.1 N ⋅ m, 2.34 N ⋅ m and 2.53 N ⋅ m respectively. Compared with the torque ripple when only the fundamental voltage is contained, the torque ripples increases by 19%, 35%, 46% respectively.

The following conclusions can be obtained from the above analysis: Compared to when the fundamental voltage only is contained, the torque ripple obviously increases by the influence of voltage harmonic. The torque ripple linearly increases with the increase of the voltage harmonic amplitude. When the 98th or 104th voltage harmonic is contained, the increase speed of the torque ripple is approximately two times that the increase of the amplitude of the voltage harmonic.

3.2. The influence of voltage harmonic initial phase angle on the torque ripple

The U = U _m sin (ωt + 𝜑) is a complete voltage source wave. The (ωt + 𝜑) is the phase angle of the voltage source wave, and when the t is 0, 𝜑 is the initial phase angle of the voltage source wave.

The finite element method is used to analyze the influence of initial phase angle on the torque ripple. The initial phase angle of the voltage harmonic increases 30 degrees each time.

Figure 5 shows the torque ripple rate with initial phase angle of different harmonic voltage. It can be obtained from the figure that the torque ripple rates of 98th and 104th voltage harmonics are both below 2%. Therefore, it can be concluded that the initial phase angle of voltage harmonic has little effect on the torque ripple, and does not cause the change of the torque ripple.

Fig. 5.

Torque ripple at different harmonic initial phase angle.

4. Decoupling analysis of torque ripple

4.1. Analysis of the torque ripple in time harmonics and space harmonics

Fig. 6.

Torque of three kinds of excitation.

In order to compare and analyze the influences of time harmonic and space harmonic on torque ripple, the torque curve in one cycle is compared and analyzed. Figure 6(a) gives the torque curves under the fundamental voltage and the additional 98th voltage harmonic. Figure 6(b) gives the torque curves under the fundamental voltage and the additional 104th voltage harmonic.

From Fig. 6 it can be seen that the torque ripple is obviously increased when the harmonic is contained. The torque curve is smoother when only the fundamental voltage is contained. From Fig. 6(a) it can be seen that the torque ripple caused by space harmonic is 1.7 N ⋅ m when the fundamental voltage is contained. When the 98th voltage harmonic is also contained, the torque ripple is 2.1 N ⋅ m, and the torque ripple increases by 0.4 N ⋅ m, accounting for 19% of the total torque ripple.

From Fig. 6(b), it can be seen that the torque ripple is 2.2 N ⋅ m when the 104th voltage harmonic is also contained. The torque ripple increases by 0.5 N ⋅ m, accounting for 23% of the total torque ripple.

From the above analysis, it can be obtained that the presence of time harmonic voltage can cause large torque ripple.

4.2. Effect of higher harmonic on motor torque ripple

It can be seen from the previous section that when the voltage contains harmonic components, it has a great influence on the torque ripple. In order to analyze the torque ripple in detail, this section analyses the variation of torque when the 98th current harmonic or the 104th current harmonic only is contained. Figure 7 shows the torque curves with only 98th current harmonic and only 104th current harmonic in the winding.

Fig. 7.

Torque curve with 98th current harmonic or 104th current harmonic.

From Fig. 7, we can get that when only 98th current harmonic is contained, the maximum torque is 0.37 N ⋅ m. When only 104th current harmonic is contained, the maximum torque is 0.48 N ⋅ m.

In Fig. 6, the torque ripple is 1.7 N ⋅ m, when the fundamental voltage is contained. The additional 98th voltage harmonic and additional 104th voltage harmonic torque ripple are 2.1 N ⋅ m and 2.2 N ⋅ m respectively. They differ in 0.4 N ⋅ m and 0.5 N ⋅ m, and there are small difference between the maximum torque of only 98th current harmonic and the maximum torque 104th current harmonic. It is further verified that the time harmonic has great influence on the torque ripple.

4.3. The influence of motor cogging torque on torque ripple

Cogging torque is an inherent characteristic of PMSM. It can cause motor vibration and noise [17,18]. In order to distinguish the effect of voltage harmonic on the torque ripple, the cogging torque is separated. The finite element analysis method is used to analyze the cogging torque of the prototype.

Fig. 8.

The cogging torque of a prototype.

The cogging torque curve of the prototype is given in Fig. 8, and the cogging torque is 0.2 N ∙ m. Combined with Fig. 6, the torque ripple caused by the 98th time harmonic is 0.4 N ⋅ m and the torque ripple caused by the 104th time harmonic is 0.5 N ⋅ m. The cogging torque accounts for half of them.

The prototype is Delta’s ECMA series SPMSM with rated power of 3 kW and rated speed of 1500 r/min. The conclusion is obtained based on the research of this prototype. The detailed limited technical parameters of the prototype are shown in Table 3.

Table 3

Prototype technical parameters

Limited technical parameters
Brand	DELTA
Model	ECMA-F11830RS
Rated power	3 kW
Rated speed	1500 rpm
Rated torque	19.1 N ⋅ m
Motor length	202.1 mm
Motor weight	18.5 kg
Motor shaft diameter	35 mm
Flange	180 mm ∗ mm
Motor shaft length	79 mm

The following conclusions can be obtained that the torque ripple caused by the time harmonic is two times of the cogging torque. Therefore, when the torque ripple is studied, more attention should be paid to the influence of time harmonic on torque ripple.

5. Analysis the influence mechanism of voltage harmonics on torque ripple

Torque ripple is mainly caused by current variation and air gap flux density variation. The above two factors will be analyzed to reveal the mechanism of torque ripple in the next.

5.1. Analysis of current in motor windings

When the input voltage contains harmonic, the harmonic current is formed in the three phase windings. Table 4 shows the current harmonic data when the motor is operating under different conditions.

Table 4
Amplitude of current harmonic under different voltages harmonic order

Harmonic order Amplitude of current harmonic under different conditions

Fundamental 98th harmonic 104th harmonic

1 12.8 A 12.8 A 12.8 A

5 0.14 A 0.14 A 0.14 A

7 0.015 A 0.015 A 0.015 A

98 0.1 A

104 0.1 A

Harmonic order	Amplitude of current harmonic under different conditions
1	12.8 A	12.8 A	12.8 A
5	0.14 A	0.14 A	0.14 A
7	0.015 A	0.015 A	0.015 A
98		0.1 A
104			0.1 A

From Table 4 it can be seen that, when only the fundamental voltage is contained, the fundamental current amplitude is 12.8 A, and the 5th current harmonic amplitude is 0.14 A, accounting for 1.1% of the fundamental. The 7th current harmonic amplitude is 0.015 A, accounting for 0.12% of the fundamental current. When the 98th voltage harmonic is contained, the amplitude of the 98th current harmonic is 0.1A, accounting for 0.8% of the fundamental current.

The equation of current calculation is shown in Eq. (4) $\begin{eqnarray}\displaystyle {\dot{I}}={\displaystyle \frac{\dot{U}}{R+j{\omega}L}}. & & \displaystyle\end{eqnarray}$ (4)

From Eq. (4), it can be seen that the voltage harmonic frequency generated by the inverter is very high, so the current harmonic is very small. Although the current ripple is very small, it can still cause the torque ripple of the motor.

5.2. Motor air gap flux density analysis

The effect of current on torque ripple has been analyzed. The effect of magnetic field on torque ripple is analyzed in this section. The existence of voltage harmonic causes the distortion of the magnetic field [19]. Studying the variation of the electromagnetic field can analyze the root cause of torque ripple [20]. In this section, the 98th voltage harmonic is taken as an example to analyze the change of the air gap magnetic density.

Fig. 9.

Air gap magnetic density curve under different states.

The curve 1, 2 and 3 represents the distributions curve of the air gap magnetic density with the additional 98th voltage harmonic and only the fundamental voltage and only the 98th voltage harmonic, respectively.

It can be seen from curve 2 that, the air gap magnetic field is not a standard sinusoidal curve with the fundamental voltage. The reason is that the space harmonic makes the air gap magnetic density distortion, causing the motor torque ripple.

Comparing curve 1 with curve 2, when the motor input voltage contains 98th harmonic, the variation of air gap flux density is very small. It can be seen that when a small amount of voltage harmonic is contained to the fundamental voltage, the air gap flux density will not change significantly. Although the change is very small, it can still cause the variation of torque ripple. Combined with Fig. 5, this can be explained. This is because of the reason of the main magnetic field waveform, which makes the change not obvious.

In order to eliminate the influence of the main magnetic field, the air gap magnetic density is analyzed when the windings only contains 98th harmonic voltage.

Curve 3 shows that when the main magnetic field is ignored and only 98th voltage harmonic is contained, there is a slight change in air gap flux density. Although the change of air gap magnetic density is very small, it can still cause large torque ripple.

6. Conclusions

In this paper, a 1500r/min 3kW SPMSM is taken as an example. The finite element method is used to analyze and calculate the electromagnetic field. The influence of voltage harmonic on the torque ripple is studied and the mechanism of torque ripple is revealed. The following conclusions could be obtained:

1. The high-frequency harmonics generated by the controller can increase torque ripple. The torque ripple is1.73 N ⋅ m when only the fundamental voltage is contained. However, the torque ripple increased by 18%, when the amplitude of the 98th voltage harmonic is 20 V. When the voltage harmonic amplitude increases by 10%, the torque ripple nearly increases by 20%. The torque ripple shows a linearly increasing trend with the increase of the voltage harmonic amplitude.

2. Under the different initial phase angles, the torque ripple with 98th voltage harmonic is below 2%. The initial phase angle of the voltage harmonics has little effect on the torque ripple. This rule is still applicable to other higher harmonics. Therefore, it is not necessary to consider the initial phase angle too much in the motor control system.

3. The torque ripple caused by space harmonics is 1.7 N ⋅ m when the fundamental voltage is contained. When the 104th time voltage harmonic exists, the torque ripple is 2.2 N ⋅ m and it increases by 29%. The time voltage harmonics can cause 23% torque ripple, which is two times of the cogging torque. Therefore, when studying the torque ripple, more attention should be paid to the influence of time harmonics on the motor torque ripple.

4. Compared with the value of the main magnetic field, 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 large torque ripple.

Footnotes

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

Jin

Park

Kum

and Lee

, Magnetic flux waveform estimation for fast efficiency map calculation in permanent magnet synchronous motors, International Journal of Applied Electromagnetics and Mechanics 56(3) (2018), 373–386, doi:10.3233/JAE-170042.

Chen

Deng

and Deng

, An analytical model of unbalanced magnetic pull for PMSM used in electric vehicle: numerical and experimental validation, International Journal of Applied Electromagnetics and Mechanics 54(4) (2017), 583–596, doi:10.3233/JAE-160121.

Yao

Hou

and Wang

, Current sensor fault diagnosis and adaptive fault-tolerant control of PMSM drive system based on differential algebraic method, International Journal of Applied Electromagnetics and Mechanics 53(3) (2017), 551–565, doi:10.3233/JAE-160090.

Hong

Joo

Lee

and Woo

, Effects of the pole-slot combination on the PMSM of an integrated motor propulsor for an unmanned underwater vehicle considering its electric performance, noise and vibration, International Journal of Applied Electromagnetics and Mechanics 52(3-4) (2016), 1689–1695, doi:10.3233/JAE-162162.

Qiu

Tang

Yang

and Wang

, Effects of driving modes on permanent magnet motor electromagnetic and temperature fields at limit conditions, COMPEL-The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 35(6SI) (2016), 2045–2062, doi:10.1108/COMPEL-04-2016-0148.

Hara

Ajima

Tanabe

Watanabe

Hoshino

and Oyama

, Analysis of vibration of permanent magnet synchronous motor with distributed winding for thePWM method of voltage source inverters, IEEE Energy Conversion Congress and Exposition (2017), 5438–5444, doi:10.1109/TIA.2018.2847620.

Han

Liu

and Ma

, Research of the influence of different PWM inverters on the eddy current losses of induction motors, in: 2011 International Conference on Electrical Machines and Systems, Beijing, 2011, pp. 1–6. doi:10.1109/ICEMS.2011.6073730.

Taniguchi

Inoue

Takeda

and Morimoto

, A PWM strategy for reducing torque-ripple in inverter-fed induction motor, IEEE Transactions on Industry Applications 30(1) (1994), 71–77, doi:10.1109/28.273623.

Liang

Pei

Chai

and Cheng

, Equivalent stator slot model of temperature field for high torque-density permanent magnet synchronous in-wheel motors accounting for winding type, COMPEL-The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 35(2) (2016), 713–727, doi:10.1108/COMPEL-02-2015-0040.

10.

Zhu

Z.Q.

and Li

G.J.

, Influence of stator topologies on average torque and torque ripple of fractional-slot SPM machines with fully closed slots, IEEE Transactions on Industry Applications 54(3) (2018), 2151–2164, doi:10.1109/TIA.2018.2799178.

11.

Liu

and Deng

, Torque ripple minimization of PMSM based on robust ILC via adaptive sliding mode control, IEEE Transactions on Power Electronics 33(4) (2018), 3655–3671, doi:10.1109/TPEL.2017.2711098.

12.

Bondre

V.S.

and Thosar

A.G.

, Study of control techniques for torque ripple reduction in BLDC motor, in: 2017 Innovations in Power and Advanced Computing Technologies (i-PACT), Vellore, 2017, pp. 1–6. doi:10.1109/IPACT.2017.8245051.

13.

Zhu

Zhang

Xie

and Zhao

, Method of reducing noise and torque ripple of switched reluctance motor, in: 2017 Chinese Automation Congress (CAC), Jinan, 2017, pp. 2761–2765.

14.

Hsieh

M.F.

and Hsu

Y.S.

, An investigation on influence of magnet arc shaping upon back electromotve force waveforms for design of permanent-magnet brushless motors, IEEE Transactions on Magnetics 41(10) (2005), 3949–3951, doi:10.1109/TMAG.2005.854975.

15.

Dai

Keyhani

and Sebastian

, Torque ripple analysis of a permanent magnet brushless DC motor using finite element method, in: IEMDC 2001. IEEE International Electric Machines and Drives Conference (Cat. No. 01EX485), Cambridge, MA, 2001, pp. 241–245. doi:10.1109/IEMDC.2001.939306.

16.

Qiu

Wei

Yang

and Fan

, Influence of different frequency harmonic generated by rectifier on high-speed permanent magnet generator, Journal of Electrical Engineering Technology 13(5) (2018), 1956–1964, doi:10.5370/JEET.2018.13.5.1956.

17.

Keloth

Mijas

Manu

P.A.

Thomas

Menon

V.M.

and Praveen

R.P.

, Analysis of cogging torque reduction techniques of a slotless PMBLDC motor, in: 2014 Annual International Conference on Emerging Research Areas: Magnetics, Machines and Drives (AICERA/iCMMD), Kottayam, 2014, pp. 1–6.

18.

Tudorache

Trifu

Ghita

and Bostan

, Improved mathematical model of pmsm taking into account cogging torque oscillations, Advances in Electrical and Computer Engineering 12(3) (2012), 59–64, doi:10.4316/AECE.2012.03009.

19.

Fan

and Wen

, Armature-reaction magnetic field analysis for interior permanent magnet motor based on winding function theory, IEEE Transactions on Magnetics 49(32) (2013), 1193–1201, doi:10.1109/TMAG.2012.2224358.

20.

Qiu

Tang

Yuan

Yang

and Cui

, Analysis of the super high-speed permanent magnet generator under unbalanced load condition, IET Electric Power Applications 11(8) (2017), 1492–1498, doi:10.1049/iet-epa.2016.0669.

Harmonic order	Amplitude of current harmonic under different conditions
	Fundamental	98th harmonic	104th harmonic
1	12.8 A	12.8 A	12.8 A
5	0.14 A	0.14 A	0.14 A
7	0.015 A	0.015 A	0.015 A
98		0.1 A
104			0.1 A

Influence of inverter voltage harmonics on the torque ripple of surface permanent magnet synchronous motor

Abstract

Keywords

1. Introduction

2. Prototype parameters and inverter output voltage harmonic analysis

2.1. Prototype parameters

2.2. Experimental study

3.1. Effect of voltage harmonic amplitude on torque ripple

4.1. Analysis of the torque ripple in time harmonics and space harmonics

5.1. Analysis of current in motor windings

Table 4 Amplitude of current harmonic under different voltages harmonic order Harmonic order Amplitude of current harmonic under different conditions Fundamental 98th harmonic 104th harmonic 1 12.8 A 12.8 A 12.8 A 5 0.14 A 0.14 A 0.14 A 7 0.015 A 0.015 A 0.015 A 98 0.1 A 104 0.1 A

Footnotes

Acknowledgements

References

Table 4
Amplitude of current harmonic under different voltages harmonic order

Harmonic order Amplitude of current harmonic under different conditions

Fundamental 98th harmonic 104th harmonic

1 12.8 A 12.8 A 12.8 A

5 0.14 A 0.14 A 0.14 A

7 0.015 A 0.015 A 0.015 A

98 0.1 A

104 0.1 A