induction motor harmonics voltage waveform analysis based

https://jurnaleeccis.ub.ac.id/

p-ISSN : 1978-3345, e-ISSN(Online): 2460-8122

Jurnal EECCIS Vol. 14, No. 2, Agustus 2020

pp 63-67

Manuscript submitted on June 2020, accepted and published on August 2020

Induction Motor Harmonics Voltage Waveform

Analysis based on Machine Construction Akhlaqul Karomah1, Wiyono2, Hari Soekotjo3

1,2,3 Electrical Engineering Department, Brawijaya University, Malang, Indonesia

Email: [email protected], [email protected], [email protected]

Abstract— This paper discussed about harmonic

analysis in an induction motor. Harmonics on

induction motor appear due to the machine

construction specially to its slots. The analysis of those

harmonic will be one of the problems in the machine

observation and design. In this paper a simulated

computation of the flux magnet and emf induction

voltage containing harmonic is proposed and

discussed. FEMM simulation software is used and the

result is compared to the mathematical analysis. The

result shows that the emf induction harmonics wave

derived from mathematic modelling and FEMM

conform each other. Each of proposed methods can

be used in the machine design or the evaluation

analysis. Index Terms—harmonic, induction motor

I. INTRODUCTION

Harmonics on electrical motor can cause several

conditions to induction motor. In an induction motor,

harmonics reduce motor’s efficiency because copper and

iron in stator and rotor become hard to magnetize. High

eddy current and hysteresis losses appear due to

harmonics.[1]

The high current density from eddy current generated

by the high frequency harmonics leakage fields of the

rotor air gap. It creates high secondary winding losses

and significant heating. Heat can cause the decrease of

insulation on winding therefore lifetime of motor become

shorten. [2] Harmonics with high dV/dt affect partial

discharge in winding and fasten the degradation of

winding insulation.

Harmonics are caused by stator and rotor design with

its slots. The slot design of rotor and stator create

different harmonics wave. Harmonics due to construction

of rotor slot from the electric machinary is called “slot

harmonics” [3]

Non uniformity of the airgap caused by stator and rotor

slotting, winding concentration, rotor eccentricity and

saturation are the main sources of harmonic fields in she

airgap of induction machines. [3]

The problem of this research is the difficulty of

knowing the slot harmonics. In order to find the slot

harmonics equation, the formula is derived from several

basic magnetic flux density and the slot characteristics.

After finding the slot harmonics equation, the wave result

from FEMM simulation from the same induction motor

are compared.

Estimation in harmonic electromagnetic fields in

induction motors is considered important due to the

design trends of smaller size, higher output and the

spread of inverter drives in recent years [4].

II. METHOD

A. Basic Parameters

Induction motor construction design is made by defining

the basic parameter as follow: TABLE I

BASIC PARAMETERS

No Parameters Value

1 N (total winding) 160

2 L (motor’s length) 0,4 m

3 f (linier frequency) 50Hz

4 ω (angular velocity) 3000 rot/s

5 Number of poles 3

6 Rotor current (max) 10

7 Stator Slot Opening 0,1 m

8 Rotor Slot Opening 0,095m

9 Stator inner radius 0,16 m

10 Rotor outer radius 0,165 m

11 Machine length 0,4 m

12 Stator slot number 18

13 Rotor slot number 14

14 µ0 (air permeability) 1

15 θ (rotating angle) 0 – 360

16 k (orde) 1 - 180

B. Induction Motor Construction Design with FEMM

Induction motor is designed by making FEMM software

version 4.2 made by David Meeker. Parameters from sub

chapter 2.1 are used to design the motor construction with

the design result can be seen here in picture 2.1:

Fig.1. Machine Construction Design with FEMM

Then, make the design analysis Fig. 1 by doing Mesh

analysis on FEMM with the result can be seen in Fig. 2.

Jurnal EECCIS Vol. 14, No. 2, Agustus 2020, p-64


Fig. 2. Magnetic Field Lines Analysis Result

The next step is to define magnetic field line by making

contour. Contour line is made in air gap between stator

and rotor, and the result is shown in Fig. 3.

Fig. 3. Flux Density Graph B

Fig. 3 shows |B| value, B real and B imaginer, B real

value had a sine form with harmonics. B value is used to

define EMF by using LUA coding, B value from LUA

analysis is put for slot 1 that is rotated from 0 degree to

360 degree with 1 degree difference.

TABLE II

B VALUE FROM SLOT 1

(ϴ 0) B (Tesla) Brata2

B1 B2 B3 B4 B5 (Tesla)

0 2,631 0,569 0,634 1,011 2,354 1,44

1 2,01 0,566 0,71 1,095 3,419 1,56

2 1,99 0,59 0,791 1,143 3,272 1,557

3 1,991 0,621 0,884 1,152 3,046 1,539

4 1,992 0,758 0,9 1,08 2,693 1,485

5 2,027 0,815 0,939 1,009 2,347 1,427

6 2,049 0,925 0,924 0,918 1,963 1,356

7 2,147 1,028 0,945 0,824 1,763 1,342

8 2,44 1,091 0,922 0,737 1,706 1,379

9 2,785 1,17 0,972 0,67 1,675 1,455

10 3,085 1,269 0,878 0,587 1,69 1,501

11 3,285 1,239 0,78 0,542 1,769 1,523

12 3,367 1,094 0,656 0,573 1,931 1,524

... ... ... ... ... ... ...

349 2,264 0,946 0,783 0,589 1,879 1,292

350 2,648 1,021 0,724 0,541 1,906 1,368

351 2,94 1,062 0,689 0,523 1,983 1,439

352 3,086 0,919 0,581 0,56 2,137 1,457

(ϴ 0) B (Tesla) Brata2

B1 B2 B3 B4 B5 (Tesla)

353 3,092 0,872 0,627 0,58 2,293 1,493

354 3,02 0,822 0,539 0,616 2,499 1,499

355 2,9 0,765 0,532 0,671 2,725 1,519

356 2,751 0,709 0,539 0,731 2,934 1,533

357 2,575 0,66 0,522 0,804 3,108 1,534

358 2,383 0,624 0,543 0,873 3,234 1,532

359 2,194 0,593 0,589 0,962 3,381 1,544

360 2,631 0,569 0,634 1,011 2,354 1,44

C. EMF Induction from FEMM Design

EMF Induction equation from FEMM can be

derived from several basic equation and the result is

𝐸 = 𝑁𝑘𝑣𝐵𝐿 2𝜋𝑠𝑖𝑛𝑋

𝑅 (1)

Using Table I and Table II as a data input to the equation

(1) so the EMF result can be seen in Table III.

TABLE III

EMF VALUE

(ϴ 0)

Brata2

(Tesla)

E (EMF)

(volt)

0 1,439898 0

1 1,559891 4,730921

2 1,557162 9,443852

3 1,538954 13,99658

4 1,484577 17,99632

5 1,427363 21,61857

6 1,355862 24,62901

7 1,341558 28,41196

8 1,37922 33,35696

9 1,45469 39,54585

10 1,501487 45,3096

11 1,523024 50,50152

.. ... ...

349 1,292216 -43,5505

350 1,368187 -42,0331

351 1,439327 -39,9153

352 1,45667 -36,0288

353 1,492662 -32,4324

354 1,499425 -28,0625

355 1,518639 -23,8388

356 1,532798 -19,4276

357 1,533719 -14,7971

358 1,531509 -10,1359

359 1,54391 -5,53734

360 1,439898 -0,79744

By using Excel software the data from Table III is

implemented on a graph and the result is shown in Fig. 4.

Fig. 4. EMF Induction Graph in Volt v.s Rotated Angle(0)



D. EMF Induction with Mathematic Modelling

EMF Induction equation derives from several equation:

𝐸 = 𝑁𝜔𝜇0

2

𝜋

1

𝛿[∑

1

𝑛𝐼𝑘𝑠𝑜𝑛𝐾𝑝𝑛𝐹𝑛(𝑟) cos(𝑛𝜃)]

𝑛

sin (𝑛𝜃) (2)

Data on Table I is used to support equation (2) so the

EMF graph induction is shown in Fig. 5.

Fig. 5. EMF Graph in volt and Rotated Angle in Degree

III. RESULT AND ANALYSIS

A. EMF Analysis from FEMM v.s. Mathematic Modelling

EMF graph from FEM analysis and mathematic

modelling has a similar form and value, to get to know

further so we can find by verifying both of the graphs

using Excel and the result is in Fig. 6.

Fig. 6. EMF Graph using FEMM v.s. Mathematic Modelling

Graph 3.1 shows that EMF graph from FEMM analysis

is similar to EMF from mathematic modelling. The

similarity is sine graph form with a slight difference in

the amplitude and the harmonics total.

B. Harmonics

Calculating and analyzing harmonics signal spectrum

generally use DFT (Discrete Fourier Transform). Using

Forrier transform discrete to get the spectrum frequency,

spectrum amplitude, and spectrum energy density in

digital signal. From this parameter the signal source is

derived from basic signal and harmonics signal, therefore

the DFT transfer function is

𝑋(𝑘) = ∑ 𝑋(𝑛). 𝑊𝑁𝑘𝑛𝑁−1

𝑛=0 , where 𝑊𝑁 = 𝑒−𝑗2𝜋/𝑁 (3)

with:

X(k) : frequency spectrum and frequency index- k

X(n) : digital data

k : index frequency of k

n : sampling from 0,1,2,3……,N-1

N : total sampling

Equation analysis (3.1), shows that X(k) is a EMF

induction spectrum-> E (k), X(n) is a EMF induction data

digital-> E(n), so the equation (3.1) can be written:

𝐸(𝑘) = ∑ 𝐸(𝑛). 𝑒−𝑗2𝜋𝑘𝑛

𝑁𝑁−1𝑛=0 (4)

Inside program coding value j=-1 is unknown so

another function with the same value from Euler:

𝑒−𝑗2𝜋𝑘𝑛

𝑁 = cos (2𝜋𝑘𝑛

𝑁) − 𝑗𝑠𝑖𝑛 (

2𝜋𝑘𝑛

𝑁),

From equation (3.2) become;

𝐸(𝑘) = ∑ 𝐸(𝑛). (cos (2𝜋𝑘𝑛

𝑁) − 𝑗𝑠𝑖𝑛 (

2𝜋𝑘𝑛

𝑁))𝑁−1

𝑛=0 (5)

Equation (3.3) sjows that cos is a real value or ER(k) can

be written in a equation form as follows;

𝐸𝑅(𝑘) = ∑ 𝐸(𝑛). cos (2𝜋𝑘𝑛

𝑁)𝑁−1

𝑛=0 , (6)

In a matrix form:

|

|

𝐸𝑅(1)𝐸𝑅(2)𝐸𝑅(3)

.

.

.𝐸𝑅(𝐾)

|

|

=

|

|

cos (2𝜋1∗0

𝑁) cos (

2𝜋2∗0

𝑁) . . . cos (

2𝜋𝐾∗0

𝑁)

cos (2𝜋1∗1

𝑁) cos (

2𝜋2∗1

𝑁) . . . cos (

2𝜋𝐾∗1)

𝑁)

.

..

cos (2𝜋1∗(𝑁−1)

𝑁)

.

..

.

.

..

.

.

..

.

.

..

.

.

..

cos (2𝜋𝐾∗(𝑁−1)

𝑁)

|

|

|

|

𝐸(0)𝐸(1)𝐸(2)

.

.

.𝐸(𝑁 − 1)

|

|

and sin is the imaginer value or EM(k), and the imaginer

part can be written:

𝐼𝑀(𝑘) = ∑ 𝐼(𝑛). sin (2𝜋𝑘𝑛

𝑁)𝑁−1

𝑛=0 , (7)

In matrix can be written;

|

|

𝐸𝑀(1)𝐸𝑀(2)𝐸𝑀(3)

.

.

.𝐸𝑀(𝐾)

|

|

=

|

|

sin (2𝜋1∗0

𝑁) sin (

2𝜋2∗0

𝑁) . . . sin (

2𝜋𝐾∗0

𝑁)

sin (2𝜋1∗1

𝑁) sin (

2𝜋2∗1

𝑁) . . . sin (

2𝜋𝐾∗1)

𝑁)

.

..

sin (2𝜋1∗(𝑁−1)

𝑁)

.

..

.

.

..

.

.

..

.

.

..

.

.

..

sin (2𝜋𝐾∗(𝑁−1)

𝑁)

|

|

|

|

𝐸(0)𝐸(1)𝐸(2)

.

.

.𝐸(𝑁 − 1)

|

|

C. Harmonics EMF Induction from FEMM

Analysis for EMF spectrum can be done by Matlab

software. Matrix from equation (4) and (5) can be written

in Matlab code and the result:

-300

-200

-100

0

100

200

300

1

24

47

70

93

11

6

13

9

16

2

18

5

20

8

23

1

25

4

27

7

30

0

32

3

34

6

GG

L In

du

ksi (

Vo

lt)

Angle (Degree)

EMF INDUCTION FEMM VS MATHEMATIC MODELLING

GGL by Pemodelan Rumus

GGL by Analisis FEM



TABLE IV

EMF SPECTRUM FROM FEM

The graph form can be shown in Fig. 7 as follows:

Fig. 7. Spectrum Graph EMF from FEMM

Table IV and Fig. 7 shows that k in order 1 as a basic

frequency have the highest amplitude with 219,074 Volt,

it shows that basic EMF is 219,074 Volt. While the

harmonics appeared in:

k = 2, EMFharmonisa = 12,92 volt




D. EMF Harmonics Analysis from Mathematic Modelling

Analyzing EMF spectrum can be done using Matlab

software. Matrix from the equation (3.4) and equation

(3.5) is put on Matlab coding so the result can be seen

here:

TABLE V

EMF SPECTRUM FROM MATHEMATIC MODELLING

The graph form can be seen in Fig. 8.

Fig. 8. EMF Spectrum Graph from Mathematic Modelling

Table V and Fig. 8 shows that k in order 1 as a basic

frequency has the highest amplitude with 247,396 Volt,

it shows that EMF basic is 247,396 Volt. While the

harmonics appeared in:



IV. CONCLUSION

The mathematic modelling of harmonics equation that

have been designed can be used to find the harmonics of

induction motor. The emf induction waveform from

mathematic modelling and FEMM simulation waveform

conform each other with its sine graph form with a slight

difference in the amplitude and the harmonics total. With

the final equation obtained, the magnitude of any slot

harmonic for any machine construction such as geometry

of stator and rotor slots can be calculated.

REFERENCES

[1] Kunihiro N, Nishihama K. Investigation into Loss Reduced Rotor

Slot Structure by Analyzing Local Behaviors of Harmonic

Magnetic Fluxes of Inverter Feeding Induction Motor. IEEE



Energy Conversion Congress and Exposition (ECCE). 2015: 263-

268.

[2] Haodong L, Keith W, Rotor Design to Reduce Secondary

Winding Harmonic Loss for Induction Motor in Hybrid Electric

Vehicle Application. IEEE Energy Conversion Congress and

Exposition (ECCE). 2016.

[3] Yamazaki K. Induction Motor Analysis Considering both

Harmonics and End Effects using Combination of 2D and 3D

Finite Element Method. IEEE International Electric Machines and

Drives Conference Record. 1997: 231-233.

[4] Zhu Q. Instantaneous Magnetic Field Distribution in Permanent

Magnet Brushless dc Motors, Part IV: Magnetic Field on Load Z.

IEEE Transactions on Magnetics. 1993; 29: 152-158.

[5] Zhu, Z, Howe D, Instantaneous magnetic field distribution in

brushless permanent magnet DC motors. III. Effect of stator

slotting. Magnetics, IEEE Transactions; 1993; 29: 143-151.

[6] Prashanth S, Sameer N, Ankit D. Analytical Determination of Slot

Harmonics content of Air-Gap Magnetic Field for an Induction

Machine. IEEE Power & Energy Society General Meeting. 2015:

978-982

[7] David H.S., Electromagnetics and Applications, Department of

Electrical Engineering and Computer Science, Massachusetts

Institute of Technology

Cambridge, 2011

[8] Vahaj, Amir Abar; Rahideh A; etall; Exact Two-Dimensional

Analytical Calculations for Magnetic Field, Electromagnetic

Torque, UMF, Back-EMF, and Inductance of Outer Rotor Surface

Inset Permanent Magnet Machines; Department of Electrical and

Electronics Engineering, Shiraz University of Technology,

Shiraz, Iran; 2019

induction motor harmonics voltage waveform analysis based

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