Finite Element Analysis Of 3-phase Im With Pwm Inverter

Finite Element Analysis of 3-Phase Induction Motor with PWM Inverter Jeong-Jong Lee, Hyuk Nam, Young-Kyon Kim, Jung-Pya Hang, Don-Ha Hwang* Department of Electrical Engineering o f Changwon National University, Korea Industry Applications Research Lab., Korea Electrotechnology Research Institute* Phone: 82-55-262-5966 Fax: 82-55-263-9956 E-mail: wave95@,korea.com A b l m c f - This paper deals with the finite element analysis of 3-phase induction motor with PWM(Pulse Width Modulated) inverter fed. When a motor i s driven by P\VM inverter, i t s input and output power i s different from those of commercial (sinusoidal) supply, because PWR.1 inverter voltage contains high frequency components. Therefore, in order t o analyze the motor performance precisely, the transient analysis lo express PWkI inverter output voltage i s required. This paper presents the method o f constitution o f variable time step transient analysis for calculating the P W M inverter voltage. The result shows the difference o f current in motor between commercial and PWM inverter voltage.

1. INTRODUCrlON

drive with sinusoidal drive. II.METHOD

A.

PCVM inverter circuit modeling

To simulate the transient analysis of induction motor, the voltage has to be defined at each time step. In sinusoidal waveform simulation, voltage and time-step can be calculated easily. However, determining the voltage and time step in PWM inverter is not easy. Fig. 2 shows the inverter circuit. General switching method is shown in Fig.3, where triangular waveform is compared with sinusoidal waveform. and time-steD and voltage are determined. The motor specifications &e shown in Table 1. -

Recently, pulse width modulated (PWM) inverters are widely used to feed rotation machines because they allow essy control of amplitude and frequency o f the voltage excitation by adjusting the number and the size of the pulses. And many studies for PWM In invener-fed electric inverter circuit have been repotted [I]-[;]. machines, the characteristics such as efficiency. cumill waveforms, and generated torque or force are ditferent from those of sinusoidal voltage fed ones. In induction motor, the efiect o f PWM inverter is more significant than other type motors, because of skin effect and secondzuy current, which contains high frequency ripples. In that case, the average voltage of inverter output is equal to sinusoidal input. And high frequency voltage can decrease motor pefonnance. In order to estimate the effect of PWM inveneer fed induction motor, it is required to simulate the PWM inveller circuit and induction motor model, which can be expressed by finite element tnethod (FEM). However, there are several problems in simulating the PWM inverter. Firstly, FEM requires too long computation time due to lots o f time steps. Secondly, there are too many PWM voltage waveforms to simulate. But in recent years, the computer system is developed to be vely fast. And it is possible to analyze the characteristic of induction motor, which is supplied by PWM inverter. The finite element formulation must be coupled to is extemal circuit model when dealing with non-sinusoidal sources because of the iteration between the electric and magnetic models. In driving an induction motor with PWM inverter, the performance of the motor varies. In a PWM inverter supply, the voltage profile consists of control method. Therefore, the PWM invener voltase also varies. In order to analyze the state of the PWM inverter, FE analysis method is used for time transient analysis. The pefonnance of an induction motor with PWM invener drive is compared with that of sinusoidal drive. In the result, the torque characteristicsofsinusoidal drive and PWM inverter appearance. This paper presents the torque distribution of 3-phase induction motor comparing PWM inverter

Fig, I.35kwclarr 3-phs inductim motor

ib, 0 -FE

+'C

Ar

Scul,l~rarml,lr

CllllD -It,>

Fig. 2. Calculating PWM inverter switchingtime step

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'TABLE I SPECIFICATIONSO F THE INDUClION MOTOR Specification Input raltagc Rated Output Rated Speed Pole number Foundation Freqocncy Connection

B.

The input current of PWM inverter is compared with that of sinusoidal wavefoim Fig. 4., where the effect of PWM inverter appears. In this analysis, in order to reduce simulation time, sinusoidal waveform is applied to PWM analysis. After phase current reaches to steady state, PWM voltage is applied as input. In Fig. 4, point A is tuming point fiom sinusoidal wavefomi to PWM voltaxe. Fig.6. shows the equipotential line of 3-phase induction motor in steady state. In steady state, flu depth is deeper than transient state because ofthe current flow of secondary conductor.

V;,lue

380 (line-to-line)

35 (kN') 1770 4

60(Hr) Udt8

Time stepping FEM

2-D time-stepping finite element metliod is used for the analysis o f the magnetic field. The goveming equation for 2-D FE analysis is given by (1) .....

where

.4

,,

is the z-component of magnetic vector potential, is the

1

permeability, U is conductivity of material, J l ' is the exciting current density ofthe primary winding [ I]. And, Voltage equations should consider each phase as follow,

-400 -6004

.

, 20.0m

0.0

,

.

.

40.0m

, 6D.Om

Time

V,

.

dl,, d4" IoR, + (L, + L,,,) di + dt

100.0m l i .Om

8O.Om

(5)

Fig. 4. Input currentof3-pliae induction niotor. 80 60

where

J/, , R,

and

$e7

are the phase voltage, inductanceand flux

linkage ofeach phase, respectively. Lc,and L,,8are winding inductance of2dimension and winding leakage inductance is phase inductance. In this respectively, the sum of L,, and L#3, paper, 2dimension FEM is used for the analysis. Therefore, it is possible to calculate L ~,,while L,,, is not. Therefore. L,>,is calculated by equivalent method [4]. 111. RESIJLT AND DlSCllSSlON A.

lripur vollage

Fig3 shows the phase voltage of induction motor at 2 kHz of PWM frequency. The motor is connected as Delta winding, and experiment and simulation are perfonned from the frequency of 2 kHz to 20 kHz.

40 20 c

c

are t 3

0 -20 -40 -60

-

8

O

90.0m

i

. , 95.0m

,

,

.

,

100.0m 105.0m Time ( 5 )

.

, 110.0m

I

1

115.01n

Fig 5. The c m n t m n i view o f b x B in Fig. 4

Fiq. 6. Stfadysme Equipotentialofllle induction n1otor.

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Fig. 7 shows the torque ripple in steady state. The sinusoidal waveform torque is larzer than PWM method. Fig. 8. shows the torque according to PWM carrier frequency. In Fig. 8 siiiiulation and experiment result of the PWM inverter and the sinusoidal drive are represented with x-axis ignored. The speed is 1770 Tin i n all simulations,but experimental result varies. In this paper, inechanical equation is ignored to reach iated speed as fast as possible. Fig. 9 shows the primary conductor loss. It is calculated by the iesistance loss equation. As the PWM frequency becomes high, the less orimarv conductor loss is shown.

Fig. I O shows the secondary conductor loss. As PWM frequency is lower, the conductor loss increases. Table 2 shows efficiency according to the voltage. The efficiency of sinusoidal voltage is profitable Ban PWM inverter supply. -2-

t

0

2

4

6

8

10

12

PWM sinusoidal Simulation

sinusoidal experimen

14

16

18

20

I

Frequency [kHr]

Fig. IO. Secondary condudorloss

TABLE 2 POWERDISTRIBUTION

250

200

-5

41.4 38.1 40.6

Sinusoidal experience PWM simulation (SkHz) PWM saperience (8kHr)

1v.

150

37.8 34.4 36.8

91.4 90.2 90.6

CONCLUSION

I

a) 7

'J too

2

--t

-t-

sinewave simulatim sinewave experience

---t pw,n Iimulatlon

50

experience

+-pwni

0

2

E tmj

I

6

8 10 I? 14 Frequency lkHzl

16

18

20

REFERENCES 0,

t

sinusoidal si8wlation .: Sinusoidal experience --ic pvin, simulation '2 p r m experience

,

.-- l .o 0

This paper presents the analysis of 3-phase induction motor with PWM inverter using finite element method. By using PWM inverter, the conductor loss increases, while torque decreases. And conductor loss can be increased due to the increase of motor temperature. Therefore, the method that does not use PWM inveiier is reasonable for motor drive. But, in recent years, PWM inverter is widely used for transient current protection and motor speed controls. Therefore, design need to consider the effect of the loss due to PWM inverter.

2

4

6

8

10

12

,

, 14

,

, . , 16

18

,

,

.

[I] In-Soung Jung, Dong-Seak tlyun, "Dynamic cliaracteristics of I'M linear synchronous motor driven by PWM inverter by finite element analysis", IEEE Trans. on Mognelics, vol. 2, no. 5, September, 1999, pp 3697-3699. [2] S. L. Ho, et. al. "A combined finite elemencdomain elimination method for minimizing torque ripples in invertevfed AC motor drive system", IEEE Trans. on Mognelic.?, vol. 36, no. 4, July, 2000, pp 1817-1 821. [3] G.H. Jang. et. al, "Finite-elemcnt analysis of an electromechanical tield of a BLDC !motor considering speed control and mechanical flexibility", IEEE J r o m on Mognerics. vol. 38, no. 2, March, 2002, pp 945-948.

20

Frequency [kHz] Fig. 9. Ihnary conductor loss

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