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Title Characteristics of Condenser-excited Single-phase Induction Motor

Author(s) Ishizaki, Takemitsu; Fujii, Tomoo; Ishikawa, Sadao; Hirasa, Takao

Editor(s)

CitationBulletin of University of Osaka Prefecture. Series A, Engineering and nat

ural sciences. 1970, 19(1), p.75-86

Issue Date 1970-09-30

URL http://hdl.handle.net/10466/8137

Rights

75

Characteristics of Condenser-excited Single-phase

Induction Motor

Takemitsu IsHizAKi*, Tomoo FuJn*, Sadao IsHiKAwA*

and Takao HiRAsA*

(Received June 15, 1970)

This paper deals with the theoretical equation to estimate the characteristics of

the condenser-excited single-phase induction motor and its experimental characteristics.

Its characteristics at rated frequency 60(Hz) varied with size of exciting cendenser.

Optimum operation can be obtained at minimized negative-phase sequence current.In optimum operation of sample motor, no-load current decrease by 60 percent, full

load eMciency increase 10 percent, and pulsating torque of double stator frequency

which introduce vibration and noise to motor decrease 30.--.70 percent compared with

the ordinary single-phase induction motor

The optimum value C,p of exciting condenser, in which optimqm characteristics

can be obtained, vary with frequency f and magnetizing inductance ldi. Relation among

them is simply represented as

C,pf21ip==constant

Tests are caried out over frequency range from 30 (Hz) to 70 (Hz) in order to verify

this relation. The speed of condenser-excited motor can be controlled more smoothly,

silently, and eficiently than ordinary single-phase induction motor. Use of exciting

condenser for single-phase induction motor in the speed control systems is suggested

in this paper.

1. Introduction

The single-phase induction motors are very widely used in appliances, in

business, and in industry. They find interesting applicatiQns in automatic control

devices of various kinds.

In previous papersi,2) control characteristics of condenser-excited single-phase

induction motor driven by thyristor inverter wete reported, and its controlling

characteristics indicated such excellent results that were never obtained by the

ordinary single-phase induction motor. !n this case, the wave form of the source

voltage which is supplied to the motor by inverter is a very distorted one. Very

little work has been done to estimate the control characteristics of condenser-

excited motor driven by the ordinary sinusoidal wave source.

This paper deals with the theoretical equation to estimate the charecteristics

of the condenser-excited single-phase induction motor and its experimental charac-

teristics driven by sinusoidal wave source over frequency range from 30(Hii) to

70 (H]z).

* Department oE EIectrical Engineering, College of Engineering.

76 T. IsHizAK!, T. FuJii, S. IsHiKAwA and T. HmAsA

2. Condenser-excited Single-phase Induetion Motor ･

2-1. Principle Condenser-excited motor resembles condenser motor except

for connection of the stator windings. They are connected as shown in Fig. 1.

The main winding M is connected to a single-phase source and the auxiliary

winding A is short circuited through a condenser C. WheB the motor is in run-

ning condition, a voltage E. is generated in the auxiliary winding by the rota-

tion of rotor in the field which is energized from the voltage V;.. The auxiliary

winding current 4 in the condenser C, is out of phase with the current 1in in the

main winding M: Both currents are equivalent to two-phase exciting currents

and can generate the rotating field in the motor. Such a motor can be called

"condenser-excited single-phase induction motor3)" because of the condenser C

serves for the excitation of the motor. This motor has no starting torque, but if

started by auxiliary means, it will continue to run eMciently and noislessly.

ImM

Vm Em1

Rotor

t'"'-'N n

la'

;.i:-:-･:

Ea

A

.Fig. 1 Connection of Condenser-excited motor.

2-2. Calculation of characteristics The stator windings of the motor indi-

cated in Fig. 1, are in electrical space quadrature each other and may have un-

equal turns. The voltage equations in stator circuits can be written as follows

1;M."+IIfxM.)lrx',)?Z=+=EVlah-o]' (')

where r., ra and x., x. are the effective resistances and leakage reactances of the

windings M; A, respectively; x,=1/2zfC is a capacitive reactance of C; and E. is

the counter emf generated in the winding ML Method of symmetrical co-ordinates

is applied to eq. (1). Then the positive- and negative-phase sequence components

of the stator phase currents are

Characteristics of Condenser-excited Single･Phase lnduction A4btor 77

li)=r}(L.-ja4), 1>v==S(Iin+ja4) ,(2)

where a(=Nh/AI;.) is the effective turn ratio. Note that axlh is the current in

winding A referred to winding ML The positive- and negative-phase sequence

components of the applied voltage and the induced emfs are

V>-VN=-SVin (3) Ep=-ll-(Em-j-}Ea), EN=='ll-(Em+jiEh) (4)

The positive- and negative-phase sequence components of the sum of the external

impedance and the leakage impedance of the stator phase windings are

zp == -ll-(rm -mZ/÷+i'(Xm -':÷/ +i/ ))) '' (s)

zN=- -l}-(rm +-Z/-+,'(xm+i/ -i/ )) J ,

When the rotor is running at a slip s, the positive- and negative-phase sequence

components of the rotor and magnetizing impedance Z> and IN as viewed from

winding M are given by the equivalent circuits shown in Fig. 2. Therefore Zi,

and Z)v can be written as follows

Ep - 1 ('lil' )x2¢+ 1'( (-22'÷)2x¢+x2x¢(x2+x¢))

Zi' === fp - ju1¢ + r,/sl+7'x, == (-li'+)2+(x2+xth)2

ZAr"":EfyN` '= ik + r,/(i2 -is)+ix, = ( 2r-2s )X2Q+( i2(r-5(s2)r-,2i)lill+x¢x)2,x¢(x2+x¢))

EiE RN +J'X}v (7)Equations (1) to (7) can be solved for the positive- and negative-phase sequence

E, x,y Zp' rs2 EN t xiZ. r2 ･..

2-s

Fig.

(a)2 Equivalent

components winding.

circuits

of the

(b)representing (a) the positive and (b) negative-phase sequence

rotor and magnetizing impedances as viewed from the main

78 T. IsHIzAKr, T. FuJii, S. IsH!KAwA and T. HTRAsA

currents, giving

ZN-Zp+Ztv Ti]. IP= 4Ziv+zN(Zi)+Z}v)+zN2-zp2 '-2- (8)

- ZN-Zp+Zi' V;n fy - lpZN+ZN(4+Ztv)+2iv2-gp2 '-'27 (9)

Considering that xc is a variable and rearranging these equations,

- (r.+a2RN)+1'(x.+a2Xlv)-1'xc li'- Bi+1'B2+(Di+1'D,)xc 'Vh (10)

I},-(ra+Ba,2.R,P.B);.i'IXs,+.ai2.DX,>)}7i'XC･vh - (ii)

where

Bi == (2a2(RpRN - XpX}v) + (a2r. + r.)(Rp + RN)

-(a2x.+xa)(.X))+.X]v)+2(rmra-xmxa))

B2 = (2a2(RpX}v + RNXi,) + (a2r. + r.)(.X> + .Xlv) (12) +(a2x.+xa)(Rp+RN)+2(xmra+xarm))

Di=rXp+.Xltv+2x.

D2 == - (Rp + RN +2r.)

It can easily be seen from eqs. (10) and (11) that locus of currents are circles.

Therefore circle diagram given by eqs. (10) and (11) is immediately applicable to

the study of motor.

From eqs. (2), the stator phasor currents can be written,

Ih-fp+fy ) G-j'(b-fy)/a j (13)

The torque in synchronous watts developed by the motor is

T==2(I2pRp-I2NRN) (W) (14)In addition to the torque Z double-stator- frequency torque pulsation is produced

in the single-phase induction motor. This pulsating torque is unavoidable in a

single-phase motor because of the pulsation in instanteneous power input inherent

in a single-phase circuit. It tend to make the motor noiser than a poly-phase

motor. Its peak value TV5ny7) is represented by

7V -= 21blxll>vlxlZi}-Ztsrl (VV) (is)

Let P be' the ratio of 7V to 7; then P may be called "pulsating torque factor".

p- 7v/Tx loo (%) a6)Input and output power and eficiency of the motor can be written as follows

#..-'=#,-t,;.se E,:M,,} ,,,,

Characteristics of Condenser･excited SingiePhase induction Mbtor 79

where e is phase difference between Vin and 1in.

3. Experimental results

Motor employed for the tests is a condenser start single-phase induction

motor. Its specifications and circuit constants are indicated in Table 1. A torque-

meter serves as the motor load.

Table 1 Specifications and circuit constants of condenser start singie-phase induction motor

Specifications

Voltage 1oo (V)'frequency 60150 (Hz)

No. of poles 4 Circuit constants in (2)

rotor referred to main winding

magnetizing reactance referred

main winding '

auxiliary winding

Effective turns ratio

output 2oo (W) speed 173011440 (rpra) Starting condenser 150 (ptF)

- r2 =2.84 x2 == 1.96to main winding xdi ==59.72

r.=1.97 x. = 1.96･ ra=9･75 Xa = 4.91"NhlAT].==a =1.59

Note; Value of reactances obtained on the frequency 60 (Hz)

3-1.No-load tests The slip of motor at no-load running is nearly equals to

O.O05. The circle diagrams of the positive- and negative-phase sequence currents

4), 1>v at slip s=O.O05, frequencyf =60(th) and Vin=100( V), are shown in Fig. 3.

In this figure 1le)(15) and I>v(15), Iin(15) and 4(15) indicate the positive- and

negative-phase sequence currents, main and auxiliary winding currents at C=15(ptF);

1))(O), 11v(O) and 1;.(O) indicate the currents of ordinary single-phase motor which has

no exciting condenser i.e. C=O. Phase difference angle between Iin(15) and 4(15)

equals to 72 deg.. After this, number in the parentheses of current, input a,

torque pulsation factor P etc. indicate the capacity of exciting condenser in ptE

The no-load running tests are carried out over the frequency range from 30(HIEr)

to 70 (H]z). The exprimental characteristics of lh, 4, R and power factor cosevs.C

at Vin==100(V),f=60(lle), s=O.oo5 are shown in Fig. 4. As compared with values

of ordinary single-phase induction motor, 1in/L.(O), R/A(O), fl/P(O) vs. C charac-

teristics are shown in Fig. 5. In this figure, I;./L.(O) and R/R(O) are indicated

experimental results, P/P(O) are indicated the theoretical values because of the

pulsating torques were not measured in these tests. This pulsating torque tend

to make the motor noisier than a poly-phase motor, can be minimized by use of

the exciting condenser for the motor. Optimum no-load running can be obtained at

minimum input and minimum pulsating torque.

From Fig. 5, it is readily seen that (1) no-load input i.e. no-load loss and pulsat-

ing torque factor are minimum at C=t15(pt"F), i.e. optimum no-load running is

obtained at this point; (2) in optimum operation, no-load current, loss and pulsating

80 T. IsHizAKi, T. FuJii, S. IsmKAwA and T. HiRAsA

torque factor decrease by 40, 33 and 72 percent, respectively, compared

ordinary single-phase motor operation; (3)I}. is minimum at C=t30(ptF), the

mized current Iin.i. decrease 73 percent.

with

mini-

o ･k oN

Ia (15)Vm

l. (1 5)'ala (15)

oi

civcdSe

Xg

l.(ls)

o,

I,(O)=I,(O)

f =60(Hz)

Vm ==1oo (V)

s=O.O05

Im (15)

Im(O)

Fig. 3 Circle diagrams of the positive and negative-phase sequence currents.

Characteristics of Condenser-excited Single-Phase induction Mbtor 81

3PO

200･A}

ac

loe

p

:.

-e

B

H

5

4

3

2

1

o

lag -"- "･ lead

f=oo(Hz)

V.t=100(V)

s=O,O05

sseto

p

l , t E l 1 I i l l 1 i l 1 l ' ,,lN" t

l 9'N

E 1

' l t 1 l l

1.0

O.8

O,6

O.4

O.2

,r;,,

Pi

o

as

8v

: main

: input

Fig.

O lo 2o 3e 4o sc C ("F)

winding current Ib: auxiliary winding current

power cose: power factpr4 No-load characteristics Iin, lb, Pi and cos e vs. C.

n

cr

Hi

250

2oo

sV 150eq

sar･

e:H

100

50

o.

g)i!(!Al

)(5ii"

2xk5{-

Fig. 5

'

o

No-load

le 2o C 'CptF) }

P: torque pulsation

P(O): va!ue of P at

incharacteristics 1in(O) ･

30

factor

c=o ,F)lr

p)(o) and

40

p vs. C.p(o)

82 T. IsHizAKi, T, FuJu, S. IsHIKAwA and T. HiRAsA

3-2. Simplified equation to determine optimum value of condenser The

optimum value of condenser in which the negative-phase sequence current I)v is

minimized, is determined by the condition the dl)v/dC=O. This calculation gives

trouble. For simplicity, r., x., r., x. and x2 are neglected compare with r2/s,

becouse of sc tO at no-load running of the motor. Optimum condenser Cop is given

11 COPf ta2ox¢ = 4z2aaf21di (pe F) (18)

where ldi==xab/2of is a magnetizing inductance.

The value of condenser at minimum main winding current denoted as C.i

' CmiN- 2.2alaf21¢ ==2Cbp (ptF) (19)

'75

:.

4

3

6:E 2

･gHE I

,50

as

go

25

N

N

N Vmx

Nx ×

N x3 lm mtn XXxN

--N N

%. rQ)

N "N ...NC N ..}N-N N

--)

1oo

s v50 E >

oo 30 40 50 60･ 70 f (Hz)

Fig. 6 Frequency characteristics at no-load Cop and lh,min vs. f:

Eq. (19) is verified by no-load test as shown in Fig. 4, 5.

Frequency characteristics of Cop and L..i. are shown in Fig. 6. In this test,

the supplied valtage V]. of the motor are regulated to be nearly proportional to

the frequency of power source for maintained the constant field flux i.e. constant

exciting current Iin(O) at f<50(th), and equals to the rated valtage 100( V) at f:}ir50

(Hiz) as shown in Fig. 6. Experimental curves for Cbp and L..in are indicated by the

solid lines, and the theoretical values by the dotted lines. Fairy agreement between

the experimental and theoretical curves is seen from Fig. 6. No-load tests verified

eqs. (18) and (19).

3-3. Load tests The load tests at rated speed i.e. rated 'slip are carried out

over the frequency range from 30(lle) to 70(H]i). The experimental characteristics

Characteristics of Condenser-excited Single-Phase lnduction Mbtor 83

of I., I., output 1b and eMciency qvs. C at V;.-100(V), f==50(th), SetO.04 i.e.

speed 1440(rPnz) are shown in Fig. 7. It is seen that optimum and minimum

current running can be obtained at C=t20 (pt17) and Cor40 (ptF), respectively. Fig. 8

shows characteristics of op and I;. at V;.=100(V>, f=50(th) n==1440(rpm), where

op (20) and I. (20) represent values of n and Ili, at optimum running; v(40), lh(40)

and op (O), I. (O) represent the values at minimum current and ordinary single phase

5

4 rm se 250 ny

200 :t3 ' p 60 n f=5[}(Hz) ge )..e v "l50 V.==loo(v) t2 40' - s=o,e4 " aO 1oo Xo

1 20 se

oo o o lo 2e .3o 4o so C (" F)

Fig. 7 Load characteristics I., I., Po and n vs. C.

running, respectively. It can be seen, from Fig. 8, that n(20) is larger than n(O),

ny (40) is smaller than op (O) at power range from no-load to 25 percent over load.

I./I.(O), n/q(O), jPb/,Pb(O), P/P(O) vs. C characteristics are shown in Fig. 9, for

compared the values gf ordinary single-phase motor with ones of condenser-excited

60

Rv 40

"

20

,o

5

4

?LV

3

s

2

1

I.<O)

1.CZO>

n (ISS> n kO>

x.kNS)

f==50(Hz)

V.-100(V)

s ==O.04

1 (4e)

o

Fig. 8

50

Load

loo lso 2ee " (W)characteristics l. and op vs. Po.

･250

t

84 T. IsHizAKi, T. FuJn, S. IsHiKAwA and T. HiRAsA

, 'Ff=oo(Hz) 140 Vm==100(V) s=O,on

120 ' 9 Po v Pe(O) 6 t,lg loo 6- 't' ' eql9 jeq 'ik2'.so ')2})' e,s,

Fr6 -l:'

60

O lo 2o 3e 4o ' C(# F) .e`"' Fig.9 Load characteristics tlli/io), p:(Oo), -p-eo) and op(opo) vs･ C･

motor at rated speed 1730(ilPm) i.e. f-60(Ile). In that figure, P/P(O) are indicated

theoretical values, and others are experimental ones. From Fig. 9, it is seen that

current Ih(15) and pulsating torque factor B(15) at optimum full load running

decreased by 10 and 30 percent than I(O) and n(O) respectively; Pb(15) and op(15)

increase 10 and 12 percent than R)(O) and n(O).

Frequency characteristics of full load running are shown in Fig. 10. In these

' 60I . 300 ' Vm leo

1io nias

v.'co> 40 75 20U 1oo o % L. 5. 50' .i.(o) - U A . nm-S > Im min ,2o V n<O) ' 50 .100 "

4

"3s-. 2

1･

o

Fig.

25

o･

laop

10

30 ,40, 50 460 .f {Ht)

(a)Freqnency characteristics at

nmax and op(O) vs. f:

o.70

s=O.04 (a) Cop,

to

inmin

e

30

and Gop

40

f

vs. L

50

(Hz)

(b)

60

Pbmax,

70

Pb(O),

Characteristics of Condenser･excited Single-Phase lnduction Mbtor 85

tests as well as no-load frequency tests, the supplied voltage Vin of the motor are

regulated to be nearly proportional to the frequency of power source at f<50(th)

and equal to the rated voltage 100(V) at f}i50(Ile) and the slip is kept the rated

value O.04. Cop, l.(O), I..in and I},op vs. f characteristics are shown in Fig. 10(a),

where I.op indicate the auxiliary winding current at optimum running. Pbmax,

Ib(O), op... and n(O) are shown in Fig. 10(b), it is readily seen that high output

power and high ethciency at small main input current of motor can be obtained by

the use of exciting condenser. Full load tests as well as no-load tests verified the

following relation

Copf21¢t tle

Discussion of frequency characteristics and torque pulsation are omitted in

this paper, it will be reported later publication.

4. Conclusion

The running characteristics of condenser-excited single-phase induction motor

vary with exciting condenser which is connect to auxiliary winding. Optimum

running motor can be obtained at minimized negative-phase sequence current.

The optimum value Cop of exciting condenser, in which optimum characteristics

can be obtained, is represented by eq. (18) i.e.

Cop yle/(f21th)

The theoritical calculations and experimental tests carried out over frequency

ranges from 30(th) to 70(Ile), verified this relation.

In optimum no-load running of the sample motor at rated frequency, source

current, loss and pulsation torque factor decrease by '40, 33 and 72 percent, respec-

tively, as compared with values of ordinary single-phase operation in which motor

has no exciting condenser.

In optimum full-load running at rated frequency, it is shown that source current

and pulsating torque factor decrease by 10 and 30 percent; output power and

eMciency are increased by 10 and 12 percent as compared with values of ordinary

single-phase operation.

The speed of condenser-excited motor can be controlled more smoothly, silently

and eMciently than ordinary single-phase motor. Use of exciting condenser for

single-phase induction motor in the speed control systems is suggested in this

paper.

References

1) S. Ishikawa, A. !chiriki, M. Okita and T. Ishizaki, Lecture 2a-18 in Annual Meating of Kansai

Branch of LE.E. of Japan, (November 1967). 2) K. Taniguchi, T. Fujii and T. Ishizaki, Lecture 3-14 in Annual Meating of Kansai Branch of

E.I.E. of Japan, (November 1968).

86 T. rsHlzAK!, T. Fum, S. IsHIKAwA and T. HIRASA

3)4)5)6)

7)

T. Hasumi. OHM, 37, 13 (1950).S. Miyairi. J.I.E.E. of Japan, 74, 31 (1954).

J. Kibe, S. Mito and K. Kamimura, J.I.E.E. of

A. Morishita, J. Kataoka, H. Watanabe and S.

of Japan, (March 1969).

T. Yokozuka, E. Baba, M. Ohki and Y. Koztt,Japan, (April 1970).

Japan, 82, 190 (1962).

Okuda, Lecture 559 in Annual Meating of LE.E.

Lecture 518 in Annual Meating of I.E.E. of

/