Abstract: In this paper a static switched capacitor with an auxiliary three-phase stator winding, which is only magnetically coupled to the stator main winding, is explored for improving the starting and operating power factor of a three-phase induction motor. The scheme improves the power factor of the motor without compromising significantly on other performances. Important advantages of the scheme include preventing harmonics in the line current, and eliminating regeneration possibility as well as preventing high inrush currents at starting

Jimoh, A. A.

Nicolae, Dan-Valentin

English

University of Johannesburg Institutional Repository

Performance Analysis of a Three-Phase Induction Motor with Capacitance Injection A.A. Jimoh, member IEEE and D.V. Nicolae, member IEEE Department of Electrical Engineering, Tshwane University of Technology Private Bag X07, 0116 Pretoria North, South Africa jimohaa@tut.ac.za danaurel@yebo.co.zaAbstract — In this paper a static switched capacitor with an auxiliary three-phase stator winding, which is only magnetically coupled to the stator main winding, is explored for improving the starting and operating power factor of a three-phase induction motor. The scheme improves the power factor of the motor without compromising significantly on other performances. Important advantages of the scheme include preventing harmonics in the line current, and eliminating regeneration possibility as well as preventing high inrush currents at starting.  Index Terms — Three-phase machines, Induction motors, Reactive compensation, Power factor correction.  I. INTRODUCTION Generally, an induction machine requires reactive power for operation. Thus its power factor is inherently poor, and it is worse especially at starting and when running with light loads.  The power factor of an induction machine has been observed to be poor also when operating with power electronics converter. At starting the input power to an induction motor is mainly reactive. It draws 6-10 times its rated current at about 0.2 power factor, and takes a second or so to come to speed, where the power factor significantly improves to above 0.6, depending on the load. This initial high current at a poor power factor normally affects the loads nearby and limits the application range of the machine. A motor with a high start-stop operation, in addition to being a nuisance to the surrounding loads, will have an overall poor power factor performance. To improve the power factor of induction machine requires a means of reactive power compensation. Several techniques, which have been suggested for achieving this, include [1] synchronous compensation, fixed capacitors, fixed capacitor with switched inductor, solid-state power factor controller, and switched capacitors. Most of these techniques suffer certain drawback or another. The synchronous compensation technique is complex and not cost effective. Other techniques incorporate directly the connection of capacitors, which lead to the problems of voltage regeneration and over-voltages, and very high inrush current during starting. Techniques incorporating controlled switches in the stator winding circuit generate large harmonic currents in the machine and in the line. A variety of stator winding configurations incorporating capacitors have also been proposed [2].  Most of these configurations introduce asymmetry problems in the machine.  The static switch capacitor has also been used for single-phase induction motors [3-5] with inconclusive results. II. PROPOSED MODEL In this paper a method is proposed which overcomes most of the drawbacks noted above. The method makes use of two three-phase windings on the stator. One set, the main winding, is connected in star to the source. The other set is in delta configuration and has the SSC connected to it as shown in Fig. 1. It is only magnetically coupled to the main winding. All windings have the same shape and pitch, but may have different turn numbers and wire sizes; usually smaller in order to be accommodated in the slots together with the stator. The windings are arranged in slots such that there is no phase shift between the two windings.  Fig. 1: The high power factor three phase induction machine  The static switching is such that only the required level of reactive compensation is allowed. A SSC is Lb???? ???VaVbVcABCWaWbWcSaLaCaCbCcScLcconnected in parallel to each phase of the delta winding so as to prevent high inrush of currents during switching. The fact that the capacitor circuit is only magnetically coupled to the main winding eliminates the injection of harmonics into the system.  After delta-star transformation of the auxiliary windings and based on transformer approach of the induction motor, the electric model per phase of the proposed machine is shown in Fig. 2. The couplings between the elements of the machine are presented as ideal transformers with ka: the turn’s ratio between auxiliary winding and stator (ka < 1), kr: the turn’s ratio between rotor and stator (kr < 1) and kra: the turn’s ratio between rotor and auxiliary winding (kra <1).   Fig. 2 Per-phase model The elements from the Fig. 2 are: rs – stator series resistance Xs – stator leakage reactance rr – rotor resistance  Xr – rotor leakage reactance  ra – auxiliary winding resistance  Xa – rotor leakage reactance  s – the slip Xc – capacitive reactance  Xlc – very small inductive reactance for di/dt thyristor  protection III. SIMULATION MODEL It is going to be further proven that the capacitive reactance introduced in the circuit via the thyristor switch improves the power factor of the motor. In this regard a simulation model has been built. The simulation model (see Fig. 3) has been built using Matlab-Power System Block Set. It is closely following the electric model from Fig. 2. The parameters of a 4 kW induction motor have been used for validation of the proposed model.   The key element in this model is the variable resistor of the rotor which depends upon the slip; the simulation block has been performed in the same way as the principle of variable inductor from the demo library. The variation of the slip – the second important simulation parameter has been realized using a repeating sequence generator which varies from 1 (corresponding to the initial starting moment) to the respective value for a given torque.   	    	 	 0Ia rms Iar tRr/s sXrXc Sw PF2 2P/ P +QXlVaV IP QFig. 3 Simulation model  In order to find the torque – speed/slip variation, a set of simulations have been done using the default 4 kW induction motor – four poles model supplied from a 380 V / 50 Hz three-phase source with 100 kVA short-circuit level and X/R = 7. By giving different values for torque (Tm) the other parameters of the motor have been deducted as presented in the Table I. TABLE I 4 KVA INDUCTION MOTOR PARAMETERS Tm(N.m) Isa (A) n(rpm) s PF 0 3.84  1498.7  0.00087  0.06 1 3.85  1496.2  0.00253  0.12 5 4.1  1485.6  0.0096  0.36 10  4.72  1471.7  0.01887  0.58 15  5.63  1457.2  0.02853  0.717 18  6.35  1448  0.03467  0.772 A. Steady state parameters  Fig. 4 shows the steady state parameters of the motor for 1 N.m torque and C = 60 µF and Fig. 5 same parameters for C = 100 µF.  rs jXs ra jXa1: kaIa1: kr1: kra jXrrr / s-jXlc jXlVaFig. 4 Steady state parameters for C = 60 µF  Fig. 5 Steady state parameters for C = 100 µF  As can be noticed from the above figures, the capacitance improves the power factor. An optimum value for the injection capacitance has been considered the value which produces a power factor of approximately 0.95 lagging. If a perfect unity power factor is considered, then any variation of the electrical, mechanical or thermal parameters could produce a leading power factor which will increase significantly the current drawn. B. Minimum capacitance determination  Next set of simulation has been performed to determine the value of the compensating capacitor when the motor naturally runs at “high power factor” for a torque of 18 N.m. The “slip generator” has been set to produce a variation between 1 and 0.03467 with duration of 0.3 sec. Then the capacitor has been varied until the power factor came, lagging, close to unity. The results are presented in the Table II and the optimum value should be 40 µF.  TABLE II POWER FACTOR VERSUS COMPENSATING CAPACITOR MINIMUM VALUE DETERMINATION C(µF)  0 10  20  30  40  50  60 Isa (A)  6.35  6.42  6.62  6.95  7.44  8.1  8.92 PF  0.77  0.82  0.87  0.92  0.95  0.97  0.99 C. Maximum capacitance determination  In the previous set of simulations a “high” slip with a “high” power factor (PF) has been taken and the capacitance C had been increased for power factor improvement while the firing angle was zero. Table III presents the power factor as a function of the compensating capacitor for a 1 N.m torque; the “slip generator” has been set to produce a variation between 1 and 0.00253 with duration of 0.2 sec. When the capacitor has been increased above 120 µF, the power factor became leading and the current in steady state increased above inrush current. Thus, the optimum value for the capacitor is 100 µF.  TABLE III POWER FACTOR VERSUS COMPENSATING CAPACITOR MAXIMUM VALUE DETERMINATION C(µF)  0 20  40  60  80  100  120 Isa (A)  2.25  2.05  1.78  1.62  2.05  3.85  4.9 PF  0.13  0.19  0.33  0.61  0.91  0.96  0.99 D. Starting current  To validate the reduction of the starting current, the torque has been set for 18 N.m which means s = 0.0347, the starting time 0.3 sec and compensating capacitor C = 50 µF. The result is shown in Fig. 6 and, as can be noticed, the over-current is about 15 percentages higher.   Fig. 6 Starting current  E. Capacitor switching   From the above simulations, it results that the value of the compensating capacitor should be between 40 and 100 µF.  The next step into validation of the proposed model was to determine the effect of the switching of the capacitor upon the parameters of the motor. For          !Time (sec)Relativeamplitude(V,A) isa (t) * 10vsa (t)PF * 100         !Time (sec) Relativeamplitude(V,A)isa (t) * 10 vsa (t) PF * 100      ! " #  Phasecurrent(A)Time (sec) this purpose, C has been split in two parallel capacitors: a fixed value of 40 µF and a 60 µF in series with the switch. Then, the torque was at 1 N.m and the firing angle (Q) has been adjusted between 00(corresponding to 1 msec) to 1620 (corresponding to 9 msec). The results are presented in the Table VII.  TABLE IV POWER FACTOR VERSUS FIRING ANGLE Q(0) 0 36  54 72  90 108  126  144  162 Isa(A)  3.85  3.8  5.2  3.32  2.51  4.8  1.87  1.76  1.82 PF  0.96  0.95  0.68  0.88  0.8  0.46  0.68  0.51  0.49 Fig. 7 shows the power factor variation versus firing angle.  Fig. 7 Power factor versus firing angle IV. SWITCHING INFLUENCE As presented above the variation of the firing angle produced the variation of the equivalent capacitor and consequently the power factor could be adjusted which is the main purpose of this proposed model. It also can be observed that the lumped parameters model has a smooth variation of the power factor versus firing angle while the model based on linear transformer has a very non-linear variation. This fact can be explained due to the complexity of the model which implies some resonances; this is also followed by the drawn current. One other aspect to be mentioned is the level of distortions introduced by the switching into the supply current. For exemplification, the firing angle of 900has been chosen. Fig. 8 shows that the shape of the supply (isa) current is not affected much and the harmonics content is quit small (see Fig. 9), while the current through the switch (icsw) displays relative high distortions. This, as stated in the introduction is due to inductive coupling between auxiliary winding and the stator.  Fig. 8 Supply and switched capacitor currents  Fig. 9 Supply current: harmonic content  At a closer look, the main component which affects the distortions of the supply current is the third harmonic that is very much diminished when one considers the three-phase model.  V. EXPERIMENTAL RESULTS In order to practically validate the proposed model, a motor has been modified by adding the auxiliary windings. The same scheme of splitting the capacitor C in two: a fixed value of 40 µF and a 60 µF in series with the switch has been used. The mechanic load has been set for rated and the firing angle adjusted from 00 to 1800.The starting current has been observed for an unmodified motor (see Fig. 10) and for a modified motor (see Fig. 11). In both oscilloscope-graphs, the time-base was 0.5 sec/div and the vertical was 20 A/div. It is possible to notice the inrush current is very Firing angle (0)1.00.9 0.8 0.70.60.5 0 36 72 108 144 180 Powerfactor** ***** * *"# "# " " # # # #Time (sec) Relativeamplitude(V,A)vsa (t) icsw (t) isa (t)    ! #     ! #   $%&' "Frequency (Hz) Phasecurrent(A)much reduced for the modified motor while the steady state is a little bit higher.  Fig. 10 Unmodified motor: starting current  Fig. 11 Modified motor: starting current  The results of measuring the motor are presented in the Table V. Parameters Va and Ia are the voltage and current per phase. The motor has been loaded with 50 % of the nominal torque.  TABLE V MEASURED PARAMETERS Q(0) 0 36  72  108  144  180 Va(V)  220  220  220  220  220  220 Ia(A)  1.61  1.65  1.75  1.96  1.84  1.86 P(W)  891  875  839  818  787  764 S(VA)  1061  1093  1156  1297  1215  1232 The power factor and active power per phase have been observed and the results are presented in Fig. 12 and 13 respectively. It is to be noticed the same very non-linear variation of the power factor versus firing angle. But the active power drawn from the supply it is a little bit higher due to the extra current flowing through auxiliary winding.  Fig. 12 Power factor versus firing angle; experimental results  Fig. 13 Active power versus firing angle: experimental results  It has been also of interest the influence of the switching upon the curve torque versus load; the results are presented in Fig.14; the influence of the switching is very small.  Fig.14 Curves torque versus loading for various angle  2 &. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... .. .. .............................................. ........................................................................................................................................................................................... . . . . . . .1) [scopedan] .C H2   20  A     0 .5  s2&. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... .. .. .............................................. ........................................................................................................................................................................................... . . . . . . .1) [ sco pedan] .CH2   20  A     0 .5  sFiring angle (0)0.850.800.750.700.650.600 36 72 108 144 180**** *** * * *Powerfactor1.2 1.1 1.0 0 36 72 108 144 180 Activepower(pu)***** * *** *Firing angle (0)(*+,  ST??????????STSTSSSSSSTTTTTTTS?STQ ' Q ' "Q '   #)!) ))#)!) ))()*-VI. CONCLUSIONS In this paper, a three-phase induction motor with an auxiliary three-phase stator winding, which is only magnetically coupled to the stator main winding and capacitance injection is explored for improving the starting current and operating power factor. The scheme improves the power factor and starting current while keeping a low level of distortion of the supply current. The efficiency of this new motor is not satisfactory yet and future research should be done to optimize it. Also experimentations of the proposed modification on various ranges of power should be done.  REFERENCES [1] M.A. El-Sharkawi, S.S. Venkata, T.J. Williams, and N.G. Butler, “An Adaptive Power Factor Controller for Three-Phase Induction Generators”, Paper 84 SM 672-2 presented at the IEEE/PES 1984 Summer Meeting, Seattle, Washington, July 15-20 1984. [2] Wu Hanguang, Chen Xiumin, Lu Xianliang, and You Linjuan, “An Investigation on Three-phase Capacitor Induction Motor”, Proceedings of the Third Chinese International Conference on Electrical Machines, August 29-31, 1999, Xi’an, China, pp. 87-90. [3] T.A. Lattemer, D.W. Novotni and T.A. Lipo, “Single-Phase Induction Motor with an Electronically controlled Capacitor”, IEEE Transaction on Industry Applications, Vol. 27, No.1, Jan./Feb., 1991, pp. 38-43 [4] E.I. Panov, H.L. Patev, G.S. Donev, T.T. Gatev and V.P. Ivanova, “Research into a class of reactive one-port with controlled parameters”, Proceedings of National Conference “Electronic Technologies”, Sozopol, Bulgaria, 1995 [5] J. Faiz and M. Tarafdar-Haque, “Minimization of starting time and improvement of performance of a capacitor-run single-phase induction motor”, Proceedings of ELMA Conference,Varna, Bulgaria, 1993, pp. 147-152  

Performance analysis of a three-phase induction motor with capacitance injection

Jimoh, A.A.

Nicolae, D.V.

Name not available

Performance Analysis of a Three-Phase 
Induction Motor with Capacitance Injection 
A.A. Jimoh, member IEEE and D.V. Nicolae, member IEEE 
Department of Electrical Engineering, Tshwane University of Technology 
Private Bag X07, 0116 Pretoria North, South Africa 
jimohaa@tut.ac.za danaurel@yebo.co.za
Abstract — In this paper a static switched capacitor with 
an auxiliary three-phase stator winding, which is only 
magnetically coupled to the stator main winding, is 
explored for improving the starting and operating power 
factor of a three-phase induction motor. The scheme 
improves the power factor of the motor without 
compromising significantly on other performances. 
Important advantages of the scheme include preventing 
harmonics in the line current, and eliminating 
regeneration possibility as well as preventing high 
inrush currents at starting.  
Index Terms — Three-phase machines, Induction 
motors, Reactive compensation, Power factor correction. 
 
I. INTRODUCTION 
Generally, an induction machine requires reactive 
power for operation. Thus its power factor is 
inherently poor, and it is worse especially at starting 
and when running with light loads.  The power factor 
of an induction machine has been observed to be poor 
also when operating with power electronics converter. 
At starting the input power to an induction motor 
is mainly reactive. It draws 6-10 times its rated 
current at about 0.2 power factor, and takes a second 
or so to come to speed, where the power factor 
significantly improves to above 0.6, depending on the 
load. This initial high current at a poor power factor 
normally affects the loads nearby and limits the 
application range of the machine. A motor with a high 
start-stop operation, in addition to being a nuisance to 
the surrounding loads, will have an overall poor 
power factor performance. 
To improve the power factor of induction machine 
requires a means of reactive power compensation. 
Several techniques, which have been suggested for 
achieving this, include [1] synchronous compensation, 
fixed capacitors, fixed capacitor with switched 
inductor, solid-state power factor controller, and 
switched capacitors. Most of these techniques suffer 
certain drawback or another. The synchronous 
compensation technique is complex and not cost 
effective. Other techniques incorporate directly the 
connection of capacitors, which lead to the problems 
of voltage regeneration and over-voltages, and very 
high inrush current during starting. Techniques 
incorporating controlled switches in the stator 
winding circuit generate large harmonic currents in 
the machine and in the line. A variety of stator 
winding configurations incorporating capacitors have 
also been proposed [2].  Most of these configurations 
introduce asymmetry problems in the machine.  
The static switch capacitor has also been used for 
single-phase induction motors [3-5] with inconclusive 
results. 
II. PROPOSED MODEL 
In this paper a method is proposed which 
overcomes most of the drawbacks noted above. The 
method makes use of two three-phase windings on the 
stator. One set, the main winding, is connected in star 
to the source. The other set is in delta configuration 
and has the SSC connected to it as shown in Fig. 1. It 
is only magnetically coupled to the main winding. All 
windings have the same shape and pitch, but may 
have different turn numbers and wire sizes; usually 
smaller in order to be accommodated in the slots 
together with the stator. The windings are arranged in 
slots such that there is no phase shift between the two 
windings. 
 
Fig. 1: The high power factor three phase induction machine 
 
The static switching is such that only the required 
level of reactive compensation is allowed. A SSC is 
Lb
?
?
?
? ?
?
?
Va
VbVc
A
BC
Wa
Wb
Wc
Sa
La
Ca
Cb
Cc
Sc
Lc
connected in parallel to each phase of the delta 
winding so as to prevent high inrush of currents 
during switching. The fact that the capacitor circuit is 
only magnetically coupled to the main winding 
eliminates the injection of harmonics into the system.  
After delta-star transformation of the auxiliary 
windings and based on transformer approach of the 
induction motor, the electric model per phase of the 
proposed machine is shown in Fig. 2. The couplings 
between the elements of the machine are presented as 
ideal transformers with ka: the turn’s ratio between 
auxiliary winding and stator (ka < 1), kr: the turn’s 
ratio between rotor and stator (kr < 1) and kra: the 
turn’s ratio between rotor and auxiliary winding (kra <
1).  
 
Fig. 2 Per-phase model 
The elements from the Fig. 2 are: 
rs – stator series resistance 
Xs – stator leakage reactance 
rr – rotor resistance  
Xr – rotor leakage reactance  
ra – auxiliary winding resistance  
Xa – rotor leakage reactance  
s – the slip 
Xc – capacitive reactance  
Xlc – very small inductive reactance for di/dt thyristor 
 protection 
III. SIMULATION MODEL 
It is going to be further proven that the capacitive 
reactance introduced in the circuit via the thyristor 
switch improves the power factor of the motor. In this 
regard a simulation model has been built. 
The simulation model (see Fig. 3) has been built 
using Matlab-Power System Block Set. It is closely 
following the electric model from Fig. 2. The 
parameters of a 4 kW induction motor have been used 
for validation of the proposed model.  
 The key element in this model is the variable 
resistor of the rotor which depends upon the slip; the 
simulation block has been performed in the same way 
as the principle of variable inductor from the demo 
library. The variation of the slip – the second 
important simulation parameter has been realized 
using a repeating sequence generator which varies 
from 1 (corresponding to the initial starting moment) 
to the respective value for a given torque. 
 


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0
Ia rms Iar 
t
Rr/s 
sXr
Xc Sw 
PF2 2P/ P +Q
Xl
Va
V I
P Q
Fig. 3 Simulation model 
 
In order to find the torque – speed/slip variation, a 
set of simulations have been done using the default 4 
kW induction motor – four poles model supplied from 
a 380 V / 50 Hz three-phase source with 100 kVA 
short-circuit level and X/R = 7. By giving different 
values for torque (Tm) the other parameters of the 
motor have been deducted as presented in the Table I. 
TABLE I 
4 KVA INDUCTION MOTOR PARAMETERS 
Tm
(N.m) 
Isa 
(A) 
n
(rpm) 
s PF 
0 3.84 
 
1498.7 
 
0.00087 
 
0.06 
1 3.85 
 
1496.2 
 
0.00253 
 
0.12 
5 4.1 
 
1485.6 
 
0.0096 
 
0.36 
10 
 
4.72 
 
1471.7 
 
0.01887 
 
0.58 
15 
 
5.63 
 
1457.2 
 
0.02853 
 
0.717 
18 
 
6.35 
 
1448 
 
0.03467 
 
0.772 
A. Steady state parameters 
 Fig. 4 shows the steady state parameters of the 
motor for 1 N.m torque and C = 60 µF and Fig. 5 
same parameters for C = 100 µF. 
 
rs jXs ra jXa1: kaIa
1: kr
1: kra jXr
rr / s
-jXlc 
jXl
Va
Fig. 4 Steady state parameters for C = 60 µF 
 
Fig. 5 Steady state parameters for C = 100 µF 
 
As can be noticed from the above figures, the 
capacitance improves the power factor. 
An optimum value for the injection capacitance 
has been considered the value which produces a 
power factor of approximately 0.95 lagging. If a 
perfect unity power factor is considered, then any 
variation of the electrical, mechanical or thermal 
parameters could produce a leading power factor 
which will increase significantly the current drawn. 
B. Minimum capacitance determination  
Next set of simulation has been performed to 
determine the value of the compensating capacitor 
when the motor naturally runs at “high power factor” 
for a torque of 18 N.m. The “slip generator” has been 
set to produce a variation between 1 and 0.03467 with 
duration of 0.3 sec. Then the capacitor has been 
varied until the power factor came, lagging, close to 
unity. The results are presented in the Table II and the 
optimum value should be 40 µF. 
 
TABLE II 
POWER FACTOR VERSUS COMPENSATING CAPACITOR 
MINIMUM VALUE DETERMINATION 
C
(µF) 
 
0 10 
 
20 
 
30 
 
40 
 
50 
 
60 
Isa 
(A) 
 
6.35 
 
6.42 
 
6.62 
 
6.95 
 
7.44 
 
8.1 
 
8.92 
PF 
 
0.77 
 
0.82 
 
0.87 
 
0.92 
 
0.95 
 
0.97 
 
0.99 
C. Maximum capacitance determination 
 In the previous set of simulations a “high” slip 
with a “high” power factor (PF) has been taken and 
the capacitance C had been increased for power factor 
improvement while the firing angle was zero. Table 
III presents the power factor as a function of the 
compensating capacitor for a 1 N.m torque; the “slip 
generator” has been set to produce a variation 
between 1 and 0.00253 with duration of 0.2 sec. 
When the capacitor has been increased above 120 µF, 
the power factor became leading and the current in 
steady state increased above inrush current. Thus, the 
optimum value for the capacitor is 100 µF. 
 
TABLE III 
POWER FACTOR VERSUS COMPENSATING CAPACITOR 
MAXIMUM VALUE DETERMINATION 
C
(µF) 
 
0 20 
 
40 
 
60 
 
80 
 
100 
 
120 
Isa 
(A) 
 
2.25 
 
2.05 
 
1.78 
 
1.62 
 
2.05 
 
3.85 
 
4.9 
PF 
 
0.13 
 
0.19 
 
0.33 
 
0.61 
 
0.91 
 
0.96 
 
0.99 
D. Starting current  
To validate the reduction of the starting current, 
the torque has been set for 18 N.m which means s = 
0.0347, the starting time 0.3 sec and compensating 
capacitor C = 50 µF. The result is shown in Fig. 6 
and, as can be noticed, the over-current is about 15 
percentages higher.  
 
Fig. 6 Starting current 
 
E. Capacitor switching  
 From the above simulations, it results that the 
value of the compensating capacitor should be 
between 40 and 100 µF. 
 The next step into validation of the proposed 
model was to determine the effect of the switching of 
the capacitor upon the parameters of the motor. For 
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A) isa (t) * 10
vsa (t)
PF * 100
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Time (sec) 
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Time (sec) 
this purpose, C has been split in two parallel 
capacitors: a fixed value of 40 µF and a 60 µF in 
series with the switch. Then, the torque was at 1 N.m 
and the firing angle (Q) has been adjusted between 00
(corresponding to 1 msec) to 1620 (corresponding to 9 
msec). The results are presented in the Table VII. 
 
TABLE IV 
POWER FACTOR VERSUS FIRING ANGLE 
Q
(0) 0 36 
 
54 72 
 
90 108 
 
126 
 
144 
 
162 
Isa
(A) 
 
3.85 
 
3.8 
 
5.2 
 
3.32 
 
2.51 
 
4.8 
 
1.87 
 
1.76 
 
1.82 
PF 
 
0.96 
 
0.95 
 
0.68 
 
0.88 
 
0.8 
 
0.46 
 
0.68 
 
0.51 
 
0.49 
Fig. 7 shows the power factor variation versus 
firing angle. 
 
Fig. 7 Power factor versus firing angle 
IV. SWITCHING INFLUENCE 
As presented above the variation of the firing 
angle produced the variation of the equivalent 
capacitor and consequently the power factor could be 
adjusted which is the main purpose of this proposed 
model. It also can be observed that the lumped 
parameters model has a smooth variation of the power 
factor versus firing angle while the model based on 
linear transformer has a very non-linear variation. 
This fact can be explained due to the complexity of 
the model which implies some resonances; this is also 
followed by the drawn current. 
One other aspect to be mentioned is the level of 
distortions introduced by the switching into the supply 
current. For exemplification, the firing angle of 900
has been chosen. Fig. 8 shows that the shape of the 
supply (isa) current is not affected much and the 
harmonics content is quit small (see Fig. 9), while the 
current through the switch (icsw) displays relative high 
distortions. This, as stated in the introduction is due to 
inductive coupling between auxiliary winding and the 
stator. 
 
Fig. 8 Supply and switched capacitor currents 
 
Fig. 9 Supply current: harmonic content 
 
At a closer look, the main component which 
affects the distortions of the supply current is the third 
harmonic that is very much diminished when one 
considers the three-phase model. 
 
V. EXPERIMENTAL RESULTS 
In order to practically validate the proposed 
model, a motor has been modified by adding the 
auxiliary windings. The same scheme of splitting the 
capacitor C in two: a fixed value of 40 µF and a 60 µF 
in series with the switch has been used. The mechanic 
load has been set for rated and the firing angle 
adjusted from 00 to 1800.
The starting current has been observed for an 
unmodified motor (see Fig. 10) and for a modified 
motor (see Fig. 11). In both oscilloscope-graphs, the 
time-base was 0.5 sec/div and the vertical was 20 
A/div. It is possible to notice the inrush current is very 
Firing angle (0)
1.0
0.9 
0.8 
0.7
0.6
0.5 
0 36 72 108 144 180 
Po
we
rf
act
or
*
* *
*
*
*
* * *
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Time (sec) 
Re
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am
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vsa (t) 
icsw (t) 
isa (t) 
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Frequency (Hz) 
Ph
ase
cu
rre
nt
(A
)
much reduced for the modified motor while the steady 
state is a little bit higher. 
 
Fig. 10 Unmodified motor: starting current 
 
Fig. 11 Modified motor: starting current 
 
The results of measuring the motor are presented 
in the Table V. Parameters Va and Ia are the voltage 
and current per phase. The motor has been loaded 
with 50 % of the nominal torque. 
 
TABLE V 
MEASURED PARAMETERS 
Q(0) 0 36 
 
72 
 
108 
 
144 
 
180 
Va(V) 
 
220 
 
220 
 
220 
 
220 
 
220 
 
220 
Ia(A) 
 
1.61 
 
1.65 
 
1.75 
 
1.96 
 
1.84 
 
1.86 
P(W) 
 
891 
 
875 
 
839 
 
818 
 
787 
 
764 
S(VA) 
 
1061 
 
1093 
 
1156 
 
1297 
 
1215 
 
1232 
The power factor and active power per phase have 
been observed and the results are presented in Fig. 12 
and 13 respectively. It is to be noticed the same very 
non-linear variation of the power factor versus firing 
angle. But the active power drawn from the supply it 
is a little bit higher due to the extra current flowing 
through auxiliary winding. 
 
Fig. 12 Power factor versus firing angle; experimental results 
 
Fig. 13 Active power versus firing angle: experimental results 
 
It has been also of interest the influence of the 
switching upon the curve torque versus load; the 
results are presented in Fig.14; the influence of the 
switching is very small. 
 
Fig.14 Curves torque versus loading for various angle 
 
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VI. CONCLUSIONS 
In this paper, a three-phase induction motor with 
an auxiliary three-phase stator winding, which is only 
magnetically coupled to the stator main winding and 
capacitance injection is explored for improving the 
starting current and operating power factor. The 
scheme improves the power factor and starting current 
while keeping a low level of distortion of the supply 
current. 
The efficiency of this new motor is not 
satisfactory yet and future research should be done to 
optimize it. Also experimentations of the proposed 
modification on various ranges of power should be 
done.  
REFERENCES 
[1] M.A. El-Sharkawi, S.S. Venkata, T.J. Williams, and N.G. 
Butler, “An Adaptive Power Factor Controller for Three-Phase 
Induction Generators”, Paper 84 SM 672-2 presented at the 
IEEE/PES 1984 Summer Meeting, Seattle, Washington, July 15-
20 1984. 
[2] Wu Hanguang, Chen Xiumin, Lu Xianliang, and You Linjuan, 
“An Investigation on Three-phase Capacitor Induction Motor”, 
Proceedings of the Third Chinese International Conference on 
Electrical Machines, August 29-31, 1999, Xi’an, China, pp. 87-
90. 
[3] T.A. Lattemer, D.W. Novotni and T.A. Lipo, “Single-Phase 
Induction Motor with an Electronically controlled Capacitor”, 
IEEE Transaction on Industry Applications, Vol. 27, No.1, 
Jan./Feb., 1991, pp. 38-43 
[4] E.I. Panov, H.L. Patev, G.S. Donev, T.T. Gatev and V.P. 
Ivanova, “Research into a class of reactive one-port with 
controlled parameters”, Proceedings of National Conference 
“Electronic Technologies”, Sozopol, Bulgaria, 1995 
[5] J. Faiz and M. Tarafdar-Haque, “Minimization of starting time 
and improvement of performance of a capacitor-run single-
phase induction motor”, Proceedings of ELMA Conference,
Varna, Bulgaria, 1993, pp. 147-152 
 


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Performance analysis of a three-phase induction motor with capacitance injection

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