Download Three-Phase Induction Motor Operating from Single

Electric Power Systems Research 73 (2005) 121–128
Three-phase induction motor operating from single-phase
supply with an electronically controlled capacitor
Nabil A. Ahmed
Department of Electrical and Electronics Engineering, Assiut University, Assiut 71516, Egypt
Received 27 October 2003; received in revised form 26 May 2004; accepted 20 June 2004
Available online 25 September 2004
Abstract
In this paper the performance of a three-phase induction motor operating from single-phase supply with a new electronically controlled
capacitor using an electronic switch in series with a fixed capacitor to achieve a minimum unbalance of the motor phase voltages at all
loading conditions is proposed. No mechanical or centrifugal switch is used here. Basic system operation, theoretical analysis, simulated and
experimental results in comparison with conventional operation using one and two fixed capacitors are presented in this paper. The optimum
effective capacitor value can be on-line adjusted at any operating speed by periodically changing the duty cycle of the controlled switch to
achieve minimum unbalance in phase voltages to improve the motor performance at different speeds.
© 2004 Elsevier B.V. All rights reserved.
Keywords: Controlled capacitor; Duty cycle; Induction motor; Minimum unbalance
1. Introduction
The three-phase supply system in now available worldwide, except perhaps in some rural areas where only a singlephase supply is available. Single-phase motors are the most
common form in the lower horse-power ranges, but they
become uneconomical for ratings above about 0.5 kW and
therefore an increasing tendency to use standard three-phase
motors supplied from single-phase supply if the three-phase
supply is not available [1–3]. In many applications it may be
become necessary to use three-phase induction motor on a
single-phase supply system. For example, it has been found
technically and economically advantageous to install initially
a single wire earth return (SWER) system for rural electrification in remote and hilly regions. As the load demand increases, the SWER system can be converted to regular threephase power system. Irrigation pump sets, which often form
the major load on the system, may use either a single-phase
or a three-phase motor with a capacitor phase converter, the
latter having the advantages that it can be used directly when
E-mail address: [email protected].
0378-7796/$ – see front matter © 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.epsr.2004.06.007
the three-phase supply is installed later. Another example is
the portable pump sets which must operate with three- or
single-phase supply depending on what is available at the
site [4].
It is well known that when an three-phase induction motor is connected to a single-phase supply system, no starting torque is developed unless the motor has some form of
a poly-phase primary winding in which poly-phase voltages
are induced. This form can be achieved by connecting a phase
capacitor in series with one of the motor phases. The function
of the capacitor is to generate a leading phase so that the motor operates as a near balanced two-phase machine. For this
reason, the capacitor value must be carefully chosen according to the motor impedance. Unfortunately, this impedance
changes dramatically from starting to running. The problems
incurred in this aspect are essentially those of selecting the
value of the capacitor to give satisfactory starting and running
performance.
Many papers have proposed different control techniques
to improve the performance of three-phase induction motor
operating from single-phase supply and well documented in
the literature [3–9]. These papers conclude that the overall
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N.A. Ahmed / Electric Power Systems Research 73 (2005) 121–128
rating of a three-phase motor operating with single-phase
supply, with proper choice of the capacitor phase converter,
could be as high as 70% of a balanced rating three-phase
motor for the same frame size. This makes the three-phase
motor almost as good as a well designed single-phase motor.
Further, the three-phase motor is cheaper than single-phase
motor.
There are many different criteria are used to optimize the
capacitor size such as minimum unbalance of the phase voltages, power factor, input power, efficiency, torque or the input
current to give satisfactory operation of the motor [4,7,9,14].
This paper uses the criteria of minimum unbalance of the
phase voltages at all motor speeds. It can be shown that ideally
the capacitor should be varied continuously with the speed
of the machine, but in practice the choice is limited to two
set capacitor values, as in the case of split-phase motors, one
is used for starting period to increase the starting torque and
the other is used during running condition at normal speed to
improve the efficiency and the motor performance [3–5], the
change-over being effected manually by means of a centrifugal switch; the most common failure is that the switch will
ultimately fail to open when needed. Moreover, if the speed
of the motor is changed for any reason such as the applications required variable speed operation or even due to any
change in the loading conditions, the value of the fixed running capacitor becomes not suitable and another value of the
running capacitor must be selected. To the author’s knowledge, continuously adjusting the capacitor size with the speed
of three-phase induction motors connected to single-phase
supplies is not yet discussed.
A controlled capacitor has been proposed and used to improve the performance of split-phase induction motors by
Lipo et al. [10–13]. The system uses a dc charged capacitor
switched by a bidirectional switch represented by a transistor
H-bridge. The switch is short-circuited and opened for each
cycle; low switching frequency. Also, the switch is closed at
the instant the voltage across the capacitor reaches zero; thus
a zero voltage switching must be performed.
The object of this paper is to introduce an alternative configuration of the controlled capacitor by using a fixed capacitor in series with an electronic switch and to supply a
continuously variable capacitance to three-phase induction
motors operating from single-phase supplies. No mechanical
or centrifugal switch is used, high switching frequency can
be used and no zero voltage switching must be performed.
By suitably adjusting the duty cycle of the electronic switch,
the required value of the capacitor can be achieved according to the desired motor performance. The other distinctive
feature in this paper is the implementation of an on line adjustment of the controlled capacitor and the validation of the
developed mathematical model by computer simulation and
experimental work.
The system consists of three major elements: an induction
motor, a switch controlled capacitor and a control circuit.
A large capacitor required for starting is permanently connected in series with one of the motor phases and a single
unidirectional switch is used with the aid of a diode bridge
rectifier to constitute a bidirectional switch representation.
It is quite clear that the scheme is simple as it composes of
only one controlled switch which is essential for reliability
and effective cost. The paper is organized as follows: a mathematical model for three-phase induction motor operating
with single-phase supply is given in Section 2. This model is
established by using instantaneous symmetrical component
and a steady state equivalent circuit is derived. The principle
of a controlled capacitor is proposed in Section 3 and then
the duty cycle of the controlled capacitor to obtain minimum
unbalance of the phase voltages can be determined. Section
4 provides both simulated and experimental results. Finally
concluding remarks are given in Section 5.
2. Mathematical model
Since the stator windings of the three-phase induction motor operating with single-phase supply are not identical, it is
necessary to use a transformation technique in order to obtain
the physical variables. The instantaneous symmetrical component transformation is used to obtain voltage and current
equations as positive and negative components. This technique has been adopted in formulating the dynamic equations
of three-phase induction motors operating from single-phase
supply [5,14]. In this analysis, all the machine parameters are
assumed constant. Core losses, magnetic saturation and mmf
space harmonics are neglected.
For the stator winding of a star-connected three-phase induction motor connected to a single-phase supply with electronically controlled capacitor represented in Fig. 1, where
two winding connected directly to the supply (phases a and
b) while the phase c winding is connected to the supply
through the capacitor, zero sequence quantities would be absent (three-wire system) and the sum of the three-phase currents is always to be zero. Further, the negative sequence
quantities are always the complex conjugates of the corresponding positive sequence quantities. Thus, only the positive sequence quantities are required for complete solution.
Fig. 1. Stator connection of single-phase operation of three-phase induction
motor with electronically controlled capacitor.
N.A. Ahmed / Electric Power Systems Research 73 (2005) 121–128
123
The terminal voltage relations for the stator circuit fed from
single-phase supply and connected in Fig. 1 are
1
va −
iC dt − vc = 0,
vs = va − vb ,
C
va −
XC
ic − vc = 0
P
(5)
where XC = 1/ωC is the capacitive reactance.
While the current relations are
ia + ib + ic = 0,
Fig. 2. Positive sequence operational equivalent circuit.
is = ia + ic ,
ib = −is
(6)
Applying the instantaneous symmetrical component analysis
Following the instantaneous symmetrical components
transformation and from the positive and negative sequence
equivalent circuit of three-phase induction motor shown in
Fig. 2, the resulting performance equations in terms of sequence quantities and motor parameters will be [14,15]:
1
2
−
vs = √ {v+
s (1 − a ) + vs (1 − a)},
3
1 +
XC +
2
0 = √ {vs (1 − a) + v−
(ais + a2 i−
s (1 − a ) −
s )} (7)
p
3
+
+
+
v+
s = (Rs + Xls p)is + Xm p(is + ir ),
By combining Eqs. (3) and (7), the performance Eqs. (1) and
(2), can be simplified as
√
vs = 3(Rs isx + Xs pisx + Xm pi)
v+
r
1 − j(γ/P)
Rr
+
+
=
+ Xlr p i+
r + Xm p(is + ir )
1 − j(γ/P)
0=
− (Rs isy + Xs pisy + Xm piry ),
(1)
0 = Rr irx + Xr pirx + Xm pisx + γ(Xr iry + Xm isy ),
where γ is the p.u. mechanical speed (ωm ) with the synchronous speed (ωs ) as the base speed, p the operator
(1/ω)(d/dt) and ω the supply radian frequency.
By the same way the negative sequence operational equivalent circuit is obtained directly by replaced j by −j in (1):
0 = Rr iry + Xr piry + Xm pisy − γ(Xr irx + Xm isx ),
√
0 = 3(Rs isx + Xs pisx + Xm pirx ) + Rs isy + Xs pisy
−
−
−
v−
s = (Rs + Xls p)is + Xm p(is + ir ),
where Xs = Xls + Xm , Xr = Xlr + Xm .
Substituting from (3) into (4), a simplified expression for
the developed electromagnetic torque results as
v+
r
1 + j(γ/P)
Rr
−
−
=
+ Xlr p i−
r + Xm p(is + ir )
1 + j(γ/P)
0=
(2)
i+
s = isx + jisy ,
v+
r = vrx + jvry ,
i+
r = irx + jiry
(3)
where, the corresponding negative sequence terms would just
be the complex conjugate. The developed electromagnetic
torque in terms of sequence quantities can be expressed as
Te =
jXm + −
−
(i i − i+
s ir )
ωs r s
Te =
(8)
2Xm
(irx isy − isx iry )
ωs
(9)
and the mechanical balance torque equation is
Eqs. (1) and (2) are complex. Therefore, it is convenient for
simulation to write these equations in terms of their real and
imaginary parts. Thus, the positive sequence voltages and
currents which are complex numbers can be written in terms
of their real and imaginary parts as
v+
s = vsx + jvsy ,
1 XC
XC
+ Xm piry + √
isx +
isy
P
3 P
(4)
dωm
+ Fωm + TL = Te ,
P
Te − TL − Fωm
pωm =
ω
J
J
(10)
where F is the friction coefficient.
The independent variables of the system can be considered as isx , isy , irx , iry and γ. Eqs. (8)–(10) are all non-linear
equations as they involve product of variables, i.e. current
with current or current with speed. The numerical techniques
must be used to evaluate the system performances at different
instants of time starting from the initial values to run-up calculations. The computation was started by defining the motor
applied voltage vs and the initial values for all variables were
set to zero.
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N.A. Ahmed / Electric Power Systems Research 73 (2005) 121–128
3. Optimization of the capacitor size
and
From (8) it is easy to understand that the capacitive reactance needed varies with the speed and the parameters of the
motor. The proper selection of the capacitor value plays an
important role in determining the machine performance. For
satisfactory operation of three-phase induction motor with
single-phase supply, it is essential to carefully select the size
of the motor capacitor C or the value of the capacitor reactance XC such that the effect of negative sequence currents
is considerably reduced if not totally eliminated so that the
undesirable features such as vibration and noise can be kept
at a low level. There are different criteria for selecting the optimum value of XC ; these criteria are minimum unbalance in
stator phase windings voltage, minimum negative sequence
voltage and zero negative sequence voltage. Here, the criterion of minimum unbalance in the stator winding voltages
and zero negative sequence voltage has been used. The value
of the capacitor that yields minimum unbalance yields also
maximum efficiency [7]. Expressions for the value of the capacitor that can achieve the above requirements can be found
in [5,14].
D=
3.1. Principles of the controlled capacitor
The switched capacitor circuit shown in Fig. 1 consists of
two main parts: a fixed ac capacitor and an electronic switch.
The switch must allow bidirectional current flow as in a mechanical switch. The switch is short circuited and opened periodically using symmetrical pulse width modulation (PWM)
technique which is simple and easy to implement. No detection of zero crossing of the capacitor voltage is required compared with the switched capacitor proposed in [10–13] where
the switch is closed at the instant the voltage across the capacitor reaches zero; thus zero voltage switching is not required.
Also, the switch in [10–13] is closed and opened one time
for each supply cycle. In the proposed circuit, the switch can
be switched many times in each supply cycle and therefore a
high switching frequency can be used. Using a high switching frequency for the switched capacitor leads to very short
off periods of the switched capacitor. Therefore, the charging
periods of the fixed capacitor, while the switched capacitor
is off, become very small and consequently a little voltage
difference between the capacitors at the instant of switching is performed to avoid any current spikes at the switching
instant. By opening and closing the switch periodically, the
effective value of the capacitor appears to be smaller than the
actual value. Therefore, a controlled capacitor is presented
in this section by using a fixed capacitor in series with an
electronic switch. A single unidirectional switch is used with
the aid of a diode bridge rectifier to constitute a bidirectional
switch representation as shown in Fig. 1. The relationship
can be approximately expressed as
XCeffective = XCreal
T
XCreal
=
Ton
D
(11)
Ton
T
(12)
where XCreal is the real capacitive reactance, XCeffective is the
effective capacitive reactance, T = Ton + Toff is the switching period of the electronic switch, D is the duty cycle, let
XC = 1/jωC, and substitute into (11), then we can obtain
Ceffective = DCreal
(13)
From Eq. (13) when the switch is closed (D = 1.0), Ceffective
is equal to Creal . On other hand, when the shorting interval
of the switch is decreased, Ceffective will become small until
it equals zero at D = 0 and it is easy to adjust the value of the
effective capacitor by changing the shorting interval of the
switch. A switched capacitor can change the effective capacitor value from large to small when the speed of the motor is
increased and it provides an effective method of overcoming
the difficulty associated with the need for a variable capacitor.
The hardware circuit consists of three parts: a sawtooth
generator, comparator circuit and isolation and driving circuit. The speed of the motor is sensed by a tachometer which
aligns with the motor shaft. The electronic switch in series
with the capacitor is realized by an IGBT. The switching
signal of the switch can be easily obtained by comparing a
dc signal having variable amplitude with a high frequency
sawtooth signal has a constant amplitude. The dc signal amplitude can be selected as a function of the motor speed to
give the required value of the short-circuited and opened periods (duty cycle) of the switch. By suitably adjusting the duty
cycle, the required effective value of the capacitor, Fig. 4, can
be obtained and minimum unbalanced can be achieved. Also,
by adjusting the capacitor size, the backward field would be
eliminated or at least minimized with resulting improving in
efficiency, torque pulsations and power factor.
The proposed system eliminates the use of any mechanical
or centrifugal switches which is located inside the motor. This
avoids the possibility of the switch failure and leads to less
operational and maintenance cost and improves the system
reliability.
4. Performance evaluation
In this section, the performance characteristics of the system under consideration will be evaluated and thoroughly
investigated for given loading conditions.
4.1. Test machine
To verify the proposed analysis and modeling of threephase induction motor operating from single-phase supply
with an electronically controlled capacitor, an experimental prototype is implemented. A 1.8 kW, 220 V, 50 Hz, 7.8 A
three-phase wound rotor induction motor connected in star
for single-phase operation as shown in Fig. 1 and has the
N.A. Ahmed / Electric Power Systems Research 73 (2005) 121–128
125
Table 1
Induction motor parameters
Parameter
Symbol
Value
Stator resistance
Rotor resistance
Stator leakage reactance
Rotor leakage reactance
Magnetizing reactance
Moment of inertia
Number of poles
Capacitor
Rs
Rr
Xls
Xlr
Xm
J
P
C
2.53 ()
0.90 ()
3.01 ()
0.6946 ()
78.5 ()
0.016 (Kg m2 )
4
330 (␮F)
parameters shown in Table 1 [14–15] is used in this paper.
The motor is mechanically coupled to a dc generator, which
by adjusting its field voltage provides a variable load torque
to the motor. The shaft speed is measured using a tachometer mounted on the same shaft couples the motor and the dc
generator.
4.2. Results and discussions
Based on the machine parameters described in Table 1,
an optimal capacitive reactance achieving minimum unbalance and zero negative sequence voltage are demonstrated in
Fig. 3. This figure shows that a small capacitive reactance XC ;
large capacitor size; during the starting period and large XC ;
small capacitor; during the running period for best running
conditions are required. It must be evident that XC must be
continuously adjusted to keep minimum unbalance or zero
negative sequence voltage at different speeds.
From Fig. 3, it can be seen that the capacitor required
for minimum unbalance reaches its maximum value at stand
still. After that point the capacitor related to minimum unbalance begins to decrease as the speed increases. It is clear that
one can choose an optimal path to control the capacitor and
achieve a minimum unbalance as shown in Fig. 3. However,
it is difficult to realize a continuously adjustable mechanical capacitor. The proposed switched capacitor can change
Fig. 3. Optimal starting curve of the capacitive reactance as a function of
motor speed.
Fig. 4. Effective capacitive reactance of a 330 ␮F controlled capacitor.
the effective capacitor and provides an effective method of
overcoming the difficulty associated with the need for a continuously variable capacitor.
Fig. 4 shows the computed and measured variations of
the effective capacitive reactance for a 330 ␮F capacitor;
switched in accordance with the principle proposed in this
paper; with the duty cycle of the electronic switch. For practical use of the proposed controlled capacitor with the threephase induction motor operating from single-phase supply, a
small fixed capacitor of 9.4 ␮F is connected in parallel with
the controlled capacitor as shown in Fig. 1 to produce a path
for the motor current of phase c during the off periods of
the controlled switch and to complete the required starting
optimal capacitor to 340 ␮F as depicted in Fig. 3.
The experimental duty cycle required for the electronic
switch to keep minimum unbalance in motor phase voltages
at all operating speeds is shown in Fig. 5, which shows that
the duty cycle is higher when the motor is near the standstill
mode and then gradually decreases as the motor starts. When
the speed of the motor closes to the synchronous speed, the
duty cycle will reduce near zero value due to the fact that the
Fig. 5. Duty cycle as a function of the motor speed.
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N.A. Ahmed / Electric Power Systems Research 73 (2005) 121–128
Fig. 6. Simulated and experimental speed–time response at no load. (a) One capacitor, (b) two capacitors, (c) proposed controlled capacitor.
value of the optimal capacitor is decreased as the speed is
increased as shown in Fig. 3.
For the purpose of comparison, three different techniques
for testing the same motor are studied. The motor was started
and running with one capacitor value (330 ␮F), two capacitor
values; one for starting (330 ␮F) and the other for running
(50 ␮F); and with a 330 ␮F capacitor switched in accordance
with the principle proposed in this paper. The effect of the
capacitor on the motor performance will be studied in the
following.
Simulated and measured starting and steady state responses of the motor speed for the three cases at no load
are shown in Fig. 6. While Fig. 7 shows the speed responses for the same three cases when the motor operating under a load of 3.0 N m. It can be seen that when
the capacitor is switched in accordance with the principle proposed in this paper, the acceleration time becomes
shorter compared to that of the other two cases and the
decrease in starting time is more apparent at load condition as shown in Fig. 7. Apart from the good agreement between the simulated and experimental speed responses, it is noticeable that there are evident undulations in the motor speed in Figs. 6(a) and 7(a) because
the running fixed capacitor is far from the optimal value.
These speed ripples become less remarkable with two fixed
and proposed switched capacitor. Steady state results of
Figs. 6 and 7(a) and (b) give near results because the value
of the running fixed capacitor is good selected to be near the
optimal value.
Fig. 8 shows a comparison of computed and experimental
supply current at starting for the same three cases under a load
of 3.0 N m. Although the current is almost the same during
the starting period, the current at steady state is still high
for the one capacitor value, decreased when using the two
capacitor values. However, when the capacitor is switched
in accordance with the principle proposed in this paper, the
steady state current is more reduced. Also, the starting period
becomes shorter especially at load condition as demonstrated
in Fig. 8(c).
Fig. 9 shows the computed electromagnetic torque responses at starting for the three cases under a load of 3.0 N m.
It can be noted that although the capacitor is not selected
according to the criteria of minimum pulsating torque, the
pulsating torque is reduced with the two value operating capacitor and more improved with the continuously controlled
capacitor.
Comparing between (b) and (c) of Figs. 6–9, one may
notice that the advantage improvement in the motor performance using the proposed switched capacitor is achieved at
starting only when compared the results with that of two
fixed capacitor technique, this is because the value of the
two fixed capacitors are carefully selected, specially the running one, to be near the optimal value required to give the
criteria of minimum unbalance at the specified particular operating speed. If the speed is changed for any reason (such
as speed control or even due to the loading conditions),
the value of the fixed running capacitor becomes not suitable and another value of the running capacitor must be
N.A. Ahmed / Electric Power Systems Research 73 (2005) 121–128
127
Fig. 7. Simulated and experimental speed–time response at a load of 3 Nm. (a) One capacitor, (b) two capacitors, (c) proposed controlled capacitor.
selected. The effect of the switched capacitor in the motor
performance can be easily noticed by comparing between
(a) and (c) at the steady state of Figs. 6–9 because the running fixed capacitor becomes far from the optimal desired
value.
In view of the obtained results, it can be concluded that
with continuously adjusting the capacitor size, it is possible
to achieve very satisfactory transient and steady-state performance of three-phase induction motor operating from singlephase supply.
Fig. 8. Simulated and experimental stator current a load of 3 N m. (a) One capacitor, (b) two capacitors, (c) proposed controlled capacitor.
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N.A. Ahmed / Electric Power Systems Research 73 (2005) 121–128
performance at different speeds. Experimental results validated the analytical results and a good agreement between
the simulated and experimental results is achieved. The results in this paper present a step toward the design of some
optimal switched capacitor techniques.
References
Fig. 9. Simulated electromagnetic torque at a load of 3 N m. (a) One capacitor, (b) two capacitors, (c) proposed controlled capacitor.
5. Conclusions
The design and implementation of a controlled capacitor for a three-phase induction motor operating from singlephase supply has been presented by using a fixed capacitor in
series with an electronic switch. The proposed system eliminates the use of mechanical or centrifugal switches which
is located inside the motor. This avoids the possibility of the
switch failure and leads to less operational and maintenance
cost and improves the system reliability. The optimum effective capacitor value can be on-line adjusted at any operating
speed by periodically changing the duty cycle of the controlled switch to achieve minimum unbalance in phase voltages or any other optimization criteria to improve the motor
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