INTRODUCTION
Singlephase induction motors are as ubiquitous as they are useful, serving
as the prime power sources for a seemingly limitless array of smallhorsepower
applications in industry and in the home, especially in Heating, Ventilation
and Air Conditioning (HVAC) systems (Chomat, 2003;
Li and Cathey, 2006).
In many applications, it may be necessary to use a threephase induction motor
on a singlephase supply system. For example, it has been found technically
and economically advantageous to initially install a Single Wire Earth Return
(SWER) system for rural electrification in remote and hilly regions (Ahmed,
2005).
Utilizing of Friction braking may lead to break wearing, bearing amortization,
thermal cracks and thermallyexcited vibration due to the temperature rise resulting
from the braking process (Talati and Jalalifar, 2008).
Therefore, electric braking is necessary to solve these problems.
In zero sequence braking, three stator phases are connected in series across
a single phase AC source. Such a connection is known as a zero sequence connection.
The switching arrangement, from normal threephase to zero sequence operation,
is extremely simple when the motor has a deltaconnected stator and can be structured
as in Fig. 1 (Ahmed, 2005; Dubey,
2002).
The developed torque of a three phase induction motor is significantly reduced
when a condenser is inserted in series in one of the supply lines (Sreenivasan,
1959).

Fig. 1: 
Zero sequence braking of a threephase induction motor operating
from singlephase supply with a controlled capacitor 
Also, zerosequence parameters and parameter variations can be determined (Grantham,
1983).
The magnetomotive force caused by cophasal currents (or zero sequence) produces
a magnetic field having three times the number of poles for which the machine
is actually wound (Dubey, 2002) because of evolving third
spatial harmonics as a result of summing the phasemagnetizing forces (Chycbar,
1967). Thus the motor works momentarily in regenerative braking mode and
generated energy is supplied to the source or energy storage device (Bai
et al., 2005). Braking could be used almost up to onethird of synchronous
speed if the load torque is less than the maximum torque (Dubey,
2002), otherwise motor speed will fall to zero.
For the fixed value of motor terminal voltage, the braking torque is not regulated
and the motor has a strict speedtorque characteristic nature. The speed is
conventionally controlled using either winding tappings, variac, autotransformer,
or series impedance (AbdelHalim, 1999). In order to
control the braking torque and, consequently, the nature of the mechanical characteristics,
it is necessary to vary the motor terminal voltage. Use of controlledvoltage
supply leads to difficulty and complexity of the electric drive system. So,
in this case and for the ease of control and balance (Obea
et al., 2007), it is more convenient to use series impedance (capacitors),
where the phaseshift capacitor may play the role of voltagedivider. Thus,
changing the motor terminal voltage is available by regulating the value of
condensercapacitance. Since the value of capacitance can be controlled electronically,
braking control will become smooth and one capacitor can be used (Ahmed,
2005). Motor behavior was investigated at three values of capacitance.
The aims of this study are to investigate and discuss the behavior of a threephase
induction motor operating from singlephase supply when steadystate zerosequence
braking is used. For this purpose, simulation is carried out and braking time
is monitored for variable values of capacitance and rotor resistance.
MODELING OF MOTOR OPERATION
Expressions used to simulate the motor operation can be obtained from the equivalent
circuit when the machine works on regenerative braking (Pillai,
2004), Fig. 2 shows the equivalent circuit for both positive
and negative sequence components.
From this circuit, voltage and current equations are:

Fig. 2: 
Perphase equivalent circuit 
Resolving currents and voltages into symmetrical components (Alshamasin,
2005, 2009; Popescu et al.,
2005) gives:
Substituting the voltage and current values from Eq. 3 and
4 into Eq. 1, yields:
Solving Eq. 5 and 6 gives:
By the obtained symmetrical components of voltages, maximum torque values can
be determined as:
Then the developed motor torque will be:
Where:
For the same motor, the critical slip value when it is fed from singlephase
supply voltage (S_{er}) differs from that (S_{er3}) of threephase
operation mode (fed from three phase supply voltage) and S_{cr} = 2.25S_{cr3}
(Feelts, 1970). Hence, the number of poles increases,
so the rotor resistance under each stator pole decreases. Also, the capacitor
affects the critical slip, so:
where, coefficient (k) can be found for a particular motor by experiment.
SIMULATION AND RESULTS
Conventional braking technique (Regenerative, plugging, dynamic) for three
phase motor operating from three phase supply were discussed and advantages
and disadvantages were stated by Rongmei et al.
(2012). This study investigates the behavior of the three phase motor fed
from single phase supply when it is braked by zero sequence method.
In order to investigate the motor characteristics, simulation by using lab
VIEW software was carried out. The motor used for simulation and experimental
in this study was 3.75 hp, four poles, 220 volt, three phase induction motor.
The motor data are as follows:
• 
Stator resistance: 
1.95 Ohm 
• 
Rotor resistance: 
3.12 Ohm 
• 
Stator reactance: 
3.43 Ohm 
• 
Rotor reactance: 
3.43 Ohm 
• 
Magnetizing reactance: 
3.40 Ohm 
• 
Magnetizing reactance: 
71.4 Ohm 
• 
Rated speed: 
1370 rpm 
Figure 3 shows the mechanical characteristics of motor regenerative
braking for three values of capacitance (C = 100, 200, 300 μF).
It is obviously seen from Fig. 3 that capacitance (C) plays
the role of the horizontal parameter affecting the amplitude of torque.
To illustrate the influence of capacitance and resistance on the motor braking,
the behavior of the motor was investigated experimentally. The motor shaft is
coupled to a DC generator (load) whose inertia is five times the motor’s
value Fig. 4.
Figure 5 shows the oscillogram of the speed dynamic characteristics
(transient characteristics) for the slipring motor with different values of
capacitance (C) and resistance (R_{2add}). The sampling time has been
set to 0.1 sec.

Fig. 3: 
Speedtorque characteristics 

Fig. 4: 
Experimental setup of system 

Fig. 5(ae): 
Instantaneous speed vs. time when the motor operates in the
braking mode for, (a) Natural characteristic, (b) C = 50 μF, R_{add}
= 0 Ω , (c) C = 50 μF, R_{add} = 6.9 Ω, (d) C = 200
μF, R_{add} = 0 Ω and (e) C = 50 μF, R_{add}
= 6.9 Ω 
It is noticeable that increasing the added resistance or capacitance results
in decreasing the braking time. Fig. 5e shows that inserting
resistance into the rotor circuit with high value of capacitance in the stator
circuit will lead to selfexcited braking and short stopping time. Uniform decelerations
are obtained for almost all portions of the curves.
Superior to other braking methods, utilizing of capacitor and rotor resistance
in zero sequence braking gives the ability to control the braking time and satisfy
fast stopping due to the uniform of the braking current. Unlike the dc injection
braking system, the braking current due to the zero sequence will flow in all
the three windings of the stator and also distribution of magnetic field due
to the braking current will be more uniform (Kostelnicek,
2001). Also, zero sequence braking does not need additional voltage source
which requires additional devices (Nasir, 2012). More
devices will lead to complexity of the braking circuit and existence of harmful
harmonics (Letenmaier et al., 1991; Alshamasin,
2005).
Regenerative brake is an energy recovery mechanism (Cholula
et al., 2005) but braking drops off at lower speed and cannot bring
the motor to a complete halt (Pengyu et al., 2009).
Frequent plugging (counter current braking) can create serious overheating (Rongmei
et al., 2012), moreover, there is a possibility of reversing the
motor rotation if the zero speed detector fails to remove the braking as soon
as the motor speed reached to zero rpm (Dubey, 2002).
CONCLUSIONS
A mathematical model is developed for steadystate zerosequence braking performance
of a threephase induction motor operating from singlephase supply with a controlled
capacitor. The obtained mechanical characteristics show that t his kind of braking
can be used for both squirrelcage and woundrotor motors alike, since it does
not require large rotor resistance. Intensive and selfexcited braking could
be caused if resistance is inserted into the rotor circuit with high value of
capacitance in the stator circuit, which ensures rapid stopping of induction
motors. Results show that the braking time can be controlled by changing the
capacitance and rotor resistance values.
This method, compared with the dynamic braking connection which requires a
DC source or AC source with high rotor circuit resistance, is worthy of serious
consideration.