Hilmi Fadhil Amin
Salahaddin University-Erbil
Electrical Enginnering Department hilmi_fadhil @yahoo.com
ABSTACT
This paper deals the simulation of variable speed drives using wound rotor induction motor, controlled by variation of an external rotor resistance by a parallel electronic chopper. A through analysis of the steady state performance of the system is presented, with low value of filter in rotor side. The effect of chopper frequency and duty cycle on the rotor rectified current ripple current, rotor phase current and torque developed are investigated. The simulink MATLAB toolbox is used to simulate the response of the drive performance. The high chopper frequency tend to improvement the performance of wound rotor induction motor drive system such as, rotor rectified current, rotor phase current, speed smoothing with reducing the torque pulsation and ripple of rotor rectified current.
Keywords : Chopper frequency, ripple, rotor rectified current, duty cycle, wound rotor induction motor.
1-Introduction:
Induction motors are a constant speed machine which account for 90% of the electrical drive used in industry. Induction motors are usually constructed to work with a small value of slip, normally less than
5% at full load. Therefore the deviation of the motor speed from the synchronous speed is practically very small. However, there are certain applications that requires enormous variation of the motor speed[1].
With the increase in availability of high current power electronic devices, smooth and quick variation of external resistance introduced in the rotor circuit of wound rotor induction motor to control its speed, can be accomplished electronically. Schemes employing chopper controlled resistance can be used to obtain a constant torque, constant speed or any desired characteristics by using a proper feedback circuit along with it. Such circuits are widely used in industrial application where the drive operation is intermittent such as, hoists, cranes, conveyers, lifts, excavators and high starting torque are more important with low starting current to avoid voltage dip.
The wound rotor induction motor(WRIM) offers a lot of flexibility for wide range of speed control compared to squirrel cage motor[2,3]. The torque depends on motor resistance. Therefore, increasing the rotor resistance will at a constant torque causes a proportionate increase in the motor slip with a result decrease in rotor speed. Thus, the speed for a given load torque may be varied by varying the rotor resistance. The function of this resistance is to introduce voltage at rotor frequency, which oppose the voltage induced in rotor winding.
The main demerit of this method of control is that energy is dissipated in rotor circuit resistance, internal and external, and this energy is wasted in the form of heat. Because of the waste-fullness of this method, it is used where speed change are needed for short duration only[4,5]. With the recent progress in power semiconductor technology, these undesirable features of the conventional rheostat control scheme can be eliminated by using a three phase uncontrolled bridge rectifier and a chopper controlled external resistance as shown in fig.(1). Where f r
is the rotor frequency, f ch
is the chopper frequency and R x
is the external resistance. The rectifier bridge acts as an electronic frequency changer (EFC), so that the machine will chiefly see the effect of EFC switching at rotor frequency. With the high frequency switching effects of the chopper, which is a power switch electronically monitored by a control module.
This system consequently lose the capacity to control rotor current waveform by pulse width modulation of ES [4].

In this paper the effect of chopper frequency, duty cycle on the rotor current, rotor rectifier current, speed and torque pulsation are investigated. Then, simulation results are presented and compared with theoretical concepts .
2-Analysis and Derivation of Open Loop Chopper Circuit Models:
The conventional resistance control scheme can be eliminated by using a three phase rectifier bridge and chopper controlled external resistance as shown in fig.(2). A chopper is a power switch electronically monitored by a control circuit. When the chopper is in the “on” mode the equivalent external resistance
R eq
in the rotor circuit is R f
, where R f
is smoothing inductor filter resistance. When the chopper is in the
“off” mode, the equivalent external resistance in the rotor circuit is (R f
+R x
). If the chopper is periodically regulated so that, in each chopper period, it is “on” for the some time but is “off” for the rest. It is possible to obtain variation of equivalent resistance R eq
between R f
and (R f
+R
X
). Thus the chopper electronically alter the external resistance R x
in continuos and contact less manner.
Fig.(1) Fundamental structure of electronic rotor cascade Fig.(2) Block diagram of chopper circuit consisting of WRIM, rotor , rectifier and resistively loaded.
Exact analysis is tedious, involving the phasor calculation for motor fundamental and harmonic quantities and step by step analysis of nonlinearities in the rectifier-chopper circuit [6,7]. The simple classical relation of rotor rms current and rotor rectified current I dc obtains:
I
= dc
3
I r
...( 1 )
2
When I dc
is the average value of the rectified rotor current and I r
is the rotor rms phase current. The power losses in stator and rotor resistance for all three phase I dc
2
(sR
1
+ R
2
) in dc side. Because of leakage reactance of rotor and stator in motor winding there is a voltage reduction of 3
ω
( l
1
+ l
2
)/
π
from the terminal voltage of rectifier voltage. Fig.(3) gives a chopper circuit current waveform. The system may be represented by the dc circuit model as shown in fig.(4), where T ch
is the chopper period.
Fig.(3) Rectifier chopper current waveform. Fig.(4) Dc Equivalent circuit.
(
Where E is the average value of rectified rotor voltage at standstill, E
2
is the rotor phase voltage and l
1
+ l
2
) is the total leakage inductance per phase referred to the rotor.
E
=
3
π
6
E
2
...( 2 )
For the chopper circuit waveforms in fig.(3), let t
1
is on-period, t
2
is off period, neglecting the voltage drop due to the commutation over lap of diode bridge, current during “on” mode is given by; i
1
=
I
1
( 1
− exp .
− t
τ on )
+ i
01 exp .
−
τ t on ...( 3 ) and during “off” mode, i
2
=
I
2
( 1
− exp .
− t
τ off )
+ i
02 t exp .
−
τ off ...( 4 )

Where
τ on
=
L f
R f
+
2 ( l
1
+
+
2 sR
1
+ l
2
)
2 R
2
,
τ
0 ff
=
R f
Lf
+
2
+ sR
2 (
1 l
+
1
+ l
2 R
2
2
+
)
R x
, I
1
=
R f sE
+
2 sR
1
+
2 R
2
& I
2
=
R f
+
2 sR
1 sE
+
2 R
2
+
R x
The i
01 and i
02
are initial values of current for “on” and “off’ mode, respectively. If the chopper frequency is very high with low value of smoothing inductor such that[8];
τ t
1 on
<<
1 and
τ t
2 off
<<
1 ...( 5 ) It can be shown that[9];
I dc
=
( R f sE
+
2 sR
1
+
2 R
2
)
+
τ t
2 ch
R x
...( 6 )
Therefore the equivalent resistance, R eq
=
R x τ t
2 ch
...( 7 )
This equation show that R eq
is proportional to the off period of the chopper circuit. This is show the external resistance in the rotor circuit can be varied by controlling the duty cycle (D) of the chopper period. If the duty cycle D=t
1
/T ch
, then the eq.(7) may be written as R eq
= R x
(1-D). The rotor copper losses is given by; sp g
= sEI dc
–2sR
1
I rms
2
…(8)
Where p g
is air gap power I rms
is rms value of I dc
. If the chopper frequency is high, then I dc
≅
I rms
, therefore;
sp g
= sEI dc
–2sR
1
I dc
T= sp g
/s
ω s
2
,Then the developed torque(T) in N.m ;
=(E-2R
1
I dc
)I dc
/
ω s
…(9)
Neglecting the voltage drop across the stator resistance(R
1
), the eq.(9) used to obtain torque for various slip for different on-off times.
T=E I dc
/
ω s
…(10)
Referring to fig.(3), using the high switch power transistor such as SIT,IGBT and power MOSFET for chopper switching permit a high chopper frequency, with reducing of smoothing inductor;
/
∆
I/ = /i
01
– i
02
/ << I dc
…(11)
For low value of smoothing inductor the above equation is satisfied if (f ch
>>f r
). Higher the chopper frequency, lower the ripple in the rotor rectified current and consequently the torque ripple. Also high values of f ch
are required to avoid any interaction between the chopper frequency and the output frequency of rectifier for all slip values. According to maximum peak-to-peak ripple in rotor rectified current, can be approximated to (E/4f ch
L)[10]. The smoothing inductor (1mH) is used, but with high chopper frequency to compensate the minimal value of smoothing inductor. Eliminating or reducing the smoothing inductor reduce the volume and then the cost of system drives. The minimum value of external resistance R x
, 50
Ω is used, which gives the required operation in the speed torque characteristics to half of full load speed.
3-Performance Characteristics:
Torque –speed characteristics
To investigate the effects of the chopper frequency, a 1.5 hp, 380 volt, 4 pole, 50Hz, WRIM was used for calculation and investigation of results. The computed torque speed curve for different frequencies with the duty cycle fixed at 0.8 and 0.5 are shown in fig.(5 & 6) respectively. At high chopper frequency (f ch
>10kHz) with 0.8 duty cycle, torque speed curve give essentially the same results. But for 0.5 duty cycle give the approximately the same results at chopper frequency greater than 1kHz.
Fig.(5) Torque Speed characteristics for 0.8 duty cycle at Fig.(6) Torque Speed characteristics for 0.5 duty cycle at different chopper frequency. different chopper frequency

Rotor rectified current
The low value of smoothing inductor was used. Though, as in other similar applications, the presence of inductance will have reduced the fluctuations in current. The dc link current waveforms shows very clearly the ripple components at six times rotor frequency. The computed rotor chopper current for 0.8 and
0.5 duty cycle are shown in fig.(7& 8) respectively. Increasing the chopper frequency, the ripple in rotor rectified current decreases. Fig.(9&10) show the ripple in rotor rectified current against speed for 0.8 and
0.5 duty cycle at different value of chopper frequency. Fig.(11a&11b) show the ripple in rotor rectified current against duty cycle for rotor speed 1350rpm and 1425rpm respectively. Fig.(12a&12b) show the variation of ripple in rotor rectified current against chopper frequency at 0.8 and 0.5 duty cycle respectively. Fig.(13a&13b) show the rotor rectified current response at normal operation of 0.8 duty cycle for 1kHz and 50Hz chopper frequency respectively. The variation in rotor rectified current from minimum to maximum current level is larger in 50Hz chopper frequency.
Fig.(7) Rotor chopper current against Fig.(8) Rotor chopper current against Fig.(9) Ripple in rotor rectified current motor speed at 0.8 duty cycle. motor speed at 0.5 duty cycle. against motor speed at 0.8 duty cycle.
Fig.(10) Ripple in rotor rectified current Fig.(11) Ripple in rotor rectified current against duty cycle
against motor speed at 0.5 duty cycle. a- at 1425rpm, b- at 1325rpm
Fig.(12) Ripple in rotor rectified current against chopper Fig.(13) Rotor rectified current response at 0.8 duty frequency a- at D= 0.8 b- at D= 0.5 cycle a- f ch
=1kHz b-f ch
= 50Hz

Rotor Phase Current
The rotor current is approximately composed of alternating square pulse of (2
π
/3) duration. Due to the leakage reactance of rotor and stator windings, the commutation of current between diodes in the rectifier bridge is no longer instantaneous. There is a period of current overlap where by two phase carry current simultaneously. Fig.(14a&14b) show the rotor phase current response at normal operation at 0.8 and 0.5 respectively for 1kHz chopper frequency. Fig.(15a&15b) show the rotor phase current response at normal operation at 0.8 and 0.5 respectively for 50Hz chopper frequency.
Speed and Torque Performance
The rotor speed of WRIM is affected by a chopper frequency and duty cycle. Fig.(16a&16b) show the steady state speed response at 0.8 duty cycle for 1kHz and 50Hz chopper frequency respectively. Also
Fig.(17a&17b) show the electromagnetic torque response at 0.8 duty cycle for 1kHz and 50Hz chopper frequency respectively.
Fig(14)Rotor current at Fig(15) Rotor current at Fig.(16)Rotor speed at D=0.8, Fig(17)Electromagnetic torque at f ch
=1kHz, a- D=0.8, b-D=0.5 f ch
=50Hz, a- D=0.8, b-D=0.5 a=f ch
=1kHz, b- f ch
=50Hz D=0.8, a=f ch
=1kHz, b- f ch
=50Hz
4-Conclusion:
The wound rotor induction motor offers a lot of flexibility for wide range of speed control compared to the squirrel cage motor. With high switching ability of power electronic devices, the effect of chopper frequency at different duty cycle of motor performance is studied. The scheme provides continuos and contactless adjustment of rotor resistance by electronic means. The feasibility of the system and verification of theoretical results is demonstrated. It is anticipated that such simple scheme will find applications in many industrial drive system. The results shown that with low value of chopper frequency may cause fluctuations in motor speed and torque pulsation. Increasing the chopper frequency decrease the ripple in rotor rectified current, harmonic rotor current, speed variation and improvement the electromagnetic torque waveforms.
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