ELECTROMECHANICAL TRANSIENT OF SERIES CONNECTED THREE PHASE SLIP
RING INDUCTION MOTORS
R.M.Hamouda
M.A. Badr
A.I. Alolah
EE Dept., King Saud University, P.O.Box 800
Riyadh 11421, Saudi Arabia
EE Dept., College of Eng., Ain
Shams University, Cairo, Egypt
induction motors represents one of such modes. This mode
of operation was almost completely ignored due to the
The series connected represents a peculiar mode of operation of three
phase slip-ring induction motors. When the rotor is connected in series belief that the motor would be unable to start at all. This is
with the stator with opposite phase sequence, the motor can start and reach true if the rotor winding is connected in the same sequence
a speed close to synchronous speed. It has been also shown that the motor as that of the stator winding. However, the authors have
under this mode can operate at double synchronous speed. The main proven that if the rotor phase sequence is opposite to that of
objectives of this paper is to develop a mathematical model along with a
computer simulation, whereby the transient behaviour of the series the stator, the motor can start and reach a speed close to
connected induction motor can be analyzed, particularly during the synchronous speed [6]. On the other hand it has been
starting period and synchronous speed operation. The torsional dynamic shown that if the series connected three phase induction
elyects become serious when one of the torsional modes of the motor-shaft motor is driven to a speed double its synchronous speed,
assembly resonates with one of the pulsating torque components of the
overall electromagnetictorque. Therefore, the effect of torsional dynamics the motor can continue running as a synchronous motor at
this speed. Other authors have pointed out this fact but they
has been taken into considerations.
dealt with the problem from the control point of view and
K eywordr: Induction motors, Transient analysis, Series
nothing
was mentioned about how the motor will reach
cmnection
such a speed [7].In addition, no information regarding the
stability limits of the motor under this mode of operation
List of Symbols
p.u instantaneousvalue of voltage and cumnt, respectwely
was given.
Abstract
p.u w and peak value of supply line to neutral voltages,
respectively
p.u. damping coefficient of mass, and its inertia in seconds,
respectively
p.u stiffness of the shaf? section connecting motor with the
load
p.u inductance, resistance and reactance, respectively
p.u magnetizing reactance and maximum mutual inductance
between stator and rotor phases, respectively
p.u motor and load torque, respectively
p.u transfer torque between motor and load
time in seconds ,d/d(o t) and slip, respectively
motor rotor and load position angles
synchronous and rotor speed, respectively
supply frequency in d s e c and p.u rotor speed, respectively
Subscripts
A, B, C
a, b, c
r, s
1, m
statorphases
rotor phases
rotor and stator, respectively
leakage and magnetizing, respectively
I. Introduction
Conventional balanced operation and starting of three
phase induction motors, in general, and three phase slip
ring induction motors in particular, have been well
understood and investigated over the extent of this century.
Theories concerning such a conventional mode of
operation have been well established and published in
numerous publications. However, little interest has been
directed to investigate the behaviour of these motors under
peculiar modes of operation, especially under transient
c.onditions[I ,2].
Recently, the authors have suggested several modes of
operation of three hase slip ring induction motor t2-61. The
series connected operation of three phase slip-ring
0-7803-5935-6/00/$10.00 (c) 2000 IEEE
The main objectives of this paper is to develop a
mathematical model along with a computer simulation,
whereby the transient behaviour of the series connected
induction motor can be analyzed, particularly during the
starting period and synchronous speed operation. The
torsional dynamic effects become serious when one of the
torsional modes of the motor-shaft assembly resonates with
one of the pulsating torque components of the overall
electromagnetic torque. Therefore, the effect of torsional
dynamics has been taken into considerations.
II. Basic Principle
I. Asynchronous mode of operation
When the motor windings are connected in series as shown
in Fig. 1, the interaction between the magnetic fields and
torques produced by both the stator and rotor can be
analyzed as follows r61:
i) The supply cu%nts that flow into the stator winding
produce a uniform magnetic field M,, rotating w.r.t.
stator by U,. By induction action hisIinduces another
uniform magnetic field Mr2 in the rotor rotating
w.r.t. rotor by (ns-n). The interaction between these
two fields produces a uniform induction torque Cl.
Due to this torque the motor can continue running in
the direction of My/,
ii) The supply currents that flow into the rotor winding
produce a uniform magnetic field Mrl rotating w.r.t.
rotor by n,. Due to the reversal of the phase
sequence the direction of M,,will be opposite to that
of MsI.
By induction M,,induces another uniform
magnetic field Ms2 in the stator rotating w.r.t. stator
by (ns-n). The interaction between Mr,and Ms2
produces a uniform induction torque
acting on
r2
260
the stator in the direction of Mr,. Due to the
principle of action and reaction'there will be a
torque exerted on the rotor in the opposite direction
and consequently will be in the direction of T,I.
iii) The interaction between M,,and M,/produces a
pulsating torque Tp with no average value.
Consequently the motor can not continue running
due to this torque.
[RJ =Diag [r, r, r, rr rr r r ] , and [LJ is the system
inductance matrix as given in the Appendix.
From the above, it can be realized that:
0
VA
The summation of T,],
and Tp makesthemotor
start and continue running as an induction motor, i.e.
n n,.
if both the stator and rotor have the same sequence,
T,Iy d T,3 would have opposite directions. Their
magnitude is equal at standstill and the motor has no
useful starting torque.
If the rotor is driven at twice the synchronous speed,
i.e n=2n, MrI will be rotating w.r.t. stator by n,.
Accordingly,
and MrI will be rotating at the same
speed and direction, which means that Tpwill be a
uniform synchronous torque.
- Motor
Load
"I
Rotor
Stator
Fig.I: (a) mechanical system .(b) Connection of the series slip ring
induction motor with opposite phase sequence
The voltage equation representing the series connected
mode of operation can be obtained by manipulating eq.( 1)
using the following connecting equations:
[vs
11. Synchronous mode of operation
J = (c11[VI
(2)
(3)
The series connected slip ring induction motor can operate ril =rc2Iriwl
synchronously at twice its rated synchronous speed [6]. where:
This requires an external prime mover to drive the motor at
2 4 with its rotor winding having a phase sequence opposite
to that of its stator winding and then connected to a three
v, cos (at+120)
phase supply after disconnecting the prime mover. With
these requirements satisfied and as stated above, the
100
conditions for uniform torque production are met and the
motor can operate as a synchronous motor at Zn,. However,
010
100100
at this speed, both T,, and X 3 oppose the torque component
001
T,,. This reduces the net uniform electromagnetic torque
010001
100
and hence the pull out torque of the motor. Consequently,
001010
the motor under this mode of operation suffers from two
001
drawbacks: (i) the loading margin is very narrow and (ii)
010
the need for an external prime mover to start and run the
where the rotor is connected in a sequence opposite to that
motor at a speed of 2n,.
of the stator. Substituting from eq.(2) and (3) in eq.(l)
yields:
III. Transient Analysis
A. Voltage equations
The system under study comprises a star connected three
phase slip ring induction motor with the stator and rotor
connected in series as shown in Fig. 1. The mathematical
model of the system in the original phase values reference
frame, is as given below.
I=
[v]'[vA
vB
I+ [ RI[i 1
vC
[ i ] = [ i A i B i,
va
i,
(1)
'b
ib
'c
COS
e,+ x
11
I
B. The current state space model
The stator and rotor currents in addition to the rotor speed
and position are chosen as the state variables. The current
space model can be derived as follows:
I'
i,
0-7803-5935-6/00/$10.00 (c) 2000 IEEE
I= Diag [(rs +rr
(rs +rr
(rs +rr
cos e, - 0.5 COS e, - 0.5
[ L , , ] = ~ xco~e,-o.5
,
C O S ~ , + X c0se,-o.5
cos e, - 0.5 cos e,- 0.5 cos e, + x
wherex= r+xl/Xm,
e,= ut, e2= ut-120, e3-wt+120.
[&,e
[
The voltage equation of the system is:
[ v P [ L I[i
where
In normalized form:
26 1
HI is the normalized inertia of massi and is given by:
H: = 2a,H,
The equations describing the unforced, undamped
mechanical system may be rearranged into the following
form:
The required state space model can be expressed as:
~ [ i s e] = [ A
where:
1
[ise
[ A I=- L,, I-'
I+[B
I[vse
1,
[GJe
[
1
(6)
(9)
I= [&,, I-'
<:.Electromagnetic Torque equation
The developed electromagnetic torque can be obtained as
the partial derivative of the energy stored in the mutually
coupled inductive circuits with respect to the rotor position
angle 0 ,. Accordingly, the torque in p.u can be expressed
as:
-'IO
-!
lo
1
1
72
CL
3
N'
F
I
-12
4
1
3 .o
0.0
t, sec
6.0
D. Mechanical system
The mechanical system consists of two masses as shown in
Fig.1. This system is represented as two inertias
interconnected by one torsional spring (the connecting
shaft), and can be described by two second-order
differential equations of the form [4]:
f
+
N.Results
The transients of the motor under normal connection when
started against 0.2 p. u load by applying the rated voltage to
its stator are shown in Fig.2. The response shows clearly
the excitation of the mechanical system natural frequency
mode (23.5 Hz). The maximum excitation occurs when the
frequency of one of the electromagnetic torque components
coincides with the natural frequency of the shaft. The
transfer torque T,I indicates that the electrical system
provides negative damping to this frequency mode at lower
speed. Once the motor speed exceeds the critical value at
which resonance occurs, the electrical system provides
positive damping to this oscillatory mode. In this case the
shaft will experience high stresses, about 7.0p.u.This is
because of the slow speeding up process of the motor that
will give a longer time for the electromechanical resonance
to take place even under a small level of pulsating torque.
The starting transients when the motor is connected in
series as shown in Fig.1 and loaded by 0.2 p.u torque is
sho n in Fig.3(a) when V=l.O p.u, and in Fig3(b) when
V= 3 p.u. The results indicate that the motor can not start
at the rated voltag under even under light load. At a
supply voltage of 3 p.u, the motor can start easily in a
time reduced by 45% compared with the conventional
direct on line starting. This advantage is obtained on the
expense of high torsional stresses on the shaft (about 12
p.u) due to the high level of pulsating torque components.
Once the motor speed reaches the running value, the
currents, electromagnetic torque and shaft torsional stress
become low. Stator and rotor voltage variations for the case
of Fig.3(b) are shown in Figd. It can be notedthatthe
stator and rotor voltages of the motor under series
connection do not exceed the rated values.
9
Fig.2 Starting transients of the motor when started under conventional
method at V=l.Op.u and against 0.2p.u load
[TI= [H*]P2 +[DIP
The system under study has only one natural fiequency in
the subsynchronous frequency zone. To assume the worst
condition the mechanical damping is neglected during the
study.
[Kl )[el
where
V. Conclusions
In this paper the series mode of operation of three phase
slip ring induction motors has been investigated. The rotor
windings are connected in series with that of the stator.
This mode allows the motor to operate from a supply with
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262
a voltage higher than the rated one. The results indicate
that: (i) under this mode, the motor can not start unless the
rotor phase sequence is in opposite of that of the stator, (ii)
the motor can not start under the rated voltage, (iii) at 133
supply voltage the motor under series mode is faster in
starting than the conventional mode, and (iv) the stator and
rotor voltages of the motor under series connection do not
e r<ceedthe rated values
4.
M.A. Badr, M.A. Abdel-halim and A.1. Alolah"A Nonconventional
Method for Fast Starting of Three Phase Wound Rotor Induction
Motors", IEEE Trans,Vol.EC-I 1(4), 1996, pp.701-707.
5.
M.A. Abdel-halim, M.A. Badr and A.I. Alo1ah"Smooth Starting of
Slip Ring Induction Motors", IEEE Trans.,Vol.EC-12(4), 1997,
pp.317-322.
6.
M.A. Badr, A.I. AIolah and A.F. A1marshood"Transient
Performance of Series Connected Three Phase Slip-Ring Induction
Motors", IEEE Trans. on Energy Conversion, Paper 97-036,
accepted for publication.
81
7. Ho, E. and Sen, P.
* * A High Performance Parameter-Insensitive
Drive Using a SeriesConnected Wound-Rotor Induction Motor",
IEEE Tw.. VoI.IA-25(6), 1989, pp.1132-1138.
2
m
.-
f
a
2
i
i
-a
0.0
I-
3
n
t<
\-
I-
-a
- I
0.0
3.0
6.0
t, sec
I
0
3
t, sec
6
Fig.4: Stator and rotor voltages when the motor is s ed under series
connection and against 0.2p.u load, V= 3p.u
Y
VI. Appendix
The rating of the motor under study is 220 V, 60 Hz,IkW
and its p.u. parameters are:
rl ~0.015,X,,, =4.0, X I =X2 = 0.09, r2=0.015,H 1 ~ ~ 2 2 6 . 2 ,
H~~~565.5,
K12=30.0.
a
U
i
I-
-10
-12
!
$*..r"
4
0.0
0.0
1
3.0
6.0
t. sec
(b)
Fig.3: Starting transients of the motor when started under cries
connection and against 0.2p.u load, (a) V=l.Op.u, @) V= 3p.u
3
W .References
I.
Alger, P."Induction Machines", Book, Gordon and Breach,New
York,2" ed., 1970.
2.
Say, M."AItemating Current Machines". Book.Pitman. England,
2 nd ed., 1984.
3.
M.A. Badr, A.I. Alolah and M.A. Abdel-halim"A Capacitor Start
Three. Phase Induction MotoS, IEEE Trans.. V0l.EC-10(4),1995,
pp.675-680.
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263
The relation between the inductance matrix elements and
the machine reactances in per unit &e:
L, =Lrr=M=2X,l3, L,r=X,, L,=X, X,=X,=X,