5. PERFORMANCE CHARATERISTICS OF IM The equivalent circuits derived in the preceding section can be used to predict the performance characteristics of.
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5. PERFORMANCE CHARATERISTICS OF IM
The equivalent circuits derived in the preceding section can be used to predict the performance characteristics of the induction machine.
The out put parameters of IM are speed and torque and their inter relation during starting ,steady state and braking are going to be seen.
The important performance characteristics in the steady state are:
- the efficiency- power factor - current- starting torque - maximum (or pull-out) torque and - so forth.
Steady state operating characteristics of an IM can be shown graphically as the shaft load increases from zero to full load.
These operating characteristics during starting, steady state, and braking are governed mainly by:-
- rotor resistance,
- air gap length, and
- shape of stator and rotor slots
4.1. Determination of induced TORQUE-SPEED characteristics of IM.
• When TORQUE-SPEED or POWER-SLIP characteristics are required, applying Thevenin's theorem is convenient.•Thevenin's theorem states that, “any linear circuit that can be separated by two terminals from the rest of the system can be replaced by a single voltage source in series with an equivalent impedance”. i.e.
V1
X1R1
Xm
Pag
I1 Io
'
2I
'
2X
SR '
2Zf
a
b
Fig. 5.1. EQUIVALENT CIRCUIT OF IM WITHOUT CORE LOSS.Fig. 5.1. EQUIVALENT CIRCUIT OF IM WITHOUT CORE LOSS.
• Applying Thevenin's theorem for equivalent circuit of IM shown in fig. 5.1, the circuit consisting of r1, x1, xm, and source voltage can be replaced by an equivalent voltage source Ve and equivalent impedance Ze = Re + jxe.
m
me xxjR
jxjxRZ
11
11 ,11
1
m
me xxjR
jxVV
Ve
Re Xe
Fig.5.2. Thevenin`s equivalent circuit
• Where,
Ve – Voltage appearing across terminals a,b with rotor circuit
disconnected from points a & b.
Ze – Impedance viewed from terminals a,b towards the voltage
source with the source voltage short circuited.
• For most IMs , under normal operating conditions, (X1+Xm) >> R1,and therefore R1 can be neglected.
Thus,
mm
m
me xxXwhere
X
xV
xx
xVV
11
1
1
1
1 ,;
1
1
1
1
1
1
1
1
X
xxj
X
xR
xx
xjx
xx
xRjXRZ mm
m
m
m
meee
• From the fig. 5.2, rotor current is:-
• We know that, per phase induced torque is:-
ee
e
xxjsr
R
VI
22
2
s
rIT
se
222.
1
Where, m – is the no. stator phases.
s
r
xxsr
R
VmT
ee
e
se
2
22
2
2
2
..
andKmV
ts
e ,
thenXxx e ,2
s
r
Xsr
R
KT
e
te
2
22
2
.
•If
NS
N0
S01
At low value of slips
( TS)
At large value of slip
( T1/S)
Tmax
Fig .5.3 Torque-speed characteristics
TST
Torque
Ns
.2Ns
speed
slip
Gen. regionMot. region
Braking
region
- Ns
-100 -50 0 50 100 150 200
torque
00.51.01.52.0 -0.5 -1.0
SmT
Ts
tar
Tm
ax
Full load oper. point
Fig
. 5.
4 T
orq
ue-
slip
cu
rve
of
IM
in
dif
fere
nt
mo
de
of
op
erat
ion
.
- T
ma
x
• Depending on the value of slip, an IM can have the following operating regions.
a) Motoring mode , 1 > S > 0 - the corresponding speed values are ZERO (s = 1.0) and synchronous speed (S = 0).
b) Generating mode , S < 0 - the rotor speed is above synchronous speed.
c) Breaking mode , S > 1 – This condition can be achieved by driving the rotor with a prime mover opposite to the direction of rotating magnetic field.
( eg. plugging action)
4.2. Determining maximum internal torque of IM
• Maximum torque is referred as Stalling torque; Pull out torque or Break down torque.
• Maximum internal torque can be obtained by using the maximum power transfer theorem of a circuit theory.
i.e. power transfer becomes max. when the load impedance is equal to the source impedance. and Torque in IM is max. when power delivered to load r2/s is max.
V1
X1R1
Rc Xm
Pag
I1 Io
Ic Im
a
II 2'
2 2
2'
2 XaX
S
Ra
S
R 2
2'
2 12
'
2 EaEE E1
Fig. 5.5.(fig.3.5b) Exact equivalent circuit diagram of IM.
• As per the exact equivalent circuit diagram of IM, max. power delivered to r2/s is attained when load resistance r2/s(referred rotor variable resistance) becomes equal to the impedance of the voltage source. i.e. from fig. 5.2 it can be seen that,
2222
22 XRxxRs
reee
mT
Thus, Max. slip at which maximum torque occurs is
222
2 ; xxXXR
rS e
e
mT
We know that, s
r
Xsr
R
KT
e
te
2
22
2
.
222222
22
22
22
22
2 XXRRXRR
XRK
XXRR
XRKT
eeee
et
ee
et
em
2222
22
2 XRRXR
XRKT
eee
et
em
222 XRR
KT
ee
tem
Where,
s
e
s
et n
mVmVK
2
22
2xxX e
1rRe
• These equations show that,
a) Slip at which maximum torque occurs is
directly proportional to rotor Resistance r2.
b) Maximum torque is independent of r2.
• This means that, if rotor resistance r2 is increased by inserting external resistance in the rotor circuit (in case of WRIM), the max. internal torque is Unaffected; but slip at which it occurs is affected proportionally.
• From the equation of Tem, it can be seen that,
a) Tem is directly proportional to the square of applied stator voltage.( Kt ∞ V1)
b) Tem is reduced by increasing stator resistance r1 (i.e.Re)
c) Tem is reduced by an increase in stator and rotor leakage reactance (x1 of stator and x2 of) rotor
• Thus, to obtain higher maximum torque, the air –gap between rotor and stator must be kept as small as possible in which mutual flux will be maximum and leakage reactance could be minimum.
• Typical TORQUE-SPEED curves for an IM with variable rotor circuit resistance and the effect of rotor resistance on the stator current are shown below
T
NS N
sm1sm2sm3
r21r22r23
r24
r24>r23>r22>r21
Slip
Fig.5.6. IM Torque-speed curve with different values of r2
Tmax
NS
N0
S01
Fig.5.7 Effect of rotor resistance r2 on stator current-slip charact.
Sta
tor
curr
ent
, p
.u.
Tor
que
Ts
tar
r22
r21
r23
r24
r24 > r23 > r22 > r21
Sta
tor
curr
.
4.3. Starting torque of IM - Tst,
s
r
Xsr
R
KT
e
te
2
22
2
.
We know that, the Induced motor torque is:
AT starting, slip S = 1.00, thus torque at starting is:-
2
22
2
.r
Xsr
R
KT
e
test
Induced motor torque Te in terms of max. torque Tem.
s
r
xxsr
R
VmT
ee
e
se
2
22
2
2
2
..
mT
emT
e
e
sem s
r
xxsr
R
VmT 2
2
22
2
.
s
r
Xsr
R
XRR
T
T
e
ee
em
e 2
22
2
22
.2
s
r
Xsr
X
T
T
em
e 2
22
2
.2
If Re is neglected, the equation becomes,
s
Xs
XsXsX
s
r
Xsr
X
T
T mT
mTem
e ..
2.
2
2
2
22
2
sss
s
s
Xs
XsXs
X
T
T
mT
mTmT
mTem
e
1
2..
.
2
2
22
2
mT
mTem
e
ss
ssT
T
2
mT
mT
eme
ss
ssT
T
2
Summary of performance characteristics.
• Speed• Torque• Stator current• Pf• Efficiency
Speed, Torque,
Stator current, Pf,
Efficiency
Pout
Fig. 5.8. Operating characteristics of IM.
0.2
1.0
1.0
Speed
Torque
Stator current
Pf
Efficiency
KEY
stator slots Shape effect on operating charac.• For a given slot area, slot shape can be:-
- More deep, less width
- Less depth, more width• Slot leakage flux is directly proportional to slot depth.• IMs with deeper slots have more leakage reactance, and more
leakage reactance results in less Tstar, less Tem and less SmT (look corresponding formula)
• Slots can also be
- open
- Semi closed
- closed.• Open slots have less leakage reactance than semi-closed slots
and semi-closed slots have less leakage reactance than closed slots.
Air-gap Effect on operating charac.• If the air-gap length is increased, air gap flux which must be
constant requires more magnetisation current.
• This reduces cosθ0,and cosθrat . In order an IM to have better power factor, the air-gap length must be as small as is mechanically possible.
- For open type slots, the air-gap is larger, so that more Im is
required which results poor operating power factor. However,
they have less leakage reactance, therefore better Test and Tem.
- For semi closed slots, the air-gap length is smaller, thus small
Im is required and cosθrat is better. But they have more
leakage reactance ,therefore reduced Test and Tem.
Thus, during designing an IM, a compromise is made between the operating power factor and Test,Tem to obtain optimum operating characteristics for a given working condition..
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