Transcript Elec467 Power Machines & Transformers

Elec467 Power Machines &
Transformers
Electric Machines by Hubert, Chapter 5
Topics: Induction machines classifications,
performance, applications, and operation.
Torque-speed
Torque-speed characteristics of basic NEMA designs for
squirrel-cage induction motors. In this chapter we will learn
what effect the rotor resistance has on these designs.
Rotor designs
The way the rotor is physically designed has a direct effect on
the torque-speed plot because it guides the flux field.
Induction motor equivalent circuit
The actual parameters of a motor are display above and labeled.
The value for each parameter are considered per phase.
Modification to text
Delete the 2nd equal sign in the first four equations on page 178 of the text.
Students are reminded of the role the turns ratio plays in
referring the components Rr and XBR to the stator side of the
equation and the inverse relationship the turns ratio has with
the voltage and current.
Induction motor equivalent circuit
Rr, X1 are changed into R2, X2 by application of the turns ratio squared, a2,
and I2 is Ir divided by a and E2 is EBR multiplied by a.
Equivalent circuit definitions for
Fig. 5-4
R1 = RS per Fig. 5-4
In these definitions the operative word is “per phase”. The equivalent circuit
represents 1 phase of the three thus the power isn’t determined by the power
in one phase but by multiplying the power for one phase by 3. Also, voltage
and current measurements are line values that have to be changed to phase
values. Since we assume a wye-connected motor/generator and we use one
in the lab then VL=√3 VØ and IL = IØ.
Formulas from Fig. 5-4
 R1  jX 1
V
Z in
E2 Z 2

R2
s
E2 Z 0 
Z1  Z P
Z2Z0

Z2  Z0

I1Z P
from page 179 of the text
R fe jX M
R fe  jX M
 jX 2
Locked rotor

I2 

V
R
R1  jX 1  2
s
 jX 2
Equation 5-3. By rearranging circuit of Fig. 5-4 and emphasizing that I2
and V are vectors, their magnitude can be taken… and T D derived.
After some more math you can find the
value of R2 the rotor resistor so that TD
occurs at block rotor:
R2, s 1  R12  ( X 1  X 2 ) 2
TD 
(5-8)
21.21V 2 R2
s

2
R 
 R1  2 s    X 1  X 2   ns



2
(5-5)
More math
Since
Thus
R
R1  2  X 1  X 2 
s
V
Vs
I2 

R2 s
R2
2
2
R 

R 
2
 R1  2    X 1  X 2    2 
s 

 s  s 0.03
21.21V 2 s
TD 
R2 ns
The observation made from all this math:
Changing the value of rotor resistance will change the slip at
which TD,max occurs, but will not change the value of TD,max
This is the means and methods for the different motor
designs seen in the first slide.
The substitutions above are valid for normal running of an induction
motor. Normal running is defined as operating between no load
and 15% overload with rated voltage and rated frequency. The slip
under these conditions is very small <0.03. See Figure 5-7 on the
next slide for the straight-line approximation.
Rotor current & Torque
Fig. 5-7
Wound-rotor motor
Torque-slip curves for wound-rotor
The rotor rheostat setting changes the
slip that TD,max occurs. For example,
maximum resistance generates curve
5. Minimum resistance puts you on
curve 1. For no-load this would mean
the intercept of curve 5 at s=1 gives
140% torque over rated load; the motor
would start to turn if the load doesn’t
exceed 140% of rated load. If you had
a rated load of 100% then the motor
increase speed up to s=.7 Thus for
any given constant load, such as 100%
rated load (in bold on figure) changing
the rheostat changes the slip which in
effect the shaft rotation or speed the
motor is rotating. The formula nr =sns
is a method for variable speed control
of motors.
Fig. 5-9
Name plate details
Derating
Imbalances in the 3Ø line voltage
overheats motors. Motors should
be run at a lower horsepower
using the factors determined
from the chart for Figure 5-13
When a motor is stopped by
switching off the line voltage, the
rotor continues to turn sending
voltage back out thru the stators.
Out-of-phase starts can create inrush current of 200% rated values.
Large motors >50 hp are
adversely affected by
starts. There are limits on
lifetime starts with waiting
periods between starts
DC tests
This test is used
to determine R1
First find RDC from
voltage & current
2nd
RDC 
select the type of winding
VDC
I DC
RDC  2R1,wye
R1,wye 
RDC
2
RDC 
R1, 2R1,
R1,  2R1,

R1,  1.5RDC
2
R1,
3
Blocked Rotor Test
This test
determines
X1 , X2 and R2
Calculate the
values solving
the formulas
below left to
right, top to
bottom:
V , BR 
VL , BR
3
Equivalent circuit assumptions IO<<IR
Z BR 
V , BR
I BR
RBR  PBR
X BR  X1  X 2
Assign values to X1, X2 according to the Table 5.10, if
motor type unknown assume X1 = X2
3I
2
BR
R2  RBR  R1
Power, voltage
and current are
taken from
measurements
while the rotor is
blocked.
IBR is the
average of the
two amp meter
readings.
2
2
X BR  Z BR
 RBR
No-load test
This test
determines
XM and
combined
core, friction
and windage
losses
Step 1
I M  I fe
I M  IO
Equivalent circuit
assumptions
To match up lab symbols to text:
XBR = Xeq RBR=Req and
PXX = sum of watt meters give 3Ø power
S NL  3V I
Calculate 3Ø apparent power
NL NL using line voltage
Step 2
2
2
QNL  S NL
 PNL
Step 3
Similarly using an approximation of the magnitude IM>>Ife as 10:
PNL  310* I NL 
2
Reactive power for all 3 phases
X NL 
PNL
R1  R fe  
 R1  R fe
2
310*I NL 
QNL
Calculate 1-Ø reactive power
2
3I NL
Step 4
X M  X NL  X1
Two additional formulas
Use as an approximation of Rfe:
PNL  I NL 
2
PNL
R1  R fe   2  R1  R fe
I NL 
Use the following equation for Pf,w and Pstray:
Pf ,w  Pstray  PNL I NL  R1  Pcore
2
Generation overview
In the above power generating system, assume the line voltage is driving
the motor at near synchronous rotor speed ns with the turbine steam valve
turned off. If the steam was let in, the turbine would turn faster causing nr
to be larger than ns thus creating a negative slip. When this occurs the flux
field at the gap reverses and the motor begins providing current to the line.
Transition plots
motoring to generator
The above graphs show the motor action that we’re familiar with and the
generator action which appear much like an inverted mirror image of the
motor side. The limits of operation in either case are between the two
extreme values: Breakdown and Pushover.
Overlay current
Graph (b) shows the overlay of the torque curve with the expected line
current. The current’s value doesn’t really go negative as one would
expect with a DC current; because its AC, the current is constantly
reversing. The exciting current exists in the motor when generating
and is supplied by the line current.
Self-Excited Generators
When an induction motor is run as a
generator, it is called an induction
generator. Induction generators can be
driven by a diesel or gasoline motor and
can be set up in remote locations (like
your backyard). While AC input voltage is
necessary for the exciting circuit to work,
enough voltage can be created without
connecting the generator to the electrical
grid. This is accomplished by connecting
3 capacitors across the input terminal of
the motor which are essentially the output
terminals of the generator.
Residue
magnetism in the rotor creates a small
voltage output and the capacitors build up
the voltage over time to provide the
exciting current, IO, to the stators. When
this occurs, the generator provides power
on its output terminals.
Stopping the motor
• A simple way to stop the motor is to simply disconnect the motor
from the AC line and let it coast to a stop. In order to lock the rotor,
it requires a mechanical application.
• Another method to stop the rotor quickly is to interchange two of
the AC line supply before its comes to a rest. This reverses the
motor’s electric field causing the motor to attempt to rotate in the
opposite direction.
• This is called PLUGGING. It will create slip values greater than one
because nr becomes negative after the rotor comes to a rest as the
rotor begins rotating in the opposite direction.
• Torque values and current surges created during this operation can
become excessive and destroy the motor unless it was designed for
this operation. See Figure 5-9 for the plot of torque values greater
than one.
Dynamic Braking
Dynamic braking is the slowing down of a machine by connecting the motor to a
braking circuit. There are two types of braking circuits: DC injection or
capacitive braking. Seen above is DC injection that operates by opening the
contactor on the input AC lines and closing thru the contactors from the braking
circuit that is rectifying the AC signal with diodes. Connecting the motor to a DC
circuit causes the stators to become permanent magnets and replaces the
rotating field with a static field that will also hold the rotor in place at rest.
Constrains on motor operation