INDUCTION MOTOR TESTS
(No-Load Test, Blocked Rotor Test)
The equivalent circuit parameters for an induction motor can be
determined using specific tests on the motor, just as was done for the
transformer.
No-Load Test
Balanced voltages are applied to the stator terminals
at the rated frequency with the rotor uncoupled from
any mechanical load. Current, voltage and power
are measured at the motor input. The losses in the
no-load test are those due to core losses, winding
losses, windage and friction.
Blocked Rotor Test
The rotor is blocked to prevent rotation and
balanced voltages are applied to the stator
terminals at a frequency of 25 percent of the
rated frequency at a voltage where the rated
current is achieved. Current, voltage and
power are measured at the motor input.
In addition to these tests, the DC resistance of the stator winding should be
measured in order to determine the complete equivalent circuit.
No-Load Test
The slip of the induction motor at no-load is very low. Thus, the
value of the equivalent resistance
in the rotor branch of the equivalent circuit is very high. The no-load rotor
current is then negligible and the rotor branch of the equivalent circuit can
be neglected. The approximate equivalent circuit for the no-load test
becomes
Induction machine
equivalent circuit for
no-load test
Note that the series resistance in the no-load test equivalent circuit is not
simply the stator winding resistance. The no-load rotational losses
(windage, friction, and core losses) will also be seen in the no-load
measurement. This is why the additional measurement of the DC
resistance of the stator windings is required. Given that the rotor current
is negligible under no-load conditions, the rotor copper losses are also
negligible. Thus, the input power measured in the no-load test is equal to
the stator copper losses plus the rotational losses.
where the stator copper losses are given by
From the no-load measurement data (VNL, INL, PNL) and the no-load
equivalent circuit, the value of RNL is determined from the no-load
dissipated power.
The ratio of the no-load voltage to current represents the no-load
impedance which, from the no-load equivalent circuit, is
and the blocked rotor reactance sum Xl1 + Xm1 is
Note that the values of Xl1 and Xm1 are not uniquely determined by the noload test data alone (unlike the transformer no-load test). The value of the
stator leakage reactance can be determined from the blocked rotor test. The
value of the magnetizing reactance can then be determined.
Blocked Rotor Test
The slip for the blocked rotor test is unity since the rotor is stationary.
The resulting speed-dependent equivalent resistance
goes to zero and the resistance of the rotor branch of the equivalent circuit
becomes very small. Thus, the rotor current is much larger than current in
the excitation branch of the circuit such that the excitation branch can be
neglected.
The resulting equivalent circuit for the blocked rotor test is shown in the
figure below.
Induction machine
equivalent circuit for
blocked rotor test
The reflected rotor winding resistance is determined from the dissipated
power in the blocked rotor test.
The ratio of the blocked rotor voltage and current equals the blocked rotor
impedance.
The reactance sum is
Note that this reactance is that for which the blocked rotor test is
performed. All reactances in the induction machine equivalent circuit are
those at the stator (line) frequency. Thus, all reactances computed based
on the blocked rotor test frequency must be scaled according to relative
frequencies (usually, a factor of 4 since TBR is usually 0.25TNL). The actual
distribution of the total leakage reactance between the stator and the rotor
is typically unknown but empirical equations for different classes of motors
(squirrel-cage motors) can be used to determine the values of Xl1 and Xl2N.
The following is a description of the four different classes of squirrel-cage
motors.
Class A Squirrel-Cage Induction Motor - characterized by normal
starting torque, high starting current, low operating slip, low rotor
impedance, good operating characteristics at the expense of high starting
current, common applications include fans, blowers, and pumps.
Class B Squirrel-Cage Induction Motor - characterized by normal
starting torque, low starting current, low operating slip, higher rotor
impedance than Class A, good general purpose motor with common
applications being the same as Class A.
Class C Squirrel-Cage Induction Motor - characterized by high
starting torque, low starting current, higher operating slip than Classes A
and B, common applications include compressors and conveyors.
Class D Squirrel-Cage Induction Motor - characterized by high
starting torque, high starting current, high operating slip, inefficient
operation efficiency for continuous loads, common applications are
characterized by an intermittent load such as a punch press.
Motor
Squirrel-cage Class A
Squirrel-cage Class B
Squirrel-cage Class C
Squirrel-cage Class D
Wound rotor
Blocked Rotor Leakage
Reactance Distribution
Xl1 = 0.5XBR
Xl1 = 0.4XBR
Xl1 = 0.3XBR
Xl1 = 0.5XBR
Xl1 = 0.5XBR
Xl2N = 0.5XBR
Xl2N = 0.6XBR
Xl2N = 0.7XBR
Xl2N = 0.5XBR
Xl2N = 0.5XBR
Using these empirical formulas, the values of Xl1 and Xl2N can be determined
from the calculation of XBR from the blocked rotor test data. Given the
value of Xl1, the magnetization reactance can be determined according to
Example (No-Load/Blocked Rotor Tests)
The results of the no-load and blocked rotor tests on a three-phase, 60
hp, 2200 V, six-pole, 60 Hz, Class A squirrel-cage induction motor are
shown below. The three-phase stator windings are wye-connected.
No-load test
Frequency = 60 Hz
Line-to-line voltage = 2200 V
Line current = 4.5 A
Input power = 1600 W
Blocked-rotor test
Frequency = 15 Hz
Line-to-line voltage = 270 V
Line current = 25 A
Input power = 9000 W
Stator resistance
2.8 S per phase
Determine (a.) the no-load rotational loss (b.) the parameters of the
approximate equivalent circuit.
(a.)
(b.) The voltage at the input terminals of the per-phase equivalent circuit,
given the wye connected stator windings, is
The equivalent circuit for the induction motor is shown below.
INDUCTION MACHINE TORQUE AND POWER
(MACHINE PERFORMANCE CHARACTERISTICS)
In order to simplify the determination of torque and power equations
from the induction machine equivalent circuit, we may replace the network
to the left of the reflected components by a Thevenin equivalent source.
The Thevenin voltage (open-circuit voltage) for the stator portion of the
equivalent circuit (to the left of the air gap) is
The Thevenin impedance (impedance seen after shorting V1) is
Inserting the Thevenin equivalent source into the induction machine
equivalent circuit yields the following equivalent circuit.
From the equivalent circuit, the total real power per phase that crosses the
air gap (the air gap power = Pair gap) and is delivered to the rotor is
The portion of the air gap power that is dissipated in the form of ohmic loss
(copper loss) in the rotor conductors is
The total mechanical power (Pmech) developed internal to the motor is equal
to the air gap power minus the ohmic losses in the rotor which gives
or
According to the previous equations, of the total power crossing the air gap,
the portion s goes to ohmic losses while the portion (1!s) goes to
mechanical power. Thus, the induction machine is an efficient machine
when operating at a low value of slip. Conversely, the induction machine
is a very inefficient machine when operating at a high value of slip. The
overall mechanical power is equal to the power delivered to the shaft of the
machine plus losses (windage, friction).
The mechanical power (W) is equal to torque (N-m) times angular
velocity (rad/s). Thus, we may write
where T is the torque and T is the angular velocity of the motor in radians
per second given by
where Ts is the angular velocity at synchronous speed. Using the previous
equation, we may write
Inserting this result into the equation relating torque and power gives
Solving this equation for the torque yields
Returning to the Thevenin transformed equivalent circuit, we find
Note that the previous equation is a phasor while the term in the torque
expression contains the magnitude of this phasor. The complex numbers
in the numerator and denominator may be written in terms of magnitude
and phase to extract the overall magnitude term desired.
The magnitude of the previous expression is
Inserting this result into the torque per phase equation gives
This equation can be plotted as a function of slip for a particular induction
machine yielding the general shape curve shown in Figure 5.17 (p.234). At
low values of slip, the denominator term of Rw2N/s is dominate and the
torque can be accurately approximated by
where the torque curve is approximately linear in the vicinity of s = 0. At
large values of slip (s.1 or larger), the overall reactance term in the
denominator of the torque equation is much larger than the overall
resistance term such that the torque can be approximated by
The torque is therefore inversely proportional to the slip for large values of
slip. Between s = 0 and s = 1, a maximum value of torque is obtained. The
maximum value of torque with respect to slip can be obtained by
differentiating the torque equation with respect to s and setting the
derivative equal to zero. The resulting maximum torque (called the
breakdown torque) is
and the slip at this maximum torque is
If the stator winding resistance Rw1 is small, then the Thevenin
resistance is also small, so that the maximum torque and slip at maximum
torque equations are approximated by
INDUCTION MACHINE EFFICIENCY
The efficiency of an induction machine is defined in the same way as
that for a transformer. The efficiency (0) is the ratio of the output power
(Pout) to the input power (Pin).
The input power is found using the input voltage and current at the stator.
The output power is the mechanical power delivered to the rotor minus the
total rotational losses.
The internal efficiency (0int) of the induction machine is defined as the ratio
of the output power to the air gap power which gives
The internal efficiency gives a measure of how much of the power
delivered to the air gap is available for mechanical power.
Example (Induction machine performance characteristics)
A three-phase, 460 V, 1740 rpm, 60 Hz, four-pole, wound-rotor
induction motor has the following equivalent circuit parameters:
Rw1 = 0.25S
Rw2N = 0.2S
Xl1 = Xl2N = 0.5S
Xm1 = 30S
The rotational losses are 1700W. Determine (a.) the starting current when
starting direct on full voltage (b.) the starting torque (c.) the full-load slip
(d.) the full-load current (e.) the ratio of starting current to full-load current
(f.) the full-load power factor (g.) the full-load torque (h.) the air-gap power
(i) the machine efficiency (j) the slip at which maximum torque is
developed (k.) the maximum torque
3 = 265.58 V. The induction
The line-to-neutral voltage is V1 = 460/%&
motor equivalent circuit is shown below.
(a.) For calculations involving starting values, the rotor is assumed to be
stationary so that s = 1. The input impedance seen by the source V1
at start is
The stator input current I1 (starting current) is
(b.)
(c.) The full-load slip is the slip at the rated speed.
(d.) The full load current is found using the full-load slip. The input
impedance at start-up is modified to include the slip-dependent term.
(e.) The ratio of starting current to full-load current is
(f.)
(g.)
(h.)
(i)
PFfl = cos(19.71o) = 0.941 lagging
(j.)
(k.)
INDUCTION MOTOR STARTING
Since induction motors can draw significant currents on startup, there
are alternate techniques that can be used to reduce the magnitude of the
startup currents. Large startup currents can cause problems to the power
system if the lines supplying the motor do not have enough capacity. If the
large startup current causes a voltage dip, the starting torque is reduced,
since the torque varies with the square of the voltage.
Direct-On-Line Starting - the induction motor is connected directly
to the line voltage on startup.
Reduced Voltage Starting - a reduced voltage is applied to start the
motor and slowly increased to the rated value (using an
autotransformer).
Addition of Resistances - insert resistances in series with the motor
at startup, short resistors when the motor gains speed.
Wye-Delta Switching - if the stator windings are normally deltaconnected, the windings can be wye-connected during startup
to provide a lower startup voltage, then switched back to delta
as the machine approaches full speed.
INDUCTION MOTOR SPEED CONTROL
The induction motor is basically a constant speed motor given a
constant voltage source operating at a constant frequency. As the load
torque increases, the motor speed varies by only a small percentage of the
rated speed. There are some techniques that allow for control of the
induction motor speed.
Pole Changing - By changing the stator winding connections, the
total number of poles can be modified, only discrete speed changes
are available.
Line frequency variation - the synchronous speed of the motor, and
thus the machine speed, can be changed by simply varying the
line frequency.
Line voltage control - the speed of the induction motor can be
changed over a small range for a given load by varying the line
voltage (see Figure 5.29, p.255).