INDUCTION MOTOR TESTS(No-Load Test, Blocked Rotor Test)

The equivalent circuit parameters for an induction motor can bedetermined using specific tests on the motor, just as was done for thetransformer.

No-Load Test Balanced voltages are applied to the stator terminalsat the rated frequency with the rotor uncoupled fromany mechanical load. Current, voltage and powerare measured at the motor input. The losses in theno-load test are those due to core losses, windinglosses, windage and friction.

Blocked Rotor Test The rotor is blocked to prevent rotation andbalanced voltages are applied to the statorterminals at a frequency of 25 percent of therated frequency at a voltage where the ratedcurrent is achieved. Current, voltage andpower are measured at the motor input.

In addition to these tests, the DC resistance of the stator winding should bemeasured in order to determine the complete equivalent circuit.

No-Load Test

The slip of the induction motor at no-load is very low. Thus, thevalue of the equivalent resistance

in the rotor branch of the equivalent circuit is very high. The no-load rotorcurrent is then negligible and the rotor branch of the equivalent circuit canbe neglected. The approximate equivalent circuit for the no-load testbecomes

Induction machineequivalent circuit for

no-load test

Note that the series resistance in the no-load test equivalent circuit is notsimply the stator winding resistance. The no-load rotational losses(windage, friction, and core losses) will also be seen in the no-loadmeasurement. This is why the additional measurement of the DCresistance of the stator windings is required. Given that the rotor currentis negligible under no-load conditions, the rotor copper losses are alsonegligible. Thus, the input power measured in the no-load test is equal tothe 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-loadequivalent circuit, the value of RNL is determined from the no-loaddissipated power.

The ratio of the no-load voltage to current represents the no-loadimpedance 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 no-load test data alone (unlike the transformer no-load test). The value of thestator leakage reactance can be determined from the blocked rotor test. Thevalue 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 circuitbecomes very small. Thus, the rotor current is much larger than current inthe excitation branch of the circuit such that the excitation branch can beneglected.

The resulting equivalent circuit for the blocked rotor test is shown in thefigure below.

Induction machineequivalent circuit for

blocked rotor test

The reflected rotor winding resistance is determined from the dissipatedpower in the blocked rotor test.

The ratio of the blocked rotor voltage and current equals the blocked rotorimpedance.

The reactance sum is

Note that this reactance is that for which the blocked rotor test isperformed. All reactances in the induction machine equivalent circuit arethose at the stator (line) frequency. Thus, all reactances computed basedon the blocked rotor test frequency must be scaled according to relativefrequencies (usually, a factor of 4 since TBR is usually 0.25TNL). The actualdistribution of the total leakage reactance between the stator and the rotoris 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-cagemotors.

Class A Squirrel-Cage Induction Motor - characterized by normalstarting torque, high starting current, low operating slip, low rotorimpedance, good operating characteristics at the expense of high startingcurrent, common applications include fans, blowers, and pumps.

Class B Squirrel-Cage Induction Motor - characterized by normalstarting torque, low starting current, low operating slip, higher rotorimpedance than Class A, good general purpose motor with commonapplications being the same as Class A.

Class C Squirrel-Cage Induction Motor - characterized by highstarting torque, low starting current, higher operating slip than Classes Aand B, common applications include compressors and conveyors.

Class D Squirrel-Cage Induction Motor - characterized by highstarting torque, high starting current, high operating slip, inefficientoperation efficiency for continuous loads, common applications arecharacterized by an intermittent load such as a punch press.

Blocked Rotor Leakage Motor Reactance Distribution

Squirrel-cage Class A Xl1 = 0.5XBR Xl2N = 0.5XBRSquirrel-cage Class B Xl1 = 0.4XBR Xl2N = 0.6XBRSquirrel-cage Class C Xl1 = 0.3XBR Xl2N = 0.7XBRSquirrel-cage Class D Xl1 = 0.5XBR Xl2N = 0.5XBRWound rotor Xl1 = 0.5XBR Xl2N = 0.5XBR

Using these empirical formulas, the values of Xl1 and Xl2N can be determinedfrom the calculation of XBR from the blocked rotor test data. Given thevalue 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, 60hp, 2200 V, six-pole, 60 Hz, Class A squirrel-cage induction motor areshown below. The three-phase stator windings are wye-connected.

No-load test Frequency = 60 HzLine-to-line voltage = 2200 VLine current = 4.5 AInput power = 1600 W

Blocked-rotor test Frequency = 15 HzLine-to-line voltage = 270 VLine current = 25 AInput power = 9000 W

Stator resistance 2.8 S per phase

Determine (a.) the no-load rotational loss (b.) the parameters of theapproximate 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 equationsfrom the induction machine equivalent circuit, we may replace the networkto the left of the reflected components by a Thevenin equivalent source.

The Thevenin voltage (open-circuit voltage) for the stator portion of theequivalent 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 machineequivalent circuit yields the following equivalent circuit.

From the equivalent circuit, the total real power per phase that crosses theair 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 equalto 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 tomechanical power. Thus, the induction machine is an efficient machinewhen operating at a low value of slip. Conversely, the induction machineis a very inefficient machine when operating at a high value of slip. Theoverall mechanical power is equal to the power delivered to the shaft of themachine plus losses (windage, friction).

The mechanical power (W) is equal to torque (N-m) times angularvelocity (rad/s). Thus, we may write

where T is the torque and T is the angular velocity of the motor in radiansper second given by

where Ts is the angular velocity at synchronous speed. Using the previousequation, 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 torqueexpression contains the magnitude of this phasor. The complex numbersin the numerator and denominator may be written in terms of magnitudeand 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 inductionmachine yielding the general shape curve shown in Figure 5.17 (p.234). Atlow values of slip, the denominator term of Rw2N/s is dominate and thetorque can be accurately approximated by

where the torque curve is approximately linear in the vicinity of s = 0. Atlarge values of slip (s.1 or larger), the overall reactance term in thedenominator of the torque equation is much larger than the overallresistance term such that the torque can be approximated by

The torque is therefore inversely proportional to the slip for large values ofslip. Between s = 0 and s = 1, a maximum value of torque is obtained. Themaximum value of torque with respect to slip can be obtained bydifferentiating the torque equation with respect to s and setting thederivative equal to zero. The resulting maximum torque (called thebreakdown torque) is

and the slip at this maximum torque is

If the stator winding resistance Rw1 is small, then the Theveninresistance is also small, so that the maximum torque and slip at maximumtorque equations are approximated by

INDUCTION MACHINE EFFICIENCY

The efficiency of an induction machine is defined in the same way asthat 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 thetotal rotational losses.

The internal efficiency (0int) of the induction machine is defined as the ratioof the output power to the air gap power which gives

The internal efficiency gives a measure of how much of the powerdelivered 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-rotorinduction 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 whenstarting 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 isdeveloped (k.) the maximum torque

The line-to-neutral voltage is V1 = 460/%&3 = 265.58 V. The inductionmotor equivalent circuit is shown below.

(a.) For calculations involving starting values, the rotor is assumed to bestationary so that s = 1. The input impedance seen by the source V1at 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 inputimpedance at start-up is modified to include the slip-dependent term.

(e.) The ratio of starting current to full-load current is

(f.) PFfl = cos(19.71o) = 0.941 lagging

(g.)

(h.)

(i)

(j.)

(k.)

INDUCTION MOTOR STARTING

Since induction motors can draw significant currents on startup, thereare alternate techniques that can be used to reduce the magnitude of thestartup currents. Large startup currents can cause problems to the powersystem if the lines supplying the motor do not have enough capacity. If thelarge 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 directlyto the line voltage on startup.

Reduced Voltage Starting - a reduced voltage is applied to start themotor and slowly increased to the rated value (using anautotransformer).

Addition of Resistances - insert resistances in series with the motorat startup, short resistors when the motor gains speed.

Wye-Delta Switching - if the stator windings are normally delta-connected, the windings can be wye-connected during startupto provide a lower startup voltage, then switched back to deltaas the machine approaches full speed.

INDUCTION MOTOR SPEED CONTROL

The induction motor is basically a constant speed motor given aconstant voltage source operating at a constant frequency. As the loadtorque increases, the motor speed varies by only a small percentage of therated speed. There are some techniques that allow for control of theinduction motor speed.

Pole Changing - By changing the stator winding connections, thetotal number of poles can be modified, only discrete speed changesare available.

Line frequency variation - the synchronous speed of the motor, andthus the machine speed, can be changed by simply varying theline frequency.

Line voltage control - the speed of the induction motor can bechanged over a small range for a given load by varying the linevoltage (see Figure 5.29, p.255).