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 no- load 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. Blocked Rotor Leakage Motor Reactance Distribution Squirrel-cage Class A Xl1 = 0.5XBR Xl2N = 0.5XBR Squirrel-cage Class B Xl1 = 0.4XBR Xl2N = 0.6XBR Squirrel-cage Class C Xl1 = 0.3XBR Xl2N = 0.7XBR Squirrel-cage Class D Xl1 = 0.5XBR Xl2N = 0.5XBR Wound rotor Xl1 = 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.