Induction Motor Parameter Measurement

Transcription

1 Induction Motor Paraeter Measureent Induction Motor Paraeter Measureent Introduction Since its invention by Nikola Tesla in the 800s, the induction otor has reained the ost popular type of otor for industry applications. The priary advantage of the induction otor is it's straightforward rotor construction leading to low-cost, ruggedness, and low-aintenance requireent. Induction otor odel As with other electrical achines, an equivalent electric circuit can be developed for the purpose of gaining insight into the otors operation. The per-phase equivalent circuit of an induction otor is shown in Figure. The circuit ipedances are defined (in Ohs) by the following: R X X R c X 2 R 2 stator resistance stator leakage reactance agnetizing reactance achine core loss resistor rotor leakage reactance rotor resistance The terinals a and n represent the a-phase and neutral points of a wye-connected induction otor. Siilar equivalent circuits exist for the b- and c- phases with all quantities having the sae values but lagging the a-phase by 20 o and 240 o respectively.

2 Induction Motor Paraeter Measureent 2 Note that the core loss resistor eleent is added to account for hysteresis and eddy currents. Since these losses are a function of frequency, this ter is only approxiate and is soeties not included in the odel. The circuit electrical quantities are: V ˆ Î Î 2 V ˆ Î s otor phase voltage (V) stator current into otor phase (A) rotor current (A) voltage across agnetizing circuit (V) agnetizing current (A) per unit slip Herein, the hat sybol ^ represents a phasor. The agnitude of the phasor is denoted by the variable of the sae nae (i.e. I is the agnitude of Î ). The phase voltage V ˆ is used as the phasor reference with an angle of zero. The per unit slip s is defined by s ω ω ω s = () s In (), ω is the rotor echanical speed and ω s is the synchronous speed of the stator poles which is a function of the electrical frequency of the excitation source V ˆ and the nuber of stator poles. For a achine operating at a frequency f, the synchronous speed can be calculated (in rad/sec) fro 2 ωs = (2π f ) (2) poles To copute the per-phase input ipedance of the induction otor, it is convenient to define the stator, agnetizing, rotor, and "field" ipedances respectively as The input ipedance is then given by Z = + (3) R j X Z = (4) Rc j X R2 Z 2 = + j X 2 (5) s Z = Z Z (6) f 2 Zin = Z + Zf = Z θ (7)

3 Induction Motor Paraeter Measureent 3 It should be noted that the angle of the input ipedance is the negative of the angle of Î since the phase voltage is used as the reference. The cosine of this angle is the power factor pf = cos(θ ) (8) Three siple laboratory tests can be used to deterine the circuit odel ipedance paraeters. These tests are described below. Measuring equivalent circuit odel paraeters The siplest eleent to deterine is the stator resistance R which can be easured with an oheter. However, for large achines it is usually easured with a DC source so that it can be deterined at the rated value of current; thereby including the increase in resistance with teperature rise. Fro Figure, it can be seen that if a DC source is used the input ipedance contains only R since the inductors will act as short circuits. Figure 2 shows the per-phase equivalent circuit that exists when a DC voltage is applied to the A-phase. The applied DC voltage and resulting DC current are easured and the stator resistance is calculated fro V DC R = (9) I DC After deterining the stator resistance, a blocked rotor test is perfored on the induction otor. This involves physically blocking the rotor and applying a low voltage so that rated current flows in the stator windings. Under these conditions, the echanical speed ω is zero and therefore the slip is unity. This results in the rotor ipedance Z 2 being uch saller than the agnetizing ipedance Z. As a result, the current flowing in the agnetizing ipedance can be neglected and the equivalent circuit only involves the stator and rotor ipedances as shown in Figure 3. By easuring the voltage, current, and input power, the blocked rotor ipedance can be calculated by

4 Induction Motor Paraeter Measureent 4 V,bl Q bl Z = bl tan (0) I,bl Pbl The real and iaginary parts of this ipedance deterine the su of the stator and rotor resistances and reactances respectively as { } R + = () R2 Re Zbl { } X + = (2) X 2 I Zbl With this inforation, the rotor resistance can be deterined since the stator resistance was found using the DC resistance test. In order to deterine the stator and rotor leakage reactances, a second equation is necessary. Table I displays the necessary relationship between X and X 2 for the ost coon types of industrial induction otors. These are classified by the National Electrical Manufacturers Association (NEMA). Table I. NEMA class otor data. NEMA class A X = X 2 NEMA class B X = (2/3) X 2 NEMA class C X = (3/7) X 2 NEMA class D X = X 2 NEMA classes are based on the otor perforance which is a function of otor geoetry. Perforance characteristics include speed regulation, stall torque, and starting current. The ost coon type of induction otor is the NEMA class B since its perforance is a good coproise of the perforance characteristics.

5 Induction Motor Paraeter Measureent 5 The reaining paraeters R c and X can be deterined fro a no-load test. If the otor is operating at rated voltage and without a load, the echanical speed is close to synchronous and the slip is zero (neglecting echanical friction load). With a slip of zero, the rotor ipedance goes to infinity and the equivalent electric circuit is that shown in Figure 4. As with the blocked rotor test, the voltage, current, and input power are easured and the no-load input ipedance is calculated fro V,nl Q nl Z nl = tan (3) I,nl Pnl The no-load "field" ipedance can be found by using R and X fro the previous tests. If a no-load "field" adittance is defined by fnl nl ( R j X ) Z = Z + (4) fnl Y fnl = (5) Z then the agnetizing ipedance eleents can be calculated fro R c = (6) Re X { Y } fnl = (7) I { Y } fnl

6 Induction Motor Paraeter Measureent 6 Laboratory Software Screen-shots of the laboratory software are shown in Figure 4. The Test Type allows selection between the three tests. For the DC resistance test (shown in the top of Figure 4), a bar is included for coanding a dc current into the otor. The voltage, current, and power can be logged. When the Test Type is set to "No Load" the eters change fro DC to AC and voltage and current wavefor plots appear. Note that this progra already divides the line-to-line voltage by 3 so that line-to-neutral voltages are displayed and logged. The blocked rotor test screen is siilar to the no-load test screen with the exception that the data is logged with a different label.

7 Induction Motor Paraeter Measureent 7 Laboratory Work Laboratory Induction Motors The laboratory induction otors are standard NEMA class B industrial achines with ratings shown in the table below. poles = 4 f = 60Hz n =725RPM V = 208V I = 3.A P =hp LL L DC Resistance Test Connect the induction otor to the Sorenson DC power supply through the eter panel as shown in Figure 5. Select "DC Test" fro the tab in the coputer progra and click "Zero DC Offset". Energize the Sorenson power supply. On the coputer screen, increase the coanded current to 3A. Note by the achine naeplate that this is close to the rated current. Log the data by clicking Add. Reduce the coanded current to zero and switch off the Sorenson power supply. Note that this resistance was easured fro line-to-line. The per-phase stator resistance will be half of the value calculated fro this easureent. Blocked Rotor Test Connect the induction otor to the source panel as shown in Figure 6. Select "Blocked Rotor" fro the tab in the coputer progra. Make sure the source voltage is set to zero and then switch on the source panel circuit breaker. Hold the otor shaft and increase the source voltage until rated current is reached. Note that this will be a relatively low voltage (with the source knob set to about 20%). Log the data by clicking Add. Decrease the source panel voltage to zero and switch off the source panel. No-Load Test For the no-load test, the sae electrical connections as the blocked rotor test (Figure 6) will be used. Change the test type in the software to "No Load". Switch on the source panel circuit breaker and increase the voltage to 00%. At this point, the otor has rated voltage applied and is operating near synchronous speed. Log the data by clicking Add. Decrease the source voltage to zero and switch the circuit breaker off. shaft

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10 Induction Motor Paraeter Measureent 0 Calculations and Questions. Based on the achine ratings, copute the slip at rated speed. Also copute the torque (in Newton-eters), input power (in Watts), and power factor at rated speed. 2. Using the DC resistance test easureents, coputer the stator resistance. 3. Using the blocked rotor test, copute the rotor resistance as well as the stator and rotor leakage reactances. Use the relationship in Table I to deterine the distribution of leakage reactances. 4. Fro the no-load test data, deterine the agnetizing reactance and the core loss resistance. 5. Copile the coplete set of achine paraeters in a table along with the achine ratings. List the ratings in etric units (e.g. Watts and rad/s).