49 239 three phase induction machine the magnetizing

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Unformatted text preview: ted by a very high resistive branch representing the rotor circuit. The reactance of this parallel combination is almost the same as X m . Therefore the total reactance X NL , measured at no load at the stator terminals, is essentially X 1 + X m . The equivalent circuit at no load is shown in Fig.4.11a. (a) No-load equivalent circuit (b) Blocked-rotor equivalent circuit. (c) Blocked-rotor equivalent circuit for improved value for R2 . Fig.4.11 The primary phase voltage can be obtained from the following equation: 240 Chapter Four V1 = VLL V / Phase 3 (4.30) Then the no-load impedance can be obtained as following: Z NL = V1 I1 (4.31) The no-load resistance is: RNL = PNL 3I12 (4.32) The no-load reactance is: 2 2 X NL = Z NL − RNL (4.33) In the IEEE recommended equivalent circuit we assume that X 1 + X m = X NL (4.35) Then from no load test we only get the value of X 1 + X m Locked-rotor test Under rated line voltage, when the rotor of an induction motor is locked, the stator current I P is almost six times its rated value. Furthermore, the slip s is equal to one. This means that R2 / s is equal to R2 , where R2 is the resistance of the rotor reflected into the stator. Because I p is much greater than the exciting current I o , we can neglect the magnetizing branch. This leaves us with the circuit of Fig.4.8 (without magnetizing branch), 241 Three-Phase Induction Machine composed of the leakage reactance X, the stator resistance R1 , and the reflected rotor resistance R2 / s . Their values can be determined by measuring the voltage, current, and power under locked-rotor conditions, as follows: a. Apply reduced 3-phase voltage to the stator and gradually increase it from zero until the stator current is about equal to its rated value. Sometimes it is recommended to use lower frequency than the rated to avoid the errors due to skin effect in the rotor circuit. b. Take readings of VLL BL (line-to-line), I1 BL , and the total 3-phase power PBL (Fig.4.12). So, for the blocked-rotor test the slip is 1. In the equivalent circuit of Fig.4.9, the magnetizing reactance X m is shunted by the ′ ′ ′ ′ low-impedance branch R2 + jX 2 . Because X m >> R2 + jX 2 , the impedance X m can be neglected and the equivalent circuit for the blocked-rotor test reduces to the form shown in Fig.4.11b. From the blocked-rotor test, the blocked-rotor resistance is: RBL = PBL 3I12 (4.36) BL The blocked-rotor impedance at frequency of blocked rotor test is: 242 Chapter Four Z BL fBL = V1 BL (4.37) I1 BL The blocked-rotor reactance at frequency of blocked rotor test is: X BL fBL = (Z 2 BL fBL 2 − RBL ) (4.38) Its value at rated frequency is: X BL = X BL * fBL Rated Frequency (4.39) Frequency at blocked rotor test ′ X BL ≅ X 1 + X 2 (4.40) ′ assume, X 1 = X 2 (at rated frequency) ′ then X 1 and X 2 can be obtained. From no load test we know that X 1 + X m = X NL and X 1 are known then the magnetizing reactance is : X m = X NL − X 1 (4.41) ′ Comments: The rotor equivalent resistance R2 plays an important role in the performance of the induction machine. So, an ′ accurate determination of R2 is recommended by the IEEE as follows: The blocked resistance RBL is the sum of R1 and an equivalent ′ ′ resistance, say R, which is the resistance of R2 + jX 2 in parallel with X m as shown in Fig.4.11c; therefore, Three-Phase Induction Machine 2 Xm R= 2 R′ 22 ′ ′ R2 + ( X 2 + X m ) 243 (4.42) ′ ′ If X 2 + X m >> R2 , as is usually the case, 2 X′ + Xm ′ R R2 = 2 Xm (4.43) 2 Xm or R ≅ X ′ + X R2 ′ 2 m (4.44) Now R = RBL − R1 . So, we can use this value of R to determine ′ R2 from equation (4.43) More elaborate tests are conducted on large machines, but the above-mentioned procedure gives results that are adequate in most cases. Fig.4.12 A locked-rotor test permits the calculation of the total leakage reactance x and the total resistance (R1 + R2 ). From these results we can determine the equivalent circuit of the induction motor. 244 Chapter Four Example 4.2 A no-load test conducted on a 30 hp, 835 r/min, 440 V, 3-phase, 60 Hz squirrel-cage induction motor yielded the following results: No-load voltage (line-to-line): 440 V No-load current: 14 A No-load power: 1470 W Resistance measured between two terminals: 0.5 Ω The locked-rotor test, conducted at reduced voltage, gave the following results: Locked-rotor voltage (line-to-line): 163 V Locked-rotor power: 7200 W Locked-rotor current: 60 A Determine the equivalent circuit of the motor. Solution: Assuming the stator windings are connected in wye, the resistance per phase is: R1 = 0.5 / 2 = 0.25 Ω From the no-load test: The primary phase voltage can be obtained from the following equation: V1 = VLL 440 = = 254V / Phase 3 3 Three-Phase Induction Machine 245 Then, the no-load impedance can be obtained as following: Z NL = V1 254 = = 18.143 Ω I1 14 The no-load resistance is: RNL = PNL 1470 = = 2.5 Ω 3I12 3 *14 2 The no-load reactance is: 2 2 X NL = Z NL − RNL = 1...
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This document was uploaded on 03/12/2014 for the course ENGINEERIN electrical at University of Manchester.

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