School of Electronic & Electrical Engineering University of Leeds (2019/2020 Session) ELEC3565 1 | P a g e ELEC 3565 ELECTRIC MACHINE Induction Motor Parameters Identification Laboratory 1 INTRODUCTION The objectives are to give an insight into how the induction motor works and how it can be described in terms of an equivalent circuit. The equivalent circuit parameters are derived from two simple tests [see (iii) and (iv) below], none of which involves supplying large amounts of’ power to the motor. 2 EXPERIMENTAL WORK Read Appendix A (which explains the equivalent circuits for Locked-Rotor and No-Load tests). The motor is a 3-phase, 50 Hz, 4-pole, cage induction machine rated for output power 2.2kW at 1420rpm. In the experiment, the motor should be delta (∆) – connected. The rated voltage for ∆ connection is 230 V, and the rated line current is 8.5 A. i) Measure the stator winding resistance (cold, i.e. ambient temperature); ii) The motor is supplied from 3-phase variable autotransformer (variac) which is connected to the 3-phase, 50 Hz, 110 V laboratory mains. Connect the motor and instruments as shown in Fig.1 below. (Pay attention to connections of wattmeter terminals.) Using the phasor analysis, it can be shown that the sum of readings of the two wattmeters, including the sign of each reading, gives the total (3 phase) real (active) input power. iii) No-Load test: Raise the voltage from the 3-ph autotransformer (variac) to approximately 230V and measure the voltage, line current and input power. After the measurement reduce the voltage to zero. iv) Locked-Rotor test: Raise the voltage to a level which gives the rated current to the motor and measure the voltage, line current and input power. After the measurement reduce the voltage to zero. SWITCH OFF THE MAINS SUPPLY. Disconnect the motor and measure the stator winding resistance (warm). Summary of results: No-load test: R1(cold) = Ω, Vph = V, Iph = ூಽ √ଷ = A, P3ϕ = Pwattmeter1 + Pwattmeter2 = W, Pph = యഝ ଷ = W Locked-rotor test: Vph = V, Iph = ூಽ √ଷ = A, R1(warm) = Ω, P3ϕ = Pwattmeter1 + Pwattmeter2 = W, Pph = యഝ ଷ = W. Use the results of the short-circuit (Locked-Rotor) and open-circuit (No-Load) tests to derive the parameters of the equivalent circuit (see Appendix A). Check that these are sensible. W1 V Fig. 1 Vph I Iph W2 V A MOTOR Red Yellow Blue School of Electronic & Electrical Engineering University of Leeds (2019/2020 Session) ELEC3565 2 | P a g e APPENDIX A: Equivalent Circuit Parameters Determination Fig 2 shows the equivalent circuit for one phase of the 3-phase induction motor. Note that it is very similar to that of a transformer, with ‘primary’ and ‘secondary’ becoming ‘stator’ and ‘rotor’ respectively. There is one vital difference: the mechanical output power of the motor is represented by the power dissipated in the resistance R2′(1-s)/s. Note that this resistance changes with slip, reflecting the fact that the mechanical power is a function of slip. When the slip is zero (at synchronous speed), the ‘load resistance’ becomes infinite, so there is no rotor current, and hence no output power. And when the slip is 1 (at standstill) the ‘load resistance’ becomes zero, and again there is no mechanical output power. Note that in the later condition, however, the rotor current will be large, because the ‘load resistance’ is zero (i.e. a short-circuit). The corresponding torque is of course the starting torque of the motor. I1 R1 X1 I2′ X2′ R2′ Vph Xm Rc R2′(1-s)/s Im Ic Fig.2 – The ‘per phase’ equivalent circuit of 3-phase induction motor R1 = Stator winding resistance per phase R2′ = Referred rotor resistance per phase X1+X2′ = Total referred leakage reactance per phase Xm = Magnetising reactance per phase Rc = ‘Core loss’ resistance per phase s = (no – n)/no , p.u. slip The equivalent circuit parameters (R1, R2′, X1, X2′, Xm and Rc) are derived from two tests – the ‘locked-rotor’ test and the ‘no-load’ test. Under locked-rotor condition, (s = 1) the part of the circuit to the right of the dotted line in Fig.2 becomes short-circuited, and since the impedance of the remaining elements R2′ and X2′ is much lower than the impedance of parallel-connected elements Xm and Rc which can be ignored and the per-phase equivalent circuit for locked-rotor test reduces to that shown in Fig 3. (The locked-rotor test of induction motor is equivalent to the test of a transformer with short-circuited secondary.) The supply voltage in this test must therefore be reduced. The measured quantities in the locked-rotor test (voltage, current and power) are used to evaluate values of (R1+R2′) and (X1+X2′) from equations for power per phase (Eq.1) and impedance (Eq.2), i.e. (1) (2) Knowing R1 by direct measurement in the warm state, R2′ can be calculated from Eq.1 and X1+X2′ from Eq.2. X1 and X2′ are taken to have equal value, i.e. X1 = X2′. R1+R2’ X1+X2’ Iph PphVph Fig. 3 )'( 21 2 RRIP phph 2 21 2 21 )'()'( XXRR I V ph ph School of Electronic & Electrical Engineering University of Leeds (2019/2020 Session) ELEC3565 3 | P a g e Under no-load condition, the slip (s) is very small and the impedance to the right of the dotted line in Fig.2 is much higher than that of the parallel-connected branches Xm and Rc. So the per-phase equivalent circuit for no-load test reduces to that shown to the left of Fig 4. (The no-load test of induction motor is equivalent to the test of a transformer with open secondary.) Since the currents of parallel elements Xm and Rc differ from the phase current Iph , the values of parameters Xm and Rc cannot be directly obtained from measured quantities in no-load test (voltage, current and power). Nonetheless, by applying the complex numbers notation, the parallel-connected elements Xm and Rc in the equivalent circuit for no-load test can be transformed into an equivalent series-connected elements R and X shown to the right of Fig.4. This transformation is derived in Appendix B. Series-connected elements (R1+R) and (X1+X) can now be easily calculated from Vph, Iph and Pph in similar manner as done above, i.e. by applying Eqs.(1) and (2) in which the parameters R2′ and X2′ are replaced by R and X, respectively. Knowing the reactance X1 obtained from locked-rotor test and the resistance R1 measured in the cold state, the values of R and X can be determined. Finally, the original parallel resistance Rc and reactance Xm can be obtained by resolving Eqs.(3) and (4) which yields: ܴ = ܴଶ + ܺଶܴ ܺ = ܴଶ + ܺଶܺ APPENDIX B: Transformation of parallel elements Xm and Rc into equivalent series elements R and X Applying complex numbers notation, the impedance of parallel elements Xm and Rc is expressed as ܴ ∙ ݆ܺ ܴ+ ݆ܺ = ܴ ∙ ݆ܺ ܴ+ ݆ܺ ∙ ܴ − ݆ܺ ܴ− ݆ܺ = ܴଶ ∙ ݆ܺ + ܴܺଶܴଶ + ܺଶ = ܴܺଶܴଶ + ܺଶ + ݆ܴଶ ∙ ܴܺଶ + ܺଶ The ‘real’ and ‘imaginary’ terms on the right-hand side of this expression represent respectively the resistive and reactive elements of the equivalent (series) impedance R+jX, i.e., ܴ = ܴܺଶ ܴ ଶ + ܺଶ (3) ܺ = ܴଶ ∙ ܺ ܴ ଶ + ܺଶ (4) Iph PphVph RcXm X X1R1 R X1R1 Fig 4
