###### Electric Machinery

117 SOLVED PROBLEMS

Question: 9.5

## A two-pole, single-phase induction motor has the following parameters Lmain = 80.6 mH  Rmain = 0.58 Ω Laux = 196 mH  Raux = 3.37 Ω Lr = 4.7 μH  Rr = 37.6 μΩ Lmain,r = 0.588 mH Laux,r= 0.909 mH It is operated from a single-phase, 230-V rms, 60-Hz source as a permanent-split-capacitor motor with ...

MATLAB, with its ease of handling complex numbers,...
Question: 8.3

## Consider the idealized 4/2 VRM of Example 8.1. Assume that it has a winding resistance of R = 1.5 Ω/phase and a leakage inductance Ll= 5 mH in each phase. For a constant rotor speed of 4000 r/min, calculate (a) the phase-1 current as a function of time during the interval -60° ≤ θm ≤ 0°, assuming ...

a. From Eq. 8.15, the differential equation govern...
Question: 8.4

## Consider a symmetrical two-phase 4/2 VRM whose λ-i characteristic can be represented by the following λ-i expression (for phase 1) as a function of θm over the range 0 ≤ θm ≤ 90° λ1=(0.005+0.09(90°- θm / 90°)(8.0 / 8.0+i1))i1 Phase 2 of this motor is identical to that of phase 1, and there is no ...

a. The $λ_1-i_1$ curves are shown in ...
Question: 8.2

## Consider a four-phase, 8/6 VRM. If the stator phases are excited sequentially, with a total time of T0 sec required to excite the four phases (i.e., each phase is excited for a time of T0/4 sec), find the angular velocity of the stator flux wave and the corresponding angular velocity of the rotor. ...

Figure 8.7 shows in schematic form an 8/6 VRM. The...
Question: 7.9

## A permanent-magnet dc motor is known to have an armature resistance of 1.03 Ω. When operated at no load from a dc source of 50 V, it is observed to operate at a speed of 2100 r/min and to draw a current of 1.25 A. Find (a) the torque constant Km, (b) the no-load rotational losses of the motor and ...

a. From the equivalent circuit of Fig. 7.20, the g...
Question: 8.6

## Consider again the two-phase, permanent-magnet stepping motor of Example 8.5. Calculate the rotor position which will result if the phase currents are controlled to be sinusoidal functions of a reference angle θref in the form i1=I0 cos θref i2=I0 sin θref ...

Substitution of the current expressions into the t...
Question: C.1

## A two-pole synchronous machine is carrying balanced three-phase armature currents ia = √2Ia cos ωt ib = √2Ia cos (ωt – 120°) ic = √2Ia cos (ωt + 120°) The rotor is rotating at synchronous speed ω, and the rotor direct axis is aligned with the stator phase-a axis at time t = 0. Find the direct- ...

The angle between the rotor direct axis and the st...
Question: 11.12

## The three-phase, 230-V, 60-Hz, 12-kW, four-pole induction motor of Example 6.7 and Example 11.11 is to be driven by a field-oriented speed-control system (similar to that of Fig. 11.21b) at a speed of 1740 r/min. Assuming the controller is programmed to set the rotor flux linkages λDR to the ...

We must first determine the parameters for this ma...
Question: B.2