EQUIVALENT CIRCUITS OF SYNCHRONOUS MOTORSPredicting the current and power-factor drawn from the supply by a cylindricalrotor or permanent magnet synchronous motor is possible by means of the perphase a.c. equivalent circuit shown in Figure 9.4. To arrive at such a simple circuitinevitably means that approximations have to be made, but we are seeking onlya broad-brush picture, so the circuit is perfectly adequate.In this circuit X (known as the synchronous reactance, or simply the reactance)represents the effective inductive reactance of the stator phase winding; R is the statorwinding resistance; V is the applied voltage; and E is the e.m.f. induced in the statorwinding by the rotating field produced either by the d.c. current on the rotor or by thepermanent magnet. (For the benefit of readers who are familiar with the parameters ofthe induction motor, it should be pointed out that X is equal to the sum of themagnetizing and leakage reactances, but because the effective air-gap in synchronousmachines is usually larger than in induction motors, their per-unit synchronous reactance is usually lower than that of an induction machine with the same stator winding.)The similarity between this circuit and that of the d.c. machine (Figure 3.6) andthe induction motor (Figure 5.8) is clear, and it stems from the fact that thesemachines all produce torque by the interaction of a magnetic field and currentcarrying conductors (the so-called ‘BIl’ effect). In the case of the d.c. machinethe inductance was seen not to be important under steady-state conditions becausethe current was steady (i.e. d.c.), and the resistance emerged as the dominantparameter. In the case of the synchronous motor the current is alternating, so notsurprisingly we find that the reactance is the dominant impedance and resistanceplays only a minor role, except in the case of small motors.
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