Vector Diagram of the Synchronous Motor

Author: E.E. Kimberly

A synchronous motor with its polyphase winding energized and producing a rotating set of field poles will usually have enough reluctance torque to run without load if the field structure is rotated to synchronous speed by some external driving force so that the salient poles can lock in with the rotating set of field poles as in Fig. 19-3. Such a motor when running would have a vector diagram for every phase similar to that of a simple reactance coil.

In Fig. 19-4, V is the phase voltage applied and I is the phase current for that condition of operation. The current I is Oh on the diagram and it lags V by the angle θ which is the characteristic impedance angle of the unexcited motor. The rotor salient poles lag the stator flux poles by a mechanical degrees, as in Fig. 19-3, to produce enough torque to maintain the speed.

Fig. 19-4. Synchronous-Motor Vector Diagram

If the windings on the rotor poles are then energized by direct current passed through the rotor winding in proper direction to add to the flux already in the poles, there will be a voltage E_a generated in the stator coils by the new rotor flux sweeping past them. The voltage E_a is not quite 180 deg out of time phase with V because the rotor is lagging a mechanical degrees behind the stator-produced poles. Since a mechanical degrees correspond to 2α electrical degrees (in a four-pole motor), let 2α = β, in which β is the lag angle in electrical degrees. The net voltage available for forcing current through the stator is E_z = V + E_a; and I is reduced to I₁ in the ratio I₁/I = E_z/V. But I₁ still lags E_z which produces it by θ deg.

If the voltage E_a is kept constant by keeping the direct current in the field structure constant, and the motor is then loaded, the angle β will increase to meet the new load demand. The voltage E_z will then lie on the locus acb which has gc = E_a as a radius. If E_z follows a circular locus as the shaft load varies, I₁ must also follow a circular locus dcf with radius hd. The motor power factor is cos φ. It is then apparent that the power factor of a synchronous motor with constant field excitation is no more constant regardless of load than is that of an induction motor, because φ changes as the changing load causes I₁ to move to the right or left along its locus.