Varying Field Excitation under Constant Load

Author: E.E. Kimberly

The total power input per phase in Fig. 19-5 is

Pi = VI1cosφ

[19-2]

The power P_i includes the shaft power output, if any, and the windage, friction, iron, and copper losses (all per phase). Let it be assumed that, while the motor is running with the vector conditions of Fig. 19-4, the field excitation of the rotor is increased. That increase in rotor field strength will increase E_a and cause E_z to swing counter-clockwise, carrying with it I₁ at angle θ lagging. If neither the shaft load nor the motor losses changed during the field adjustment, I₁ cos φ would remain constant but I₁ would be made to lie in a new position leading V by some phase angle φ1, as in Fig. 19-5. If φ1 = φ, the power input per phase would actually be the same as before because both load and losses would be unchanged.

Fig. 19-5. Vector Diagram of Over-Excited Synchronous Motor.

The motor under this new condition of field excitation takes from the power source not only VI₁ cos φ as a power component but also VI₁ sin φ in leading reactive volt-amperes, This is a valuable property of a synchronous motor because, if such a motor is run "over-excited" on a power system which has a preponderance of lagging power factor loads, it acts partly as a condenser and improves the over-all power factor of the system. This use is considered further in Chapter 25.

Fig 19-6. Vector Diagrams of a Synchronous Motor With Different Degrees of Field Excitation (Polyphase Winding Assumed to Be Without Copper Loss, in Accordance With Common Approximation)

If a synchronous motor had no copper losses within itself, the power input with constant shaft load would be constant regardless of any change in field excitation, as long as synchronism was maintained. In that case, if the field excitation were changed, I₁ would change but would follow a vertical locus XY shown in Fig. 19-6 for three states of field excitation. In a large motor E_z is so large compared to the IR drop in the polyphase winding that the IR drop may be neglected without introducing serious error. All the synchronous-motor vector diagrams have been drawn with the assumption that the synchronous impedance is the same at all power factors. In a salient-pole motor which has been under consideration, the impedance actually is different for different power factors but the differences within the normal or usual range of use are negligible.

The over-excited synchronous motor provides leading vars for power-factor correction at remarkably low cost per var. A motor built to furnish no leading vars but to run at unity power factor has only enough copper in its polyphase winding to enable it to take the necessary minimum current to produce rated shaft horsepower. Its field winding has only enough copper to provide enough E_a for unity power factor. Thus, a motor rated at 100 per cent power factor is built at minimum cost and is desirable when no leading vars are needed. However, by a small increase in the amount of copper used in both windings, the motor may be overexcited to produce vars at much less cost than that of the equivalent vars in static condensers. The power factor specified on the name plate of a synchronous motor is the minimum power factor leading at which the motor can be run while carrying its rated horsepower load. Fig. 19-7 shows some power-factor and current curves of a typical synchronous motor with and without load and with a wide range of field excitation. There is almost never a need to run such a motor with a lagging power factor.

Fig. 19-7. Synchronous-Motor Curves