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# V Curves and Inverted V Curves of Synchronous Motor

## Synchronous Motor V Curves

*The graphs plotted between armature current (I _{a}) and field current (I_{f}) for different constant loads are known as the V curves of the synchronous motor.*

The power factor of a synchronous motor can be controlled by changing the
field excitation, i.e., by variation of field current (I_{f}). Also, the armature current (I_{a}) changes with the change in the excitation or field current (I_{f}).

Now, let us assume that the synchronous motor is operating at no-load. If the field current (I_{f}) is increased from a small value, the armature current (I_{a}) decreases until I_{a} becomes minimum. The power factor of the motor corresponding to this minimum armature current is unity. Up to the point of minimum armature current, the motor was operating at lagging power factor. If a graph is plotted between armature current (I_{a}) and field current (I_{f}) at noload, the lowest curve in Figure-1 is obtained. In order to obtain a family of curves as shown in Figure-1, the above procedure is to be repeated for various increased loads.

Because the shape of the curves plotted between armature current (I_{a}) and field current (I_{f}) resembles the letter "V", thus these curves are known as *V curves of a synchronous motor.*

The point corresponding to unity power factor is the point at which the armature current is minimum. The curve connecting the unity power factor points (or lowest points) of all V curves for various loads is called the unity power factor compounding curve. Similarly, the compounding curves for 0.85 power factor lag and 0.85 power factor lead are shown by dotted curves in Figure-1.

Therefore, *the compounding curves may be defined as the loci of constant
power factor points on the V curves of a synchronous motor*. The compounding curves give the information about the manner in which the field current (I_{f}) of the motor should be varied to maintain constant power factor under changing loads.

Hence, the V curves are useful in adjusting the field current of the synchronous motor. From the V curves shown in Figure-1, it is clear that decreasing the field current below that for minimum armature current results in lagging power factor. Similarly, increasing the field current beyond the level of minimum armature current results in leading power factor. Therefore, by changing the field excitation of a synchronous motor, the reactive power supplied to or consumed from the power system can be controlled.

## Inverted V Curves of Synchronous Motor

*Inverted V curves of a synchronous motor are defined as the graphs plotted between power factor and field current (I _{f}) of the motor.*

A family of inverted V curves of a synchronous motor obtained by plotting the power factor versus field current is shown in Figure-2.

The peak point on each of these curves indicates unity power factor. From the curves, it can be seen that the field current (I_{f}) for unity power factor at full-load is greater than the field current (I_{f}) for unity power factor at no-load.

The inverted V curves also show that if the synchronous motor at full-load is operating at unity power factor then removal of the mechanical load from the shaft of the motor causes the motor to operate at a leading power factor.

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