The performance characteristics of a synchronous motor can be understood using v-curves and inverted v-curves. These curves show how the armature current (Ia) and the power factor of the motor change as the field current (If) is varied.

The v-curves and inverted v-curves of a synchronous motor have a parabolic shape, which means that they are curved like a parabola. When the field current (If) is varied from a low (under-excitation) to a high (over-excitation) value, the armature current (Ia) also changes. At unity power factor (PF), Ia is at a minimum, but as the field current increases further, Ia begins to increase again.

At starting, the lagging current becomes unity (i.e., the power factor is 1) and then becomes leading in nature. This means that when the motor is starting, the power factor starts at 1 (unity) and then becomes leading as the field current increases.

The v-curves and inverted v-curves of a synchronous motor are used to analyze the efficiency of the motor under no-load and on-load conditions. These curves can be used to determine the field current (If) that is required to achieve a certain power factor or to understand how the power factor of the motor changes as the field current is varied.

**V-Curves of Synchronous Motor:**

The V curves of a synchronous motor are graphs that show the relationship between the armature current (Ia) and the field current (If) for different constant loads. These curves are useful for adjusting the field current of the motor in order to control the power factor of the motor.

At no-load, if the field current (If) is increased from a small value, the armature current (Ia) decreases until it reaches a minimum. The power factor of the motor at this point is unity (i.e., 1). Up to this point, the motor was operating with a lagging power factor. If a graph is plotted between Ia and If at no-load, the lowest curve in the V curves is obtained.

To obtain a complete set of V curves, this process is repeated for various increased loads. The shape of the curves plotted between Ia and If resembles the letter "V", which is why these curves are called V curves.

The point corresponding to unity power factor (i.e., the point at which Ia is minimum) is the same for all V curves. The curve that connects these points for all V curves is called the unity power factor compounding curve. Similarly, there are compounding curves for other power factors, such as 0.85 power factor lag and 0.85 power factor lead.

The compounding curves show the field current (If) that must be maintained in order to keep the power factor of the motor constant under changing loads. For example, if the power factor of the motor needs to be kept at 0.85 lag, the field current should be adjusted according to the 0.85 lag compounding curve.

By changing the field excitation of the synchronous motor, the reactive power supplied to or consumed from the power system can be controlled. This is because increasing the field current beyond the level of minimum armature current results in a leading power factor, while decreasing the field current below the level of minimum armature current results in a lagging power factor.

**Inverted V-Curves of Synchronous Motor:**

Inverted V curves of a synchronous motor are graphs that show the relationship between the power factor and the field current (If) of the motor. These curves can be obtained by plotting the power factor versus the field current for various constant loads.

Each inverted V curve has a peak point, which indicates unity power factor (i.e., a power factor of 1). From the inverted V curves, it is clear that the field current (If) required to achieve unity power factor at full-load is greater than the field current required to achieve unity power factor at no-load.

The inverted V curves also show that if the synchronous motor is operating at unity power factor at full-load, removing the mechanical load from the shaft of the motor will cause the motor to operate at a leading power factor. This is because the field current (If) required to achieve unity power factor at no-load is lower than the field current required to achieve unity power factor at full-load. When the load is removed and the field current remains at the higher value, the power factor becomes leading.