## What are V Curves of Synchronous Motor?

**V-Curves** are a method of graphing the variation of the armature or **line current (L)** with respect to **field current (I)** in a synchronous motor keeping the input power constant or the mechanical output power constant.

The variation I_F/I_L of the motor’s line or armature current I_L with field excitation current I_F yields a **V-curve** for given power input to the motor.

The ‘V’ line also changes as the input power increases and decreases. The figure below shows how the V-line changes for different input power.

## Fig-1: V Curves

If, V = phase voltage,

I = phase current,

Cosθ = power factor.

Then the input power of a three-phase motor, P= 3VI Cosθ watts. If P and V are unchanged, then Cosθ will also change with its change.

Hence it can be seen that changing the field current not only changes the armature current but also changes the power factor.

Read more: Gauge Factor of Strain Gauge: Formula, Materials, Advantage

## V-curves drawing of Synchronous Motor

All the equipments, materials etc. required for **V-curves** drawing. They are:

1. DC supply

2. Rheostat

3. DC ammeter

4. Single phase watt meter (2)

5. Voltmeter (AC)

6. Ammeter (AC)

7. Field circuit suit

8. Coupling is provided when generator is required for motor loading. The output of the generator is measured and the input to the motor is quantified at various loads.

## Working principle of V-curves

First, the synchronous motor is started at no load. Initially, it runs as an induction motor with the help of damper winding (connected to the rotor poles). After some time the DC excitation is given through the switch. At this time the DC ammeter reading is noted. If the value of current is high, it should be understood that proper synchronism is lacking, then switch off and try to provide DC excitation again. Until the pole slip comes into proper synchronizing. In this condition, the excitation current is low and steady.

Now the armature current graph against excitation current at no-load conditions should be recorded on paper. The same process is done at full-load, half-load, \frac{1}{3} load and \frac{1}{4} load with respect to a constant load. It can also be subject to constant output or constant input. Now what is found on graph paper looks like a** V curve** and is called **V-curves**. A wattmeter, by taking readings, determines the power factor for various operating conditions.

## Fig-2: V Curves

**Taking Readings:** The readings taken are – W1, W2, A, A (dc), and V armature current readings are taken by varying the excitation at different loads.

**Calculation and drawing of curves on graph paper:** Armature current/field excitation current \frac{I_L}{I_F} is plotted on graph paper. This process is done at no-load, \frac{1}{4} th load,\frac{1}{2} th load, \frac{3}{4} th load and full-load. Power factor is plotted against excitation current on graph paper. A sample diagram of the V-curve and power factor curve is given below:

## Fig-3: V Curves

When measuring power factor two wattmeter readings are added, namely-

W_1+W_2=input\ =\sqrt{3}VI\cos\theta

\cos\theta\ =\frac{input}{\sqrt{3}VI}

## Explain the V-curves of Synchronous Motor

From the V-line, it can be seen that when the **field current** is very low, the power factor of the motor is **lagging** and very low. Besides, the armature current is relatively high at this time. As the field current gradually increases, the value of the power factor improves, and the armature current decreases.

The value of the power factor is the maximum or unity at a given field current. At this time the armature draws the least current from the line. Further increasing the field current results in a leading power factor but the value decreases to unity. As a result the armature current increases again.

Shown here are lightweight, general, and high-load** V Curves.** A review of each curve shows that the line current (armature current) is higher at low field excitation, the motor’s line current is lowest at rated excitation, and the line current is again high at high field excitation. So it can be said that in normal excitation the power factor is unity and the armature current is minimum.

High or overexcitation leads to power factor leading and high armature current flows. Low or under excitation results in power factor lagging and high armature current.

So if a synchronous motor is given a V-line of a certain power, then the power factor, line current, and field current of this motor can be known from the **V-curve.**

## Different points and positions of V-curve by power factor

Let’s say, the armature current of a synchronous motor is very high if the amount of under-excitation at no-load is much less. That is, as the field current gradually increases its armature current decreases and is minimum at normal excitation. The power factor increases to unity (1) at normal excitation.

## Fig-4: V Curves

Now increase the amount of excitation further. That is, as the overexcitation increases, the armature current of the motor increases and the power factor decreases from unity but leading. The lowest of the V-curves in the accompanying figure is the V-curve of the no-load synchronous motor.

Similarly, the V-curve is drawn by varying the field current of the synchronous motor at earth load and full load. In this curve, as the field current of the synchronous motor increases gradually from under excitation, its power factor increases from lagging and becomes unity at lower excitation. After normal excitation, on further increasing the excitation, the power factor of the motor leads to unity but decreases as shown in the figure.

Also read:

## Frequently Asked Questions

A motor whose speed does not change with load change, i.e. a motor which always rotates at a fixed speed, is called a synchronous motor.

The speed of revolving flux in the stator field is called synchronous speed.

The speed of a synchronous motor varies with the number of poles or the supply frequency.

The direction of rotation can be changed by changing the position of any two phases of a three-phase supply.

The angle by which the rotor axis of a synchronous motor lags behind the stator axis is called the torque angle.