Phasor Diagram for AC Series Motor

We will discuss here the simplest way of drawing the phasor diagram for an AC series motor. Before we draw phasor diagram, let us write the various notations for each quantity at one place. Here we will use:
R_s to represent the resistance of the series field
R_p to represent the resistance of the inter pole circuit
R_c to represent the resistance of the compensation winding
R_a to represent the resistance of the armature circuit
X_s to represent the reactance of the series field
X_p to represent the reactance of the inter pole circuit

X_c to represent the reactance of the compensation winding
X_a to represent the reactance of the armature circuit
I to represent the current in the circuit
Φ to represent the flux produced by the current I
We assume that the flux produced by the current I is in phase with the current I due to a very small lagging angle. Taking the current on the reference axis, the terminal voltage equals the sum of all the voltage drops and the counter emf.

The main advantage of the phasor diagram of the AC series motor is that we can easily obtain the phase angle for counter emf E with the help of phasor diagram.
Given below is the phasor diagram for the AC series motor.

Now let us discuss various characteristics of the AC series motor. There are five important characteristics of an AC series motor which are written below:

1. Power factor characteristics
2. Speed current characteristics
3. Torque current characteristics
4. Torque speed characteristics
5. Power output characteristics

Now let discuss each of them in detail:

Power Factor Characteristics

We can derive the expression for power factor with the help of phasor diagram given above. From the phasor diagram we write sine of angle φ as

Clearly from the above equation we can say that if we want the high value of power factor, the value of reactance and counter emf should low as minimum as possible. From point of view of loading, we have low value of power factor at over loading and it is due to the fact that the high value of current. Thus the high value of power can be achieved only if the load is very light.

Speed Current Characteristics

To understand speed current characteristics, we derive an expression for speed in terms of counter emf. Speed is proportional to counter emf, so higher counter emf means higher speed. The phasor diagram shows that counter emf is the difference between terminal voltage and voltage drops. If current causes higher voltage drops, the counter emf and motor speed decrease. Comparing AC and DC series motors: DC series motor have high counter emf due to low resistive voltage drops, resulting in higher speed. AC series motor have low counter emf due to higher resistive and reactance drops, resulting in lower speed. The speed current characteristics curve for DC series motors drops less than for AC series motors.

Torque Current Characteristics

Neglecting the small phase angle (angle between the flux and the current) and saturation effect, the torque is directly proportional to the square of the current. Thus, the variation of torque with current can be plotted as shown in the figure below:

Torque Speed Characteristics

The relation between the torque and speed can derived with the help of torque current and speed current characteristics. The torque speed characteristics are plotted as shown in the given diagram.

Power Output Characteristics

The mechanical output power of an AC series motor is calculated by multiplying the counter emf and current. Mechanical power is directly proportional to current, if we ignore the slight decrease in counter emf as current increases.




Now let us discuss some application of AC series motors:

• These motors are highly in home appliances like hair dryers, grinders, table fans, polishers and many other kitchen appliances.
• These motors are also very useful where high speed control is required like lift, cranes, etc.