Phasor Diagram for AC Series Motor

This section develops the phasor diagram for an AC series motor. Start by assigning one symbol to each circuit quantity before drawing the phasor diagram:
R_s represents the resistance of the series field
R_p represents the resistance of the interpole circuit
R_c represents the resistance of the compensating winding
R_a represents the resistance of the armature circuit
X_s represents the reactance of the series field
X_p represents the reactance of the interpole circuit

X_c represents the reactance of the compensating winding
X_a represents the reactance of the armature circuit
I represents the current in the series circuit
Φ represents the flux produced by current I
The field flux lags the current I slightly because of magnetic losses. A simplified diagram neglects this small angle and treats flux and current as in phase. With I as the reference, resistance drops are in phase with I, reactance drops lead I by 90 degrees, and terminal voltage is the vector sum of the counter emf and all voltage drops.

The phasor construction shows how the counter emf and circuit impedance drops combine to set the supply-voltage angle relative to current.
The following figure is the phasor diagram for the AC series motor.

The same relationships help explain five characteristics of an AC series motor:

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

The sections below explain each characteristic.

Power Factor Characteristics

The power factor follows from the angle between terminal voltage and current in the phasor diagram. The equation below relates sin φ to the total reactive drop and the terminal voltage.

For a fixed supply voltage, reducing total reactance or reducing current lowers the phase angle and improves power factor. At starting or overload, the counter emf is low and the high current produces a larger reactive drop, so power factor falls.

Speed Current Characteristics

Motor speed follows n = E/(kΦ), where E is counter emf and Φ is field flux. As current rises, flux rises until the magnetic circuit approaches saturation, while resistance and reactance drops also rise. The remaining counter emf and speed therefore fall as load current increases. For the same supply and current, a DC series motor has only resistive voltage drops. An AC series motor also has reactance drops, so its counter emf and speed are usually lower.

Torque Current Characteristics

Motor torque is proportional to the product of flux and armature current. If the small phase angle is neglected and the magnetic circuit is unsaturated, flux is proportional to current, so torque is proportional to the square of current. After saturation, flux increases more slowly and the torque-current curve becomes closer to linear.

Torque Speed Characteristics

Combining the torque-current and speed-current curves gives the series-motor torque-speed characteristic. High current produces high torque and lower speed. As the mechanical load falls, current and flux fall while speed rises sharply. A large series motor should not run without its connected load because its speed can become unsafe.

Power Output Characteristics

The electromagnetic power converted by the armature is approximately the counter emf multiplied by current when their small phase displacement is neglected. Shaft output is lower because mechanical and iron losses must also be subtracted. Output rises with load until increasing losses and voltage drops limit it.




Typical applications depend on motor size and design:

• Fractional-horsepower AC series and universal motors are used in hair dryers, grinders, small fans, polishers, kitchen appliances, vacuum cleaners and hand-held power tools.
• Larger AC series motors were historically used for hoists and other duties that need high starting torque. Modern variable-frequency drives have reduced their use in these applications.