Phasor Diagrams of Synchronous Motors: A Comprehensive Guide

Synchronous motors are pivotal components in industrial applications due to their constant speed operation and power factor correction capabilities. A critical tool for understanding their operation is a phasor diagram which graphically represents the relationship between voltage, current, and internal quantities like induced EMF. 

This blog explores phasor diagrams, their significance, and the various factors influencing synchronous motor performance.

What is a Synchronous Motor?

A synchronous motor is an AC motor that operates at a constant speed synchronised with the frequency of the AC supply. Unlike induction motors, the synchronous motor rotates at the same speed as the magnetic field to ensure precise speed control. It makes them ideal for applications requiring consistent speed operation.

Construction of the synchronous motor includes stator, rotor and excitation system. The stator generates a rotating magnetic field using a three-phase AC supply, while the rotor consists of a permanent magnet aligned with the stator’s magnetic field. In wound rotor designs, the excitation system supplies DC power to the rotor windings, creating the necessary magnetic field for synchronous operation. 

Watch the YouTube video by "Sabins Civil Engineering" to know about the working of synchronous motor

One of the defining features of synchronous motors is their constant speed which remains unaffected by load variations. They are also highly efficient in converting electrical energy into mechanical energy. Moreover, they can operate at a leading, lagging, or unity power factor, making them suitable for power factor correction. 

Synchronous motors are widely used in industrial applications where precise speed control is critical. Due to their efficiency, reliability, and ability to control the power factor, they become a preferred choice for diverse industrial needs.

Phasor Diagram of Synchronous Motor

A phasor diagram is a graphical representation of electrical quantities in a synchronous motor such as voltage, current, and phase relationships. It is vital to understand its operating characteristics under different load conditions.

By representing these electrical quantities as vectors in a rotating coordinate system, the phasor diagram simplifies complex AC interactions and offers insights into the synchronous motor's efficiency, power factor, and stability.

As synchronous motors operate at a constant speed synchronised with the frequency of the AC supply. The phasor diagram helps to visualise how the rotor's excitation voltage interacts with the stator's supply voltage to produce torque.

Also Read

What is a Synchronous Motor? | Construction, Working Principle and Applications

Components of a Phasor Diagram for Synchronous Motors

• Terminal Voltage (V)

Represents the voltage supplied to the stator of the synchronous motor. It serves as a reference phasor in most diagrams.

• Stator Current (I)

Represents the current drawn by the stator winding shown at a specific angle based on its load and power factor. 

• Induced EMF (Ef)

Represents the internal voltage induced by the rotor’s field excitation which is critical for determining the synchronous motor power output. 

• Synchronous Reactance (Xs)

Represents the opposition to the current flow due to the synchronous motor’s inductance, showing perpendicular to Stator Current (I).

• Power Factor Angle (ϕ)

The angle between V and I indicates whether the synchronous motor is operating in a leading, lagging, or unity power factor condition.

Importance of Phasor Diagram 

Phasor diagrams are essential in understanding the operation and performance of synchronous motors. They graphically represent the relationship between voltage, current, and other electrical parameters in the motor, enabling precise analysis of its behaviour under varying conditions. The key importance of the phasor diagram is: 

• Visualisation of electrical relationship

The phasor diagram depicts the phase relationship between stator voltage(V), stator current(I) and excitation voltage(Ef). This visualisation helps in understanding how these electrical quantities interact in real time. 

• Analysis of Power Factor

By analysing the angle between the current and voltage phasors, the power factor of the synchronous motor can be determined. This is critical for optimising the motor’s efficiency and reducing energy costs. 

• Excitation Analysis

Phasor diagrams help evaluate the effect of over-excitation and under-excitation. This is crucial for maintaining the synchronous motor’s stable operation and preventing issues like hunting and overheating. 

• Load Impact Assessment

As the synchronous motor load changes, the phasor diagram shifts and shows variation in the current magnitude and power factor. This allows engineers to predict synchronous motor performance under different load conditions.

• Fault Diagnosis

Any abnormalities in the phasor diagram indicate potential faults such as issues in excitation systems, faults in winding, uneven load etc. 

Excitation Conditions and Phasor Diagrams

The performance and power factor of a synchronous motor are closely related to the level of excitation. Excitation refers to the DC current supplied to the rotor windings which generate the magnetic field necessary for synchronous motor operation. 

The excitation condition can be classified into three types: under-excited, normally excited, and over-excited. Each condition influences the synchronous motor's power factor and load characteristics, which are illustrated with phasor diagrams.

Under-Excited Condition

In an under-excited condition, the field current (I) is insufficient to generate the required magnetic field. As a result, the back EMF (Ef) produced by the rotor is smaller than the applied voltage. This imbalance causes the synchronous motor to operate at a lagging power factor. 

Phasor Diagram Representation:

• Ef is represented as a smaller vector compared to V
• I is shown lagging V by a phase angle (ϕ), signifying inductive behaviour.
• The resultant magnetic flux is less than optimal, leading to reduced efficiency.

Normal Excitation Condition

In a normal excited condition, the field current is adjusted such that the rotor magnetic field is precisely sufficient to counterbalance the applied stator voltage (V). As a result, the back EMF (Ef) is equal in magnitude to the voltage (V). The synchronous motor operates at unity power, where the current (I) is in the phase with voltage (V). 

Phasor Diagram Representation:

• Ef aligns in both magnitude and phase with V
• I am in phase with V, forming a straight line on the phasor diagram.
• The synchronous motor operates at its most efficient point, delivering active power without reactive components.

Over-Excited Condition

In an over-excited condition, the current (I) exceeds the required level and produces a back EMF (Ef) greater than the voltage (V). The synchronous motor now operates at the leading power factor and behaves like a capacitive load.

Phasor Diagram Representation:

• E is represented as a larger vector compared to V
• I lead by V a phase angle (ϕ), indicating capacitive behaviour.
• The resultant magnetic flux is higher than optimal, which can lead to excessive heating if not controlled. 

Also Read

Load Characteristics of Synchronous Motor

Conclusion

Phasor diagrams are a cornerstone of synchronous motor analysis, providing invaluable insights into their performance. By visualising the interplay of voltage, current, and back EMF, one can design, operate, and maintain synchronous motors more effectively. Whether adjusting excitation to optimise power factor or mastering phasor diagrams ensures the reliable and efficient operation of synchronous motors in diverse applications.