What is Phasor Diagram for Synchronous Motor?

Encyclopedia
08/17/2024

What is Phasor Diagram for Synchronous Motor?

Phasor Diagram Definition

A phasor diagram for a synchronous motor shows the relationships between various electrical quantities like voltage and current.

9bc16c7564c829cfbdd752fa0badcc88.jpeg

Ef to represent the excitation voltage

Vt to represent the terminal voltage

Ia to represent the armature current

Θ to represent the angle between terminal voltage and armature current

to represent the angle between the excitation voltage and armature current

δ to represent the angle between the excitation voltage and terminal voltage

ra to represent the armature per phase resistance.

Reference Phasor

Vt is the reference phasor, with armature current and excitation voltage being plotted in relation to it.

Opposite Phases

The armature current is in phase opposition to the excitation emf in a synchronous motor.

Power Factor Operations

Different power factor operations (lagging, unity, leading) affect the expressions for the excitation emf, using components of terminal voltage and armature current.

47c2b279412ebb497c17a6aaa4f81029.jpeg

 Motoring operation at lagging power factor.

Motoring operation at lagging power factor: In order to derive the expression for the excitation emf for the lagging operation we first take the component of the terminal voltage in the direction of armature current Ia. Component in the direction of armature current is VtcosΘ.

As the direction of armature is opposite to that of the terminal voltage therefore voltage drop will be –Iara hence the total voltage drop is (VtcosΘ – Iara) along the armature current. Similarly we can calculate the voltage drop along the direction perpendicular to armature current. The total voltage drop comes out to be (Vtsinθ – IaXs). From the triangle BOD in the first phasor diagram we can write the expression for excitation emf as

Motoring operation at unity power factor.

Motoring operation at unity power factor: In order to derive the expression for the excitation emf for the unity power factor operation we again first take the component of the terminal voltage in the direction of armature current Ia. But here the value of theta is zero and hence we have = δ. From the triangle BOD in the second phasor diagram we can directly write the expression for excitation emf as

d9d9284a6e9f5bb3e1a557dc1840ed9b.jpeg

Motoring operation at leading power factor.

Motoring operation at leading power factor: In order to derive the expression for the excitation emf for the leading power factor operation we again first take the component of the terminal voltage in the direction of armature current Ia. Component in the direction of armature current is VtcosΘ. As the direction of armature is opposite to that of the terminal voltage therefore voltage drop will be (–Iara) hence the total voltage drop is (VtcosΘ – Iara) along the armature current. Similarly we can calculate the voltage drop along the direction perpendicular to armature current. The total voltage drop comes out to be (Vtsinθ + IaXs). From the triangle BOD in the first phasor diagram we can write the expression for excitation emf as

b700ff88c140e247006993dcfeb1c021.jpeg

 Advantages of Phasor Diagrams

  • Phasors are highly useful for gaining physical insight into the operation of the synchronous motors.

  • We can derive mathematical expressions for various quantities easily with the help of phasor diagrams.

Encyclopedia

The Electricity Encyclopedia is dedicated to accelerating the dissemination and application of electricity knowledge and adding impetus to the development and innovation of the electricity industry.

What is a  Synchronous Motor Drive?
What is a Synchronous Motor Drive?
What is a Synchronous Motor Drive?Synchronous Motor OverviewSynchronous motors are not self-starting, which presents a unique challenge. To understand their starting methods, it’s essential to briefly know about the types of supply and the components of the motor, specifically the rotor and the stator.The stator of synchronous motors are similar to that of an induction motors but the only difference lies in the rotor, the rotor of the synchronous motors are given DC supply.Before exploring how s
Encyclopedia
08/22/2024
Phasor Diagram of Synchronous Generator
Phasor Diagram of Synchronous Generator
Phasor Diagram DefinedA phasor diagram is a graphical representation of the phase relationships between different electrical quantities in an AC circuit, specifically used here for synchronous generators.Drawing BasicsEf which denotes excitation voltageVt which denotes terminal voltageIa which denotes the armature currentθ which denotes the phase angle between Vt and Iaᴪ which denotes the angle between the Ef and Iaδ which denotes the angle between the Ef and Vtra which denotes the armature per
Encyclopedia
08/19/2024
Armature Winding
Armature Winding
Armature winding definitionThe armature winding in an alternator is the arrangement of coils to generate electricity and is essential to its operation.Type of armature windingSingle-phase armature windingSingle-phase armature windings can be centralized or distributed.Centralized armature windingWhen the number of slots on the armature equals the number of poles in the machine, the central winding is used. This winding type provides maximum output voltage, but is not always fully sinusoidal. The
Encyclopedia
08/17/2024
Power Derivation  in Synchronous Motors
Power Derivation in Synchronous Motors
Power Flow in Inductive CircuitsPower flow through an inductive impedance involves voltage sources and a load with a resistor and inductor.Phasor DiagramsPhasor diagrams visually represent voltages and currents in a circuit, helping to understand power conditions.Power Equation of Synchronous GeneratorThe power equation of a synchronous generator relates the voltage, current, and phase angles to determine power output.Maximum Power Output ConditionsMaximum power output in alternators and synchro
Encyclopedia
08/17/2024
Inquiry
Download
Experts Electrical is dedicated to serving the personnel in the global power industry.
Join Experts Electrical, not only can you discover power equipment and power knowledge, but also canhnd like - minded friends!