- Electrical Machines - Discussion
- Electrical Machines - Resources
- Electrical Machines - Quick Guide
- Power Developed by Synchronous Motor
- Equivalent Circuit and Power Factor of Synchronous Motor
- Working of 3-Phase Synchronous Motor
- Losses and Efficiency of 3-Phase Alternator
- Output Power of 3-Phase Alternator
- Armature Reaction in Synchronous Machines
- Working of 3-Phase Alternator
- Construction of Synchronous Machine
- Introduction to 3-Phase Synchronous Machines
- Methods of Starting 3-Phase Induction Motors
- Speed Regulation and Speed Control
- Characteristics of 3-Phase Induction Motor
- Three-Phase Induction Motor on Load
- Construction of Three-Phase Induction Motor
- Three-Phase Induction Motor
- Single-Phase Induction Motor
- Introduction to Induction Motor
- Applications of DC Machines
- Losses in DC Machines
- Types of DC Motors
- Back EMF in DC Motor
- Working Principle of DC Motor
- Types of DC Generators
- EMF Equation of DC Generator
- Working Principle of DC Generator
- Types of DC Machines
- Construction of DC Machines
- Types of Transformers
- Three-Phase Transformer
- Efficiency of Transformer
- Losses in a Transformer
- Transformer on DC
- Ideal and Practical Transformers
- Turns Ratio and Voltage Transformation Ratio
- EMF Equation of Transformer
- Construction of Transformer
- Electrical Transformer
- Fleming’s Left Hand and Right Hand Rules
- Concept of Induced EMF
- Faraday’s Laws of Electromagnetic Induction
- Rotating Electrical Machines
- Singly-Excited and Doubly Excited Systems
- Energy Stored in a Magnetic Field
- Electromechanical Energy Conversion
- Electrical Machines - Home
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- Questions and Answers
- UPSC IAS Exams Notes
Working of 3-Phase Alternator
A 3-phase alternator is a synchronous machine that converts mechanical energy into 3-phase electrical energy through the process of electromagnetic induction.
As we discussed in previous chapters, a 3-phase alternator, also called a 3-phase synchronous generator, has a stationary armature and a rotating magnetic field. In the three-phase alternator, the rotor winding (serves as field winding) is energized from a DC supply and alternate north and south poles are developed on the rotor.
Operation of Three-Phase Alternator
When the rotor is rotated (say in anticlockwise direction) by a prime mover (engine, turbine, etc.), the stator winding (serves as armature winding) is cut by the magnetic flux of the rotor poles. Due to electromagnetic induction, an EMF is induced in the armature winding. This induced EMF is alternating one because the north and south poles of the rotor alternately pass the armature winding conductors. We can determine the direction of the induced EMF by Fleming’s right hand rule.
The electrical equivalent circuit of a star-connected armature winding and dc field winding three-phase alternator is shown in Figure-1.
![Phasor Diagram](/electrical_machines/images/phasor_diagram.jpg)
When the rotor is rotated a three-phase voltage is generated in the armature winding. The magnitude of generated voltage depends upon the speed of the rotation of rotor and the DC excitation current. However, the magnitude of generated voltage in each phase of the armature is the same, but displaced by 120° electrical from each other in space as shown in the phasor diagram.
Frequency of Generated Voltage
In a three-phase alternator, the frequency of generated voltage depends upon the speed of rotation and the number of field poles in machine.
Let
N = speed of rotation in RPM
P = number of field poles
Then, the frequency of generated voltage is given by,
$$mathrm{mathit{f}:=:frac{mathit{NP}}{120}:mathrm{Hz}:cdot cdot cdot (1)}$$
It should be noted that N is the synchronous speed because the alternator is a synchronous machine whose rotor always rotates at the synchronous speed.
EMF Equation of Three-Phase Alternator
The mathematical relation which gives the value of EMF induced in the armature winding of a three-phase alternator is termed as its EMF equation.
Let
N = speed of rotation in RPM
P = number of field poles on rotor
$phi$ = flux per pole in weber
Z = number of armature conductors per phase
Then, in one revolution, each stator conductor is cut by a flux of $mathit{Pphi }$ Weber, i.e.,
$$mathrm{mathit{dphi }:=:mathit{Pphi }}$$
Also, time taken to complete one revolution is,
$$mathrm{mathit{dt }:=:frac{60}{mathit{N}}}$$
Therefore, the average EMF induced in each armature conductor is,
$$mathrm{mathrm{EMF :per:conductor}:=:mathit{frac{dphi }{dt}}:=:frac{mathit{Pphi }}{(60/mathit{N})}:=:frac{mathit{Pphi N}}{mathrm{60}}}$$
Since Z is the total number of conductors in the armature winding per phase, then
$$mathrm{mathrm{Avg.:EMF:per:phase, }mathit{E_{av}/mathrm{phase}}:=:mathit{Z imes }frac{mathit{Pphi N}}{mathrm{60}}}$$
$$mathrm{ecause mathit{N}:=:frac{120mathit{f}}{mathit{P}}}$$
Then,
$$mathrm{mathit{E_{av}/}mathrm{phase}:=:frac{mathit{Pphi Z}}{60} imes frac{120mathit{f}}{mathit{P}}:=:2mathit{fphi Z}:mathrm{Volts}}$$
Now, the RMS value of generated EMF per phase is given by,
$$mathrm{mathit{E_{mathrm{RMS}}/}mathrm{phase}:=:left ( mathit{E_{av}/mathrm{phase}} ight ) imes mathrm{form:factor}}$$
In practice, we consider that a three-phase alternator generates a sinusoidal voltage, whose form factor is 1.11.
$$mathrm{mathit{E_{mathrm{RMS}}/}mathrm{phase}:=:2mathit{fphi Z} imes 1.11}$$
$$mathrm{ herefore mathit{E_{mathrm{RMS}}/}mathrm{phase}:=:2.22mathit{fphi Z}:mathrm{volts}:cdot cdot cdot (2)}$$
Sometimes, number of turns (T) per phase rather than number of conductors per phase are specified. In that case, we have,
$$mathrm{mathit{Z}:=:2mathit{T}}$$
$$mathrm{ herefore mathit{E_{mathrm{RMS}}/}mathrm{phase}:=:mathit{E_{ph}}:=:4.44mathit{fphi Z}:mathrm{volts}:cdot cdot cdot (3)}$$
The expressions in equations (2) & (3) are known as EMF equation of three-phase alternator.
Numerical Example (1)
What is the frequency of the voltage generated by a three-phase alternator having 6 poles and rotating at 1200 RPM?
Solution
Given data,
P = 6;
N = 1200 RPM
$$mathrm{mathrm{Frequency,}mathit{f}:=:frac{mathit{NP}}{120}:=:frac{1200 imes 6}{120}}$$
$$mathrm{ hereforemathit{f} :=:60:Hz}$$
Numerical Example (2)
The armature of a 4-pole, 3-phase, 50 Hz alternator has 24 slots and 10 conductors per slot. A flux of 0.03 Wb is entering the armature from one pole. Calculate the induced EMF per phase.
Solution
$$mathrm{mathrm{Total:number:of:conductors}:=:24 imes 10:=:240}$$
$$mathrm{mathrm{Number:of:conductors:per:phase,}mathit{Z}:=:frac{240}{3}:=:80}$$
$$mathrm{ herefore mathit{E_{ph}}:=:2.22mathit{fphi Z}:=:2.22 imes 50 imes 0.03 imes 80}$$
$$mathrm{mathit{E_{ph}}:=:266.4:V}$$
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