
- Electrical Machines - Home
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- DC Machines
- Construction of DC Machines
- Types of DC Machines
- Working Principle of DC Generator
- EMF Equation of DC Generator
- Derivation of EMF Equation DC Generator
- Types of DC Generators
- Working Principle of DC Motor
- Back EMF in DC Motor
- Types of DC Motors
- Losses in DC Machines
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- DC Generator
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- Stepper vs DC Motors
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- DC Machines Commutation
- DC Motor Characteristics
- Synchronous Generator Working Principle
- DC Generator Characteristics
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- DC Motor Voltage & Power Equations
- DC Generator Efficiency
- Electric Breaking of DC Motors
- DC Motor Efficiency
- Four Quadrant Operation of DC Motors
- Open Circuit Characteristics of DC Generators
- Voltage Build-Up in Self-Excited DC Generators
- Types of Armature Winding in DC Machines
- Torque in DC Motors
- Swinburne’s Test of DC Machine
- Speed Control of DC Shunt Motor
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- DC Motor of Speed Regulation
- Hopkinson's Test
- Permanent Magnet DC Motor
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- DC Servo Motor Theory
- DC Series vs Shunt Motor
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- Induction Motors
- Introduction to Induction Motor
- Single-Phase Induction Motor
- 3-Phase Induction Motor
- Construction of 3-Phase Induction Motor
- 3-Phase Induction Motor on Load
- Characteristics of 3-Phase Induction Motor
- Speed Regulation and Speed Control
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- 3-Phase Induction Motor Working Principle
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- Induction Motors Power Flow Diagram & Losses
- Determining Induction Motor Efficiency
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- Induction Motor Inverted or Rotor Fed
- High Torque Cage Motors
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- 3-Phase Induction Motors Starting Torque
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- 3-Phase Induction Motor - Rotating Magnetic Field
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- Winding EMFs in 3-Phase Induction Motors
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- Single-Phase Induction Motor Performance Analysis
- Linear Induction Motor
- Single-Phase Induction Motor Testing
- 3-Phase Induction Motor Fault Types
- Synchronous Machines
- Introduction to 3-Phase Synchronous Machines
- Construction of Synchronous Machine
- Working of 3-Phase Alternator
- Armature Reaction in Synchronous Machines
- Output Power of 3-Phase Alternator
- Losses and Efficiency of an Alternator
- Losses and Efficiency of 3-Phase Alternator
- Working of 3-Phase Synchronous Motor
- Equivalent Circuit and Power Factor of Synchronous Motor
- Power Developed by Synchronous Motor
- More on Synchronous Machines
- AC Motor Types
- Induction Generator (Asynchronous Generator)
- Synchronous Speed Slip of 3-Phase Induction Motor
- Armature Reaction in Alternator at Leading Power Factor
- Armature Reaction in Alternator at Lagging Power Factor
- Stationary Armature vs Rotating Field Alternator Advantages
- Synchronous Impedance Method for Voltage Regulation
- Saturated & Unsaturated Synchronous Reactance
- Synchronous Reactance & Impedance
- Significance of Short Circuit Ratio in Alternator
- Hunting Effect Alternator
- Hydrogen Cooling in Synchronous Generators
- Excitation System of Synchronous Machine
- Equivalent Circuit Phasor Diagram of Synchronous Generator
- EMF Equation of Synchronous Generator
- Cooling Methods for Synchronous Generators
- Assumptions in Synchronous Impedance Method
- Armature Reaction at Unity Power Factor
- Voltage Regulation of Alternator
- Synchronous Generator with Infinite Bus Operation
- Zero Power Factor of Synchronous Generator
- Short Circuit Ratio Calculation of Synchronous Machines
- Speed-Frequency Relationship in Alternator
- Pitch Factor in Alternator
- Max Reactive Power in Synchronous Generators
- Power Flow Equations for Synchronous Generator
- Potier Triangle for Voltage Regulation in Alternators
- Parallel Operation of Alternators
- Load Sharing in Parallel Alternators
- Slip Test on Synchronous Machine
- Constant Flux Linkage Theorem
- Blondel's Two Reaction Theory
- Synchronous Machine Oscillations
- Ampere Turn Method for Voltage Regulation
- Salient Pole Synchronous Machine Theory
- Synchronization by Synchroscope
- Synchronization by Synchronizing Lamp Method
- Sudden Short Circuit in 3-Phase Alternator
- Short Circuit Transient in Synchronous Machines
- Power-Angle of Salient Pole Machines
- Prime-Mover Governor Characteristics
- Power Input of Synchronous Generator
- Power Output of Synchronous Generator
- Power Developed by Salient Pole Motor
- Phasor Diagrams of Cylindrical Rotor Moto
- Synchronous Motor Excitation Voltage Determination
- Hunting Synchronous Motor
- Self-Starting Synchronous Motor
- Unidirectional Torque Production in Synchronous Motor
- Effect of Load Change on Synchronous Motor
- Field Excitation Effect on Synchronous Motor
- Output Power of Synchronous Motor
- Input Power of Synchronous Motor
- V Curves & Inverted V Curves of Synchronous Motor
- Torque in Synchronous Motor
- Construction of 3-Phase Synchronous Motor
- Synchronous Motor
- Synchronous Condenser
- Power Flow in Synchronous Motor
- Types of Faults in Alternator
- Miscellaneous Topics
- Electrical Generator
- Determining Electric Motor Load
- Solid State Motor Starters
- Characteristics of Single-Phase Motor
- Types of AC Generators
- Three-Point Starter
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- Distribution Factor
- Electrical Machines Basic Terms
- Synchronizing Torque Coefficient
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- Metadyne
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- CVT vs PT
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- Stator and Rotor in Electrical Machines
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- Discussion
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 Flemings 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.

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 $\mathit{P\phi }$ Weber, i.e.,
$$\mathrm{\mathit{d\phi }\:=\:\mathit{P\phi }}$$
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,
$$\mathrm{\mathrm{EMF \:per\:conductor}\:=\:\mathit{\frac{d\phi }{dt}}\:=\:\frac{\mathit{P\phi }}{(60/\mathit{N})}\:=\:\frac{\mathit{P\phi N}}{\mathrm{60}}}$$
Since Z is the total number of conductors in the armature winding per phase, then
$$\mathrm{\mathrm{Avg.\:EMF\:per\:phase, }\mathit{E_{av}/\mathrm{phase}}\:=\:\mathit{Z\times }\frac{\mathit{P\phi N}}{\mathrm{60}}}$$
$$\mathrm{\because \mathit{N}\:=\:\frac{120\mathit{f}}{\mathit{P}}}$$
Then,
$$\mathrm{\mathit{E_{av}/}\mathrm{phase}\:=\:\frac{\mathit{P\phi Z}}{60}\times \frac{120\mathit{f}}{\mathit{P}}\:=\:2\mathit{f\phi Z}\:\mathrm{Volts}}$$
Now, the RMS value of generated EMF per phase is given by,
$$\mathrm{\mathit{E_{\mathrm{RMS}}/}\mathrm{phase}\:=\:\left ( \mathit{E_{av}/\mathrm{phase}} \right )\times \mathrm{form\:factor}}$$
In practice, we consider that a three-phase alternator generates a sinusoidal voltage, whose form factor is 1.11.
$$\mathrm{\mathit{E_{\mathrm{RMS}}/}\mathrm{phase}\:=\:2\mathit{f\phi Z}\times 1.11}$$
$$\mathrm{\therefore \mathit{E_{\mathrm{RMS}}/}\mathrm{phase}\:=\:2.22\mathit{f\phi Z}\:\mathrm{volts}\:\cdot \cdot \cdot (2)}$$
Sometimes, number of turns (T) per phase rather than number of conductors per phase are specified. In that case, we have,
$$\mathrm{\mathit{Z}\:=\:2\mathit{T}}$$
$$\mathrm{\therefore \mathit{E_{\mathrm{RMS}}/}\mathrm{phase}\:=\:\mathit{E_{ph}}\:=\:4.44\mathit{f\phi Z}\:\mathrm{volts}\:\cdot \cdot \cdot (3)}$$
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
$$\mathrm{\mathrm{Frequency,}\mathit{f}\:=\:\frac{\mathit{NP}}{120}\:=\:\frac{1200\times 6}{120}}$$
$$\mathrm{\therefore\mathit{f} \:=\:60\:Hz}$$
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
$$\mathrm{\mathrm{Total\:number\:of\:conductors}\:=\:24\times 10\:=\:240}$$
$$\mathrm{\mathrm{Number\:of\:conductors\:per\:phase,}\mathit{Z}\:=\:\frac{240}{3}\:=\:80}$$
$$\mathrm{\therefore \mathit{E_{ph}}\:=\:2.22\mathit{f\phi Z}\:=\:2.22\times 50\times 0.03\times 80}$$
$$\mathrm{\mathit{E_{ph}}\:=\:266.4\:V}$$