
- 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
- Applications of DC Machines
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- DC Generator
- DC Generator Armature Reaction
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- Stepper vs DC Motors
- DC Shunt Generators Critical Resistance
- 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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- Permanent Magnet DC 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
- Methods of Starting 3-Phase Induction Motors
- More on Induction Motors
- 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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- Single-Phase Induction Motor Performance Analysis
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- 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
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- 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
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- Synchronous Motor Excitation Voltage Determination
- Hunting Synchronous Motor
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- Effect of Load Change on Synchronous Motor
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- Output Power of Synchronous Motor
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- V Curves & Inverted V Curves of Synchronous Motor
- Torque in Synchronous Motor
- Construction of 3-Phase Synchronous Motor
- Synchronous Motor
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- Power Flow in Synchronous Motor
- Types of Faults in Alternator
- Miscellaneous Topics
- Electrical Generator
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- Solid State Motor Starters
- Characteristics of Single-Phase Motor
- Types of AC Generators
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- Electrical Machines Basic Terms
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- Stator and Rotor in Electrical Machines
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Losses and Efficiency of an Alternator
Losses in an Alternator
The losses that occur in an alternator can be divided into the following categories −
Copper Losses or I2R Losses
The copper losses or I2R losses occur in the armature winding and rotor winding of the alternator. These losses occur due to the resistance of the windings.
$$\mathrm{\text{Armature Winding cu Loss } \:=\: I^{2}_{a} R_{a}}$$
$$\mathrm{\text{Rotor Winding cu Loss } \:=\: I^{2}_{r} R_{r}}$$
Core Losses
The core losses or iron losses occur in the pole faces, teeth and stator core of the alternator. The core losses in the alternator occur because the various iron parts of the machine are subjected to the varying magnetic field. The core losses consist of eddy current loss and hysteresis loss.
$$\mathrm{\text{Core Losses, } \: P_{i} \:=\: \text{ Hysteresis Loss } \:(P_{h}) \:+\: \text{ Eddy Current Loss }\:(P_{e} )}$$
Hysteresis Loss
The hysteresis loss occurs in the cores of the alternator since any given iron part is subjected to magnetic reversal as the magnetic field varies. When the magnetic reversal occurs, some amount of power has to be spent to overcome the magnetic friction, which is called as hysteresis loss. The hysteresis loss is given by,
$$\mathrm{\text{Hysteresis Loss, } \: P_{h} \:=\: K_{h} \: {B^{1.6}_{max}}\:f \: V \: Watts}$$
Eddy Current Loss
When the armature and rotor cores of the alternator are subjected to the changing magnetic field, an EMF is induced in the cores which circulates eddy currents in the cores. The power loss due to these eddy currents is known as eddy current loss and is given by,
$$\mathrm{\text{Eddy Current Loss, } \:P_{e} \:=\: K_{e}\:{B^{2}_{max}}\:f^{2}\:t^{2}\:V\:Watt}$$
Mechanical Losses
In the alternators, there are two types of mechanical losses viz. friction losses and windage losses. The friction losses occur due to the friction in the moving parts such as bearings etc. while the windage losses occur due to the friction between the moving parts of the machine and the air inside the alternator's casing.
$$\mathrm{\text{Mechancial Losses = Friction Losses + Windage Losses}}$$
Miscellaneous Losses
All the losses in the alternator which cannot be easily accounted for are known as miscellaneous losses. The miscellaneous losses in the alternator may be result of the following −
- Distorted flux due to the effect of armature reaction.
- Non-uniform distribution of the current over the cross-section of the armature conductors, etc.
In practice, the miscellaneous losses are taken to be 1% of the full-load losses.
Note −
- The core losses and mechanical losses together are known as rotational losses, i.e.,
$$\mathrm{\text{Rotational Losses, }\:P_{r} \:=\: \text{ Core Losses + Mechanical Losses}}$$
- All the losses occur in the alternator are converted in to heat and result in the increase of temperature and decrease in the efficiency of the alternator.
Efficiency of Alternator
The efficiency of the alternator is defined as the ratio of output power to input power. Therefore, the per unit efficiency of the alternator is given by,
$$\mathrm{Efficiency, \: \eta \:=\: \frac{\text{Output Power }\:(P_{out})}{\text{Input Power }\:(P_{in})}}$$
Also, the percentage efficiency is,
$$\mathrm{Efficiency, \: \eta \:=\: \frac{\text{Output Power }\:(P_{out})}{\text{Input Power }\:(P_{in})}\:\times\:100 \: =\:\frac{P_{out}}{P_{out} \:+\: Losses} \: \times \: 100}$$
Expression for Efficiency of Alternator
Consider a 3-phase alternator which is supplying a load at lagging power factor.
Let,
V = Terminal Voltage per Phase
Ia = Armature Current per Phase
cosφ = Power Factor of The Load
Therefore, the power output of the alternator is given by,
$$\mathrm{P_{out} \:=\: 3VI_{a} \: \cos \phi}$$
The armature copper losses of the alternator are,
$$\mathrm{\text{Armature cu Losses } \:=\: 3{I^{2}_{a}} R_{a}}$$
And the field winding losses are,
$$\mathrm{\text{Field Winding Losses } \:=\: V_{f}\:I_{f}}$$
Where,
- Vf is the DC voltage across the rotor field winding, and
- If is the DC current through the rotor field winding.
Also, the rotational losses are given by,
$$\mathrm{\text{Rotational Losses, } \: P_{r} \:=\: \text{ Core Losses + Mechanical Losses}}$$
Now, if Pmisc represents the miscellaneous losses in the alternator, then
$$\mathrm{\text{Total Losses } \:=\: 3{I^{2}_{a}} R_{a} \:+\: V_{f} \: I_{f} \:+\: P_{r} \:+\: P_{misc}}$$
As the rotor of the alternator rotates at a constant speed so that the rotational losses are constant. Also, the field winding losses are constant. If the miscellaneous losses are also assumed to be constant, then
$$\mathrm{\text{Total Constant Losses, }\:P_{C} \:=\: P_{r} \:+\: P_{misc} \:+\: V_{f}\:I_{f}}$$
The copper losses in the armature winding vary as the square of armature current in the armature winding. As the armature current varies and hence the armature copper losses. For this reason, the armature copper losses are also known as variable losses.
$$\mathrm{\therefore \: \text{ Variable Losses } \:=\: 3{I^{2}_{a}}R_{a}}$$
Therefore, the efficiency of the alternator can be written as,
$$\mathrm{\eta \:=\: \frac{P_{out}}{P_{out} \:+\: Losses} \:=\: \frac{3VI_{a}\:\cos \phi}{3VI_{a}\:\cos \phi \:+\: 3{I^{2}_{a}}R_{a} \:+\: P_{C}}}$$
Condition for Maximum Efficiency of Alternator
The efficiency of the alternator will be maximum when the variable losses are equal to the constant losses of the machine, i.e.,
$$\mathrm{\text{Variable Losses = Cosntant Losses}}$$
$$\mathrm{\Rightarrow \: 3{I^{2}_{a}}R_{a} \:=\: P_{C}}$$
In practice, the maximum efficiency of an alternator occurs at about 85% of full load.