
- Electrical Machines - Home
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- Fleming's Left Hand and Right Hand Rules
- Transformers
- Electrical Transformer
- Construction of Transformer
- EMF Equation of Transformer
- Turns Ratio and Voltage Transformation Ratio
- Ideal Transformer
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- Transformer Working Principle
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- 3 to 12-Phase Transformers
- Scott-T Transformer Connection
- Transformer kVA Rating
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- Transformer DC Supply Issue
- Equivalent Circuit Transformer
- Simplified Equivalent Circuit of Transformer
- Transformer No-Load Condition
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- OTI WTI Transformer
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- Isolation vs Regular Transformer
- Dry vs Oil-Filled
- 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
- More on DC Machines
- DC Generator
- DC Generator Armature Reaction
- DC Generator Commutator Action
- Stepper vs DC Motors
- DC Shunt Generators Critical Resistance
- DC Machines Commutation
- DC Motor Characteristics
- Synchronous Generator Working Principle
- DC Generator Characteristics
- DC Generator Demagnetizing & Cross-Magnetizing
- 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
- Speed Control of DC Series Motor
- DC Motor of Speed Regulation
- Hopkinson's Test
- Permanent Magnet DC Motor
- Permanent Magnet Stepper Motor
- DC Servo Motor Theory
- DC Series vs Shunt Motor
- BLDC Motor vs PMSM Motor
- 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
- 3-Phase Induction Motor Rotor Parameters
- Double Cage Induction Motor Equivalent Circuit
- Induction Motor Equivalent Circuit Models
- Slip Ring vs Squirrel Cage Induction Motors
- Single-Cage vs Double-Cage Induction Motor
- Induction Motor Equivalent Circuits
- Induction Motor Crawling & Cogging
- Induction Motor Blocked Rotor Test
- Induction Motor Circle Diagram
- 3-Phase Induction Motors Applications
- 3-Phase Induction Motors Torque Ratios
- Induction Motors Power Flow Diagram & Losses
- Determining Induction Motor Efficiency
- Induction Motor Speed Control by Pole-Amplitude Modulation
- Induction Motor Inverted or Rotor Fed
- High Torque Cage Motors
- Double-Cage Induction Motor Torque-Slip Characteristics
- 3-Phase Induction Motors Starting Torque
- 3-phase Induction Motor - Rotor Resistance Starter
- 3-phase Induction Motor Running Torque
- 3-Phase Induction Motor - Rotating Magnetic Field
- Isolated Induction Generator
- Capacitor-Start Induction Motor
- Capacitor-Start Capacitor-Run Induction Motor
- Winding EMFs in 3-Phase Induction Motors
- Split-Phase Induction Motor
- Shaded Pole Induction Motor
- Repulsion-Start Induction-Run Motor
- Repulsion Induction Motor
- PSC Induction Motor
- 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
- Four-Point Starter
- Ward Leonard Speed Control Method
- Pole Changing Method
- Stator Voltage Control Method
- DOL Starter
- Star-Delta Starter
- Hysteresis Motor
- 2-Phase & 3-Phase AC Servo Motors
- Repulsion Motor
- Reluctance Motor
- Stepper Motor
- PCB Motor
- Single-Stack Variable Reluctance Stepper Motor
- Schrage Motor
- Hybrid Schrage Motor
- Multi-Stack Variable Reluctance Stepper Motor
- Universal Motor
- Step Angle in Stepper Motor
- Stepper Motor Torque-Pulse Rate Characteristics
- Distribution Factor
- Electrical Machines Basic Terms
- Synchronizing Torque Coefficient
- Synchronizing Power Coefficient
- Metadyne
- Motor Soft Starter
- CVT vs PT
- Metering CT vs Protection CT
- Stator and Rotor in Electrical Machines
- Electric Motor Winding
- Electric Motor
- Useful Resources
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- Discussion
Losses in DC Machines
In DC machines (generator or motor), the losses may be classified into three categories namely,
- Copper losses
- Iron or core losses
- Mechanical losses
All these losses appear as heat and hence raise the temperature of the machine. They also reduce the efficiency of the machine.
Copper Losses
In dc machines, the losses that occur due to resistance of the various windings of the machine are called copper losses. The copper losses are also known as I2R losses because these losses occur due to current flowing through the resistance of the windings.
The major copper losses that occur in dc machines are as,
$$\mathrm{\mathrm{Armature\:copper\:loss}\:=\:\mathit{I_{a}^{\mathrm{2}}R_{a}}}$$
$$\mathrm{\mathrm{Series\:field\:copper\:loss}\:=\:\mathit{I_{se}^{\mathrm{2}}R_{se}}}$$
$$\mathrm{\mathrm{Shunt\:field\:copper\:loss}\:=\:\mathit{I_{sh}^{\mathrm{2}}R_{sh}}}$$
In dc machines, there is also a brush contact loss due to brush contact resistance. In practical calculation, this loss is generally included in armature copper loss.
Iron Losses
The iron losses occur in core of the armature of a DC machine due to rotation of the armature in the magnetic field. Because these losses occur in core of the armature, these are also called core losses.
There are two types iron or core losses namely hysteresis loss and eddy current loss.
Hysteresis Loss
The core loss that occurs in core of the armature of a dc machine due to magnetic field reversal in the armature core when it passes under the successive magnetic poles of different polarity is called hysteresis loss. The hysteresis loss is given by the following empirical formula,
$$\mathrm{\mathrm{Hysteresis\:loss,}\mathit{P_{h}}\:=\:\mathit{k_{h}B_{max}^{\mathrm{1.6}}fV}}$$
Where, $\mathit{k_{h}}$ is the Steinmetzs hysteresis coefficient, $\mathit{B_{max}}$ the maximum flux density,f is the frequency of magnetic reversal, and V is the volume of armature core.
The hysteresis loss in dc machines can be reduced by making the armature core of such materials that have a low value of Steinmetzs hysteresis coefficient like silicon steel.
Eddy Current Loss
When the armature of a DC machine rotates in the magnetic field of the poles, an EMF is induced in core of the armature which circulates eddy currents in it. The power loss due to these eddy currents is known as eddy current loss. The eddy current loss is given by,
$$\mathrm{\mathrm{Eddy\:current\:loss,}\mathit{P_{e}}\:=\:\mathit{k_{e}B_{max}^{\mathrm{2}}f^{\mathrm{2}}t^{\mathrm{2}}V}}$$
Where,$\mathit{K_{e}}$ is a constant of proportionality, and tis the thickness of lamination.
From the expression for eddy current loss it is clear that the eddy current loss depends upon the square of thickness of lamination. Therefore, to reduce this loss, the armature core is built up of thin laminations that are insulated from each other by a thin layer of varnish.
Mechanical Losses
The power losses due to friction and windage in a dc machine are known as mechanical losses. In a dc machine, the friction loss occurs in form of bearing friction, brush friction, etc. while the windage loss occurs due to air friction of rotating armature.
The mechanical losses depend upon the speed of the machine. But these losses are practically constant for a given speed.
Note− Iron or core losses and mechanical losses together are known as stray losses.
Constant and Variable Losses
In DC machines, we may group the above discussed losses in the following two categories −
- Constant Losses
- Variable Losses
Those losses in a DC machine that remain constant at all loads are called constant losses. These losses include − iron losses, shunt field copper loss, and mechanical losses.
Those losses in a DC machine that vary with load are known as variable losses. The variable losses in a DC machine are − armature copper loss and series field copper loss.
Total losses in a DC machine = Constant losses + Variable losses
Note − Iron losses and mechanical losses together are known as stray losses, i.e.
Strey Losses = Iron losses + Mechanical losses
Losses in a Transformer
The power losses in a transformer are of two types −
- Iron or Core Losses
- Copper Losses
Iron or Core Losses
The irons losses consist of hysteresis and eddy current losses and occur in the core of the transformer due to alternating flux. The iron losses of the transformer can be determined by the open-circuit test.
$$\mathrm{\text{Hysteresis Loss,} \:P_{h} \: = \: K_{h} \: B_{max}^{1.6} \:fV \: \text{ Watts }}$$
$$\mathrm{\text{Eddy Current Loss,} \:P_{e} \: = \: K_{e} \: B_{max}^{2} \:f^{2}t^{2}V \: \text{ Watts }}$$
Also,
$$\mathrm{\text{Iron or core Losses, } \:P_{i} \: = \: P_{h} \: + \: P_{e} \: = \: \text{ Constant Losses}}$$
The hysteresis losses can be minimised using silicon steel whereas the eddy current losses can be reduced using core made up of thin laminations.
Copper Losses
Copper losses occur in the primary and secondary windings of the transformer due to their resistance. These can be determined by short circuit test.
$$\mathrm{\text{Copper Losses, } \:P_{cu} \: = \: I_{1}^{2}R_{1} \: + \:I_{2}^{2}R_{2}}$$
Losses in Rotating AC Machines
The losses occur in rotating AC machines are also same as those are in DC machines. These losses can be classified into two categories as −
Fixed or Constant Losses
- Stator iron loss
- Friction and windage loss
Variable Losses
- Stator Copper Loss
- Rotor Copper Loss
Electric Machine Efficiency
The efficiency of an electric machine is defined as the ratio of the output power to the input power, i.e.
$$\mathrm{\text{Efficiency, } \: \eta \: = \: \frac{\text{Output Power }\:(P_{0})}{\text{Input Power}\:(P_{i})}}$$
$$\mathrm{\because\: \text{Input Power } \: = \: \text{Output Power } \: + \: \text{ Losses}}$$
$$\mathrm{\therefore \: \text{ Efficiency, } \: \eta \: = \: \frac{\text{Output Power}\:(P_{0})}{\text{Output Power }\:(P_{0}) \: + \: \text{ Losses}} \: = \: \left(1 \: + \: \frac{\text{Output Power }\:(p_{0})}{\text{ Losses}}\right)}$$
Numerical Example #1
The armature resistance of a compound long shunt DC motor is 0.0858 Ω. It has shunt and series field resistances of 60 Ω and 0.06 Ω respectively. The motor draws a total current of 100 A. If the shunt field current and series field current are 2 A, determine the total cu loss of the motor.
Solution
Armature Current,
$$\mathrm{I_{a} \: = \: I_{r} \: + \: I_{sh} \: = \: 100 \: + \: 2 \: = \: 102}$$
Therefore, Armature Cu Loss,
$$\mathrm{= \: I_{a}^{2}R_{a} \: = \: 102^{2} \: \times \: 0.0858 \: = \:892.66 \: W}$$
Series Field Cu Loss,
$$\mathrm{= \: I_{se}^{2}R_{se} \: = \: I_{a}^{2}R_{se} \: = \: 102^{2} \: \times \: 0.06 \: = \: 624.24 \: W}$$
Shunt Field Cu Loss,
$$\mathrm{= \: I_{sh}^{2}R_{sh} \: = \: 2^{2} \: \times \: 60 \: = \: 240 \: W}$$
∴ Total Cu Losses,
$$\mathrm{P_{cu} \: = \: I_{a}^{2}R_{a} \: + \: I_{se}^{2}R_{se} \: + \: I_{sh}^{2}R_{sh}}$$
⇒ Total Cu Losses,
$$\mathrm{P_{cu} \: = \: 892.66 \: + \: 624.24 \: + \: 240 \: = \: 1756.9 \: W}$$
Numerical Example #2
A power transformer has a core material for which hysteresis coefficient is 120 J/m3and eddy current-loss coefficient is 250. Its volume is 10000 cm3 and the maximum flux density is 1.18 Wb/m2 . The core is built up of thin laminations of thickness 8 mm. What is the total iron/core loss in watts, if the frequency of the alternating current is 50 Hz?
Solution
The hysteresis power loss is given by,
$$\mathrm{P_{h} \: = \: K_{h}B_{max}^{1.6} \: fV}$$
$$\mathrm{= \: 120 \: \times \: (1.18)^{1.6} \: \times \: 50 \: \times \: 10000 \: \times \: 10^{-6}}$$
$$\mathrm{= \: 78.19 \: W}$$
And, the eddy current loss is given by,
$$\mathrm{P_{e} \: = \: K_{e}B_{max}^{2} \: f^{2}t^{2} \: V}$$
$$\mathrm{= \: 250 \: \times \: (1.18)^{2} \: \times \: 50^{2} \: \times \: (8 \: \times \: 10^{-3})^{2} \: \times \: 10000 \: \times \: 10^{-6}}$$
$$\mathrm{= \: 0.557 \: W}$$
Therefore,
Total core losses = $\mathrm{78.19 \: + \: 0.557 \: = \: 78.747 \: W}$
Numerical Example #3
In a 25 kVA transformer, the iron loss is 250 W and full load copper loss is 400 W. Find the efficiency at full load at 0.8 power factor lagging.
Solution
Full Load Output,
$$\mathrm{P_{0} \: = \: 25 \: \times \: 0.8 \: = \: 20 \: kW}$$
Total Full Load Losses,
$$\mathrm{= \: 250 \: + \: 400 \: = \: 650 \: W \: = \: 0.65 \: kW}$$
Full Load Input Power,
$$\mathrm{P_{i} \: = \: 20 \: + \: 0.65 \: = \: 20.65 \: kW}$$
Therefore, Full Load Efficiency,
$$\mathrm{\eta \: = \: \frac{P_{0}}{P_{i}} \: \times \: 100 \: = \: \frac{20}{20.65} \: \times \: 100 \: = \: 96.85\%}$$