
- Electrical Machines - Home
- Basic Concepts
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- Faraday’s Laws of Electromagnetic Induction
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- Fleming's Left Hand and Right Hand Rules
- Transformers
- Electrical Transformer
- Construction of Transformer
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- Transformer Working Principle
- Single-Phase Transformer Working Principle
- 3-Phase Transformer Principle
- 3-Phase Induction Motor Torque-Slip
- 3-Phase Induction Motor Torque-Speed
- 3-Phase Transformer Harmonics
- Double-Star Connection (3-6 Phase)
- Double-delta Connection (3-6 Phase)
- Transformer Ratios
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- Transformer DC Supply Issue
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- Transformer No-Load Condition
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- OTI WTI Transformer
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- Isolation vs Regular Transformer
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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
- 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
- Quick Guide
- Resources
- Discussion
Power Flow Diagram and Losses of Induction Motor
The 3-phase input power fed to the stator of a 3-phase induction motor is given by,
$$\mathrm{P_{is} \:=\: \sqrt{3} \: V_{L}I_{L} \: \cos \varphi_{i} \: = \: 3 V_{sph} I_{sph} \: \cos \varphi_{i}}$$
Where,
- VL = Line voltage
- IL = Line current
- Vsph = Stator phase voltage
- Isph = Stator phase current
- cos ϕi = input power factor
Stator Losses
- Stator copper losses or I2R losses in the stator winding resistances, which are given as follows −
$$\mathrm{P_{scu} \: = \: 3 I_{sph}^{2} R_{sph}}$$
- Hysteresis and eddy current losses in the stator core, which are known as stator-core losses and are given by −
$$\mathrm{P_{sC} \:=\: P_{sh} \:+\: P_{se}}$$
Therefore, the power output of the stator will be,
$$\mathrm{P_{os} \:=\: P_{is} \: - \: P_{scu} \: - \: P_{sC}}$$
This output power of the stator (Pos) is transferred to the rotor of the machine across the air-gap between the stator and the rotor. It is also known as air-gap power (Pg) of the machine. Hence,
$$\mathrm{\text{Power output of stator } \: (P_{os}) \:=\: \text{ Air gap power } \: (P_g) \:=\: \text{ Input\:power\:to\:rotor } \: (P_{ir})}$$
Rotor Losses
- Rotor copper losses or I2R losses in the rotor resistance, which are given by,
$$\mathrm{P_{rcu} \:=\: 3 \: I_{2}^{2} R_{2}}$$
- Rotor core losses or hysteresis and eddy current losses, which are given as follows −
$$\mathrm{P_{rC} \:=\: P_{rh} \:+\: P_{re}}$$
- Friction and windage losses (Pfw)
- Stray load losses (Pmisc) consisting of all the losses which are not included in the above losses like losses due to harmonic fields.
Mechanical Power Developed (Pm)
If the rotor copper losses are subtracted from the rotor input power (Pg or Pir), then the remaining power is converted from electrical power to mechanical power. It is known as developed mechanical power(Pm).
$$\mathrm{\text{Developed mechanical power, } \: P_{m} \:=\: P_{ir} \: - \: P_{rcu}}$$
$$\mathrm{\Rightarrow \: P_{m} \:=\: P_{g} \:-\: P_{rcu} \:=\: P_{g} \:-\: (3I_{2}^{2}R_{2})}$$
Therefore, the output power of the motor is given by,
$$\mathrm{P_{o} \:=\: P_{m} \:-\: P_{fw} \:-\: P_{misc}}$$
The power Po is known as useful power or shaft power.
Rotational Losses
At the starting and during the acceleration, the rotor core losses are high and decreases with the increase in the speed of the motor. The friction and windage losses are zero at start and increases with the increases in the speed.
Consequently, the sum of core losses and friction and windage losses is approximately constant with varying speed of the motor. Hence, these losses may lumped together and are called as rotational losses and given as follows −
$$\mathrm{P_{\text{rotational losses}} \:=\: P_{C} \:+\: P_{fw} \:+\: P_{misc}}$$
Then, the output power of the motor is given by,
$$\mathrm{P_{o} \:=\: P_{m} \:-\: P_{\text{rotational losses}} \:=\: P_{o} \:=\: P_{m} \:-\: P_C \:-\: P_{fw} \:-\: P_{misc}}$$
The power diagram of the induction motor is shown in the figure below.
