Master Electrical Machines

Interactive simulations for understanding electrical machines - Learn and Enjoy!

🎓 Track Your Learning Journey

Create a free account to save your progress and unlock personalized features!

Login

or

Register

Or continue without account - click any simulator to start!

📬 Stay Updated!

Subscribe to get notified about new simulators, features, and educational content. We regularly add new machines and improve existing simulations.

🚀 New Simulators - Get notified when we add new electrical machine simulators
📚 Learning Content - Receive updates on new tutorials and guides
⚡ Feature Updates - Be the first to know about new features

Subscribe for Updates

We respect your privacy. Your email will only be used for platform updates.

Synchronous Machines

Explore synchronous motors and generators with field excitation control, phasor diagrams, and power factor correction

Motor Generator Phasors

Induction Machines

Deep dive into asynchronous motors and generators with slip analysis, torque curves, and rotor dynamics

Asynchronous Squirrel Cage Torque-Speed

Machine Construction

Visualize the internal construction, windings, magnetic circuits, and mechanical assembly of electrical machines

Stator Rotor Windings

Learning Paths

Beginner

Fundamentals

  • Magnetic circuits basics
  • Electromagnetic induction
  • AC fundamentals
  • Power in AC systems
Intermediate

Machine Theory

  • Rotating magnetic fields
  • Equivalent circuits
  • Performance characteristics
  • Testing methods
Advanced Level

Advanced Analysis

  • Finite element analysis
  • Harmonic analysis
  • Thermal modeling
  • Fault diagnosis

Synchronous Machine Simulator

Interactive simulation of synchronous motors and generators with real-time parameter control

Mode: Motor
Speed: 1500 RPM

Terminal Voltage Vt (3-Phase Waveforms)

Phasor Diagram (V, E, I)

Power Factor Indicator

Machine Parameters

Operation Mode

Power Factor Control

Measured Values

Armature Current (Ia): 0 A
Power Factor (cos φ): 0.8
Mechanical Power: 0 W
Internal EMF (E): 0 V

Synchronous Machine Operation

A synchronous machine operates on the principle of electromagnetic induction. When a three-phase stator winding is supplied with balanced AC voltages, a rotating magnetic field is produced at synchronous speed:

ns = 120f / P

where f is the supply frequency and P is the number of poles.

The rotor, equipped with field windings, produces a constant magnetic field when DC excitation is applied. When the rotor field locks with the rotating stator field, the machine operates at synchronous speed - neither slipping nor lagging.

Key Insight: Synchronous machines can operate at exactly synchronous speed only. If the mechanical load exceeds the stability limit, the machine loses synchronism and stalls.

Synchronous Machine Equations

Phasor Equation (Motor Mode)
E = Vt + Ia(Ra + jXs)

where E is the induced EMF, Vt is terminal voltage, Ia is armature current, Ra is armature resistance, and Xs is synchronous reactance.

Power Equations
P = √3 Vt Ia cos(φ)
Pmech = √3 Vt Ia cos(φ) - 3Ia²Ra
Torque
T = Pmech / ωs

Synchronous Machine Construction

Stator (Armature Winding)
  • Laminated silicon steel core to minimize eddy current losses
  • Three-phase distributed winding (usually 60° or 120° phase spread)
  • Double-layer winding for better harmonic distribution
Rotor (Field Winding)
  • Salient Pole: Used for low-speed machines (hydro generators)
  • Cylindrical Rotor: Used for high-speed machines (turbo generators)
  • Field winding supplied with DC through slip rings or brushless exciter
Excitation System
  • DC exciter mounted on the same shaft
  • Automatic Voltage Regulator (AVR) for voltage control

Per-Phase Equivalent Circuit

Synchronous Impedance
Zs = Ra + jXs

Xs = Xl + Xa

Power-Angle
P = (EV/Xs) sin(δ)
Pro Tip: Xd determines stability

Induction Machine Simulator

Explore asynchronous motors and generators with slip analysis and torque-speed characteristics

Slip: 0%
Speed: 0 RPM

Torque-Speed Characteristic

Machine Parameters

Operation Control

Rotor Type

Calculated Values

Synchronous Speed: 1500 RPM
Actual Speed: 0 RPM
Slip (s): 0%
Developed Torque: 0 Nm
Efficiency: 0%

Induction Machine Operation

The induction machine operates on the principle of transformer action with rotating parts. The stator winding creates a rotating magnetic field (RMF) that rotates at synchronous speed:

ns = 120f / P

The rotating magnetic field induces currents in the rotor conductors, which then create their own magnetic field. The interaction between the stator and rotor fields produces torque.

Key Concept - Slip: The rotor always rotates at a speed less than synchronous speed. The difference is expressed as slip:

s = (ns - nr) / ns

When s = 0 (nr = ns), no relative motion exists between the RMF and rotor, so no EMF is induced - the machine acts as a synchronous machine.

Did You Know? In the generating mode (negative slip), the rotor is driven above synchronous speed, causing the induced rotor currents to reverse, and the machine delivers electrical power to the grid.

Induction Machine Equations

Equivalent Circuit (Per Phase)

The induction machine is modeled as a transformer with the rotor represented as a short-circuited secondary. The slip appears as a variable resistance in the rotor circuit:

R2/s = R2 + R2(1-s)/s

The second term represents the mechanical load converted to electrical resistance.

Torque Equation
T = (3 × V1² × R2/s) / (ωs × [(R1 + R2/s)² + (X1 + X2)²])

The torque-slip characteristic shows:

  • Starting torque at s = 1
  • Pull-out (maximum) torque at s = R2/√((R1+R2)² + (X1+X2)²)
  • Stable operating region for 0 < s < smax
Power Flow
Pair-gap = Pmech / (1-s)
Protor-cu = s × Pair-gap

The slip directly represents the fraction of air-gap power converted to rotor copper losses.

Starting Methods for Induction Motors

Induction motors draw 5-7 times rated current at starting. Various methods are used to reduce starting current:

Direct On-Line (DOL)

Simplest method - full voltage applied directly. High starting current but maximum torque.

Star-Delta

Stator winding connected in star during start (reduced voltage), then switched to delta.

Auto-Transformer

Reduced voltage applied via autotransformer, with taps at 50%, 65%, or 80% voltage.

Soft Starter

Thyristor-controlled voltage ramp for smooth starting with current limit.

Variable Frequency Drive (VFD)

Best method - controls voltage and frequency simultaneously for optimal starting performance.

Wound Rotor - External Resistance

Adding external resistance to rotor circuit increases starting torque and reduces starting current.

DC Motor Simulator

Interactive simulation of DC motors - shunt, series, and compound

Motor Parameters

Readings

Speed:0 RPM
Armature Current:0 A
Back EMF:0 V
Efficiency:0%

Transformer Simulator

Interactive simulation of power transformers with phasor diagrams, waveforms, and equivalent circuit

Voltage & Current Waveforms

Phasor Diagram

Equivalent Circuit

Input Parameters

Load Parameters

Transformer Parameters

Measured Values

Secondary V:0 V
Primary I:0 A
Secondary I:0 A
Efficiency:0%
Power:0 VA
Voltage Regulation:0%

PMSM Simulator

Permanent Magnet Synchronous Machine with vector control

Current Waveforms

d-q Axis Vectors

Operating Parameters

Current Control (Vector Control)

Measurements

Speed:0 RPM
Torque:0 Nm
Power:0 W
Efficiency:0%
Frequency:0 Hz
Voltage:0 V

Electrical Machine Learning Center

Comprehensive educational resources on electrical machine fundamentals

Learning Objectives

🎯

1. Machine Topologies

Understand the structure and operating principles of various electrical machine topologies including DC, induction, synchronous, and PMSM machines.

⚡

2. Application Selection

Select an appropriate electrical machine topology for a given application based on performance requirements, cost, and efficiency.

🔄

3. Torque Production

Explain the torque production process in electrical machines using electromagnetic principles and the Lorentz force equation.

📐

4. Machine Sizing

Comprehend the principles of electrical machine sizing including thermal limits, torque density, and power rating calculations.

🧲

5. Windings

Understand the basics of electrical machine windings including lap and wave windings, distributed vs concentrated windings.

🔧

6. Materials

List and apply the most important materials used in magnetic circuits and windings including electrical steel, copper, and permanent magnets.

Machine Types & Operating Principles

DC Machines

+

DC machines convert electrical energy to mechanical energy (motor) or vice versa (generator). They consist of a stator (field windings) and rotor (armature) with commutator.

E = kΦn (EMF equation)
T = kΦIa (Torque equation)

Applications: DC motors widely used in industry, electric vehicles, robotics where variable speed control is needed.

Induction Machines

+

Induction machines operate on the principle of transformer action. The stator creates a rotating magnetic field that induces currents in the rotor.

ns = 120f/P (Synchronous speed)
s = (ns - n)/ns (Slip)
T = (3V²R₂/sωs) / ((R₁+R₂/s)² + (X₁+X₂)²)

Applications: Most widely used motor in industry (pumps, fans, compressors) due to rugged construction and low cost.

Synchronous Machines

+

Synchronous machines run at constant speed (synchronous speed) determined by frequency and number of poles. Can operate as motor or generator.

ns = 120f/P (Synchronous speed)
E = 4.44fNΦk (Generated EMF)
T = (3VEsinδ)/Xsωs (Power angle equation)

Applications: Power generation (hydro, thermal generators), large industrial motors, power factor correction.

Permanent Magnet Synchronous Machines (PMSM)

+

PMSM uses permanent magnets instead of field windings, providing higher efficiency and power density. Requires vector control for operation.

Te = 1.5P/2 [ΦmIq + (Ld-Lq)IdIq]

Vector Control: Decouples torque and flux components for precise control.

Applications: Electric vehicles, wind turbines, servo drives, aerospace.

Machine Calculations

Induction Machine Calculations

Synchronous Speed: 1500 RPM

Synchronous Machine Calculations

Apparent Power calculation shown

Power & Torque

Torque: 63.66 Nm

Efficiency Calculation

Efficiency: 80%

Materials in Electrical Machines

Electrical Steel

Types: Grain-oriented (GO) and Non-oriented (NO) steel

Properties: High permeability, low core loss (0.5-5 W/kg at 1.5T, 50Hz)

Applications: Stator and rotor cores

Thickness: 0.35mm, 0.5mm, 0.65mm laminations

Copper

Properties: High conductivity (5.96×10⁷ S/m), low resistivity (1.68 μΩ·cm)

Forms: Round wire, rectangular busbar, litz wire (for high frequency)

Temperature: Class F (155°C) or Class H (180°C) insulation

Current Density: 3-6 A/mm² typical

Permanent Magnets

Types: Ferrite, AlNiCo, SmCo, NdFeB

NdFeB: Highest energy product (up to 52 MGOe), max temp 200°C

SmCo: Good up to 350°C, expensive

Ferrite: Low cost, low energy product, max temp 300°C

Insulation Materials

Classes: A (105°C), E (120°C), B (130°C), F (155°C), H (180°C)

Types: Enamel (magnet wire), paper, Mylar, epoxy, varnish

Key Property: Dielectric strength (typically 20-200 kV/mm)

📝 Knowledge Quiz

Test your understanding of electrical machines!

1

What is the EMF equation of a DC machine?

2

What is the synchronous speed formula for a 50Hz, 4-pole motor?

3

In synchronous machines, what happens if the load angle (δ) exceeds 90°?

4

What is the main advantage of PMSM over induction motors?

5

What happens to the core losses in a transformer when frequency increases?

6

What is the typical efficiency of commercial silicon solar cells?

Your Quiz Progress

0 / 6 Correct

V2G Simulator

Vehicle-to-Grid Technology - Electric Vehicle Grid Integration

24-Hour Price Curve

EV Battery

Time & Grid

Charging Mode

Status

Power:0 kW
Battery:50%
Capacity:37.5 kWh
Grid Price:$0.12/kWh
Grid Demand:5 kW
Cost:$0.00
V2G Profit:$0.00

Power Electronics Simulator

Interactive simulation of DC-DC converters and inverters

Input Parameters

Switching

Components

Output Readings

Vout:0 V
Iout:0 A
Ripple:0 %
Efficiency:0 %

Converter Theory

Buck Converter (Step-Down)

Reduces voltage while increasing current. Output voltage is always less than input.

Vout = Vin × D

Where D is the duty cycle (0-1). The inductor smooths the output current, and the capacitor reduces output voltage ripple.

Wind Turbine Simulator

Interactive simulation of wind turbine power generation

Power Curve

Wind Conditions

Turbine Control

Output

Power:0 kW
Rotor Speed:0 RPM
Cp:0%
TSR:0

Solar Panel Simulator

Interactive simulation of solar PV system power generation

IV Curve

Solar Conditions

Panel Setup

Output

Power:0 kW
Voltage:0 V
Current:0 A
Daily Energy:0 kWh
Efficiency:0%

Machine Construction & Anatomy

Interactive exploration of electrical machine components and their assembly

Hover over components

Explore the internal construction of electrical machines

Select Component

Construction Animation

Cross-Section Views

Synchronous Machine

Induction Machine

Magnetic Field Distribution