Basic Electrical and Electronics Engineering (EE 103) – Chapter 2
This chapter provides a comprehensive overview of Electrical Machines, covering the fundamental principles and operational characteristics of transformers, induction motors, DC motors, and synchronous generators. Understanding these electrical machines is crucial for electrical engineering applications. These electrical machines form the backbone of modern power systems and industrial applications.
Chapter Information
Chapter 2: Electrical Machines (14 hours) – 18 marks
Course: Basic Electrical and Electronics Engineering (EE 103), I Year I Part
Description: This guide provides complete Electrical Machines notes covering transformers, induction motors, DC motors, synchronous generators, and electromagnetic principles as per IOE syllabus.
Credit: Asst. Prof. Shahabuddin Khan
Table of Contents
External Resources
For further reading on electrical machines, check out these authoritative resources:
Detailed Chapter Notes
2.1 Faraday’s Law of Electromagnetic Induction
The principle of electromagnetic induction is the foundation upon which all electrical machines operate. Michael Faraday, through his experiments, formulated two fundamental laws.
Faraday’s First Law:
This law states that whenever the magnetic flux linked with a circuit or conductor changes, an electromotive force (EMF) is induced in it. The existence of an induced EMF depends solely on the change in flux linkage, regardless of whether the circuit is closed or open.
Faraday’s Second Law:
This law quantifies the induced EMF. It states that the magnitude of the induced EMF is directly proportional to the rate of change of magnetic flux linkages.
Mathematically, the induced EMF (e) is given by:
\[ e = -N \frac{d\phi}{dt} \]
Where:
N is the number of turns in the coil.
dΦ/dt is the rate of change of magnetic flux.
The negative sign is a consequence of Lenz’s Law.
Lenz’s Law:
Lenz’s Law provides the direction of the induced EMF and current. It states that the direction of the induced current will be such that it creates a magnetic field that opposes the very change in flux that produced it.
2.2 Dynamically and Statically Induced EMFs
An EMF can be induced in a conductor through two primary mechanisms, based on how the change in flux linkage is achieved.
Dynamically Induced EMF
A dynamically induced EMF is generated when a conductor moves through a stationary magnetic field, or when a magnetic field moves past a stationary conductor. In either case, there is relative motion between the conductor and the magnetic field. This is the principle behind the operation of electrical generators, which are essential electrical machines.
The magnitude of the dynamically induced EMF is given by:
\[ e = B l v \sin(\theta) \]
Where:
B is the magnetic flux density (in Tesla).
l is the length of the conductor within the magnetic field (in meters).
v is the velocity of the conductor relative to the field (in m/s).
θ is the angle between the direction of motion of the conductor and the magnetic field. The EMF is maximum when the conductor moves perpendicular to the field (θ=90°).
Statically Induced EMF
A statically induced EMF is generated in a conductor that is stationary within a stationary magnetic field, where the magnitude of the field itself changes over time. This changing magnetic field produces a change in flux linkage, inducing an EMF. This principle is fundamental to the operation of transformers, which are crucial electrical machines. Statically induced EMF can be further categorized into:
- Self-Induced EMF: This is the EMF induced in a coil due to the change in current flowing through the coil itself. The changing current creates a changing magnetic flux that links the coil, inducing an opposing EMF.
It is given by: \[ e = -L \frac{di}{dt} \]
Where L is the self-inductance of the coil.
- Mutually Induced EMF: This is the EMF induced in a coil due to a change in current in a neighboring coil. The changing flux produced by the first coil links with the second coil, inducing an EMF in it. This is the working principle of a transformer.
It is given by: \[ e = -M \frac{di_1}{dt} \]
Where M is the mutual inductance between the two coils.
2.3 Transformer
2.3.1 Introduction of Single-Phase Transformer
A transformer is a static AC device that transfers electrical energy from one electrical circuit to another through the process of electromagnetic induction. It is commonly used to increase (step-up) or decrease (step-down) voltage levels without changing the frequency of the supply. Transformers are fundamental electrical machines in power systems.
2.3.2 Working Principle of Transformer
The operation of a transformer is based on the principle of mutual induction.
- An alternating voltage source is connected to the primary winding.
- This causes an alternating current to flow through it, which produces a time-varying magnetic flux in the transformer’s core.
- Since the secondary winding is wound on the same core, this changing flux links with the secondary winding.
- According to Faraday’s law of electromagnetic induction, this flux linkage induces an alternating EMF in the secondary winding.
2.3.3 Components of Transformer
- Laminated Core: Provides a low-reluctance path for the magnetic flux. It is made of thin, insulated silicon steel laminations to minimize eddy current loss.
- Windings: Two sets of insulated copper windings, the primary (connected to the source) and the secondary (connected to the load).
- Insulation: Insulating material (like paper or varnish) is used to insulate the windings from each other and from the core.
- Transformer Tank: A steel tank that houses the core and windings, filled with insulating oil.
- Transformer Oil: Provides insulation and acts as a coolant to dissipate heat.
- Conservator: A small cylindrical tank mounted above the main tank to allow for the expansion and contraction of oil.
- Breather: Contains silica gel to absorb moisture from the air entering the conservator.
- Cooling Tubes/Radiators: Help in cooling the transformer oil through natural circulation.
- Bushings: Insulators used to connect the winding terminals to the external circuit safely.
2.3.4 Transformation Ratio (K)
The transformation ratio is the ratio of the secondary voltage to the primary voltage. For an ideal transformer:
\[ K = \frac{E_2}{E_1} = \frac{N_2}{N_1} = \frac{I_1}{I_2} \]
- If K > 1, it is a step-up transformer (N₂ > N₁).
- If K < 1, it is a step-down transformer (N₂ < N₁).
- If K = 1, it is an isolation transformer (N₂ = N₁).
2.3.5 EMF Equation of Transformer
The alternating flux in the core can be represented as ϕ = ϕₘ sin(ωt).
The instantaneous EMF induced in the primary winding is:
\[ e_1 = -N_1 \frac{d\phi}{dt} = -N_1 \phi_m \omega \cos(\omega t) = N_1 \phi_m (2\pi f) \sin(\omega t – 90^\circ) \]
The RMS value of the induced EMF in the primary winding is:
\[ E_1 = \frac{E_{max1}}{\sqrt{2}} = \frac{2\pi f N_1 \phi_m}{\sqrt{2}} = 4.44 f N_1 \phi_m \]
Similarly, the RMS value of the induced EMF in the secondary winding is:
\[ E_2 = 4.44 f N_2 \phi_m \]
Where:
- f is the supply frequency (Hz)
- N₁, N₂ are the number of turns in the primary and secondary windings
- Φₘ is the maximum value of flux in the core (Webers)
2.3.6 Types of Transformers
- Based on Construction: Core Type and Shell Type
- Based on Voltage Level: Step-up and Step-down
- Based on Application: Power Transformers (for transmission), Distribution Transformers (for local distribution), Instrument Transformers (Current Transformer – CT, Potential Transformer – PT for measurement), and Autotransformers (single winding)
2.3.7 Load and No-Load Operation
- No-Load Operation: When the secondary winding is open-circuited, the transformer draws a small no-load current (I₀) from the source. This current establishes the magnetic flux in the core and supplies the core losses. It has two components: a magnetizing component (Iₘ) and a core loss component (I_w)
- Load Operation: When a load is connected to the secondary, a secondary current (I₂) flows. This current creates a demagnetizing flux. To counteract this, the primary winding draws an additional load component of current (I₁′) from the source. The total primary current is the vector sum of the no-load current and the load component (I₁ = I₀ + I₁′)
2.3.8 Ideal and Practical Transformer
- Ideal Transformer: A hypothetical transformer with no losses. Its windings have zero resistance, there are no core losses (hysteresis or eddy current), and there is no magnetic leakage (all flux is confined to the core). Its efficiency is 100%
- Practical Transformer: A real-world transformer that has winding resistances, core losses, and magnetic leakage. Its efficiency is always less than 100%
2.3.9 Losses and Efficiency
- Core (or Iron) Losses (Pᵢ): These losses occur in the core and are constant, regardless of the load
- Hysteresis Loss: Due to the repeated reversal of magnetization in the core material
- Eddy Current Loss: Due to circulating currents induced in the core material itself. Minimized by using a laminated core
- Copper Losses (P_cu): These are I²R losses in the primary and secondary windings. They are variable and depend on the square of the load current
Efficiency (η): The ratio of output power to input power
\[ \eta = \frac{\text{Output Power}}{\text{Input Power}} = \frac{\text{Output Power}}{\text{Output Power} + \text{Core Loss} + \text{Copper Loss}} \]
The condition for maximum efficiency is when the variable copper losses are equal to the constant core losses (P_cu = Pᵢ)
2.3.10 Applications
Transformers are essential in AC power systems for:
- Stepping up voltage for efficient long-distance power transmission
- Stepping down voltage for safe distribution and use by consumers
- Impedance matching in electronic circuits
- Providing electrical isolation between circuits
2.4 Three Phase Induction Motor
2.4.1 Construction
A three-phase induction motor consists of two main parts:
- Stator: The stationary outer part, which consists of a steel frame, a laminated core with slots, and a three-phase winding distributed in the slots
- Rotor: The rotating inner part, which consists of a laminated cylindrical core and a rotor winding
2.4.2 Rotating Magnetic Field (RMF)
When the three-phase stator winding is connected to a balanced three-phase AC supply, a system of currents flows that produces a magnetic field. This magnetic field is constant in magnitude but rotates in space at a constant speed, known as the synchronous speed (Nₛ)
\[ N_s = \frac{120 f}{P} \]
Where f is the supply frequency and P is the number of stator poles
2.5 DC Motors
2.5.1 Construction
A DC machine consists of a stationary part (stator) and a rotating part (rotor)
- Stator (Field System): Yoke (outer frame), pole cores, pole shoes, and field windings (which produce the main magnetic field)
- Rotor (Armature): Armature core (laminated steel cylinder with slots), armature windings (housed in the slots), a commutator (segmented copper ring), and brushes (carbon blocks that conduct current to/from the commutator)
2.5.2 Working Principle
The operation is based on the Lorentz Force Principle
- Current is supplied to the field windings, creating a magnetic field
- Current is also supplied to the armature windings via the brushes and commutator
- The current-carrying armature conductors are now in the magnetic field and experience a force
- This force creates a torque, causing the armature to rotate
- The commutator’s function is crucial: it reverses the direction of current in each armature coil as it passes from one magnetic pole to the next, ensuring that the torque is always in the same direction, resulting in continuous rotation
2.6 Synchronous Generator (Alternator)
2.6.1 Construction
An alternator also has a stator and a rotor. However, its arrangement is the reverse of a DC machine
- Stator (Armature): The stationary part that houses the three-phase armature winding, where the voltage is generated
- Rotor (Field System): The rotating part that carries the field winding. This winding is excited by a DC source (via slip rings) to create the magnetic poles. There are two types of rotors:
- Salient Pole Rotor: Has projecting poles and is used for low-speed alternators (e.g., in hydroelectric plants)
- Cylindrical Rotor: Has a smooth, non-salient pole construction and is used for high-speed turbo-alternators (e.g., in thermal or nuclear plants)
2.6.2 Working Principle
The operation is based on Faraday’s Law of Electromagnetic Induction
- A DC current is passed through the rotor field winding to create a magnetic field
- A prime mover (like a turbine) rotates the rotor at a constant speed, called the synchronous speed (Nₛ)
- As the magnetic field of the rotor rotates, it cuts through the stationary conductors of the stator armature winding
- This induces a three-phase sinusoidal EMF in the stator windings
The frequency of the generated EMF is synchronized with the rotor speed:
\[ f = \frac{P N_s}{120} \]
2.6.3 EMF Equation
The RMS value of the induced EMF per phase (E_ph) in the stator windings is given by:
\[ E_{ph} = 4.44 K_p K_d f \phi T_{ph} \]
Where:
f is the frequency of the induced EMF
Φ is the flux per pole
T_ph is the number of turns in series per phase
K_d is the Distribution Factor (accounts for the winding being distributed in several slots)
K_p is the Pitch Factor (accounts for the winding being short-pitched)
2.6.4 Applications
Synchronous generators, or alternators, are the primary source of almost all the electrical energy consumed in the world. They are used in all major power generation stations, including:
- Hydroelectric Power Plants
- Thermal Power Plants (coal, gas)
- Nuclear Power Plants
They are responsible for producing the power that is fed into the electrical grid
PDF Notes
Disclaimer
The educational materials provided on this website are intended as supplementary resources to support your learning journey. These study materials are sample documents designed to help students understand complex concepts in Basic Electrical and Electronics Engineering.
We have made every effort to ensure the accuracy of the content. However, we recommend students to refer to standard textbooks and consult with professors for authoritative explanations. These materials should be used as references only.