This module covers theory only - numerical problems are not expected.
1. Working Principle of Single-Phase Transformer
What is a Transformer?
A transformer is a static electrical device that transfers electrical energy from one circuit to another through electromagnetic induction, without any change in frequency.
It works on the principle of Faraday's Law of Electromagnetic Induction and mutual induction between two coils.
Principle of Operation
The working principle of a transformer can be explained in the following steps:
Primary Winding Connection: When an AC voltage is applied to the primary winding, an alternating current flows through it.
Magnetic Flux Production: This alternating current produces an alternating magnetic flux in the iron core.
Flux Linkage: The magnetic flux links with both the primary and secondary windings through the common iron core.
EMF Induction: According to Faraday's law, this changing magnetic flux induces an EMF in both windings.
Secondary Voltage: The induced EMF in the secondary winding causes a voltage to appear across its terminals, which can supply power to a load.
Basic Transformer Construction
Key Points about Transformer Operation
Transformer works only with AC supply (needs changing flux)
It does NOT work with DC (constant flux = no induced EMF)
There is no electrical connection between primary and secondary
Energy transfer is through magnetic coupling
Frequency remains unchanged from primary to secondary
Transformer is a static device (no moving parts)
2. Types of Single-Phase Transformers
2.1 Based on Construction
Core Type Transformer
In core type transformer, the windings surround the core. The core has two limbs, and each limb carries both primary and secondary windings.
Windings are cylindrical and placed on the core limbs
Better cooling of windings
Easy to repair and maintain
Used for high voltage applications
Core Type
Shell Type Transformer
In shell type transformer, the core surrounds the windings. The core has three limbs, with windings on the central limb only.
Windings are sandwiched between core sections
Better mechanical protection for windings
More material required for core
Used for low voltage, high current applications
Shell Type
2.2 Based on Voltage Transformation
Step-Up Transformer
Increases voltage from primary to secondary.
N₂ > N₁ (more secondary turns)
V₂ > V₁ (output voltage higher)
I₂ < I₁ (output current lower)
Application: Power transmission from generating station
Step-Down Transformer
Decreases voltage from primary to secondary.
N₂ < N₁ (fewer secondary turns)
V₂ < V₁ (output voltage lower)
I₂ > I₁ (output current higher)
Application: Distribution, electronic power supplies
2.3 Other Classifications
Type
Description
Application
Power Transformer
High capacity, used at generating stations
Power transmission
Distribution Transformer
Medium capacity, step-down type
Distribution to consumers
Instrument Transformer
CT (Current) and PT (Potential) for measurement
Metering and protection
Auto Transformer
Single winding acts as both primary and secondary
Voltage regulation, starters
Isolation Transformer
1:1 ratio, provides electrical isolation
Safety, noise reduction
3. Transformation Ratio
What is Transformation Ratio?
The transformation ratio (also called turns ratio or voltage ratio) is the ratio of the number of turns in the secondary winding to the number of turns in the primary winding.
Transformation Ratio Formulas
K = N₂/N₁ = V₂/V₁ = I₁/I₂
Where:
K = Transformation ratio
N₁, N₂ = Number of turns in primary and secondary
V₁, V₂ = Primary and secondary voltages
I₁, I₂ = Primary and secondary currents
For Step-Up Transformer: K > 1
For Step-Down Transformer: K < 1
Important Relationships
Voltage ratio equals turns ratio: V₂/V₁ = N₂/N₁
Current ratio is inverse of turns ratio: I₂/I₁ = N₁/N₂
Power remains same (ideal): V₁I₁ = V₂I₂
If voltage increases, current decreases proportionally (and vice versa)
4. Ideal and Practical Transformer
4.1 Ideal Transformer
An ideal transformer is a theoretical concept with 100% efficiency and no losses.
Assumptions for Ideal Transformer:
Winding resistance is zero (no copper loss)
No leakage flux (all flux links both windings)
Permeability of core is infinite (no magnetizing current needed)
No core losses (hysteresis and eddy current losses are zero)
Ideal Transformer Equations
V₁/V₂ = N₁/N₂ = I₂/I₁
V₁I₁ = V₂I₂ (Input power = Output power)
Efficiency = 100%
4.2 Practical Transformer
A practical transformer has various losses and imperfections that reduce its efficiency.
Characteristics of Practical Transformer:
Winding Resistance: Both windings have some resistance → Copper losses
Leakage Flux: Some flux doesn't link both windings
Core Losses: Due to hysteresis and eddy currents in the core
Magnetizing Current: Required to establish flux in the core
Efficiency is less than 100% (typically 95-99% for power transformers)
Parameter
Ideal Transformer
Practical Transformer
Winding Resistance
Zero
Has finite resistance
Leakage Flux
Zero (100% coupling)
Some flux leakage exists
Core Losses
Zero
Hysteresis + Eddy current losses
Magnetizing Current
Zero
Required to establish flux
Efficiency
100%
95% - 99%
Existence
Theoretical only
Real world
5. Transformer Losses
Transformer losses can be divided into two main categories: Core Losses (Iron Losses) and Copper Losses.
5.1 Core Losses (Iron Losses)
Core losses occur in the magnetic core of the transformer. These losses are constant as long as the voltage and frequency remain constant, regardless of the load.
Hysteresis Loss (Ph)
Loss due to the reversal of magnetization in the core material during each AC cycle.
Core material resists change in magnetization
Energy is lost as heat in each cycle
Depends on: Frequency, flux density, core material
Reduced by: Using silicon steel with low hysteresis coefficient
Eddy Current Loss (Pe)
Loss due to circulating currents induced in the core by the changing magnetic flux.
Changing flux induces EMF in the core itself
This causes currents to flow in the core (eddy currents)
These currents cause I²R heating
Reduced by: Using laminated core (thin sheets insulated from each other)
Laminated Core to Reduce Eddy Currents
Laminations break up eddy current paths, reducing losses
5.2 Copper Losses
Copper Loss (Pcu)
Copper losses occur due to the resistance of the winding conductors. When current flows through the windings, power is dissipated as heat (I²R loss).
Pcu = I₁²R₁ + I₂²R₂
Where R₁, R₂ are the resistances of primary and secondary windings.
Copper losses are variable - they depend on the load current
At no load: Copper loss is very small (only magnetizing current)
At full load: Copper loss is maximum
Copper loss ∝ (Load)² or I²
Summary of Transformer Losses
Loss Type
Cause
Nature
Reduction Method
Hysteresis Loss
Magnetic reversal
Constant
Use silicon steel
Eddy Current Loss
Circulating currents in core
Constant
Use laminated core
Copper Loss
Winding resistance
Variable (∝ I²)
Use thick conductors
6. Efficiency of Transformer
Definition
Efficiency of a transformer is the ratio of output power to input power, usually expressed as a percentage.
Efficiency Formula
η = (Output Power / Input Power) × 100%
η = (Output / (Output + Losses)) × 100%
η = (Input − Losses) / Input × 100%
Condition for Maximum Efficiency
The efficiency of a transformer is maximum when:
Copper Loss = Core Loss
Pcu = Pi (iron loss)
This is an important condition. At maximum efficiency, the variable losses (copper) equal the constant losses (iron).
Factors Affecting Efficiency
Load: Efficiency varies with load - maximum at a specific load
Power Factor: Efficiency is higher at unity power factor
Core Material: Better core material reduces iron losses
Large power transformers have efficiency of 98-99%
Small transformers may have efficiency of 90-95%
Transformers are among the most efficient electrical machines. Even small improvements in efficiency result in significant energy savings over the transformer's lifetime.
7. Applications of Transformer
Power System Applications
Power Generation: Step-up transformers at power plants to increase voltage for efficient transmission
Power Transmission: Transmitted at high voltages (132kV, 220kV, 400kV) to reduce I²R losses
Power Distribution: Step-down transformers to reduce voltage for distribution (11kV, 440V, 230V)
Generation 11kV - 25kV
↓ Step-Up
Transmission 132kV - 400kV
↓ Step-Down
Distribution 11kV - 33kV
↓ Step-Down
Consumer 415V / 230V
Other Applications
Application
Type of Transformer
Purpose
Electronic Power Supplies
Step-down
Provide low voltage DC to electronics
Battery Chargers
Step-down
Charge batteries at appropriate voltage
Welding
Step-down
High current, low voltage for welding
Measurement (CT, PT)
Instrument transformer
Measure high voltage/current safely
Impedance Matching
Audio transformer
Match impedance in audio systems
Electrical Isolation
Isolation transformer
Safety and noise reduction
Voltage Regulation
Auto transformer
Variable voltage output
Transformers must be properly rated for their application. Using an undersized transformer can lead to overheating, reduced efficiency, and potential failure.
Summary: Single Phase Transformer
Topic
Key Points
Working Principle
Mutual induction between two magnetically coupled coils; Faraday's law