Transformers

Transformers are one of the most important devices in electrical engineering and power systems. They enable efficient voltage conversion, energy transfer, and isolation in AC circuits. By understanding transformers, one can grasp the principles of electromagnetic induction, energy conservation, and power distribution across electrical networks.

This post covers transformers in detail, including working principles, types, construction, theory, efficiency, applications, and examples.

1. Introduction to Transformers

A transformer is an electrical device that transfers electrical energy between two or more circuits via electromagnetic induction. It can step up or step down voltage levels without changing the frequency of the AC supply.

Key features:

Only works with AC (Alternating Current)
No mechanical moving parts (static device)
Relies on Faraday’s Law of Electromagnetic Induction

2. Historical Background

Michael Faraday (1831): Discovered electromagnetic induction.
William Stanley and Lucien Gaulard (1880s): Developed early practical transformers.
Transformers revolutionized electricity distribution by enabling high-voltage transmission to reduce losses and low-voltage utilization for safety.

3. Construction of a Transformer

3.1 Basic Components

Core:
- Made of laminated silicon steel to reduce eddy current losses.
- Provides a path for magnetic flux.
Primary Winding:
- Connected to the input AC supply.
- Generates magnetic flux in the core.
Secondary Winding:
- Induced EMF appears here.
- Delivers energy to the load.

3.2 Core Types

Shell Type: Core surrounds windings.
Core Type: Windings surround the central limb of the core.
Toroidal Type: Circular core with windings around it; compact and efficient.

4. Working Principle of Transformers

Transformers operate based on Faraday’s Law:

AC in the primary winding produces a time-varying magnetic flux in the core.
This changing flux links with the secondary winding.
According to Faraday’s Law:

Es=−NsdΦdt\mathcal{E}_s = -N_s \frac{d\Phi}{dt}Es=−NsdtdΦ

NsN_sNs = number of turns in secondary coil
Φ\PhiΦ = magnetic flux

Key Concept: No electrical connection exists between primary and secondary; energy is transferred magnetically.

5. Transformer Equations

5.1 Turns Ratio

VsVp=NsNp\frac{V_s}{V_p} = \frac{N_s}{N_p}VpVs=NpNs

VsV_sVs = secondary voltage
VpV_pVp = primary voltage
NsN_sNs, NpN_pNp = turns in secondary and primary

5.2 Step-Up and Step-Down Transformers

Step-Up: Ns>NpN_s > N_pNs>Np, Vs>VpV_s > V_pVs>Vp
Step-Down: Ns<NpN_s < N_pNs<Np, Vs<VpV_s < V_pVs<Vp

5.3 Current Relation

Assuming ideal transformer (no losses): IsIp=NpNs\frac{I_s}{I_p} = \frac{N_p}{N_s}IpIs=NsNp

Power conservation: VpIp=VsIsV_p I_p = V_s I_sVpIp=VsIs

6. Ideal Transformer

Assumptions:

No losses (no resistance in windings).
Core is perfectly magnetic (infinite permeability).
No leakage flux (all flux links both windings).

For ideal transformer: Vs=NsNpVpV_s = \frac{N_s}{N_p} V_pVs=NpNsVp Is=NpNsIpI_s = \frac{N_p}{N_s} I_pIs=NsNpIp Pp=PsP_p = P_sPp=Ps

7. Real Transformer

7.1 Losses in Transformers

Copper Losses:
- Due to resistance of windings (I2RI^2 RI2R).
Iron Losses:
- Hysteresis Loss: Due to reversal of magnetization in core.
- Eddy Current Loss: Circulating currents in the core.
Leakage Flux:
- Part of magnetic flux does not link secondary winding.
Magnetizing Current:
- Small current required to magnetize the core.

7.2 Efficiency

η=PoutPin×100%\eta = \frac{P_{\text{out}}}{P_{\text{in}}} \times 100\%η=PinPout×100%

Power transformers: 95–99% efficient.

8. Types of Transformers

8.1 Based on Voltage

Step-Up Transformer: Increases voltage.
Step-Down Transformer: Decreases voltage.

8.2 Based on Construction

Core Type
Shell Type
Toroidal Transformer

8.3 Based on Phase

Single-Phase Transformers
Three-Phase Transformers

8.4 Special Types

Auto-Transformer: Primary and secondary share some windings; smaller and economical.
Isolation Transformer: Same voltage but isolates circuits.
Instrument Transformer: Step down high voltage/current for meters (CT and PT).

9. Transformer on Load

When connected to a load, secondary draws current.
Primary current adjusts to maintain magnetic flux.
Voltage regulation measures change in secondary voltage from no-load to full-load:

Voltage Regulation=Vno load−Vfull loadVfull load×100%\text{Voltage Regulation} = \frac{V_{\text{no load}} – V_{\text{full load}}}{V_{\text{full load}}} \times 100\%Voltage Regulation=Vfull loadVno load−Vfull load×100%

10. Phasor and Equivalent Circuit

Ideal transformer: no losses, perfect coupling.
Real transformer: represented by series resistances (primary and secondary), leakage reactances, and magnetizing branch.

Equivalent circuit helps in:

Predicting voltage drops
Calculating efficiency
Analyzing short-circuit and load conditions

11. Transformer Testing

Open-Circuit Test:
- Measures core (iron) losses.
- Primary connected to rated voltage; secondary open.
Short-Circuit Test:
- Measures copper losses.
- Primary voltage reduced until rated current flows; secondary shorted.
Polarity Test:
- Determines relative polarity of windings.

12. Energy and Power Relations

12.1 Energy Transfer

Energy is stored in the magnetic field of the core during AC cycle.
EMF induced in secondary ensures power transfer without direct connection.

12.2 Power Conservation

Pprimary≈Psecondary+lossesP_{\text{primary}} \approx P_{\text{secondary}} + \text{losses}Pprimary≈Psecondary+losses

Ideal transformer: Pp=PsP_p = P_sPp=Ps
Real transformer: Ps=Pp−lossesP_s = P_p – \text{losses}Ps=Pp−losses

13. Applications of Transformers

13.1 Power Transmission

Step-up high voltage for long-distance transmission to reduce I²R losses.
Step-down voltage for domestic or industrial use.

13.2 Electrical Isolation

Isolation transformers separate sensitive devices from supply for safety.

13.3 Instrument Transformers

Current Transformer (CT): Step-down high current for measurement.
Potential Transformer (PT): Step-down high voltage for measurement.

13.4 Electronics

Impedance matching, signal transfer, audio transformers, voltage stabilization.

14. Advantages of Transformers

Efficient power transfer with minimal losses.
Easy voltage conversion without moving parts.
Enables long-distance AC power transmission.
Electrical isolation for safety.
Compact and durable design.

15. Limitations of Transformers

Only works with AC; cannot be used for DC.
Subject to core losses (hysteresis and eddy currents).
Requires heavy magnetic cores for high power ratings.
Voltage regulation affected by load variations.

16. Modern Transformer Design Considerations

Core Material: High-grade silicon steel or amorphous steel to reduce losses.
Cooling: Oil-immersed or air-cooled for thermal management.
Insulation: Prevents breakdown at high voltages.
Minimizing Leakage Flux: Ensures high efficiency.
Compact Toroidal Designs: Reduce weight and electromagnetic interference.

17. Practical Examples and Calculations

Example 1: Step-Down Transformer

Primary voltage: 230 V, 1000 turns
Secondary voltage: 23 V
Find secondary turns:

VsVp=NsNp⇒Ns=VsVpNp=23230⋅1000=100 turns\frac{V_s}{V_p} = \frac{N_s}{N_p} \Rightarrow N_s = \frac{V_s}{V_p} N_p = \frac{23}{230} \cdot 1000 = 100 \text{ turns}VpVs=NpNs⇒Ns=VpVsNp=23023⋅1000=100 turns

Example 2: Power Transfer

Transformer rating: 5 kVA, 230/115 V, full load current:

Is=PVs=5000115≈43.5 AI_s = \frac{P}{V_s} = \frac{5000}{115} \approx 43.5 \text{ A}Is=VsP=1155000≈43.5 A Ip=PVp=5000230≈21.7 AI_p = \frac{P}{V_p} = \frac{5000}{230} \approx 21.7 \text{ A}Ip=VpP=2305000≈21.7 A

Example 3: Efficiency Calculation

Output power: 4.8 kW
Total losses: 200 W

η=PoutPin×100=48004800+200×100≈96%\eta = \frac{P_{\text{out}}}{P_{\text{in}}} \times 100 = \frac{4800}{4800+200} \times 100 \approx 96\%η=PinPout×100=4800+2004800×100≈96%