Auto-Transformer Fundamentals
Auto-Transformer Definition
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Definition: Single winding transformer with electrical connection between primary and secondary
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Key Feature: No electrical isolation between input and output
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Construction: Continuous winding with intermediate tap
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Terminals: Three terminals - High (H), Low (L), and Common (X)
GATE Important Point
Auto-transformer combines both electromagnetic induction and electrical conduction for energy transfer.
GATE Exam Focus
Remember: Auto-transformer is NOT suitable when electrical isolation is required.
Working Principle
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Electromagnetic Induction: Flux linkage between turns
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Electrical Conduction: Direct current flow through common winding
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Energy Transfer: Approximately 85% electromagnetic + 15% conduction
Energy Distribution
Voltage and Current Relations
Transformation Ratio and Voltage Relations
GATE Key Formulas
GATE Important
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Voltage transformation follows same law as conventional transformer
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Current distribution is different due to common winding
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Typical voltage ratios: 2:1 to 3:1 for economic benefits
Current Relations - Step Down Auto-Transformer
Current Equations (Step-Down)
Current Equations (Step-Up)
GATE Tip
Common winding current \(I_c\) carries the difference between primary and secondary currents.
Power and Efficiency Analysis
Power Relations
Power Equations
GATE Important Formula
Copper Saving Ratio:
Efficiency Analysis
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Higher efficiency than conventional transformers (95-98%)
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Reduced copper losses in common winding section
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Same iron losses as conventional transformers
Efficiency Formula
GATE Key Point
Auto-transformer efficiency is higher because:
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Reduced \(I^2R\) losses in common winding
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Less copper required for same power rating
Advantages and Disadvantages
Advantages - GATE Perspective
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Higher efficiency \((2-3\%\) better than conventional)
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Reduced size and cost due to copper saving
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Better voltage regulation (lower impedance)
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Lower losses in common winding
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Improved power factor at light loads
Economic Benefits
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Cost reduction proportional to \((1 - 1/K)\)
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Weight reduction due to less copper
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Smaller size for same power rating
Disadvantages - GATE Important
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No electrical isolation - major limitation
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Higher short-circuit current due to direct connection
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Limited voltage ratio applications (economical up to \(3:1\))
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Safety concerns - common neutral point
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Harmonic transfer between primary and secondary
GATE Critical Point
Auto-transformers are NOT used when:
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Electrical isolation is required
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High voltage ratios are needed (\(>3:1\))
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Safety is a primary concern
GATE Problem Solving
GATE Problem Type 1
Problem Statement
A 10 kVA, 400V/200V auto-transformer is connected as step-down. Load current is 50 A at 0.8 pf lagging. Calculate:
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Transformation ratio
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Primary current
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Common winding current
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Power transferred electromagnetically and conductively
Solution
GATE Problem Type 2
Problem Statement
Calculate the copper saving in an auto-transformer with transformation ratio \(2.5:1\) compared to a conventional transformer of same rating.
Solution
GATE Tip
Higher the transformation ratio, greater the copper saving (up to practical limits).
GATE Important Formulas - Quick Reference
Must Remember for GATE
GATE Memory Tips
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Auto-transformer = Higher efficiency + No isolation
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Copper saving increases with transformation ratio
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Suitable for voltage ratios up to \(3:1\)
Applications
GATE Relevant Applications
Power Systems:
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Voltage regulation
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Transmission interconnection
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Distribution voltage control
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Reactive power compensation
Industrial Applications:
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Motor starting (reduced current)
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Voltage stabilizers
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Laboratory equipment
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Lighting control
GATE Focus Areas
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Motor starting applications (current reduction)
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Voltage regulation in power systems
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Efficiency calculations and comparisons
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Economic analysis (copper saving)
Summary
GATE Exam Summary
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Definition: Single winding transformer with electrical connection
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Key Feature: No electrical isolation between primary and secondary
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Efficiency: Higher than conventional transformers (95-98%)
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Copper Saving: \((1 - 1/K) \times 100\%\)
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Applications: Limited by lack of isolation
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Voltage Ratio: Economical up to 3:1
GATE Quick Check
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Can you calculate transformation ratio, currents, and power distribution?
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Do you know when NOT to use auto-transformers?
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Can you compare efficiency with conventional transformers?