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Educational use: ElectraCore supports learning and preliminary checks. It does not replace a competent electrician or engineer. Verify results, equipment data, and current local regulations before installation or live work.
Courses/Three-Phase Systems/Transformers

lesson · 9min · Lesson 25 of 28

Turns ratio and voltage/current transformation

Course syllabusCourse overview
01Three-Phase Fundamentals
  1. ReadWhy three-phase?: advantages over single-phase
  2. ReadGeneration of three-phase voltages
  3. ReadPhase sequence: L1, L2, L3
  4. ReadPhasor representation of three-phase
  5. quizPhase fundamentals quiz
02Star (Wye) Connection
  1. ReadStar connection topology
  2. ReadLine voltage = √3 × phase voltage: proof
  3. ReadNeutral current in star systems
  4. exerciseStar circuit analysis problems
03Delta Connection
  1. ReadDelta connection topology
  2. ReadLine current = √3 × phase current: proof
  3. ReadCirculating currents in delta
  4. exerciseDelta circuit analysis problems
04Three-Phase Power
  1. ReadActive, reactive, and apparent power
  2. ReadPower factor in three-phase
  3. ReadTwo-wattmeter method
  4. ReadPower correction capacitor sizing
  5. quizThree-phase power quiz
05Three-Phase Induction Motors
  1. ReadHow induction motors work
  2. ReadMotor nameplate data and efficiency classes
  3. ReadStarting currents and starting methods
  4. ReadDOL starters: design and wiring
  5. ReadStar-delta starters: wiring and timing
06Transformers
  1. ReadTransformer construction and principles
  2. ReadTurns ratio and voltage/current transformation
  3. ReadThree-phase transformer connections
  4. quizTransformer quiz
  5. quizFinal assessment
Lesson · 9min
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In this lesson

PurposeCore theoryWorked exampleKnowledge checkSources

In this lesson

PurposeCore theoryWorked exampleKnowledge checkSources
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ElectraCore lesson handout

Turns ratio and voltage/current transformation

Three Phase Systems · Lesson 25 · Advanced

AdvancedReview: professional review pending

Purpose

Apply the ideal turns-ratio relationships for voltage, current and apparent power while distinguishing nameplate ratios from loaded terminal values.

Before you beginTransformer principle · Ratios

Learning objectives

  • Use voltage ratio
  • Use inverse current ratio
  • Check apparent power
  • Qualify regulation and losses

For an ideal transformer, voltage follows turns ratio and current changes inversely so apparent power is conserved. Real winding drop, leakage reactance, magnetising current and loss modify measured values.

TRANSFORMER FLUX AND VECTOR GROUPTRANSFORMER FLUX AND VECTOR GROUPHVLVV1/V2 = N1/N2ratio · impedance · vector group

Core theory

For consistent winding quantities, V1/V2 = N1/N2 = a. The ideal current relation is I1/I2 = N2/N1 = 1/a.

Ideal input and output apparent power are equal. Real input active power exceeds output active power by losses, and secondary terminal voltage varies with load magnitude and power factor.

Three-phase calculations must state whether voltages/currents are winding phase or external line quantities and account for star/delta connection before applying the turns ratio.

Terms, symbols, and units
TermMeaningSymbolUnit
Turns ratioPrimary turns divided by secondary turnsaNot applicable
Voltage regulationChange in secondary terminal voltage from no-load to stated loadNot applicableNot applicable
Rated apparent powerDeclared transformer loading basisSVA
V1/V2 = N1/N2 = a; I1/I2 = 1/a

Ideal winding voltage follows turns and current follows the inverse ratio.

Ratios dimensionless
Worked exampleAn ideal 11 kV/400 V three-phase transformer supplies 250 kVA. Find line-current magnitudes on both sides.

Assumptions: Balanced three-phase line quantities; Ideal transformer.

  1. HV: I1 = 250000/(√3×11000) ≈ 13.12 A.
  2. LV: I2 = 250000/(√3×400) ≈ 360.8 A.
  3. Check: Current ratio 360.8/13.12 ≈ 27.5, inverse of 400/11000.

HV line current is approximately 13.12 A; LV line current approximately 360.8 A.

Reasonableness check: Lower voltage requires proportionally higher current for the same apparent power.

Common mistakes
  • Applying voltage ratio to current in same direction
  • Mixing line and phase values
  • Treating nameplate voltage as exact under load

Where this appears in practice

Ratio analysis supports selection, metering, protection, fault studies and commissioning checks.

SafetyA low-voltage winding can deliver extremely high fault current, and a supposedly isolated winding can be backfed. Ratings do not prove safe isolation.
Local code checkConfirm the current machinery, motor, transformer, control-panel, installation, EMC and energy-efficiency requirements; exact nameplate, manufacturer and coordination data; fault level, earthing, isolation, guarding and stored-energy controls. Training calculations do not authorise energisation, rewiring, paralleling or starter commissioning.

Knowledge check

Why does ideal secondary current rise when voltage is stepped down?

Apparent power conservation requires the inverse current ratio. Real losses slightly increase required input power.

Answer: Apparent power conservation requires the inverse current ratio. Real losses slightly increase required input power.

Practical exercise

Repeat the example at 100 kVA and verify both sides give the same ideal apparent power.

Summary

  • Voltage follows turns ratio
  • Current follows inverse ratio
  • Connection and regulation matter

Sources and review

  • IEC 60034-30-1: Efficiency classes of line-operated AC motors: IEC; 2025; International
  • IEC 60076-3: Power transformers: insulation and dielectric tests: IEC; 2013+A1:2018; International
  • The safe isolation of plant and equipment (HSG253): Health and Safety Executive; Second edition; Great Britain

Editorial review date: 2026-08-22. Professional electrical review is pending.

Educational material for learning and preliminary checks. Verify current local requirements and exact equipment instructions. This lesson does not replace competent professional work.

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