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Courses/Three-Phase Systems/Three-Phase Power

lesson · 9min · Lesson 15 of 28

Power factor in three-phase

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
THREE-PHASE · 120° APARTL1 · L2 · L3STARY: Vʟ=√3·VₚΔ: Iʟ=√3·IₚDELTA
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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

Power factor in three-phase

Three Phase Systems · Lesson 15 · Intermediate

IntermediateReview: professional review pending

Purpose

Interpret three-phase power factor as active-to-apparent power ratio and distinguish displacement from distortion effects.

Before you beginThree-phase power · Harmonics

Learning objectives

  • Define true power factor
  • Explain lagging and leading
  • Separate displacement and distortion
  • Predict current impact

Power factor is P/S. For a sinusoidal load it equals cosφ, but nonlinear loads can have distortion power factor even when fundamental voltage and current appear nearly in phase.

THREE-PHASE POWER TRIANGLETHREE-PHASE POWER TRIANGLEQPSS² = P² + Q²P = √3 VL IL PF

Core theory

For fixed active power and line voltage, lower true power factor requires higher rms line current, increasing conductor loss, voltage drop, equipment loading, and potentially tariff cost.

Displacement power factor describes the fundamental-frequency voltage-current angle. True power factor includes harmonic distortion and equals total active power divided by total apparent power.

Correction must match the operating profile. Fixed capacitors can overcorrect at light load, interact with harmonics, or affect embedded generation behavior; measurement over representative time is necessary.

Terms, symbols, and units
TermMeaningSymbolUnit
True power factorRatio of total active power to total apparent powerPFNot applicable
Displacement factorCosine of the fundamental voltage-current phase angleNot applicableNot applicable
Distortion factorReduction in power factor caused by nonsinusoidal currentNot applicableNot applicable
PF = P/S = P/(√3 VL IL)

Use total rms line quantities and active power for a balanced three-phase load.

dimensionless
Worked exampleA balanced load takes 30 kW from 400 V at true PF 0.75. Estimate line current.

Assumptions: Balanced rms line quantities.

  1. Rearrange: IL = P/(√3 VL PF).
  2. Substitute: IL = 30000/(1.732 × 400 × 0.75).
  3. Calculate: IL ≈ 57.7 A.

Line current is approximately 57.7 A.

Reasonableness check: At unity PF the same load would draw about 43.3 A, so poorer PF correctly increases current.

Common mistakes
  • Equating all PF with cosφ
  • Calling low PF wasted active energy
  • Correcting from one instantaneous reading

Where this appears in practice

Power-factor analysis affects distribution capacity, loss, generator/inverter loading, and billing.

SafetyDo not attach correction equipment based on clamp-current readings alone; harmonics, switching duty, protection, discharge, and resonance require engineered assessment.
Local code checkConfirm nominal voltage and frequency, source/earthing arrangement, conductor and protective-device duties, meter category and connection method, harmonic/resonance conditions, capacitor-bank product and discharge provisions, and the current local installation standard. Balanced 230/400 V examples are analytical models, not approval of a site design.

Knowledge check

Can a load have near-unity displacement factor but lower true PF?

Yes. Distorted current can reduce true PF without a large fundamental phase angle.

Answer: Yes. Distorted current can reduce true PF without a large fundamental phase angle.

Practical exercise

Compare line current for the same 30 kW load at PF 0.75, 0.90, and 1.00.

Summary

  • True PF is P/S
  • Lower PF increases current
  • Distortion and displacement are different

Sources and review

  • IEC 60038: IEC standard voltages: IEC; 2009+A1:2021; International
  • IEC 61921: Low-voltage power-factor-correction banks: IEC; 2017; International
  • Harmonics and Power Quality Analysis webinar Q&A: IET; Current online guidance; United Kingdom

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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