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Courses/Three-Phase Systems/Three-Phase Power

lesson · 10min · Lesson 16 of 28

Two-wattmeter method

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 · 10min
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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

Two-wattmeter method

Three Phase Systems · Lesson 16 · Intermediate

IntermediateReview: professional review pending

Purpose

Apply the two-wattmeter method to three-wire systems and interpret positive, zero, or negative readings safely.

Before you beginThree-phase power · Meter polarity

Learning objectives

  • Describe connections conceptually
  • Sum readings for active power
  • Derive balanced-load reactive information
  • Handle negative readings correctly

Two wattmeters can determine total active power in a three-phase three-wire system because Kirchhoff current law removes one independent line current. The method can measure balanced or unbalanced active power, but PF-angle formulas add a balance assumption.

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

Core theory

Each wattmeter current element is placed in a different line and its voltage element referenced to the remaining line according to the instrument method. Total active power is W1 + W2 with algebraic signs.

For a balanced sinusoidal load, Q = √3(W1 − W2) under the declared connection/sign convention and tanφ = √3(W1 − W2)/(W1 + W2). Swapping meter identities reverses the Q sign.

At PF below 0.5 one reading becomes negative; at PF 0.5 one becomes zero. Reverse a connection only according to the instrument procedure and retain the reading's negative algebraic sign.

Terms, symbols, and units
TermMeaningSymbolUnit
WattmeterInstrument measuring active power from voltage and current channelsNot applicableNot applicable
Algebraic sumSum retaining positive and negative signsNot applicableNot applicable
Three-wire systemThree line conductors with no load neutral current pathNot applicableNot applicable
P = W1 + W2; tanφ = √3(W1 − W2)/(W1 + W2)

The angle relation requires a balanced sinusoidal load and declared connection convention.

W for P; ratio dimensionless
Worked exampleTwo readings are 8 kW and 2 kW for a balanced load. Find total P and PF using the stated convention.

Assumptions: Balanced sinusoidal load; W1 = 8 kW, W2 = 2 kW.

  1. Power: P = 8 + 2 = 10 kW.
  2. Angle: tanφ = √3(8−2)/(8+2) = 1.039.
  3. PF: φ ≈ 46.1°, so PF = cosφ ≈ 0.693.

Total active power is 10 kW and power-factor magnitude is approximately 0.693.

Reasonableness check: Both readings are positive, consistent with PF above 0.5.

Common mistakes
  • Discarding a negative reading
  • Using the PF formula on unbalanced loads
  • Changing connections while energised

Where this appears in practice

The method is used in meters, commissioning, laboratories, and diagnosis of three-wire loads.

SafetyPower measurement is live multi-line work with line-to-line voltage. Use rated equipment, fused leads where applicable, barriers, PPE, and a manufacturer-approved connection procedure.
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

How is total active power found when one wattmeter reads negative?

Add the readings algebraically. Do not replace the negative value with its magnitude.

Answer: Add the readings algebraically. Do not replace the negative value with its magnitude.

Practical exercise

Calculate P and PF magnitude for three fictional reading pairs, including one negative reading.

Summary

  • Two readings give total active power
  • Signs matter
  • PF derivation assumes balance

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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