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Courses/Three-Phase Systems/Delta Connection

lesson · 8min · Lesson 10 of 28

Delta connection topology

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 · 8min
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

Delta connection topology

Three Phase Systems · Lesson 10 · Intermediate

IntermediateReview: professional review pending

Purpose

Trace voltage and current paths in a closed delta and distinguish branch quantities from line quantities.

Before you beginThree-phase phasors · Kirchhoff current law

Learning objectives

  • Draw delta topology
  • Identify phase branches
  • Relate line and phase voltage
  • Recognise open-delta and circulating-current limits

A delta connects three phase impedances end-to-end in a closed loop, with each line conductor attached to a junction. Each branch is therefore directly across a line-to-line voltage.

DELTA VOLTAGE AND CURRENT PATHSDELTA VOLTAGE AND CURRENT PATHSL1L2L3Vph = VLIL = √3 Iph · 30° shift

Core theory

In an ideal delta, phase voltage equals line voltage: Vph = VL. There is normally no neutral point because no branch terminates at a common star junction.

Each line current is the phasor difference of the two branch currents meeting at that line terminal; it is not simply the current in one branch.

A closed delta can provide a path for zero-sequence or triplen components and for currents caused by unequal induced phase voltages. Whether a delta is suitable depends on equipment design, protection, heat, and harmonic duty.

Terms, symbols, and units
TermMeaningSymbolUnit
DeltaClosed three-branch connection with line terminals at the junctionsNot applicableNot applicable
Phase currentCurrent through one delta branchIphA
Line voltageVoltage between two line terminalsVLV
Worked exampleA balanced 400 V delta has 40 Ω resistive impedance in each branch. Find phase current.

Assumptions: Balanced sinusoidal source; Pure resistance.

  1. Voltage: In delta, Vph = VL = 400 V.
  2. Branch: Iph = Vph/Zph.
  3. Calculate: Iph = 400/40 = 10 A.

Each delta branch current is 10 A.

Reasonableness check: Every 40 Ω branch is directly connected across 400 V.

Common mistakes
  • Dividing delta phase voltage by √3
  • Calling phase current line current
  • Assuming every delta suppresses every harmonic

Where this appears in practice

Delta windings appear in motors, transformers, heating banks, and harmonic/zero-sequence control arrangements.

SafetyA delta can remain energised line-to-line with no neutral present. Prove isolation at every terminal and consider stored or induced energy.
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

What is the voltage relationship for an ideal delta branch?

Vph = VL. Each branch spans two line terminals.

Answer: Vph = VL. Each branch spans two line terminals.

Practical exercise

Label all branch-current directions and terminal line currents on a paper delta, then write KCL at each junction.

Summary

  • Delta is a closed loop
  • Phase voltage equals line voltage
  • Line current is a vector difference

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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