--- title: "Star and delta connection relations" subject: "Basic Electrical Engineering" chapter: 8 key: "semester_1/basic_electrical_engineering:phase-line-relations-star-delta" source: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/phase-line-relations-star-delta site: BCT Engineering --- # Star and delta connection relations Basic Electrical Engineering · Chapter 8: Three-Phase Circuit Analysis - Asked in: 2070 Chaitra, 4 marks; 2069 Asar, 6 marks (asked 2 times) - Video: [Star and Delta Connection - Explained | TheElectricalGuy](https://www.youtube.com/watch?v=-PuVmOLr5K8) — Gaurav J - TheElectricalGuy - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/phase-line-relations-star-delta - Whole chapter: https://www.bctengineer.com/md/semester_1/basic_electrical_engineering/chapter-8 ## Question What are the two ways of connecting a 3-phase system? Draw their phasor diagrams and write down the relationship between phase and line voltages and phase and line current for these system. ## Short answer In star connection, V_L = √3 V_ph and I_L = I_ph; line voltage leads phase voltage by 30°. In delta connection, V_L = V_ph and I_L = √3 I_ph; line current lags phase current by 30°. Neutral is available only in star. ## Answer The two ways of connecting a three-phase system are **star (Y)** and **delta (Δ)**. #### 1. Star connection One end of each of the three phase windings is joined at a common neutral point N. The other ends are the line terminals R, Y and B. ```text R ● \ ● N ── (neutral, 4th wire) / \ Y ● ● B ``` Phasor diagram (RYB sequence, V_RN as reference): ```text V_BN (+120°) V_RY = V_RN − V_YN ↖ ↗ (leads V_RN by 30°) ↖ ↗ ↖ ↗ ↖ ↗ 30° ●─────────────────► V_RN (0°) ↙ ↙ V_YN (−120°) ``` **Relations:** - Line voltage V_L = √3 V_ph (each line voltage leads its phase voltage by 30°) - Line current I_L = I_ph #### 2. Delta connection The windings are joined end to start to form a closed loop. The lines are connected to the three junctions. ```text R / \ / \ Y─────B ``` Phasor diagram of currents (I_RY as reference). The line current is I_R = I_RY − I_BR: ```text I_BR (+120°) ↖ ↖ ●──────────────────► I_RY (0°) ↙ ↘ ↙ ↘ I_YB (−120°) ↘ I_R = I_RY − I_BR (lags I_RY by 30°) ``` For a balanced load the magnitude of I_R is √3 I_ph, and it lags the phase current I_RY by 30°. **Relations:** - Line voltage V_L = V_ph - Line current I_L = √3 I_ph #### Summary | Quantity | Star | Delta | |---|---|---| | Line voltage | √3 V_ph | V_ph | | Line current | I_ph | √3 I_ph | | Phase angle between line and phase quantity | V_L leads V_ph by 30° | I_L lags I_ph by 30° | | Power (balanced) | √3 V_L I_L cos φ | √3 V_L I_L cos φ | | Neutral | available | not available | For both, P = 3 V_ph I_ph cos φ, where φ is the angle between phase voltage and phase current. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which are the two ways of connecting a 3-phase system? A. Series and parallel B. Star and delta C. Open and closed D. Positive and negative Answer: B. Three-phase systems are connected in star (Y) or delta (Δ). (Key point: Two connections) 2. In a balanced star connection: A. V_L = V_ph, I_L = √3 I_ph B. V_L = √3 V_ph, I_L = I_ph C. V_L = √3 V_ph, I_L = √3 I_ph D. V_L = V_ph, I_L = I_ph Answer: B. Star has V_L = √3 V_ph and I_L = I_ph. (Key point: Star relations) 3. In a balanced delta connection, the line current: A. Equals the phase current B. Is √3 times the phase current and lags it by 30° C. Is 1/√3 of the phase current D. Leads the phase current by 30° Answer: B. I_L = √3 I_ph and I_L lags I_ph by 30°. (Key point: Delta relations) 4. Which power formula applies to both star and delta balanced loads? A. 3 V_L I_L cos φ B. √3 V_L I_L cos φ C. V_L I_L cos φ D. √3 V_ph I_ph cos φ Answer: B. P = √3 V_L I_L cos φ = 3 V_ph I_ph cos φ for both. (Key point: Power formula) ## Related in Basic Electrical Engineering - [Compare star and delta connection](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Acompare-star-delta-three-phase) — Basic Electrical Engineering, chapter 8 - [Star load (8+j6) line, phase current](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Astar-load-8j6-400v-ryb) — Basic Electrical Engineering, chapter 8 - [Delta load (15+j20) phase and line currents](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Adelta-load-15j20-220v-phasors) — Basic Electrical Engineering, chapter 8 - [Current in 20Ω using star-delta transformation](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Astar-delta-current-20-ohm-2v) — Basic Electrical Engineering, chapter 2 - [Current I using star-delta transformation](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Astar-delta-current-i-19v) — Basic Electrical Engineering, chapter 2 - [Star system with three loads, neutral current](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Astar-three-loads-400v-neutral-current) — Basic Electrical Engineering, chapter 8 ## Related in other subjects - [Scott connection for three-phase to two-phase](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ascott-connection) — Electrical Machines I, chapter 2 - [Three-phase connections and series RC phasor](https://www.bctengineer.com/question.md?key=semester_1%2Ffundamental_of_electrical_and_electronics_engineering%3Athree-phase-connections-series-rc) — Fundamental of Electrical and Electronics Engineering, chapter 3 - [Delta/star 120 kVA transformer values](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Adelta-star-120kva-line-phase-values) — Electrical Machine, chapter 2 - [Significance of components; phasor voltages](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Asymmetrical-components-significance-voltages) — Power System Analysis II, chapter 4