--- title: "Transformer location for three villages (A)" subject: "Transmission and Distribution System Design" chapter: 7 key: "semester_8/transmission_and_distribution_system_design:three-villages-transformer-location-a" source: https://www.bctengineer.com/q/semester_8/transmission_and_distribution_system_design/three-villages-transformer-location-a site: BCT Engineering --- # Transformer location for three villages (A) Transmission and Distribution System Design · Chapter 7: Distribution System Design - Asked in: 2071 Magh, 6 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_8/transmission_and_distribution_system_design/three-villages-transformer-location-a - Whole chapter: https://www.bctengineer.com/md/semester_8/transmission_and_distribution_system_design/chapter-7 ## Question Three villages A, B and C are situated at an equal distance of 0.6 km from each other and their respective loads are 20 kW, 50 kW and 30 kW. Find their distribution transformer location relative to the location of village A assuming yourself as an electrical engineer. ## Short answer Place transformer at the load centre: coordinates (0.39 km, 0.156 km) from A, distance 0.42 km at 21.8° from line AB towards C. This minimizes LT voltage drop and losses. ## Answer The distribution transformer should be placed at the **load centre** (centre of gravity of the loads), because this minimises the load moment ($\sum P_i d_i$), and so the LT voltage drop and loss. Since the villages are 0.6 km from **each other**, they form an equilateral triangle of side 0.6 km. ```text C (30 kW) /\ 0.6 / \ 0.6 / T \ /______\ A (20 kW) 0.6 B (50 kW) ``` #### Coordinates (A at origin, AB along x-axis) | Village | Load (kW) | x (km) | y (km) | |---|---|---|---| | A | 20 | 0 | 0 | | B | 50 | 0.6 | 0 | | C | 30 | 0.3 | 0.5196 | #### Load centre $$ \begin{aligned} \bar x &= \frac{\sum P_ix_i}{\sum P_i} = \frac{20(0)+50(0.6)+30(0.3)}{100} = \frac{39}{100} = 0.39\ \text{km}\\ \bar y &= \frac{\sum P_iy_i}{\sum P_i} = \frac{30(0.5196)}{100} = 0.156\ \text{km} \end{aligned} $$ Distance from A: $$ d = \sqrt{0.39^2+0.156^2} = 0.42\ \text{km},\quad \theta = \tan^{-1}\frac{0.156}{0.39} = 21.8^\circ $$ #### Engineering judgement - The transformer is located about **0.42 km from A**, at **21.8° from line AB towards C**, i.e. pulled towards B, the largest load. - In practice it is placed at the nearest accessible point (road side, public land) to this centre. The demand of 100 kW needs about 118–125 kVA (at 0.85–0.8 p.f.), which is more than a 100 kVA unit can carry, so the next standard size (160 or 200 kVA, allowing for growth) would be chosen. **Answer: Transformer at (0.39 km, 0.156 km) from A, i.e. 0.42 km from A at 21.8° to AB towards C.** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why is the distribution transformer placed at the load centre? A. It minimises the sum of load x distance, reducing LT drop and loss B. It equalises the distance to all villages C. It puts the transformer at the heaviest load D. It is the geometric centre of the triangle Answer: A. Load centre (centre of gravity) minimises load-moment, so LT voltage drop and loss are least. (Key point: Load centre principle) 2. Villages 0.6 km from each other form what shape? A. A straight line B. A right-angled triangle C. An isosceles triangle with a 1.2 km base D. An equilateral triangle of side 0.6 km Answer: D. Equal mutual distances give an equilateral triangle. (Key point: Geometry) 3. How is the x-coordinate of the load centre computed? A. Sum of x_i divided by 3 B. Sum of P_i x_i divided by sum of P_i C. Sum of P_i divided by sum of x_i D. Largest load's x Answer: B. It is the load-weighted average of the coordinates; here x = 39/100 = 0.39 km. (Key point: Load centre formula) 4. Where is the transformer relative to the loads? A. At the midpoint of the triangle B. Pulled towards C, the smallest load C. Pulled towards B, the largest load D. Exactly at A Answer: C. The weighted centre shifts towards the largest load B (50 kW), at 0.42 km from A. (Key point: Location result) ## Close variants set in other exams - [Transformer location for three villages (B)](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Athree-villages-transformer-location-b) — Transmission and Distribution System Design, chapter 7, asked 2× ## Related in Transmission and Distribution System Design - [Capacitor size, feeder with three equal loads](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Acapacitor-size-equal-loads-ohms) — Transmission and Distribution System Design, chapter 7 - [Selecting distribution transformer size and location](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Atransformer-size-and-location) — Transmission and Distribution System Design, chapter 7, asked 2× ## Related in other subjects - [Circular arch: two rolling loads 20 kN and 30 kN](https://www.bctengineer.com/question.md?key=semester_4%2Ftheory_of_structures_i%3Aarch-circular-100m-20kn-30kn-25m) — Theory of Structures I, chapter 6, asked 2× - [Four loads on 50 m girder: BM at 20 m, absolute](https://www.bctengineer.com/question.md?key=semester_4%2Ftheory_of_structures_i%3Afour-loads-100-150-200-150-50m) — Theory of Structures I, chapter 5 - [Cable 20 m: three loads, length and area](https://www.bctengineer.com/question.md?key=semester_4%2Ftheory_of_structures_i%3Acable-20m-three-loads-0-96m-dip) — Theory of Structures I, chapter 7