---
title: "Best substation location from load figure"
subject: "Industrial Power Distribution and Illumination"
chapter: 4
key: "semester_6/industrial_power_distribution_and_illumination:substation-location-figure"
source: https://www.bctengineer.com/q/semester_6/industrial_power_distribution_and_illumination/substation-location-figure
site: BCT Engineering
---

# Best substation location from load figure

Industrial Power Distribution and Illumination · Chapter 4: Distribution Substation of Industrial Plant

- Asked in: 2072 Magh, 4 marks
- Video: [substation service area with n feeders | optimal location of substation | EDS | lecture 8](https://www.youtube.com/watch?v=27Zs2v6psdE) — Reddaiah Polisetty
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/industrial_power_distribution_and_illumination/substation-location-figure
- Whole chapter: https://www.bctengineer.com/md/semester_6/industrial_power_distribution_and_illumination/chapter-4

## Question

In the figure below, select the best option for setting the sub-station with suitable justifications. [Figure: a site plan on x-y coordinates (x axis marked 10, 80, 85, 100; y axis marked 10, 20, 28, 50, 60) with five loads: W1 = 200 kVA at (10, 20), W2 = 10 kVA at (80, 60), W3 = 12 kVA at (100, 50), W4 = 10 kVA at (85, 28), W5 = 12 kVA at (100, 10).]

## Short answer

Compute load centre: x̄ = Σ(Si·xi)/ΣSi = 6050/244 = 24.80 m; ȳ = Σ(Si·yi)/ΣSi = 5600/244 = 22.95 m. Result near W1 at (25, 23) m. Locate substation here to minimise cable length, losses, and voltage drop, since W1 is 82% of load.

## Answer

The best site for a substation is at or near the **load centre** (centre of gravity of the loads), because it gives the least load × distance product, so LT cable cost, voltage drop and losses are minimum.

#### Load centre calculation
| Load | kVA | x | y | kVA·x | kVA·y |
|---|---|---|---|---|---|
| W1 | 200 | 10 | 20 | 2000 | 4000 |
| W2 | 10 | 80 | 60 | 800 | 600 |
| W3 | 12 | 100 | 50 | 1200 | 600 |
| W4 | 10 | 85 | 28 | 850 | 280 |
| W5 | 12 | 100 | 10 | 1200 | 120 |
| Total | 244 | | | 6050 | 5600 |

```text
x̄ = Σ W·x / Σ W = 6050 / 244 = 24.80
ȳ = Σ W·y / Σ W = 5600 / 244 = 22.95
```

#### Selection and justification
- The load centre is at about **(24.8, 23.0)**, very close to W1 (10, 20).
- W1 (200 kVA) is 82 % of the total load, so the substation should be placed **next to W1**, on the side facing the other loads.
- The heavy 200 kVA current then travels only a few metres, while only the small loads (10–12 kVA, low current) need long cables to the right side of the site, where voltage drop can be handled with modest cable sizes.
- Placing it at the geometric middle of the site (around x = 55) or near W2–W5 would make the large W1 feeder long and costly, with high losses.

**Answer: locate the substation near W1, at about (25, 23)** (or the option in the figure nearest to this point), subject to access, safety and HT line route.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What formula gives the x position of the load centre?
   A. Sum(x) / number of loads
   B. Sum(W x) / Sum(W)
   C. Sum(W) / Sum(x)
   D. Sum(W y) / Sum(W)
   Answer: B. Weighted by kVA. (Key point: Load centre formula)

2. What is the load centre for the given loads?
   A. About (55, 35)
   B. About (80, 50)
   C. About (10, 20) exactly
   D. About (24.8, 23.0)
   Answer: D. x = 6050/244 = 24.80 and y = 5600/244 = 22.95. (Key point: Result)

3. Why place the substation next to W1?
   A. W1 is the farthest load
   B. W1 is about 82% of the load, so its feeder should be shortest
   C. W1 has the smallest current
   D. The site middle is always best
   Answer: B. Small loads can use long cables with modest sizes. (Key point: Justification)

## Related in Industrial Power Distribution and Illumination

- [Power/light sub-circuits and cable for 50 kW, 60 kW](https://www.bctengineer.com/question.md?key=semester_6%2Findustrial_power_distribution_and_illumination%3Asub-circuits-cable-50kw-60kw) — Industrial Power Distribution and Illumination, chapter 5, asked 4×
- [Distribution substation site selection factors](https://www.bctengineer.com/question.md?key=semester_6%2Findustrial_power_distribution_and_illumination%3Asubstation-site-location-factors) — Industrial Power Distribution and Illumination, chapter 4
- [Substation site criteria and H-pole BOQ](https://www.bctengineer.com/question.md?key=semester_6%2Findustrial_power_distribution_and_illumination%3Asubstation-site-boq-h-pole) — Industrial Power Distribution and Illumination, chapter 4
- [Cable size MDB to SDB1 (80 kW) and SDB2 (10 kW)](https://www.bctengineer.com/question.md?key=semester_6%2Findustrial_power_distribution_and_illumination%3Acable-mdb-sdb-80kw-10kw) — Industrial Power Distribution and Illumination, chapter 5, asked 5×
- [Substation capacity and diversity factor from load pattern](https://www.bctengineer.com/question.md?key=semester_6%2Findustrial_power_distribution_and_illumination%3Aabc-complex-load-pattern) — Industrial Power Distribution and Illumination, chapter 1
- [Importance of distribution substation with SLD](https://www.bctengineer.com/question.md?key=semester_6%2Findustrial_power_distribution_and_illumination%3Adistribution-substation-importance-sld) — Industrial Power Distribution and Illumination, chapter 4

## Related in other subjects

- [Sony-Samsung Markov, 80/85, 60% users](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Amarkov-sony-samsung-80-85) — Simulation and Modeling, chapter 5
- [Best financing option; EBIT Rs 350,000](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Abest-option-two-options-ebit-350000) — Project Engineering, chapter 6
- [Capital structure; best option by EPS, three options](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Abest-option-eps-three-options-c70) — Project Engineering, chapter 6
- [Coordinates of instrument station O and station A](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aresection-pwd-instrument-station-a) — Surveying II, chapter 5