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Best substation location from load figure

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.

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).]

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

LoadkVAxykVA·xkVA·y
W1200102020004000
W2108060800600
W312100501200600
W4108528850280
W512100101200120
Total24460505600
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.

✓ Answer checked by Claude Opus 5.5 (high effort)

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