---
title: "Substation capacity and diversity factor from load pattern"
subject: "Industrial Power Distribution and Illumination"
chapter: 1
key: "semester_6/industrial_power_distribution_and_illumination:abc-complex-load-pattern"
source: https://www.bctengineer.com/q/semester_6/industrial_power_distribution_and_illumination/abc-complex-load-pattern
site: BCT Engineering
---

# Substation capacity and diversity factor from load pattern

Industrial Power Distribution and Illumination · Chapter 1: Introduction

- Asked in: 2072 Asoj, 4 marks
- 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/abc-complex-load-pattern
- Whole chapter: https://www.bctengineer.com/md/semester_6/industrial_power_distribution_and_illumination/chapter-1

## Question

The load pattern of ABC complex is:

| Time | (0:00-4:00) | (4:00-8:00) | (8:00-12:00) | (12:00-16:00) | (12:00-16:00) | (16:00-20:00) | (20:00-24:00) |
|---|---|---|---|---|---|---|---|
| Load of Block-A in KVA | 5 | 13 | 18 | 9 | 16 | 22 | 8 |
| Load of Block-B in KVA | 7 | 19 | 22 | 34 | 17 | 14 | 6 |
| Load of Block-C in KVA | 3 | 12 | 16 | 24 | 40 | 35 | 4 |

Calculate: i) Capacity of substation required. ii) Diversity factor.
(The fifth column is printed as (12:00-16:00) a second time in the paper.)

## Short answer

Combined loads per 4-hour interval: max total = 73 kVA (second 12-16 interval). Substation capacity = 73 kVA (practically 100 kVA standard). Individual max demands: A=22, B=34, C=40 kVA; sum=96 kVA. Diversity factor = 96/73 = 1.315. Substation sized for simultaneous peak, not sum of individual peaks.

## Answer

The fifth column repeats "(12:00–16:00)"; it is taken as a separate 4-hour interval as printed, giving 7 intervals of data.

#### Step 1: Combined load in each interval

| Interval | A | B | C | Total (kVA) |
|---|---|---|---|---|
| 0–4 | 5 | 7 | 3 | 15 |
| 4–8 | 13 | 19 | 12 | 44 |
| 8–12 | 18 | 22 | 16 | 56 |
| 12–16 | 9 | 34 | 24 | 67 |
| 12–16 (2nd) | 16 | 17 | 40 | **73** |
| 16–20 | 22 | 14 | 35 | 71 |
| 20–24 | 8 | 6 | 4 | 18 |

#### Step 2: Capacity of substation
The substation must supply the highest combined (simultaneous) load:

```text
Max demand of complex = 73 kVA
```

**Answer (i): Required substation capacity = 73 kVA** (in practice the next standard transformer, **100 kVA**, would be installed).

#### Step 3: Diversity factor
Individual maximum demands:

```text
Block A max = 22 kVA
Block B max = 34 kVA
Block C max = 40 kVA
Sum         = 96 kVA

Diversity factor
 = Σ individual MDs / Max demand of system
 = 96 / 73
 = 1.315
```

**Answer (ii): Diversity factor = 1.32.**

Because the blocks reach their peaks at different times, the substation needs only 73 kVA instead of 96 kVA.

## Check yourself

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

1. How is the substation capacity found?
   A. By adding the individual block maxima
   B. By averaging all intervals
   C. From the highest combined (simultaneous) load of all blocks in any interval
   D. By taking the largest single block load
   Answer: C. The substation supplies the peak of the sum of the blocks. (Key point: Combined load method)

2. What is the maximum combined load?
   A. 96 kVA
   B. 73 kVA
   C. 71 kVA
   D. 67 kVA
   Answer: B. In the second 12-16 interval, 16 + 17 + 40 = 73 kVA. (Key point: Peak value)

3. How is the diversity factor computed?
   A. Sum of individual maximum demands / system maximum demand
   B. System MD / sum of individual MDs
   C. Average load / MD
   D. MD / connected load
   Answer: A. Diversity factor = sum of individual MDs divided by MD of the whole system. (Key point: Diversity factor formula)

4. What is the diversity factor of the complex?
   A. 0.76
   B. 1.00
   C. 1.51
   D. 1.32
   Answer: D. Block maxima 22 + 34 + 40 = 96 kVA, and 96/73 = 1.32. (Key point: Result)

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