--- title: "Load factor of two consumers" subject: "Industrial Power Distribution and Illumination" chapter: 1 key: "semester_6/industrial_power_distribution_and_illumination:load-factor-two-consumers" source: https://www.bctengineer.com/q/semester_6/industrial_power_distribution_and_illumination/load-factor-two-consumers site: BCT Engineering --- # Load factor of two consumers Industrial Power Distribution and Illumination · Chapter 1: Introduction - Asked in: 2079 Chaitra, 4 marks - Video: [Load Factor, Diversity Factor, Plant Capacity Factor, Utilization Factor, Reserve Capacity](https://www.youtube.com/watch?v=CeVFXs6mnUU) — Electrical Minus - 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/load-factor-two-consumers - Whole chapter: https://www.bctengineer.com/md/semester_6/industrial_power_distribution_and_illumination/chapter-1 ## Question Define Load Factor. Consumer A has a load of 20 kW for 5 hrs and Consumer B has a load of 5 kW for 20 hrs. Find the load factor for both consumers and explain the significance of the load factor based on energy expenditure and utility point of view. ## Short answer Load factor = average load / maximum demand = energy/(max demand × hours). For A: 100 kWh/(20 kW×24 h) = 0.208; for B: 100 kWh/(5 kW×24 h) = 0.833. High load factor (B) means lower fixed cost per kWh for utility and lower demand charge for consumer, even with same energy use. ## Answer **Load factor** is the ratio of the average load to the maximum demand over a given period (day, month or year): ```text Load factor = Average load / Maximum demand = Energy consumed / (Max demand × hours) ``` It is always ≤ 1 and shows how evenly the load is used. #### Calculation (period = 1 day = 24 h) Each consumer's maximum demand is its constant load. ```text Consumer A: Energy = 20 kW × 5 h = 100 kWh Avg load = 100 / 24 = 4.167 kW LF(A) = 4.167 / 20 = 0.2083 Consumer B: Energy = 5 kW × 20 h = 100 kWh Avg load = 100 / 24 = 4.167 kW LF(B) = 4.167 / 5 = 0.8333 ``` **Answer: Load factor of A = 0.208 (20.8%); load factor of B = 0.833 (83.3%).** #### Significance Both consumers use the **same energy, 100 kWh per day**, but: - **Utility point of view:** to supply A, the utility must keep 20 kW of generation, transformer and line capacity ready, which is used only 5 hours a day. For B only 5 kW of capacity is needed and it is used 20 hours. The fixed cost of plant per kWh sold is four times larger for A. So a high load factor (B) is better for the utility: plant is used well, cost per unit falls. - **Energy expenditure (consumer) point of view:** under a two-part tariff (demand charge per kW + energy charge per kWh), A pays the same energy charge as B but four times the demand charge (20 kW vs 5 kW). A's cost per kWh is therefore higher. Improving load factor by spreading loads over time lowers the electricity bill. - That is why utilities give lower rates to high load factor consumers and encourage off-peak use. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is load factor? A. Maximum demand divided by connected load B. Sum of individual MDs divided by system MD C. Connected load divided by average load D. Average load divided by maximum demand over a period Answer: D. Load factor = average load / maximum demand, and it is at most 1. (Key point: Definition of load factor) 2. What is the load factor of consumer A (20 kW for 5 h in 24 h)? A. 0.833 B. 0.25 C. 0.208 D. 4.167 Answer: C. Energy 100 kWh, average load 4.167 kW, and 4.167/20 = 0.208. (Key point: Calculation for A) 3. What is the load factor of consumer B (5 kW for 20 h in 24 h)? A. 0.208 B. 0.833 C. 0.5 D. 0.25 Answer: B. Energy 100 kWh, average 4.167 kW, and 4.167/5 = 0.833. (Key point: Calculation for B) 4. Why is the higher load factor of B better for the utility? A. Less capacity is needed for the same energy and it is used more hours, so cost per kWh falls B. B uses more energy than A C. B has a higher maximum demand D. Utility capacity is idle for B Answer: A. Both use 100 kWh, but A needs four times the capacity, used only 5 hours a day. 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