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Load factor and demand factor numerical

Short answer

Connected load = 1360 W (12×80W lamps + 4×100W heaters). Daily energy = 5440 Wh (8 lamps×6h + 4 heaters×4h). Average load = 226.67 W. Demand factor = 1500/1360 = 1.103; load factor = 226.67/1500 = 0.151 (15.1%). Note: demand factor >1 indicates probable heater rating error (should be 1000W).

A consumer has the following connected loads: 12 lamps of 80 W each and 4 heaters of 100 W each. His maximum demand is 1500 W. On the average consumer uses 8 lamps 6 hours a day and each heater for 4 hours a day. Find load factor and demand factor.

Formulas used

Demand factor = Maximum demand / Connected load
Load factor   = Average load / Maximum demand
Average load  = Energy per day / 24 h

Connected load

Lamps   : 12 × 80 W  =  960 W
Heaters :  4 × 100 W =  400 W
Connected load       = 1360 W

Daily energy and average load

Lamps   : 8 × 80 W × 6 h  = 3840 Wh
Heaters : 4 × 100 W × 4 h = 1600 Wh
Energy per day            = 5440 Wh
Average load = 5440 / 24  = 226.67 W

Factors

Demand factor = 1500 / 1360   = 1.103
Load factor   = 226.67 / 1500 = 0.1511

Answer (data as printed): load factor = 0.151 (15.1%), demand factor = 1.10.

Note on the data: a demand factor greater than 1 is not possible, because the maximum demand cannot exceed the connected load. The heater rating is almost certainly 1000 W (the standard textbook version of this problem). With 4 heaters of 1000 W:

Connected load = 960 + 4000           = 4960 W
Energy/day = 3840 + 4×1000×4          = 19840 Wh
Average load = 19840 / 24             = 826.67 W
Demand factor = 1500 / 4960           = 0.3024
Load factor   = 826.67 / 1500         = 0.5511

Answer (heaters 1000 W): demand factor = 0.302, load factor = 0.551 (55.1%).

✓ Answer checked by Claude Opus 5.5 (high effort)

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