Buller-Woodrow Loss Factor
Estimates the loss factor of a distribution feeder from its load factor using the empirical Buller-Woodrow relation: loss factor = k × load factor + (1 − k) × load factor squared. The loss factor is the ratio of average loss to peak loss over the period, and it is what turns the instantaneous loss measured at peak hour into energy lost over the month without needing a recorded load curve. Because Joule loss varies with the square of the current, the loss factor always sits below the load factor, and the lower the load factor the lower the ratio between them: at a load factor of 0.20 the loss factor is under half of it, while at 0.80 it sits around 86% of its value. The coefficient k is an input rather than fixed at 0.30, the classic Buller-Woodrow value for distribution networks, because utilities recalibrate k between 0.15 and 0.50 according to the feeder load profile. Enter the load factor for the period and the coefficient k.
Result
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Loss Factor: From Peak Loss to Monthly Energy
Anyone sizing technical losses on a feeder rarely has an 8,760-hour load curve at hand. What they have is a power flow solved at peak, which returns the instantaneous loss in kilowatts, and the monthly energy bill. Multiplying peak loss by the 730 hours in a month inflates the answer badly: the feeder spends most of its time well below peak, and Joule loss falls with the square of the current. The loss factor bridges the gap — multiply it by the peak loss and by the hours in the period and you get the energy that actually turned into heat in the copper.
Buller and Woodrow write the loss factor as k × LF + (1 − k) × LF², a weighted blend of linear and quadratic behaviour. LF is the load factor for the period, average demand over peak demand: an urban residential feeder usually lands between 0.45 and 0.60; a three-shift industrial customer runs past 0.80; a seasonal irrigation spur drops under 0.30. The coefficient k sits in a field instead of being pinned at 0.30, the classic value the authors gave for distribution networks, since every utility recalibrates it between 0.15 and 0.50 to match the feeder profile — a higher k pulls the loss factor toward the load factor. The screen defaults return 0.3768.
The relation is empirical, fitted on real load curves, and it never replaces metering where metering exists. The true loss factor always falls between LF² and LF, a band the formula honours for any k from 0 to 1; inside that band, though, the deviation reaches a few points whenever the peak is narrow and isolated, as on a spur feeding an irrigation pump or an arc furnace. Two unit slips wreck the result: the load factor goes in as a fraction, and typing 55 instead of 0.55 trips the invalid-value warning, since the check rejects any factor above 1. And the loss factor scales lost power, never billed energy.
Frequently asked questions
Why is the loss factor (0.3768) smaller than the load factor (0.55)?
What value of k should I use when the utility publishes none?
How do I turn the loss factor into kilowatt-hours lost in a month?
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.