PW-B3 · Power and power factor

Load and demand: it is the overlap, not the sum

No one builds equipment by adding up the ratings of every load, because loads reach their peaks at different times and rarely all at once. Drag the peaks of two loads apart, watch the combined maximum demand become smaller than the sum, and learn the three ratios that measure that gap.

Drag the two peaks apart

The daily curves of two loads are drawn. Dragging the handle moves the peak time of the second load: when the two peaks overlap the gold combined curve rises up to double, and the further apart in time they are, the lower the combined maximum sinks. Equipment is built for exactly this combined maximum.

Drag the handle left and right to move the second load's peak time. The horizontal axis is the hour of the day; the first load peaks at 9 o'clock and the second can be placed 0 to 11 hours later. The two curves have peaks of the same height.

Composite maximum demand and diversity factor

F_div ≈ 1.18

ΣP_i = 2.00   P_g ≈ 1.69   (· P_inst)

Building for the sum is too big

If every household in an apartment block used its rated power at the same moment, the transformer would have to be enormous. In reality someone cooks while someone else sleeps, and the peaks scatter across the day. So equipment is sized not to the sum of ratings but to the combined maximum demand that actually appears at one time.

Diversity factor · how staggered the peaks

Diversity factor = sum of individual maximum demands / combined maximum demand. When the peaks overlap completely the combined value equals the sum and the diversity factor is 1; the more the times differ, the smaller the combined value and the larger than 1 the diversity factor. A large diversity factor means the transformer can be sized that much smaller, which is why the diversity factor rose as the combined peak sank in the curves you dragged. For two loads with peaks of the same height, the diversity factor is largest when they are completely apart, approaching 2.

Demand and load factors · the other two

A single customer does not use all of its installed capacity at once either, and that ratio is demand factor = maximum demand / installed capacity ≤ 1. How even the use is over the day is measured by load factor = average demand / maximum demand; the closer the load factor is to 1, the less the equipment sits idle and the more fully it is used. With demand factor, diversity factor and load factor together, equipment can be sized much smaller and more efficiently than the sum of ratings.

ObserveF_div = ΣP_iP_g

Diversity = sum of individual maxima / composite maximum.

ChooseF_div ? 1

When peaks are apart the combined value is smaller, so the diversity factor is 1 or more.

Fill inP_g = ΣP_i / ?

Composite maximum = individual sum / diversity factor.

On your ownF_dem = P_max / ?

Demand factor = maximum demand / installed capacity.

Back to the first screen

With the two peaks stacked, the combined value was double (diversity factor 1), and the further apart the times, the lower the combined maximum sank and the larger the diversity factor grew. What the equipment must withstand is not the sum but exactly this combined maximum demand. Diversity factor, demand factor and load factor are all ratios that measure, from different angles, the distance between the sum of ratings and the amount actually used at once, and that distance is what lets a transformer be chosen smaller than the sum, yet not too small.

Loads and demand factor: equipment is built not for the sum of ratings but for the combined maximum demand. Diversity factor = sum of individual maximum demands / combined maximum demand ≥ 1 (because peaks are offset), demand factor = maximum demand / installed capacity ≤ 1 (not all used at once), load factor = average demand / maximum demand (1 for perfectly even use). Together the three make equipment smaller than the sum, yet not too small.

The next step

With the size and ratios of power in hand, the next unit (PW-B4) works out how to measure that power. Three-phase power cannot be measured with a voltmeter and an ammeter alone; the phase has to be taken into account. In the two-wattmeter method, which uses 2 single-phase wattmeters to measure the power of a three-phase 3-wire system without a neutral, we follow why the sum of the two readings is the total active power.