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Making Sense of Peak Load Cost Allocations

Fortnightly Magazine - March 15 1995

the utility testified that much

of the $14.8-million cost of the initial capacity of

8 million of gallons/day (MMgd) was fixed and would have been incurred regardless of the capacity of the plant because the "laboratory, laboratory equipment, control room, control system, administrative area, chemical feed area, maintenance shop, river intake, pumping chambers, site improvements, etc. are necessary no matter what the production capacity of the plant might be." This cost information supports the basic idea that as daily demand rises, so does the cost of meeting that demand, though much less than proportionally. One can interpret this cost data either linearly (em assuming a large fixed cost ($11.5 million) and a very low linear (proportional) incremental cost ($400,000 per MMgd) (em or using a power function (sixth root). The proportional assumption implicitly assumes that the cost of additional capacity was $1.9 MMgd when, in fact, the cost of additional capacity was $200,000 to $400,000 MMgd. That is, using a proportional assumption could skew the result by a factor of five to 10.

Implications for Rate Design

When significant economies of scale are present, it is clearly inappropriate to allocate costs and set rates in proportion to the demand placed on the system. The less-than-proportional nature of the cost relationship has to be taken into account. One way of doing this would be to simply replace the proportional assumption with the appropriate n-th root assumption. Consider the example in Table 2:

Residential peak demand is three times average use, while industrial use is flat across the year. The commercial class falls in between. An allocation of costs in proportion to peak load would boost the residential cost share by 40 percent compared to an allocation based upon average or commodity use. Industrial customers, on the other hand, would see an allocation only half as large as suggested by commodity usage under a proportional peak load allocator. Traditionally, such divergent allocations would be justified on the basis that the delivery system "had to be designed to meet peak loads." But if the cost of meeting peak loads increases only with the fourth root of the capacity, an allocation much closer to the commodity allocation would be appropriate. The residential peak allocator would rise only 11 percent above the commodity allocation, not 40 percent above it. The industrial allocation would fall 14 percent below the commodity allocator, not 50 percent below it. (Note: The fourth root allocator is calculated by taking the fourth root of the ratio of peak to average usage, then multiplying this times the average use. The sum of these class values is then used as the denominator in calculating the percentage allocator for each class.) Clearly, the economic-engineering assumption makes a significant difference in cost allocation.

The same would be true in the design of peak-period prices. If the demands in excess of the average annual level are assigned solely to peak-period usage, as Figure 2 indicates, peak period rates dramatically exceed offpeak levels (em by 200 percent where the peak load is twice the average load, as in the