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Making Sense of Peak Load Cost Allocations

Fortnightly Magazine - March 15 1995

square of the diameter. The installed cost of the pipe, however, increases much more slowly than the diameter, for two reasons. First, the installation costs often are unrelated to the size of the pipe. Installation requires a right-of-way, opening and closing a ditch, and resurfacing. Most of these costs are not affected by whether the pipe diameter is 6, 8, or 10 inches. Secondly, the cost of the pipe itself often does not increase in proportion to the diameter. This certainly is true of smaller diameter pipes.

These two economic-engineering relationships compound the cost of capacity. If pipe capacity rises with the square of the diameter, and cost rises (very conservatively) only with the square root of the diameter, then the cost of delivery capacity rises only with the fourth root of capacity needs.

This relationship exists for electric transmission and distribution lines, too, where the peak capacity of the line increases with the square of the voltage, but the installed cost of a line increases much less than proportionally with voltage. As a result, the installed cost of electric lines can increase as slowly as the sixth root of the design capacity.

Figure 1 contrasts the proportional assumption with a cube- or fourth-root assumption. While the proportional cost assumptions would suggest that costs rise rapidly as one seeks to meet peak loads,

the fourth-root relationship suggested by actual

economics-engineering relationships indicates that costs do not vary much with peak loads. Figure 2 applies these two cost-allocation approaches to the calculation of peak and offpeak costs using the base-excess approach widely favored in the water industry. For peak loads three times greater than offpeak loads, the proportional assumptions would suggest that peak costs per unit climb to five times the offpeak cost. If, on the other hand, we make use of the actual relationship, the peak costs per unit rise only 63 percent above offpeak costs (em not 400 percent above.

Utilities Understand Their Capacity Costs

Utility planners know that capacity costs do not increase in proportion to the peak. This is evident, for instance, in the choices utilities make in designing transmission and distribution systems. Because additional delivery capacity can be obtained so cheaply by laying a somewhat larger line, utilities almost always install what is at the time redundant capacity in their delivery systems. The cost of removing and replacing transmission and distribution lines is so much higher than the cost of initially installing a slightly larger line that utilities as standard practice install the next larger line than projections of future demand indicate as appropriate.

If utility planners recognize the significant economies of scale associated with increasing delivery capacity, why should cost analysts not do the same? They should allocate costs on the same empirical economics-engineering relationships that are used to plan the delivery system.

Significant economies of scale are not limited to pipeline systems. One can find them in electric transmission and distribution, in natural gas storage, and in water treatment, to name just a few. Consider the water treatment plant costs in Table 1:

In this example,