Model Assumptions

This statistical model is based upon the following assumptions:

1. The electrical demand is represented by a linear load-duration curve, as shown in Figure 2. Thus, for a typical year, the facility has a demand D that varies between an upper value Du (annual maximum) and a lower value D1 (annual minimum). This implies the electrical load is uniformly distributed between the maximum and minimum demands. The facility operates T hours per year.

Demand Period,

Figure 1. Sample record for a uniformly distributed random demand.

Figure 2. Load—Duration Curve for uniformly distributed demand.

2. There is an even energy or consumption rate Ce ($/kWh) throughout the year.

3. There is an even demand rate Cd ($/kW/month) for every month of the year.

4. There is a same demand peak Du for every month. Demand ratchet clauses are not applicable in this case.

5. The equipment's annual ownership or amortization unit installed cost ($/kW/year) is constant for all sizes of PSGs. The unit ownership or rental cost ($/kW/year) is considered independent of unit size. Ownership, rental or lease annualized costs are denoted by Ac.

6. A PSG set is installed to reduce the peak demand by a maximum of g kW, operating t hours per o year.


Consider a facility with the load-duration characteristic shown in Figures 1 and 2. For a unit consumption cost Ce, the annual energy or consumption cost (without PSG) for the facility is

AEC = T D1 • Ce + 1/2 T (Du - D1) Ce Which is equivalent to

Next, considering a peak demand Du occurs every month, the annual demand cost is defined by

Thus, the total annual cost for the facility is

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