In the case of simple buyback, the generators use the threshold control scheme as previously described. If the buyback cost is greater than the equivalent cost of gas, then all the generators run and the excess is sold to the utility or power exchange. The number of generators installed depends on the projected income the process operator expects to earn from selling electricity. This control method finds the incremental sum of all fuel used to get the total cost for the hour:

Total Cost = A\$kWhGRID + A\$BtuGRID - A\$kWhBUYBACK

The A\$ term implies that the gas and electric costs are evaluated on an incremental monthly (i.e., billing period) basis except for real time pricing rates. For example, the change of the grid electricity bill is

A\$kWhGRID = M\$(kWh1, kWh2,..., kWhN-1, kWhN) - M\$(kWh1, kWh2,..., kWhN-1)

where M\$ is the monthly bill amount (including consumption and demand fees, surcharges, and taxes) based on N hourly electricity use values for that billing period. This allows the bills to be calculated, including any time-of-use and block components. Unfortunately, these latter components also affect the linearity of the cost function — the cost function is not necessarily linear under these conditions. That is, the electricity used and the utility bill are not related in a simple linear fashion.

The algorithm for determining whether or not to use buyback, therefore, should (1) determine the loads on the building for a given hour, (2) calculate the total cost function for all integral numbers of generators operating, from zero to the number installed, and (3) determine which number of operating generators minimizes the total cost function. That is the number of generators that will operate that hour to maximize financial benefit.

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