## 714 Optimal Control

Ideally, on-site generation is operated using an algorithm that reduces the operating cost such that the cost to the building operator is minimized every hour. If the building is subject to a real-time pricing rate schedule, then the optimization can be trivial; the costs of grid electricity and locally produced electricity are compared at each hour; and, when the former is more expensive, the on-site generators are operated. However, more conventional rate structures such as block rates and time-of-use rates, with accumulation over a billing period, can make the calculation of instantaneous "next kWh" costs much more difficult. In that case, the electricity bill CELEC at any given hour is:

where OKWH is the utility function used to calculate the bill based on consumption, is the function used for demand, kWhBLDG(l) is the total electric load at hour 1, kWhGEN(l) is the kWh offset from the on-site generation equipment at hour 1, and so forth. The calculation must be performed for each hour of the billing period to account for variations in the hourly load, any time-of-use components of the utility rate, and any ambient temperature or solar dependencies of the generation equipment. If the generators use natural gas to produce electricity (an internal combustion engine, combustion turbine, microturbine, or fuel cell), then a similar calculation is performed for the gas consumption. Assuming no demand component for gas, the total gas bill up to hour k of the billing period is given as

where BtuGEN is the incremental gas consumption of the generation equipment at each hour. Note that kWhGEN, kWGEN, and BtuGEN can have zero values at any hour depending on whether or not the generation equipment is operating for that hour. To determine if the generators should operate at hour k+1, the total cost CELEC + CGAS should be evaluated twice: once using values for the terms kWhGEN, kWGEN, and BtuGEN based on the estimated generator performance, and then again with these values set to zero. If the former is greater than the latter, the generators should not be run for that hour.

## Solar Stirling Engine Basics Explained

The solar Stirling engine is progressively becoming a viable alternative to solar panels for its higher efficiency. Stirling engines might be the best way to harvest the power provided by the sun. This is an easy-to-understand explanation of how Stirling engines work, the different types, and why they are more efficient than steam engines.

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