Analysis of Error in Using Simplified Models to Approximate the Heating or Cooling Output of Fan Coil Units for Energy Cost Allocation Purposes

Energy cost allocation systems apportion heating and/or cooling costs among the individual apartments in centrally-metered buildings based on some measure of relative energy use or thermal comfort. The most commonly used systems measure one or more parameters related to the thermal output of the terminal element, but do not measure enough parameters to provide a calibratable measurement of output. Further, they typically assume that heating or cooling output is linearly proportional to a quantity which may be a single temperature, a difference between two temperatures, or an average of two temperatures. This paper assesses how well various simple linear models approximate the true relative heating or cooling output of fan coil units under various ranges of application conditions. It further assesses the improvement possible in using non-linear models that follow the known form of the heat transfer relationship.

Few of the simple models perform well over a very wide range of application conditions, but quite a number perform well over certain limited ranges of application conditions. These more limited ranges of conditions are found in many buildings because of HVAC system control strategies. In other buildings, it is possible to correct for the variation in some parameter, such as fan speed, and thus to effectively reduce the range of conditions that must be captured by the model. Allocation schemes based on a heat transfer relationship expressed in terms of log mean temperature difference did not model true heat output any better than linear models, unless all four temperatures were assumed to be measured. 

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Analysis of Error in Using Simplified Models to Approximate the Heating or Cooling Output of Fan Coil Units for Energy Cost Allocation Purposes