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Figure 5-11 + c3 (Tout ) + c4 (Tout )2 -10 0 10 20 30 40 50 (Tout) outdoor temperature (oF) Figure 5-10 + k3 (Tout ) + k4 (Tout )2 -10 0 10 20 30 40 50 (Tout) outdoor temperature (oF) ⎡k + k (T )⎤ ⎣12s⎦ (Qh) heating capacity (Btu/hr) ⎡c + c (T )⎤ ⎣12s⎦ COP The modeling equations for the heat pump’s heating capacity and COP are based on curve fitting, which provides an approximation of performance over a range of operating conditions. These modeling equations may not accommodate the performance characteristics of all air- to-water heat pumps, or the characteristics of all building loads or heating distribution systems. In some cases, designers may need to use other modeling methods to achieve accurate simulation. Any models developed should be checked to see if they can replicate published performance information with reasonable accuracy. It’s also important to remember that curve fitting is based on specific ranges of data. The equations developed from curve fitting should only be applied within those ranges of data unless specific constraints are imposed, such as limiting maximum heating capacity and COP values under very desirable operating conditions. Check with heat pump manufacturers to verify such constraints. SEASONAL AVERAGE COP It is possible to use performance information for the heat pump and the building’s hydronic heating distribution system, combined with bin temperature data for a given location, to calculate a “project-adjusted” seasonal average COP. This involves determining the required supply water temperature for each bin, using this temperature along with the corresponding outdoor temperature and the heat pump’s COP data (or model) to determine the COP for that bin. The operating hours of the heat pump in each bin are calculated. These values cannot exceed the actual hours in each bin. The operating hours in each bin are multiplied by the COP for that bin. These multiplications are summed and then divided by the total heat pump operating hours over the heating season to get a project-adjusted average COP for the heating season. These calculations are best done using a spreadsheet. When this method was applied to the previously discussed building near Boston, along with the constraint that the maximum COP could not exceed 4.5, and the heating capacity could not exceed 72,000 Btu/hr, the seasonal average COP of the heat pump was 3.49. This is an excellent performance number that is comparable to, if not higher than, what the seasonal average COP of a geothermal heat pump of the same capacity, and applied under the same conditions, might be. This seasonal average COP is based on the full outdoor temperature range for an average Boston winter, which ranges from -10oF to a high of 70oF. Additional spreadsheet-based analysis of this example project indicates that the total space heating energy required for the building for an average Boston winter is 194.3 MMBtu ( 1 MMBtu = 1,000,000 Btu). Of this, the heat pump supplied 185.0 MMBtu (about 95% of total), 44PDF Image | Heat Pump Systems 2020
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