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Three-ton cold-climate heat pump on a 36,000 Btu/h design load: thermal and economic balance points, bin season with gas backup, and the Appendix M HSPF

ToolHeat Pump Balance Point
SourceU.S. Department of Energy (2016). Uniform Test Method for Measuring the Energy Consumption of Central Air Conditioners and Heat Pumps. 10 CFR Part 430, Subpart B, Appendix M, Code of Federal Regulations, revised as of 1 January 2016. Sections 4.2 and 4.2.1 (Equations 4.2-1, 4.2-2, 4.2.1-1 to 4.2.1-5, Tables 17 and 18); U.S. Environmental Protection Agency (2022). ENERGY STAR Program Requirements for Central Air Conditioner and Heat Pump Equipment, Version 6.1 (cold-climate criteria); U.S. Environmental Protection Agency (2025). Emission Factors for Greenhouse Gas Inventories.
LevelProfessional

Problem

A house loses 36,000 Btu/h at a 5 °F design temperature and needs no heat above 65 °F. A variable-speed heat pump delivers 38,000 Btu/h at 47 °F and 28,500 Btu/h at 5 °F, with a 95 % gas furnace as backup; electricity costs 0.15 per kWh and gas 1.60 per therm. Find the thermal and economic balance points, the supplemental heat at design, the switchover setting, the seasonal energy, cost and CO2 on Region IV bins, the payback against the furnace alone, and the HSPF of a single-speed unit by the DOE test procedure.

Inputs to Enter

  • Load line: design heat loss 36,000 Btu/h at 5 °F, balance temperature 65 °F (600 Btu/h per °F)
  • Maximum capacity points (°F, Btu/h, kW): −13 22,000 3.60; 5 28,500 3.75; 17 32,000 3.70; 35 35,500 3.45; 47 38,000 3.10; 62 41,000 2.75; minimum capacity points: −13 9,000 1.60; 5 10,500 1.45; 17 11,500 1.25; 35 12,500 1.00; 47 13,000 0.85; 62 14,000 0.75; quadratic fits
  • Defrost derate table: 17 °F 1.00; 35 °F capacity 0.90, power 0.985; 45 °F 1.00; C_D 0.25
  • Gas furnace 0.95, 1.60 per therm, 100,000 Btu and 5.306 kg CO2 per therm; electricity 0.15 per kWh, 0.350 kg CO2 per kWh; switchover at the warmer balance point
  • Bins: Table 17 Region IV fractional hours × 5,643 h (62 °F 745 h down to −8 °F 6 h)
  • Economics: heat pump 14,000, incentive 2,000, furnace and air conditioner avoided 10,000; escalation 2 % electricity, 3 % fuel; discount 3 %; 15 years
  • Cooling: 36,000 Btu/h at SHR 0.75 against 30,000 total and 24,000 sensible; SEER 16; Table 16 fractions × 2,000 h
  • Appendix M: H1 36,000 Btu/h and 3,000 W, H2 28,500 and 2,850, H3 21,000 and 2,650; Region IV, minimum DHR
Open the Heat Pump Balance Point tool (loaded with this example)

Answers

  • Thermal balance point 13.79 °F (capacity = load); minimum-capacity crossover 43.63 °F
  • Break-even COP = 0.95 · 0.15 · 29.307 / 1.60 = 2.610; economic balance point 23.27 °F; switchover setting 24 °F (cost governs)
  • At 5 °F: capacity 28,179 Btu/h, COP 2.22, 78.3 % of the design load, shortfall 7,821 Btu/h (2.292 kW); capacity at 5 °F is 73.5 % of that at 47 °F
  • Season: load 80.99 MMBtu, heat pump 57.94 MMBtu (71.5 %), compressor 5,195 kWh at a seasonal COP of 3.27, furnace 242.7 therms; defrost penalty 280 kWh
  • Annual cost 1,167.64 and 3,106 kg CO2, against 1,364.07 and 4,524 kg for the gas furnace alone
  • Extra first cost 2,000.00, saving 196.43 a year, simple payback 10.2 years, NPV 1,814.53, SIR 1.91, IRR 11.95 %
  • With electric resistance backup instead: seasonal COP 2.909 (HSPF equivalent 9.93), resistance 385 kWh
  • Cooling: oversize ratio 1.20, sensible ratio 1.13, 1,474 kWh
  • Appendix M: minimum DHR 36,000 → 35,000 Btu/h; Σ n BL = 10,746.3 Btu/h, Σ e = 1,209.68 W, Σ RH = 129.20 W; HSPF 8.03

Notes

The tool's default inputs are this case; press Submit. The equipment points, prices, costs and bin-hour totals are illustrative, not a printed example: Appendix M prints no worked HSPF number, so the HSPF is checked by hand on the 17 °F and 47 °F bins (BL 21,560 and 8,085 Btu/h) and against an independent numpy implementation. Checked by test_heat_pump_balance_point.php (950 checks): fits against numpy.polyfit, balance points against scipy brentq on 40 seeded pairs, the bin season against an independent implementation on the default and 20 seeded systems with the identity heat pump + backup = load in every bin, NPV and IRR against numpy, and the page in both unit systems.