Dual Fuel Heat Pump Switchover: Gas, Oil or Propane

The house load is $Q_L(T)=UA\max(T_b-T,0)$. Following the temperature-bin approach described in ASHRAE Handbook—Fundamentals, 2017, Chapter 19, delivered heat and equipment input are accumulated as $\sum_j Q(T_j)h_j$. This is a steady temperature-only bin model, not an hourly building heat-balance simulation.

Capacity and COP are independently interpolated linearly through 47, 17, 5 and −5 °F, in the NEEP cold-climate data format. Values above 47 °F are held at the 47 °F point. Below −5 °F the heat pump is disabled. The user may set an earlier compressor lockout. Default equipment data are from GREE extended ratings, April 2023, page 3, first (70 °F return-air) column; these are manufacturer operating data, not an AHRI seasonal rating.

The user-selected extra defrost factors are $Q_{HP}=Q_{table}(1-d_Q w)$ and $COP=COP_{table}(1-d_C w)$, with $w=\exp[-((T-0\,^{\circ}C)/(5\,K))^2]$. This smooth near-freezing envelope is a stated scenario assumption, not a NEEP or AHRI correlation. Set both penalties to zero if the entered data already include the relevant defrost loss.

Fuel heat content converts the purchase price to $c_f=p_f/(H_f\eta_f)$ per delivered kWh. The economic equality is $COP_*=p_e/c_f$. The search includes every performance knot. It merges consecutive equal-margin linear pieces into equality intervals and separately brackets isolated crossings for Brent root finding. An equality interval begins and ends at its actual performance knots, independent of scan resolution. Full-range equality requires equality at all scanned temperatures and knots, allowing only floating-point round-off. The recommended single lockout is the warmest temperature below which any economic or capacity constraint fails, also bounded by the compressor lockout. If multiple crossovers occur, this conservative single setting skips isolated colder heat-pump-favourable intervals.

The all-electric case supplies up to available heat-pump capacity and supplies the rest with COP-1 resistance heat. Dual fuel runs the heat pump alone above the selected threshold and the furnace alone below it. Furnace-only supplies all heat at AFUE. Uniform hours within each 5 °F bin are integrated with midpoint quadrature, splitting bins at the switch, compressor lockout, balance temperature and performance knots. CO₂ is electricity times the grid factor plus fuel input times the EIA combustion coefficient.

• Constant UA, heating balance temperature, AFUE and marginal prices; adequate backup output to meet the load.
• The same entered COP applies at partial house load; modulation, cycling, distribution losses, standby and auxiliary electricity are not separately resolved.
• Default UA is an illustrative small-house case. Boston TMY3 is independent of the national fuel-price examples.
• Extra defrost reductions of 0.08 for COP and 0.05 for capacity are editable scenario assumptions. The 0.30 kg/kWh grid factor is illustrative.
• EIA heat contents: 100,000 Btu/therm, 138,500 Btu/US gal oil, 91,452 Btu/US gal propane. Combustion factors are 52.91, 74.14 and 62.88 kg CO₂ per million Btu, respectively (EIA, September 2024).
• The Boston histogram is derived from 8,760 EPW dry-bulb records, lower-inclusive and upper-exclusive. Its 380 hours at 80 °F or warmer require no heat within the allowed balance-temperature range.

Performance is supported from −5 °F to the heating balance temperature, with endpoint holding above 47 °F. Never extend operation below the coldest entered point without additional manufacturer data. An absent economic boundary is shown as an unavailable temperature and explained by the economic interpretation; the controller still chooses a finite threshold. A finite equal-cost interval is distinguished from an isolated crossover. Its economic boundary is the warmest internal edge where costs cease to be unequal; the warmest interval's endpoints are listed under How it’s calculated. A missing capacity crossing means no capacity balance within the supported interval.

Custom annual bins cover −40 to 80 °F, with a separate warmer-hours count. Do not put hours colder than −40 °F into the first bin; use a more extensive weather model for those climates. Uniform temperature distribution within a 5 °F band loses actual within-bin weather detail, so finer quadrature does not recover that information. Refine the sample count and crossover scan under Advanced to test numerical stability; plotted curves use 241 samples of the implemented model.

The design-temperature backup outputs are sizing requirements, not checks of installed equipment. The single dual-fuel threshold enforces non-simultaneous operation. Thermostat dead bands, setback recovery, utility lockouts, backup delays, line-length corrections, multi-head diversity and equipment-specific defrost controls are outside the model. AFUE is used as an effective fuel-to-heat efficiency; blower and burner auxiliary electricity are excluded.

Price basis: 2025 EIA US residential electricity 0.173 USD/kWh and gas 15.34 USD/1,000 ft³ (about 1.48 USD/therm using 1,036 Btu/ft³); oil 6.138 USD/US gal and propane 2.820 USD/US gal for 2 November 2026, checked 6 November 2026. These are dated comparison inputs, not live local tariffs. CO₂ excludes methane leakage, refrigerant loss and other life-cycle emissions. This calculator does not implement AHRI 210/240 certification or a code compliance calculation.