modelHeatPumpPartialLoad

Information

1. Purpose of model

Semi-empirical heat pump model whose coefficient of performance (COP) depends on both the temperature lift and the partial load. The model requires only two fitting parameters (b₁, b₂) and is intended for energy system simulations where a low parametrization effort and a high computational efficiency are required.

2. Level of detail, physical effects considered, and physical insight

L1: Explicit algebraic COP correlation without states, derived from the entropy and energy balance of the inner (refrigerant) cycle. Physical effects considered:

• Temperature lift via the Carnot COP of the refrigerant temperatures T_hot (condensing) and T_cold (evaporating)
• Partial load via an empirical correlation for the internal entropy generation rate (exponential in the heat flow rate, linear in T_hot/T_cold − 1)
• Heat transfer between refrigerant and secondary fluids via constant temperature differences (3 K for liquids, 8 K for gases)
• Steady-state energy balance of the heat sink fluid with real fluid properties (TILMedia)

Physical insight: The COP approaches the Carnot COP for a vanishing internal entropy generation rate and never exceeds it. For a positive temperature lift the COP is positive. The COP tends to zero for very small and for very large heat flow rates, so that the second-law efficiency COP/COP_Carnot has its maximum at partial load.

3. Limits of validity

- Only for subcritical cycles with pure or nearly azeotropic refrigerants (e.g. R410A, R134a).

- The correlation for the internal entropy generation rate was established from measurements of a single heat pump (Abid et al. 2021b). It may deviate for other designs, e.g. two-stage cycles or cycles with economiser.

- Heat transfer is modelled with constant temperature differences only. They are fixed (3 K for liquids, 8 K for gases) and cannot be parametrized.

- Steady state: no thermal inertia, no on/off cycling, no minimum partial load, no capacity limit (the heat flow set point is always met) and no defrosting.

- No pressure loss on the heat sink side.

4. Interfaces

heatFlowSet: set point of the heat flow rate to the heat sink in W; negative values mean heat supplied to the heat sink (Signal, input)

sourceTemperature: inlet temperature of the heat source in K (Signal, input)

electricConsumption: electric power consumption of the heat pump in W, positive (Signal, output)

portA: heat sink fluid inlet, e.g. return of a heating network (Fluid, inlet)

portB: heat sink fluid outlet, e.g. supply of a heating network (Fluid, outlet)

5. Nomenclature

heatFlowSet

electricConsumption

COP

COP_c_inner

T_hot

T_cold

sinkTemperature

deltaT_sink

deltaT_source

b1

b2

portA.m_flow

portB.m_flow

hIn

hOut

portA.p

portB.p

6. Governing Equations

Refrigerant temperatures from constant temperature differences to the secondary fluids (3 K for liquids, 8 K for gases):

Empirical correlation for the internal entropy generation rate, linear in the temperature ratio and exponential in the heat flow rate:

Inserting the correlation into the balances and solving for COP = Q̇_hot/P_el gives the explicit COP correlation with the Carnot COP of the refrigerant temperatures:

Electric power consumption:

Steady-state energy balance of the heat sink fluid; the heat flow rate follows the set point:

Mass balance and pressure of the heat sink fluid (no pressure loss):

7. Remarks for Usage

- Sign convention: heatFlowSet < 0 means heat supplied to the heat sink. For heatFlowSet ≥ -1 W the heat pump is off; then COP = 0, electricConsumption = 0 and the heat sink fluid leaves with unchanged specific enthalpy.

- The mass flow rate of the heat sink fluid has to be imposed externally, e.g. by a pump or a mass flow boundary. A zero mass flow rate (division by zero) is caught by a minimum mass flow rate of 1e-5 kg/s.

- The supply temperature is not controlled; it results from the energy balance of the heat sink fluid.

- Requires an inner simCenter (TransiEnt.SimCenter); the heat sink medium defaults to simCenter.fluid1.

- The model terminates the simulation if T_hot ≤ T_cold while the heat pump is on.

- heatSinkType and heatSourceType select the temperature difference between refrigerant and secondary fluid (Liquid: 3 K, Gas: 8 K).

- Parametrization: choose a predefined heat pump with selectHP or set useCustomizedParameter = true and define b1_custom and b2_custom. The fit requires at least two operating points with different heat flow rates, which should cover a range of heat flow rates as wide as possible. For the fit, T_hot and T_cold are calculated with the same constant temperature differences as in the model.

Predefined parameter sets:

8. Validation

The COP correlation was validated against measurement data of four heat pumps: an air-to-water heat pump with R410A (Abid et al. 2021a), a water-to-water heat pump with R134a (Skye 2022) and the brine-to-water heat pumps ecoGEO+ 45 kW and 60 kW with R410A (ECOFOREST 2025). The mean absolute percentage error (MAPE) of the COP lies between 1.8 % and 7.4 %.

Tested in check model "HeatPump_PartialLoad.TestHeatPumpPartialLoad"

9. References

Abid, M.; Hewitt, N.; Huang, M.-J.; Wilson, C.; Cotter, D., 2021a: Performance Analysis of the Developed Air Source Heat Pump System at Low-to-Medium and High Supply Temperatures for Irish Housing Stock Heat Load Applications. Sustainability 13(21), 11753, doi:10.3390/su132111753.

Abid, M.; Hewitt, N.; Huang, M. J.; Wilson, C.; Cotter, D., 2021b: Experimental Study of the Heat Pump with Variable Speed Compressor for Domestic Heat Load Applications.

Skye, H. M., 2022: Data for NIST Technical Note: Validation and Optimization with a Vapor Compression Cycle Model Accounting for Refrigerant Thermodynamic and Transport Properties. National Institute of Standards and Technology (NIST), https://data.nist.gov/od/ds/ark:/88434/mds2-2613/Experiment%20-%20All%20-%20Rev_1_5.zip.

ECOFOREST, 2025: Technical Datasheets Heat pumps (ecoGEO+ series), DS_HP_EN_v2025_01.

10. Version History

Model created by Michael Vieth (michael.vieth@tuhh.de) on 02.10.2026

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