TP-12: Heat Pumps

Overview

TP-12 models the performance of electric heat pumps providing space heating and hot water services to a dwelling. The calculation determines the coefficient of performance (CoP), thermal capacity, and total electrical energy input at each timestep, accounting for varying source and sink temperatures, part-load operation, and backup heater contribution.

The methodology follows the DAHPSE method (CALCM-01), developed for SAP 2012 and SAP 10.2, which is itself based on a draft of BS EN 15316-4-2:2017. Heat pump performance is derived from standardised test data collected under EN 14825, which provides capacity and CoP measurements at a set of defined operating conditions. The model interpolates between these test points using Carnot CoP ratios and exergetic efficiency to predict performance across the full range of operating conditions encountered during a simulation year.

The heat pump model supports multiple source types (air, ground, water, exhaust air, heat network), multiple sink types (water, air, glycol), and two control strategies: on/off and variable-speed (modulating). A backup heater, operating in top-up or substitute mode, covers demand when the heat pump cannot meet the load or operates outside its limits.

Inputs

Heat Pump Configuration

EN 14825 Test Data

Each test data record contains:

Test data is provided for up to four design flow temperatures. Each design flow temperature has five test records (A through D, plus F for the bivalent/TOL condition). Records are sorted by test temperature in ascending order.

Calculation

Source Temperature

The source temperature ${\theta }_{source}$ depends on the heat pump type and is determined at each timestep.

For air-source heat pumps, the source temperature equals the external air temperature from the weather data:

${\theta }_{source}={\theta }_{ext}$

For ground-source heat pumps, the source temperature is a linear function of external air temperature, clamped between 0 °C and 8 °C:

${\theta }_{source}=\text{clamp}(0.25806\cdot {\theta }_{ext}+2.8387,0,8)[°C]$

For water-source (ground) heat pumps, the source temperature equals the annual average air temperature:

${\theta }_{source}={\theta }_{ext,annual}$

For water-source (surface) heat pumps, the source temperature equals the monthly average air temperature:

${\theta }_{source}={\theta }_{ext,monthly}$

For heat network source heat pumps, the source temperature is a fixed distribution temperature declared as an input.

For exhaust air heat pumps (MEV and MVHR types), the source temperature is the internal air temperature from the previous timestep. For the mixed exhaust air variant, the source temperature is a weighted mix of outdoor and indoor air:

${\theta }_{source}=r_{ext}\cdot {\theta }_{ext}+(1-r_{ext})\cdot {\theta }_{int}$

where $r_{ext}$ is the external air ratio. When the external temperature exceeds a declared maximum threshold, or when the mixed temperature falls below a declared minimum threshold, only the indoor air temperature is used.

Carnot CoP

The Carnot CoP provides the theoretical maximum performance and is used as a reference for the exergetic efficiency method. It is calculated from source and outlet temperatures in Kelvin:

${\text{CoP}}_{Carnot}=\frac{T_{outlet}}{T_{outlet}-T_{source}}$

A minimum temperature difference of $\Delta T_{min}=6$ K is enforced between source and sink to prevent unrealistically high Carnot CoP values when the temperature lift is small:

${\text{CoP}}_{Carnot}=\frac{T_{outlet}}{\max (T_{outlet}-T_{source},\Delta T_{min})}$

Derived Quantities from Test Data

Several derived quantities are pre-computed from the EN 14825 test records for each design flow temperature.

Temperature Spread at Test Conditions

The temperature spread at test conditions $\Delta {\theta }_{test}$ depends on the design flow temperature:

Exergetic Efficiency

For each test record, the Carnot CoP is calculated from the test source and outlet temperatures, and the exergetic efficiency is the ratio of measured CoP to Carnot CoP:

${\eta }_{exer}=\frac{{\text{CoP}}_{measured}}{{\text{CoP}}_{Carnot}}$

Theoretical Load Ratio

The theoretical load ratio at each test point is calculated relative to the coldest test condition (index 0 after sorting by test temperature):

$L{R}_{theo}=\frac{{\text{CoP}}_{Carnot}}{{\text{CoP}}_{Carnot,cld}}\cdot {\left(\frac{T_{outlet,cld}\cdot T_{source}}{T_{source,cld}\cdot T_{outlet}}\right)}^{N_{exer}}$

where $N_{exer}=3.0$ is the exergy weighting exponent.

Regression Coefficients

A second-order polynomial regression is fitted to the test temperature vs. CoP data for each design flow temperature:

${\text{CoP}}_{reg}({\theta }_{test})=c_0+c_1\cdot {\theta }_{test}+c_2\cdot {\theta }_{test}^2$

These coefficients are used for the non-air-source CoP calculation.

Average Degradation Coefficient and Capacity

The average degradation coefficient and average capacity are computed from the non-bivalent test conditions (A, B, C, D) for each design flow temperature. These averages are used when the source temperature does not vary during testing.

Interpolation Between Design Flow Temperatures

When test data is available for more than one design flow temperature, all derived quantities (CoP, capacity, degradation coefficient, load ratios, exergetic efficiencies) are linearly interpolated between the design flow temperatures using the actual operating flow temperature (converted to Celsius) as the interpolation variable. When test data exists for only one design flow temperature, that single set of values is used directly.

CoP at Operating Conditions

The CoP calculation follows one of two paths depending on whether the source temperature varies with operating conditions.

Air-Source or Variable Flow Temperature During Test

For air-source heat pumps, or when variable flow temperature control was enabled during testing, the CoP is determined through the exergetic efficiency method.

Step 1: Carnot CoP at operating conditions.

${\text{CoP}}_{Carnot,op}=\frac{T_{output}}{\max (T_{output}-T_{source},6)}$

Step 2: Load ratio at operating conditions. For each design flow temperature, the load ratio at operating conditions is:

$L{R}_{op}=\max \left(1.0,\frac{{\text{CoP}}_{Carnot,op}}{{\text{CoP}}_{Carnot,cld}}\cdot {\left(\frac{T_{outlet,cld}\cdot T_{source}}{T_{output}\cdot T_{source,cld}}\right)}^{N_{exer}}\right)$

The result is interpolated between design flow temperatures.

Step 3: Exergetic efficiency at operating conditions. The test data records whose theoretical load ratios bracket the operating load ratio are identified. The exergetic efficiency is linearly interpolated:

${\eta }_{exer,op}={\eta }_{exer,below}+\frac{({\eta }_{exer,below}-{\eta }_{exer,above})\cdot (L{R}_{op}-L{R}_{below})}{L{R}_{below}-L{R}_{above}}$

Step 4: CoP at operating conditions.

${\text{CoP}}_{op}=\max (1.0,{\eta }_{exer,op}\cdot {\text{CoP}}_{Carnot,op}\cdot f_{spread})$

where $f_{spread}$ is the temperature spread correction factor (defined below).

Non-Air-Source with Fixed Flow Temperature During Test

For ground-source and water-source heat pumps where the flow temperature was fixed during testing, the CoP at operating conditions uses the polynomial regression:

${\text{CoP}}_{op}=f_{spread}\cdot (c_0+c_1\cdot {\theta }_{ext}+c_2\cdot {\theta }_{ext}^2)\cdot \frac{T_{output}\cdot (T_{outlet,cld}-T_{source,cld})}{T_{outlet,cld}\cdot \max (T_{output}-T_{source},6)}$

where ${\theta }_{ext}$ is the external air temperature in Celsius, $T_{outlet,cld}$ and $T_{source,cld}$ are the outlet and source temperatures from the coldest test record (in Kelvin), and the regression coefficients $c_0,c_1,c_2$ are evaluated using external temperature in Celsius (matching the units used to fit the regression). The result is interpolated between design flow temperatures.

Degradation Coefficient at Operating Conditions

The degradation coefficient is determined alongside the CoP.

For air-source or variable-flow-temp-during-test heat pumps, the degradation coefficient is interpolated from the test records bracketing the operating load ratio, following the same bracket-finding logic as the exergetic efficiency:

$C_{d,op}=C_{d,below}+\frac{(C_{d,below}-C_{d,above})\cdot (L{R}_{op}-L{R}_{below})}{L{R}_{below}-L{R}_{above}}$

The result is clamped to $[0.9,1.0]$ for water and glycol sinks, or $[0.0,0.25]$ for air-sink space heating.

For non-air-source heat pumps with fixed flow temperature during test, the average degradation coefficient across test conditions A through D is used, interpolated between design flow temperatures.

Temperature Spread Correction

The temperature spread correction accounts for the difference between the emitter temperature spread in operation and the temperature spread under standard test conditions. For each design flow temperature:

$f_{spread}=1-\frac{(\Delta {\theta }_{test}-\Delta {\theta }_{emitter})/2}{T_{output}-\Delta {\theta }_{test}/2+\Delta T_{cond}-T_{source}+\Delta T_{evap}}$

where:

• $\Delta {\theta }_{test}$ is the temperature spread at test conditions (K)
• $\Delta {\theta }_{emitter}$ is the design temperature spread of the emitter system (K)
• $\Delta T_{cond}=5.0$ K, the average temperature difference between heat transfer medium and refrigerant in the condenser
• $\Delta T_{evap}$ is the average temperature difference in the evaporator: 15.0 K for air-source fluid, 10.0 K for water-source fluid

The result is interpolated between design flow temperatures. For hot water services, the temperature spread correction is set to 1.0 (no correction applied).

Thermal Capacity at Operating Conditions

The method for calculating thermal capacity at operating conditions depends on source type and test configuration.

Non-Air-Source, Fixed Flow Temperature During Test

When the source temperature does not vary during testing, the average capacity across test conditions A through D is used, interpolated between design flow temperatures:

$Q_{cap,op}={\overline{Q}}_{cap,A\text{-}D}$

Air-Source or Variable Flow Temperature During Test (Modulating)

For modulating heat pumps, the capacity at operating conditions scales from the coldest test record:

$Q_{cap,op}=Q_{cap,cld}\cdot {\left(\frac{T_{outlet,cld}\cdot T_{source}}{T_{output}\cdot T_{source,cld}}\right)}^{N_{exer}}$

Air-Source or Variable Flow Temperature During Test (On/Off)

For on/off heat pumps, the capacity is interpolated linearly between the coldest condition and test condition D using the temperature difference:

$Q_{cap,op}=Q_{cap,cld}+(Q_{cap,D}-Q_{cap,cld})\cdot \frac{\Delta T_{cld}-\Delta T_{op}}{\Delta T_{cld}-\Delta T_D}$

where:

• $\Delta T_{cld}=T_{outlet,cld}-T_{source,cld}$
• $\Delta T_D=T_{outlet,D}-T_{source,D}$
• $\Delta T_{op}=T_{output}-T_{source}$

Running Time

The running time for each service within a timestep is determined by the energy demand and thermal capacity:

$t_{required}=\frac{Q_{output,limited}}{Q_{cap,op}}$

$t_{available}=(t_{step}-t_{running,other})\cdot \left(1-\frac{t_{start}}{t_{step}}\right)$

$t_{running}=\min (t_{required},t_{available})$

where $t_{running,other}$ is the time already committed to higher-priority services within the same timestep, and $t_{start}$ accounts for any delay before the service can begin (e.g. emitter cool-down time).

Energy Output Limiting

When the required output temperature exceeds the heat pump's upper operating limit ${\theta }_{limit}$, the energy output is scaled down proportionally:

$Q_{output,limited}=Q_{output,required}\cdot \frac{T_{limit}-T_{scaling}}{T_{output}-T_{scaling}}$

where $T_{scaling}$ is the return temperature (or cold water feed temperature for hot water service). If the achievable temperature difference $(T_{limit}-T_{scaling})$ is less than the minimum flow-return difference $\Delta {\theta }_{min}$, the energy output is zero.

Backup Heater Logic

The backup heater activates under the following conditions, provided backup control is not set to "None":

1. Outside operating limits. The source temperature is at or below the minimum operating limit, or the return feed temperature exceeds the maximum (for water/glycol sinks).
2. Inadequate capacity (substitute mode). The energy demand exceeds what the heat pump can deliver within the timestep, the backup delay time has elapsed, and the backup heater can provide more energy than the heat pump (for substitute mode). In substitute mode, when the backup heater takes over, the heat pump compressor is switched off entirely.
3. Cost-effectiveness (hybrid systems). For hybrid heat pump/boiler systems with a cost schedule, the heat pump is replaced by the boiler when:

$\frac{C_{hp}}{{\text{CoP}}_{op}}>\frac{C_{boiler}}{{\eta }_{boiler}}$

where $C_{hp}$ and $C_{boiler}$ are the fuel costs from the schedule and ${\eta }_{boiler}$ is the boiler efficiency.

When the backup heater operates in top-up mode, it supplements the heat pump output up to the remaining demand. The total energy delivered is:

$Q_{delivered,total}=Q_{delivered,HP}+Q_{delivered,backup}$

The backup energy output is capped at the maximum backup power multiplied by the time available:

$Q_{backup}=\min (P_{backup,max}\cdot t_{available},Q_{required}-Q_{delivered,HP})$

For hybrid systems with a boiler, the backup energy is delegated to the boiler model (see TP-14: Boilers) rather than using the simple backup heater.

Energy Input Calculation

The energy input calculation is performed at the end of each timestep, after all services have reported their demand.

Load Ratio

The load ratio determines whether the heat pump operates in on/off or continuous (modulating) mode:

$LR=\frac{t_{running}}{t_{step}}$

For space heating services, $t_{running}$ is the aggregate running time across all space heating zones.

The minimum continuous load ratio $L{R}_{cont,min}$ depends on the control type:

• On/off control: $L{R}_{cont,min}=1.0$ (the heat pump cannot modulate, so any load ratio below 1.0 triggers on/off operation).
• Modulating control: $L{R}_{cont,min}$ is interpolated between $L{R}_{min,low}$ and $L{R}_{min,55}$ based on the output temperature, if test data at 55 °C is available. Otherwise, $L{R}_{cont,min}=L{R}_{min,low}$.

The heat pump operates in on/off mode when $0<LR<L{R}_{cont,min}$.

Compressor Energy Input: Continuous Operation

When the heat pump runs continuously ($LR\ge L{R}_{cont,min}$), the compressor energy input is:

$E_{input,HP}=\frac{Q_{delivered,HP}}{{\text{CoP}}_{op}}$

Compressor Energy Input: On/Off Operation

When cycling ($LR<L{R}_{cont,min}$), additional energy is consumed due to transient inertia effects. The compressor power at minimum load is:

$P_{comp,min}=\frac{Q_{cap,op}}{{\text{CoP}}_{op}}\cdot L{R}_{cont,min}$

The power penalty due to on/off cycling inertia (from CALCM-01, section 4.5.10) is:

$P_{inertia}=P_{comp,min}\cdot \frac{{\tau }_{onoff}\cdot LR\cdot (1-LR)}{{\tau }_{service}}$

where ${\tau }_{service}$ is the time constant for the service type:

• Water heating: ${\tau }_{service}=1560$ s
• Space heating (water or glycol sink): ${\tau }_{service}=1370$ s
• Space heating (air sink): ${\tau }_{service}=120$ s

The compressor energy input for on/off operation is:

$E_{input,HP}=\frac{\left(\frac{Q_{cap,op}}{{\text{CoP}}_{op}}\cdot (1+f_{aux})+P_{inertia}\right)\cdot t_{running}}{D_{divisor}}$

where $f_{aux}=0$ for electric heat pumps, and $D_{divisor}$ is a correction factor. For most configurations $D_{divisor}=1.0$, except for hot water service with an air-sink heat pump:

$D_{divisor}=1-C_{d,op}\cdot \left(1-\frac{LR}{L{R}_{cont,min}}\right)$

Ancillary Energy (Off-Cycle Losses)

After the primary energy input is calculated, ancillary energy consumption during the off-cycle is added for services operating in on/off mode. This represents compressor standstill losses:

$E_{ancillary,off}=(1-C_{d,op})\cdot \frac{P_{comp,min}}{L{R}_{cont,min}}\cdot \max \left(t_{remaining}-\frac{LR}{L{R}_{cont,min}}\cdot t_{step},0\right)$

This ancillary energy applies only when the service is on, the heat pump ran during this timestep, no lower-priority service subsequently ran, and the system is not an air-sink providing hot water. For on/off operation, the ancillary energy is divided by $D_{divisor}$ and added to the compressor energy input.

Auxiliary Energy (Standby, Crankcase Heater, Off Mode)

Auxiliary energy consumption during the non-running portion of the timestep follows the logic from CALCM-01, section 4.7:

• Heating service active: standby power and crankcase heater power are applied for the remaining time $t_{remaining}=t_{step}-t_{running,total}$.
• Only water heating active: standby power only for the remaining time.
• No services active: off-mode power for the full timestep.

$E_{aux}=\{\begin{array}{ll}{t}_{remaining}\cdot (P_{standby}+P_{crank})& \text{if heating on}\\ t_{remaining}\cdot P_{standby}& \text{if water only}\\ t_{step}\cdot P_{off}& \text{if all off}\end{array}$

Total Energy Input

The total energy input to the heat pump for each service is:

$E_{input,total}=E_{input,HP}+E_{input,backup}+E_{circ,heating}+E_{circ,source}+E_{fan,warmair}$

where:

• $E_{circ,heating}=t_{running}\cdot P_{circ}$ is the heating circulation pump energy
• $E_{circ,source}=t_{running}\cdot P_{source}$ is the source-side circulation pump energy
• $E_{fan,warmair}=t_{running}\cdot P_{fan}$ for warm air distribution systems (replacing $E_{circ,heating}$ in that case)

Energy Extracted from Source

The energy extracted from the heat source (environment or heat network) is the difference between heat delivered and electrical energy consumed by the compressor:

$E_{source}=Q_{delivered,HP}-E_{input,HP}$

This is reported separately on the relevant energy supply for heat network sources.

Continuous Running Tracking

The model tracks whether the heat pump runs continuously across consecutive timesteps to manage backup heater delay logic. If the heat pump occupies the entire timestep ($t_{remaining}=0$), the continuous running counter accumulates. If there is any idle time within a timestep, the counter resets to zero. The backup heater is permitted to activate only after the continuous running time exceeds $t_{delay}$.

Exhaust Air Heat Pumps

For exhaust air heat pumps (MEV, MVHR, Mixed types), additional logic applies:

1. Test data interpolation by air flow rate. When test data is provided at multiple air flow rates, the capacity, CoP, and degradation coefficient are interpolated to match the actual exhaust air throughput of the ventilation system.
2. Overventilation ratio. If the lowest tested air flow rate exceeds the ventilation system throughput, an overventilation ratio is computed. This ratio adjusts the effective ventilation rate during heat pump operation, modifying the throughput factor applied to the zone:

$f_{throughput}=\frac{(t_{step}-t_{running})+r_{overvent}\cdot t_{running}}{t_{step}}$

3. Mixed exhaust air. The mixed variant uses a proportion of external air blended with internal exhaust air. The external air ratio $r_{ext}$ determines the mix. When the external temperature exceeds a maximum threshold or the mixed temperature drops below a minimum threshold, only internal air is used.

Outputs

Assumptions

• A minimum temperature difference of 6 K between source and sink is enforced in the Carnot CoP calculation to prevent unrealistically high values at low temperature lifts (CALCM-01, section 4.5.3).
• The exergy weighting exponent $N_{exer}$ is fixed at 3.0.
• The fraction of energy input dedicated to auxiliaries $f_{aux}$ is zero for all electric heat pumps.
• The backup heater operates at 100% efficiency when not delegated to a separate boiler model.
• Ground-source temperature is a linear function of external air temperature, clamped to 0-8 °C. This is a simplification; actual ground loop temperatures depend on soil properties and borehole depth.
• Water-source (ground) temperature is assumed constant at the annual average air temperature. Water-source (surface) temperature uses the monthly average air temperature.
• Time spent on different services within a timestep is assumed to be evenly distributed, so the proportional time available for each service is reduced by the ratio of time already committed.
• The time constant for on/off cycling inertia differs by service type: 1560 s for water heating, 1370 s for space heating with water/glycol distribution, and 120 s for warm air distribution.
• The temperature spread correction uses fixed values for condenser temperature difference (5 K) and evaporator temperature difference (15 K for air-source, 10 K for water-source), per BS EN 15316-4-2.
• Buffer tank losses, when a buffer tank is present, are added to the energy demand the heat pump must satisfy. Recoverable losses contribute to internal gains.

Cross-references

• TP-01: Overview and Climate Data: timestep structure and simulation parameters
• TP-03: External Conditions: external air temperature, annual and monthly averages used for source temperature
• TP-04: Space Heating Demand: space heating energy demand that the heat pump must satisfy
• TP-06: Ventilation and Infiltration: exhaust air throughput for EAHP; throughput factor adjustment
• TP-09: Hot Water Demand: hot water energy demand driving the water heating service
• TP-10: Pipework and Ductwork Losses: distribution losses added to the heat pump load
• TP-11: Hot Water Storage: cylinder temperatures providing flow and return temperatures for the water heating service
• TP-14: Boilers: hybrid boiler backup heater model
• TP-16: Heat Emitters: flow and return temperatures, emitter design temperature spread
• TP-17: Controls: service on/off scheduling, setpoints, and modulation control