TP-15: Heat Batteries | HEM Reference

Overview

Heat batteries store thermal energy in phase change materials (PCMs) and release it on demand for space heating and hot water services. The PCM undergoes a solid-liquid phase transition within a defined temperature band, absorbing and releasing large quantities of energy at a near-constant temperature. This makes heat batteries well suited to time-shifting electrical energy from off-peak periods into thermal demand periods.

The heat battery model in the Home Energy Model represents the storage medium as a series of discrete thermal zones. Each zone tracks its own temperature and exchanges energy with a water circuit via an internal heat exchanger. The model covers four principal operations: electric charging, hydraulic discharge (energy delivery to services), simultaneous charge and discharge, and standby heat losses.

The calculation uses a sub-timestep iterative approach. The main HEM timestep (typically one hour) is subdivided into shorter intervals (of the order of seconds) to capture the transient heat exchange between the PCM zones and the flowing water. Fluid properties, heat transfer coefficients, and zone temperatures are updated at each sub-timestep.

Inputs

Parameter	Symbol	Unit	Description
Number of units	$N_{u ni t s}$	--	Number of heat battery units installed
Rated charge power	$P_{c ha r g e}$	kW	Maximum electrical charging power per unit
Maximum rated losses	$P_{l oss}$	kW	Maximum standby heat loss rate per unit
Maximum temperature	$T_{ma x}$	degC	Upper temperature limit when fully charged
Phase transition upper temperature	$T_{pt, u pp er}$	degC	Upper bound of the PCM phase change band
Phase transition lower temperature	$T_{pt, l o w er}$	degC	Lower bound of the PCM phase change band
Heat capacity above phase transition	$C_{ab o v e}$	kJ/K	Effective heat capacity per zone above $T_{pt, u pp er}$
Heat capacity during phase transition	$C_{d u r in g}$	kJ/K	Effective heat capacity per zone within the phase change band
Heat capacity below phase transition	$C_{b e l o w}$	kJ/K	Effective heat capacity per zone below $T_{pt, l o w er}$
Heat exchanger surface area	$A_{h e x}$	m2	Total internal heat exchanger surface area per unit
Heat transfer coefficient A	$A_{h t c}$	--	Empirical log-linear regression parameter for UA
Heat transfer coefficient B	$B_{h t c}$	--	Empirical log-linear regression parameter for UA
Capillary diameter	$d_{c a p}$	m	Internal diameter of heat exchanger capillary tubes
Velocity at 1 l/min	$v_{1}$	m/s	Water velocity in the heat exchanger at a flow rate of 1 l/min
Flow rate	$\dot{V}$	l/min	Volumetric water flow rate through the heat exchanger
Electricity for circulation pump	$P_{p u m p}$	kW	Electrical power consumed by the circulation pump during operation
Electricity standby	$P_{s t an d b y}$	kW	Electrical power consumed in standby mode
Simultaneous charge/discharge flag	--	--	Whether the battery may charge electrically whilst discharging to a service
Number of zones	$N_{z o n es}$	--	Number of discrete thermal zones (default 8)
Sub-timestep duration	$Δ t_{hb}$	s	Internal iterative timestep (default 20 s)
Minimum run time	$t_{min}$	s	Minimum duration the battery must run once activated (default 120 s)

Calculation

Thermal Zone Model

The PCM storage medium is discretised into $N_{z o n es}$ zones arranged in series along the water flow path. Each zone holds a uniform temperature $T_{z}$ and has a piecewise-linear enthalpy-temperature relationship governed by three heat capacity values corresponding to the regions above, within, and below the phase change band.

All zones are initialised to $T_{ma x}$ at the start of the simulation, representing a fully charged state.

Fluid Properties

The water kinematic viscosity is approximated as a quadratic function of the average circuit temperature:

$ν = a \cdot T_{a v g}^{2} + b \cdot T_{a v g} + c$

where:

$T_{a v g} = (T_{in} + T_{o u t}) /2$ is the mean of inlet and outlet temperatures degC
$a = 1.45238 \times 1 0^{- 10}$ m2/(s.degC2)
$b = - 2.48238 \times 1 0^{- 8}$ m2/(s.degC)
$c = 1.432 \times 1 0^{- 6}$ m2/s

The Reynolds number at a reference flow rate of 1 l/min is:

$R e_{1} = \frac{v _{1} \cdot d _{c a p}}{ν}$

where:

$v_{1}$ is the water velocity at 1 l/min m/s
$d_{c a p}$ is the capillary tube diameter m
$ν$ is the kinematic viscosity m2/s

The mass flow rate is derived from the volumetric flow rate:

$\overset{m}{˙} = \frac{V ˙}{60} \cdot ρ_{w}$

where:

$\dot{V}$ is the volumetric flow rate l/min
$ρ_{w} = 1.0$ kg/l (water density)

Heat Transfer Coefficient

The overall heat transfer coefficient for the heat exchanger is determined from an empirical log-linear correlation derived from test data:

$U A = A_{h t c} \cdot ln (R e_{1} \cdot \dot{V}) + B_{h t c} [W/K]$

where:

$A_{h t c}$ and $B_{h t c}$ are empirical regression parameters
$R e_{1}$ is the Reynolds number at 1 l/min
$\dot{V}$ is the flow rate l/min

The heat transfer capacity in kW/K is:

$h_{h e x} = \frac{U A \cdot A _{h e x}}{1000}$

where $A_{h e x}$ is the heat exchanger surface area m2.

Outlet Temperature

For each zone in normal (discharge or simultaneous) mode, the outlet water temperature is derived from the energy balance between the PCM zone and the flowing water. The governing equation is:

$\dot{Q}_{z} = \overset{m}{˙} \cdot c_{w} \cdot (T_{w, o u t} - T_{w, in}) = h_{h e x} \cdot (T_{z} - \frac{T _{w, in} + T _{w, o u t}}{2})$

where:

$\dot{Q}_{z}$ is the heat transfer rate from the zone kW
$\overset{m}{˙}$ is the water mass flow rate kg/s
$c_{w}$ is the specific heat capacity of water kWh/(kg.K)
$T_{z}$ is the zone temperature degC
$T_{w, in}$ is the inlet water temperature to the zone degC
$T_{w, o u t}$ is the outlet water temperature from the zone degC
$h_{h e x}$ is the heat transfer capacity kW/K

Solving for the outlet temperature gives:

$T_{w, o u t} = \frac{2 \cdot h _{h e x} \cdot T _{z} - h _{h e x} \cdot T _{w, in} + 2 \cdot m ˙ \cdot c _{w}^{'} \cdot T _{w, in}}{2 \cdot m ˙ \cdot c _{w}^{'} + h _{h e x}}$

where $c_{w}^{'} = c_{w} \times 3600$ converts the specific heat capacity to kJ/(kg.K) for consistency with the energy transfer units.

The energy transferred from each zone during a sub-timestep of duration $Δ t$ is:

$Q_{z} = \overset{m}{˙} \cdot c_{w}^{'} \cdot (T_{w, o u t} - T_{w, in}) \cdot Δ t [kJ]$

The outlet of one zone becomes the inlet of the next, creating a cascaded heat exchange path through the battery.

Zone Energy and Temperature Update

Piecewise Enthalpy Model

The relationship between energy stored and zone temperature is piecewise-linear across three regions. The energy required to move a zone from its current temperature $T_{z}$ to a target temperature $T_{t a r g e t}$ depends on which regions the temperature traverses:

Zone above phase transition ( $T_{z} \geq T_{pt, u pp er}$ ):

$Q_{r e q} = C_{ab o v e} \cdot (T_{z} - T_{t a r g e t})$

Zone within phase transition ( $T_{pt, l o w er} \leq T_{z} < T_{pt, u pp er}$ ):

If $T_{t a r g e t} > T_{pt, u pp er}$ :

$Q_{r e q} = C_{ab o v e} \cdot (T_{pt, u pp er} - T_{t a r g e t}) + C_{d u r in g} \cdot (T_{z} - T_{pt, u pp er})$

Otherwise:

$Q_{r e q} = C_{d u r in g} \cdot (T_{z} - T_{t a r g e t})$

Zone below phase transition ( $T_{z} < T_{pt, l o w er}$ ):

The calculation sums contributions from each region the temperature must traverse to reach $T_{t a r g e t}$ , using $C_{b e l o w}$ , $C_{d u r in g}$ , and $C_{ab o v e}$ as appropriate.

Temperature Update After Energy Transfer

After an energy transfer $Q_{t r an s f}$ (positive for discharge, negative for charging), the new zone temperature is computed by inverting the piecewise enthalpy model. The algorithm determines how much of the transferred energy falls within each thermal region and computes the corresponding temperature change:

$Δ T_{1} + Δ T_{2} + Δ T_{3} = total temperature change$

$T_{z}^{n e w} = T_{z} - (Δ T_{1} + Δ T_{2} + Δ T_{3})$

where:

$Δ T_{1}$ is the temperature change in the region above $T_{pt, u pp er}$ , computed as $Q / C_{ab o v e}$
$Δ T_{2}$ is the temperature change within the phase transition band, computed as $Q / C_{d u r in g}$
$Δ T_{3}$ is the temperature change below $T_{pt, l o w er}$ , computed as $Q / C_{b e l o w}$

The algorithm proceeds sequentially through the regions. If the energy transfer exhausts one region (the zone temperature reaches a boundary), the residual energy is applied to the next region using the corresponding heat capacity.

Electric Charging

When the charge control signal is active, the battery charges electrically at the rated power $P_{c ha r g e}$ . The charging energy budget for a sub-timestep of duration $Δ t$ is:

$Q_{ma x} = - P_{c ha r g e} \cdot \frac{Δ t}{3600} \cdot 3600 [kJ]$

The negative sign indicates energy flowing into the battery (raising zone temperatures).

During charging-only mode, zones are processed in reverse order (from the zone furthest from the inlet to the zone nearest the inlet). No water flows through the heat exchanger; the electrical energy is distributed across zones to raise their temperatures towards the target:

$T_{t a r g e t} = T_{ma x} \cdot f_{c ha r g e}$

where $f_{c ha r g e}$ is the target charge fraction from the charge control (typically 1.0, giving $T_{t a r g e t} = T_{ma x}$ ).

Each zone receives charging energy until it reaches $T_{t a r g e t}$ or the charging budget is exhausted.

Simultaneous Charge and Discharge

When the simultaneous charge/discharge flag is set and the charge control is active, the battery may charge electrically whilst simultaneously discharging to a service. In this mode, the charging energy budget is combined with the discharge energy transfer at each zone.

The logic operates per zone:

If the zone is below $T_{t a r g e t}$ and the water is withdrawing energy (positive $Q_{t r an s f}$ ), the charging budget first compensates the withdrawn energy, then pushes the zone temperature towards $T_{t a r g e t}$ .
If the zone is below $T_{t a r g e t}$ and the water is adding energy (negative $Q_{t r an s f}$ , as when return water is warmer than the zone), the combined charging and inlet energy is applied up to $T_{t a r g e t}$ .
If the zone is already at or above $T_{t a r g e t}$ , the charging budget offsets any energy withdrawn by the water flow, preventing unnecessary depletion.

The net energy consumed from the electrical supply for charging during simultaneous operation is tracked and reported at the end of the timestep.

Standby Heat Losses

At the end of each HEM timestep, standby losses are applied to all zones whose temperature exceeds 22 degC. The total loss energy budget for the full timestep is:

$Q_{l oss} = P_{l oss} \cdot Δ t_{s t e p} [kJ]$

where $Δ t_{s t e p}$ is the timestep duration in seconds. This budget is divided equally among all zones:

$Q_{l oss, z} = \frac{Q _{l oss}}{N _{z o n es}} [kJ per zone]$

Each zone's temperature is then updated using the piecewise enthalpy model. If a zone temperature is at or below 22 degC, no loss is applied to that zone.

Demand Energy (Service Delivery)

When a service (space heating or hot water) demands energy from the heat battery, the model runs an iterative sub-timestep loop:

The required energy per unit is $E_{d e man d} = E_{r e q u i r e d} / N_{u ni t s}$ .
Any residual energy stored in the pipework from a previous minimum-run overshoot is credited first, reducing the effective demand.
At each sub-timestep, the zone processing loop computes the outlet temperature and energy transfer across all zones.
If the outlet temperature exceeds the required service temperature $T_{o u tp u t}$ , the energy delivered is accumulated. The next sub-timestep duration is estimated from the remaining demand and the instantaneous power.
If the outlet temperature falls below $T_{o u tp u t}$ , the battery can no longer deliver useful energy at the required temperature. If some energy has already been delivered, the battery continues running for the minimum run time $t_{min}$ to complete the water loop, storing any excess energy as pipework residual.
The sub-timestep is capped at $Δ t_{hb}$ and must not exceed the time remaining in the HEM timestep.
The Reynolds number is recalculated at each sub-timestep using the updated outlet temperature.

The total energy delivered to the service is:

$E_{d e l i v er e d} = E_{d e l i v er e d, u ni t} \cdot N_{u ni t s}$

Time Availability

Multiple services may draw from the battery within a single HEM timestep. The time available for each service is reduced by time already spent on prior services:

$t_{a v ai l} = (Δ t_{s t e p} - t_{r u nnin g}) \cdot (1 - \frac{t _{s t a r t}}{Δ t _{s t e p}})$

where:

$Δ t_{s t e p}$ is the HEM timestep duration hours
$t_{r u nnin g}$ is the cumulative time already spent on services this timestep hours
$t_{s t a r t}$ is the start time offset within the timestep hours

Maximum Energy Output

The maximum energy the battery can deliver at a given output temperature is estimated by running a read-only simulation over the full HEM timestep. This uses a coarser sub-timestep (five times $Δ t_{hb}$ , capped at 100 s) for computational efficiency. The simulation iterates through sub-timesteps, accumulating delivered energy while the outlet temperature remains above $T_{o u tp u t}$ . Zone temperatures are not committed to the battery state, so this calculation does not alter the stored charge.

Hot Water Temperature Estimation

A similar read-only simulation estimates the hot water temperature the battery can deliver. A nominal volume (20 litres) is drawn through the battery at the rated flow rate. The simulation sub-steps through the draw period, updating zone temperatures (on a copy) and Reynolds numbers at each step. The final outlet temperature is returned as the estimated hot water delivery temperature.

Auxiliary Energy

At the end of each timestep, auxiliary electrical consumption is calculated:

$E_{a ux} = t_{r u nnin g} \cdot P_{p u m p} + t_{r e mainin g} \cdot P_{s t an d b y}$

where:

$t_{r u nnin g}$ is the total time the battery ran during the timestep hours
$t_{r e mainin g} = Δ t_{s t e p} - t_{r u nnin g}$ hours
$P_{p u m p}$ is the circulation pump power kW
$P_{s t an d b y}$ is the standby power kW

Timestep End Sequence

At the end of each HEM timestep, the following operations are performed in order:

Auxiliary energy consumption is calculated and recorded against the energy supply.
Standby heat losses are applied to all zones.
If the charge control is active, the remaining time in the timestep is used for electric charging.
The total electrical energy consumed for charging (including any simultaneous charging during service delivery) is recorded against the energy supply, scaled by $N_{u ni t s}$ .
Per-timestep accumulators (total running time, energy charged) are reset.

Outputs

Quantity	Symbol	Unit	Description
Energy delivered to service	$E_{d e l i v er e d}$	kWh	Thermal energy delivered per service per timestep
Energy charged	$E_{c ha r g e d}$	kWh	Electrical energy consumed for charging per timestep
Auxiliary energy	$E_{a ux}$	kWh	Electrical energy for pump and standby per timestep
Standby losses	$Q_{l oss}$	kWh	Thermal energy lost from the battery per timestep
Zone temperatures	$T_{z}$	degC	Temperature of each thermal zone at end of timestep
Hot water temperature	$T_{h w}$	degC	Estimated delivery temperature for hot water service
Maximum energy output	$E_{ma x}$	kWh	Maximum deliverable energy at a given output temperature

Assumptions

The PCM storage medium is represented by a one-dimensional series of well-mixed thermal zones. No spatial temperature gradients exist within a single zone.
The piecewise-linear enthalpy-temperature model uses three constant heat capacities (above, during, and below the phase transition). The real phase change enthalpy curve is idealised as a linear ramp between $T_{pt, l o w er}$ and $T_{pt, u pp er}$ .
The heat exchanger performance is characterised by a log-linear correlation $U A = A \cdot ln (R e \cdot \dot{V}) + B$ , derived from laboratory test data. This is assumed valid across the operating range.
Water kinematic viscosity uses a quadratic fit, not a full thermodynamic property table. Accuracy is limited to the typical operating range of hydronic circuits (approximately 0 to 100 degC).
Water density is taken as a constant 1.0 kg/l regardless of temperature.
Standby losses are applied uniformly across all zones above 22 degC. The 22 degC threshold is a fixed assumption representing a nominal room temperature.
Pipework energy residuals carry over between services within a timestep but are not carried across timesteps.
The battery is initialised fully charged ( $T_{z} = T_{ma x}$ for all zones) at the start of the simulation.
The minimum run time constraint (default 120 s) means that once activated, the battery continues circulating water even after the demand is met. Excess energy is stored as pipework residual.
The maximum energy output estimation uses a coarser timestep (up to 100 s) and may slightly overestimate the true deliverable energy.
All thermal losses are assumed to be to the exterior, regardless of the battery's physical location within the dwelling.

Cross-references

TP-04: Space Heating Demand -- space heating demand drives the energy request to the heat battery service
TP-09: Hot Water Demand -- hot water usage events generate the thermal energy demand for the water heating service
TP-10: Pipework and Ductwork Losses -- distribution losses between the heat battery and point of use
TP-16: Heat Emitters -- emitter model requests energy at specified flow and return temperatures
TP-17: Controls -- charge control determines when the battery charges; service controls determine when services are active
TP-18: PV and Battery -- electrical energy supply for charging; potential for PV-divert charging strategies