TP-13: Storage Heaters | HEM Reference

Overview

Electric storage heaters charge a thermal core using off-peak electricity and release stored heat into the dwelling over the following hours. The model tracks the state of charge (SOC) as a scalar quantity between 0 and 1, with SOC-dependent power output curves governing both minimum (case losses) and maximum (active discharge) heat release rates. An ordinary differential equation (ODE) governs the evolution of SOC, energy charged, and energy delivered within each simulation timestep.

Two physical configurations are modelled: fan-assisted units, which use an internal fan to boost convective output, and damper-only (static) units, which rely on natural convection controlled by an air damper. Both types may include a direct-acting electric element for instant backup when stored energy is insufficient to meet demand.

Charge control strategies determine how much energy to store and when charging is permitted. Four logic types are supported: Manual, Automatic, CELECT, and HHRSH (High Heat Retention Storage Heater). The HHRSH strategy uses heating degree hours to estimate next-day demand and adjusts the target charge accordingly, informed by a heat retention ratio derived from a simulated 16-hour standby test per BS EN 60531.

Inputs

Parameter	Symbol	Unit	Description
Charging power	$P_{in}$	kW	Electrical power consumed during charging
Instant backup power	$P_{in s t an t}$	kW	Rated power of direct-acting electric element (0 if absent)
Storage capacity	$C_{s t or e}$	kWh	Total thermal energy the core can hold at full charge
Air flow type	—	—	Fan-assisted or damper-only
Convective fraction	$f_{co n v}$	—	Fraction of heat output delivered convectively (0 to 1)
Fan power	$P_{f an}$	W	Electrical power consumed by the fan (0 for damper-only units)
Number of units	$n$	—	Count of identical storage heater units in the zone
Minimum output curve	$P_{min} (S)$	kW	Piecewise-linear power output as a function of SOC, damper closed / fan off
Maximum output curve	$P_{ma x} (S)$	kW	Piecewise-linear power output as a function of SOC, damper open / fan running
Charge control logic	—	—	One of: Manual, Automatic, CELECT, HHRSH
Target charge schedule	$S_{t a r g e t}$	—	SOC target (0 to 1) per day, from the charge control
Temperature charge cut	$θ_{c u t}$	°C	Room air temperature above which charging is suppressed

SOC-Power Output Curves

The minimum and maximum output curves are supplied as ordered arrays of (SOC, power) pairs. Each array must span the full SOC range from 0.0 to 1.0. At any SOC, the maximum output power must be greater than or equal to the minimum output power. Between data points, power is obtained by linear interpolation.

$P_{min} (S) = lerp (S, S_{min}, P_{min})$

$P_{ma x} (S) = lerp (S, S_{ma x}, P_{ma x})$

Where:

$S$ is the current state of charge (dimensionless, 0 to 1)
$S_{min}$ , $P_{min}$ are the SOC and power vectors for minimum output
$S_{ma x}$ , $P_{ma x}$ are the SOC and power vectors for maximum output
$lerp$ denotes piecewise-linear interpolation

The minimum output curve represents unavoidable case losses: the heat that escapes through the heater casing when no active output is requested. The maximum output curve represents the heat release rate when the damper is fully open or the fan is running.

Calculation

State of Charge ODE

The state of charge, energy charged, and energy delivered are governed by a coupled ODE system integrated over each simulation timestep $Δ t$ (in hours):

$\frac{d S}{d t} = \frac{- P _{d i sc ha r g e} ( S ) + P _{c ha r g e} ( S )}{C _{s t or e}}$

$\frac{d E _{c ha r g e d}}{d t} = P_{c ha r g e} (S)$

$\frac{d E _{d e l i v er e d}}{d t} = P_{d i sc ha r g e} (S)$

Where:

$S$ is the state of charge (dimensionless)
$P_{d i sc ha r g e} (S)$ is the discharge power kW, equal to $P_{min} (S)$ or $P_{ma x} (S)$ depending on the output mode
$P_{c ha r g e} (S)$ is the charge power kW, determined by the charging logic
$C_{s t or e}$ is the storage capacity kWh
$E_{c ha r g e d}$ and $E_{d e l i v er e d}$ are cumulative energies kWh

The system is integrated using an adaptive Runge-Kutta (RK45) method. A terminal event halts integration if SOC reaches zero, preventing unphysical negative charge.

Charging Logic within the ODE

During each timestep, the charge power applied within the ODE depends on the current SOC relative to the target:

$P_{c ha r g e} (S) = ⎩ ⎨ ⎧ P_{in} min (P_{d i sc ha r g e} (S), P_{in}) 0 if S < S_{t a r g e t} if S \geq S_{t a r g e t} and S_{t a r g e t} > 0 otherwise$

When the SOC has reached the target, charging is reduced to offset discharge only, maintaining the SOC at the target level. When no charging is active ( $S_{t a r g e t} = 0$ ), the charge rate is zero throughout the timestep.

Target Charge Determination

The target charge $S_{t a r g e t}$ for a given timestep depends on the charge control logic type.

Manual

The target is read directly from the input schedule:

$S_{t a r g e t} = S_{sc h e d u l e}$

No temperature feedback is applied.

Automatic

An internal thermostat modulates charging. If the zone air temperature $θ_{ai r}$ exceeds the charge cut temperature $θ_{c u t}$ , charging is suppressed entirely:

$S_{t a r g e t} = {0 S_{sc h e d u l e} if θ_{ai r} > θ_{c u t} otherwise$

CELECT

A CELECT-type controller uses electronic sensors throughout the dwelling linked to a central control device. It monitors individual room sensors and optimises the charging of storage heaters individually. The charge logic follows the same temperature-cut structure as Automatic control:

$S_{t a r g e t} = {0 S_{sc h e d u l e} if θ_{ai r} > θ_{c u t} otherwise$

HHRSH (High Heat Retention Storage Heater)

A high heat retention storage heater, as defined in BS EN 60531, must have a heat retention of not less than 45%. It incorporates a timer, electronic room thermostat, and fan to control heat output. The HHRSH logic estimates the next day's heating demand from heating degree hours and adjusts the target charge to store sufficient energy.

The energy to store is estimated by comparing future and past heating degree hours:

$E_{s t or e} = \frac{H D H _{f u t u r e}}{H D H _{p a s t}} \times \sum E_{d e man d}$

Where:

$H D H_{f u t u r e}$ is the sum of heating degree hours for the next 24 hours, using forecast external temperatures
$H D H_{p a s t}$ is the sum of heating degree hours for the preceding 24 hours, using observed external temperatures
$\sum E_{d e man d}$ is the total energy demand recorded over the preceding 24 hours

Heating degree hours for a set of hourly temperatures are calculated as:

$H D H = \sum_{i} max (θ_{ba se} - θ_{e x t, i}, 0)$

where $θ_{ba se}$ is the zone setpoint temperature °C and $θ_{e x t, i}$ is the external air temperature °C at hour $i$ .

During the initial 24 hours of simulation, insufficient historical data is available. In this case, the heater defaults to a full charge:

$E_{s t or e} = P_{in} \times 24 [kWh]$

The target SOC for HHRSH is then derived from the energy to store, the current stored energy, and the heat retention ratio:

$E_{s t or e d} = S \times C_{s t or e}$

$E_{a dd} = ⎩ ⎨ ⎧ C_{s t or e} - E_{s t or e d} \frac{1}{R _{r e t}} \times (E_{s t or e} - E_{s t or e d}) if R_{r e t} \leq 0 if R_{r e t} > 0$

$S_{t a r g e t, H H R S H} = clip (S + \frac{E _{a dd}}{C _{s t or e}}, 0, 1)$

Where:

$E_{s t or e d}$ is the energy currently held in storage kWh
$R_{r e t}$ is the heat retention ratio (dimensionless)
$E_{a dd}$ is the energy that must be added kWh

The final HHRSH target charge is capped by the schedule target to respect off-peak periods:

$S_{t a r g e t} = min (S_{sc h e d u l e}, S_{t a r g e t, H H R S H})$

Heat Retention Ratio

The heat retention ratio $R_{r e t}$ quantifies what fraction of stored energy remains after a 16-hour standby period at minimum output, following BS EN 60531. It is calculated once at initialisation by integrating the SOC ODE from a fully charged state ( $S = 1.0$ ) over 16 hours with no charging and minimum output:

$\frac{d S}{d t} = \frac{- P _{min} ( S )}{C _{s t or e}}, S (0) = 1.0$

$R_{r e t} = S (16)$

The result is a value between 0 and 1. A value of 0.45 or greater qualifies the unit as a high heat retention storage heater under BS EN 60531.

Energy Output Calculation

Each timestep, the model evaluates the energy deliverable under both minimum and maximum output modes. The ODE system is integrated for the full timestep duration in each mode, yielding:

$Q_{min}$ : energy delivered at minimum output kWh per unit
$Q_{ma x}$ : energy delivered at maximum output kWh per unit
$E_{c ha r g e d}$ : energy drawn from the electricity supply for charging kWh per unit
$t_{u se d}$ : active discharge time hours

The minimum output $Q_{min}$ represents the unavoidable case losses. The maximum output $Q_{ma x}$ represents the most heat the unit can release within the timestep.

Demand Matching

When the zone requests energy $E_{d e man d}$ kWh, the demand is first divided equally among the installed units:

$e_{d e man d} = \frac{E _{d e man d}}{n}$

The model then selects the appropriate operating point:

Minimum output exceeds demand ( $Q_{min} > e_{d e man d}$ ): The heater delivers $Q_{min}$ regardless; there is no mechanism to reduce case losses below the minimum. The zone receives more heat than requested.
Demand within range ( $Q_{min} \leq e_{d e man d} \leq Q_{ma x}$ ): The heater delivers exactly $e_{d e man d}$ . The active discharge time is scaled proportionally:

$t_{u se d} = t_{u se d, ma x} \times \frac{e _{d e man d}}{Q _{ma x}}$

Maximum output insufficient ( $e_{d e man d} > Q_{ma x}$ ): The heater delivers $Q_{ma x}$ from storage. The remaining unmet demand is supplied by the instant backup element, if present:

$E_{in s t an t} = min (e_{d e man d} - Q_{ma x}, P_{in s t an t} \times Δ t) [kWh per unit]$

After determining the energy delivered, the state of charge is updated:

$S_{n e w} = clip (S + \frac{E _{c ha r g e d} - E _{d e l i v er e d}}{C _{s t or e}}, 0, 1)$

Fan Energy

For fan-assisted units, the fan consumes electrical energy proportional to the active discharge time when operating above minimum output:

$E_{f an} = \frac{P _{f an}}{1000} \times t_{u se d} [kWh per unit]$

Where $P_{f an}$ is the fan power W and $t_{u se d}$ is the time the fan runs hours. Fan energy is zero for damper-only units.

Total Energy from Supply

The total electrical energy drawn from the supply in each timestep accounts for charging, instant backup, and fan power across all units:

$E_{s u ppl y} = n \times (E_{c ha r g e d} + E_{in s t an t} + E_{f an}) [kWh]$

Total Energy Delivered to Zone

The total thermal energy delivered to the zone from all units is:

$E_{z o n e} = n \times (E_{d e l i v er e d} + E_{in s t an t}) [kWh]$

The convective fraction $f_{co n v}$ determines how this heat is split between convective and radiative components in the zone heat balance.

Outputs

Quantity	Symbol	Unit	Description
Energy delivered (storage)	$E_{d e l i v er e d}$	kWh	Heat released from thermal core per unit per timestep
Energy charged	$E_{c ha r g e d}$	kWh	Electrical energy consumed for charging per unit per timestep
Energy instant	$E_{in s t an t}$	kWh	Energy from direct-acting backup element per unit per timestep
Fan energy	$E_{f an}$	kWh	Electrical energy consumed by fan per unit per timestep
State of charge	$S$	—	Fraction of storage capacity currently held (0 to 1)
Heat retention ratio	$R_{r e t}$	—	SOC remaining after 16 hours standby at minimum output
Total energy to zone	$E_{z o n e}$	kWh	Total heat delivered to zone from all units per timestep
Total energy from supply	$E_{s u ppl y}$	kWh	Total electrical energy drawn from supply per timestep

Assumptions

The thermal core is treated as a single lumped mass. Internal temperature distribution within the core is not modelled; the SOC is a scalar quantity representing the ratio of stored energy to capacity.
SOC-dependent output power curves are piecewise-linear interpolations of test data. No physical model of core temperature or insulation conductance is used; the curves are empirical.
Charging and discharging occur simultaneously within a timestep. The ODE integrates both processes concurrently, which permits the SOC to rise or fall depending on the balance of charge and discharge power.
The instant backup element is assumed to operate at 100% efficiency (electrical energy converts directly to heat).
Fan power is consumed only when the unit is operating above minimum output (i.e. when the fan or damper is actively engaged). At minimum output, the fan is not running.
Case losses (minimum output) are always delivered to the zone. There is no mechanism to suppress heat release below the minimum output curve.
The heat retention ratio is calculated once at initialisation from the minimum output curve and storage capacity. It does not vary with ambient conditions or ageing.
For HHRSH charge control, the first 24 hours of simulation use a default full-charge strategy because insufficient demand history is available to estimate next-day requirements.
All units within a zone are identical. The demand is divided equally among them, and per-unit results are scaled by the number of units.

Cross-references

TP-01: Overview and Climate Data: external air temperature data used in HHRSH heating degree hour calculations
TP-03: External Conditions: provides external temperature for charge control logic and heating degree hour forecasting
TP-04: Space Heating Demand: determines the energy demand that storage heaters must meet each timestep
TP-16: Heat Emitters: convective fraction determines how storage heater output enters the zone heat balance
TP-17: Controls: charge control logic types (Manual, Automatic, CELECT, HHRSH) and setpoint control