TP-18: PV and Battery | HEM Reference

Overview

TP-18 calculates electrical energy generation from photovoltaic (PV) panels and the charge/discharge behaviour of electrical battery storage. PV generation is determined from solar irradiance on the panel surface, adjusted for system performance, shading, and inverter efficiency. Battery storage shifts surplus generation in time, subject to capacity limits, round-trip efficiency losses, state of health degradation, and temperature-dependent capacity reduction.

The PV calculation follows BS EN 15316-4-3:2017 for the energy yield methodology. Inverter efficiency curves are derived from empirical data. The battery model uses a single-node energy balance with one-way efficiency derived from the round-trip charge/discharge efficiency.

Inputs

Photovoltaic system

Parameter	Symbol	Unit	Description
Peak power	$P_{p k}$	kW	Electrical power at 1 kW/m² irradiance and 25 °C
Ventilation strategy	—	—	One of: unventilated, moderately ventilated, strongly or forced ventilated, rear surface free
Pitch	$β$	degrees	Tilt angle from horizontal (0° = horizontal, 90° = vertical)
Orientation	$γ$	degrees	Azimuth of panel normal ( $- 180$ to $180$ ; south = 0°, east = 90°, west = $- 90$ °)
Base height	$h_{ba se}$	m	Height of the lowest panel edge above ground
Panel height	$h_{p an e l}$	m	Physical height of the panel along its surface
Panel width	$w$	m	Width of the panel
Inverter peak DC power	$P_{in v, D C}$	kW	Maximum DC power input the inverter accepts
Inverter peak AC power	$P_{in v, A C}$	kW	Maximum AC power the inverter can deliver
Inverter location	—	—	Whether the inverter is inside or outside the dwelling
Inverter type	—	—	String inverter or optimised (micro) inverter

Battery storage

Parameter	Symbol	Unit	Description
Nominal capacity	$C_{n o m}$	kWh	Maximum energy storage at rated conditions
Round-trip efficiency	$η_{r t}$	—	Charge/discharge round-trip efficiency (0 to 1)
Battery age	$a$	years	Age of battery at start of simulation
Minimum charge rate	$\dot{Q}_{min}$	kW	Minimum power below which PV charging is rejected
Maximum charge rate	$\dot{Q}_{c h, ma x}$	kW	Maximum power the battery accepts during charging
Maximum discharge rate	$\dot{Q}_{d i s, ma x}$	kW	Maximum power the battery can deliver during discharge
Battery location	—	—	Inside or outside the dwelling
Grid charging	—	—	Whether charging from the electricity grid is permitted

Calculation

PV energy generation

Solar irradiance at the panel surface

The direct and diffuse components of solar irradiance on the tilted panel surface, $I_{so l, d i r}$ and $I_{so l, d i f}$ (W/m²), are obtained from TP-03: External Conditions using the panel pitch $β$ and orientation $γ$ . See TP-08: Solar Gains and Shading for the irradiance decomposition method.

Shading factors

Shading reduction factors for direct and diffuse radiation, $f_{s h, d i r}$ and $f_{s h, d i f}$ , are calculated from the panel geometry (base height, projected height, and width) and any defined shading obstacles, following the methodology in TP-08: Solar Gains and Shading.

The projected height of the panel is:

$h_{p r o j} = h_{p an e l} \times sin (β)$

where $β$ is the panel pitch in radians.

System performance factor

The system performance factor $f_{p er f}$ accounts for losses from wiring, module mismatch, soiling, and inverter inefficiency. Values are taken from Table C.4, Annex C of BS EN 15316-4-3:2017, adjusted upward by a factor of $0.85/0.80$ based on empirical UK performance data:

Ventilation strategy	$f_{p er f}$
Unventilated	0.81
Moderately ventilated	0.85
Strongly or forced ventilated	0.87
Rear surface free	0.87

The "rear surface free" category uses the same factor as "strongly or forced ventilated". BS EN 15316-4-3:2017 section 6.2.4.7.2 assigns a factor of 1.0 to rear surface free installations, but this would imply zero system losses despite section 6.2.4.7.5 stating that the factor accounts for inverter and other losses. The specification therefore treats rear surface free identically to strongly ventilated.

Inverter shading inefficiency

When the direct shading factor $f_{s h, d i r} < 1$ , partial shading on the panel reduces inverter conversion efficiency beyond the reduction in incident radiation. This effect depends on the inverter type.

The inverter shading efficiency factor $η_{s h}$ is modelled as a two-piece quadratic function of the direct shading factor $f_{s h, d i r}$ :

$η_{s h} = min (1, {a \cdot f_{s h, d i r}^{2} + b \cdot f_{s h, d i r} + c d \cdot f_{s h, d i r}^{2} + e \cdot f_{s h, d i r} + g if f_{s h, d i r} < f_{t h r es h} if f_{s h, d i r} \geq f_{t h r es h})$

The coefficients and threshold for each inverter type are:

Coefficient	String inverter	Optimised inverter
$f_{t h r es h}$	0.70	0.42
$a$	2.7666	2.7666
$b$	$- 4.3397$	$- 4.3397$
$c$	2.2201	2.2201
$d$	$- 1.9012$	$- 0.2024$
$e$	4.8821	0.4284
$g$	$- 1.9926$	0.7721

When $f_{s h, d i r} = 1$ (no direct shading), $η_{s h} = 1$ .

The lower portion of the curve (below $f_{t h r es h}$ ) shares the same coefficients for both inverter types. The upper portion diverges: string inverters suffer greater efficiency loss under partial shading than optimised (micro) inverters, which condition power at the module level.

These curves are derived from empirical data on normalised power output under partial panel covering, disaggregating the inverter efficiency effect from the reduction in incident radiation.

Solar irradiation

The solar irradiation at the panel surface for the timestep, combining direct and diffuse components with their respective shading factors, is:

$E_{so l} = (I_{so l, d i r} \times f_{s h, d i r} + I_{so l, d i f} \times f_{s h, d i f}) \times \frac{Δ t}{1000} [kWh/m²]$

where $Δ t$ is the timestep duration in hours and the factor of 1000 converts W to kW.

DC energy input

The DC energy input to the inverter is calculated per BS EN 15316-4-3:2017:

$E_{D C} = \frac{E _{so l} \times P _{p k} \times f _{p er f} \times η _{s h}}{0.972 \times I _{r e f}}$

where:

$I_{r e f} = 1 kW/m²$ is the reference solar irradiance
The divisor $0.972$ removes the inverter efficiency component that is already embedded in $f_{p er f}$ (from BS EN 15316-4-3:2017), since inverter DC-to-AC conversion is applied separately

Inverter DC-to-AC efficiency

The inverter conversion efficiency varies with load. The ratio of rated output is:

$r = \frac{m i n ( P _{in p u t} , P _{in v, D C} )}{P _{in v, D C}}$

where $P_{in p u t} = E_{D C} /Δ t$ is the instantaneous DC power input in kW.

When $r = 0$ , the inverter efficiency $η_{in v} = 0$ . Otherwise, the efficiency is the minimum of three empirical curves (expressed as percentages):

$η_{1} = 97.2 \times (1 - \frac{0.18}{1 + e ^{21 r}})$

$η_{2} = 0.5 \times cos (π r) + 96.9$

$η_{3} = 97.2 \times tanh (30 r)$

$η_{in v} = \frac{m i n ( η _{1} , η _{2} , η _{3} )}{100}$

This three-curve system captures the rapid efficiency rise at low load fractions, the plateau at mid-range, and the slight droop near full load. The curves are fitted to measured performance data for residential-scale inverters.

AC energy output

The AC energy produced in the timestep is capped at both the inverter DC input limit and the AC output limit:

$E_{A C} = min (min (E_{D C}, P_{in v, D C} \times Δ t) \times η_{in v}, P_{in v, A C} \times Δ t) [kWh]$

The first inner minimum prevents the DC energy exceeding the inverter's rated DC input capacity. The result, after applying the inverter efficiency, is then capped at the inverter's AC power rating multiplied by the timestep duration.

Energy lost to inverter conversion and capping is:

$E_{l os t} = E_{D C} - E_{A C} [kWh]$

The AC energy produced is supplied to the energy supply connection, where it offsets electrical demand. Any surplus may charge a battery or be exported.

Battery charge and discharge

State of health

The battery's state of health (SoH) degrades linearly with age:

$S oH = max (1 - 0.04 \times a, 0)$

where $a$ is the battery age in years. This represents a 4% capacity loss per year, reaching 60% remaining capacity at 10 years.

The effective maximum capacity is:

$C_{ma x} = C_{n o m} \times S oH$

One-way efficiency

The round-trip efficiency $η_{r t}$ is decomposed into equal one-way charge and discharge efficiencies:

$η_{o w} = η_{r t}$

The reverse one-way efficiency, used when converting stored energy back to delivered energy, is:

$η_{o w, r e v} = \frac{1}{η _{o w}}$

Temperature-dependent capacity

For batteries located outside the dwelling, capacity is reduced at low temperatures. The temperature capacity factor $f_{t e m p}$ is:

$f_{t e m p} = {1.0 0.8496 + 0.01208 \times T_{ai r} - 0.000228 \times T_{ai r}^{2} if T_{ai r} > 20 °C otherwise$

where $T_{ai r}$ is the external air temperature in °C from TP-03: External Conditions. The result is clamped to the range 0, 1.

For batteries located inside the dwelling, $T_{ai r}$ is fixed at 20 °C, giving $f_{t e m p} = 1$ .

State of charge

The state of charge at any point is:

$S o C = \frac{E _{s t or e d}}{C _{ma x}}$

where $E_{s t or e d}$ is the current energy stored in the battery (kWh), clamped to the range 0, 1 for rate calculations.

Maximum charge and discharge energy

The maximum energy that can be charged in a timestep is:

$E_{c h, ma x} = \dot{Q}_{c h, ma x} \times Δ t [kWh]$

The maximum energy that can be discharged in a timestep is:

$E_{d i s, ma x} = - \dot{Q}_{d i s, ma x} \times Δ t [kWh]$

The discharge value is negative by convention (energy leaving the battery).

Charging

When surplus energy is available (negative electrical demand $E_{d e man d} < 0$ ), the battery charges. The supply power must exceed the minimum charge rate $\dot{Q}_{min}$ for PV charging to proceed. Grid charging, when permitted, bypasses this minimum rate check.

The energy available to enter the battery is:

$E_{a v ai l} = min (- E_{d e man d} \times η_{o w} \times S oH \times f_{t e m p}, E_{c h, ma x})$

The stored energy is then updated:

$E_{s t or e d}^{'} = min (C_{ma x}, max (0, E_{s t or e d} + E_{a v ai l}))$

The energy accepted by the battery (the actual change in stored energy) is:

$E_{a cce pt e d} = E_{s t or e d}^{'} - E_{s t or e d}$

The energy drawn from the supply to achieve this charge is:

$E_{s u ppl y} = \frac{E _{a cce pt e d}}{η _{o w}}$

The charging time within the timestep is tracked to prevent over-charging when multiple charge events occur in a single timestep. If the remaining time in the timestep has been fully consumed by charging, no further charge is accepted.

Discharging

When there is electrical demand ( $E_{d e man d} > 0$ ), the battery discharges. During grid-charging periods, discharge is suppressed (maximum discharge is set to zero).

The energy available from the battery is:

$E_{a v ai l} = \frac{m a x ( - E _{d e man d} , E _{d i s, ma x} )}{η _{o w}} \times S oH \times f_{t e m p}$

Note that $E_{d i s, ma x}$ is negative, so $max (- E_{d e man d}, E_{d i s, ma x})$ selects the less negative value (smaller magnitude), limiting discharge to either the demand or the maximum discharge rate.

The stored energy update and clamping follow the same logic as charging. The energy delivered to the supply is:

$E_{d e l i v er e d} = - E_{a cce pt e d} \times η_{o w}$

where $E_{a cce pt e d}$ is negative during discharge. The delivered energy is therefore positive, representing energy returned to the electrical supply.

Timestep reset

At the end of each timestep, the cumulative charging time counter is reset to zero in preparation for the next timestep.

Outputs

Quantity	Symbol	Unit	Description
PV energy produced	$E_{A C}$	kWh	AC electrical energy generated per timestep
PV energy lost	$E_{l os t}$	kWh	Energy lost to inverter conversion and capping per timestep
Battery state of charge	$S o C$	—	Ratio of stored energy to effective maximum capacity
Battery energy accepted	$E_{a cce pt e d}$	kWh	Change in stored energy per charge/discharge event
Energy to/from supply	—	kWh	Net energy exchanged with the electrical supply per event

Assumptions

The system performance factor $f_{p er f}$ is constant for a given ventilation strategy. It does not vary with temperature, irradiance level, or panel age.
The inverter efficiency component embedded in $f_{p er f}$ from BS EN 15316-4-3:2017 is approximately 0.972 (97.2%). This is removed before applying the explicit inverter efficiency curve.
The inverter DC-to-AC efficiency curve is fitted to residential-scale inverter data and does not vary by manufacturer or rated power.
Inverter shading inefficiency applies only to the direct radiation component. Diffuse shading affects the whole panel approximately uniformly and is accounted for separately through the reduction in incident radiation.
Battery state of health degrades linearly at 4% per year, based on manufacturer warranty data (60% remaining capacity at 10 years). This is intentionally conservative.
The one-way charge and discharge efficiencies are assumed equal, each being the square root of the round-trip efficiency.
Charge and discharge rates are currently independent of state of charge. The model includes placeholder functions for SoC-dependent rate limiting, but these return 1.0 (no reduction) pending further empirical evidence.
For batteries located inside the dwelling, the ambient temperature is fixed at 20 °C regardless of actual zone temperatures.
The battery starts each simulation with zero stored energy.
There is no explicit self-discharge model. Energy losses occur only through charge/discharge efficiency, state of health degradation, and temperature-dependent capacity reduction.

Cross-references

TP-01: Overview and Climate Data -- climate data provides solar irradiance and external temperature inputs
TP-03: External Conditions -- direct and diffuse solar irradiance on tilted surfaces; external air temperature for battery capacity adjustment
TP-08: Solar Gains and Shading -- shading reduction factors for direct and diffuse radiation on PV panels