Calculator methodology:
data, formulas and sources

1. How the calculator works

The calculator simulates a full year, day by day (365 days), at the location entered. For each day it estimates the thermal and electrical demand, the output of photovoltaics and of any wind turbine, and checks how BioGS-1.0, electrical storage and thermal storage cover the difference. It then sizes the system: number of BioGS-1.0 units, photovoltaic power, battery capacity and puffer (thermal buffer tank) volume.

2. Climate data

Reference photovoltaic production. The calculator asks PVGIS for the yield of 1 kWp with system losses of 14%. The yield is calculated on the horizontal plane and is then corrected with the exposure factors described below.

Climate normalization (heating only). The degree days of the typical year (base 20 °C) are divided by those of 2023, and the ratio, limited between 0.8 and 1.3, multiplies the heat loss. This is needed because 2023 was warmer than average across much of Italy and must not lead to heating being underestimated.

Altitude correction. The ERA5 temperature refers to cells of about 30 km, whose mean altitude may differ from that of the site. The altitude difference between cell and site, multiplied by a gradient of 0.45 °C per 100 m, corrects the temperature (correction limited between -4 and +8 °C).

Italian climate zone. For locations in Italy the proxy derives the climate zone (A-F, DPR 412/93) from the degree days of the typical year.

3. Thermal demand

3.1 Space heating

Simplified daily balance, inspired by EN ISO 13790 and EN ISO 52016:

Q = max(0, H × 24 × (T interna − T esterna) × fattore climatico − η × (apporti interni + apporti solari))

• H: specific heat loss of the building, in W/K = h_spec × floor area × shape factor × height factor.
• T interna: 20 °C, or the target temperature entered by the user.
• Internal gains: 3 W per m² of floor area.
• Solar gains: daily irradiance × 0.03 m² of equivalent solar area per m² of floor area (windows about 15% × solar factor 0.6, with shading and orientation).
• η: gain utilization factor, with parameter a = 4 (building of medium thermal inertia).
• Height factor: average height / 2.7 m, limited between 0.85 and 1.3.

Insulation level (h_spec in W/m²K, calibrated on a detached house of about 100 m² on two floors, with reference to TABULA/EPISCOPE and to Italian and European legal limits):

APE energy class (Italian energy performance certificate; locations in Italy only). If entered, it takes precedence over the insulation level. The class is relative to a reference building (DM 26/06/2015), so h_spec = 1.1 × the ratio between the EPgl,nren of the class and that of the reference building (midpoint of the band), then multiplied by a climate zone factor and limited to the range of the insulation levels.

The zone factor reflects the fact that the APE reference building has less stringent requirements in warm zones (2019/2021 U-values, DM 26/06/2015).

Building type (share of heat-losing envelope relative to the detached house):

Declared thermal consumption. If the user enters their own annual thermal consumption, that value always takes precedence over the model and is distributed across the days with the seasonal shape of the physical model.

3.2 Domestic hot water and appliances

• Domestic hot water: 50 liters per person per day, heated to 45 °C, distributed uniformly over the year. The temperature rise starts from the mains water temperature, approximated by the mean annual air temperature of the place (limited between 5 and 22 °C).
• Washing machine and dishwasher: 100 and 150 cycles per year per person, 15 and 10 equivalent liters per cycle, with a mean washing temperature of 50 °C. Water preheated by the puffer is assumed to be available up to 40 °C: this share is a thermal load, the remainder stays electrical.
• Number of people: if not specified, 3 people are assumed.

3.3 Swimming pool and greenhouse

• Swimming pool: 200 thermal kWh per m³ per year, concentrated in the summer months, plus 20 electrical kWh per m³ per year for recirculation and filtration, uniform over the year.
• Greenhouse: physical calculation day by day, kWh = U × area × (T target − T external) × 24 / 1000, with U in W/m²K equal to 6.2 (single cover), 4.0 (double), 3.4 (rigid), from Rutgers Cooperative Extension values.
• If the declared consumption already includes pool or greenhouse, the annual total does not change: the model uses them only to give the chart the correct seasonal shape.

4. Electrical demand

• Base consumption: this is the annual electrical consumption entered by the user. If not entered, the calculator estimates it: 300 kWh plus 900 kWh per person.
• Lighting: 8% of the base consumption is redistributed across the days in proportion to the actual hours of darkness at the place, calculated with an astronomical formula from latitude and day of the year (it also handles midnight sun and polar night). The daily factor is limited between 0.3 and 3. The annual total does not change.
• Electric car: 0.18 kWh per km, uniform throughout the year, if not already included in the declared consumption.
• Air conditioner: only if the user states they have one and declares the cooled area. Cooling demand = 0.035 kWh per m² cooled per cooling degree day (threshold 26 °C), multiplied by the solar factor of the site and divided by a SEER of 3.2.
• Pool recirculation: see section 3.3.
• Farm: in the months of May-September the pelletizing and drying loads are added (see section 7).

5. Photovoltaics, wind and storage

Photovoltaics. Daily production is the PVGIS yield of 1 kWp multiplied by the installed power and by an exposure factor:

The base yield is the PVGIS yield on the horizontal plane and the gain due to tilt is not credited: this is a conservative choice, which tends to underestimate the production of a pitched roof by a few percentage points.

If the available area is specified, photovoltaics is limited to 1 kWp every 5 m².

Wind. This is an optional integration: the installed power is set by the user. The yield does not derive from a historical wind series but from three wind categories of the site.

Electrical storage. The capacity is the smallest that eliminates the annual electrical deficit, with a minimum of 5 kWh and a maximum equal to the lesser of 60 kWh and two days of average consumption. If the limit is reached, the result flags it.

6. BioGS-1.0 and daily simulation

Product data used in the calculation (real operating conditions):

BioGS-1.0 always cogenerates heat and electricity together, in a fixed ratio: the two outputs cannot be chosen independently.

Dispatch order, for each day:

1. Photovoltaics and wind cover the electrical demand first.
2. Any renewable surplus first charges the battery, up to its free capacity.
3. The remaining surplus is converted into heat, up to the thermal demand of the day and never beyond.
4. The heat still missing is produced by BioGS-1.0. At the same time it generates the associated electricity, which covers the remaining electrical deficit. The number of operating hours is determined by the thermal demand (thermal priority) or by the electrical demand, if this requires more hours.
5. Any residual electrical deficit is discharged from the battery and, if that is not enough, remains as grid import.

The battery carries its state of charge from one day to the next (this is the only point of the calculation where days are not independent), starting from a steady-state level obtained with a first pass over the year. Since the surplus charges the battery first, a smaller part becomes heat and BioGS-1.0 works a few more hours.

Sizing.

• BioGS-1.0 units: the minimum number for which, on every day of the year, the required operating hours do not exceed 24, with the battery sized for that number of units.
• Photovoltaics: the minimum power that, with the battery within the autonomy limit, eliminates the annual electrical deficit (tolerance 0.05 kWh/year), found by bisection. The calculator also indicates the day of the year that determines this sizing.
• Puffer: the volume derives from the maximum daily mismatch between heat production and demand. A typical hourly profile of thermal demand is used: 30% between midnight and 6 a.m., 15% between 6 and 9, 15% between 9 and 18, 40% between 18 and midnight. The PV surplus is concentrated between 11 and 15; BioGS-1.0 runs a single continuous cycle, with a start time chosen to minimize the mismatch. The liters are obtained with a temperature difference of 25 °C and 1.163 Wh per liter per °C.

7. Farm: from biomass to pellet

The agricultural pathway assesses whether the farm's waste is enough to fuel BioGS-1.0.

• Conversion to equivalent pellet: dry mass = quantity × (1 − moisture); pellet = dry mass / 0.9, multiplied by a process yield of 95% (grinding plus pelletizing). If the biomass is already pellet, the yield is 1.
• Grinding: wood chips 11 kWh/t (fine shredding); logs and brushwood 30 kWh/t (chipping plus fine shredding).
• Press: throughput of 15 kg/h per installed kW (66.7 kWh/t), 6 net working hours per day, smallest commercial size among 3, 4, 5.5, 7.5, 11, 15, 18.5, 22, 30, 37, 45, 55 and 75 kW that completes the campaign.
• Campaign: drying and pelletizing in the months of May-September, when there is more energy surplus.
• Drying: down to 14% moisture, with 1 thermal kWh per kg of evaporated water. The user chooses whether to use BioGS-1.0 heat (added to the thermal demand) or natural drying. The dryer fans absorb 3% of the heat.
• Shells and stones: ready to use, without grinding. They are dried only if they exceed 10% moisture. They can be at most 40% of the total fuel (technical constraint of BioGS-1.0).
• Mix: own waste is used first (at 2.4 kg/h) until exhausted, then purchased certified A1 or A2 pellet (at 2.2 kg/h) for the remaining hours. The calculator also indicates what share of the hours is covered by own waste.

Sources for the process data: Forest Research UK (2011), "Wood pellets production"; MDPI Sustainability 17(1):140 (2024); MDPI Energies 16(13):4894 (2023); TCPEL, "Biomass Hammer Mill" guide.

8. Biomass, biochar and CO₂

The value is a sequestration potential and not a certified carbon credit. No carbon permanence factor is applied: it will be added when further analyses become available.

9. Reliability of the result

The calculator indicates a reliability level based on three real data points: electrical consumption, thermal consumption and a precise address (with street or house number).

10. Model limitations

• it is a preliminary estimate, not a detailed engineering design;
• dispatch is daily, not hourly; the hourly profile is used only to size the puffer;
• the climate is that of 2023 normalized for heating, not a forecast;
• wind is an average yield per category, not a historical series;
• the mains water temperature is approximated by the mean annual air temperature;
• thermal demand depends on the quality of the building data entered;
• CO₂ sequestration is a potential without a permanence factor.

11. References

PVGIS (JRC, European Commission);
ERA5 (Copernicus Climate Change Service, ECMWF);
Open-Meteo;
OpenStreetMap (Nominatim, Photon);
EN ISO 13790 and EN ISO 52016;
DM 26/06/2015 (energy classification);
DPR 412/93 (climate zones);
TABULA/EPISCOPE;
Rutgers Cooperative Extension (greenhouse coverings).