How does energie27 calculate? The model

An hourly model of one household: 8,760 hours (365 × 24) with generation, consumption, battery and car, then consumption from and feed-in to the grid × the price of that hour. It runs entirely in the browser (TypeScript, no libraries); only postcode, orientation and tilt go through our server to PDOK and PVGIS. The explanation in plain language is in How does this calculator work?; this page is also available as A4 (pdf) download.

Input: 25 parameters

Solar panels (8): number of panels, watt peak, orientation, kWh per kWp, age, degradation per year, measured annual yield and the distribution over the months.
Household (6): annual consumption, workdays at home during the day, share of shiftable consumption that runs smartly, weeks away, the daytime share and the night-time share.
Car (5): annual consumption, charging moment, charging power, three phases and workdays the car is at home during the day.
Heat pump and air conditioning (2): the annual consumption of each.
Battery (3): capacity, power and losses (round-trip loss, standby, usable share, AC or DC).
Weather (1): the year whose hourly KNMI weather distributes the yield.

Calibration tunes three of them to the annual statement: the annual consumption, the daytime share and the night-time share (see below). That is the starting point for simulating all scenarios. Contract and prices come on top of that separately.

Hourly balance

net = consumption + car + heat pump + air conditioning + standby + battery charging − generation − battery discharging
consumption = max(net, 0) and feed-in = max(−net, 0), for every hour

Hourly prices: the day-ahead prices (EnergyZero), converted to Dutch time. The duplicate hour in October is averaged, the missing hour in March copied; 29 February is dropped.

Generation

annual yield = panels × watt peak × kWh per kWp × (1 − age × degradation)

The kWh per kWp and the monthly distribution come from PVGIS 5.3 (14% system losses, no shade); east-west is the average of two calculations. Without PVGIS: 925 kWh per kWp × a factor for orientation and tilt.
The months are redistributed with the sunshine KNMI measured in the year of the hourly prices: weight = base × max(0, 1 + 0.85 × (sun ÷ normal − 1)), then normalized so the annual yield stays the same. The 0.85: sunny years are warmer and KNMI measures on a flat surface.
The shape over the day is a solar arc, sin(πx) to the power 1.3 × a Gaussian weighting around solar noon, shifted by orientation (1.2 hours for south-east and south-west, 2.4 hours for east and west). For any orientation other than south the arc itself is skewed (time warped with a power), so the peak really falls at that hour: checked against the position of the sun and the meter of an east-facing roof. Each hour is scaled by the measured global radiation (KNMI, hourly values) relative to the monthly average for that hour, at most 5×; each month is then brought back exactly to the monthly yield.
Measured annual yield is converted to a normal year with the sunshine at the three nearest KNMI stations, weighted by 1 ÷ distance.

Consumption

Two own daily profiles (away during the day and home during the day) with a monthly factor from 0.86 in summer to 1.20 in December. On 0 to 5 workdays the home profile; weekends always count as home. The annual total stays the same.
Weeks away per month (0 to 4, in the middle of the month; default 1 in February, May, July and August): 30% standby consumption, even over the day (with a base load only that); the other days scale up.
Base load (optional, in watts): the same every hour, also on holiday, at most 90% of household consumption; the rest follows the daily profiles.
Shiftable consumption (washing machine, dishwasher and dryer: 530 kWh per year, at most 30%) goes greedily to the hours with the largest solar surplus, at most 2 kW per hour; with a dynamic contract the rest goes to the cheapest hours.
Heat pump: the annual consumption you enter, or an estimate from gas: (gas − cooking) × 8.79 kWh per m³ × 0.9 ÷ SCOP (3.5 with radiators, 4.2 with underfloor heating). A fixed monthly distribution (17% in January, 2% in the summer months) and a daily profile; 25% (hot water) is shiftable, if the hot water comes from the heat pump.
Water heater (under Hot water: heat pump water heater or electric water heater): by default 700 or 2,200 kWh per year, about the same every day (10% more in winter, 10% less in summer). Without control it heats up at 7–9 and 18–21 h. Smart-controlled it goes to the solar surplus first, at the power of the water heater (0.5 kW, electric 2 kW), and the rest to the cheapest hours of that day (without hourly prices at night). It shifts within a day, not across days.
Air conditioning: m² × 50 to 90 W per m² × 400 full-load hours ÷ SEER 5.5; from May to September, mainly between 15:00 and 17:00, scaled per day by that day's sun.

Electric car

0.17 kWh per km, including charging losses. In the evening: from 18:00 at full power. During the day: up to 3.7 kW from 10:00. On solar surplus: the hours with the largest surplus, from 1.4 kW (4.1 kW for a charger that does not switch to 1 phase). On hourly price: sessions of 20 kWh (within a month) in the cheapest hours when the car is at home (weekends unless the car is away during the day then). Controlled by the supplier: the same sessions, spread evenly over the cheapest half of those hours, with at most a third of the charging power.

Home battery

Efficiency per direction is the square root of (1 − round-trip loss), default 10% round-trip loss; 90% of capacity usable; 30 W standby; DC-coupled charging from solar × 1.06.
Self-consumption: greedy per hour, charge surplus and discharge deficit, within power and state of charge; not from the grid.
Smart on hourly prices: dynamic programming over a grid of the state of charge (10 to 60 steps of about 0.1 kWh). Every day a horizon of 48 hours (today and tomorrow, the day-ahead prices), solved by backward induction; only the first 24 hours are executed. The charge left at the end is valued at the lowest feed-in price in the horizon. A perfect forecast of sun and consumption. Planned on an average (median) supplier; every supplier is billed on the same flows.
Imbalance trading: a table (capacity × power × customer share), precomputed with TenneT's quarter-hour imbalance prices, trilinearly interpolated and added to smart control.

Price and bill

dynamic: consumption × (market price × 1.21 + mark-up + energy tax) − feed-in × (market price × 1.21 + feed-in rule) + 12 × fixed costs per month
fixed: consumption × (supply rate + energy tax) − feed-in × (compensation − feed-in costs) − tier + 12 × fixed costs per month
bill = electricity + grid costs − tax reduction

Mark-up and energy tax include VAT; VAT is added only to the market price. With curtailment, no feed-in at a negative price.
Fixed contracts: the model contract with a 1-year fixed rate. A tier (staffel) is an amount per month per band of annual feed-in.
Net metering (the past year): with a fixed contract on the annual balance; with a dynamic contract, energy tax and mark-up are refunded on the smaller of total feed-in and total consumption.
Grid costs per grid operator (via the postcode) and connection, pro rata per day across tariff periods.
Price change only on market prices: (1 + i) to the power of the number of years between the past year and the calculation year, with i from PBL (Climate and Energy Outlook), otherwise from CPB. Energy tax follows the table per year.

Calibration to the annual statement

Three parameters, fitted to the kWh consumed, consumed at the off-peak rate and fed in on the annual statement: household consumption (a fixed-point correction on consumption − feed-in), the daytime share, the weight of consumption in sunny hours (bisection in 20 steps, between 0.25 and 3), and the night-time share, the weight of consumption between 23:00 and 7:00, fitted to consumption at the off-peak rate (workdays 23:00–7:00 and the weekend; bisection between 0.25 and 4). At most three alternating rounds, five with all three. The result applies to the past year, the calculation year and all comparisons.

Testing

Over 200 automated tests with golden values and invariants: the energy balance closes, the state of charge stays within usable capacity, smart control is never more expensive than self-consumption, net metering never more expensive than without, a larger battery never feeds in more, calibration hits its targets, and the difference per option equals the difference of two calculations.

Limitations

Hourly values average out short peaks: self-consumption without a battery comes out 2 to 5 percentage points too high.
A perfect forecast: smart control and imbalance trading rather too favourable.
Heat pump and air conditioning follow a fixed pattern, not the temperature; the SCOP is a seasonal average.
Charging on solar surplus is an upper limit: the car is not always at home.
The difference between two choices is more reliable than the amount itself.

Questions and feedback about the model are welcome: info@magict.nl. Reuse only with attribution (energie27.nl).