Model a UK home solar PV installation: system size, install cost, sunlight hours and electricity prices, and watch cumulative savings overtake the install cost at the payback year.
Annual generation ≈ system size (kW) × daily sunlight hours × 365 × a performance ratio of 0.8 (losses from inverter efficiency, wiring, temperature and soiling). Each year the panels degrade by about 0.5%, while grid electricity is inflated by 3% per year. Annual saving = self-used kWh × electricity price + exported kWh × export tariff. Payback is the first year cumulative savings reach the install cost.
Electricity you generate and use immediately is worth the full retail price you would otherwise have paid; electricity you export to the grid is worth only the (much lower) export tariff. A battery raises the self-use fraction from a typical 30-40% to 60-70%, which is usually a bigger lever on payback than adding more panels.
Panels are warrantied for 25-30 years and typically lose about 0.5% of output per year, so year-25 generation is roughly 12% lower than year one. Because electricity prices tend to rise faster than panel output falls, later years of the system's life are usually its most valuable — a rising price times a slowly falling generation still grows the annual saving.
This simulation models a UK home solar PV installation over its 25-year warrantied life. Annual electricity generation is system size × daily sunlight hours × 365 days × an 0.8 performance ratio, degrading roughly 0.5% a year. Each unit of that electricity is worth either the full retail electricity price (if used on-site) or the lower export tariff (if sent back to the grid), and the retail price itself is assumed to inflate 3% a year. Cumulative savings are plotted against the flat install cost, and the year they cross is the payback period.
A red flat line is the one-off install cost. A green curve is cumulative savings, growing faster in later years as electricity prices rise faster than panel output degrades. Where the green curve crosses the red line (marked with a pulsing yellow dot and dashed guide) is the payback year — after that, every pound saved is pure return on the investment.
Drag System size and Install cost to size the installation, Daily sunlight hours to reflect your region (2-3h for cloudy northern sites, 4-6h for sunny southern ones), and Electricity price / Export tariff / Self-use fraction to model your tariff and habits. The three presets show a small south-facing roof, a large north-facing roof, and a battery-equipped system with high self-use.
Raising the self-use fraction from 40% to 65% (roughly what a home battery achieves) often shortens payback more than adding another kW of panels, because self-used electricity is worth several times more per kWh than exported electricity under a typical UK export tariff.
The performance ratio captures real-world losses that never show up on a panel's headline efficiency rating — inverter conversion losses, cable resistance, panels running hotter than their rated test temperature, dust and soiling, and slight shading. A well-installed UK system typically achieves a performance ratio around 0.75-0.85, so 0.8 is a reasonable mid-range estimate.
Because most UK export tariffs pay only a few pence per kWh, while retail electricity costs several times as much. Every kWh you generate and use yourself avoids buying a full-price unit from the grid, while every exported kWh only earns the much smaller export rate — so self-use is worth far more per unit than export.
Most manufacturers warranty output at around 80-87% of the original rating after 25 years, which corresponds to roughly 0.4-0.6% degradation per year. This simulation uses 0.5% a year as a representative figure, meaning year-25 generation is about 12% lower than year one.
3% is a commonly used long-run planning assumption for UK household electricity price inflation, roughly tracking general inflation over long periods, though real-world prices have been far more volatile year to year (including sharp spikes and falls). It is a simplification used here to keep the model illustrative rather than a market forecast.
It multiplies the first year's generation in kWh by approximately 0.000233 tonnes of CO2 per kWh, a commonly cited grid carbon-intensity factor for displaced grid electricity. It is an approximation — actual grid carbon intensity varies by time of day, season and year as the generation mix changes.