This chapter covers the physics and engineering of solar photovoltaic systems with enough depth to understand sizing calculations and production estimates — without requiring an electrical engineering degree.
A silicon photovoltaic cell converts photons (light) into electron flow (current) via the photovoltaic effect. When photons with sufficient energy hit the silicon junction, they excite electrons across a bandgap, creating a voltage. Connect many cells in series and parallel to form a panel (also called a module).
Key quantities:
A typical residential panel: 400–440 Wp rated, ~2.0 m² area, ~22% efficiency.
Irradiance (W/m²) is the instantaneous solar power per unit area. It peaks near 1,000 W/m² at noon on a clear summer day.
Peak Sun Hours (PSH) normalizes daily solar energy to equivalent hours at 1,000 W/m²:
PSH = Daily irradiation (Wh/m²) / 1,000 (W/m²)
If a location receives 5.0 kWh/m²/day of solar energy, it has 5.0 PSH/day.
PSH depends on:
| City | Country | Annual kWh/m²/yr | Avg PSH/day | Jan PSH | Jul PSH |
|---|---|---|---|---|---|
| Seville | Spain | 1,900 | 5.2 | 2.8 | 7.8 |
| Nice | France | 1,700 | 4.7 | 2.5 | 7.1 |
| Rome | Italy | 1,750 | 4.8 | 2.6 | 7.4 |
| Madrid | Spain | 1,800 | 4.9 | 2.7 | 7.6 |
| Barcelona | Spain | 1,700 | 4.7 | 2.5 | 7.0 |
| Lyon | France | 1,500 | 4.1 | 1.9 | 6.5 |
| Paris | France | 1,300 | 3.6 | 1.6 | 5.8 |
| Brussels | Belgium | 1,200 | 3.3 | 1.4 | 5.5 |
| Berlin | Germany | 1,200 | 3.3 | 1.3 | 5.6 |
| Amsterdam | Netherlands | 1,100 | 3.0 | 1.2 | 5.0 |
| London | UK | 1,050 | 2.9 | 1.1 | 4.9 |
| Dublin | Ireland | 1,000 | 2.7 | 1.0 | 4.7 |
| Stockholm | Sweden | 1,050 | 2.9 | 0.6 | 5.8 |
| Helsinki | Finland | 950 | 2.6 | 0.3 | 5.5 |
| Lisbon | Portugal | 1,950 | 5.3 | 3.0 | 7.9 |
| Athens | Greece | 1,900 | 5.2 | 2.8 | 7.8 |
| Bucharest | Romania | 1,450 | 4.0 | 1.8 | 6.8 |
| Warsaw | Poland | 1,100 | 3.0 | 1.0 | 5.4 |
| New York | USA | 1,400 | 3.8 | 2.5 | 5.5 |
| Chicago | USA | 1,300 | 3.6 | 2.0 | 5.6 |
| Los Angeles | USA | 1,950 | 5.3 | 4.2 | 6.5 |
| Denver | USA | 1,800 | 4.9 | 3.8 | 6.4 |
| Miami | USA | 1,900 | 5.2 | 4.2 | 6.1 |
| Seattle | USA | 1,100 | 3.0 | 1.5 | 5.0 |
| Toronto | Canada | 1,300 | 3.6 | 1.9 | 5.6 |
| Montreal | Canada | 1,250 | 3.4 | 1.6 | 5.5 |
| Sydney | Australia | 1,700 | 4.7 | 5.0 | 3.2 |
| Melbourne | Australia | 1,500 | 4.1 | 4.5 | 2.5 |
| Auckland | New Zealand | 1,350 | 3.7 | 4.5 | 2.5 |
| Tokyo | Japan | 1,300 | 3.6 | 2.8 | 3.9 |
| Singapore | Singapore | 1,550 | 4.2 | 4.1 | 4.3 |
Source: PVGIS (EU JRC), Global Solar Atlas. Values are approximate and vary with specific micro-siting.
Efficiency = Rated Power (Wp) / (Panel Area (m²) × 1,000 W/m²)
For a 420 Wp panel with area 1.95 m²:
Efficiency = 420 / (1.95 × 1000) = 21.5%
Monocrystalline silicon panels (dominant residential technology as of 2024) achieve 20–23% efficiency. Bifacial panels can add 5–15% in favorable conditions (light-colored roofs, elevated mounting).
Solar panels lose efficiency as they heat up. The typical temperature coefficient is −0.35% to −0.40% per °C above the STC temperature of 25°C.
On a hot summer day, panel temperature can reach 60–70°C (20–40°C above ambient due to solar absorption). This represents a 12–17% power reduction from rated:
Power_actual = Power_rated × [1 + TempCoeff × (T_cell − 25°C)]
= 420 W × [1 + (−0.0038) × (65 − 25)]
= 420 W × [1 − 0.152]
= 356 W
Ironically, cold sunny winter days can produce more than rated power if irradiance is high.
The rated power of your panels is never what reaches your appliances. Losses stack multiplicatively:
| Loss factor | Typical range | Typical value |
|---|---|---|
| Temperature derating | 5–15% | 8% |
| Soiling (dust, bird droppings) | 2–10% | 5% |
| Shading (partial, nearby objects) | 0–25% | 5% (varies widely) |
| Wiring losses (DC + AC) | 1–3% | 2% |
| Inverter efficiency | 2–5% loss | 97% inverter |
| Mismatch (panel variation) | 1–3% | 2% |
| Total system efficiency | ~80% |
The widely-used performance ratio (PR) captures all losses combined:
Annual yield (kWh) = Installed peak power (kWp) × Annual PSH × PR
With PR = 0.80 and Paris-level irradiation (1,300 kWh/m²/yr = 1,300 PSH/yr):
1 kWp system → 1,300 × 0.80 = 1,040 kWh/year
This figure — kWh per kWp per year — is called specific yield. Rough ranges:
| Climate zone | Specific yield (kWh/kWp/yr) |
|---|---|
| Northern Europe (UK, Benelux) | 850–1,100 |
| Central Europe (France, Germany) | 1,000–1,350 |
| Southern Europe (Spain, Italy) | 1,350–1,600 |
| US Southwest | 1,400–1,700 |
| US Northeast | 1,100–1,400 |
| Australia (most of country) | 1,300–1,600 |
The inverter converts the DC output of the panels into AC electricity your home can use.
All panels in series → one central inverter. Simple and cost-effective. Weakness: if one panel is shaded, the whole string output drops.
One inverter per panel (mounted on the roof). Each panel operates at its individual maximum power point. Advantage: shading or soiling on one panel does not affect others. Cost: 20–30% higher than string system.
Each panel has a DC optimizer that tracks its individual maximum power point; the string inverter handles the AC conversion. Intermediate cost and performance.
A string inverter with an integrated battery charger/controller. Handles solar input, battery charge/discharge, and grid interaction in one unit. Required for grid-tied solar + battery systems.
The ideal orientation in the northern hemisphere is true south, at a tilt of ~30–40° from horizontal. Deviations reduce yield:
| Orientation | Relative yield vs. optimal |
|---|---|
| South, 30–40° | 100% (reference) |
| South, 15° (flatter) | 95% |
| South, 60° (steeper) | 92% |
| SE or SW, 35° | 92–95% |
| East or West, 35° | 75–82% |
| North, 35° | 55–65% |
| Flat (0°) | 85–90% |
East+West split: Some installers mount panels on both sides of a pitched roof. Total yield is slightly less than a pure south system, but the generation profile is broader (earlier morning and later afternoon production), which can improve self-consumption.
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