Solar

Photovoltaic (PV) cells turn sunlight directly into electricity. Learn how cells work, I–V and P–V curves, maximum power point tracking, temperature and irradiance effects, energy yield, and how to size and string a rooftop system.

A PV cell is a large silicon diode. Photons with enough energy knock electrons free, and the cell's built-in electric field sweeps them into a current. Cells are wired into modules (panels), modules into strings, and strings feed an inverter that converts DC to grid AC.

Solar is now the cheapest new electricity in much of the world. Designing a PV system means understanding how much energy the site produces, how temperature and shading affect output, and how to match panels to the inverter safely.

An analogy

A solar panel is like a water wheel under a rain shower: more sunshine is heavier rain (more current), but how hard it can push (voltage) is fixed by the wheel's design — and on a hot day the wheel gets sluggish.

How a PV cell works

Silicon is doped to form a p–n junction. Light creates electron–hole pairs; the junction's field separates them, producing a current roughly proportional to irradiance. The cell's voltage (~0.6–0.7 V) is set by the junction, so modules put 60–144 cells in series.

Ratings and STC

Panels are rated at Standard Test Conditions: 1000 W/m², 25 °C cell temperature, AM1.5 spectrum. A '400 W' panel produces 400 W only under those conditions; real output depends on sun angle, clouds, dirt and temperature.

I–V curve and MPPT

A PV module's current stays near I_sc until the voltage approaches V_oc, where it falls sharply. Power peaks at the 'knee' — the maximum power point. Because the MPP moves with irradiance and temperature, inverters and charge controllers run MPPT algorithms (perturb-and-observe, incremental conductance) to track it continuously.

Temperature and shading

Voltage falls ~0.3 %/°C as cells heat, so a panel at 65 °C loses about 14 % power. Cold mornings raise V_oc — the worst case for inverter voltage limits. Partial shading of a few cells can collapse a whole string's output; bypass diodes and module-level power electronics (optimisers, micro-inverters) mitigate it.

System design and grid integration

String design keeps V_oc at the coldest temperature below the inverter's maximum and V_mp at the hottest above its MPPT minimum. Grid-tied inverters must meet grid codes (anti-islanding, voltage/frequency ride-through, reactive power support). High solar penetration creates the 'duck curve' — a steep evening ramp — driving demand for storage.

Cell technologies

Mono-PERC, TOPCon and heterojunction silicon reach 22–24 % module efficiency; bifacial modules harvest reflected light from behind; perovskite–silicon tandems have exceeded 33 % in the lab by capturing more of the spectrum.

Formulas

• Cell model: I = I_sc − I₀(e^{V/(nV_T)} − 1)
• Fill factor: FF = P_mp / (V_oc · I_sc)
• Efficiency: η = P_mp / (G · A)
• Daily energy: E = kWp × PSH × PR
• Temperature correction: P(T) = P_STC · [1 + γ(T_cell − 25 °C)], γ ≈ −0.35 %/°C

Worked example: Daily energy from one panel

Given: 400 W panel; 5 peak sun hours; Performance ratio 0.80

Find: Average daily energy.

• E = 0.4 kW × 5 h × 0.80 = 1.6 kWh/day
• Per year ≈ 584 kWh

Answer: 1.6 kWh/day

Worked example: Hot-day output and cold-day voltage

Given: P_STC = 400 W, γ = −0.35 %/°C; V_oc = 49.5 V, β = −0.28 %/°C; Cell 65 °C (summer), −10 °C (winter)

Find: Summer power and winter V_oc.

• Summer: ΔT = +40 °C → −14 % → 344 W
• Winter: ΔT = −35 °C → +9.8 % → V_oc = 54.35 V

Answer: 344 W when hot; 54.4 V V_oc when cold

Common mistakes

• Wrong: Sizing strings using STC voltage only. — Right: Check cold-weather V_oc against the inverter maximum and hot-weather V_mp against its MPPT minimum.
• Wrong: Mixing panel orientations on one MPPT input. — Right: Differently oriented or shaded strings need separate MPPT inputs or module-level electronics.

Applications

• Rooftop & commercial: Homes and businesses offset daytime use and export surplus under net-metering or feed-in tariffs.
• Utility-scale farms: Single-axis trackers and bifacial modules deliver some of the lowest-cost electricity ever produced.
• Off-grid: Solar + battery systems power telecom sites, water pumps and villages beyond the grid.

Key takeaways

• PV cells are illuminated diodes; current ∝ irradiance, voltage set by the junction.
• MPPT holds the array at its knee-point maximum power.
• Heat reduces power; cold raises V_oc — design strings for both extremes.
• Energy = kWp × PSH × PR.

Going further

• Bypass diodes and hot spots: A shaded cell in a string can become reverse-biased and dissipate the string's power as heat; bypass diodes (typically one per 20–24 cells) route current around shaded sections.
• Degradation: Modules lose ~0.3–0.5 %/year (LID, LeTID, PID, UV). Warranties guarantee ~85–90 % output after 25–30 years; yield models include this.
• Inverter clipping and DC/AC ratio: Designers often install 1.2–1.4× more DC capacity than inverter AC rating: the inverter clips a little at noon but produces more energy in mornings, evenings and cloudy weather.