5.3 The I-V Curve, Irradiance, Temperature and Shading
Key Takeaways
- The I–V curve is plotted as current against voltage; Isc is current at zero volts, Voc is voltage at zero current, and Pmax is Vmp × Imp at the knee of the curve
- Irradiance primarily scales current: Isc and Imp rise and fall almost in proportion to W/m², while Voc changes only weakly
- Voc falls as cell temperature rises and rises in the cold, so string open-circuit voltage at the lowest expected temperature is the inverter maximum-DC-voltage problem (the 1.2 multiplier is calculated in a later chapter)
- A typical silicon module power temperature coefficient is about −0.3 to −0.4 %/°C; treat that as an industry typical, not a handbook pass figure
- A series string's current is limited by the weakest illuminated cell unless bypass diodes conduct; near versus far shade is qualitative here, with MGD 005 quantitative later
Quick Answer: Handbook v1.3, 3.1.4(a), requires the I–V curve, short-circuit current behaviour, irradiance and temperature effects, and shading. Isc is the current with the output shorted (voltage = 0). Voc is the voltage with the output open (current = 0). Vmp and Imp are the voltage and current at maximum power, and Pmax = Vmp × Imp. Irradiance mostly moves the curve up and down (current). Temperature mostly moves it left and right (voltage). Shade in a series string limits current to the weakest illuminated cell unless bypass diodes conduct.
The I–V curve you must be able to sketch
Plot current (I) on the vertical axis and voltage (V) on the horizontal axis. A healthy illuminated module (or string) traces a curve that starts at Isc on the current axis and ends at Voc on the voltage axis. Between those intercepts the curve is high and fairly flat (a current source) then falls steeply (a voltage source). The maximum-power point sits at the "knee": the rectangle Vmp × Imp is the largest area you can draw under the curve. Manufacturers quote Pmax at STC (1000 W/m², 25 °C cell temperature, AM1.5). Real roofs are rarely STC.
Fill factor is Pmax divided by the Isc × Voc rectangle. You do not need a handbook numerical fill-factor pass mark; you do need to know that a family of curves with a sharp knee is healthier than a sloppy, collapsed knee from mismatch, damage, or heavy shade.
Short-circuit current behaviour in one sentence: Isc is set by how many photons are creating carriers that the junction can collect. It is therefore almost proportional to irradiance, only slightly dependent on temperature (a small positive coefficient), and brutally dependent on series shading, because a dark cell cannot pass the current the bright cells want to push.
How the curve moves — right, left, up, down
| Change on the module | What happens on the I–V plot | What happens to power |
|---|---|---|
| Irradiance up (more W/m²) | Curve moves up: Isc and Imp rise almost in proportion | Pmax rises, roughly with current |
| Irradiance down | Curve moves down: Isc and Imp fall | Pmax falls |
| Cell temperature down (colder) | Curve moves right: Voc and Vmp rise | Pmax usually rises (silicon) |
| Cell temperature up (hotter) | Curve moves left: Voc and Vmp fall | Pmax falls |
| Hard shade on one series cell, diodes not conducting | Current of that substring collapses toward the shaded cell's photocurrent | Pmax collapses; reverse-biased cell can heat (hot spot) |
| Bypass diode conducts around the shaded substring | That substring is bypassed; remaining substrings still contribute | Pmax reduced by about that substring, not by the whole module |
Irradiance also nudges Voc a little (logarithmic), and temperature nudges Isc a little. Exam answers that say "irradiance only changes voltage" or "heat only changes current" are the wrong axes.
Worked qualitative example: 1000 vs 500 W/m², and 25 °C vs 0 °C vs 50 °C
Hold the module at 25 °C cell temperature first, so temperature is not mixing into the irradiance story.
At 1000 W/m² (STC irradiance) you are on the nameplate curve: Isc ≈ Isc_stc, Voc ≈ Voc_stc, Pmax ≈ Pmax_stc.
At 500 W/m² and the same 25 °C, irradiance has halved. Isc approximately halves. Imp follows. Voc does not halve. Open-circuit voltage varies only weakly (logarithmically) with light, so the curve is much shorter in height and only a little shorter in width. Pmax is therefore about half, slightly worse than a perfect half if Voc has sagged a little. A 2922 candidate who halves Voc when the sun goes behind thin cloud has mixed up the axes.
Now hold irradiance at 1000 W/m² and move cell temperature.
At 25 °C you are back on the STC voltage. At 0 °C the cells are 25 °C colder. Voc moves right — higher. Isc changes only slightly: it has a small positive temperature coefficient, so colder cells have slightly lower Isc, but the Voc rise still dominates and Pmax is higher than at 25 °C. A typical silicon power temperature coefficient of about −0.3 to −0.4 %/°C (industry typical, not a handbook pass mark and not a UK-specific invented constant) means a 25 °C drop is very roughly 8–10% more power than STC at the same 1000 W/m². Use the datasheet coefficient on a real design; use the typical band only to sense the size of the effect.
At 50 °C the cells are 25 °C hotter than STC. Voc moves left — lower. Pmax is lower by a similar ballpark 8–10% using that same typical coefficient. This is a clear, still, dark-roof summer afternoon: plenty of irradiance, disappointing watts. Thin-film often (not always) loses a little less power per degree; still label any coefficient you quote as typical, not as a 2922 handbook number.
Why cold Voc is an inverter problem
String voltage is the sum of module voltages. The highest Voc occurs at the lowest cell temperature, not on the hottest day. The inverter has a maximum DC input voltage. If a long string's cold Voc exceeds that rating, you risk inverter damage or a forbidden operating region. A later chapter works the arithmetic, including the common UK 1.2 multiplier on STC Voc as a simple cold-weather allowance. This chapter only plants the physics: temperature moves the curve left and right; cold moves it right; that right-hand Voc is what you check against the inverter.
Hot weather does the opposite to voltage: Voc and Vmp fall, so a string that was comfortable at STC can drop out of the MPPT window on a hot roof. That is a minimum-voltage / summer problem, not the maximum-voltage / winter problem. Do not reverse them in a scenario question.
Shading: near, far, and the weakest cell
Cells in a module, and modules in a string, are usually in series. Series current is one current. A cell that is dark acts like a poor current source in that loop. The unshaded cells try to drive Isc through it; the shaded cell becomes reverse-biased and dissipates power as heat — the hot-spot mechanism — unless a bypass diode in the junction box forward-biases and takes that substring out of the current path. Diode arrangement and testing sit in a later chapter. Qualitatively: without a conducting bypass diode, the string current is limited by the weakest illuminated cell.
Near shade is a hard, close obstruction — a chimney, vent pipe, dormer cheek, aerial, or a tree within a short distance of the array. The shadow has a sharp edge. On a clear day it can wipe a whole cell or substring for hours of high-sun geometry. Far shade is distant — a hill, a far building, a far tree line. It shows on a sun-path as a horizon that eats low morning or evening sun rather than punching a hard rectangle into the array at noon. Far shade is often more about lost winter hours than a single black cell at midday.
Do not invent a shade-factor percentage here. MGD 005 (Solar PV Shade Evaluation Procedure) is the MCS method for turning a shade assessment into a shade factor for yield estimates; that quantitative procedure is a later chapter. This chapter only requires the electrical idea: shade reduces the photocurrent of the affected cells, series connection spreads that penalty, and bypass diodes are the module's local relief valve.
A practical 2922 survey still notes both kinds of shade. A chimney on a south plane is near shade you can often design around with layout, power electronics at module level, or more bypassed substrings. A hill due south-west is far shade you cannot move; you record it and let MGD 005 (later) price the lost resource instead of pretending STC Isc will appear at 16:00 in December.
Putting the four effects on one mental model
- More light → more current (up). Half the irradiance, about half Isc, Voc almost unchanged.
- Colder cells → more voltage (right). That is the inverter max-voltage check, later with the 1.2 allowance.
- Hotter cells → less voltage (left) and less Pmax. Typical silicon −0.3 to −0.4 %/°C power, labelled typical.
- Shade on a series cell → that cell caps current until a bypass diode conducts; near shade is a hard local shadow, far shade is a horizon story, MGD 005 waits until the quantitative chapter.
If you can move a finger on an I–V sketch and say which way irradiance, temperature and shade push it, you have 3.1.4(a) in the form the knowledge test can actually use.
On the I–V curve of a PV module, what is the main effect of changing irradiance, and what happens to Voc compared with Isc?
Why is string open-circuit voltage at the lowest expected cell temperature the quantity compared with the inverter's maximum DC voltage?
A chimney casts a hard shadow across one cell in a series string. What limits the string current if the bypass diodes have not yet conducted, and how is that different from far-horizon shade?