Connect a realistic module to a virtual load, look inside a silicon cell, and build a day’s energy from changing light and time.
Enable JavaScript to change the conditions and run the interactive experiment.
Light makes charge carriers available in the cell. A connected circuit can carry electrical energy to a load, but the voltage and current depend on that connection. Useful power is their product. Both an open circuit and an ideal short circuit deliver zero terminal power for different reasons.
A bright panel has its largest terminal voltage, but the circuit is open. How much power reaches an external load?
Power is voltage multiplied by current. An available voltage with no load current gives zero delivered power. Compare the virtual short: current is large, but voltage is zero.
Sunlight carries energy. Silicon can absorb some of it and excite an electron, leaving a hole. The electronic charges are already in the material; electrons do not arrive from the Sun. Photovoltaic conversion is different from first heating the panel and then using that heat as a power source.
Doping creates regions with different majority-carrier populations. A typical instructional silicon cell can have a thin n-type emitter over a p-type base. The junction and carrier transport help charges reach appropriate metal contacts. The broad p and n regions are not simply whole slabs carrying large net positive or negative charges.
A generated electron and hole can contribute to current if they reach suitable contacts. Some carriers recombine before collection. Absorption, transport, separation, recombination and collection are distinct processes. Our enlarged cutaway follows selected events, rather than claiming a measured microscopic efficiency or a complete device-transport solution.
A module combines cells. With a load connected, the panel can deliver direct current: DC. The load affects the voltage and current at the terminals. Cable markers in the model indicate conventional current qualitatively; electron drift in a metal is in the opposite direction. The semiconductor story and terminal circuit operate at different levels of description.
An open circuit has zero load current, even when voltage is available. An ideal short has zero terminal voltage even though current can flow. In each case V × I is zero. Between them, the curve has a maximum-power point. A very high voltage or a very high current alone does not identify it.
Uniformly reducing light primarily reduces available current; the voltage also changes, but not in the same simple proportion. Cell temperature has its own effect. The resistance that best matches one condition need not be the best at another. Pin a curve and change one input at a time to make a clear comparison.
The live calculation uses the historical CEC/SAM row for Canadian Solar Inc. CS6K-300MS in the 2019-03-05 archive distributed by pvlib 0.15.2. It represents 60 series cells. At effective irradiance 1000 W/m² and cell temperature 25°C, its maximum is about 32.60 V × 9.20 A = 299.92 W. A reference rating describes conditions and an operating point; it is not an unconditional output or universal ceiling.
I = IL − I0 expm1((V + I Rs)/a) − (V + I Rs)/Rsh. IL is light-generated current, I0 is the diode saturation parameter, Rs is series resistance, and Rsh is shunt resistance. This equivalent circuit describes terminal behavior; it does not mean separate ordinary resistors and one discrete diode are visibly packed inside each wafer. The module-level a already includes the number of series cells.
The archived reference parameters are IL = 9.702283 A, I0 = 7.211832 × 10⁻¹¹ A, a = 1.549486 V, Rs = 0.262808 Ω and Rsh = 1116.523926 Ω. The CEC temperature adjustment uses alpha_sc = 0.003250 A/K with Adjust = 4.822110%. The manufacturer’s February 2019 V5.571 sheet has the same model name but some different electrical values. We use that dated drawing for factual physical dimensions and the archived row for electrical calculations; the revisions are not merged into a fictitious single specification.
The CEC auxiliary equations adjust photocurrent, diode saturation current, thermal voltage and shunt resistance with temperature and effective irradiance. Temperature is converted to kelvin internally. At the same 1000 W/m², increasing cell temperature from 25°C to 55°C reduces the modeled maximum from about 299.9 W to 263.2 W while short-circuit current rises slightly. Air temperature is a different quantity and needs an additional thermal/environmental model to predict cell temperature.
The implementation parameterizes the curve by internal diode voltage d = V + I Rs. It solves the short-circuit endpoint, open-circuit endpoint and maximum of P = VI using bracketed roots. A resistive load intersects the curve at V = Rload I. The operating point satisfies both relations; it is not a dot placed arbitrarily along a decorative curve.
A watt is a joule per second, a rate of energy transfer. For constant time blocks, energy in watt-hours is the sum of power in watts multiplied by duration in hours. Our invented 25°C day uses 400 W/m² for 2 hours, 1000 for 3 hours and 200 for 1 hour. Ideal matching gives about 1.198939 kWh. A fixed 3.54347826 Ω load gives about 1.019534 kWh before other system losses.
Uniform dimming applies the same effective irradiance to every cell. A partial shadow can create different conditions across series cells and substrings, changing reverse-bias and bypass behavior. Its effect depends on topology and operating conditions. Shading 10% of the area does not imply exactly 10% less power. Our uniform-module solver does not predict that case.
A roof module delivers DC. An inverter may convert it to AC for appliances or a grid connection. A battery can store energy in some systems, but it is not required for photovoltaic conversion itself. Inverters, batteries and wiring have separate limits and losses that are outside our single-module readouts.
A maximum-power controller changes the electrical operating point as conditions change. Our Find maximum power button shows the mathematical optimum of the present curve. It is an ideal benchmark, not the tracking dynamics, efficiency or limits of a particular commercial controller.
A panel’s reference watt rating is a power value. A day’s watt-hours or kilowatt-hours require the power history. Multiplying a rating by every hour between sunrise and sunset usually ignores changing light, temperature, loading and losses.
A panel can feel warm while its available electrical power is below its cooler value at the same illumination. That is a controlled comparison: it does not mean sunshine is harmful or that a warmer day always generates less total energy.
At the same reference conditions, compare these rounded points: 9.69 V and 9.69 A; 32.60 V and 9.20 A; 37.93 V and 3.79 A; 39.70 V and zero A; zero V and 9.70 A. Multiply each voltage by its current. Circle the largest result and explain why the largest voltage is not the winner.
Draw voltage horizontally and current vertically. For each point, sketch a rectangle from the origin to the point. Compare their areas. Then compare the best load at 1000 and 400 W/m² using Vmp/Imp: about 32.60/9.20 and 32.56/3.69 ohms. One fixed resistance does not match both perfectly.
Use rounded power cards: 120 W for two hours, 300 W for three hours, and 59 W for one hour. Draw power against time. Multiply each height by its duration and add: 240 + 900 + 59 = 1199 Wh, or 1.199 kWh. These rounded cards approximate the model’s default ideal day.
Make the last card two hours long instead of one. Predict the extra energy: another 59 Wh. Next write whether this model can answer each question: an open circuit, a hotter cell at the same light, and a tree shadow over selected cells. Explain what information is missing for the shadow.
Which operating point transfers the most power, and how much energy does a changing day deliver?
Paper and data only. No roof access, live terminal measurements, wiring changes, installation access or physical short circuit. The activity measures arithmetic and reasoning, not a household installation’s output.
Absorbed light, which can create collectable charge carriers Light supplies energy. The electronic charges are in the material and circuit; ordinary conversion does not consume silicon as exhaust.
Transport and collection at suitable contacts, with a connected external circuit Generation alone is insufficient. Carriers can recombine; transport, separation and collection matter, and the external circuit determines the operating point.
0 W P = VI = 39.7 × 0 = 0. Volts are not watts; current is also needed.
32.60 V × 9.20 A The products are about 93.9 W, 299.9 W and 143.8 W. The middle point has the largest product, even though it has neither the largest voltage nor the largest current.
Short-circuit current falls to about 3.88 A while open-circuit voltage remains near 38.28 V Photocurrent responds roughly proportionally to light. The voltage relation is nonlinear and changes much less proportionally in this comparison.
263.2 W The model’s maximum power falls even though short-circuit current rises slightly. Cell temperature affects semiconductor behavior independently of the supplied light level.
1199 Wh Multiply power by each duration before adding: 120 × 2 + 300 × 3 + 59 × 1 = 1199 Wh, or 1.199 kWh.
No; cell conditions, interconnection and bypass behavior need a more detailed model Partial shading is different from evenly dimming all cells. Neither a simple area fraction nor a universal zero-output rule is justified.
Supports the light-to-carrier-to-external-circuit explanation, without treating heat as the required first conversion stage.
US Department of Energy · Photovoltaic cell basicsTonio Buonassisi, 2.627, 2013, slides 3 and 6. The original cutaway does not copy course or third-party figures.
MIT OCW · Charge extractionThe microscopic sequence is qualitative; quantitative terminal behavior comes from a separate documented equivalent-circuit model.
MIT OCW · Device fundamentalsSupports equation form and module/cell distinctions. The lesson solves this equation through its internal diode voltage.
Sandia PVPMC · Single-diode equivalent circuitModel name Canadian Solar Inc. CS6K-300MS; database SAM 2018.11.11 r2, row date 1/3/2019. Reference values and row provenance are downloadable locally.
pvlib 0.15.2 · Archived CEC module databaseReference band-gap constants and module-level units are preserved. The scalar browser solver is original.
pvlib 0.15.2 · CEC auxiliary equationsUsed to check equation definitions and version-specific behavior. The lesson does not multiply module-level a_ref by the cell count again.
pvlib · Versioned first-party implementationPage 2, V5.571. Its electrical ratings differ from the older archived row. No product photograph, diagram, logo or CAD is copied.
Canadian Solar · February 2019 physical referenceOur watt and watt-hour results are at DC module terminals, before omitted system components and losses.
SAM · Module model documentationThe public lesson does not turn a shaded-area slider into an unsupported power forecast.
pvlib · Partial module shading exampleSupports the rooftop application and keeps the optional inverter/battery outside the module calculation.
US Department of Energy · PV Cells 101Independent subject review is pending.
Read the sources and model assumptionsClose a switch. Follow a complete path. Give current a second route and discover what changes.
Interactive explorationLook through a phone, separate a battery’s layers, and trace two different journeys. One happens inside the cell. The other powers the world outside.
Power a motor. Reverse its direction. Add a load and watch speed, current and turning force find a new balance.