Solar Cell Equivalent Circuit Model
A solar cell can be modeled by an equivalent electrical circuit. The simplest model includes a current source representing the photogenerated current (\(I_L\)), in parallel with a diode representing the p-n junction. A more accurate model adds a parallel shunt resistance (\(R_{sh}\)) for leakage currents and a series resistance (\(R_s\)) for contact and bulk material resistance.
The equivalent circuit model is a powerful tool for understanding and analyzing the electrical behavior of a solar cell. It abstracts the complex semiconductor physics into a simple circuit diagram with a few key components. The core of the model is an ideal current source that produces a current, \(I_L\), directly proportional to the incident light intensity. This represents the generation of electron-hole pairs by photons.
In parallel with this current source is a diode. This diode models the behavior of the p-n junction itself. In the dark, the solar cell is just a diode, and its current-voltage (I-V) characteristic follows the ideal diode equation. When illuminated, some of the photogenerated current is shunted through this internal diode, a process known as recombination, which does not contribute to the output current. The total output current \(I\) is therefore the photogenerated current minus the diode current: \(I = I_L – I_D\).
For a more realistic representation, two parasitic resistances are added. A series resistance, \(R_s\), accounts for the resistance of the metal contacts, the emitter, and the bulk semiconductor material. It causes a voltage drop that reduces the terminal voltage and the fill factor. A shunt resistance, \(R_{sh}\), is placed in parallel with the diode and current source. It represents leakage paths for the current across the p-n junction, often due to manufacturing defects. A low shunt resistance provides an alternate path for the photogenerated current, reducing the current delivered to the load. The governing equation for this single-diode model is: \(I = I_L – I_0 \left[ \exp\left(\frac{V+IR_s}{n k_B T/q}\right) – 1 \right] – \frac{V+IR_s}{R_{sh}}\), where \(I_0\) is the diode saturation current and \(n\) is the ideality factor.
UNESCO Nomenclature: 2205
– Electronics
Precursors
- development of diode theory (shockley diode equation)
- ohm’s law
- kirchhoff’s circuit laws
- invention of the p-n junction solar cell
Applications
- predicting solar cell performance under varying conditions
- characterizing solar panels in manufacturing (i-v curve tracing)
- designing maximum power point tracking (mppt) algorithms
- simulating the behavior of large photovoltaic arrays
Potential Innovations Ideas
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Related to: equivalent circuit, solar cell model, series resistance, shunt resistance, diode, photocurrent, i-v curve, fill factor.