ELEC5206 Chap.2 The Single Diode Model and PV Output Curves
The Single Diode Model and PV Output Curves
The modelling lecture turns the PV curve into an equation you can simulate. A crystalline cell is a p-n junction with a large light-absorbing surface, so it is modelled as a photocurrent source in parallel with one diode: the ideal single-diode model.
Its three unknowns, the photocurrent, the saturation current and the ideality factor, are identified at standard test conditions from the short-circuit point, the open-circuit point and the maximum power point. The lecture then shows how irradiance and temperature update the photocurrent, the open-circuit voltage and the saturation current in a fixed order, and how one cell model scales to a module or string.
Lab 3 builds exactly this model for the lab module in MATLAB and Simulink, so the chapter is also preparation for that report.
What this chapter covers
- 01
Why a PV generator is neither a voltage source nor a current source
- 02
The Shockley diode equation, saturation current and ideality factor
- 03
The ideal single-diode model and its three unknowns
- 04
Identifying the photocurrent from short circuit at STC
- 05
Open-circuit and MPP equations solved together for the remaining parameters
- 06
Photocurrent, open-circuit voltage and saturation current updated for weather
- 07
The irradiance correction factor: lecture fit and lab rule of thumb
- 08
Scaling a cell model to a module or string
Worked example · free
Updating the cell model for a warm, hazy hour
- 1Photocurrent: iph = (800/1000) × 8.38 × (1 + 0.0006 × 10) = 6.704 × 1.006 = 6.744 A.
- 1Open-circuit voltage: vOC = 0.614 × (1 − 0.0033 × 10) × 0.989 = 0.614 × 0.967 × 0.989 = 0.587 V.
- 1Saturation current at 308 K: AnkT/q = 1.48 × 0.02657 = 0.03932 V, so is = 6.744/(e0.587/0.03932 − 1) = 6.744/e14.94 = 2.2 × 10−6 A.
Key terms
- Ideality factor
- The diode parameter An that sets how sharply the I-V curve bends at its knee.
- Saturation current
- The reverse-bias diode current is that scales the exponential term of the cell model.
- Photocurrent
- The light-generated current source in the cell model, proportional to irradiance and equal to the short-circuit current in the ideal model.
- Thermal voltage
- The quantity kT/q, about 0.0257 V at 25 °C, that appears in every diode exponent.
The Single Diode Model and PV Output Curves FAQ
Why is the ideality factor kept constant when the weather changes?
The lecture identifies it once, offline, from the three STC points and then treats it as a cell property. Only the photocurrent, open-circuit voltage and saturation current are recalculated as irradiance and temperature change, which keeps the real-time model cheap enough to run inside a system simulation.
How do I solve for the saturation current and ideality factor without a computer?
Divide the MPP equation by the open-circuit equation. Because both exponentials are huge, the minus-one terms can be dropped, leaving one exponential in the difference between the two voltages. Take a logarithm to find the exponent, then back-substitute into the open-circuit equation for the saturation current.
Why does the lab use a different temperature formula from the lecture?
The lab writes the open-circuit voltage change additively, in volts per degree for one cell, and uses a linear rule for the irradiance factor because the module datasheet gives no table. The lecture multiplies by a percentage coefficient and fits a quadratic. Both are valid; state the form you use.
How does a cell model become a module or string model?
Multiply the voltage axis by the number of cells in series. Series cells carry one current, so the photocurrent and short-circuit current stay those of a single cell while every voltage scales by the cell count. The lecture's Simulink block uses one gain for this, covering a cell, a module or a string.
Exam move
Write the diode equation and the ideal single-diode model from memory, then practise the three-point identification by hand with a datasheet of your own choosing until the division trick is automatic. Next drill the four update equations in order and check your result by confirming that the curve still passes through the new open-circuit voltage.
Finally connect the chapter to Lab 3: the per-cell values, the fsolve call and the Simulink blocks are the same mathematics in software. Keep one worked identification on your revision sheet with every intermediate number visible.
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