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Summary

The Martin & Ruiz Recombination Model extends the standard single diode model by adding a recombination term to account for additional current losses in the depletion region. This model is implemented in PlantPredict as OneDiodeRecombination and includes two additional parameters: built-in voltage (VbiV_{bi}) and recombination parameter (di2/utdi_2/u_t). The recombination term becomes significant at low irradiance levels where recombination losses dominate over shunt resistance losses. The model modifies both the photocurrent calculation and the circuit equation solution.

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Inputs

NameSymbolUnitsDescription
Standard Five Parameters—variousIph,I0,Rs,Rsh,γI_{ph}, I_0, R_s, R_{sh}, \gamma (scaled)
Built-in VoltageVbiV_{bi}VBuilt-in junction voltage per cell
Recombination Parameterdi2/utdi_2/u_t—Recombination current parameter
Number of CellsNsN_s—Cells in series
Short-Circuit CurrentIscI_{sc}AScaled short-circuit current

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Outputs

NameSymbolUnitsDescription
PhotocurrentIphI_{ph}APhotocurrent including recombination correction
Max Power PointVmp,Imp,PmpV_{mp}, I_{mp}, P_{mp}V, A, WMaximum power point values
Open-Circuit VoltageVocV_{oc}VOpen-circuit voltage

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Detailed Description

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Photocurrent Calculation with Recombination

If Isc≤0I_{sc} \leq 0: Iph=0I_{ph} = 0 Otherwise: Iph=Isc+I0(eIscRsα−1)+IscRs/Rsh1−di2/utNsVbi−IscRsI_{ph} = \frac{I_{sc} + I_0 (e^{I_{sc} R_s \alpha} - 1) + I_{sc} R_s / R_{sh}}{1 - \frac{di_2/u_t}{N_s V_{bi} - I_{sc} R_s}} where:
  • Vbi,scaled=Ns×VbiV_{bi,scaled} = N_s \times V_{bi}
  • di2/utdi_2/u_t is the recombination parameter
  • α=q/(kTNsγ)\alpha = q/(k T N_s \gamma)

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Circuit Equation with Recombination

I=Iph−I0(eαV−1)−VRsh−(di2/ut)IphVbi,scaled−VI = I_{ph} - I_0 (e^{\alpha V} - 1) - \frac{V}{R_{sh}} - \frac{(di_2/u_t) I_{ph}}{V_{bi,scaled} - V} The additional term (di2/ut)IphVbi,scaled−V\frac{(di_2/u_t) I_{ph}}{V_{bi,scaled} - V} represents recombination current losses.

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Maximum Power Point Solution

Uses Newton-Raphson iteration with modified derivatives accounting for recombination term. Convergence tolerance: ∣V1−V2∣<0.0001|V_1 - V_2| < 0.0001 V Current rounded to 5 decimal places (vs 4 for standard model).

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Open-Circuit Voltage

Solved using advanced diode Lambert W function method with recombination parameters.

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References

  • Martin, N., & Ruiz, J. M. (2001). Calculation of the PV modules angular losses under field conditions by means of an analytical model. Solar Energy Materials and Solar Cells, 70(1), 25–38.
  • King, D. L., Boyson, W. E., & Kratochvil, J. A. (2004). Photovoltaic array performance model. SAND2004-3535, Sandia National Laboratories.