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Summary

Parameter Translation scales the five standard parameters from reference conditions (typically : 25 °C, 1000 W/m²) to actual operating conditions. PlantPredict applies physics-based scaling relationships for , , , , , and . All parameters are scaled before solving the single-diode circuit equation. The two additional parameters of the seven-parameter model (di2/μτd_i^2/\mu\tau and VbiV_{bi}) are not scaled, so this procedure applies similarly to both model variants.

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Inputs

NameSymbolUnitsDescription
Series ResistanceRs,refR_{s,ref}ΩSeries resistance at reference conditions
Shunt ResistanceRsh,refR_{sh,ref}ΩShunt resistance at reference conditions
Diode Ideality Factorγref\gamma_{ref}—Ideality factor at reference conditions
Saturation CurrentI0,refI_{0,ref}ASaturation current at reference conditions
Short-Circuit CurrentIsc,refI_{sc,ref}AShort-circuit current at reference conditions
Reference TemperatureTrefT_{ref}°CReference temperature (typically 25 °C)
Reference IrradianceGrefG_{ref}W/m²Reference irradiance (typically 1000 W/m²)
Cell TemperatureTcT_c°COperating cell temperature (from temperature model)
Total Effective POA IrradianceGPOA,tot,eff′G'_{POA,tot,eff}W/m²Total effective POA irradiance after DC system losses
Temp. Coeff. of Ideality Factorαγ\alpha_{\gamma}1/°CLinear temperature coefficient of diode ideality factor
Ideality Factor Polynomial Coefficientsaγ,bγ,cγ,dγa_\gamma, b_\gamma, c_\gamma, d_\gamma1/°C, 1/°C², 1/°C³, 1/°C⁴Polynomial temperature coefficients for ideality factor
Temp. Coeff. of Short-Circuit CurrentαIsc\alpha_{I_{sc}}1/°CLinear temperature coefficient of short-circuit current
DC Wiring ResistanceRDC,moduleR_{DC,module}ΩPer-module DC equivalent series resistance
Dark Shunt ResistanceRsh,0R_{sh,0}ΩShunt resistance at zero irradiance
Shunt ExponentRsh,expR_{sh,exp}—Exponential dependency coefficient (default = 5.5)
Recombination Parameterdi2/μτd_i^2/\mu\tauVRecombination parameter for 7-parameter single-diode model
Built-in VoltageVbiV_{bi}VBuilt-in junction voltage per cell for 7-parameter single-diode model
Bandgap VoltageEgE_geVSemiconductor bandgap
Number of CellsNsN_s—Cells in series

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Outputs

NameSymbolUnitsDescription
Series ResistanceRsR_sΩScaled series resistance
Shunt ResistanceRshR_{sh}ΩScaled shunt resistance
Diode Ideality Factorγ\gamma—Scaled ideality factor
Saturation CurrentI0I_0AScaled saturation current
Short-Circuit CurrentIscI_{sc}AScaled short-circuit current
PhotocurrentIphI_{ph}AScaled photocurrent

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Detailed Description

The general of a PV cell is described by: I=Iph−I0(exp⁡ ⁣(q(V+IRs)NskTcγ)−1)−V+IRsRsh−(di2/μτ)⋅IphNsVbi−(V+IRs)I = I_{ph} - I_0 \left(\exp\!\left(\frac{q(V + IR_s)}{N_s k T_c \gamma}\right) - 1\right) - \frac{V + IR_s}{R_{sh}} - \frac{(d_i^2/\mu\tau) \cdot I_{ph}}{N_s V_{bi} - (V + IR_s)} where q=1.602×10−19q = 1.602 \times 10^{-19} C is the elementary charge and k=1.381×10−23k = 1.381 \times 10^{-23} J/K is the Boltzmann constant. The first five parameters—photocurrent IphI_{ph}, saturation current I0I_0, ideality factor γ\gamma, series resistance RsR_s, and shunt resistance RshR_{sh}—define the 5-parameter model. The last term, governed by the recombination parameter di2/μτd_i^2/\mu\tau and VbiV_{bi}, is an optional extension used by the 7-parameter model to improve accuracy at low irradiance. For the 5-parameter model, di2/μτ=0d_i^2/\mu\tau = 0 and this term vanishes. Module datasheets characterize these parameters at reference conditions (typically 25 °C, 1000 W/m²). Since cell temperature and irradiance vary continuously during operation, each parameter must be scaled from reference to actual conditions before solving the circuit equation. Additionally, a per-module DC equivalent series resistance is added to account for wiring losses. The scaling relationships below are applied at every simulation time step. All temperatures are converted to Kelvin before use in the equations below. Throughout, ΔT=Tc−Tref\Delta T = T_c - T_{ref} denotes the temperature difference from reference conditions.

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Series Resistance

The per-module DC wiring resistance RDC,moduleR_{DC,module} is added to the reference value: Rs=Rs,ref+RDC,moduleR_s = R_{s,ref} + R_{DC,module}

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Shunt Resistance

Shunt resistance increases at low irradiance due to reduced minority carrier concentration. The exponential model below, aligned with PVsyst (Mermoud & Lejeune, 2010), is an empirical fit that interpolates between a finite dark shunt resistance Rsh,0R_{sh,0} at zero irradiance and the reference value at STC: Rsh=Rsh,ref+(Rsh,0−Rsh,ref)exp⁡(−Rsh,expGPOA,tot,eff′Gref)R_{sh} = R_{sh,ref} + (R_{sh,0} - R_{sh,ref}) \exp\left(-R_{sh,exp} \frac{G'_{POA,tot,eff}}{G_{ref}}\right) where:
  • Rsh,refR_{sh,ref} is the reference shunt resistance, typically defined at STC
  • Rsh,0R_{sh,0} is the dark shunt resistance (at G=0G = 0 W/m²)
  • Rsh,expR_{sh,exp} is the exponential dependency coefficient (default 5.5)
Note that PlantPredict uses Rsh,refR_{sh,ref} directly rather than computing an intermediate base value Rsh,baseR_{sh,base}. As a result, RshR_{sh} evaluated at GPOA,tot,eff′=GrefG'_{POA,tot,eff} = G_{ref} does not exactly equal Rsh,refR_{sh,ref}—it includes a residual term (Rsh,0−Rsh,ref)⋅e−Rsh,exp(R_{sh,0} - R_{sh,ref}) \cdot e^{-R_{sh,exp}}. For the default Rsh,exp=5.5R_{sh,exp} = 5.5, this residual is less than 0.5% of (Rsh,0−Rsh,ref)(R_{sh,0} - R_{sh,ref}).

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Diode Ideality Factor

PlantPredict supports two models for the temperature dependence of the diode ideality factor. The linear model is the standard approach, aligned with PVsyst. The polynomial model provides additional flexibility for technologies where the ideality factor exhibits nonlinear temperature dependence, as observed by Sauer et al. (2015). Linear model: γ=γref(1+αγΔT)\gamma = \gamma_{ref} (1 + \alpha_{\gamma} \Delta T) The coefficient αγ\alpha_{\gamma} is typically derived during parameter extraction from the temperature coefficient of maximum power (βPmp\beta_{P_{mp}}) reported on the module datasheet. It is chosen so that the fully scaled single-diode model reproduces the correct temperature coefficient of power. Polynomial model: γ=γref(1+aγΔT+bγΔT2+cγΔT3+dγΔT4)\gamma = \gamma_{ref} (1 + a_{\gamma} \Delta T + b_{\gamma} \Delta T^2 + c_{\gamma} \Delta T^3 + d_{\gamma} \Delta T^4) where aγ,bγ,cγ,dγa_{\gamma}, b_{\gamma}, c_{\gamma}, d_{\gamma} are polynomial coefficients. In practice, these are derived by fitting the single-diode model to measured I-V curves at multiple temperatures, extracting γ\gamma at each temperature, and then fitting a 4th-degree polynomial to γ\gamma as a function of ΔT\Delta T.

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Saturation Current

The saturation current I0I_0 represents the recombination current of charge carriers across the solar cell in the dark. Its temperature dependence follows from the intrinsic carrier concentration nin_i, where ni2∝T3exp⁡(−Eg/kT)n_i^2 \propto T^3 \exp(-E_g / kT) and EgE_g is the . The ideality factor γ\gamma in the exponent accounts for non-ideal recombination: I0=I0,refTc3Tref3exp⁡(qEgkγ(1Tref−1Tc))I_0 = I_{0,ref} \frac{T_c^3}{T_{ref}^3} \exp\left(\frac{q E_g}{k \gamma} \left(\frac{1}{T_{ref}} - \frac{1}{T_c}\right)\right)

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Short-Circuit Current

Short-circuit current scales linearly with irradiance and is corrected for temperature using the coefficient αIsc\alpha_{I_{sc}} (typically from the module datasheet): Isc=Isc,refGPOA,tot,eff′Gref(1+αIscΔT)I_{sc} = I_{sc,ref} \frac{G'_{POA,tot,eff}}{G_{ref}} (1 + \alpha_{I_{sc}} \Delta T)

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Photocurrent

The photocurrent IphI_{ph} is obtained by evaluating the I-V equation at V=0V = 0 and solving for IphI_{ph} to ensure that I(V=0)=IscI(V=0) = I_{sc}: Iph=Isc+I0(exp⁡ ⁣(q IscRsk Tc Ns γ)−1)+IscRsRsh1−di2/μτNsVbi−IscRsI_{ph} = \frac{I_{sc} + I_0 \left(\exp\!\left(\frac{q \, I_{sc} R_s}{k \, T_c \, N_s \, \gamma}\right) - 1\right) + \frac{I_{sc} R_s}{R_{sh}}}{1 - \frac{d_i^2/\mu\tau}{N_s V_{bi} - I_{sc} R_s}} For the 5-parameter model, di2/μτ=0d_i^2/\mu\tau = 0 and the relationship simplifies to: Iph=Isc+I0(exp⁡ ⁣(q IscRsk Tc Ns γ)−1)+IscRsRshI_{ph} = I_{sc} + I_0 \left(\exp\!\left(\frac{q \, I_{sc} R_s}{k \, T_c \, N_s \, \gamma}\right) - 1\right) + \frac{I_{sc} R_s}{R_{sh}}

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References

  • Mermoud, A., & Lejeune, T. (2010). Performance assessment of a simulation model for PV modules of any available technology. 25th European Photovoltaic Solar Energy Conference, Valencia, Spain.
  • Sauer, K. J., Roessler, T., & Hansen, C. W. (2015). Modeling the irradiance and temperature dependence of photovoltaic modules in PVsyst. IEEE Journal of Photovoltaics, 5(1), 152–158.
  • De Soto, W., Klein, S. A., & Beckman, W. A. (2006). Improvement and validation of a model for photovoltaic array performance. Solar Energy, 80(1), 78–88.