Module Parameter Generation

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Summary

Module Parameter Generation is the process by which PlantPredict converts user-supplied module characterization data into the full set of parameters required by Parameter Translation and the 5-Parameter Model or 7-Parameter Model. PlantPredict supports four input paths—Basic Data (datasheet), IEC 61853-1 Key I-V Points, Full I-V Curves, and PVsyst PAN file import—and invokes the same core solver for each. The solver determines $I_{ph,ref}$, $I_{0,ref}$, and $\gamma_{ref}$ at reference conditions by simultaneously imposing that the generated reproduces the reference $I_{sc}$, $V_{oc}$, and $(V_{mp}, I_{mp})$. Shunt resistance $R_{sh,ref}$, dark shunt resistance $R_{sh,0}$, series resistance $R_{s,ref}$, the recombination parameter $d_i^2/\mu\tau$ (7-parameter only), and the linear temperature dependence of $\gamma$ are set by technology-specific empirical rules, iterative bracketing searches, and a power-temperature-coefficient matching routine.

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Inputs

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Outputs

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Detailed Description

PlantPredict provides four entry paths for creating a module file, all of which ultimately populate the same single-diode parameter set. The Key I-V Points and Full I-V Curves paths first reduce the supplied data to basic datasheet-equivalent values (and, when enough points are available, to temperature coefficients and a relative-efficiency curve); the PAN file path parses PVsyst’s parameters directly and regenerates the derived quantities. The Basic Data path operates on datasheet values from the outset.

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Technology Constants

Before any solve, PlantPredict assigns technology-specific physical constants and empirical multipliers based on the selected cell technology. These seed the shunt-resistance heuristic, the initial guess for $\gamma_{ref}$, and the recombination-model defaults: The default $R_{sh,exp}$ is 5.5 and the default heat-absorption coefficient is 0.9. For the 5-parameter model, $V_{bi}$ is not used because the recombination term is set to zero.

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Shunt Resistance

The reference shunt resistance is set from the I-V curve slope near $V_{mp}$ using a technology-dependent multiplier $m_{R_{sh}}$: $$R_{sh,ref}^{raw} = m_{R_{sh}} \cdot \frac{V_{mp}}{I_{sc} - I_{mp}}$$ $R_{sh,ref}^{raw}$ is then quantized to a round value (10 Ω below 200 Ω, 20 Ω between 200 and 250 Ω, 50 Ω between 250 and 3000 Ω, 500 Ω above 3000 Ω) to stabilize downstream iteration against near-identical inputs. The dark shunt resistance is obtained by applying a second technology-dependent multiplier $m_{R_{sh,0}}$ to the quantized $R_{sh,ref}$, then quantizing again (50 Ω below 500 Ω, 100 Ω between 500 and 2000 Ω, 500 Ω above 2000 Ω): $$R_{sh,0} = \text{quantize}\!\left(m_{R_{sh,0}} \cdot R_{sh,ref}\right)$$

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Core System of Equations

At reference conditions ($T_{ref} = 25\,°\mathrm{C}$, $G_{ref} = 1000\,\mathrm{W/m^2}$), the three unknowns $\gamma_{ref}$, $I_{0,ref}$, and $I_{ph,ref}$ are the simultaneous solution of the single-diode equation evaluated at the three key I-V points. Let $$V_{th,ref} = \frac{N_c \, k \, T_{ref}}{q}$$ with $q = 1.602 \times 10^{-19}$ C and $k = 1.381 \times 10^{-23}$ J/K. Using the recombination-extended form (the 5-parameter system is recovered by setting $d_i^2/\mu\tau = 0$), the residual system is: Open-circuit point ($V = V_{oc}, I = 0$): $$0 = I_{ph,ref}\!\left(1 - \frac{d_i^2/\mu\tau}{N_c V_{bi} - V_{oc}}\right) - I_{0,ref}\!\left(\exp\!\frac{V_{oc}}{\gamma_{ref} V_{th,ref}} - 1\right) - \frac{V_{oc}}{R_{sh,ref}}$$ Short-circuit point ($I = I_{sc}, V = 0$): $$0 = -I_{sc} + I_{ph,ref}\!\left(1 - \frac{d_i^2/\mu\tau}{N_c V_{bi} - I_{sc} R_{s,ref}}\right) - I_{0,ref}\!\left(\exp\!\frac{I_{sc} R_{s,ref}}{\gamma_{ref} V_{th,ref}} - 1\right) - \frac{I_{sc} R_{s,ref}}{R_{sh,ref}}$$ Maximum-power point ($V = V_{mp}, I = I_{mp}$): $$0 = -I_{mp} + I_{ph,ref}\!\left(1 - \frac{d_i^2/\mu\tau}{N_c V_{bi} - (V_{mp} + I_{mp} R_{s,ref})}\right) - I_{0,ref}\!\left(\exp\!\frac{V_{mp} + I_{mp} R_{s,ref}}{\gamma_{ref} V_{th,ref}} - 1\right) - \frac{V_{mp} + I_{mp} R_{s,ref}}{R_{sh,ref}}$$ The system is solved by the Levenberg–Marquardt non-linear least-squares algorithm with a patience limit of 1000 iterations. The initial guesses follow from substituting the technology-dependent $\gamma_0$ into the short-circuit approximation: $$I_{ph}^{(0)} = I_{sc}\!\left(1 + \frac{R_{s,ref}}{R_{sh,ref}}\right), \qquad I_0^{(0)} = I_{sc} \exp\!\left(-\frac{q \, V_{oc}}{k \, T_{ref} \, N_c \, \gamma_0}\right), \qquad \gamma^{(0)} = \gamma_0$$ The solver returns $\gamma_{ref}$, $I_{0,ref}$, and $I_{ph,ref}$ conditional on $R_{s,ref}$ and $R_{sh,ref}$; $R_{s,ref}$ is determined separately by the searches below.

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Maximum Series Resistance Search (5-parameter)

For the 5-parameter model, $R_{s,ref}$ is bracketed by the largest value for which the core system admits a physically meaningful solution—specifically, where the ratio $I_{0,ref}/I_{ph,ref}$ remains above $10^{-12}$:

1. Start at $R_{s,ref} = 0$.
2. Increase $R_{s,ref}$ by $\Delta R = 0.1\,\Omega$; re-solve the core system. Repeat while $I_{0,ref}/I_{ph,ref} > 10^{-12}$ or until 1000 iterations are performed.
3. Back off by $\Delta R$, set $\Delta R \leftarrow \Delta R / 10$, and repeat.
4. After three refinement passes ($\Delta R = 0.1, 0.01, 0.001\,\Omega$), the final value is $R_{s,\max}$.

The generated module’s $R_{s,ref}$ is then set by the EIR-tuning step described below; $R_{s,\max}$ serves as the upper bound.

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Maximum Series Resistance and Recombination Search (7-parameter, CdTe)

For the 7-parameter model, two quantities must be bracketed before the core solve: Maximum recombination parameter. Hold $R_{s,ref} = 0.1\,\Omega$ and iterate $d_i^2/\mu\tau$ upward from 0 using the same zero-in schedule ($\Delta = 0.1, 0.01, 0.001$, three passes) while $I_{0,ref}/I_{ph,ref} > 10^{-12}$. The resulting upper bound $\left(d_i^2/\mu\tau\right)_{\max}$ is then reduced to 90 % for use in the module: $$\frac{d_i^2}{\mu\tau} = 0.9 \cdot \left(\frac{d_i^2}{\mu\tau}\right)_{\max}$$ Maximum series resistance. With $d_i^2/\mu\tau$ fixed at the 90 % value, repeat the three-pass bracketing search on $R_{s,ref}$ as in the 5-parameter case to obtain $R_{s,\max}$. The final reference series resistance is set to half the maximum: $$R_{s,ref} = 0.5 \cdot R_{s,\max}$$ The core Levenberg–Marquardt system is then solved once at these values of $R_{s,ref}$ and $d_i^2/\mu\tau$ to finalize $\gamma_{ref}$, $I_{0,ref}$, and $I_{ph,ref}$.

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Series Resistance Tuning to Effective Irradiance Response

When only datasheet values are available (no user-supplied EIR targets), the 5-parameter series resistance is tuned so that the module reaches a technology-dependent default relative efficiency $\eta_{rel}^{target}$ (0.97 for c-Si, 0.95 for CdTe and CIGS) at 200 W/m² and 25 °C. The relative efficiency is defined as: $$\eta_{rel}(G, T) = \frac{P_{mp}(G, T)}{P_{mp,STC} \cdot G / G_{ref}}$$ Starting from $R_{s,ref} = 0.2 \cdot R_{s,\max}$, the algorithm increments $R_{s,ref}$ by $\Delta R$, re-solves the core system, and re-evaluates $\eta_{rel}(200\,\mathrm{W/m^2})$ until either $\eta_{rel}$ falls inside the window $(0.97001, 0.975)$ or $R_{s,ref}$ exceeds $0.95 \cdot R_{s,\max}$. Two refinement passes ($\Delta R = 0.01, 0.001\,\Omega$) tighten the result. A small margin of $10 \Delta R$ is added at the end to compensate for the last under-shoot. When explicit EIR targets are provided at 200, 400, 600, and 800 W/m² at 25 °C, the tuning minimizes a weighted root-mean-square error against those targets: $$\varepsilon = \sqrt{\frac{1}{N} \sum_{G \in \{200,400,600,800\}} w_G \left(\eta_{rel}^{target}(G) - \eta_{rel}^{model}(G)\right)^2}$$ with weights $w_{200} = 0.4$, $w_{400} = 0.6$, $w_{600} = 0.8$, $w_{800} = 1.0$. A coarse two-step direction probe at $\Delta R = 0.1\,\Omega$ selects increase or decrease, followed by a refined walk at $\Delta R = 0.01\,\Omega$ until the error stops decreasing, the upper bound $R_{s,\max}$ is reached, or the lower bound of $0.05 \cdot R_{s,\max}$ is reached.

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Finalizing the Power Temperature Coefficient ($\mu_\gamma$)

The linear temperature dependence of the diode ideality factor $\mu_\gamma$ (the $\alpha_\gamma$ appearing in Parameter Translation) is set so that the generated module reproduces the datasheet $\beta_{P_{mp}}$. The algorithm evaluates $P_{mp}$ at 25 °C and at 45 °C under the scaled parameters and defines the effective model temperature coefficient: $$\mu_{P_{mp}} = \frac{1}{P_{mp}(25\,°\mathrm{C})} \cdot \frac{P_{mp}(45\,°\mathrm{C}) - P_{mp}(25\,°\mathrm{C})}{45 - 25}$$ Starting from $\mu_\gamma = 0.01\,\%/°\mathrm{C}$, a direction probe evaluates $\mu_{P_{mp}}$ at three trial values and selects the sign that reduces the error $\beta_{P_{mp}}/100 - \mu_{P_{mp}}$. The algorithm then walks $\mu_\gamma$ in that direction with an increment of $\pm 0.111 \cdot \mu_\gamma$ and four successive refinement passes (each dividing the increment by 20 and the convergence tolerance by 10). Convergence is reached when $|\beta_{P_{mp}}/100 - \mu_{P_{mp}}| < \varepsilon$; the final $\beta_{P_{mp}}$ returned by the module is the one produced by the converged $\mu_\gamma$.

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Computing $\alpha$ and Module Thermal Quantities

The dimensionless exponent prefactor $\alpha$ used by the single-diode solver is: $$\alpha = \frac{q}{k \, N_c \, \gamma_{ref} \, T_K}$$ with $T_K$ the reference cell temperature in Kelvin. For modules with a non-default reference ($T_{ref} \neq 25\,°\mathrm{C}$ or $G_{ref} \neq 1000\,\mathrm{W/m^2}$), $\alpha$ is recomputed from the scaled $\gamma$ at the target reference.

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Extraction from Key I-V Points (IEC 61853-1)

The Key I-V Points path accepts a matrix of $(T, G, I_{sc}, V_{oc}, I_{mp}, V_{mp}, P_{mp})$ readings. An STC point ($T = 25\,°\mathrm{C}$, $G = 1000\,\mathrm{W/m^2}$) is mandatory. When additional temperatures above 25 °C are present at $G = 1000\,\mathrm{W/m^2}$, the temperature coefficients are fitted by ordinary linear regression and normalized to %/°C: $$\beta_{P_{mp}} = \frac{\partial P_{mp}/\partial T}{P_{mp,STC}} \cdot 100, \qquad \alpha_{I_{sc}} = \frac{\partial I_{sc}/\partial T}{I_{sc,STC}} \cdot 100, \qquad \beta_{V_{oc}} = \frac{\partial V_{oc}/\partial T}{V_{oc,STC}} \cdot 100$$ When irradiances other than 1000 W/m² are present, relative efficiency targets are derived per temperature group for use in the EIR tuning step above: $$\eta_{rel}(G_i, T_j) = \frac{P_{mp}(G_i, T_j)}{P_{mp}(G = 1000\,\mathrm{W/m^2}, T_j) \cdot G_i / G_{ref}}$$ The extracted STC quantities and coefficients are then passed to the core pipeline as if they had been entered on the datasheet.

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Extraction from Full I-V Curves

For each supplied $(T, G)$ curve, PlantPredict first filters out points at the origin and any points with negative current or voltage. A curve must contain at least 40 data points after filtering. The key I-V quantities are then computed:

• Short-circuit current $I_{sc}$: if a point with $V = 0$ exists, its current is used; otherwise a linear regression on $I(V)$ restricted to $V \leq V_{\max}/20$ is fitted and the $V = 0$ intercept is returned.
• Open-circuit voltage $V_{oc}$: if a point with $I = 0$ exists, its voltage is used; otherwise a linear regression on $V(I)$ restricted to $I \leq I_{\max}/20$ returns the $I = 0$ intercept.
• Maximum power $P_{mp} = \max(I \cdot V)$; the corresponding $(V_{mp}, I_{mp})$ are the data-point coordinates at that maximum.

The resulting per-curve Key I-V rows feed the Key I-V Points pipeline above.

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Import from a PVsyst PAN File

PlantPredict imports text-based PVsyst PAN files (v6.8.0 and later). Binary PAN files are not supported and raise a parse error. The importer reads key–value lines and maps PVsyst fields onto ModuleDTO fields, with unit conversions where necessary: After mapping, PlantPredict applies technology-specific defaults. CdTe modules are assigned the First Solar POR spectral response with the Lee & Panchula two-variable coefficients; other technologies receive the generic c-Si Lee & Panchula coefficients with spectral response off by default. The PV model is set to 1-Diode Recombination for CdTe and 1-Diode otherwise. The core generator (GenerateModuleParametersAdavanced) is then invoked to re-derive $I_{ph,ref}$, $I_{0,ref}$, $\gamma_{ref}$, $\mu_\gamma$, and $\alpha$ consistent with the imported $R_{s,ref}$ and $R_{sh,ref}$. Finally, the nameplate $P_{mp,STC}$ is restored to the PAN value (overriding any shift introduced by regeneration) and a fixed set of defaults is applied:

• Heat absorption coefficient 0.9; Sandia convective coefficient −0.075; Sandia conductive coefficient −3.56; cell-to-module temperature difference 3 °C; heat-balance conductive coefficient 29.
• Back-side mismatch 3 %.
• Module mismatch coefficient 0.5 % for CdTe, 1.0 % otherwise.
• Light-induced degradation 0 for CdTe, 1.5 % for all other technologies.
• Linear degradation 0.5 %/year.
• Module shading response set to Linear for CdTe and to Fractional Electrical Shading otherwise, with a 100 % electrical shading effect.
• Default ASHRAE IAM $b_0 = 0.05$; the Sandia IAM polynomial and the tabular IAM use PlantPredict-fitted defaults. If the PAN file contains an IAMProfile block, its $(\theta, f)$ pairs are imported verbatim. If no profile is provided but FrontSurface = fsARCoating is present, an ARC-specific default table is used; otherwise a generic no-ARC table is used.

The resulting module can be further tuned via the Advanced inputs (GenerateModuleParametersAdavanced) or optimized against measured EIR data (OptimizeSeriesResistance) using the same core routines described above.

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Parameter Validation

PlantPredict enforces range checks on generated parameters; if any fall outside the intervals below, generation fails with an “out of range” error: The generated module is then passed to Parameter Translation at every simulation time step to produce the operating-condition values consumed by the 5-Parameter Model or the 7-Parameter Model.

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References

• 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. DOI: 10.1016/j.solener.2005.06.010
• 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.
• Levenberg, K. (1944). A method for the solution of certain non-linear problems in least squares. Quarterly of Applied Mathematics, 2(2), 164–168. DOI: 10.1090/qam/10666
• Marquardt, D. W. (1963). An algorithm for least-squares estimation of nonlinear parameters. Journal of the Society for Industrial and Applied Mathematics, 11(2), 431–441. DOI: 10.1137/0111030
• IEC 61853-1:2011. Photovoltaic (PV) module performance testing and energy rating — Part 1: Irradiance and temperature performance measurements and power rating. International Electrotechnical Commission.
• Lee, M., & Panchula, A. (2016). Spectral correction for photovoltaic module performance based on air mass and precipitable water. 2016 IEEE 43rd Photovoltaic Specialists Conference (PVSC), 1351–1356. DOI: 10.1109/PVSC.2016.7749836