> ## Documentation Index
> Fetch the complete documentation index at: https://docs.plantpredict.com/llms.txt
> Use this file to discover all available pages before exploring further.

# Parameter Translation

export const SeriesResistance = () => <Tooltip tip="Combined ohmic resistance of cell metallization, interconnects, and wiring in the module current path; causes I²R losses.">
    series resistance
  </Tooltip>;

export const BuiltInVoltage = () => <Tooltip tip="Contact potential across a semiconductor junction at equilibrium, equal to the difference in chemical potential between the two sides in isolation.">
    built-in voltage
  </Tooltip>;

export const Recombination = () => <Tooltip tip="Loss of photo-generated electron-hole pairs before collection as electrical current; reduces cell output.">
    recombination
  </Tooltip>;

export const SaturationCurrent = () => <Tooltip tip="Reverse-bias leakage current of the diode in the single-diode model; represents charge carrier recombination.">
    saturation current
  </Tooltip>;

export const BandgapEnergy = () => <Tooltip tip="Minimum energy to excite an electron across the semiconductor junction; determines spectral response (1.12 eV for c-Si).">
    bandgap energy
  </Tooltip>;

export const Photocurrent = () => <Tooltip tip="Light-generated current in a PV cell; slightly exceeds short-circuit current due to internal losses at V = 0.">
    photocurrent
  </Tooltip>;

export const ShortCircuitCurrent = () => <Tooltip tip="Maximum current from a PV cell when terminals are connected (V = 0); scales approximately linearly with irradiance.">
    short-circuit current
  </Tooltip>;

export const DiodeIdealityFactor = () => <Tooltip tip="Dimensionless parameter (typically 1–2) characterizing how closely a PV cell junction follows ideal diode behavior.">
    diode ideality factor
  </Tooltip>;

export const ShuntResistance = () => <Tooltip tip="Parasitic resistance across the PV cell junction from manufacturing defects; allows leakage current that reduces output.">
    shunt resistance
  </Tooltip>;

export const IVCurve = () => <Tooltip tip="Current-voltage characteristic of a PV cell or module; the operating point on this curve determines power output.">
    I-V curve
  </Tooltip>;

export const SingleDiodeModel = () => <Tooltip tip="Equivalent circuit representing a PV cell as a current source, diode, and resistances to predict I-V behavior.">
    single-diode model
  </Tooltip>;

export const STC = () => <Tooltip tip="Standard Test Conditions: 1000 W/m² irradiance, 25 °C cell temperature, AM1.5G spectrum; the reference conditions for rating PV modules.">
    STC
  </Tooltip>;

## Summary

Parameter Translation scales the five standard <SingleDiodeModel /> parameters—<Photocurrent />, <SaturationCurrent />, <DiodeIdealityFactor />, <SeriesResistance />, and <ShuntResistance />—from reference conditions (typically <STC />: 25 °C, 1000 W/m²) to actual operating conditions using physics-based scaling relationships. PlantPredict also scales <ShortCircuitCurrent /> for use in downstream calculations. All parameters are scaled before solving the single-diode circuit equation. The two additional parameters of the seven-parameter <Recombination /> model ($d_i^2/\mu\tau$ and $V_{bi}$) are not scaled, so this procedure applies similarly to both model variants.

## Inputs

| Name                                        | Symbol                                   | Units                     | Description                                                                                                    |
| ------------------------------------------- | ---------------------------------------- | ------------------------- | -------------------------------------------------------------------------------------------------------------- |
| **Series Resistance**                       | $R_{s,ref}$                              | Ω                         | Series resistance at reference conditions                                                                      |
| **Shunt Resistance**                        | $R_{sh,ref}$                             | Ω                         | Shunt resistance at reference conditions                                                                       |
| **Diode Ideality Factor**                   | $\gamma_{ref}$                           | —                         | Ideality factor at reference conditions                                                                        |
| **Saturation Current**                      | $I_{0,ref}$                              | A                         | Saturation current at reference conditions                                                                     |
| **Short-Circuit Current**                   | $I_{sc,ref}$                             | A                         | Short-circuit current at reference conditions                                                                  |
| **Reference Temperature**                   | $T_{ref}$                                | °C                        | Reference temperature (typically 25 °C)                                                                        |
| **Reference Irradiance**                    | $G_{ref}$                                | W/m²                      | Reference irradiance (typically 1000 W/m²)                                                                     |
| **Cell Temperature**                        | $T_c$                                    | °C                        | Operating cell temperature (from [temperature model](/models/dc-performance/overview#cell-temperature-models)) |
| **Total Effective POA Irradiance**          | $G'_{POA,tot,eff}$                       | W/m²                      | Total effective POA irradiance after [DC system losses](/models/dc-performance/dc_system_losses)               |
| **Temp. Coeff. of Ideality Factor**         | $\alpha_{\gamma}$                        | 1/°C                      | Linear temperature coefficient of diode ideality factor                                                        |
| **Ideality Factor Polynomial Coefficients** | $a_\gamma, b_\gamma, c_\gamma, d_\gamma$ | 1/°C, 1/°C², 1/°C³, 1/°C⁴ | Polynomial temperature coefficients for ideality factor                                                        |
| **Temp. Coeff. of Short-Circuit Current**   | $\alpha_{I_{sc}}$                        | %/°C                      | Linear temperature coefficient of short-circuit current                                                        |
| **DC Wiring Resistance**                    | $R_{DC,module}$                          | Ω                         | Per-module [DC equivalent series resistance](/models/dc-performance/dc_wiring_resistance)                      |
| **Dark Shunt Resistance**                   | $R_{sh,0}$                               | Ω                         | Shunt resistance at zero irradiance                                                                            |
| **Shunt Resistance Exponent**               | $R_{sh,exp}$                             | —                         | Exponential dependency coefficient (default = 5.5)                                                             |
| **Recombination Parameter**                 | $d_i^2/\mu\tau$                          | V                         | Recombination parameter for 7-parameter single-diode model                                                     |
| **Built-in Voltage**                        | $V_{bi}$                                 | V                         | Built-in junction voltage per cell for 7-parameter single-diode model                                          |
| **Bandgap Energy**                          | $E_g$                                    | eV                        | Semiconductor bandgap                                                                                          |
| **Number of Cells in Series**               | $N_c$                                    | —                         | Cells in series within module                                                                                  |

***

## Outputs

| Name                      | Symbol   | Units | Description                  |
| ------------------------- | -------- | ----- | ---------------------------- |
| **Series Resistance**     | $R_s$    | Ω     | Scaled series resistance     |
| **Shunt Resistance**      | $R_{sh}$ | Ω     | Scaled shunt resistance      |
| **Diode Ideality Factor** | $\gamma$ | —     | Scaled ideality factor       |
| **Saturation Current**    | $I_0$    | A     | Scaled saturation current    |
| **Short-Circuit Current** | $I_{sc}$ | A     | Scaled short-circuit current |
| **Photocurrent**          | $I_{ph}$ | A     | Scaled photocurrent          |

***

## Detailed Description

The general <IVCurve /> of a PV cell is described by:

$$
I = I_{ph} - I_0 \left(\exp\!\left(\frac{q(V + IR_s)}{N_c k T_c \gamma}\right) - 1\right) - \frac{V + IR_s}{R_{sh}} - \frac{(d_i^2/\mu\tau) \cdot I_{ph}}{N_c V_{bi} - (V + IR_s)}
$$

where $q = 1.602 \times 10^{-19}$ C is the elementary charge and $k = 1.381 \times 10^{-23}$ J/K is the Boltzmann constant.

The first five parameters—photocurrent $I_{ph}$, saturation current $I_0$, ideality factor $\gamma$, series resistance $R_s$, and shunt resistance $R_{sh}$—define the [5-parameter model](/models/dc-performance/5_parameter_model). The last term, governed by the recombination parameter $d_i^2/\mu\tau$ and <BuiltInVoltage>built-in junction voltage</BuiltInVoltage> $V_{bi}$, is an optional extension used by the [7-parameter model](/models/dc-performance/7_parameter_model) to improve accuracy at low irradiance. For the 5-parameter model, $d_i^2/\mu\tau = 0$ 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](/models/dc-performance/dc_wiring_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, $\Delta T = T_c - T_{ref}$ denotes the temperature difference from reference conditions.

### Series Resistance

The per-module [DC wiring resistance](/models/dc-performance/dc_wiring_resistance) $R_{DC,module}$ is added to the reference value:

$$
R_s = R_{s,ref} + R_{DC,module}
$$

### 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 $R_{sh,0}$ at zero irradiance and the reference value at STC:

$$
R_{sh} = R_{sh,ref} + (R_{sh,0} - R_{sh,ref}) \exp\left(-R_{sh,exp} \frac{G'_{POA,tot,eff}}{G_{ref}}\right)
$$

where:

* $R_{sh,ref}$ is the reference shunt resistance, typically defined at STC
* $R_{sh,0}$ is the dark shunt resistance (at $G = 0$ W/m²)
* $R_{sh,exp}$ is the exponential dependency coefficient (default 5.5)

Note that PlantPredict uses $R_{sh,ref}$ directly rather than computing an intermediate base value $R_{sh,base}$. As a result, $R_{sh}$ evaluated at $G'_{POA,tot,eff} = G_{ref}$ does not exactly equal $R_{sh,ref}$—it includes a residual term $(R_{sh,0} - R_{sh,ref}) \cdot e^{-R_{sh,exp}}$. For the default $R_{sh,exp} = 5.5$, this residual is less than 0.5% of $(R_{sh,0} - R_{sh,ref})$.

### 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:**

$$
\gamma = \gamma_{ref} (1 + \alpha_{\gamma} \Delta T)
$$

The coefficient $\alpha_{\gamma}$ is typically derived during parameter extraction from the temperature coefficient of maximum power ($\beta_{P_{mp}}$) 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:**

$$
\gamma = \gamma_{ref} (1 + a_{\gamma} \Delta T + b_{\gamma} \Delta T^2 + c_{\gamma} \Delta T^3 + d_{\gamma} \Delta T^4)
$$

where $a_{\gamma}, b_{\gamma}, c_{\gamma}, d_{\gamma}$ are polynomial coefficients. In practice, these are derived by fitting the single-diode model to measured I-V curves at multiple temperatures, extracting $\gamma$ at each temperature, and then fitting a 4th-degree polynomial to $\gamma$ as a function of $\Delta T$.

### Saturation Current

The saturation current $I_0$ represents the recombination current of charge carriers across the solar cell in the dark. Its temperature dependence follows from the intrinsic carrier concentration $n_i$, where $n_i^2 \propto T^3 \exp(-E_g / kT)$ and $E_g$ is the <BandgapEnergy />. The ideality factor $\gamma$ in the exponent accounts for non-ideal recombination:

$$
I_0 = I_{0,ref} \frac{T_c^3}{T_{ref}^3} \exp\left(\frac{q E_g}{k \gamma} \left(\frac{1}{T_{ref}} - \frac{1}{T_c}\right)\right)
$$

### Short-Circuit Current

Short-circuit current scales linearly with irradiance and is corrected for temperature using the coefficient $\alpha_{I_{sc}}$ (typically from the module datasheet, in %/°C; converted to 1/°C before use in the equation below):

$$
I_{sc} = I_{sc,ref} \frac{G'_{POA,tot,eff}}{G_{ref}} (1 + \alpha_{I_{sc}} \Delta T)
$$

### Photocurrent

The photocurrent $I_{ph}$ is obtained by evaluating the I-V equation at $V = 0$ and solving for $I_{ph}$ to ensure that $I(V=0) = I_{sc}$:

$$
I_{ph} = \frac{I_{sc}\!\left(1 + \frac{R_s}{R_{sh}}\right) + I_0 \left(\exp\!\left(\frac{q \, I_{sc} R_s}{k \, T_c \, N_c \, \gamma}\right) - 1\right)}{1 - \frac{d_i^2/\mu\tau}{N_c V_{bi} - I_{sc} R_s}}
$$

For the 5-parameter model, $d_i^2/\mu\tau = 0$ and the relationship simplifies to:

$$
I_{ph} = I_{sc}\!\left(1 + \frac{R_s}{R_{sh}}\right) + I_0 \left(\exp\!\left(\frac{q \, I_{sc} R_s}{k \, T_c \, N_c \, \gamma}\right) - 1\right)
$$

***

## 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. DOI: [10.1109/JPHOTOV.2014.2364402](https://doi.org/10.1109/JPHOTOV.2014.2364402)
* 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](https://doi.org/10.1016/j.solener.2005.06.010)