Parameter Translation

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Summary

Parameter Translation scales the five single diode model parameters from Standard Test Conditions (STC: 25°C, 1000 W/m²) to actual operating conditions. PlantPredict applies physically-based scaling relationships for series resistance, shunt resistance, diode ideality factor, saturation current, short-circuit current, and photocurrent. Temperature scaling uses linear or polynomial relationships, while irradiance scaling uses exponential relationships for shunt resistance and linear relationships for photocurrent. All parameters are calculated before solving the single diode circuit equation.

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Inputs

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Outputs

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Detailed Description

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Series Resistance Scaling

$$R_s = R_{s,ref} (1 + \alpha_{R_s} (T_{actual} - T_{ref}))$$ where $\alpha_{R_s}$ is temperature coefficient of series resistance. In PlantPredict implementation: $\alpha_{R_s} = 0$ (not used), so: $$R_s = R_{s,ref}$$ Then add DC wiring resistance: $$R_s \leftarrow R_s + R_{s,DC}$$

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Shunt Resistance Scaling

$$R_{sh} = R_{sh,ref} + (R_{sh,0} - R_{sh,ref}) \exp\left(-R_{sh,exp} \frac{G_{actual}}{G_{ref}}\right)$$ where:

• $R_{sh,ref}$ is shunt resistance at STC
• $R_{sh,0}$ is dark shunt resistance (at $G = 0$)
• $R_{sh,exp}$ is exponential dependency coefficient

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Diode Ideality Factor Scaling

Linear model: $$\gamma = \gamma_{ref} (1 + \alpha_{\gamma} (T_{actual} - T_{ref}))$$ where $\alpha_{\gamma}$ is linear temperature dependence coefficient. Nonlinear model (OneDiodeRecombinationNonLinear): $$\Delta T = T_{actual} - T_{ref}$$ $$\gamma = \gamma_{ref} (1 + a_{\gamma} \Delta T + b_{\gamma} \Delta T^2 + c_{\gamma} \Delta T^3 + d_{\gamma} \Delta T^4)$$ where $a_{\gamma}, b_{\gamma}, c_{\gamma}, d_{\gamma}$ are polynomial coefficients.

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Alpha Parameter

$$\alpha = \frac{q}{k T_{actual} N_s \gamma}$$ where:

• $q = 1.602 \times 10^{-19}$ C (elementary charge)
• $k = 1.381 \times 10^{-23}$ J/K (Boltzmann constant)
• $T_{actual}$ in Kelvin
• $N_s$ is number of cells in series
• $\gamma$ is scaled ideality factor

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Saturation Current Scaling

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

• $E_g$ is bandgap voltage (eV)
• All other parameters as defined above

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Short-Circuit Current Scaling

$$I_{sc} = I_{sc,ref} \frac{G_{actual}}{G_{ref}} (1 + \alpha_{I_{sc}} (T_{actual} - T_{ref}))$$ where $\alpha_{I_{sc}}$ is temperature coefficient of short-circuit current (typically 0.0003 to 0.0006 /K).

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Photocurrent Scaling

Standard model (OneDiode): $$I_{ph} = I_{sc,ref} \frac{G_{actual}}{G_{ref}} (1 + \alpha_{I_{sc}} (T_{actual} - T_{ref}))$$ (Same as $I_{sc}$ for standard model) Advanced model (OneDiodeRecombination): If $I_{sc} \leq 0$: $$I_{ph} = 0$$ Otherwise: $$I_{ph} = \frac{I_{sc} + I_0 (e^{I_{sc} R_s \alpha} - 1) + I_{sc} R_s / R_{sh}}{1 - \frac{di_2/u_t}{N_s V_{bi} - I_{sc} R_s}}$$ where:

• $di_2/u_t$ is recombination parameter
• $V_{bi}$ is built-in voltage per cell
• $N_s$ is number of cells in series

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References

• King, D. L., Boyson, W. E., & Kratochvil, J. A. (2004). Photovoltaic array performance model. SAND2004-3535, Sandia National Laboratories.
• 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.