pvlib.singlediode.bishop88

pvlib.singlediode.bishop88(diode_voltage, photocurrent, saturation_current, resistance_series, resistance_shunt, nNsVth, d2mutau=0, NsVbi=inf, breakdown_factor=0.0, breakdown_voltage=-5.5, breakdown_exp=3.28, gradients=False)

Explicit calculation of points on the IV curve described by the single diode equation. Values are calculated as described in [1].

The single diode equation with recombination current and reverse bias breakdown is

\[I = I_{L} - I_{0} \left (\exp \frac{V_{d}}{nN_{s}V_{th}} - 1 \right ) - \frac{V_{d}}{R_{sh}} - \frac{I_{L} \frac{d^{2}}{\mu \tau}}{N_{s} V_{bi} - V_{d}} - a \frac{V_{d}}{R_{sh}} \left (1 - \frac{V_{d}}{V_{br}} \right )^{-m}\]

The input diode_voltage must be \(V + I R_{s}\).

Warning

• Usage of d2mutau is required with PVSyst coefficients for cadmium-telluride (CdTe) and amorphous-silicon (a:Si) PV modules only.

• Do not use d2mutau with CEC coefficients.

Parameters:

• diode_voltage (numeric) – diode voltage \(V_d\) [V]

• photocurrent (numeric) – photo-generated current \(I_{L}\) [A]

• saturation_current (numeric) – diode reverse saturation current \(I_{0}\) [A]

• resistance_series (numeric) – series resistance \(R_{s}\) [ohms]

• resistance_shunt (numeric) – shunt resistance \(R_{sh}\) [ohms]

• nNsVth (numeric) – product of thermal voltage \(V_{th}\) [V], diode ideality factor \(n\), and number of series cells \(N_{s}\) [V]

• d2mutau (numeric, default 0) – PVsyst parameter for cadmium-telluride (CdTe) and amorphous-silicon (a-Si) modules that accounts for recombination current in the intrinsic layer. The value is the ratio of intrinsic layer thickness squared \(d^2\) to the diffusion length of charge carriers \(\mu \tau\). [V]

• NsVbi (numeric, default np.inf) – PVsyst parameter for cadmium-telluride (CdTe) and amorphous-silicon (a-Si) modules that is the product of the PV module number of series cells \(N_{s}\) and the builtin voltage \(V_{bi}\) of the intrinsic layer. [V].

• breakdown_factor (float, default 0) – fraction of ohmic current involved in avalanche breakdown \(a\). Default of 0 excludes the reverse bias term from the model. [unitless]

• breakdown_voltage (float, default -5.5) – reverse breakdown voltage of the photovoltaic junction \(V_{br}\) [V]

• breakdown_exp (float, default 3.28) – avalanche breakdown exponent \(m\) [unitless]

• gradients (bool) – False returns only I, V, and P. True also returns gradients

Returns:

tuple – currents [A], voltages [V], power [W], and optionally \(\frac{dI}{dV_d}\), \(\frac{dV}{dV_d}\), \(\frac{dI}{dV}\), \(\frac{dP}{dV}\), and \(\frac{d^2 P}{dV dV_d}\)

Notes

The PVSyst thin-film recombination losses parameters d2mutau and NsVbi should only be applied to cadmium-telluride (CdTe) and amorphous- silicon (a-Si) PV modules, [2], [3]. The builtin voltage \(V_{bi}\) should account for all junctions. For example: tandem and triple junction cells would have builtin voltages of 1.8[V] and 2.7[V] respectively, based on the default of 0.9[V] for a single junction. The parameter NsVbi should only account for the number of series cells in a single parallel sub-string if the module has cells in parallel greater than 1.

References

[1]

“Computer simulation of the effects of electrical mismatches in photovoltaic cell interconnection circuits” JW Bishop, Solar Cell (1988) DOI: 10.1016/0379-6787(88)90059-2

[2]

“Improved equivalent circuit and Analytical Model for Amorphous Silicon Solar Cells and Modules.” J. Mertens, et al., IEEE Transactions on Electron Devices, Vol 45, No 2, Feb 1998. DOI: 10.1109/16.658676

[3]

“Performance assessment of a simulation model for PV modules of any available technology”, André Mermoud and Thibault Lejeune, 25th EUPVSEC, 2010 DOI: 10.4229/25thEUPVSEC2010-4BV.1.114

Examples using pvlib.singlediode.bishop88

Calculating power loss from partial module shading

Calculating power loss from partial module shading