pvlib.singlediode.bishop88(diode_voltage, photocurrent, saturation_current, resistance_series, resistance_shunt, nNsVth, d2mutau=0, NsVbi=inf, gradients=False)[source]

Explicit calculation of points on the IV curve described by the single diode equation 1.


  • Do not use d2mutau with CEC coefficients.

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

  • diode_voltage (numeric) – diode voltages [V]

  • photocurrent (numeric) – photo-generated current [A]

  • saturation_current (numeric) – diode reverse saturation current [A]

  • resistance_series (numeric) – series resistance [ohms]

  • resistance_shunt (numeric) – shunt resistance [ohms]

  • nNsVth (numeric) – product of thermal voltage Vth [V], diode ideality factor n, and number of series cells Ns

  • d2mutau (numeric) – PVSyst thin-film recombination parameter that is the ratio of thickness of the intrinsic layer squared \(d^2\) and the diffusion length of charge carriers \(\mu \tau\), in volts [V], defaults to 0[V]

  • NsVbi (numeric) – PVSyst thin-film recombination parameter that is the product of the PV module number of series cells Ns and the builtin voltage Vbi of the intrinsic layer, in volts [V], defaults to np.inf

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


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


The PVSyst thin-film recombination losses parameters d2mutau and NsVbi are only 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.



“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


“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


“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