pvlib.ivtools.sde.fit_sandia_simple¶
-
pvlib.ivtools.sde.fit_sandia_simple(voltage, current, v_oc=None, i_sc=None, v_mp_i_mp=None, vlim=0.2, ilim=0.1)[source]¶ Fits the single diode equation (SDE) to an IV curve.
- Parameters
voltage (ndarray) – 1D array of float type containing voltage at each point on the IV curve, increasing from 0 to
v_ocinclusive. [V]current (ndarray) – 1D array of float type containing current at each point on the IV curve, from
i_scto 0 inclusive. [A]v_oc (float, default None) – Open circuit voltage. If not provided,
v_ocis taken as the last point in thevoltagearray. [V]i_sc (float, default None) – Short circuit current. If not provided,
i_scis taken as the first point in thecurrentarray. [A]v_mp_i_mp (tuple of float, default None) – Voltage, current at maximum power point. If not provided, the maximum power point is found at the maximum of
voltagetimescurrent. [V], [A]vlim (float, default 0.2) – Defines portion of IV curve where the exponential term in the single diode equation can be neglected, i.e.
voltage<=vlimxv_oc. [V]ilim (float, default 0.1) – Defines portion of the IV curve where the exponential term in the single diode equation is significant, approximately defined by
current< (1 -ilim) xi_sc. [A]
- Returns
photocurrent (float) – photocurrent [A]
saturation_current (float) – dark (saturation) current [A]
resistance_series (float) – series resistance [ohm]
resistance_shunt (float) – shunt (parallel) resistance [ohm]
nNsVth (float) – product of thermal voltage
Vth[V], diode ideality factorn, and number of series cellsNs. [V]
- Raises
RuntimeError if parameter extraction is not successful. –
Notes
Inputs
voltage,current,v_oc,i_scandv_mp_i_mpare assumed to be from a single IV curve at constant irradiance and cell temperature.fit_sandia_simple()obtains values for the five parameters for the single diode equation 1:\[I = I_{L} - I_{0} (\exp \frac{V + I R_{s}}{nNsVth} - 1) - \frac{V + I R_{s}}{R_{sh}}\]See
pvlib.pvsystem.singlediode()for definition of the parameters.The extraction method 2 proceeds in six steps.
In the single diode equation, replace \(R_{sh} = 1/G_{p}\) and re-arrange
\[I = \frac{I_{L}}{1 + G_{p} R_{s}} - \frac{G_{p} V}{1 + G_{p} R_{s}} - \frac{I_{0}}{1 + G_{p} R_{s}} (\exp(\frac{V + I R_{s}}{nN_sV_{th}}) - 1)\]The linear portion of the IV curve is defined as \(V \le vlim \times v_{oc}\). Over this portion of the IV curve,
\[\frac{I_{0}}{1 + G_{p} R_{s}} (\exp(\frac{V + I R_{s}}{nN_sV_{th}}) - 1) \approx 0\]Fit the linear portion of the IV curve with a line.
\[I &\approx \frac{I_{L}}{1 + G_{p} R_{s}} - \frac{G_{p}}{1 + G_{p}R_{s}} V &= \beta_{0} + \beta_{1} V\]The exponential portion of the IV curve is defined by \(\beta_{0} + \beta_{1} \times V - I > ilim \times i_{sc}\). Over this portion of the curve, \(\exp((V + IR_s)/{nN_sV_{th}}) \gg 1\) so that
\[\exp(\frac{V + I R_{s}}{nN_sV_{th}}) - 1 \approx \exp(\frac{V + I R_{s}}{nN_sV_{th}})\]Fit the exponential portion of the IV curve.
\[\begin{split}\log(\beta_{0} - \beta_{1} V - I) &\approx \log(\frac{I_{0}}{1 + G_{p} R_{s}} + \frac{V}{nN_sV_{th}} + \frac{I R_{s}}{nN_sV_{th}}) \\ &= \beta_{2} + \beta_{3} V + \beta_{4} I\end{split}\]Calculate values for
IL, I0, Rs, Rsh,andnNsVthfrom the regression coefficents \(\beta_{0}, \beta_{1}, \beta_{3}\) and \(\beta_{4}\).
References