Figure 7.6: Change in series resistance, Rs, as a function of the number of cumulative cuts.
Black and blue circles refer to String B. For the blue circles, n disconnected ribbons means that the external ribbon was cut in positions 1 to 7, and the central ribbon was cut from position 1 to n. Lines are linear fits.
As Figure 7.6 shows, the increase in Rsis higher when disconnections are in the external ribbon rather than in the central ribbon. This justifies the corresponding trend for the loss in FF and the Pmaxseen in Figure 7.2. When the external ribbon is already completely disconnected for all cells in a string, each cut in the central ribbon increases the Rsby around 13%, with an impact on Rsapproximately three times higher compared to when the external ribbon is disconnected.
7.3 Modeling the performance of cells/strings with an inhomoge-neous distribution of the series resistance
In the following, we present a simplified model that was implemented in LT-SPICE (version 4.23I) to simulate the electrical performance of a string with disconnected ribbons. The experimental results presented in Section 7.2 are utilized here to validate the model. This model was set up by Jacques Levrat from CSEM [3].
7.3.1 The electrical model
In the previously described experiments, ribbons are cut sequentially forcing the electrical current to be collected through the neighboring ribbon(s). The symmetry of the three-busbar H-pattern invites us to consider the cell as three sub-cells connected in parallel, each being represented by a two-diode model featuring one internal Rs, one shunt resistance Rshand
two saturation currents (I01and I02) with ideality factors n1= 1 and n2= 2, respectively. To reproduce the current redistribution within the cell when one ribbon has been severed, the internal series resistor has been removed from the grid resistance terms, i.e. RG,fand RG,b, for the front and the rear side, respectively. The reason is that these terms relate to lateral transport and should be considered separately as they are involved differently when one ribbon path is missing. The exact scheme considered is depicted in Figure 7.7.
To extract the diode parameters experimentally, one of the cells was measured in the four-terminal configuration within the module environment. A nonlinear fit of the IV curve provides the following diode parameters: J01= 5.2· 10−10A/cm2, J02= 1.1· 10−5A/cm2, Rsh= 40Ω cm2. The internal series resistance (free of the grid contribution) is derived from the fitting of the full module measurement yielding Rs= 4 mΩ cm2. As the cell is monofacial, RG,fcorresponds to the resistance between two front busbar and RG,bto the rear metal blanket resistance value between two backside ribbons. A four-terminal measurement yields RG,f= 25 mΩ and RG,b= 1 mΩ . As all ribbons are the same size, they are modeled by a single-value contribution Rribbon
= 3 mΩ. The only adjustable parameter of the model is the parasitic resistance Rconnector
induced by the crocodile connectors used during the IV measurement. Experimental data were accurately fitted with Rconnector= 3 mΩ.
Figure 7.7: Schematic representation of the LT-SPICE model considered to simulate the 6 × 1 cell string.
7.3.2 Comparison of experimental and simulation results
When only the central ribbon is disconnected (String A), the simulated IV curves fit the measured ones with good accuracy for the different steps, as can be seen in Figure 7.8. The variation of the Pmaxand of the FF obtained from the simulations also closely reproduce the
7.3. Modeling the performance of cells/strings with an inhomogeneous distribution of the series resistance measurements, with a relative error always less (in absolute value) than 1% for the Pmaxand 0.50% for the FF. For the Rsthe relative error is around −10% in the extreme cases of 6 and 7 cuts, where the simulated curves are slightly above the measured ones, whereas for the other cases it is on average −7.22%. This discrepancy can be attributed to the fact that, as mentioned, the value of series resistance estimated from the measurements is the Roc, which is generally higher than the true value of Rsdetermined by fitting the IV curve with the two-diode equation and obtained from the simulations.
Figure 7.8: IV curves of String A: measured (dots) and simulated (lines). The central ribbon is sequentially cut between consecutive cells.
In the configuration in which both an external and the central ribbons are disconnected (String B), our model also predicts the variation of the electrical parameters with a good accuracy.
Figure 7.9 illustrates the relative change of Pmaxand Rswith respect to initial values at each step. As we proceed in cutting the external ribbon, the trend of the simulated values closely follows the measured one. Further, the model is able to reproduce with a good approximation the change in the slope observed experimentally as soon as the central ribbon starts to be disconnected too (corresponding to points 8 to 14 in the x-axis). In this case as well, the overlap of simulated and measured IV curves is very good (see Figure 7.10). It is worth noticing that our model is able not only to reproduce the variation in the curve slope close to the open-circuit point (correlated with Rs), but also the peculiar shape of the IV curve of a cell in which part of the cell is affected by a high series resistance as discussed in Section 7.2.2. Table 7.1 summarizes the Pmaxand Rsvalues obtained from simulations and measurements, and their differences normalized by the measured values.
Figure 7.9: Relative variation of Pmax(top) and of Rs(bottom) for String B with respect to initial values as a function of the number of disconnected points. The values from 0 to 7 cuts are the same as in Figure 7.2 (Ext) and Figure 7.6 (Ext).
Figure 7.10: IV curves of String B: measured (dots) and simulated (lines). First the external ribbon is cut sequentially between adjacent cells (black) until all seven positions are discon-nected, then the central ribbon is also cut sequentially from each cell (blue). A good agreement is observed.