Introduction to I-V Curves

An I − V curve indicates the relationship between current and voltage for a solar cell or module. Thus for a single I − V curve, the dataset usually consists of several data points of voltage V and the associated current I. As is shown in Figure 1, a standard I − V curve has the shape of a concave curve with nearly no change of current at small voltage, and a sharp decrease of current at a certain voltage point.

Solar cell parameters in I − V curves are important in evaluating the performance and degradation of PV modules. These performance parameters include the maximum power point P_mp, short-circuit current I_sc, open-circuit voltage V_oc, shunt resistance R_sh, series resistance R_s, and fill factor FF. The first five of these parameters are illustrated in Figure 1. I_sc is defined as the current at zero voltage (the y-intercept of the I − V curve), while V_oc is the voltage at zero current (the x-intercept). R_sh is equivalent to the negative of inverse slope of the I − V curve near I_sc. R_s is equivalent to the negative of inverse slope of the I − V curve near V_oc. P_mp is the maximum product of current and voltage on the I − V curve. FF is defined as the ratio of the maximum power from the solar cell to the product of V_oc and I_sc, it measures the “squareness” of the solar cell. FF is not shown in Figure 1 directly, but can be calculated with the equation

$Figure 1: A standard $I-V$ curve and $I-V$ features. $I-V$ curve shows the relationship between current($I$) and voltage ($V$). $I-V$ features are maximum power point ($P_{mp}$), short-circuit current ($I_{sc}$), open-circuit voltage ($V_{oc}$), shunt resistance ($R_{sh}$), series resistance ($R_s$), and fill factor ($FF$)$

Figure 1: A standard I − V curve and I − V features. I − V curve shows the relationship between current(I) and voltage (V). I − V features are maximum power point (P_mp), short-circuit current (I_sc), open-circuit voltage (V_oc), shunt resistance (R_sh), series resistance (R_s), and fill factor (FF)

We define the in the I − V curves as how many typical I − V curve shapes appear in the current-voltage relationship. The standard I − V curve shown in Figure 1 is said to have only one step. There are cases (e.g. when it is cloudy) where several steps are present in a single I − V curve due to activation of the bypass diodes. An example of I − V curves with steps is demonstrated in Figure 2. This I − V curve looks like a combination of three standard I − V curves. This pattern of I − V curves is an indication of mismatch between different areas of the array of module under test. This may be caused by a partial shading of the PV array or damage of PV cells, causing bypass diodes to activate. If a step is caused by partially shaded array, then the step would be transient and disappear from future I − V curves. However, if the PV cell is damaged, then the step would be permanent.

Figure 2: An example of I − V curve that has three steps. The I − V curve is a combination of three standard I − V curves. There are three local maximum power point for each standard I − V curves. Out of these three, one is the global maximum power point.

Load data and run code to extract I − V features

library(ddiv)
## Use the example IV curve data that has two steps
## Load the IV curve data set
data(IV_step2)
IV2 <- data.frame(IV_step2)
#?IV_step2

## Calculate number of steps in IV curve
IVsteps(IV2$I,IV2$V,plot.option=FALSE)

## $step
## [1] 2
## 
## $xsep
##       V1
## 1 10.596

## Extract two sets of IV features for each sub IV curves
IVExtractResult(IV2,plot.option=FALSE)

##   step            Isc                Rsh              Voc              Rs
## 1    2 V1#1.732#1.917 V1#2732.708#46.831 V1#68.612#37.133 V1#34.319#1.082
##                Pmp            Imp              Vmp             FF    Cutoff
## 1 V1#17.841#55.137 V1#1.692#1.646 V1#10.544#33.489 V1#15.01#77.46 V1#10.596

- Load data and run code to extract I − V features

Introduction to I − V Curves

Load data and run code to extract I − V features