Imagine that you have a voltage source in series with some source resistance feeding power to a variable load. The relationship between load voltage, load current, and cell current can be drawn as follows in Figure 1.
Figure 1 The load voltage versus cell and load current for a circuit where the voltage source is in series with some source resistance feeding power to a variable load.
If by multiplying load voltage times load current, we examine power delivery to the load versus load resistance where the result is a curve that looks like an upside-down soup bowl (Figure 2).
Figure 2 Power to the load (load voltage*load current) versus cell and load current.
For some specific source resistance value, we can plot a horizontal line on our graph (Figure 3).
Figure 3 Adding a specific numerical value for the source resistance.
If we next add a curve to plot the varying load resistance value (Figure 4), we find that the point of maximum power delivery to the load corresponds to equality between the load resistance to the source resistance. Of course, this is expected to be so, but we should also note that the equality of interest is really between the load resistance and the dynamic value of the source resistance as opposed to that part’s value of static resistance.
Figure 4 Discovery of the peak power point by finding the equality between the load resistance to the source resistance.
This last remark may seem trivial, but as we shall now show, it is NOT trivial at all.
From Linear Technology (a name of fond memory today) at this now inoperative URL, we had the following sketch of a photovoltaic (PV) assembly’s characteristics shown in Figure 5.
Figure 5 Solec S-70C PV panel power curve while facing the sun.
Graphically extracting some numbers from the current versus voltage curve and fitting a descriptive equation to those numbers, we find the following in Figure 6.
Figure 6 A numerical representation of the PV device shown in Figure 5.
Again, we multiply the load voltage times the cell and load current to see the curve of the power delivery to the load and we also draw the dynamic resistance of the photovoltaic device (Figure 7).
Figure 7 Current, power and dynamic resistance curves for the Solec S-70C PV device, the dynamic resistance of the PV here is no longer the static horizontal line we saw in Figure 3.
Note now that the dynamic resistance of the photovoltaic device is not a horizontal line. The dynamic resistance of the photovoltaic device is now a variable. We also note that the power curve is no longer symmetrical but has instead taken a lean over to the viewer’s right.
Identifying the point of maximum power to the load or identifying the peak power point, we see the following in Figure 8.
Figure 8 Discovery of the peak power point for the Solec S-70C PV device.
We find that the peak power point is located where the load resistance equals the dynamic source resistance of the PV device.
If you want to get as much power delivery as possible out of a PV device, the load resistance needs to match the dynamic source impedance of that device.
Please note that in order to make these sketches more viewable, the vertical axis presentation of resistance is not linear in Ohms but has been made proportional to log (1+Ohms).
John Dunn is an electronics consultant, and a graduate of The Polytechnic Institute of Brooklyn (BSEE) and of New York University (MSEE).
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