| 8 | “I assumed that the photoelectric effect in the cell would produce constant voltage and variable current, quanta being what they are.” |
The total photo current (Iph) is always directly proportional to the solar irradiance (E). For silicon, that's about 1/2 amp per watt of irradiance. But as can be reasoned from the simple solar cell model below, the only way to get 100% of Iph from the cell is by driving it into a short circuit load. However, the goal of an inverter is not to maximize the current out of the solar cell, but rather to present such a load to the solar cell that it maximizes solar cell output power.
Referring again to the model, it can be seen that the theoretical maximum power point will be reached when the load resistance = Vd/Id. This model, as with all models, is only an approximation of an actual real-world device, and you could certainly choose to make a model that is more sophisticated, by including such additional internal components as Rs, Rp, Cp, etc., but the model shown should provide an adequate first level approximation to answer the questions you asked.
To get an idea just how sophisticated the control loop of an inverter has to be in order to maximize the power from the solar cell, take a look at this I-V curve from a typical solar panel consisting of 36 individual solar cells and illuminated at a specific level of irradiance. Note that as irradiance falls the curve recedes both down and to the left. Compounding the difficulty of designing the inverter, is whether it will be a grid tie inverter or a stand alone inverter. The former requires that it always be putting out maximum power, irrespective of whether that power is feeding the house or the grid. But in the latter case, it must tune its output to the load requirements of the house (and any storage system).
As a fellow engineer, you are of course familiar with the practice humorously referred to as "specsmanship", where manufacturers try hiding the bad news about their product in the smallest print at the bottom of the page or obscured in overly convoluted technical detail. One of the best examples of specsmanship in the field of inverter design and marketing is the efficiency rating. A certain model may have 90% efficiency when you only compare the input voltage and current to the output voltage and current. BUT that does not necessarily mean that the inverter was properly designed to present the ideal load to the solar cell, so as to extract the solar cell's maximum power. In other words your 90% efficient inverter may only be 80% efficient when actually connected to a real live solar cell.
--Boot Hill