@ Mr. IGH: I guess by "Roadie" you mean me. I don't see where I'm confused. I agree with you that we don't have a proper understanding of the generator and its model. I certainly do not have one. If you have one, please give a good description of it (such as in item 2 below). However, I don't see that you have presented a good model of the generator.

1. If you are correct that the hubgen will produce a constant current into a zener load, then the hubgen must be a Norton source when in that region (below saturation) of operation. Hence in that region the generator is linear, while the load is non-linear since it isn't resistive.

2. Do you have data that shows the saturation of the Shimano generator at 12vrms? Is the saturation independent of loading? What I'd really believe is measurements of voltage and current with resistive loads, with speed and resistance varied as parameters, and some scope photos (or the computer equivalents) to see the onset of saturation. I'd also see those as a strong basis for a generator model.

3. I think the saturation you are talking about is due to the magnetic materials, not the winding. The winding is wire, which is copper or aluminum, and those metals do not saturate, unless you are talking about failures such as melting or insulation burning and creating short circuits. Magnetic materials, however, do saturate.

4. Now a systems perspective: any valid generator model has to accommodate the variations in real-world use: single headlamp, headlamp with taillamp, dual parallel headlamps, series headlamps, and the variations of lighting systems with mobile device charging.

Usually electric machines produce a higher open-circuit voltage with shaft speed. I don't see why we have to throw out that principle for bike generators. One thing it implies is that for loads with a higher input resistance than the generator winding resistance, this voltage variation will be measurable as you speed up the bike wheel.

Keep talking?