The Living Force
I've been wondering about this too. I wanted to introduce a first-approximation 1/r heliocentric isotropic (at least on the ecliptic) electrical field with unknown amplitude and to determine geometrically, according to the relative positions of the planets, the probabilities for localized discharges. Thinking about it appeared that it required a programming of the type of the "travelling salesman problem" which may appear a little severe for such a simplified model for the electric solar system. Is the book offering a more straightforward approach for the problem?
Interesting. I get what you're saying, although I think the problem is even more complex based on what I've read. I think your idea of using a 1/r heliocentric isotropic electric field is probably the best way to approximate the idea of the solar capacitor, but each planet seems to have a different potential to discharge based its their size, orbital position (as well as its perihelion I'd imagine), and maybe other factors yet unknown to us (such as the positions of moons, etc.)
If Nelson is correct in his findings, then it seems that the probability for solar discharge seems to be based more on the number of 0, 180, 90, 45, etc. degree alignments among all the planets in a given time frame (could be hours or even days, Nelson isn't exactly clear). But it also seems to depend on which planets are doing the aligning. He mentions alignments between Mercury and another outer planet as being one of the main initiating factors in most solar disturbances/discharges. Alignments among the outer planets, or even some of the inner planets like Earth and Mars cause little activity on the Sun until Mercury starts aligning with them. Once Mercury creates a hard angle between itself and another planet (particularly Jupiter of Saturn), then that can set off a lot of discharging activity; the character of which depends on other alignments happening at the time. Like I said, these alignments don't have to be direct (as in oppositions and conjunctions), they can be any harmonic of these angles, although oppositions and conjunctions seem to be the strongest in terms of producing the most electrical discharge activity. It seems like the solar capacitor likes to have certain 90 degree harmonic geometry between the planets for discharging activity to occur.
Then there is the stuff about the trines and their associated harmonics, and how they tend to act as act as a stabilizing factor for the solar capacitor. Nothing in my study of electricity really explains this satisfactorily. But according to Nelson trines and their harmonics seem to stabilize electrical activity on the Sun, or within the solar capacitor.
Of course, Nelson never considered anything like comets as being a factor. These seem to have a much higher potential to discharge the solar capacitor, although it probably depends on the comet's orbital eccentricity, its size, position among the planets and maybe even composition. Also, how does the sun's hypothetical companion play into this, or any other outer-planets that have yet to be discovered, for that matter? Interestingly, could we infer the position of some of these undiscovered bodies based on anomalous discharging factors once we get it all ironed out?
Then the big question is how does this impact Earth weather? What is really needed here is a massive data-mining operation sifting through the data from the last century, correlating it with planetary alignments and Earth's position within such alignments. Then we might be able to discern some patterns in the data about how the planets affect weather down here.
Really, if you're interested, I would recommend reading Nelson's book. It's pretty short and focused on this topic and he gives a lot of examples. You might get some good ideas on different models to test.