The only way that the energy input by donation can be represented by money is by issue of money for free within the black box, each token representing some Joules of donated energy recieved and put to use, to all people.
Relating economics/dollars to energy, especially electricity and solar production, is quite tricky. Your keyword in this is "and put to use". Using existing grids without storage capacity simply dumps off much of the energy generated to ground except in times of extreme heat during the day.
Any generation up to the existing capacity of the grid has no value to anyone until storage can be improved. Our grid system is completely hodge-podge and disjointed and there is no storage solution on the horizon that can scale up to the demand.
That is quite a backlog of free money owed, to all people, it seems to me.
A penny saved is a penny earned. The cheapest way to introduce solar generation is to make each household independent, or as close to it as possible, and then use the grid as the ground dump so that excess capacity can be utilized without investing more in the grid. Eventually, the goal of solar generation should be stand-alone building processes with a more reasonable demand for storage.
Either way, the currency-issuing government can "afford" it as long as the required resources and labor are potentially available. The money for any endeavor to make our society more efficient/productive never has to be "found" or "collected".
This is a solid explanation for the reason why inflation is happening, and won't stop until free money is issued, massive free money is needed to recover the value of currencies, according to the principals of Austrian Economics, which says all issue of money must be balanced with issue of product, because in the end it is the product which is the thing of value, not the money, I believe.
Austrian economists are monetarists who believe the opposite of what you are proposing. They see any increase in the money supply as inflationary whether it is balanced with a product or not. They are firm believers in fighting inflation by cutting back public purpose spending and raising interest rates to curtail employment, which has made them very popular with industry and finance.
Their definition of "product" in this context is very limited in scope, primarily that sold by a company for a profit, and certainly doesn't include anything the government would provide funding for, much less a massive injection of dollars to pay for donated energy.
