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The capacitor solution has risks too. One of the things a lead-acid battery brings is a voltage somewhat independent of the load. As such, it helps keep the voltages constant versus wandering. A capacitor is going to show an immediate voltage drop under a current load ... it is how they work. In contrast, battery chemistry just increases its activity to sustain the voltage while current varies.
It is an interesting challenge, trying to put together a capacitor system substitute for a lead-acid battery. I'll have to think about it.
Bob Wilson
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2019 Tesla Model 3 Std. Range Plus - 215 mi EV
2017 BMW i3-REx - 106 mi EV, 88 mi mid-grade
Retired engineer, Huntsville, AL
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