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Understand you are in new territory and I tend to be a conservative engineer. So I would probably do a lot of checking before trying to substitute a nominal 12.x VDC battery for the 13.8 VDC generated by the inverter.
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This has been done before so hopefully I will be able to get some specific info before I do anything:
http://www.veva.bc.ca/articles/PHCdemoArticle080211.pdf
I will try to get some information from the owner, who is a member of VEVA and has rebuilt several Prii:
http://peopleshybrid.com/index.htm
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One wild thought, a 24 VDC deep discharge battery could be stepped down using a switching power supply to just about any lower voltage fairly easily and efficiently.
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I like that idea better. 24V is better because it seems to be easier to find and implement a down converter than a boost converter. Also, I will need at least 2 batteries if the overhead is indeed 300+ watts. I'm not concerned about the extra weight because it's well known that cutting ICE electrical overhead outweighs the added weight of batteries. Ha Ha.
Questions to be answered assuming a 12V nominal system:
Will the lower voltage (under 13.5V) set codes? My guess is that it might if it gets too low. Prii with dying 12V batteries exhibit all kinds of strange behaviours. Although a dying battery will probably be sub 10V under load. The graham scanner sees 11.3 on mine with the hybrid system off so there seems to be some flexibility.
I noticed, from the EWD that there seem to be quite a few different blocks or busses. I was thinking, If there was a simple way to keep the DC-DC happy by leaving it to run the ECU's, or at least the engine bus then it would be less likely to set any codes. I have noticed on my van that some sensors (eg. coolant temp) read low when the voltage gets low.
What is the electrical efficiency of the THS from ICE (35%eff) to MG(?%Eff) to battery(?%Eff) to DC-DC(?%Eff) to 12V? How does it compare to a regular ICE(20%Eff) belt(?%Eff) Alternator(45%Eff) 12V?
Is the DC-DC a simple load based unit? Will it just supply what is asked of it and no more?
What happens to a stock Prius if the DC-DC goes offline while driving? If the car still operates then we know it would be possible to simply substitute the 12V supply. (better if 13.5V)
Will it be a simple/desireable thing to supply some blocks with 12V and some with the DC-DC?
Should I have a relay set up to switch between systems for long trips when the batteries get low?
Fun stuff.