In preparation for my dissertation proposal (hopefully sometime this semester), I’ve been diligently patching all potential logical flaws in my research assumptions. One of the overarching assumptions that I had been operating on was the inadequacy of existing energy storage prognostics techniques (batteries in particular) for non-constant loads. My brief original forays into the literature indicated this to be true, but I never independently confirmed this fact until Friday. Well, my treacherous spelunking in the literature allowed me to differentiate existing prediction algorithms, and I found that a shocking number or algorithms rely on an archaic empirical relationship, Peukert’s law. This law directly relates the run time of the battery to the current drawn. The peculiarity of battery systems, modeled by Peukert’s law, is the total available charge diminishes given higher currents (in other words, the efficiency of the battery drops). However, I ran some tests with real battery draw data and confirmed what a paper by Doerffel in 2006 illustrated… the invalidity of Peukert’s law in a vast majority of realistic cases.
The first tests that I ran used battery data with constant currents. In this case, Peukert’s law should apply. Accounting for the uncertainties in the parameters, we can generate the probability distribution of predictions. As shown in the figure, Peukert’s correlation is well founded. However, if we look at real battery data given a periodic load (on/off only), this correlation crumbles. As I mentioned above, a shocking number of published techniques still rely on this empirical correlation for prediction for realistic systems… completely discounting the inaccuracy. Dynamic battery models, on the other hand, directly account for variability in the load… given Occum’s razor, simpler prediction actually requires dynamic models.
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