Lead acid RLC equivalent

A significant 4 extra parts:

1. Voltage of the voltage source varying with degree of charge, maybe in volts close to 12.65 + 1/10 of log of ratio of percentage charged to

100% (applicable during discharge as opposed to during charge).

1. Voltage of the voltage source equated to be inside the battery being higher than above during charge and by a different formula, leading to hysteresis between charge and discharge for this voltage source. This voltage source equated to be in the battery has maybe 13.8 volts or so at 85-90% of full charge while charging is being done. (And above something like 13.8 volts applied often results in electrolysis of the water in the electrolyte.)

2. Resistance inversely proportional to percentage charged, and maybe 15 milliohms at full charge, applicable to discharge - maybe, somewhat likely higher during charge and varying less with degree of charge during charge than during discharge.

1. Significant nonlinear parallel resistance, maybe equivalent to 6 diodes in series (current changes by factor of 10 per change of per-cell voltage by .1 volt). The question here becomes what such diodes are that conduct many 10's of mA or around 100 mA at 2.35 volts and a few mA at 2.1 volts. I consider these to be hypothetical vaporware lime-green LEDs.

===========================

I might be wrong about .1 volt per cell per factor-of-10-degree-of-charge. I give slight chance that this is doubled due to 2 electrons per molecular reaction, although over-80%-charged during discharge still has the voltage source usually being 12.6-12.7 volts, meaning that 12.1 volts could mean about 30% charged rather than 10% charged (as in percentage above deepest rock bottom of electrolyte becoming non-acidic pH of 6-7, as opposed to percentage of being charged above the deepest level of discharge that is "reasonably safe" if some recharge comes soon to avoid damage by the "sulfation" mechanism).

Beyond that: I sense that the chemistry adds parallel capacitance of value that is unsteady but generally of value of a few farads.

- Don Klipstein ( snipped-for-privacy@misty.com)

"More complex than that" -- whatever you choose for "that".

The basic model for NiCd batteries is a Thevinin equivalent circuit with a voltage that's astonishingly constant* and a resistance that varies markedly with charge level. Beyond that there's the multi-farad capacitance that Don mentioned in parallel with the output and in series with it's own resistance that varies somewhat with charge level.

There's probably a career to be made just out of modeling battery discharge curves.

• Connect a seemingly dead flat NiCd cell to a voltmeter and wait 30 minutes -- unless the cell is really truly damaged you'll see something close to 1.2 or 1.25V after things settle out.

--
www.wescottdesign.com

st

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The information on batteries is really amazingly scarce for something so important in the day of electric cars, hybrids, etc.

In the days I was heavily into charger design, I rolled my own battery impedance tester using a high side current sense and external BJT buffered op amp circuit. The idea was to draw both AC and DC from the battery at a specific DC current, then use the AC variation to compute the impedance by monitoring the AC voltage on the battery. It worked well, but the trouble is if you need to do such testing at various states of charge and current drawn, the data gets out of hand pretty fast. Plus it is time consuming, so you can't test too many batteries to check for unit to unit variation.

I put this circuit into one of the trade mags and got quite a few responses, so there are clearly a number of people that want this information. All the callers were rolling their own testers. [One caller was a researcher in the chem department of a university doing some battery testing for the CIA. ]

Such testing of all types of batteries would make a great federal grant for a university. It is an interesting field of study since the ideal candidate would have both a chemical engineering and electrical engineering degree.

Ok, how about HF response? Are cells generally any better or worse than, say, electrolytics? Point being, would I need any bypass between cell and a switching supply? If that "big capacitor" is actually a big capacitor with no ESL and rated ESR, that would seem to suggest electrolytics aren't needed.

Tim

-- Deep Friar: a very philosophical monk. Website:

On Sun, 2 Aug 2009 21:25:56 -0700, Tim Williams wrote (in article ):

[Cross-posted to sci.chem.electrochem.*]

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I'm not sure about lead acid, but AC impedance is a technique I investigated as a method of detecting if the user inserted alkaline or secondary cells. I found this in a text book on batteries,but it was on I borrowed.

I once saw a simulator that was used to test battery chargers. It had some huge honking power resistor (I don't remember what the resistance was, presumably enough to draw 40 amps at 24V (it was for industrial chargers)) and an array of about a dozen of those BMF caps about three times the size of a 40 oz. beer can. (~8" tall, ~3" diam.)

As far as just powering stuff, why not just a plain ol' ordinary power supply? The only way to determine the battery characteristics is to use a real battery.

Good Luck! Rich

At least Li-Ion cells have bad HF response. I this out when our MFG supplier had changed an electrolytic to a high-ESR type. When the system powered up one section (abt.

40uF tantalums, switched with a low-Rdson FET), the battery voltage dropped for a few critical microseconds. This tripped the Li-Ion protection circuit, which shut down the whole system.

I suggest that you measure your batteries. If the battery ESR drops in the high frequencies only, you can get away with a very small cap.

The water does not contribute to capacitance (other than allowing chemical reactions). The battery can be charged and discharges "just" like a capacitor. A good, charged car battery can have an internal resistance in the region of 10 milliohms.

It seems like the basic charge mechanism equates to quite a few farads

- 30 kF for 100 AH @ 12 V.

--
John
(100 AH = 360,000 coulombs, C = Q/V)

In "Battery Models for Use in Electric Vehicles and Battery Energy Storage Systems" Sutanto/Chan/Fok from EPE'99, the authors suggest four or five models to cover battery dynamics over load and ranges of SOC, including the overload condition.

The simpler models mirror early measurements by DeBardelaben (Intelec'88).

At high frequencies, there are also inductive terms that are not normally considered in a dynamically decoupled system.

RL

Please post anything you happen onto. I'm always on the lookout for data sufficient to generate accurate Spice models. Thanks!

...Jim Thompson

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