Simple Battery Power Question

[michael.hill]

I'm trying to develop a power budget for a robotics team I mentor. The electrical system is pretty much completely regulated, so I can't alter the power path between battery, power distribution, motor controllers or motors.  The computer we're required to use has a software means of shutting down motor controllers if the battery voltage drops below 6.8 V, so my goal is to find the maximum amount of power I can draw to never go below 7 volts.  We use marine grade 17Ah SLA batteries (~12.7V -13.5V). Impedance from the battery to the power distribution panel tends to be around 0.013-0.017 Ohms (including Rint of the battery).  If I want to determine the maximum amount of power I can draw from the battery, which voltage do I use in my calculations?

I know P = I * V, and I = V/R.  I'm relatively certain the V in P = I * V is my 7 Volts, but I'm not sure if the V in the I = V/R equation should be 7 Volts or Delta V (12.7 V - 7 V).

Any help here?

Thanks

[PSR B1257]

If I want to determine the maximum amount of power I can draw from the battery, which voltage do I use in my calculations?

None. You cant't really calculate the maximum power (i.e. the maximum current). Take a look in the datasheet.

P = I * V, and I = V/R.  I'm relatively certain the V in P = I * V is my 7 Volts,

Your lead acid battery is pretty much toast, if discharged to 7V. You have to make sure not to discharge the battery below 10V (typical figure).

Beside of that, no it isn't, nor is it

7 Volts or Delta V (12.7 V - 7 V).

The power taken from the battery (like any voltage source) is the total current multiplied by the termial voltage.

[IanB]

If your source impedance is 0.017 ohms then for every amp you draw the supply voltage will drop by 0.017 volts. So if you draw 100 A you can expect the battery voltage to decrease by 1.7 V. That is the "rough estimate" calculation. But to find out what the battery can actually do you need to refer to the data sheet as noted above.

[michael.hill]

If I want to determine the maximum amount of power I can draw from the battery, which voltage do I use in my calculations?

None. You cant't really calculate the maximum power (i.e. the maximum current). Take a look in the datasheet.

P = I * V, and I = V/R.  I'm relatively certain the V in P = I * V is my 7 Volts,

Your lead acid battery is pretty much toast, if discharged to 7V. You have to make sure not to discharge the battery below 10V (typical figure).

Beside of that, no it isn't, nor is it

7 Volts or Delta V (12.7 V - 7 V).

The power taken from the battery (like any voltage source) is the total current multiplied by the termial voltage.

We aren't concerned about the life of the battery.  They get used about 10-15 times before they're toast. It's very common in competition robotics to run them that hard and to run them about that many times. We keep about a dozen on hand at any given time.

Anyway, so at the worst case, I want my terminal voltage to be 7 Volts.  I calculate my current to be I = deltaV/R = 5.7 V / 0.017 Ohms = 335 A.  If I multiply that by the terminal voltage of 7 volts, I get P = I * V = 2347 W. 

Does that look right?

[michael.hill]

I should also mention that I'm looking for the maximum surge power.  It doesn't always run at 7 volts.  This is when motors are near or at stall (when we start driving or start pushing another robot). It had been very common to have current spikes that result in voltages < 6 volts. We generally mitigate the take-off surge by ramping the speed up over a few hundred milliseconds.

[Jeroen3]

If you do not have closed loop motor control you're basically shorting the battery through the motor windings. So if you want to sustain that, you'll have to parallel all motors, calculate the current, and take that maximum discharge current to the battery shopping sites.
You'll probably end up with either paralleled batteries or a huge car battery.

Or lithium polymer, but I think they are not allowed, right?

[michael.hill]

If you do not have closed loop motor control you're basically shorting the battery through the motor windings. So if you want to sustain that, you'll have to parallel all motors, calculate the current, and take that maximum discharge current to the battery shopping sites.
You'll probably end up with either paralleled batteries or a huge car battery.

Or lithium polymer, but I think they are not allowed, right?

The whole topography is basically set in stone and I cannot alter any power paths, btw.  Operating like this is something that has been done for years.  All I'm asking out of this thread is if that's the correct power calculation.

[Jeroen3]

Dave recently made two video's about batteries. Where he explains about the curves in the datasheets.

[michael.hill]

Yeah, he does it the way hard way. We use this: http://www.westmountainradio.com/product_info.php?products_id=cba4

Great piece of hardware. We try to get battery curves on every battery we use to assess the health (while simultaneously hurting it) every year.

We use another tool (ctr-electronics.com/Beak.html) for getting a quick assessment of Rint. It's okay, but it's got its drawbacks, it only finds the internal resistance at up to 10A.