Response Time of Battery to load jump?

PowerStarter

Joined Mar 4, 2022
16
Hello together,

a real battery has probably a response time to a load change as well, like every real system.
I would assume that an ideal battery should have an instant response. Therefore the delay in the transient response results from parasitics of the battery. The small size of those parasitics turns the ideal to a real response while keeping a wide, but finite, bandwidth and a quick response time.
A battery in a circuit should be therefore only responsible for a minor reduction of the response time.
(for this question I assumed that the battery can supply enough power)

Two questions popped up in my mind:
- Can the response time of a battery be neglected at all times?
- How much is such a response time of e.g. a ev car battery?

I would really appreciate to hear your thoughts on this topic.

Ya’akov

Joined Jan 27, 2019
5,647
I know that tests of Lithium chemistry cells out to ~200KHz didn't show any contribution to current rise time.

Other batteries may have different performance. The equivalent circuit for a battery looks like a series resistance and a one or more parallel RC pairs in a series. The values for these will influence the inherent rise time for the cell. I don't know how they vary for each chemistry.

ci139

Joined Jul 11, 2016
1,810

PowerStarter

Joined Mar 4, 2022
16
I know that tests of Lithium chemistry cells out to ~200KHz didn't show any contribution to current rise time.
I think you refer to this paper: Electrochemical Impedance Spectroscopy of a LiFePO4/Li Half-Cell
They wrote that it "behaves like a low-pass filter with a cutoff frequency of around 200 Hz". So I guess there is a delay in the voltage rise time, due to the "limitation" of frequencies. The current on the other hand can be seen as instantaneously (really short time - at least limited by the propagation of the electromagnetic wave).

When assuming the cutoff frequency at 200 Hz we would get a Tr of about 1.75ms by using the following formulas:
BW=fh-fl
Tr=0.35/BW

With Bandwidth BW, Low-Cutoff Frequency fl, High-Cutoff Frequency fh, Rising Time Tr.
The coefficient of 0.35 is used for approximation of a 1- or 2-pole filter roll-off in the frequency domain (0.45 is used by real-time oscilloscopes).

Last edited:

Ya’akov

Joined Jan 27, 2019
5,647
I think you refer to this paper: Electrochemical Impedance Spectroscopy of a LiFePO4/Li Half-Cell
They wrote that it "behaves like a low-pass filter with a cutoff frequency of around 200 Hz". So I guess there is a delay in the voltage rise time, due to the "limitation" of frequencies. The current on the other hand can be seen as instantaneously (really short time - at least limited by the propagation of the electromagnetic wave).

When assuming the cutoff frequency at 200 Hz we would get a Tr of about 1.75ms by using the following formulas:
BW=fh-fl
Tr=0.35/BW

With Bandwidth BW, Low-Cutoff Frequency fl, High-Cutoff Frequency fh, Rising Time Tr.
The coefficient of 0.35 is used for approximation of a 1- or 2-pole filter roll-off in the frequency domain (0.45 is used by real-time oscilloscopes).
Yes, that's the one. But of course because of the differences in construction and chemistry I don't think it can be generalized to all cells.

PowerStarter

Joined Mar 4, 2022
16
But I'm not quite sure why they got the instant current change, when normally a battery is seen as a voltage source.

Sure the battery can be modeled with either the
1. Thevenin model (constant voltage source battery in series with resistor) - when internal resistance low compared to load
2. Norton model (constant current source battery in parallel with resistor) - when internal resistance high compared to load

So most of the time applies the Thevenin model, where the battery is seen as a voltage source.

Can one verify my thoughts/calculations in the #4th post pls.

Ya’akov

Joined Jan 27, 2019
5,647
But I'm not quite sure why they got the instant current change, when normally a battery is seen as a voltage source.

Sure the battery can be modeled with either the
1. Thevenin model (constant voltage source battery in series with resistor) - when internal resistance low compared to load
2. Norton model (constant current source battery in parallel with resistor) - when internal resistance high compared to load

So most of the time applies the Thevenin model, where the battery is seen as a voltage source.

Can one verify my thoughts/calculations in the #4th post pls.
Where in the paper are you seeing the current vs. voltage data? I didn't try to read it in depth but the figures I see are for phase vs. frequency, reactance vs. resistance, and magnitude Z vs. frequency. Are you inferring the current vs. voltage from that data?

It appears the cell's capacitance is largely responsible for the shape of the curve from the high end to 11Hz but frankly, my only takeaway from the paper originally was the idea that at higher frequencies the cell doesn't seem to be a major contributor to rise time. This is a simplistic conclusion, though.

Maybe someone else can spend the time to dig into it further. I don't have the math to untangle their explanation of the simulation in which, I suspect, the answer to your question lies.

ci139

Joined Jul 11, 2016
1,810
guess there is a delay in the voltage rise time
just a remainder that there're various capacitors on the market