You can calculate power density using pulse technic. Charging or discharging battery as a function of C-rate (ex: 0.1C, 0.2C, 0.33C, 0.5C, 0.7C, 1C) at SOC50 for 10sec (you can determine the SOC level and time yourself), and plotting current vs end voltage of each sequence.Internal resistance and V0 are derived from slop and y-intercept respectively and you can obtain power density as follwing equation.

charge power = charge cut off voltage*(charge cut off voltage - V0)/internal resistance

discharge power = dischrage cut off voltage *(V0-discharge cut off voltage )/ internal resistance

Dear Lakshman Kumar Ventrapragada,

reading the question, I get a little confused as the power density would have to be related to either volume or weight of the battery.

Contradicting, the values you mentioned are charge (Ah) and voltage (V) which would lead to an energy (Wh) instead of a power (W).

Consequently, the result would need to be an energy density which would also make more sense in regards of a battery, denoting a volume, necessary to store a certain amount of energy (Wh/Liter) or an amount of material needed to build a certain energy storage (Wh/kg).

Regarding a battery's ability to provide power to an application and survive for a certain lifetime, power density as power/area could be correlated to the area available on the electrodes leading to W/cm².

So what specifically are you searching for?

Cheers - Martin

Dear Martin Schulz, 

I wanted power density related to weight. My specific capacitance (Ah/g) times voltage (V) will give me energy density (Wh/Kg). I am interested in calculating power density (W/Kg), so that I can fit my data on ragone plot. Thank you

Dear Soojeong Lee, 

Thank you for your response, that is helpful. Also can you kindly provide me with some reference material in this direction?

Thank you for your time. 

Dear Lakshman Kumar Ventrapragada

I have the same question of yours ( calculating power density (W/Kg)). Could you please tell me what did you find it ? Is there a direct formulation from C-Rate and capacitance ?

Thanks

Hi Hassan,

I use the following method:

Power density = current density X voltage (mid-point voltage in your discharge curve).

Ideally I think you should take the energy density and divide by time and in this case you get energy density by integrating the area below voltage vs. capacity curve.

Hope this helps.

Best wishes,

Lakshman

thanks for your answer !

Actually I have a different context of yours. I don't have curves of discharge nor current density. What I have is the typical datasheet on websites : capacity (Ah), dimesnion, Resistance, weight (kg), C-Rate & energy density (Wh/kg) . In this case do you have an idea how can we deduce power densit (W/kg) ?

Thanks for your time again

Hassan

Energy density multiplied by C-rate (XC-rate means that the battery was charged in t = 1/X hours, e.g. 10C-rate -> t = 1/10 = 0.1 h, 2C-rate -> t = 1/2 = 0.2 h, 1 C-rate -> t = 1 h, 0.5C-rate -> t= 1/0.5=2h, and so on) --> Wh/kg * C-rate = Wh/kg * (1/h) = W/kg

Take into account that for different C-rates you will obtain different energy densities and power densities. The lower the C-rate (or in other words, the lower the current), the higher the energy density and the lower the power density.

The formula for power is P(W)= IxV, as an example if you have a nominal (average) voltage of 3 V and 1 Ampere current the power is 3W then you can divide this value by the liter or kg to find the power density.

Hi Noemí Aguiló-Aguayo that would mean that Energy Density and Power Density are essentially inversely linear? Is that correct? Or is that just a way to ballpark estimate?

the power density is written as P=Wh/L. if we multiply V and I we will get the power as P=VI but how could we convert it into Wh? can we replace the current as Ah instead of I? and my second question is that should we consider the total volume of the battery/cell? or volume of the electrode?@Serkan Sevinc

Dear Evan Schein, energy and power density are not necessarily inversely proportional. It depends on how the battery responses at high C-rate, whether its internal resistance increases or not. If the internal resistance increases with the C-rate, this will cause a voltage drop that will reduce the capacity of the battery, and therefore the energy density.

For power density calculation (PD), PD= MPV * i, here MPV is mid point voltage of discharge, i is current density of discharge. i= c/t, c= discharge capacity, t is discharge time.