Specific Heat Capacity of the Battery Pack

The specific heat capacity is a measure of how much energy is necessary to raise the temperature of a system a given amount. A system with a higher specific heat capacity is said to have a higher thermal mass, meaning that with the same amount of heat, it will have a lower temperature rise.

Determining the specific heat capacity of the battery pack is important to be able to determine non steady-state thermal characteristics of the pack - how long can we produce X power through the cells before a temperature rise of X degrees occurs?

Because the battery pack is made up of many parts and many different materials with different thermal conductivities, specific heat capacities, etc., we will focus only on the materials that are physically located close to the cells, and have a good thermal coupling to the cells.

We will also assume that all the other components that are in the high current path (and thus produce heat) have a small enough power loss compared to their thermal mass that they can be neglected (relays, connectors, etc.)

Here is a table that outlines some of the materials we are using the in battery pack, and their associated thermal characteristics. The values in the table are not to be used for mathematical calculations (ans so were significantly rounded), and were only used to determine relative thermal capacities between the parts of the pack.

Unit converter used here: https://converter.eu/heat_capacity/#0.403_BTU/Pound_°F_in_Joule/Kilogram_°C

Given that the 18650s, the Nickel, and the EMS Sigma 60 have thermal conductivities a few orders of magnitude higher than the rest of the materials, only the metals will be used for the rest of the calculations (this is expected since metals and plastics are very far apart when it comes to thermal properties).

Mass of the relevant materials used in the battery pack:

To raise the temperature of the battery pack by 1 degree celcius (assuming a uniform temperature distribution), we must heat up all of the materials in the table above by 1 degree celsius.

1 Joule = 1 Watt x 1 Second

Average Specific Heat Capacity from measured data: 35.45 kJ/deg C

So, the thermal mass of the pack being 35.5kJ/deg C lines up with the testing results well within margin of error.

With this heat capacity of the pack, we are able to calculate some of the transient effects of going up hills, etc. Our strategy lead (Clarke) says that while going up a hill, a 10kW power draw for 5 minutes would be a conservative estimate for the length of a hill.

At 10kW, we are drawing 76A at nominal voltage and producing 329.2W of heat.

1W = 1J/s

329.2J/s * 5min * 60sec/min = 98.76kJ

This amount of energy will give a temperature rise of:

98.76kJ / 35.45kJ/degC = 2.79decC

Keep in mind, this is without active cooling. With this result, we are able to say that any hill that we go up will raise the pack temperature by a maximum of 3 degrees Celsius. So during cruising (before the hill) we require the pack to be under 42 degrees Celsius in order to keep the max temp under 45 degrees Celsius.

Given our conservative estimate of a cruising current of 20A which equates to 22.8W of heat. Looking at the measured results of the rate of temperature rise with the fan running (below), we were able to remove 20W of heat anywhere above roughly 7 degrees above ambient (look at where the curve flattens. So, we can essentially keep the pack at a roughly constant temperature of max 7 degrees above ambient. This allows the 3 degree rise of a hill while still maintaining temp under 45 degrees in a 35 degree ambient environment. Also, keep in mind that this 20W heat removal is assuming worst case module result scaling to pack environment.

The above discussion has concluded that we have enough cooling power to keep the pack at a maximum of 45 degrees given our worst case conservative estimates. However, the cooling and temperature distribution within the pack is NOT uniform (see below). We need to ensure as much uniformity as possible in our pack in order to be able to operate in more comfortable regions, and not having to worry about hitting a temperature limit - but also keep in mind that the 45 degrees limit will just disable regen and solar for a short time until we can cool the pack, we still have 15 degrees more headroom before hitting the discharge max temp.

This discussion is continued on the Battery Pack Temperature Distribution page.

Also to note, is that with a constant 20A draw and 22W of heat production, we can figure out how long it will take to reach the max temperature, assuming we start at 35 degrees ambient, we would be looking for a temperature rise of 10 degrees (up to 45 degrees).

35.5kJ/degC * 10degC = 355kJ

355kJ / 22J/s = 16 000 s

16 000s / 3600s/h = 4.4h

With no cooling and a 22W rate of heat production, it will take 4.4h to raise the temperature of the pack by 4 degrees. So we will definitely need to cooling the pack at least a little during the 8h days on the track or the roads.