Question

The Tesla Powerpack lithium ion battery storage system has the following specifications:

Installed Capacity – 50 KW

Storage Capacity – 210 KWh

Output voltage – 480 V

Overall efficiency – 89%

1. How long (in hours) can the Powerpack deliver the rated power?

2. How much heat is generated by the Powerpack in each charge/discharge cycle?

3. What is the output current of the Powerpack (in amps) when operated at the rated power and voltage?

Answer 1

1)

Installed Capacity – 50 KW

Storage Capacity – 210 KWh

time= Storage Capacity / Installed Capacity

t= 210/50

t=4.2 hours.

----------------------------------------------------------------------------------------------------------------------------------------------------------------------

2)

See part 3 first and come back

V(output)= 480V

I(current)= 92.708 amps

Q( heat generated ) = VxIxt

= 480 x 92.708 x 4.2

= 186899.328 J

=186.899 KJ ( 1KJ=1000J )

Number of cycles isn't mentioned. Considering the average Tesla batterypack working for around 1500 discharge cycles,

Heat energy / discharge cycles = 186899.328 / 1500 = 124.599J / cycle.

NOTE: This answer will vary depending on the number of discharge cycles of this battery. It depends on the battery specification. I have taken an average data.

----------------------------------------------------------------------------------------------------------------------------------------------------

3)

Efficiency = P(output) / P(input)

0.89 = P(output) / 50 .... input capacity given=50KW

P(output) = 50x0.89 = 44.5KW

Also,

P = V x I

44.5 x 1000 = 480 x I (1KW = 1000W = 1000 volt-amps)

I = 92.708 A.