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Exercise E1 Conversions: Battery

1. How many minutes could a consumer with $3~{\rm W}$ get supplied by an ideal battery with $10~{\rm kWh}$ ?

Solution

\begin{align*} W &= 10~{\rm kWh} &&= 10'000~{\rm Wh}\\ \\ t &= {{W }\over{P }} &&= {{10'000~{\rm Wh}}\over{3~{\rm W}}} \\ &&&= 3'333~{\rm h}= 200'000~{\rm min} \quad (= 139~{\rm days}) \end{align*}

Result

\begin{align*} t = 200'000~{\rm min} \end{align*}

2. Hard: Why is a real Lithium-ion battery with $10~{\rm kWh}$ unable to provide the given power for the calculated time?

Result

There are additional losses:

  • The battery has an internal resistance. Depending on the current the battery provides, this leads to internal losses.
  • The internal resistance of the battery depends on the state of charge (SoC) of the battery.
  • The wires also add additional losses to the system.