Consider a simplified battery model with just internal resistance and a capacity that is independent of current. We fit data for the open circuit voltage and the internal resistance of a Panasonic NCR18650G cell (high specific energy, which is important for aircraft applications). This fit is only reasonable for a SOC between 0.1 and 0.9 (we won’t operate outside those limits anyway because of degradation and max power requirements).
\[OCV = 0.39\, SOC^2 + 0.07 \, SOC + 3.7 \text{ Volts}\] \[R = 0.015\, SOC^2 - 0.025 \, SOC + 0.104 \text{ Ohms}\]The capacity of the cell is 3.55 Ah. The battery pack is arranged as follows (s means series, p means parallel):
| Submodule | 1s x 24p cells |
| Module | 20s x 1p submodules |
| Pack | 7s x 2p modules |
Now consider the following simplified aircraft mission for an eVTOL aircraft:
| Segment | Time (minutes) | Power (kW) |
| Takeoff and Climb | 1 | 250 |
| Cruise | 35 | 75 |
| Aborted Descent and Climb | 1 | 180 |
| Reserve Cruise | 5 | 75 |
| Descent and Landing | 1 | 150 |
For each segment compute the pack current, voltage, efficiency, and the new state of charge at the end of the segment. Rather than integrating, for simplicity assume that open circuit voltage and resistance are constant within each segment, defined by the state of the charge at the start of that segment. Begin the mission with a state of charge of 0.9.
Optional explore: use AI to help you integrate with small time steps, rather than using frozen properties across large time steps. If you do so you should find a final SOC of 0.171.