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Background notes

Reference material moved out of the README: how the rainflow counting feeds the stress factors, and what the data sets from the original publication contain.

Provenance

The model is based on (https://ieeexplore.ieee.org/document/7488267):

"Modeling of Lithium-Ion Battery Degradation for Cell Life Assessment" by Bolun Xu, Alexandre Oudalov, Andreas Ulbig, Göran Andersson, and Daniel S. Kirschen, IEEE Transactions on Smart Grid, vol. 9, no. 2, March 2018.

See also this related code repository: https://github.com/DaniCelis25/lithium_ion_battery_degradation_models. Modified and adjusted by Jinsong Hua with IFE data. The papers themselves are not redistributed here -- see the DOI above.

Rainflow cycle counting

Input: the SoC profile.

Output: the rainflow cycle count —

  1. cycle amplitude
  2. cycle mean value
  3. cycle number (0.5 for a half cycle, 1 for a full cycle)
  4. cycle begin time
  5. cycle end time

Estimating stress factors from the count:

  1. the DoD of the i-th cycle (δ_i) is twice the i-th rainflow cycle amplitude
  2. the average SoC of the i-th cycle (σ_i) is the i-th rainflow cycle mean value
  3. the average cycle temperature of the i-th cycle (T_c,i) is the mean temperature between the start and end times of the i-th rainflow cycle
  4. the average profile SoC (σ) is the mean value of the rainflow cycle mean values
  5. the average profile temperature (T_c) is the mean value of the temperature profile

The implementation is esf.models.cycle_counting_algorithm.CycleCounter (wrapping the vendored peak-detection and rainflow algorithms in esf/external/); its behaviour on synthetic profiles is pinned in tests/test_cycle_counting.py.

Dynamic Stress Test (DST) data from the original publication

  • Illustrate the battery's performance in mixed-cycle operations.
  • For each test, the cell starts at a set SoC level and the DST profile is applied repetitively until the set stop level is reached.
  • The cell is then recharged back to the starting level at a 1 C-rate to finish one test cycle.
  • Only the State of Health (SoH) vs. cycle number is provided; the underlying profile must be simulated to reproduce the results (see esf.simulations.dst_cycle.DSTCycleDeg).

  • Data sets (in esf/data/Ageing_Data_Org/DST_cycles/), with start/stop SoC in percent; the test room temperature is assumed 20 °C (293.15 K) based on the figure in the publication:

  • DST_25_100.csv: 100% to 25% SoC

  • DST_40_100.csv: 100% to 40% SoC
  • DST_50_100.csv: 100% to 50% SoC
  • DST_25_85.csv: 85% to 25% SoC
  • DST_25_75.csv: 75% to 25% SoC
  • DST_45_75.csv: 75% to 45% SoC
  • DST_65_75.csv: 75% to 65% SoC

C-rates (c_rate) and time-steps (delta_t in seconds) were obtained by Jinsong Hua from the publication:

delta_t = np.array(
    [18, 28, 12, 8, 16, 24, 12, 8, 16, 24, 12, 8, 16, 36, 8, 24, 8, 32, 8, 42]
)
c_rate = np.array(
    [0, -1, -2, 1, 0, -1, -2, 1, 0, -1, -2, 1, 0, -1, -8, -5, 2, -2, 4, 0]
)
# only the discharge steps; re-charging is performed at constant current of 1C

Other aging data from the original publication

In esf/data/Ageing_Data_Org/:

  • calendar_degradation/calend_deg_at_25_deg.csv — calendar aging at 25 °C for several SoC levels
  • calendar_degradation/calend_deg_at_50_SoC.csv — calendar aging at 50% SoC for several temperatures
  • cycling_degradation/cycle_nb_at_80_SoH_{LMO,LFP,NMC}.csv — cycle life to 80% SoH vs. DoD per chemistry