Demonstrate ECM Extractors

The ECM extractors assemble the required components for Equivalent Circuit model using reference performance test data.

%matplotlib inline
from matplotlib import pyplot as plt
from battdat.data import BatteryDataset
import numpy as np

Load an Example Dataset

We use an example RPT cycle from the CAMP 2023 dataset to demonstrate parameter extraction

data = BatteryDataset.from_hdf('files/example-camp-rpt.h5')

C:\Users\lward\AppData\Local\miniconda3\envs\moirae\lib\site-packages\battdat\data.py:57: UserWarning: Metadata was created in a different version of battdat. supplied=0.4.0, current=0.4.1.
  warnings.warn(f'Metadata was created in a different version of battdat. supplied={supplied_version}, current={__version__}.')

data.tables['raw_data']

	cycle_number	file_number	test_time	state	current	voltage	step_index	method	substep_index	cycle_capacity	cycle_energy
0	1	0	120.042	b'charging'	0.260548	3.450065	0	b'constant_current'	0	0.000000	0.000000
1	1	0	139.182	b'charging'	0.260090	3.470207	0	b'constant_current'	0	0.001384	0.004789
2	1	0	439.182	b'charging'	0.260014	3.487297	0	b'constant_current'	0	0.023055	0.080177
3	1	0	739.182	b'charging'	0.259937	3.493553	0	b'constant_current'	0	0.044720	0.155796
4	1	0	1039.182	b'charging'	0.260166	3.499809	0	b'constant_current'	0	0.066391	0.231572
...	...	...	...	...	...	...	...	...	...	...	...
180	1	0	41767.320	b'hold'	0.000000	3.272145	3	b'rest'	8	-0.027665	0.011427
181	1	0	41777.322	b'hold'	0.000000	3.276875	3	b'rest'	8	-0.027665	0.011427
182	1	0	41787.318	b'hold'	0.000000	3.280995	3	b'rest'	8	-0.027665	0.011427
183	1	0	41797.320	b'hold'	0.000000	3.284504	3	b'rest'	8	-0.027665	0.011427
184	1	0	41807.310	b'hold'	0.000000	3.287556	3	b'rest'	8	-0.027665	0.011427

185 rows × 11 columns

The dataset contain a single slow cycle that samples the entire capacity of the cell.

fig, axs = plt.subplots(2, 1, figsize=(3.5, 3.), sharex=True)

raw_data = data.tables['raw_data']
time = (raw_data['test_time'] - raw_data['test_time'].min()) / 3600
axs[0].plot(time, raw_data['voltage'])
axs[0].set_ylabel('Voltage (V)')
axs[1].plot(time, raw_data['current'])
axs[1].set_ylabel('Current (A)')
axs[1].set_xlabel('Time (hr)')

Text(0.5, 0, 'Time (hr)')

Determining Capacity

The MaxCapacityExtractor determines capacity by integrating current over time then measuring difference between the maximum and minimum change in charge state.

Note: Integration is actually implemented in battdat.

from moirae.extractors.ecm import MaxCapacityExtractor

cap = MaxCapacityExtractor().extract(data)
cap

MaxTheoreticalCapacity(updatable=set(), base_values=array([[1.48220808]]))

This should match up with the measured change in charge

fig, ax = plt.subplots(figsize=(3.5, 2.))

ax.plot(time, raw_data['cycle_capacity'])
ax.set_xlim(ax.get_xlim())
ax.set_ylabel('Capacity Change (A-hr)')
ax.set_xlabel('Time (hr)')

min_cap, max_cap = raw_data['cycle_capacity'].min(), raw_data['cycle_capacity'].max()
ax.fill_between(ax.get_xlim(), min_cap, max_cap, alpha=0.5, color='red', edgecolor='none')

<matplotlib.collections.PolyCollection at 0x2274cab1f90>

The width of the colored span is the estimated capacity and it spans from the lowest capacity (~11hr) and the highest (~6hr)

Open-Circuit Voltage Estimation

The OCVExtractor determines the Open Circuit Voltage by fitting a spline to voltage as a function of state of charge.

The first step is to compute the SOC from the capacity change during the cycle and the total capacity estimated by MaxCapacityExtractor. As the actual state of charge cannot be directly measured, we assume the lowest capacity change is an SOC of 0.

raw_data['soc'] = (raw_data['cycle_capacity'] - raw_data['cycle_capacity'].min()) / cap.base_values.item()

fig, ax = plt.subplots(figsize=(3.5, 2.))

ax.plot(raw_data['soc'], raw_data['voltage'])
ax.set_ylabel('Voltage (V)')
ax.set_xlabel('SOC')

Text(0.5, 0, 'SOC')

The voltage during charge and discharge are different. Moirae accounts for this by weighing points with lower current more strongly and fitting a smoothing spline.

Note: Make the spline fit data more closely by increating the number of SOC points

from moirae.extractors.ecm import OCVExtractor
ocv = OCVExtractor(capacity=cap).extract(data)

fig, ax = plt.subplots(figsize=(3.5, 2.))

ax.plot(raw_data['soc'], raw_data['voltage'], label='Data')
soc = np.linspace(0, 1, 64)
fit = ocv(soc)
ax.plot(soc, fit[0, 0, :], 'r--', label='OCV')
ax.set_ylabel('Voltage (V)')
ax.set_xlabel('SOC')

ax.legend()

<matplotlib.legend.Legend at 0x2274db7dc00>

This yields a generally-good representation of the OCV.