CALB L148N58A - 3RC Equivalent Circuit Model Parameter Extraction

Extracts 3RC equivalent circuit model parameters from HPPC and C/20 test data for 11 CALB L148N58A (58 Ah nominal, NMC 811) large-format prismatic lithium-ion cells using the Mendeley dataset.

Dataset

Source: Mendeley Data - CALB L148N58A Testing Campaign

Property	Value
Chemistry	NMC 811 (Graphite anode)
Nominal Capacity	58 Ah
Voltage Range	2.5 - 4.2 V
Dimensions (L x W x H)	148 x 27 x 106 mm
Weight	0.926 kg
Number of Cells	11
Test Temperatures	10°C, 25°C, 40°C

Dataset Structure

A Dataset for Large Prismatic Lithium-Ion Battery Cells (CALB L148N58A).../
└── CALB L148N58A testing campaign/
    ├── Raw Data/           (.xlsx files)
    └── Processed Data/     (.mat files) <-- used by this script
        ├── Temperature_10C/
        ├── Temperature_25C/
        └── Temperature_40C/
            ├── C20_Charge/       C/20 charge data
            ├── C20_Discharge/    C/20 discharge data (capacity + OCV)
            ├── HPPC_1C/          1C HPPC pulse test (R0, RC parameters)
            ├── HPPC_C3/          C/3 HPPC pulse test
            ├── EIS_test/         Electrochemical impedance spectroscopy
            ├── DV_UDDS/          UDDS driving cycle
            ├── DV_WLTP/          WLTP driving cycle
            └── DV_US06/          US06 driving cycle

3RC Equivalent Circuit Model

        R0          R1          R2          R3
  o───/\/\/──┬──/\/\/──┬──/\/\/──┬──/\/\/──┬──o
             │         │         │         │
  I(t) →     │    C1 ──┤    C2 ──┤    C3 ──┤
             │  (tau1)  │  (tau2) │  (tau3) │
             │         │         │         │
  o──────────┴─────────┴─────────┴─────────┴──o
             +                                -
                      Em(SOC)

• Em(SOC): Open-circuit voltage as a function of SOC
• R0: Ohmic resistance (instantaneous voltage drop)
• R1, tau1: Fast RC branch (tau ~ 2-4 s)
• R2, tau2: Medium RC branch (tau ~ 15-30 s)
• R3, tau3: Slow RC branch (tau ~ 50-200 s)

Methodology

1. Capacity (C/20 Discharge)

Full discharge at C/20 rate (2.9 A). Capacity is the total discharged Ah:

Capacity = integral(|I(t)| * dt) / 3600   [Ah]

Note on measured vs. nominal capacity: The nominal capacity is 58 Ah (datasheet), but the measured C/20 capacity is 53-54 Ah. This is because:

1. Incomplete initial charge: The discharge starts at 4.192 V instead of 4.200 V, meaning the cell was not fully charged to 100% SOC before the test. This accounts for approximately 1-1.5 Ah.
2. Nominal vs. actual: Datasheet capacity is measured under ideal conditions. Real-world C/20 tests typically yield 90-95% of nominal capacity.
3. Cell aging: A few formation/conditioning cycles may have been performed before testing.

The measured values (53-54 Ah) are used in the model because they represent the actual tested capacity of these specific cells, which is more accurate for simulation than the nominal value.

2. OCV / Em (C/20 Discharge)

At C/20, the current is low enough that the IR drop is negligible (~0.003 V for 2.9 A x ~0.001 Ohm). The measured voltage is therefore approximately equal to the OCV. Interpolation is performed at the SOC breakpoints:

SOC(t) = 1 - (cumulative_Ah(t) / total_capacity)
Em = interp(SOC_LUT, SOC, Voltage)

3. R0 (HPPC 1C Pulse Test)

Instantaneous voltage drop at the start of each 10s discharge pulse:

R0 = (V_before_pulse - V_instant_after) / I_pulse

Sampling rate verification: HPPC data is sampled at 10 Hz (0.1 s interval) at pulse onset. At the first sample: dV = 67.2 mV; at 0.1 s later: dV = 68.1 mV. The RC contamination is only 0.9 mV, which is negligible.

4. R1, R2, R3, tau1, tau2, tau3 (Curve Fitting)

Three-exponential fit to the 600s voltage relaxation curve after each pulse:

dV(t) = V_inf - V_rest(t)
dV(t) = A1*exp(-t/tau1) + A2*exp(-t/tau2) + A3*exp(-t/tau3)
Ri = Ai / I_pulse

Fitting bounds (optimized for 58 Ah prismatic cell with low internal resistance):

• Voltage amplitude upper bound: 0.1 V (total pulse dV ~ 0.06 V)
• tau1 range: 0.01 - 10 s
• tau2 range: 0.1 - 100 s
• tau3 range: 1 - 1000 s

HPPC Test Pattern

At each SOC point (from 100% to 0%, in ~10% steps):

Voltage
  |    V_before
  |    ──────┐
  |          |← dV_instant (R0 = dV / I)
  |          V1
  |           \
  |            \← Exponential decay (R1,R2,R3 + tau1,tau2,tau3)
  |             \_____ V_end
  |                    |
  |                    |← Current removed
  |                    V2
  |                   /
  |                  / ← Recovery (3RC relaxation -> curve fitting)
  |                 /
  |          ──────  V_inf
  └──────────────────────── Time

Sequence per SOC point: 10s discharge pulse → 600s rest → 10s charge pulse → 600s rest → 360s discharge (SOC step-down) → 3600s rest

Verification Checks Performed

Check	Result
Current sign convention	Negative = discharge (verified: V drops when I < -50 A)
HPPC sampling rate at pulse onset	10 Hz (0.1 s) — RC contamination only 0.9 mV
Rest region end detection	5 A threshold correctly captures charge pulse onset
Curve fitting convergence	RMSE < 0.1 mV for all fits

Installation and Usage

Requirements

pip install -r requirements.txt

Run

python extract_CALB_params.py

Place the Mendeley dataset in the same directory as extract_CALB_params.py.

Outputs

calb/
├── extract_CALB_params.py          Main script
├── all_cell_params.json            All parameters (JSON)
├── comparison_table.xlsx           Comparison table (Excel)
└── results/
    ├── Cell_59294/
    │   ├── batteryParameterEstimation_results_3RC_10degC.mat
    │   ├── batteryParameterEstimation_results_3RC_25degC.mat
    │   └── batteryParameterEstimation_results_3RC_40degC.mat
    ├── Cell_59485/
    │   └── ... (same 3 files)
    ├── ...
    └── Cell_60710/
        └── ...

Each .mat file contains:

Variable	Description	Size
Em	OCV vs SOC (V)	1x11
R0	Terminal resistance vs SOC (Ohm)	1x11
R1	1st RC resistance vs SOC (Ohm)	1x11
R2	2nd RC resistance vs SOC (Ohm)	1x11
R3	3rd RC resistance vs SOC (Ohm)	1x11
SOC_LUT	SOC breakpoints	1x11
tau1	1st RC time constant vs SOC (s)	1x11
tau2	2nd RC time constant vs SOC (s)	1x11
tau3	3rd RC time constant vs SOC (s)	1x11

Results

Capacity and R0 Summary (11-Cell Average)

Temperature	Measured Capacity (Ah)	Nominal Capacity (Ah)	Ratio	R0 Mean (mOhm)
10°C	53.36 ± 0.49	58	92.0%	1.958 ± 0.105
25°C	53.63 ± 0.38	58	92.5%	1.147 ± 0.078
40°C	54.19 ± 0.43	58	93.4%	0.835 ± 0.071

Cell-by-Cell Comparison (25°C)

Cell	Capacity (Ah)	R0 (mOhm)	R1 (mOhm)	R2 (mOhm)	tau1 (s)	tau2 (s)	tau3 (s)
59294	53.29	1.189	0.128	0.187	3.07	24.67	141.6
59485	53.38	1.155	0.127	0.185	3.01	24.15	136.8
59627	53.44	1.065	0.145	0.200	3.09	25.17	151.6
59690	53.59	1.157	0.124	0.180	3.04	24.52	140.9
59861	53.81	1.165	0.122	0.184	3.06	23.82	137.1
60031	54.14	1.123	0.140	0.201	3.15	24.50	147.0
60129	54.17	1.086	0.136	0.201	3.07	24.50	150.5
60195	54.04	1.100	0.126	0.174	3.08	25.21	142.6
60403	52.96	1.359	0.192	0.209	3.15	23.01	148.5
60644	53.88	1.062	0.131	0.184	3.15	23.38	142.2
60710	53.30	1.154	0.160	0.201	3.20	23.26	152.9

Cell 60403 is an outlier: lowest capacity and highest R0 (+18.5% above mean). This likely indicates cell-to-cell manufacturing variation.

Key Observations

• Temperature dependence: R0 decreases with increasing temperature (Arrhenius behavior). From 10°C to 40°C, R0 drops by 57%.
• Capacity: Slightly increases with temperature (10°C: 53.4 Ah → 40°C: 54.2 Ah).
• Cell-to-cell variation: R0 varies by ±6-7% across cells (excluding Cell 60403).
• Fit quality: 3RC curve fitting RMSE < 0.1 mV across all SOC points and temperatures.

Simulink Integration

To replace the Kokam model parameters in Simulink with CALB L148N58A parameters:

% Old (Kokam):
% results.T5C  = load('batteryParameterEstimation_results_3RC_5degC.mat');
% results.T20C = load('batteryParameterEstimation_results_3RC_20degC.mat');
% results.T40C = load('batteryParameterEstimation_results_3RC_40degC.mat');

% New (CALB L148N58A - e.g., Cell 59294):
results.T10C = load('results/Cell_59294/batteryParameterEstimation_results_3RC_10degC.mat');
results.T25C = load('results/Cell_59294/batteryParameterEstimation_results_3RC_25degC.mat');
results.T40C = load('results/Cell_59294/batteryParameterEstimation_results_3RC_40degC.mat');

% Update temperature LUT:
Battery(idx).Temperature_LUT = [10 25 40] + 273.15;  % Kelvin

% Update physical properties:
cell_thickness = 0.027;   % m
cell_width     = 0.148;   % m
cell_height    = 0.106;   % m
Battery(idx).cell_mass = 0.926; % kg

% Use measured capacity (NOT nominal 58 Ah):
Battery(idx).Capacity_LUT = [53.4 53.6 54.2]; % Ah (per temperature)

Project Structure

calb/
├── README.md                       This file
├── requirements.txt                Python dependencies
├── extract_CALB_params.py          Parameter extraction script
├── all_cell_params.json            All results (JSON)
├── comparison_table.xlsx           Cell comparison table (Excel)
├── results/                        Simulink-compatible .mat outputs
│   ├── Cell_59294/                 (11 cells, 3 .mat files each)
│   ├── Cell_59485/
│   ├── Cell_59627/
│   ├── Cell_59690/
│   ├── Cell_59861/
│   ├── Cell_60031/
│   ├── Cell_60129/
│   ├── Cell_60195/
│   ├── Cell_60403/
│   ├── Cell_60644/
│   └── Cell_60710/
└── A Dataset for .../              Mendeley raw dataset
    └── CALB L148N58A testing campaign/
        ├── Raw Data/
        └── Processed Data/