PyBatterySE

PyBatterySE — a shorthand for Python Battery State Estimation, is an open-source library for state estimation using Bayesian filters and linear parameter-varying (LPV) battery models.

Installation

Use the package manager pip to install PyBatterySE.

pip install pybatteryse

Requirements

PyBatterySE is a companion package to PyBatteryID, and utilises the models identified using PyBatteryID for state estimation. Whilst it is possible to use a custom model that follows the same format as PyBatteryID, it is recommended to use models identified using PyBatteryID for state estimation with PyBatterySE.

Basic usage

In the following, example usages of PyBatterySE have been demonstrated for performing battery state estimation, including SOC estimation, SOC observability analysis, and ageing-aware parameter and capacity estimation.

1. SOC estimation

For SOC estimation, two filter options are available: (i) extended Kalman filter (EKF), and (ii) particle filter (PF). In both cases, a StateSpace object is first constructed from the identified model, specifying which quantities form the state vector. The state is then augmented with the SOC: $x = [s \ x_1 \ \cdots \ x_n]^\top$.

Example 1: SOC estimation using EKF

import numpy as np
from pybatteryid.utilities import load_model_from_file
from pybatteryse import load_statespace_representation, load_filter

model = load_model_from_file('path/to/model.npy')
dataset = {
    'current_values': current_values,   # may contain bias/noise
    'voltage_values': voltage_values,
    'temperature_values': temperature_values,
}

# Build state-space representation
ss = load_statespace_representation(model, state_components=['s', 'overpotentials'])

# Initialize EKF
ekf = load_filter(
    ss,
    'extended_kalman_filter',
    variance_eta_u=1e-2,        # Input (current) noise variance
    variance_eta_y_e=1e-3,      # Measurement (voltage) noise variance
)

# Initial conditions
initial_state = np.array([0.5] + [0.0] * model.model_order)
initial_covariance = np.diag([1.0] + [0.1] * model.model_order)

# Run filter
state_estimates, error_covariances = ekf.run(
    dataset=dataset,
    initial_state=initial_state,
    initial_covariance=initial_covariance,
)

# Extract SOC estimates
soc_estimates = state_estimates[:, 0]

Example 2: SOC estimation using PF

import numpy as np
from pybatteryid.utilities import load_model_from_file
from pybatteryse import load_statespace_representation, load_filter

model = load_model_from_file('path/to/model.npy')
dataset = {
    'current_values': current_values,
    'voltage_values': voltage_values,
    'temperature_values': temperature_values,
}

# Build state-space representation
ss = load_statespace_representation(model, state_components=['s', 'overpotentials'])

# Initialize PF
pf = load_filter(
    ss,
    'particle_filter',
    num_particles=20,
    eta_bounds=(-4, -1),        # Uniform bounds for current-sensor bias
    variance_eta_y_e=1e-3,      # Measurement noise variance
)

# Run filter ('auto' initialises particles uniformly over the SOC domain)
state_estimates, _ = pf.run(
    dataset=dataset,
    initial_particles='auto',
)

soc_estimates = state_estimates[:, 0]

2. SOC observability analysis

SOC observability can be quantified using finite-horizon observability Gramians, which measure the accumulated sensitivity of the terminal voltage to a unit SOC perturbation over a fixed time horizon. An example is provided in examples/3_soc_observability_analysis.ipynb.

from pybatteryid.utilities import load_model_from_file
from pybatteryse import load_statespace_representation
from pybatteryse.utilities import compute_soc_observability_contributions, simulate_state_trajectory
from pybatteryse.plotter import plot_soc_vs_gramian

model = load_model_from_file('path/to/model.npy')
ss = load_statespace_representation(model, state_components=['s', 'overpotentials'])

state_trajectory = simulate_state_trajectory(ss, dataset)
gramian_contributions = compute_soc_observability_contributions(ss, state_trajectory, dataset)

plot_soc_vs_gramian(
    [(state_trajectory[:, 0], gramian_contributions['total'])],
)

3. Ageing-aware model estimation

Joint estimation of battery capacity and ageing-related model parameters can be performed by extending the state vector with the parameters to be tracked. These free parameters follow random-walk dynamics and are estimated alongside the physical states using EKF. An example is provided in examples/4_ageing_aware_model_estimation_with_ekf.ipynb.

import numpy as np
from pybatteryid.utilities import load_model_from_file
from pybatteryse import load_statespace_representation, load_filter

model = load_model_from_file('path/to/model.npy')
dataset = {
    'current_values': current_values,
    'voltage_values': voltage_values,
    'temperature_values': temperature_values,
}

# Augment state with free parameters and capacity
ss = load_statespace_representation(model, state_components=['s', 'overpotentials', 'theta_3', 'theta_6', 'capacity'])

ekf = load_filter(
    ss,
    'extended_kalman_filter',
    variance_eta_u=1e-3,
    variance_eta_y_e=1e-3,
    variance_eta_theta=1e-12,       # Process noise for theta random walks
    variance_eta_capacity=0.1,      # Process noise for capacity random walk
)

# Initial state: [soc, overpotentials..., theta_3, theta_6, capacity]
initial_state = np.array([0.5, 0.0, theta_3_mean, theta_6_mean, capacity_nominal])
initial_covariance = np.zeros((len(initial_state), len(initial_state)))

state_estimates, _ = ekf.run(
    dataset=dataset,
    initial_state=initial_state,
    initial_covariance=initial_covariance,
)

soc_est      = state_estimates[:, 0]
theta_3_est  = state_estimates[:, 2]
theta_6_est  = state_estimates[:, 3]
capacity_est = state_estimates[:, 4]

Examples

The examples/ folder contains four Jupyter notebooks along with the datasets required to run them:

#	Notebook	Description
1	1_soc_estimation_with_ekf.ipynb	SOC estimation for NMC and LFP batteries using LTI and LPV models with EKF
2	2_soc_estimation_with_pf.ipynb	SOC estimation for NMC and LFP batteries using LTI and LPV models with PF
3	3_soc_observability_analysis.ipynb	SOC observability analysis via finite-horizon observability Gramians
4	4_ageing_aware_model_estimation_with_ekf.ipynb	Recursive joint estimation of capacity and ageing parameters with EKF

Datasets are stored under examples/data/ in three sub-folders: nmc_soc_estimation/, lfp_soc_estimation/, and nmc_ageing_estimation/.