Battery Capacity Estimator (Kalman Filter)

Battery capacity estimator with Kalman filter

Since R2023b

Libraries:
Simscape / Battery / BMS / Estimators

Description

The Battery Capacity Estimator (Kalman Filter) block implements an estimator that calculates the cell capacity of a battery by using the Kalman filter algorithms.

Use this block in conjunction with another block that estimates the state of charge (SOC) of the battery, such as SOC Estimator (Kalman Filter) or SOC Estimator (Adaptive Kalman Filter).

This block supports single-precision and double-precision floating-point simulation.

Note

To enable single-precision floating-point simulation, the data type of all inputs and parameters, except for the Sample time (-1 for inherited) parameter, must be single.

For continuous-time simulation, set the Filter type parameter to Extended Kalman-Bucy filter or Unscented Kalman-Bucy filter.

Note

Continuous-time implementation of this block works only in a double-precision floating-point simulation. If you provide single-precision floating-point parameters and inputs, this block casts them to double-precision floating-point values to prevent errors.

For discrete-time simulation, set the Filter type parameter to Extended Kalman filter or Unscented Kalman filter and the Sample time (-1 for inherited) parameter to a positive value or -1.

Equations

To estimate the battery capacity, the Battery Capacity Estimator (Kalman Filter) block starts from the equations of the derivative of the capacity and the SOC:

$\begin{array}{l} \frac{d Q}{d t} = 0 \\ 0 = \frac{d S O C}{d t} + \frac{i}{3600 Q} \end{array}$

where

SOC is the state of charge.
i is the current of the battery cell.
Q is the capacity in Ampere-hour.

The first equation is the state equation. The second equation is the output equation.

For the Kalman filter algorithms, the Battery Capacity Estimator (Kalman Filter) block uses Q as the state and these process and observation functions:

$\begin{array}{l} f (Q) = 0 \\ h (Q, S O C) = \frac{d S O C}{d t} + \frac{i}{3600 Q} \end{array}$

Extended Kalman Filter

This diagram shows the structure of the extended Kalman filter (EKF):

The EKF technique relies on a linearization at every time step to approximate the nonlinear system. To linearize the system at every time step, the algorithm computes these Jacobians online:

$\begin{array}{l} F = \frac{\partial f}{\partial Q} = 0 \\ H = \frac{\partial h}{\partial Q} = - \frac{i}{3600 Q^{2}} \end{array}$

The EKF is a discrete-time algorithm. After the discretization, the Jacobians for the SOC estimation of the battery are:

$\begin{array}{l} F_{d} = 1 \\ H_{d} = - \frac{i T_{s}}{3600 Q^{2}} \end{array}$

where T_S is the sample time.

For more information about the implementation of the EKF algorithm steps, see the Extended Kalman Filter section of the SOC Estimator (Kalman Filter) block.

Extended Kalman-Bucy Filter

This diagram shows the structure of the extended Kalman-Bucy filter (EKBF):

The EKBF is the continuous-time variant of the Kalman filter. In continuous time, the prediction and correction steps are coupled.

For more information about the implementation of the EKF algorithm steps, see the Extended Kalman-Bucy Filter section of the SOC Estimator (Kalman Filter) block.

Unscented Kalman Filter

This diagram shows the structure of the unscented Kalman filter (UKF):

The EKF locally approximates nonlinear functions with the linear equations obtained from the Taylor expansion by using only the first term of the expansion. In a highly nonlinear system, these solutions are not very accurate.

The UKF uses nonlinear transformations on a set of sigma points that the algorithm chooses deterministically. This technique is called unscented transformation. The mean and the covariance matrix of the transformed points are accurate to the second order of the Taylor series expansion.

For more information about the implementation of the EKF algorithm steps, see the Unscented Kalman Filter section of the SOC Estimator (Kalman Filter) block.

Unscented Kalman-Bucy Filter

This diagram illustrates the structure of the unscented Kalman-Bucy filter (UKBF):

The derived continuous-time filtering equations of the UKBF are similar to the EKBF equations.

For more information about the implementation of the EKF algorithm steps, see the Unscented Kalman-Bucy Filter section of the SOC Estimator (Kalman Filter) block.

Examples

Estimate Battery State of Health Based on Capacity Fade

Estimate the battery capacity and state of health (SOH) by using a Kalman filter. The initial state of charge (SOC) of the battery is equal to 0.5. The estimator uses an initial condition for the SOC equal to 0.8. The battery keeps charging and discharging for 50 hours. The example estimates the battery capacity, in ampere-hour, and the SOC by using an extended Kalman Filter. The estimation error for the battery capacity is less than 4%. The SOC is estimated using an extended Kalman filter. When using fixed capacity the estimated SOC value diverges from the true value. To demonstrate the functionality of the estimator and to restrict the duration of the simulation, this example models an increased capacity fade rate.

Since R2024a
Open Model

Ports

Input

expand all

Current — Battery current
scalar | vector

Battery current, in ampere, specified as a scalar for a single cell or a vector for multiple cells. To specify this input as a vector of cell currents, select the Specify Current input as cell current(s) parameter.

CellSOC — Cell state of charge
scalar | vector

State of charge of one or multiple cells, specified as a scalar or vector of entries in the range [0, 1]. The size of this input port must be equal to the size of the InitialCellAH input port.

InitialCellAH — Cell temperature
scalar | vector

Initial cell capacity of the battery, in ampere-hour, specified as a scalar for a single cell or a vector for multiple cells. The size of this input port must be equal to the size of the CellSOC input port.

Output

expand all

CellAH — Estimated cell capacity
scalar | vector

Estimated cell capacity of the battery, in ampere-hour, returned as a scalar or a vector. The size of this output port is equal to the size of the InitialCellAH input port.

Parameters

expand all

Specify Current input as cell current(s) — Option to specify current input port as vector
`off` (default) | `on`

Option to specify the value of the Current input port as a vector of cell currents. If you select this parameter, the value at the Current input port can be a scalar or a vector of size equal to the size of the block inputs.

Filter type — Kalman filter type
`Extended Kalman filter` (default) | `Extended Kalman-Bucy filter` | `Unscented Kalman filter` | `Unscented Kalman-Bucy filter`

Type of Kalman filter that this block uses to estimate the battery cell capacity.

Alpha — Alpha coefficient
`1` (default) | scalar in the range [0, 1]

Coefficient that controls the spread of the sigma points. The block uses this parameter in its implementation of the equations for the unscented Kalman filter and the unscented Kalman-Bucy filter.

Dependencies

To enable this parameter, set Filter type to Unscented Kalman filter or Unscented Kalman-Bucy filter.

Beta — Beta coefficient
`2` (default) | nonnegative scalar

Coefficient related to the distribution. The block uses this parameter in its implementation of the unscented Kalman filter and the unscented Kalman-Bucy filter.

Dependencies

To enable this parameter, set Filter type to Unscented Kalman filter or Unscented Kalman-Bucy filter.

Kappa — Kappa coefficient
`0` (default) | scalar in the range [0, 3]

Coefficient that controls the spread of the sigma points. The block uses this parameter in its implementation of the equations for the unscented Kalman filter and the unscented Kalman-Bucy filter.

Dependencies

To enable this parameter, set Filter type to Unscented Kalman filter or Unscented Kalman-Bucy filter.

Covariance of the process noise, Q — Covariance of process noise
`3e-4` (default) | scalar

Covariance of the noise in the state.

Covariance of the measurement noise, R — Covariance of measurement noise
`5e-7` (default) | scalar

Covariance of the noise in the measurements.

Initial state error covariance, P0 — Initial state error covariance
`1e-8` (default) | scalar | matrix

Covariance of the initial state error. This parameter defines the deviation in the initialization of the state.

Sample time (-1 for inherited) — Block sample time
`1` (default) | 0 | -1 | integer

Time between consecutive block executions. During execution, the block produces outputs and, if appropriate, updates its internal state. For more information, see What Is Sample Time? and Specify Sample Time.

For inherited discrete-time operation, specify this parameter as -1. For discrete-time operation, specify this parameter as a positive integer. For continuous-time operation, specify this parameter as 0.

If this block is in a masked subsystem or a variant subsystem that supports switching between continuous operation and discrete operation, promote the sample time parameter. Promoting the sample time parameter ensures correct switching between the continuous and discrete implementations of the block. For more information, see Promote Block Parameters on a Mask.

Dependencies

To enable this parameter, set Filter type to Extended Kalman filter or Unscented Kalman filter.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2023b

Battery Capacity Estimator (Kalman Filter)

Description

Equations

Examples

Estimate Battery State of Health Based on Capacity Fade

Ports

Input

Current — Battery current scalar | vector

CellSOC — Cell state of charge scalar | vector

InitialCellAH — Cell temperature scalar | vector

Output

CellAH — Estimated cell capacity scalar | vector

Parameters

Specify Current input as cell current(s) — Option to specify current input port as vector off (default) | on

Filter type — Kalman filter type Extended Kalman filter (default) | Extended Kalman-Bucy filter | Unscented Kalman filter | Unscented Kalman-Bucy filter

Alpha — Alpha coefficient 1 (default) | scalar in the range [0, 1]

Dependencies

Beta — Beta coefficient 2 (default) | nonnegative scalar

Dependencies

Kappa — Kappa coefficient 0 (default) | scalar in the range [0, 3]

Dependencies

Covariance of the process noise, Q — Covariance of process noise 3e-4 (default) | scalar

Covariance of the measurement noise, R — Covariance of measurement noise 5e-7 (default) | scalar

Initial state error covariance, P0 — Initial state error covariance 1e-8 (default) | scalar | matrix

Sample time (-1 for inherited) — Block sample time 1 (default) | 0 | -1 | integer

Dependencies

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

Version History

See Also

Current — Battery current
scalar | vector

CellSOC — Cell state of charge
scalar | vector

InitialCellAH — Cell temperature
scalar | vector

CellAH — Estimated cell capacity
scalar | vector

Specify Current input as cell current(s) — Option to specify current input port as vector
`off` (default) | `on`

Filter type — Kalman filter type
`Extended Kalman filter` (default) | `Extended Kalman-Bucy filter` | `Unscented Kalman filter` | `Unscented Kalman-Bucy filter`

Alpha — Alpha coefficient
`1` (default) | scalar in the range [0, 1]

Beta — Beta coefficient
`2` (default) | nonnegative scalar

Kappa — Kappa coefficient
`0` (default) | scalar in the range [0, 3]

Covariance of the process noise, Q — Covariance of process noise
`3e-4` (default) | scalar

Covariance of the measurement noise, R — Covariance of measurement noise
`5e-7` (default) | scalar

Initial state error covariance, P0 — Initial state error covariance
`1e-8` (default) | scalar | matrix

Sample time (-1 for inherited) — Block sample time
`1` (default) | 0 | -1 | integer

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.