Cell Delta SOC Estimator (Kalman Filter, Variable Resistance)

State of charge estimator with cell delta Kalman filter and variable resistance

Since R2025a

• 

Libraries:
Simscape / Battery / BMS / Estimators

Description

The Cell Delta SOC Estimator (Kalman Filter, Variable Resistance) block implements an estimator that calculates the state of charge (SOC) of a battery by using the cell delta Kalman filter. The terminal resistance of the battery cell is an input to the block and can be variable. The delta SOC is the internal estimator state, the current is the control input, and the cell voltage is the measurement.

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

Note

To enable inherited 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

This equation defines the cell delta SOC:

$$\begin{array}{cc}\Delta SO{C}_i=SO{C}_i-\overline{SOC},& i=1,\dots ,N_s\end{array},$$

where SOC_i is the state of charge of cell i, $$\overline{SOC}$$ is the pack-average state of charge, and Ns is the number of series-connected cells.

This equation defines the inverse delta cell capacity:

$$\Delta A{H}_{inv,i}=A{H}_{inv,i}-\overline{A{H}_{inv}},$$

where $$A{H}_{inv,i}=\frac{1}{A{H}_i}$$ is the inverse cell capacity of cell i and $${\overline{AH}}_{inv}=\frac{1}{\overline{AH}}$$ is the average inverse capacity of the battery.

The state-space model for the delta SOC is

$$\begin{array}{l}\frac{d\Delta SO{C}_i}{dt}=-\frac{i\cdot \Delta A{H}_{inv,i}}{3600}\\ V_{t,i}=V_0\left(\overline{SOC}+\Delta SO{C}_i,\overline{T}\right)-i{R}_0-{\overline{V}}_{dyn}\end{array}$$

where Vt,i is the terminal voltage of cell i and R₀ is the terminal resistance.

For the Kalman filter algorithms, the block uses $$d\Delta SO{C}_i$$ as the state and these processes and observation functions:

$$\begin{array}{l}f\left(\Delta SO{C}_i\right)=-\frac{i\cdot \Delta A{H}_{inv,i}}{3600}\\ h\left(d\Delta SO{C}_i\right)=V_0\left(\overline{SOC}+\Delta SO{C}_i,\overline{T}\right)-i{R}_0-{\overline{V}}_{dyn}\end{array}$$

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

$$\begin{array}{l}F=\frac{\partial f}{\partial \Delta SO{C}_i}=0\\ H=\frac{\partial V_0}{\partial \Delta SO{C}_i}\end{array}$$

The EKF is a discrete-time algorithm. After the discretization, the Jacobians are:

$$\begin{array}{l}{F}_d=1\\ H_d=\frac{\partial V_0}{\partial \Delta SO{C}_i}\end{array}$$

The unscented Kalman filter uses nonlinear transformations on a set of sigma points that the algorithm chooses deterministically.

The block then computes the cell SOC using this equation:

$$SO{C}_i=\overline{SOC}+\Delta SO{C}_i.$$

The implementation of the Kalman filter for capacity estimation follows the theory in the SOC Estimator (Kalman Filter) block for the one-state model described in this section.

Examples

Explore Techniques to Estimate Battery State of Charge

Explores different techniques to estimate the state of charge (SOC) of a battery, including the Kalman filter algorithm and the Coulomb counting method. The Kalman filter is an estimation algorithm that infers the state of a linear dynamic system from incomplete and noisy measurements. This example illustrates the effectiveness of the Kalman filter in dynamically estimating the SOC of a battery, even when starting with inaccurate initial conditions and when the measurements are noisy. The SOC of a battery measures the current capacity of the battery in relation to its maximum capacity.

• Since R2024b
• Open Live Script

Assumptions and Limitations

The process and SOC noises are independent, zero mean, Gaussian noises.

Ports

Input

Current — Battery current, ampere

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.

CellVoltage — Cell voltage, volt

scalar | vector

Cell voltage, in volt, 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 CellTemperature, dInvCellAH, and CellR0 input ports.

CellTemperature — Cell temperature, K

scalar | vector

Cell temperature, 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 CellVoltage, dInvCellAH, and CellR0 input ports.

dInvCellAH — Inverse delta cell capacity, A*Hr

scalar | vector

Inverse delta 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 CellVoltage, CellTemperature, and CellR0 input ports.

CellR0 — Cell terminal resistance, ohm

scalar | vector

Terminal resistance of the cell, in ohm, 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 CellVoltage, CellTemperature, and dInvCellAH input ports.

PackSOC — Average SOC of battery pack, unitless

scalar

Average SOC of the battery pack, specified as a scalar.

Vdyn — Average dynamic overpotential voltage of battery pack, volt

scalar

Average dynamic overpotential voltage of the battery pack, in volt, specified as a scalar.

Output

CellSOC — SOC of battery cell

scalar | vector

SOC of the battery cell, returned as a scalar or a vector. The size of this output port is equal to the size of the CellVoltage, CellTemperature, and dInvCellAH input ports.

Parameters

Main

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 state of charge.

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 the process noise

0.0001 (default) | scalar

Covariance of the noise in the states.

Covariance of the measurement noise, R — Covariance of the measurement noise

0.7 (default) | scalar

Covariance of the noise in the measurements.

Initial state error covariance, P0 — Initial state error covariance

1e-3 (default) | scalar

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.

System Model

Vector of state-of-charge values, SOC (-) — SOC breakpoints

[0, .1, .25, .5, .75, .9, 1] (default) | vector of scalars in the range [0, 1]

Vector of the state of charge breakpoints defining the points at which you specify lookup data. The entries of this vector must be in strictly ascending order.

Vector of temperatures, T — Temperature breakpoints

[278, 293, 313] (default) | vector of positive scalars

Vector of temperature breakpoints defining the points at which you specify lookup data. This vector must be in strictly ascending order and greater than 0 K. The physical unit of this parameter must be the same as the physical unit of the CellTemperature input port.

Terminal resistance, R0(SOC,T), (ohm) — R0 lookup table with temperature breakpoint

[.0117, .0085, .009; .011, .0085, .009; .0114, .0087, .0092; .0107, .0082, .0088; .0107, .0083, .0091; .0113, .0085, .0089; .0116, .0085, .0089] (default) | matrix of positive entries

Lookup data for series resistance of the battery at the specified SOC and temperature breakpoints.

No-load voltage, V0(SOC,T), (V) — V₀ lookup table

[3.49, 3.5, 3.51; 3.55, 3.57, 3.56; 3.62, 3.63, 3.64; 3.71, 3.71, 3.72; 3.91, 3.93, 3.94; 4.07, 4.08, 4.08; 4.19, 4.19, 4.19] (default) | matrix of nonnegative entries

Lookup data, in volt, for open-circuit voltages across the fundamental battery model at the specified SOC. The number of rows of this matrix is equal to the size of the Vector of state-of-charge values, SOC (-) parameter. The number of columns of this matrix is equal to the size of the Vector of temperatures, T parameter.

Signal Attributes

Algorithm data type — Option to choose data type for block algorithm

Inherit: auto (default) | double | single | <data type expression>

Since R2025a

Option to choose the data type for the block algorithm, specified as one of these values:

• Inherit: auto — You can simulate the block in both single and double precision. You must explicitly provide the inputs and parameters as either single or double.

• double — The block algorithm casts all inputs and parameters to double data type.

• single — The block algorithm casts all inputs and parameters to single data type.

• <data type expression> — The block algorithm casts all inputs and parameters to the data type object you specify.

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the data type attributes. For more information, see Specify Data Types Using Data Type Assistant and Control Data Types of Signals.

References

[1] Plett, Gregory L. "Efficient Battery Pack State Estimation Using Bar-Delta Filtering,” 2009. https://api.semanticscholar.org/CorpusID:54178271.

Extended Capabilities

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

Version History

Introduced in R2025a