Estimation Equivalent Circuit Battery

Resistor-capacitor (RC) circuit battery that determines combined voltage using lookup tables

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Libraries:
Powertrain Blockset / Energy Storage and Auxiliary Drive / Network Battery

Description

The Estimation Equivalent Circuit Battery block implements a resistor-capacitor (RC) circuit battery model that determines the combined voltage of a network battery using parameter lookup tables. The tables are functions of the state-of-charge (SOC). Consider using the block for estimating battery voltage and SOC, not in system-level models.

To acquire the SOC, the block integrates the charge and discharge currents. The block implements these values as lookup tables that are functions of the SOC:

• Series resistance, R_o=ƒ(SOC)

• Battery open-circuit voltage, E_m=ƒ(SOC)

• Network resistance, R_n=ƒ(SOC)

• Network capacitance, C_n=ƒ(SOC)

To calculate the combined voltage of the battery network, the block uses these equations.

$$\begin{array}{l}{V}_T=E_m-I_{batt}{R}_o-{\displaystyle \sum _1^n{V}_n}\\ V_n={\displaystyle \underset{0}{\overset{t}{\int }}\left[\frac{I_{batt}}{C_n}-\frac{V_n}{R_n{C}_n}\right]dt}\\ SOC=\frac{-1}{C_{batt}}{\displaystyle \underset{0}{\overset{t}{\int }}{I}_{batt}}dt\\ I_{batt}=I_{in}\\ V_{out}=V_T\end{array}$$

Positive current indicates battery discharge. Negative current indicates battery charge.

The equations use these variables.

SOC	State-of-charge
Em	Battery open-circuit voltage
Ibatt	Per module battery current
Iin	Combined current flowing from the battery network
Ro	Series resistance
n	Number of RC pairs in series
Vout, VT	Combined voltage of the battery network
Vn	Voltage for n-th RC pair
Rn	Resistance for n-th RC pair
Cn	Capacitance for n-th RC pair
Cbatt	Battery capacity

Examples

Build Full Electric Vehicle Model

Build a vehicle with a motor-generator, battery, direct-drive transmission, and powertrain control algorithms using the electric vehicle (EV) reference application.

Ports

Inputs

BattCurr — Battery network current

scalar

Combined current flowing from the battery network, I_in, in A.

Output

Info — Bus signal

bus

Bus signal containing these block calculations.

Signal	Description	Variable	Units
CapVolt	Voltage for n-th RC pair	Vn	V

BattVolt — Battery output voltage

scalar

Combined voltage of the battery network, V_out, in V.

BattSoc — Battery SOC

scalar

Battery state-of-charge, SOC.

Parameters

Core Battery

Number of series RC pairs — RC pairs

1 (default) | 2 | 3 | 4 | 5

Number of series RC pairs. For lithium, typically 1 or 2.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	NumRC
Values:	1 (default) | 2 | 3 | 4 | 5
Data Types:	double

Open circuit voltage Em table data, Em — Voltage table

[3.8 3.8 3.8 3.8 3.8 3.8] (default) | array

Open-circuit voltage table, E_m, in V. Function of SOC.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	Em
Values:	[3.8 3.8 3.8 3.8 3.8 3.8] (default) | array
Data Types:	double

Series resistance table data, R0 — Resistance

[0.01 0.01 0.01 0.01 0.01 0.01] (default) | array

Series resistance table, R_o, in ohms. Function of SOC.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	R0
Values:	[0.01 0.01 0.01 0.01 0.01 0.01] (default) | array
Data Types:	double

State of charge breakpoints, SOC_BP — SOC breakpoints

[0 .2 .4 .6 .8 1] (default) | vector

State-of-charge (SOC) breakpoints, dimensionless.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	SOC_BP
Values:	[0 .2 .4 .6 .8 1] (default) | vector
Data Types:	double

Battery capacity, BattCap — Capacity

27.6250 (default) | scalar

Battery capacity, C_batt, in Ah.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	BattCap
Values:	27.6250 (default) | scalar
Data Types:	double

Initial battery capacity, BattCapInit — Capacity

27.6250 (default) | scalar

Initial battery capacity, C_batto, in Ah.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	BattCapInit
Values:	27.6250 (default) | scalar
Data Types:	double

Initial capacitor voltage, InitialCapVoltage — Voltage

0 (default) | vector

Initial capacitor voltage, in V. Dimension of vector must equal the Number of series RC pairs.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	InitialCapVoltage
Values:	0 (default) | vector
Data Types:	double

R and C Table Data

Network resistance table data, Rn — Lookup table

[0.005 0.005 0.005 0.005 0.005 0.005] (default) | array

Network resistance table data for n-th RC pair, as a function of SOC, in ohms.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	R
Values:	[0.005 0.005 0.005 0.005 0.005 0.005] (default) | array
Data Types:	double

Network capacitance table data, Cn — Lookup table

[10000 10000 10000 10000 10000 10000] (default) | array

Network capacitance table data for n-th RC pair, as a function of SOC, in F.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	C
Values:	[10000 10000 10000 10000 10000 10000] (default) | array
Data Types:	double

Cell Limits

Upper Integrator Voltage Limit, Vu — Maximum

Inf (default) | scalar

Upper voltage limit, in V.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	Vu
Values:	Inf (default) | scalar
Data Types:	double

Lower Integrator Voltage Limit, Vl — Minimum

Inf (default) | scalar

Lower voltage limit, in V.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	Vl
Values:	Inf (default) | scalar
Data Types:	double

References

[1] Ahmed, Ryan, et al. "Model-Based Parameter Identification of Healthy and Aged Li-ion Batteries for Electric Vehicle Applications." SAE International Journal of Alternative Powertrains. 4, no. 2 (2015): 233 -47. https://doi.org/10.4271/2015-01-0252.

[2] Gazzarri, Javier, Nishant Shrivastava, Robyn Jackey, and Craig Borghesani. "Battery Pack Modeling, Simulation, and Deployment on a Multicore Real Time Target." SAE International Journal of Aerospace. 7, no. 2 (2014): 207–13. https://doi.org/10.4271/2014-01-2217.

[3] Huria, Tarun, Massimo Ceraolo, Javier Gazzarri, and Robyn Jackey. “High Fidelity Electrical Model with Thermal Dependence for Characterization and Simulation of High Power Lithium Battery Cells.” IEEE^® International Electric Vehicle Conference, March 2012. https://doi.org/10.1109/ievc.2012.6183271.

[4] Huria, Tarun, Massimo Ceraolo, Javier Gazzarri, and Robyn Jackey. "Simplified Extended Kalman Filter Observer for SOC Estimation of Commercial Power-Oriented LFP Lithium Battery Cells." SAE Technical Paper Series, 2013. https://doi.org/10.4271/2013-01-1544.

[5] Jackey, Robyn A. "A Simple, Effective Lead-Acid Battery Modeling Process for Electrical System Component Selection." SAE Technical Paper Series, 2007. https://doi.org/10.4271/2007-01-0778.

[6] Jackey, Robyn A., Gregory L. Plett, and Martin J. Klein. "Parameterization of a Battery Simulation Model Using Numerical Optimization Methods." SAE Technical Paper Series, 2009. https://doi.org/10.4271/2009-01-1381.

[7] Jackey,Robyn, et al. "Battery Model Parameter Estimation Using a Layered Technique: An Example Using a Lithium Iron Phosphate Cell." SAE Technical Paper Series, 2013. https://doi.org/10.4271/2013-01-1547.

[8] Geng, Zeyang, Jens Groot, and Torbjorn Thiringer. “A Time- and Cost-Effective Method for Entropic Coefficient Determination of a Large Commercial Battery Cell.” IEEE Transactions on Transportation Electrification 6, no. 1 (March 2020): 257–66. https://doi.org/10.1109/TTE.2020.2971454.

Extended Capabilities

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

Version History

Introduced in R2017a