Estimation Equivalent Circuit Battery

Resistor-capacitor (RC) circuit battery that creates lookup tables

• Library:

• 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 you can use to create lookup tables for the Equivalent Circuit Battery block. The lookup tables are functions of the state-of-charge (SOC).

The Estimation Equivalent Circuit Battery block calculates the combined voltage of the network battery using parameter lookup tables. The tables are functions of the SOC. To acquire the SOC, the block integrates the charge and discharge currents.

Specifically, the block implements these parameters 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

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.

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.

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.

State of charge breakpoints, SOC_BP — SOC breakpoints

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

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

Battery capacity, BattCap — Capacity

27.6250 (default) | scalar

Battery capacity, C_batt, in Ah.

Initial battery capacity, BattCapInit — Capacity

27.6250 (default) | scalar

Initial battery capacity, C_batto, in Ah.

Initial capacitor voltage, InitialCapVoltage — Voltage

0 (default) | vector

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

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.

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.

Cell Limits

Upper Integrator Voltage Limit, Vu — Maximum

Inf (default) | scalar

Upper voltage limit, in V.

Lower Integrator Voltage Limit, Vl — Minimum

Inf (default) | scalar

Lower voltage limit, in V.

Model Examples

EV Reference Application

Simulate an EV model with a motor-generator, battery, direct-drive transmission, and associated powertrain control algorithms. Use the for powertrain matching analysis and component selection, control and diagnostic algorithm design, and hardware-in-the-loop (HIL) testing.

References

[1] Ahmed, R., J. Gazzarri, R. Jackey, S. Onori, S. Habibi, et al. "Model-Based Parameter Identification of Healthy and Aged Li-ion Batteries for Electric Vehicle Applications." SAE International Journal of Alternative Powertrains. doi:10.4271/2015-01-0252, 4(2):2015.

[2] Gazzarri, J., N. Shrivastava, R. Jackey, and C. Borghesani. "Battery Pack Modeling, Simulation, and Deployment on a Multicore Real Time Target." SAE International Journal of Aerospace. doi:10.4271/2014-01-2217, 7(2):2014.

[3] Huria, T., M. Ceraolo, J. Gazzarri, and R. 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, pp. 1–8.

[4] Huria, T., M. Ceraolo, J. Gazzarri, and R. Jackey. "Simplified Extended Kalman Filter Observer for SOC Estimation of Commercial Power-Oriented LFP Lithium Battery Cells." SAE Technical Paper 2013-01-1544. doi:10.4271/2013-01-1544, 2013.

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

[6] Jackey, R., G. Plett, and M. Klein. "Parameterization of a Battery Simulation Model Using Numerical Optimization Methods." SAE Technical Paper 2009-01-1381. doi:10.4271/2009-01-1381, 2009.

[7] Jackey, R., M. Saginaw, T. Huria, M. Ceraolo, P. Sanghvi, and J. Gazzarri. "Battery Model Parameter Estimation Using a Layered Technique: An Example Using a Lithium Iron Phosphate Cell." SAE Technical Paper 2013-01-1547. Warrendale, PA: SAE International, 2013.

Extended Capabilities

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