Equivalent Circuit Battery

Resistor-capacitor (RC) circuit battery

• 

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

Description

The Equivalent Circuit Battery block implements a resistor-capacitor (RC) circuit battery that you can parameterize using equivalent circuit modeling (ECM). To simulate the state-of-charge (SOC) and terminal voltage, the block uses load current and internal core temperature.

The Equivalent Circuit Battery block calculates the combined voltage of the network battery using parameter lookup tables. The tables are functions of the SOC and battery temperature. You can use the Estimation Equivalent Circuit Battery block to help create the lookup tables.

Specifically, the Equivalent Circuit Battery block implements these parameters as lookup tables that are functions of the SOC and battery temperature:

• Series resistance, R_o=ƒ(SOC,T)

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

• Battery capacity, C_batt=ƒ(T)

• Network resistance, R_n=ƒ(SOC,T)

• Network capacitance, C_n=ƒ(SOC,T)

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

$$\begin{array}{l}{V}_T=E_m-I_{batt}{R}_o-{\displaystyle \sum _1^n{V}_n}\\ V_n={\displaystyle \underset{0}{\overset{t}{\int }}\left[\frac{I_{batt}}{C_n}-\frac{V_n}{R_n{C}_n}\right]dt}\\ SOC=\frac{-1}{C_{batt}}{\displaystyle \underset{0}{\overset{t}{\int }}{I}_{batt}}dt\\ I_{batt}=\frac{I_{in}}{N_p}\\ V_{out}=N_s{V}_T\\ P_{BattLoss}=I_{batt}{}^2{R}_0+{\displaystyle \sum _1^n\frac{V_n{}^2}{R_n}}\\ L{d}_{AmpHr}={\displaystyle \underset{0}{\overset{t}{\int }}{I}_{batt}}dt\end{array}$$

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

Power Accounting

For the power accounting, the block implements these equations.

Bus Signal			Description	Equations
PwrInfo	PwrTrnsfrd — Power transferred between blocks Positive signals indicate flow into block Negative signals indicate flow out of block	PwrLdBatt	Battery network power	$\begin{array}{l}{V}_{batt}=V_{out}\text{ OR }\frac{V_{out}}{\tau s+1}\\ \\ P_{batt}=-V_{batt}{I}_{batt}\\ P_{LdBatt}= -P_{batt}\end{array}$
	PwrNotTrnsfrd — Power crossing the block boundary, but not transferred Positive signals indicate an input Negative signals indicate a loss	PwrLossBatt	Battery network power loss	$$P_{LossBatt}=-\left(I_{batt}{}^2{R}_0+{\displaystyle \sum _1^n\frac{V_n{}^2}{R_n}}\right)$$
	PwrStored — Stored energy rate of change Positive signals indicate an increase Negative signals indicate a decrease	PwrStoredBatt	Battery network power stored	$P_{StoredBatt}=P_{Batt}+P_{LossBatt}$

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
Np	Number parallel branches
Np	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
Pbatt	Battery power
PLossBatt	Negative of battery network power loss
PBattLoss	Battery network power loss
PStoredBatt	Battery network power stored
PLdBatt	Battery network power
T	Battery temperature

Examples

EV Reference Application

Simulate an EV model with a motor-generator, battery, direct-drive transmission, and associated powertrain control algorithms.

Open Script

Ports

Inputs

CapInit — Battery capacity

scalar

Rated battery capacity at the nominal temperature, Cap_batt, in Ah.

Dependencies

To create this port, select External Input for the Initial battery capacity parameter.

BattCurr — Battery network current

scalar

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

BattTemp — Battery temperature

scalar

Battery temperature, T, in K.

Output

Info — Bus signal

bus

Bus signal containing these block calculations.

Signal			Description	Variable	Units
BattCurr			Combined current flowing from the battery network	Ibatt	A
BattAmpHr			Battery energy	LdAmpHr	A*h
BattSoc			State-of-charge capacity	SOC	NA
BattVolt			Combined voltage of the battery network	Vout	V
BattPwr			Battery power	Pbatt	W
PwrInfo	PwrTrnsfrd	PwrLdBatt	Battery network power	PLdBatt	W
	PwrNotTrnsfrd	PwrLossBatt	Battery network power loss	PLossBatt	W
	PwrStored	PwrStoredBatt	Battery network power stored	PStoredBatt	W

BattVolt — Battery output voltage

scalar

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

Parameters

Block Options

Initial battery capacity — Input or parameter

Parameter (default) | External Input

Initial battery capacity, Cap_batt, in Ah.

Dependencies

Block Parameter Initial battery capacity Option	Creates
External Input	Input port CapInit
Parameter	Parameter Initial battery capacity, BattCapInit

Output battery voltage — Unfiltered or Filter

Unfiltered (default) | Filtered

Select Filtered to apply a first-order filter to the output batter voltage.

Dependencies

Setting Output battery voltage parameter to Filtered creates these parameters:

• Output battery voltage time constant, Tc

• Output battery voltage initial value, Vinit

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

[3.5042 3.5136; 3.5573 3.5646; 3.6009 3.6153; 3.6393 3.6565; 3.6742 3.6889; 3.7121 3.7214; 3.7937 3.8078; 3.8753 3.8945; 3.97 3.9859; 4.0764 4.0821; 4.1924 4.193] (default) | array

Open circuit voltage table, E_m, in V. Function of SOC and battery temperature.

Series resistance table data, R0 — Resistance

array

Series resistance table, R_o, in ohms. Function of SOC and battery temperature.

State of charge breakpoints, SOC_BP — SOC breakpoints

[0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1] (default) | vector

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

Temperature breakpoints, Temperature_BP — Battery

[293.15 313.15] (default) | vector

Battery temperature breakpoints, K.

Battery capacity table, BattCap — Capacity

[28 28] (default) | array

Battery capacity, C_batt, in Ah. Function of battery temperature.

Initial battery capacity, BattCapInit — Capacity

28 (default) | scalar

Initial battery capacity, Cap_batt, in Ah.

Dependencies

Block Parameter Initial battery capacity Option	Creates
External Input	Input port CapInit
Parameter	Parameter Initial battery capacity, BattCapInit

Initial capacitor voltage, InitialCapVoltage — Voltage

0 (default) | array

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

Output battery voltage time constant, Tc — Filter time constant

1/1000 (default) | scalar

Output battery voltage time constant, T_c, in s. Used in a first-order voltage filter.

Dependencies

Setting Output battery voltage parameter to Filtered creates these parameters:

• Output battery voltage time constant, Tc

• Output battery voltage initial value, Vinit

Output battery voltage initial value, Vinit — Filter initial voltage

4.193 (default) | scalar

Output battery voltage initial value, V_init, in V. Used in a first-order voltage filter.

Dependencies

Setting Output battery voltage parameter to Filtered creates these parameters:

• Output battery voltage time constant, Tc

• Output battery voltage initial value, Vinit

R and C Table Data

Network resistance table data, Rn — Lookup table

[0.010342 0.0012244; 0.0067316 0.0011396; 0.0051156 0.0012661; 0.0043447 0.0012265; 0.0038826 0.0011163; 0.0034226 0.0009968; 0.003346 0.0011458; 0.0033222 0.001345; 0.0033201 0.0013091; 0.0032886 0.0010986; 0.0028114 0.0010309] (default) | array

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

Network capacitance table data, Cn — Lookup table

[2287.7 11897; 6122 24515; 18460 42098; 20975 44453; 15254 33098; 10440 24492; 13903 32975; 16694 40007; 15784 35937; 12165 26430; 9118 24795] (default) | array

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

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.

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™.

Version History

Introduced in R2017a