Using MathWorks®tools, estimation techniques, and measured lithium-ion or lead acid battery data, you can generate parameters for theEquivalent Circuit Batteryblock. TheEquivalent Circuit Batteryblock implements a resistor-capacitor (RC) circuit battery with open circuit voltage, series resistance, and 1 through N RC pairs. The number of RC pairs reflects the number of time constants that characterize the battery transients. Typically, the number of RC pairs ranges from 1 through 5.
To create parameter data for theEquivalent Circuit Batteryblock, follow these workflow steps. The steps use numerical optimization techniques to determine the number of recommended RC pairs, provide initial estimates for the battery model circuit parameters, and estimate parameters to fit a model to experimental pulse discharge data. The results provide the open circuit voltage, series resistance, and RC pair parameter data for theEquivalent Circuit Batteryblock.
The workflow steps use this example script and models for a lithium-ion polymer (LiPo) battery:
Estimate battery discharge scriptExample_DischargePulseEstimation
.
ModelBatteryEstim3RC_PTBS
.
ModelBatteryEstim3RC_PTBS_EQ
.
The example battery discharge script uses a battery class to control the parameter estimation workflow.
Workflow | Description | Additional MathWorks Tooling |
---|---|---|
Step 1: Load and Preprocess Data | Load and preprocess time series battery discharge voltage and current data. |
None |
Step 2: Determine the Number of RC Pairs | Determine the number of necessary time constants (TC) for estimation. |
Curve Fitting Toolbox™ |
Step 3: Estimate Parameters | For battery discharge data, estimate and optimize:
Use a model that exercises theEstimation Equivalent Circuit Batteryblock. |
Curve Fitting Toolbox, Parallel Computing Toolbox™, Optimization Toolbox™, and金宝app®Design Optimization™ |
Step 4: Set Equivalent Circuit Battery Block Parameters | Set these block parameters:
|
None |
The workflow supports pulse discharge sequences from 100% to 0% state-of-charge (SOC).
数据需求包括:
Time series consisting of current and voltage from an experimental pulse discharge. For each experimental data set, the temperature is constant. The sample rate should be a minimum of 1 Hz, with an ideal rate at 10 Hz. This table summarizes the accuracy requirements.
Measurement | Accuracy | 理想的 |
---|---|---|
Voltage | ±5 mV | ±1 mV |
Current | ±100 mA | ±10 mA |
Temperature | ±1 °C | ±1 °C |
Change in SOC for each pulse should not be greater than 5%.
Data collection at high or low SOC might need modification to ensure safety.
Sufficient relaxation time after each pulse to ensure battery approaches steady-state voltage.
Load the battery time, voltage, and discharge data. Break up the data intoBattery.Pulse
objects. For example, load and preprocess the discharge data for a lithium-ion polymer (LiPo) battery using theStep1: Load and Preprocess Data
commands in theExample_DischargePulseEstimation
script.
Pulse Sequence
Pulse Identification
Determine how many RC pairs to use in the model. You can investigate how many RC pairs to use by executing theStep 2: Determine the Number of RC Pairs
commands in theExample_DischargePulseEstimation
script. The example script uses theBatteryEstim3RC_PTBS
model.
Compare the time constants (TC) for each pulse. This example compares three pulses.
TC Comparison, Pulse 3 of 3
Estimate the parameters. You can investigate parameter estimation by executing theStep 3: Estimate Parameters
commands in theExample_DischargePulseEstimation
script.
Inspect the voltage immediately before and after the current is applied and removed at the start and end of each pulse. The estimation technique uses the voltage for a raw calculation to estimate the open-circuit voltage (Em) and the series resistance (R0).
Parameter Tables
Use a curve-fitting technique on the pulse relaxation to estimate the RC time constant (Tau) at each SOC.
Relaxation Tau Fit
Plot the parameter and pulse sequence data and simulation comparison.
Parameter Tables
Pulse Sequence
Identify parameters and set the initial values using a linear system approach, pulse-by-pulse.
Linear Fit
Optimize the Em, R0, Rx, and Tau estimates usingSimulink Design Optimization.
Pulse Identification
Set theEquivalent Circuit Batteryblock parameters to the values determined in step 3. To investigate setting the block parameters, execute theStep 4: Set Equivalent Circuit Battery Block Parameters
commands in theExample_DischargePulseEstimation
script. The experiment ran at two constant temperatures. There are three RC-pairs. TheEquivalent Circuit Batteryblock parameter values are summarized in this table:
Parameter | Example Value |
---|---|
Number of series RC pairs |
3 |
Open circuit voltage table data, EM |
EmPrime = repmat(Em,2,1)'; |
Series resistance table data, R0 |
R0Prime = repmat(R0,2,1)'; |
State of charge breakpoints, SOC_BP |
SOC_LUTPrime = SOC_LUT; |
Temperature breakpoints, Temperature_BP |
TempPrime = [303 315.15]; |
Battery capacity table |
CapacityAhPrime = [CapacityAh CapacityAh]; |
Network resistance table data, R1 |
R1Prime = repmat(Rx(1,:),2,1)'; |
Network capacitance table data, C1 |
C1Prime = repmat(Tx(1,:)./Rx(1,:),2,1)'; |
Network resistance table data, R2 |
R2Prime = repmat(Rx(2,:),2,1)'; |
Network capacitance table data, C2 |
C2Prime = repmat(Tx(2,:)./Rx(2,:),2,1)'; |
Network resistance table data, R3 |
R3Prime = repmat(Rx(3,:),2,1)'; |
Network capacitance table data, C3 |
C3Prime = repmat(Tx(3,:)./Rx(3,:),2,1)'; |
[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 .杜松子酒和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.
Equivalent Circuit Battery|Estimation Equivalent Circuit Battery