Characterize Battery Cell for Electric Vehicles
This example shows how to characterize a battery cell for electric vehicle applications using the test method from [1]. This example estimates the parameters of BAK N18650CL-29 18650 type lithium-ion cells [2] at five different ambient temperatures. The battery hybrid pulse power characterization (HPPC) test is performed in controlled environmental chambers.
Battery Testing
A typical HPPC data is a set of discharge-charge pulses, applied to a battery at different state of charge (SOC) and at a given temperature [1]. The magnitude of the pulse depends on the cell capacity and the test temperature. At the end of every sequence of discharge-charge pulse operations, the SOC decreases by about 10% by applying a constant discharge current of C/3. A long rest time of one hour is recommended for the cells to relax after every sequence of discharge-charge pulses. This process continues until it covers all points of interest in the SOC range. For more information, see [1].
Plot Battery Test Data
A Biologic BCS-815 8-channel battery tester, equipped with standard cables, accessories, and thermocouples, performed the battery HPPC tests [3]. The test chamber maintained temperature and humidity control. To measure the temperature, the tester used the Agilent 34972A data acquisition system equipped with multiplexer capabilities (34901A 20-Channel Multiplexer). The system tested three different samples. The test was reproducible each time. The cells were tested at five different temperatures: and chamber temperatures. During the test duration, the temperature was uniform. For more information about the test procedure, see [1].
These plots show the battery test data. Each test data comprises nine pair of discharge-charge pulses. After each discharge-charge operation, a C/3 constant current (SOC sweep step) decreases the cell SOC by 10%. To read, visualize, and extract individual pulse information from the HPPC test data, use the hppcTest function.
TestTemperatures = [0 10 25 35 45]; testData = struct(); for tempIdx = 1:5 filename = strcat("hppcDataBAKcell",mat2str(TestTemperatures(tempIdx)),"degC"); loadFileName = fullfile("testDataBAKcells",filename); load(loadFileName) testData.(filename) = hppcTest(hppcData,TimeVariable="time (s)",... VoltageVariable="voltage (V)",CurrentVariable="current (A)",... ValidVoltageRange=[2.8 4.6]); figure plot(testData.(filename)) title(filename) end
The hppcTest function automatically reads the HPPC test data and identifies all the individual load pulses. This function returns an HPPCTest object that can automatically perform parameter estimation for battery equivalent circuit models. To further refine the pulses you want to filter, tabulate, and include in the parameter estimation process, define these properties:
CurrentOnThreshold— Threshold current value that indicates whether a charge or a discharge is taking place, specified as a scalar double.VoltageChangeThreshold— Threshold voltage change value that indicates whether a charge or a discharge is taking place, specified as a scalar double.ValidPulseDurationRange— Valid pulse duration range that indicates whether a pulse is valid and should be stored in theTestSummaryproperty table, specified as a1-by-2 vector of doubles.ValidVoltageRange— Valid battery voltage range that indicates whether a pulse is valid and should be stored in theTestSummaryproperty table, specified as a1-by-2vector of doubles.
To view a tabulated summary of the final identified pulses, access the TestSummary property of any of the HPPCTest objects you previously created.
disp(testData.hppcDataBAKcell25degC.TestSummary)
PulseID Directionality SOC HPPCData PulseDuration PseudoOCV_V MaximumVoltage MinimumVoltage Current_A C_rate PulseStartIndex PulseEndIndex Temperature_degC
_______ ______________ _______ _________________ _____________ ___________ ______________ ______________ _________ ______ _______________ _____________ ________________
1 "Discharge" 1 {701×6 timetable} 30 4.1745 4.1745 3.7846 -6.1869 1.8976 354 1055 25
2 "Discharge" 0.90376 {701×6 timetable} 30 4.0837 4.0837 3.7479 -6.187 1.8977 2702 3403 25
3 "Discharge" 0.80754 {702×6 timetable} 30 4.0132 4.0132 3.6652 -6.1867 1.8975 5049 5751 25
4 "Discharge" 0.71133 {701×6 timetable} 30 3.9226 3.9226 3.5775 -6.1868 1.8976 7398 8099 25
5 "Discharge" 0.61512 {701×6 timetable} 30 3.846 3.846 3.4942 -6.1868 1.8976 9746 10447 25
6 "Discharge" 0.51891 {701×6 timetable} 30 3.7353 3.7353 3.4001 -6.1871 1.8977 12094 12795 25
7 "Discharge" 0.4227 {701×6 timetable} 30 3.65 3.65 3.3236 -6.1867 1.8975 14442 15143 25
8 "Discharge" 0.32649 {701×6 timetable} 30 3.6015 3.6015 3.2652 -6.1869 1.8976 16790 17491 25
9 "Discharge" 0.23028 {701×6 timetable} 30 3.5507 3.5507 3.1931 -6.1869 1.8976 19138 19839 25
10 "Charge" 0.98415 {502×6 timetable} 10 4.1158 4.3889 4.1158 4.6393 1.423 1055 1557 25
11 "Charge" 0.88793 {502×6 timetable} 10 4.057 4.3001 4.057 4.6406 1.4233 3403 3905 25
12 "Charge" 0.79172 {502×6 timetable} 10 3.9674 4.2113 3.9674 4.6394 1.423 5751 6253 25
13 "Charge" 0.69551 {502×6 timetable} 10 3.8751 4.1175 3.8751 4.6396 1.423 8099 8601 25
14 "Charge" 0.5993 {502×6 timetable} 10 3.7905 4.0355 3.7905 4.6396 1.423 10447 10949 25
15 "Charge" 0.50309 {502×6 timetable} 10 3.6936 3.9339 3.6936 4.6405 1.4233 12795 13297 25
16 "Charge" 0.40688 {502×6 timetable} 10 3.6224 3.8602 3.6224 4.6396 1.423 15143 15645 25
17 "Charge" 0.31066 {502×6 timetable} 10 3.5695 3.8109 3.5695 4.6397 1.4231 17491 17993 25
18 "Charge" 0.21445 {502×6 timetable} 10 3.5098 3.7597 3.5098 4.6397 1.4231 19839 20341 25
Estimate Battery Parameters
The Battery Equivalent Circuit block in Simscape Battery uses the equivalent circuit modeling approach. You can capture different physical phenomena of a cell by connecting multiple resistor-capacitor (RC) pairs in series. In the Battery Equivalent Circuit block, you can select up to three RC pairs. You can derive the value of the resistance and time constant parameters from the HPPC test data.
This equation defines the voltage response of a battery cell,
where:
is the cell open-circuit potential.
is the cell ohmic resistance.
and are the cell i-th RC pair resistance and time constant values.
is the current passing through the cell.
t is the elapsed time.
All parameters in this equation can be a function of the SOC, current load, current directionality, and cell temperature. Some HPPC test standards apply the current load such that the battery SOC and temperature states do not vary significantly. Therefore, you can assume a constant temperature. This figure shows a typical discharge-charge profile used in the test standard [1].
You can estimate the ohmic resistance from the sudden voltage change at the start of a discharge or a charge pulse (for example V1 to V2 or V5 to V6). To estimate the and parameters, you can use the short voltage relaxation immediately after the discharge (V4 - V5) or the charge (V8 - V9) pulse. You can extract more time constants from the longer voltage relaxation (V12 - V14) after the SOC sweep step (V9 - V12). In this example, you use the fitecm function to estimate the , , and parameters for the battery.
Select Parameter Estimation Method
The process of parameter estimation involves minimizing the error between the predicted voltage output of the ECM and the measured battery voltage response from the HPPC test. This table shows the most typical ECMs used to represent the impedance of a battery.
To minimize the error, you iteratively adjust the model parameters, such as R0, R1, and C1, until you achieve a satisfactory error between the measured voltage and simulated voltage. There are several techniques in MATLAB® that provide this functionality inside the Model-Based Calibration Toolbox™, System Identification Toolbox™, and Curve Fitting Toolbox™. In this example, you estimate the parameters of the battery model by using an optimization-based fitting method implemented in Simscape™ Battery™. This fitting method utilizes a custom implementation of the fminsearch function.
The battery ECM parameters for a specific operating point can be different depending on which segment or section of the current pulse you use for the parameter estimation process. The load-segment parameters suit most applications. However, the best estimation segment depends on the specific end application of the battery ECM. Some methods are better suited to estimate parameters for a given segment. For example the System Identification Toolbox tfest function works best for fitting load-only dynamics. This table contains a summary of the supported options for the FittingMethod and SegmentToFit arguments of the fitecm function, depending on the chosen toolbox or method. Curve Fitting Toolbox contains good methods to estimate parameters for the relaxation segment.
Estimate Time Constants from Short Relaxation
The testData structure contains information for the pulse section and the short voltage relaxation sections. For the short-duration voltage relaxation segments and load segments, there might not be enough information to fit the time constants of the RC branches that are much greater than 10 seconds. In these cases, to perform the parameter estimation, select a 1-RC equivalent circuit. To estimate the time constants from the short relaxation segment after the pulse, use the fitecm function and specify "relaxation" for the SegmentToFit argument and a 1RC ECM for the ECM argument.
batteryEcm25degC = fitECM(testData.hppcDataBAKcell25degC,ECM=ecm(1),SegmentToFit="relaxation"); To visually verify the fit for the four first pulses, use the plot method. The time constants for the relaxation segment do not necessarily provide good fits for the load segment of the pulse. Other factors, such as the assumption of a scalar constant open-circuit voltage value, might influence the accuracy of the fit in these plots. The crucial output to verify with these plots is that the relaxation behavior matches between simulated and measured voltage points.
plot(batteryEcm25degC,1:4)
To view the time constant values, access the ParameterSummary property of the batteryEcm25degC object.
disp(batteryEcm25degC.ParameterSummary)
ID Directionality SOC Temperature_degC Current_A OpenCircuitVoltage R0 R1 Tau1 C1 FitPc
__ ______________ _______ ________________ _________ __________________ ________ _________ ______ ______ __________
1 "Discharge" 1 25 -6.1869 4.1745 0.043854 0.0098299 10.217 1039.4 0.0026152
2 "Discharge" 0.90376 25 -6.187 4.0837 0.040707 0.0094222 10.262 1089.2 0.0021524
3 "Discharge" 0.80754 25 -6.1867 4.0132 0.039485 0.0097654 11.243 1151.3 0.0019493
4 "Discharge" 0.71133 25 -6.1868 3.9226 0.039243 0.0094014 11.678 1242.1 0.0017278
5 "Discharge" 0.61512 25 -6.1868 3.846 0.03937 0.0090181 11.633 1289.9 0.0016414
6 "Discharge" 0.51891 25 -6.1871 3.7353 0.039686 0.0081095 11.185 1379.2 0.0014102
7 "Discharge" 0.4227 25 -6.1867 3.65 0.040354 0.0083378 11.252 1349.6 0.0013838
8 "Discharge" 0.32649 25 -6.1869 3.6015 0.04115 0.0085245 11.562 1356.4 0.0013272
9 "Discharge" 0.23028 25 -6.1869 3.5507 0.042858 0.0086828 11.024 1269.6 0.00164
10 "Charge" 0.98415 25 4.6393 4.1158 0.0482 0.0052075 3.8168 732.95 0.00053578
11 "Charge" 0.88793 25 4.6406 4.057 0.043691 0.0043709 4.3715 1000.1 0.0003732
12 "Charge" 0.79172 25 4.6394 3.9674 0.042342 0.0045548 4.3033 944.79 0.00035176
13 "Charge" 0.69551 25 4.6396 3.8751 0.04209 0.004625 4.1394 895 0.00032855
14 "Charge" 0.5993 25 4.6396 3.7905 0.042434 0.0047765 3.8075 797.13 0.00034043
15 "Charge" 0.50309 25 4.6405 3.6936 0.043065 0.004334 4.1386 954.92 0.00049142
16 "Charge" 0.40688 25 4.6396 3.6224 0.043463 0.0039566 4.798 1212.7 0.00033171
17 "Charge" 0.31066 25 4.6397 3.5695 0.044009 0.0038565 4.7506 1231.8 0.00029811
18 "Charge" 0.21445 25 4.6397 3.5098 0.045168 0.0040985 4.8543 1184.4 0.00032097
EstimateTime Constants from Long Relaxation
To extract the time constants from the longer voltage relaxation pulses, you must first filter the HPPC data using the hppcTest function by defining the ValidPulseDurationRange and the ValidVoltageRange name-value arguments. If you increase the minimum and maximum pulse duration thresholds, you also filter out the shorter duration pulses and you only obtain the SOC sweep pulses with the longer voltage relaxation section.
for tempIdx = 1:5 filename = strcat("hppcDataBAKcell",mat2str(TestTemperatures(tempIdx)),"degC"); loadFileName = fullfile("testDataBAKcells",filename); load(loadFileName) testData.(strcat(filename,"Long")) = hppcTest(hppcData,TimeVariable="time (s)",... VoltageVariable="voltage (V)",CurrentVariable="current (A)", ... ValidPulseDurationRange=[100 1600],ValidVoltageRange=[3 4.6]); end
To inspect the individual pulses in the HppcTest object, use the plot method.
figure
plot(testData.hppcDataBAKcell25degCLong)
title("Long relaxation pulses 25degC")
disp(testData.hppcDataBAKcell25degCLong.TestSummary)
PulseID Directionality SOC HPPCData PulseDuration PseudoOCV_V MaximumVoltage MinimumVoltage Current_A C_rate PulseStartIndex PulseEndIndex Temperature_degC
_______ ______________ _______ __________________ _____________ ___________ ______________ ______________ _________ _______ _______________ _____________ ________________
1 "Discharge" 0.98811 {1145×6 timetable} 1081 4.1416 4.1416 4.0285 -0.91589 0.28092 1557 2702 25
2 "Discharge" 0.89189 {1144×6 timetable} 1081 4.0781 4.0781 3.9534 -0.91593 0.28093 3905 5049 25
3 "Discharge" 0.79568 {1145×6 timetable} 1081 3.9949 3.9949 3.8544 -0.91594 0.28093 6253 7398 25
4 "Discharge" 0.69947 {1145×6 timetable} 1081 3.9021 3.9021 3.7672 -0.91597 0.28094 8601 9746 25
5 "Discharge" 0.60326 {1145×6 timetable} 1081 3.8171 3.8171 3.6693 -0.91604 0.28096 10949 12094 25
6 "Discharge" 0.50705 {1145×6 timetable} 1081 3.7145 3.7145 3.5944 -0.91599 0.28095 13297 14442 25
7 "Discharge" 0.41084 {1145×6 timetable} 1081 3.6413 3.6413 3.5392 -0.91597 0.28094 15645 16790 25
8 "Discharge" 0.31462 {1145×6 timetable} 1081 3.59 3.59 3.476 -0.91584 0.2809 17993 19138 25
9 "Discharge" 0.21841 {1148×6 timetable} 1082 3.5324 3.5324 3.3742 -0.91575 0.28087 20341 21489 25
To estimate the time constants from the long relaxation segment after the SOC sweep pulse, use the fitecm function.
batteryEcm25degCLong = fitECM(testData.hppcDataBAKcell25degCLong, SegmentToFit = "relaxation"); To view the time constant values, use the ParameterSummary property of the batteryEcm25degCLong object. These time constants might not produce a good fit for the load segment of the pulse.
disp(batteryEcm25degCLong.ParameterSummary)
ID Directionality SOC Temperature_degC Current_A OpenCircuitVoltage R0 R1 Tau1 C1 R2 Tau2 C2 FitPc
__ ______________ _______ ________________ _________ __________________ ________ __________ __________ __________ _________ ______ ______ __________
1 "Discharge" 0.98811 25 -0.91589 4.1416 0.037254 0.016552 3.3039 199.6 0.0061691 254.79 41301 3.7102e-06
2 "Discharge" 0.89189 25 -0.91593 4.0781 0.035967 0.019408 1.0001e-10 5.1529e-09 0.0088514 42.43 4793.6 5.0498e-05
3 "Discharge" 0.79568 25 -0.91594 3.9949 0.035675 0.027497 40.294 1465.4 0.011182 338.03 30229 2.6218e-06
4 "Discharge" 0.69947 25 -0.91597 3.9021 0.035987 1.6543e-05 1.1726e-10 7.0885e-06 0.045121 37.133 822.97 0.0019725
5 "Discharge" 0.60326 25 -0.91604 3.8171 0.036338 1e-05 0.00017667 17.667 0.030543 27.427 897.97 0.00082185
6 "Discharge" 0.50705 25 -0.91599 3.7145 0.037034 1e-05 4.4858e-07 0.044858 0.02241 34.556 1542 7.1771e-05
7 "Discharge" 0.41084 25 -0.91597 3.6413 0.037719 0.019914 1.0003e-10 5.0229e-09 0.0082379 35.722 4336.4 0.00033233
8 "Discharge" 0.31462 25 -0.91584 3.59 0.038465 0.018573 1.4823 79.809 0.030163 719.11 23841 2.0817e-05
9 "Discharge" 0.21841 25 -0.91575 3.5324 0.040896 0.024498 49.1 2004.3 0.021757 721.75 33173 7.0132e-06
Parameterize Battery Equivalent Circuit Block
To parameterize the Battery Equivalent Circuit block and visualize the verification results for all the temperatures that you specified in the TestTemperatures workspace variable, at the MATLAB Command Window, enter:
hppcSuite = hppcTestSuite([testData.hppcDataBAKcell0degC,... testData.hppcDataBAKcell10degC,... testData.hppcDataBAKcell25degC,... testData.hppcDataBAKcell35degC,... testData.hppcDataBAKcell45degC], ... Temperature=TestTemperatures); batteryEcm = fitECM(hppcSuite,SegmentToFit="loadAndRelaxation");
You can also parameterize the equivalent circuit model by selecting either the "relaxation" or "load" segment of the pulse. In addition, you can also decide to fit the model using the long voltage relaxation pulses instead.
To parameterize the Battery Equivalent Circuit block, open the CellDischargeCC model and obtain the handle to the Battery Equivalent Circuit block.
modelName = "CellDischargeCC"; open_system(modelName); blockHandle = getSimulinkBlockHandle( strcat(modelName,"/battery"));
Use the parameterizeEquivalentCircuitBlock function and close the model.
batteryEcm.ResistanceTemperatureBreakpoints = simscape.Value([10,25,35,45] + 273.15,"K"); parameterizeEquivalentCircuitBlock(batteryEcm,blockHandle,"ParameterizePseudoOCV",false) close_system(modelName,1)
To visualize the parameter trends, use the plotModelParameters method of the batteryEcm object.
plotModelParameters(batteryEcm)
Simulate Battery with Estimated Parameters
This figure shows the CellDischargeCC model.
Set the minimum and the maximum C-rates for the simulation.
oneHr = 3600; C_rate_min = 0.25; C_rate_max = 1; C_rate_del = 0.25; numCases = (C_rate_max - C_rate_min)/C_rate_del + 1;
Set the battery capacity, thermal mass, initial temperature, and initial SOC. The temperature of the cell depends on the CellThermalMass, which is equal to 200 J/K.
CellCapacityAhr = 2.8;
CellThermalMass = 200;
InitialTemperature = 305;
InitialSOC = 1;
load("ocvData.mat")Run a constant current discharge at different C rates, for a given InitialTemperature.
legendStr = strings(1,numCases); battSensorData = cell(1,numCases);
Run all simulations.
caseNum = 0; for C_rate = C_rate_min:C_rate_del:C_rate_max caseNum = caseNum + 1; legendStr(1,caseNum) = strcat(num2str(C_rate),'C rate discharge case'); BatteryConstantCurrent = -C_rate*CellCapacityAhr; batterySimTime_s = oneHr/C_rate; sim('CellDischargeCC'); ts = simlog_CellDischargeCC.battery.batteryVoltage.series.time; voltage = simlog_CellDischargeCC.battery.batteryVoltage.series.values; tempK = simlog_CellDischargeCC.battery.batteryTemperature.series.values; battSensorData{1,caseNum} = [ts voltage tempK]; end
Plot the battery voltage for different constant current discharge cases.
titleDisplay = strcat('Cell Voltage, Ambient Temperature = ',num2str(InitialTemperature-273),' degC'); figure('Name', titleDisplay); for itr = 1:numCases plot(battSensorData{1,itr}(:,1),battSensorData{1,itr}(:,2)); hold on end hold off legend(legendStr); xlabel('Time'); ylabel('Voltage'); title(titleDisplay);
Plot the battery temperature rise during the constant current discharge cases.
titleDisplay = strcat('Cell Temperature, Ambient Temperature = ',num2str(InitialTemperature-273),' degC'); figure('Name', titleDisplay); for itr = 1:numCases plot(battSensorData{1,itr}(:,1),battSensorData{1,itr}(:,3)); hold on end hold off legend(legendStr); xlabel('Time'); ylabel('Temperature (K)'); title(titleDisplay);
References
Christophersen, Jon P. "Battery Test Manual For Electric Vehicles, Revision 3". United States: N. p., 2015. Web. doi:10.2172/1186745
Zhengzhou Bak Battery Co.,LTD, "Specification For Lithium-ion Rechargeable Cell. Cell Type : N18650CL-29".
Anandaroop Bhattacharya, Subhasish Basu Majumder. "Experimental data collected with Biologic BCS-815 8-channel battery tester for battery HPPC test". Indian Institute of Technology (IIT) Kharagpur, India.
