Keithley 2450: Battery characterization

3.2 Battery Characterization

Battery selection for a specific application can depend on multiple factors: price, size, weight, safety and its electrical properties. Manufacturers are known for making dubious claims about their batteries lifetime and capacity, so the proper way to evaluate a battery is to characterize it.

Batteries are complex electrochemical devices that do not behave as constant voltage sources (Figure A). Their terminal voltage depends on the amount of charge in the battery, its temperature and the dynamics of the current being drawn. There are models of different levels of complexity that can simulate their behavior. A state of charge dependent voltage source model (Figure B) can simulate the voltage drop caused by the loss of battery charge. To simulate how the current causes a voltage drop at the terminals (Vt) a series resistor (Rs) needs to be added (Figure C). A current surge can drop Vt in non-series-resistor way, where Vt would slowly increase the voltage after the battery gets unloaded, to simulate that, an RC block needs to be added to the model (Figure D). Models can of course get much more complex, and can model self-discharge, temperature-dependence, or even the battery cell electrochemical dynamics.

Keithley provides a TSP script (Model generation script) to measure the Voc (open-circuit voltage) and equivalent series resistance (ESR) as the battery discharges. The generated data can then be used to create a battery model (Figure C) that can be used by the Keithley 2281S Battery simulator.

I decided to test the script with a 18650 Lithium battery and then plot the Voc, Vload and ESR (Rs) curves to see how they depend on the amount of charge of the battery.

The script requires to enter the "discharge current", which I set to 1 A, the cut-off voltage, which I set to 3 V, and the ESR measuring interval, which I set to 10 s. The script discharges the battery at constant current and measures the voltage (Vload), it periodically interrupts the discharge (sets the discharge current to 0 A) and measures the open circuit voltage (Voc). The ESR can then be derived as ESR = (Voc - Vload) / Idischarge. While the script discharges the battery it displays the elapsed time, the Voc, the Vload and the ESR.

After 2 hours the battery Vload hit the cut-off voltage, the discharge stopped and the data got saved into an USB drive. The script generated 2 files, one contains the raw data, and the other the battery model that can be used by the Keithley 2281S battery simulator.

The raw file contained:

TEST_PARAM.comment:,18650

SourceMeter Model:,2450
SourceMeter S/N:,00000000
SourceMeter Firmware:,1.7.1e

TEST_PARAM.terminals:,FRONT TERMINALS

TEST_PARAM.initial_voc:,4.1914849281
TEST_PARAM.vcutoff:,3

TEST_PARAM.discharge_type:,CONSTANT
TEST_PARAM.discharge_current:,1
TEST_PARAM.max_discharge_current:,1

TEST_PARAM.measure_interval:,10

TEST_PARAM.discharge_start_time:,07/03/20 14:51:05
TEST_PARAM.discharge_stop_time:,07/03/20 16:59:55

BATT_MODEL_RAW:,Index,Timestamp,Voc,Vload,ESR
BATT_MODEL_RAW:,1,0.04147066,4.1869735718,3.9285964966,0.2583770752
BATT_MODEL_RAW:,2,10.04163994,4.1751747131,3.9447231293,0.23045158386
BATT_MODEL_RAW:,3,20.04195438,4.1686229706,3.95063591,0.21798706055
BATT_MODEL_RAW:,4,30.04289712,4.1635017395,3.9475860596,0.21591567993
BATT_MODEL_RAW:,5,40.04404116,4.1592350006,3.9434394836,0.21579551697
BATT_MODEL_RAW:,6,50.04481626,4.1554431915,3.9393730164,0.21607017517
BATT_MODEL_RAW:,7,60.04562628,4.152048111,3.9423675537,0.20968055725
BATT_MODEL_RAW:,8,70.04634302,4.1489944458,3.9473381042,0.20165634155
BATT_MODEL_RAW:,9,80.04716334,4.1461925507,3.9474830627,0.19870948792
BATT_MODEL_RAW:,10,90.04737856,4.1436023712,3.9476509094,0.19595146179
BATT_MODEL_RAW:,11,100.04829772,4.1411247253,3.9458198547,0.19530487061
BATT_MODEL_RAW:,12,110.04906084,4.1387672424,3.9439659119,0.19480133057
BATT_MODEL_RAW:,13,120.05018826,4.1364307404,3.9417533875,0.19467735291
BATT_MODEL_RAW:,14,130.05060916,4.1343212128,3.9396514893,0.19466972351
BATT_MODEL_RAW:,15,140.05131596,4.1321258545,3.9372825623,0.19484329224
BATT_MODEL_RAW:,16,150.05158634,4.1300601959,3.936498642,0.19356155396
BATT_MODEL_RAW:,17,160.05184474,4.1280403137,3.9346523285,0.19338798523
BATT_MODEL_RAW:,18,170.05213434,4.126077652,3.9331703186,0.19290733337
BATT_MODEL_RAW:,19,180.05308966,4.1241550446,3.9298915863,0.19426345825
BATT_MODEL_RAW:,20,190.0534611,4.1222476959,3.926448822,0.1957988739
BATT_MODEL_RAW:,21,200.05388696,4.1203632355,3.9248046875,0.19555854797
BATT_MODEL_RAW:,22,210.05503024,4.1184978485,3.9234809875,0.19501686096
BATT_MODEL_RAW:,23,220.05631474,4.1166706085,3.9226894379,0.19398117065
BATT_MODEL_RAW:,24,230.05749754,4.1148509979,3.9226436615,0.19220733643
BATT_MODEL_RAW:,25,240.05781516,4.1130599976,3.9208621979,0.19219779968
BATT_MODEL_RAW:,26,250.05833834,4.1112728119,3.920091629,0.19118118286
BATT_MODEL_RAW:,27,260.0593152,4.1094818115,3.9175071716,0.19197463989
BATT_MODEL_RAW:,28,270.0603908,4.1077346802,3.9156265259,0.1921081543
BATT_MODEL_RAW:,29,280.06080194,4.1059894562,3.9137516022,0.192237854
BATT_MODEL_RAW:,30,290.06188338,4.1043128967,3.912569046,0.19174385071
BATT_MODEL_RAW:,31,300.0624175,4.1025085449,3.9104347229,0.19207382202
BATT_MODEL_RAW:,32,310.06318338,4.1007957458,3.9093151093,0.1914806366
BATT_MODEL_RAW:,33,320.06411186,4.0991306305,3.9074039459,0.19172668457
BATT_MODEL_RAW:,34,330.06466198,4.0974674225,3.9059638977,0.19150352478
BATT_MODEL_RAW:,35,340.06544256,4.095664978,3.9031410217,0.1925239563
BATT_MODEL_RAW:,36,350.06640894,4.0939750671,3.9018592834,0.19211578369
BATT_MODEL_RAW:,37,360.06768308,4.0922851563,3.9014205933,0.19086456299
BATT_MODEL_RAW:,38,370.0684368,4.090593338,3.9005413055,0.19005203247
BATT_MODEL_RAW:,39,380.06939068,4.0889205933,3.8992424011,0.18967819214
BATT_MODEL_RAW:,40,390.0699098,4.087266922,3.8982963562,0.1889705658
BATT_MODEL_RAW:,41,400.0707351,4.0855998993,3.8961029053,0.18949699402
BATT_MODEL_RAW:,42,410.07173234,4.0839252472,3.8947887421,0.18913650513
BATT_MODEL_RAW:,43,420.0728917,4.0823402405,3.8938293457,0.18851089478
BATT_MODEL_RAW:,44,430.0740412,4.0806236267,3.8922767639,0.18834686279
BATT_MODEL_RAW:,45,440.07472052,4.0790958405,3.891450882,0.1876449585
BATT_MODEL_RAW:,46,450.07591266,4.077419281,3.8901176453,0.18730163574
BATT_MODEL_RAW:,47,460.07613942,4.0756912231,3.8884849548,0.18720626831
BATT_MODEL_RAW:,48,470.07655048,4.0740585327,3.8873233795,0.1867351532
BATT_MODEL_RAW:,49,480.077216,4.072429657,3.8861198425,0.18630981445
BATT_MODEL_RAW:,50,490.07836948,4.0707969666,3.8853988647,0.18539810181
BATT_MODEL_RAW:,51,500.07951396,4.0691661835,3.8834381104,0.18572807312
BATT_MODEL_RAW:,52,510.08071844,4.0675601959,3.8822154999,0.18534469604
BATT_MODEL_RAW:,53,520.08164934,4.0660209656,3.8811225891,0.18489837646
BATT_MODEL_RAW:,54,530.0820863,4.0643215179,3.8794879913,0.18483352661
BATT_MODEL_RAW:,55,540.08262132,4.0627784729,3.8778133392,0.18496513367
BATT_MODEL_RAW:,56,550.0829232,4.0610961914,3.8764457703,0.18465042114
BATT_MODEL_RAW:,57,560.08408718,4.0595207214,3.8741149902,0.1854057312
BATT_MODEL_RAW:,58,570.08443458,4.0579013824,3.8733024597,0.18459892273
BATT_MODEL_RAW:,59,580.08536182,4.056312561,3.8713855743,0.18492698669
BATT_MODEL_RAW:,60,590.08609158,4.0547657013,3.8690624237,0.18570327759
BATT_MODEL_RAW:,61,600.08653976,4.0531101227,3.8673934937,0.18571662903
BATT_MODEL_RAW:,62,610.0871543,4.0515365601,3.865278244,0.18625831604
BATT_MODEL_RAW:,63,620.08754322,4.0499191284,3.8636035919,0.1863155365
BATT_MODEL_RAW:,64,630.08857226,4.0483283997,3.8625564575,0.18577194214
BATT_MODEL_RAW:,65,640.08880142,4.0467281342,3.8617916107,0.18493652344
BATT_MODEL_RAW:,66,650.08967788,4.0451526642,3.8603630066,0.18478965759
BATT_MODEL_RAW:,67,660.0898926,4.0435619354,3.8579826355,0.18557929993
BATT_MODEL_RAW:,68,670.09032444,4.0420742035,3.8564109802,0.18566322327
BATT_MODEL_RAW:,69,680.09136604,4.0404052734,3.8535423279,0.18686294556
BATT_MODEL_RAW:,70,690.09251666,4.0388336182,3.8519935608,0.18684005737
BATT_MODEL_RAW:,71,700.09357694,4.0372390747,3.8506469727,0.18659210205
BATT_MODEL_RAW:,72,710.09374676,4.0356769562,3.8489055634,0.18677139282
BATT_MODEL_RAW:,73,720.09436664,4.0340900421,3.847776413,0.18631362915
BATT_MODEL_RAW:,74,730.09489284,4.0325222015,3.8453083038,0.18721389771
BATT_MODEL_RAW:,75,740.09512284,4.0309562683,3.8430805206,0.18787574768
BATT_MODEL_RAW:,76,750.09547364,4.0293865204,3.8409404755,0.18844604492
BATT_MODEL_RAW:,77,760.0957287,4.0278129578,3.8394374847,0.18837547302
BATT_MODEL_RAW:,78,770.09605106,4.0262413025,3.8378829956,0.18835830688
BATT_MODEL_RAW:,79,780.09676726,4.0246906281,3.8364315033,0.18825912476
BATT_MODEL_RAW:,80,790.09745016,4.0231246948,3.834695816,0.18842887878
BATT_MODEL_RAW:,81,800.09769716,4.0215606689,3.8330345154,0.18852615356
BATT_MODEL_RAW:,82,810.09877796,4.0199985504,3.8322944641,0.1877040863
BATT_MODEL_RAW:,83,820.09914636,4.0184364319,3.830575943,0.18786048889
BATT_MODEL_RAW:,84,830.10033254,4.0168972015,3.8287315369,0.18816566467
BATT_MODEL_RAW:,85,840.10115234,4.0154285431,3.8272895813,0.18813896179
BATT_MODEL_RAW:,86,850.10185282,4.0137844086,3.8256187439,0.18816566467
BATT_MODEL_RAW:,87,860.10310216,4.0122375488,3.824131012,0.18810653687
BATT_MODEL_RAW:,88,870.10353326,4.0107707977,3.8224773407,0.18829345703
BATT_MODEL_RAW:,89,880.1042103,4.0092277527,3.8204059601,0.1888217926
BATT_MODEL_RAW:,90,890.1049132,4.0075931549,3.8183097839,0.18928337097
BATT_MODEL_RAW:,91,900.10536854,4.0060634613,3.8167266846,0.18933677673
BATT_MODEL_RAW:,92,910.10577336,4.0045070648,3.8143558502,0.1901512146
BATT_MODEL_RAW:,93,920.10594378,4.0029888153,3.8127250671,0.19026374817
BATT_MODEL_RAW:,94,930.10671694,4.0014419556,3.810968399,0.19047355652
BATT_MODEL_RAW:,95,940.10749688,3.9999008179,3.8080291748,0.19187164307
BATT_MODEL_RAW:,96,950.10857836,3.9983634949,3.807434082,0.19092941284
BATT_MODEL_RAW:,97,960.10967274,3.9968776703,3.8045711517,0.19230651855
BATT_MODEL_RAW:,98,970.109892,3.9952888489,3.8034439087,0.19184494019
BATT_MODEL_RAW:,99,980.1100553,3.9937648773,3.8020019531,0.19176292419
BATT_MODEL_RAW:,100,990.11088666,3.9922351837,3.8001651764,0.19207000732
BATT_MODEL_RAW:,101,1000.1117395,3.9907302856,3.7987918854,0.19193840027
BATT_MODEL_RAW:,102,1010.1124241,3.9891777039,3.7963638306,0.19281387329
BATT_MODEL_RAW:,103,1020.1135547,3.9877262115,3.7955436707,0.19218254089
BATT_MODEL_RAW:,104,1030.1141527,3.98620224,3.7940273285,0.1921749115
BATT_MODEL_RAW:,105,1040.1151561,3.9846115112,3.7928466797,0.19176483154
BATT_MODEL_RAW:,106,1050.11618,3.9830970764,3.7920207977,0.19107627869
BATT_MODEL_RAW:,107,1060.1167876,3.9815921783,3.7915115356,0.1900806427
BATT_MODEL_RAW:,108,1070.1170712,3.9800548553,3.7903270721,0.1897277832
BATT_MODEL_RAW:,109,1080.1175484,3.9785480499,3.7892799377,0.18926811218
BATT_MODEL_RAW:,110,1090.1185612,3.977142334,3.788766861,0.18837547302
BATT_MODEL_RAW:,111,1100.1190314,3.9755172729,3.7872276306,0.18828964233
BATT_MODEL_RAW:,112,1110.1193551,3.9740009308,3.7857551575,0.18824577332
BATT_MODEL_RAW:,113,1120.1199989,3.9725952148,3.7842998505,0.18829536438
BATT_MODEL_RAW:,114,1130.1205544,3.9710845947,3.7828826904,0.1882019043
BATT_MODEL_RAW:,115,1140.1208792,3.9694786072,3.7810077667,0.18847084045
BATT_MODEL_RAW:,116,1150.1211314,3.9679832458,3.779542923,0.18844032288
BATT_MODEL_RAW:,117,1160.1214676,3.9664745331,3.7780456543,0.18842887878
BATT_MODEL_RAW:,118,1170.1216419,3.9649734497,3.7767448425,0.18822860718
BATT_MODEL_RAW:,119,1180.1220134,3.963476181,3.7755413055,0.18793487549
BATT_MODEL_RAW:,120,1190.1231267,3.9619827271,3.7740383148,0.18794441223
BATT_MODEL_RAW:,121,1200.1237663,3.960483551,3.772310257,0.18817329407
BATT_MODEL_RAW:,122,1210.1247695,3.959066391,3.770740509,0.18832588196
BATT_MODEL_RAW:,123,1220.1250217,3.9575119019,3.7692432404,0.1882686615
BATT_MODEL_RAW:,124,1230.1260759,3.9560184479,3.7676353455,0.18838310242
BATT_MODEL_RAW:,125,1240.1265677,3.9545288086,3.7662220001,0.18830680847
BATT_MODEL_RAW:,126,1250.1267244,3.9530467987,3.7649974823,0.18804931641
BATT_MODEL_RAW:,127,1260.1270916,3.9515705109,3.7636451721,0.18792533875
BATT_MODEL_RAW:,128,1270.1272993,3.9501628876,3.7624759674,0.18768692017
BATT_MODEL_RAW:,129,1280.1278516,3.9485874176,3.7610664368,0.18752098083
BATT_MODEL_RAW:,130,1290.1287608,3.9471302032,3.7595767975,0.18755340576
BATT_MODEL_RAW:,131,1300.1290559,3.9457263947,3.7580509186,0.18767547607
BATT_MODEL_RAW:,132,1310.1295808,3.9442367554,3.7564506531,0.18778610229
BATT_MODEL_RAW:,133,1320.1300146,3.9427814484,3.754825592,0.18795585632
BATT_MODEL_RAW:,134,1330.1310061,3.9412136078,3.7533321381,0.18788146973
BATT_MODEL_RAW:,135,1340.1311909,3.9398365021,3.7520942688,0.18774223328
BATT_MODEL_RAW:,136,1350.1314688,3.9383583069,3.7507305145,0.18762779236
BATT_MODEL_RAW:,137,1360.1320154,3.9368152618,3.7491817474,0.1876335144
BATT_MODEL_RAW:,138,1370.1323078,3.9353561401,3.7475223541,0.18783378601
BATT_MODEL_RAW:,139,1380.1333796,3.9338798523,3.7460193634,0.18786048889
BATT_MODEL_RAW:,140,1390.134544,3.9324913025,3.7445220947,0.18796920776
BATT_MODEL_RAW:,141,1400.1350823,3.9309425354,3.742811203,0.1881313324
BATT_MODEL_RAW:,142,1410.1353242,3.9294834137,3.7411327362,0.18835067749
BATT_MODEL_RAW:,143,1420.1364242,3.9280185699,3.7390861511,0.18893241882
BATT_MODEL_RAW:,144,1430.1368941,3.926612854,3.7375202179,0.18909263611
BATT_MODEL_RAW:,145,1440.1374999,3.9250926971,3.7359104156,0.18918228149
BATT_MODEL_RAW:,146,1450.1385187,3.923658371,3.7350311279,0.18862724304
BATT_MODEL_RAW:,147,1460.1389116,3.9222011566,3.7339096069,0.18829154968
BATT_MODEL_RAW:,148,1470.1392986,3.9207458496,3.7322006226,0.18854522705
BATT_MODEL_RAW:,149,1480.1399008,3.9192848206,3.7303943634,0.18889045715
BATT_MODEL_RAW:,150,1490.140121,3.9178333282,3.7288284302,0.18900489807
BATT_MODEL_RAW:,151,1500.141015,3.91639328,3.7268924713,0.18950080872
BATT_MODEL_RAW:,152,1510.1420501,3.9149494171,3.7252426147,0.18970680237
BATT_MODEL_RAW:,153,1520.1424857,3.913520813,3.7238273621,0.18969345093
BATT_MODEL_RAW:,154,1530.1428878,3.9120788574,3.7223129272,0.18976593018
BATT_MODEL_RAW:,155,1540.1438171,3.9107017517,3.7207527161,0.18994903564
BATT_MODEL_RAW:,156,1550.144328,3.9091949463,3.7194442749,0.18975067139
BATT_MODEL_RAW:,157,1560.14454,3.9077682495,3.7179260254,0.18984222412
BATT_MODEL_RAW:,158,1570.1450214,3.9063777924,3.7167663574,0.18961143494
BATT_MODEL_RAW:,159,1580.1455874,3.9048843384,3.7153244019,0.18955993652
BATT_MODEL_RAW:,160,1590.1457759,3.903459549,3.713924408,0.18953514099
BATT_MODEL_RAW:,161,1600.1460267,3.9020442963,3.7127037048,0.18934059143
BATT_MODEL_RAW:,162,1610.1468302,3.9006137848,3.7115974426,0.18901634216
BATT_MODEL_RAW:,163,1620.1479299,3.8992595673,3.7103500366,0.18890953064
BATT_MODEL_RAW:,164,1630.1482598,3.8978424072,3.7091140747,0.18872833252
BATT_MODEL_RAW:,165,1640.1488333,3.8963336945,3.7073097229,0.18902397156
BATT_MODEL_RAW:,166,1650.1496371,3.894985199,3.7057723999,0.18921279907
BATT_MODEL_RAW:,167,1660.1508104,3.8935031891,3.7042236328,0.18927955627
BATT_MODEL_RAW:,168,1670.1512314,3.8920898438,3.70287323,0.18921661377
BATT_MODEL_RAW:,169,1680.1517068,3.8906669617,3.7014045715,0.18926239014
BATT_MODEL_RAW:,170,1690.1525194,3.889257431,3.6995849609,0.18967247009
BATT_MODEL_RAW:,171,1700.152946,3.8878517151,3.6978263855,0.19002532959
BATT_MODEL_RAW:,172,1710.1537267,3.8864307404,3.6959152222,0.19051551819
BATT_MODEL_RAW:,173,1720.1546401,3.8850917816,3.6940574646,0.19103431702
BATT_MODEL_RAW:,174,1730.1555115,3.8837089539,3.6920394897,0.19166946411
BATT_MODEL_RAW:,175,1740.1564768,3.8823013306,3.6903572083,0.19194412231
BATT_MODEL_RAW:,176,1750.1570428,3.8808994293,3.6886749268,0.19222450256
BATT_MODEL_RAW:,177,1760.1573468,3.87940979,3.6869010925,0.19250869751
BATT_MODEL_RAW:,178,1770.1577286,3.8780193329,3.6853637695,0.19265556335
BATT_MODEL_RAW:,179,1780.15886,3.876625061,3.6841316223,0.19249343872
BATT_MODEL_RAW:,180,1790.1591033,3.8752288818,3.6828079224,0.19242095947
BATT_MODEL_RAW:,181,1800.159741,3.8738327026,3.6818161011,0.19201660156
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BATT_MODEL_RAW:,381,3800.2925774,3.6509590149,3.4576034546,0.1933555603
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BATT_MODEL_RAW:,383,3820.2940702,3.6493339539,3.456413269,0.19292068481
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BATT_MODEL_RAW:,385,3840.2952435,3.647808075,3.4557991028,0.19200897217
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BATT_MODEL_RAW:,387,3860.2969595,3.6463012695,3.4549560547,0.19134521484
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BATT_MODEL_RAW:,389,3880.2979057,3.6448707581,3.4531898499,0.1916809082
BATT_MODEL_RAW:,390,3890.2985226,3.6440429688,3.4520835876,0.1919593811
BATT_MODEL_RAW:,391,3900.2991378,3.6433067322,3.4513931274,0.19191360474
BATT_MODEL_RAW:,392,3910.2997156,3.6425628662,3.4508743286,0.1916885376
BATT_MODEL_RAW:,393,3920.3006315,3.6418914795,3.4503707886,0.19152069092
BATT_MODEL_RAW:,394,3930.3013288,3.6410980225,3.4496879578,0.1914100647
BATT_MODEL_RAW:,395,3940.3015279,3.6403808594,3.4491043091,0.19127655029
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BATT_MODEL_RAW:,397,3960.3020032,3.6389198303,3.4477119446,0.19120788574
BATT_MODEL_RAW:,398,3970.3025804,3.6381988525,3.4470787048,0.19112014771
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BATT_MODEL_RAW:,401,4000.3039961,3.6361465454,3.4451980591,0.19094848633
BATT_MODEL_RAW:,402,4010.304243,3.6353569031,3.444393158,0.19096374512
BATT_MODEL_RAW:,403,4020.3044197,3.6346702576,3.4436836243,0.1909866333
BATT_MODEL_RAW:,404,4030.30484,3.6340332031,3.442905426,0.1911277771
BATT_MODEL_RAW:,405,4040.3060153,3.6332740784,3.4328422546,0.20043182373
BATT_MODEL_RAW:,406,4050.306549,3.6325874329,3.4349098206,0.1976776123
BATT_MODEL_RAW:,407,4060.3076581,3.6319007874,3.4351425171,0.19675827026
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BATT_MODEL_RAW:,409,4080.3082943,3.6305427551,3.4360046387,0.19453811646
BATT_MODEL_RAW:,410,4090.30933,3.6298713684,3.4359931946,0.19387817383
BATT_MODEL_RAW:,411,4100.3099591,3.6291923523,3.43516922,0.19402313232
BATT_MODEL_RAW:,412,4110.3109876,3.6285743713,3.435092926,0.19348144531
BATT_MODEL_RAW:,413,4120.3112645,3.6278495789,3.4346199036,0.19322967529
BATT_MODEL_RAW:,414,4130.3116564,3.6272621155,3.4340782166,0.19318389893
BATT_MODEL_RAW:,415,4140.3124607,3.6265182495,3.4335289001,0.19298934937
BATT_MODEL_RAW:,416,4150.3128079,3.6258544922,3.4330177307,0.19283676147
BATT_MODEL_RAW:,417,4160.3138703,3.6252212524,3.4326629639,0.19255828857
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BATT_MODEL_RAW:,419,4180.3151136,3.6239013672,3.4318504333,0.19205093384
BATT_MODEL_RAW:,420,4190.3156833,3.6232528687,3.4316711426,0.19158172607
BATT_MODEL_RAW:,421,4200.3168724,3.6225967407,3.4310760498,0.19152069092
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BATT_MODEL_RAW:,423,4220.3180377,3.6213607788,3.4298477173,0.19151306152
BATT_MODEL_RAW:,424,4230.3187767,3.6206817627,3.4291419983,0.1915397644
BATT_MODEL_RAW:,425,4240.3195742,3.6200447083,3.4282264709,0.1918182373
BATT_MODEL_RAW:,426,4250.3205228,3.6194038391,3.4277229309,0.1916809082
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BATT_MODEL_RAW:,428,4270.3210309,3.618221283,3.4265556335,0.19166564941
BATT_MODEL_RAW:,429,4280.3216851,3.6175270081,3.4256019592,0.19192504883
BATT_MODEL_RAW:,430,4290.322005,3.6168899536,3.4247665405,0.19212341309
BATT_MODEL_RAW:,431,4300.3228822,3.616268158,3.4243850708,0.19188308716
BATT_MODEL_RAW:,432,4310.3230709,3.6156425476,3.424030304,0.19161224365
BATT_MODEL_RAW:,433,4320.3236277,3.6150360107,3.4234733582,0.19156265259
BATT_MODEL_RAW:,434,4330.324128,3.6144065857,3.4228401184,0.19156646729
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BATT_MODEL_RAW:,438,4370.3268641,3.6119842529,3.4203414917,0.19164276123
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BATT_MODEL_RAW:,440,4390.3275646,3.6108779907,3.4193954468,0.19148254395
BATT_MODEL_RAW:,441,4400.3278167,3.6101837158,3.4187393188,0.19144439697
BATT_MODEL_RAW:,442,4410.3280298,3.6095962524,3.4183425903,0.19125366211
BATT_MODEL_RAW:,443,4420.3291916,3.6090774536,3.4178619385,0.19121551514
BATT_MODEL_RAW:,444,4430.3295194,3.6084976196,3.417049408,0.19144821167
BATT_MODEL_RAW:,445,4440.3298115,3.6078147888,3.4163665771,0.19144821167
BATT_MODEL_RAW:,446,4450.3300075,3.6072463989,3.415561676,0.1916847229
BATT_MODEL_RAW:,447,4460.3305703,3.6066932678,3.414855957,0.19183731079
BATT_MODEL_RAW:,448,4470.3314322,3.6061553955,3.4144706726,0.1916847229
BATT_MODEL_RAW:,449,4480.3326268,3.6054916382,3.4137382507,0.19175338745
BATT_MODEL_RAW:,450,4490.3336232,3.6049118042,3.4132804871,0.19163131714
BATT_MODEL_RAW:,451,4500.3347471,3.6043243408,3.4127998352,0.19152450562
BATT_MODEL_RAW:,452,4510.3358831,3.6037483215,3.4124488831,0.19129943848
BATT_MODEL_RAW:,453,4520.336818,3.6032371521,3.4123916626,0.1908454895
BATT_MODEL_RAW:,454,4530.3372652,3.6026000977,3.4122009277,0.19039916992
BATT_MODEL_RAW:,455,4540.3384872,3.6020545959,3.4118156433,0.19023895264
BATT_MODEL_RAW:,456,4550.3387597,3.6015510559,3.4114608765,0.19009017944
BATT_MODEL_RAW:,457,4560.3394534,3.6009063721,3.4109649658,0.18994140625
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BATT_MODEL_RAW:,459,4580.3407965,3.5998573303,3.4102478027,0.18960952759
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BATT_MODEL_RAW:,465,4640.3444751,3.596446991,3.4055938721,0.1908531189
BATT_MODEL_RAW:,466,4650.3454159,3.5958747864,3.4044494629,0.19142532349
BATT_MODEL_RAW:,467,4660.3459147,3.59532547,3.4043045044,0.19102096558
BATT_MODEL_RAW:,468,4670.346854,3.5947685242,3.4036865234,0.19108200073
BATT_MODEL_RAW:,469,4680.3476577,3.5942153931,3.4026603699,0.19155502319
BATT_MODEL_RAW:,470,4690.3483124,3.5936813354,3.4015426636,0.19213867188
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BATT_MODEL_RAW:,476,4750.351375,3.5903930664,3.3984565735,0.19193649292
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BATT_MODEL_RAW:,478,4770.3523168,3.5893096924,3.3981323242,0.19117736816
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BATT_MODEL_RAW:,480,4790.35387,3.5882301331,3.3962783813,0.19195175171
BATT_MODEL_RAW:,481,4800.3543432,3.5876922607,3.3955001831,0.19219207764
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BATT_MODEL_RAW:,484,4830.3562724,3.5861587524,3.3941116333,0.19204711914
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BATT_MODEL_RAW:,486,4850.3572526,3.5850830078,3.393321991,0.19176101685
BATT_MODEL_RAW:,487,4860.3581682,3.5845031738,3.3924713135,0.19203186035
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BATT_MODEL_RAW:,490,4890.3603815,3.582901001,3.3913497925,0.1915512085
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BATT_MODEL_RAW:,497,4960.3661908,3.5792236328,3.388343811,0.19087982178
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BATT_MODEL_RAW:,499,4980.3671698,3.5781555176,3.3873023987,0.1908531189
BATT_MODEL_RAW:,500,4990.3681843,3.5776252747,3.3868522644,0.19077301025
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BATT_MODEL_RAW:,505,5040.371573,3.575012207,3.3837203979,0.19129180908
BATT_MODEL_RAW:,506,5050.3717749,3.5745048523,3.3811759949,0.19332885742
BATT_MODEL_RAW:,507,5060.3725699,3.5739974976,3.3807067871,0.19329071045
BATT_MODEL_RAW:,508,5070.3734059,3.5734596252,3.3810462952,0.19241333008
BATT_MODEL_RAW:,509,5080.3737351,3.5729522705,3.3796653748,0.19328689575
BATT_MODEL_RAW:,510,5090.3744849,3.5724258423,3.3795013428,0.19292449951
BATT_MODEL_RAW:,511,5100.3752711,3.5719070435,3.3792114258,0.19269561768
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BATT_MODEL_RAW:,583,5820.4207908,3.5340461731,3.3466720581,0.18737411499
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BATT_MODEL_RAW:,622,6210.4447966,3.5094223022,3.3193206787,0.19010162354
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BATT_MODEL_RAW:,626,6250.4471447,3.5064277649,3.3135871887,0.19284057617
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BATT_MODEL_RAW:,772,7710.5420372,3.2059288025,3.0196228027,0.18630599976
BATT_MODEL_RAW:,773,7720.5430585,3.1948776245,3.0089645386,0.18591308594
BATT_MODEL_RAW:,774,7730.5438031,3.1831436157,2.9977035522,0.18544006348
BATT_MODEL_RAW.capacity:,2.1473732786

BATT_MODEL:,Index,Timestamp,Voc,Vload,ESR
BATT_MODEL:,1,7730.5023325,3.1831436157,2.9977035522,0.18544006348
BATT_MODEL:,2,7650.495255,3.2640686035,3.0777359009,0.18633270264
BATT_MODEL:,3,7580.4898867,3.3156814575,3.1293029785,0.186378479
BATT_MODEL:,4,7500.4859911,3.3556747437,3.168964386,0.18671035767
BATT_MODEL:,5,7420.4815796,3.3795433044,3.1920204163,0.18752288818
BATT_MODEL:,6,7340.4759533,3.3953514099,3.2080841064,0.18726730347
BATT_MODEL:,7,7270.4713352,3.4065589905,3.2191123962,0.18744659424
BATT_MODEL:,8,7190.4651542,3.4179229736,3.2299537659,0.18796920776
BATT_MODEL:,9,7110.4612688,3.4282264709,3.2397880554,0.18843841553
BATT_MODEL:,10,7030.4556075,3.4377288818,3.2505226135,0.18720626831
BATT_MODEL:,11,6960.4512398,3.4454574585,3.2569503784,0.18850708008
BATT_MODEL:,12,6880.4468641,3.4537086487,3.2635650635,0.19014358521
BATT_MODEL:,13,6800.4401214,3.4610519409,3.2710151672,0.19003677368
BATT_MODEL:,14,6730.4360847,3.4669036865,3.278263092,0.18864059448
BATT_MODEL:,15,6650.4301758,3.4731407166,3.2839775085,0.18916320801
BATT_MODEL:,16,6570.4258032,3.4794311523,3.2892456055,0.19018554688
BATT_MODEL:,17,6490.4207883,3.4861869812,3.2934684753,0.19271850586
BATT_MODEL:,18,6420.4174656,3.4923362732,3.3005371094,0.19179916382
BATT_MODEL:,19,6340.4116047,3.4992790222,3.30701828,0.19226074219
BATT_MODEL:,20,6260.4061137,3.5057220459,3.3118629456,0.19385910034
BATT_MODEL:,21,6180.4008271,3.5116157532,3.3215065002,0.19010925293
BATT_MODEL:,22,6110.3969702,3.5164337158,3.3266448975,0.18978881836
BATT_MODEL:,23,6030.3917126,3.5216331482,3.3346061707,0.18702697754
BATT_MODEL:,24,5950.3868213,3.5265579224,3.3391189575,0.18743896484
BATT_MODEL:,25,5870.3820229,3.5312385559,3.3445205688,0.18671798706
BATT_MODEL:,26,5800.3778782,3.5351867676,3.3478469849,0.18733978271
BATT_MODEL:,27,5720.3726829,3.5395812988,3.3520011902,0.18758010864
BATT_MODEL:,28,5640.3685612,3.5438766479,3.3568725586,0.18700408936
BATT_MODEL:,29,5570.3644598,3.5475883484,3.3607673645,0.18682098389
BATT_MODEL:,30,5490.3581199,3.5517692566,3.3647460938,0.18702316284
BATT_MODEL:,31,5410.3526477,3.5559272766,3.3682365417,0.18769073486
BATT_MODEL:,32,5330.3490065,3.5600547791,3.3718261719,0.18822860718
BATT_MODEL:,33,5260.3454953,3.5636558533,3.3746986389,0.18895721436
BATT_MODEL:,34,5180.3399209,3.5677833557,3.3775138855,0.19026947021
BATT_MODEL:,35,5100.3338004,3.5719070435,3.3792114258,0.19269561768
BATT_MODEL:,36,5020.3284673,3.5760612488,3.3851165771,0.19094467163
BATT_MODEL:,37,4950.3238036,3.5797309875,3.3886566162,0.19107437134
BATT_MODEL:,38,4870.3171038,3.5839576721,3.3920021057,0.19195556641
BATT_MODEL:,39,4790.3123993,3.5882301331,3.3962783813,0.19195175171
BATT_MODEL:,40,4720.3081082,3.5920219421,3.4002037048,0.1918182373
BATT_MODEL:,41,4640.3030044,3.596446991,3.4055938721,0.1908531189
BATT_MODEL:,42,4560.2979827,3.6009063721,3.4109649658,0.18994140625
BATT_MODEL:,43,4480.2911561,3.6054916382,3.4137382507,0.19175338745
BATT_MODEL:,44,4410.2865592,3.6095962524,3.4183425903,0.19125366211
BATT_MODEL:,45,4330.2826574,3.6144065857,3.4228401184,0.19156646729
BATT_MODEL:,46,4250.2790521,3.6194038391,3.4277229309,0.1916809082
BATT_MODEL:,47,4170.2734041,3.624622345,3.4321784973,0.19244384766
BATT_MODEL:,48,4100.2684884,3.6291923523,3.43516922,0.19402313232
BATT_MODEL:,49,4020.262949,3.6346702576,3.4436836243,0.1909866333
BATT_MODEL:,50,3940.2600573,3.6403808594,3.4491043091,0.19127655029
BATT_MODEL:,51,3870.255967,3.645614624,3.4542388916,0.19137573242
BATT_MODEL:,52,3790.2505537,3.6516342163,3.4583282471,0.19330596924
BATT_MODEL:,53,3710.2434579,3.6579742432,3.4643211365,0.19365310669
BATT_MODEL:,54,3630.2397692,3.6645507813,3.470085144,0.19446563721
BATT_MODEL:,55,3560.2343206,3.6704673767,3.4765357971,0.19393157959
BATT_MODEL:,56,3480.2293462,3.6774291992,3.4845237732,0.19290542603
BATT_MODEL:,57,3400.2235117,3.6846618652,3.4928741455,0.19178771973
BATT_MODEL:,58,3320.2170971,3.6920700073,3.5010566711,0.19101333618
BATT_MODEL:,59,3250.2126723,3.6987800598,3.5081672668,0.19061279297
BATT_MODEL:,60,3170.2072283,3.7066574097,3.5154685974,0.19118881226
BATT_MODEL:,61,3090.203365,3.7147750854,3.522983551,0.19179153442
BATT_MODEL:,62,3010.1978829,3.7231254578,3.5304489136,0.19267654419
BATT_MODEL:,63,2940.1925807,3.7306194305,3.5372200012,0.19339942932
BATT_MODEL:,64,2860.1871489,3.7393894196,3.5455665588,0.19382286072
BATT_MODEL:,65,2780.1818723,3.7484016418,3.5550079346,0.19339370728
BATT_MODEL:,66,2710.1772936,3.756526947,3.5627861023,0.19374084473
BATT_MODEL:,67,2630.1715575,3.7659835815,3.5727539063,0.19322967529
BATT_MODEL:,68,2550.1663929,3.7755336761,3.5819396973,0.19359397888
BATT_MODEL:,69,2470.1620716,3.7853775024,3.5906791687,0.19469833374
BATT_MODEL:,70,2400.1568358,3.7941417694,3.5993118286,0.1948299408
BATT_MODEL:,71,2320.1529477,3.8042888641,3.6109542847,0.19333457947
BATT_MODEL:,72,2240.1471752,3.8145847321,3.6215705872,0.1930141449
BATT_MODEL:,73,2160.1415736,3.8250637054,3.6324691772,0.1925945282
BATT_MODEL:,74,2090.1371947,3.8343429565,3.6415977478,0.19274520874
BATT_MODEL:,75,2010.1312419,3.8450679779,3.6519050598,0.19316291809
BATT_MODEL:,76,1930.1249658,3.8559169769,3.6642227173,0.19169425964
BATT_MODEL:,77,1860.1215998,3.865530014,3.6738624573,0.19166755676
BATT_MODEL:,78,1780.1173893,3.876625061,3.6841316223,0.19249343872
BATT_MODEL:,79,1700.1114753,3.8878517151,3.6978263855,0.19002532959
BATT_MODEL:,80,1620.1064592,3.8992595673,3.7103500366,0.18890953064
BATT_MODEL:,81,1550.1028573,3.9091949463,3.7194442749,0.18975067139
BATT_MODEL:,82,1470.097828,3.9207458496,3.7322006226,0.18854522705
BATT_MODEL:,83,1390.0930733,3.9324913025,3.7445220947,0.18796920776
BATT_MODEL:,84,1310.0881101,3.9442367554,3.7564506531,0.18778610229
BATT_MODEL:,85,1240.085097,3.9545288086,3.7662220001,0.18830680847
BATT_MODEL:,86,1160.079997,3.9664745331,3.7780456543,0.18842887878
BATT_MODEL:,87,1080.0760778,3.9785480499,3.7892799377,0.18926811218
BATT_MODEL:,88,1000.0702689,3.9907302856,3.7987918854,0.19193840027
BATT_MODEL:,89,930.06524628,4.0014419556,3.810968399,0.19047355652
BATT_MODEL:,90,850.06038216,4.0137844086,3.8256187439,0.18816566467
BATT_MODEL:,91,770.0545804,4.0262413025,3.8378829956,0.18835830688
BATT_MODEL:,92,700.05210628,4.0372390747,3.8506469727,0.18659210205
BATT_MODEL:,93,620.04607256,4.0499191284,3.8636035919,0.1863155365
BATT_MODEL:,94,540.04115066,4.0627784729,3.8778133392,0.18496513367
BATT_MODEL:,95,460.03466876,4.0756912231,3.8884849548,0.18720626831
BATT_MODEL:,96,390.02843914,4.087266922,3.8982963562,0.1889705658
BATT_MODEL:,97,310.02171272,4.1007957458,3.9093151093,0.1914806366
BATT_MODEL:,98,230.01602688,4.1148509979,3.9226436615,0.19220733643
BATT_MODEL:,99,150.01011568,4.1300601959,3.936498642,0.19356155396
BATT_MODEL:,100,80.00569268,4.1461925507,3.9474830627,0.19870948792
BATT_MODEL:,101,0,4.1869735718,3.9285964966,0.2583770752
BATT_MODEL.capacity:,2.1474

I wrote a short Python program (Battery.py) to process and plot the data:

The plot shows that the battery ESR stayed relatively constant at around 200 mΩ while the battery voltage dropped in a very predictable way as the battery lost charge. Besides being able to simulate a battery, the generated data can be used to compare batteries of different brands to evaluate which is better or also to evaluate how much a battery has degraded from its usage. Higher capacity and lower ESR make the battery better, but the ESR may not always be relevant. At high currents the ESR can cause a major waste of energy, but at very low currents it may have almost no negative effect, and other characteristics such as the self-discharge rate may become more relevant when deciding what type of battery to use.