Forschungsgruppe Kfz-Elektronik, Ruhr-Universität Bochum, Universitätsstr. 150, Bochum

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1 Impedance spectroscopy on lthum on cells or automotve applcatons wth optmzed measurement duraton and requency resoluton Peter Haußmann 1, Joachm Melbert 1 1 Forschungsgruppe Kz-Elektronk, Ruhr-Unverstät Bochum, Unverstätsstr. 150, Bochum peter.haussmann@est.rub.de Abstract A new mpedance spectroscopy measurement procedure or automotve battery cells s presented, whch s based on waveorm shapng. The method s optmzed towards short measurement duraton, hgh ectaton energy and ncreased requency resoluton and overcomes the lmtatons o establshed methods. For a gven spectral ampltude prole, the correspondng tme doman waveorm s derved rom the nverse dscrete Fourer transorm. Applyng an dentcal ntal phase angle or each requency component, the resultng sgnal ehbts a hgh peak-to-peak ampltude at relatvely low total ectaton energy. Ths lmts the mamum allowed energy or lnear ectaton. Alterng the phase angles randomly spreads the ectaton energy across the complete measurement duraton. Thereby, lnearty s preserved at hgher ectaton energy. By ncludng wndow unctons n the synthess concept, spectral leakage s reduced wthout changng the spectral sgnal ampltude n the requency range o nterest. A tme doman waveorm optmzed or mpedance spectroscopy on lthum on cells s syntheszed based on the proposed approach and evaluated on real automotve cells. The resultng mpedance data show good concordance wth establshed standard measurement procedures at sgncantly reduced measurement duraton and charge throughput. Addtonally, ncreased requency resoluton s acheved, enhancng the level o detal o the obtaned mpedance data. The method s used or mproved localzaton o agng eects n the cells, wthout urther stress o the cells by the measurement procedure. Keywords: electrochemcal mpedance spectroscopy, broadband ectaton, waveorm shapng, sgnal synthess, wndowed ectaton Introducton Lthum on cells or the use n electrc vehcles are subject to ongong research, ag to reach hgher energy denstes and longer letmes whle mantanng sae operaton. To reach these goals, cell chemstry s steadly optmzed. To evaluate the perormance o a cell technology, benchmark and cycle le studes are conducted. These studes rely on precse and reproducable characterzaton lke ts nternal resstance and capactance, whch are strongly nluenced by the materal composton o the cell. Thereore, analyzng the agng behavour o varous materals seperately and ts localzaton n the cell s mandatory. Electrochemcal mpedance spectrosopy (EIS) s an establshed method n the characterzaton o electrochemcal systems. By analyzng measurement data o current and voltage o a lthum on cell, the requency dependent comple mpedance Z j can be calculated. The applcaton o EIS on lthum on cells or automotve energy storage s a challengng task. Compared to other electrochemcal systems, the nternal mpedance o standard automotve lthum on cell s usually n the m range, requrng hgh current ampltudes. The most establshed approach s based on snusodal ectaton wth a gven ampltude, whch ensures quas lnear response. The mpedance s measured at a dscrete number o requences, one at a tme. Ths method s robust aganst nluences o nose, as the spectral ectaton power s concentrated on a sngle requency. However, especally or low requences n the mhz range, long measurement duratons are requred. In mpedance measurements, a dense requency resoluton s desrable. For the sngle requency approach, a large number o requences has to be chosen. Snce several perods at each requency need to be analyzed sequentally, the complete measurement procedure s very tme-consug, especally at low requences. At measurement duraton o several hours, tme-nvarance o the DUT cannot be guaranteed [1], [2]. 18. GMA/ITG-Fachtagung Sensoren und Messsysteme

2 An alternatve apporach optmzed towards short measurement duraton s based on pulse ectaton. Opposed to the stepped-sne approach, multple requences are covered smultaneously. The requency doman characterstc results rom the tme doman pulse shape. Although rectangularly shaped pulses can be syntheszed on almost any test equpment, ther spectra are less useul due to the non unorm power densty. Usng sophstcated test equpment capable o arbtrary waveorm generaton, spectrally optmzed pulse shapes lke snc ( sn()/ ) pulses are avourable [2]. By employng synthetc ectaton sgnals based on dened spectral ampltude proles, urther optmzaton o the waveorm s possble [3]. However, ectaton energy s concentrated around the man pulse slopes. Consderng the long measurement duraton requred or the analyss o low requency EIS, sgnal energy s stll lmted by the boundary condton or lnear ectaton. Broadband ectaton based on band lmted nose sgnals avods temporal energy concentraton. However, spectral ampltude s randomly dstrbuted across the observed requency range. Thereore, sutable ectaton s not guaranteed or all requences o nterest [4]. In ths work, a novel ectaton sgnal generaton method s presented, ag to combne the advantageous spectral ampltude propertes o pulse sgnals wth wde-spread tme doman characterstcs typcal o nose sgnals. Ths s acheved usng a waveorm shapng approach based on the nverse dscrete oruer transorm (IDFT) n the dgtal sgnal synthess [5], supplemented by the nherent use o wndow unctons. Fundamentals The mpedance o any electrochemcal system can be dened as the voltage response ollowng a current ectaton: v j j Z e j Z j (1) Impedance measurements on a devce-undertest (DUT) are perormed by applyng an ectaton sgnal and measurng the system response. In theory, current and voltage ectaton can be appled equvalently. In the case o low nternal mpedance n the m range and capactve behavor, voltage ectaton s not easble. Ths s the case or contemporary automotve lthum on cells. For that reason, current controlled ectaton s preerred. For the nterpretaton o EIS results, the measured mpedance s tted to an electrochemcally motvated equvalent crcut. Ths allows a lnk between the measured electrcal characterstcs and the underlyng electrochemcal processes nsde the cell. The eects observable n automotve lthum on cells can roughly be separated accordng to ther characterstc requency range. In the khz regon, nductve behavor resultng rom the geometry can typcally be dented. The Hz range s doated by double layer capactance eects at the sold electrolyte nterphase (SEI) ormed between electrodes and electrolyte. In comparson, lthum on duson processes through the electrolyte are slower by another order o magntude, deterng the mpedance n the mhz range [6]. In Fg. 1, a typcal mpedance spectrum o a lthum on cell s depcted n the Nyqust representaton, descrbng the relaton o the real and magnary part o the mpedance. Fg. 1 Nyqust plot o lthum on cell mpedance rom 10 mhz (top rgh to 1 khz (bottom le. Note the nverse magnary as chosen or the convenence. For robust model ttng, good mpedance data qualty and ntegrty s requred. Data qualty reers to requency resoluton and the sgnalto-nose rato, whch s lmted by the ectaton sgnal ampltude. Furthermore, the model ttng approach mplctly requres that the underlyng system has to be lnear, tme-nvarant and statonary. These condtons are not necessarly satsed by a lthum on cell. Typcal volatons are nonlnear behavor due to eceedng an adequate value o the ectaton ampltude, or tme varance due to temperature or state-o-charge changes durng the measurement. I one or more o these eects occur, the measurement 18. GMA/ITG-Fachtagung Sensoren und Messsysteme

3 data are unsutable or equvalent crcut ttng. Thereore, vercaton o the EIS results ntegrty s requred. The Kramers-Krong relatons descrbe the nterdependency o the real and magnary part o causal LTI-system (lnear tme nvaran transer unctons n system theory. A Kramers- Krong complance test method applcable to EIS results s presented n [7]. The algorthm s employed to valdate the measurement results n ths work. As the mpedance s dened n the requency doman, spectra calculaton usually nvolves a tme-requency doman transorm lke the dscrete Fourer transorm (DFT). For an nput tme doman sgnal consstng o k samples at the samplng requency S, the mum requency consdered by the DFT equals the recprocal value o the total samplng duraton. 1 S (2) k Tmeas Accordng to the well-known Nyqust theorem, the upper requency bound s calculated as: S ma (3) 2 mpedance at requency, the ollowng constrants have to be met: S 2 (4) 1 Tmeas (5) The requred values or the samplng requency derved rom Eq. (4) are not an ssue n state o the art measurement systems, consderng the typcal requency range o nterest. However, n the mhz range, the constrant n Eq. (5) regardng T meas mght lead to etremely long measurement duratons. 1 In theory, Tmeas s the mum requency analyzed by the DFT. However, sgnal components ehbtng a requency o lower than contrbute to the low requency range as undesred artacts o the DFT spectrum due to spectral leakage. To avod measurement errors n practcal scenaros, the number o perods n analyzed per requency s usually chosen as a multple o the mamum perod length o nterest, resultng n even longer measurement duratons. In typcal measurement scenaros, n 3 s an adequate choce. Standard mpedance spectroscopy measurement procedures A undamental requrement or any EIS method s an adequate ectaton o the DUT n the requency range o nterest. In most conventonal approach, the DUT s stmulated at only one requency at a tme usng snusodal ectaton sgnals. In lterature, ths procedure s reerred to as stepped-sne EIS. The entre ectaton energy s concentrated on a sngle requency, resultng n a convenent sgnal to nose rato. The complete measurement duraton can be calculated usng the ollowng equaton, assug n perods o m derent requences: T Meas total,sn m 1 n, (6) In the mhz-range, sgnal perods last up to 15 utes. Dependng on the desred requency range and resoluton, typcal values o T Meas, total range rom several hours up to days. In cycle le studes, such long tme rames are not avalable or characterzaton. Furthermore, tme nvarance cannot be assumed durng long measurement duratons. In order to reduce measurement duraton whle preservng the same requency resoluton, broadband ectaton usng pulse waveorms can be appled. Opposed to snusodal sgnals, multple requency components are present n the ectaton sgnal [1]. The spectral densty characterstc detere the perormance o a pulse waveorm or EIS. For most commercal test equpment, only rectangular pulses are avalable, sutable or measurements wth low demand on duraton and charge throughput. Such ectaton waveorm provdes a non-unorm power densty across the requency range o nterest resultng whch results nto a poor sgnal to nose rato. Alternatve pulse orms lke snc pulses enable a homogenous broadband ectaton [2]. The sgnal synthess can be perormed n tme doman based on the equaton: sn( 2 snc (7) 2 t Equvalently, the tme doman waveorm o the snc pulse can be nterpreted as the result o the nverse Fourer transorm o a rectangular spectral ampltude prole [8]. For pulse sgnals coverng the complete requency range o nterest, the requred measurement duraton s calculated as a multple o the perod o the mum requency o nterest: 18. GMA/ITG-Fachtagung Sensoren und Messsysteme

4 T n Meas, total, pulse (8) However, the spectral ectaton energy s shared by all requency components o the stmulus sgnal, oerng a lmted sgnal-tonose rato wth respect to each requency component. Ths can be overcome by usng multple ectaton pulses coverng derent requency ranges. I every pulse covers a relatve bandwdth o one requency decade, the overall measurement duraton or a desred bandwdth o l decades results n: T n n 10 l Meas, total, pulse 1. 1 k 1 k 1 (9) A comparson between the equatons (6) and (9) shows a sgncant reducton o measurement duraton or the pulse EIS approach compared to stepped-sne procedures. Even or spectrally optmzed pulse shapes lke snc pulses, establshed tme doman waveorms ehbt a low average sgnal energy at a hgh transent peak-to-peak ampltude, lmtng the achevable qualty o the measured mpedance spectra due to lnearty constrants. s (11) ma 100 s (12) The measurement duraton s chosen to 4 T sg n order to avod errors due to low requency artacts. The samplng requency may be chosen wth respect to the s requency range o nterest. For the unambguous denton o requency doman sgnals, both ampltude normaton A and the ntal phase angle are requred. Intally, the phase angle s chosen to: 0 (13) The resultng waveorm depcted n Fg. 2 resembles a requency modulated snc pulse and shows hgh temporal concentraton o the hghest slopes, as epected n analogy to common pulse synthess approaches. Tme doman waveorms synthess or arbtrary spectral ampltude proles In ths paper, a waveorm shapng method s developed. The desgn low can be used to synthesze tme doman waveorms based on an arbtrary spectral ampltude prole X ( ). The tme doman waveorm ( s syntheszed by applyng the IDFT to the spectral ampltude prole X ( ). The requency samplng ponts o the prole are dependent on the total sgnal duraton T sg and the samplng requency s, n accordance wth the aorementoned propertes o the (I)DFT. For each requency component, the target ampltude A s dened. 1, ma A (10) 0, otherwse In the ollowng, the target requency doman ectaton prole dened n Eq. (10) s used. It ehbts a rectangular shape wth homogenous coverage rom up to ma. As noted n equatons (11) and (12), a relatve bandwdth o one requency decade s covered, ncludng a 10 % margn above. ma Fg. 2 top: normalzed requency doman ampltude prole or a relatve bandwdth o one requency decade. 18. GMA/ITG-Fachtagung Sensoren und Messsysteme

5 Bottom: tme doman sgnals wth dentcal spectral ampltude characterstcs wthout (black) and wth (blue) phase modcaton. In EIS measurements, only the relatve phase angle between voltage and current s relevant. Thereore, the absolute ntal phase angle o each ectaton requency component may be altered arbtrarly. In ths eample, an ndvdual random phase angle s chosen or every requency component: RANDOM 0: 2 (14) Ths leads to a broadened dstrbuton o the sgnal energy n the tme doman waveorm. The transent peak-to-peak ampltude s sgncantly reduced at dentcal requency doman characterstcs. The correspondng waveorm ( s depcted n Fg. 2. wndowng (ISW) combnes the spectral leakage reducton ntroduced by the wndow uncton wth the requency doman ampltude characterstcs o the target prole. Ths s acheved by scalng the requency doman sgnal X ( ) by a requency dependent actor ( ) beore applyng the IDFT and the wndow uncton: X ISW ( ) X ( ) ( ) Hwn ( ) (16) The requred scalng actor ( ) s detered usng an teratve numerc optmzaton. The resultng waveorm s reerred to as ( ). ISW t Spectral leakage reducton usng preectaton wndow unctons Due to the random phase sht o the requency components, the rst and last samples are generally not equal. Thereore, the tme doman sgnal ( s not perodcally repeatable. Ths results n ampltude and phase errors due to spectral leakage n the DFT. In order to reduce the mpact o ths eect, ( can be multpled by a wndow uncton, resultng n the post-synthess wndowed (PSW) sgnal ( : X PSW P SW hwn ( ) X ( ) Hwn ( ) (15) In ths work, a narrow band Gaussan wndow uncton s used. The low wndow bandwdth s represented by a relatvely broad tme doman shape, as desred to mantan a wdespread temporal energy dstrbuton [9]. Besdes the desred spectral leakage reducton, the use o a wndow uncton also nluences the spectral ampltude X ( ). P SW The sgnal energy ehbts derent temporal localzaton or every requency, dependng on the phase angle. Thereore, the waveorm PSW does not ehbt the desred characterstcs, as the wndow uncton reduces the spectral ampltude o each requency to a derent etent. The requency dependent attenuaton can be avoded by ntegratng the wndow uncton nto the sgnal synthess low. Intra-synthess Fg. 3 Tme doman waveorms wth (a) no wndow uncton, post-synthess wndow uncton (b) and ntrasynthess wndow uncton (c). In (d), the spectral ampltude o all waveorms s compared. 18. GMA/ITG-Fachtagung Sensoren und Messsysteme

6 In Fg. 3, the phase moded tme doman sgnals ( (no wndowng), PSW (post synthess wndowng) and (ntra synthess wndowng) are compared n tme and requency doman. All sgnals are normalzed to a spectral ampltude o 0 db across the desred requency range. Whle the tme doman sgnal shape o PSW and are smlar at rst sght, the requency-dependent attenuaton o X ( ) s conrmed n the requency P SW doman comparson. The mamum ampltude loss s greater than 6 db, whch reduces the achevable sgnal-to-nose rato n measurement scenaros. The etended ampltude rescalng durng the synthess o avods any ampltude loss caused by the wndow uncton. In Tab. 1, a short comparson o the tme doman sgnals dscussed n ths paper s gven. All sgnals are based on a one decade rectangular spectral ampltude prole. The most sutable waveorm or EIS measurements s, whch ncludes peak ampltude reducton usng phase modcaton and reduced spectral leakage due to the nherently appled wndow uncton. Compared to the unmoded sgnal (, the transent peak-topeak ampltude o s reduced by 60 % wthout alterng the sgnal energy n the requency range o nterest. In EIS measurements, the spectral ampltude o the can be ncreased to the same etend wthout volatng lnearty constrants. Thereore, s used as ectaton sgnal or the tme doman EIS measurements presented n ths work. Measurement results For the practcal evaluaton o the proposed measurement procedure, a precson lthum on sngle cell test unt developed by our research group was used [2]. It s equpped wth a 600 A wdeband lnear dscharge current snk along wth a measurement control unt, enablng accurate measurements wth errors below 0.1 %. Furthermore, arbtrary current proles are supported at samplng rates up to 10 khz. The DUT s a sngle 26 Ah automotve cell or the use n plug-n hybrd vehcles (PHEV). All measurements are conducted at 25 C ambent temperature and 50 % state o charge. In order to very the spectral characterstcs o the proposed waveorm, t s appled to the DUT as a current prole DUT( t ). Both the target waveorm and the measured sgnal are shown n tme and requency doman n Fg. 4. The synthess concept s vered by the close consstency o the target and measured sgnal both n tme and requency doman. Tab. 1 Comparson between the dscussed tme doman waveorms wth equal target spectral ampltude prole. + (postve), o (neutral), (-) negatve Sgnal PSW ISW Rel. bandwdth 1 decade Phase sht X X X Ampltude latness Spectral leakage o Peak-to-peak ampltude relatve to Fg. 4 Prole vercaton n tme (top) and requency doman (bottom). The measured sgnal (green) closely resembles the target prole across the entre target bandwdth (10 Hz to 100 Hz). 18. GMA/ITG-Fachtagung Sensoren und Messsysteme

7 To evaluate the sutablty o the proposed mpedance s measured n the requency range rom 10 mhz to 1 khz usng both the establshed stepped-sne approach (51 requency ponts n 30 utes) and the proposed measurement procedure based on n 5 derent tme scales at a total duraton o 8 utes. The Nyqust plots o the resultng mpedance spectra are depcted n Fg. 5. The results o both procedures show good concordance, ndcatng the sutablty o the proposed tme doman method. characterstcs, requency resoluton may be chosen arbtrarly wthn the aorementoned lmtatons o the DFT. Especally at low requences, the spectrum obtaned rom the optmzed waveorm s enrched by the ncreased requency resoluton. Fg. 5 mpedance measured usng stepped sne (blue) and optmzed waveorm (green) approaches. To evaluate the data qualty o the measured spectra, a Kramers-Krong complance test s perormed on the mpedance data obtaned usng both methods. In the test procedure, an a pror Kramers-Krong complant mpedance spectrum s calculated based on the real part o the measured spectrum. A devaton between the measured and the calculated magnary part ndcates a volaton o the Kramers-Krong constrants. The magnary part resdual dstrbuton or both mpedance spectra s depcted n Fg. 6. For both spectra, a homogeneous dstrbuton o the resdual can be seen. As no sgncant devaton can be recognzed, the Kramers- Krong complance o both spectra s conrmed. The observed resdual s caused by measurement nose. Due to the ncreased avalable ectaton energy n stepped-sne measurements, a lower resdual s acheved compared to measurements based on the proposed waveorm. Fg. 6 Lnear Kramers-Krong resdual or mpedance spectra measured usng stepped-sne (blue) and waveorm shapng (green) methods. In Tab. 2, a quanttatve comparson o both measurement procedures s gven. At sgncantly reduced measurement duraton and charge throughput, ectaton based on the proposed waveorm shapng approach yelds EIS results equvalent to spectra obtaned usng the standard stepped-sne EIS procedure. The slghtly ncreased resdual or the proposed method does not compromse especally when takng the aorementoned mprovements nto account. Tab. 2 Quanttatve comparson o steppedsne and optmzed tme doman EIS measurements on an automotve lthum on cell Measurement Stepped Sne ( ) Frequency range Frequency resoluton 10 ponts per decade 10 mhz - 1 khz ISW t 24 ponts per decade * (+ 140 %) 8 utes Total duraton 30 utes (- 73 %) Charge 0,27 Ah 2,41 Ah throughput (- 88 %) Mean KK 0,05 % 0,28 % resdual * Frequency resoluton s chosen arbtrarly 18. GMA/ITG-Fachtagung Sensoren und Messsysteme

8 Concluson A waveorm shapng method to generate broadband tme doman sgnals was developed and optmzed or hgh sgnal power at low peak-to-peak ampltudes. Compared to common pulse waveorms, a 60 % decrease n peak-to-peak ampltude s acheved at a relatve bandwdth o 1 decade. The overall sgnal ampltude can be ncreased to the same etent, stll enablng lnear ectaton o the DUT. The concept was vered n smulaton and measurement. EIS results based on the optmzed tme doman waveorm show good concordance wth reerence stepped sne EIS measurements, reducng measurement duraton by 73 % and charge throughput by 88 %. In comparson to equvalent pulse ectaton schemes, a hgher ectaton ampltude s acheved by deconcentratng sgnal energy n the tme doman. Spectral dstorton caused by spectral leakage can be avoded by applyng wndow unctons wthn the waveorm shapng low. To some etent, the proposed pulse shapes resemble typcal current proles measured n real automotve drvng scenaros. Despte the lmted spectral ampltude control n real measurement scenaros, passve on-board EIS mplementatons are possble, mprovng the state-o-charge and state-o-health estmaton algorthms n the net generaton o battery management systems [10]. pp , 1986; do: / (86) [5] P. Symons, Dgtal waveorm generaton. Cambrdge, U.K.: Cambrdge Unversty Press, [6] J. P. Schmdt, T. Chrobak, M. Ender, J. Illg, D. Klotz, and E. Ivers- LFePO4 as cathode materal usng Journal o Power Sources, vol. 196, no. 12, pp , 2011; do: /j.jpowsour [7] M. Schönleber and E. Ivers-Tée, e spectra by RC elements and mplcatons or mpedance Electrochemstry Communcatons, vol. 58, pp , 2015; do: /j.elecom [8] -requency mpedance IMEKO TC4 Internatonal Symposum on Noveltes n Electrcal Measurements and Instrumentatons, vol. 1 o 15th IMEKO TC4 Internatnal Symposum on Noveltes n Electrcal Measurements and Instrumentatons Proceedngs, pp [9] ndows or harmonc analyss wth the dscrete Fourer Proc. IEEE, vol. 66, no. 1, pp , 1978; do: /PROC [10] N. Lohmann, P. Haussmann, P. Wesskamp, Automotve Drvng Data or Electrochemcal Impedance Spectroscopy on Lthum-Ion SAE Int. J. Alt. Power, vol. 4, no. 2, 2015; do: / Reerences [1] D. Klotz, M. Schönleber, J. P. Schmdt, and E. Iverscalculaton o mpedance spectra out o tme Electrochmca Acta, vol. 56, no. 24, pp , 2011; do: /j.electacta [2] N. Lohmann, P. Weßkamp, P. Haußmann, J. mpedance spectroscopy or lthum-on cells: Test equpment and procedures or agng and ast characterzaton n tme and Journal o Power Sources, vol. 273, pp , 2015; do: /j.jpowsour [3] T. Guerrero Cervera, A. P. Vega-Leal, G. Adame García, and J. Brey Sánchez, [4] synthetc wde- Internatonal Journal o Hydrogen Energy, vol. 39, no. 8, pp , 2014; do: /j.jhydene pseudorandom nose appled to a Computers & Mathematcs wth Applcatons, vol. 12, no. 6, 18. GMA/ITG-Fachtagung Sensoren und Messsysteme