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Electrochemical impedance spectroscopy based estimation of the state of charge of lithium-ion batteries
G Model EST 135 No. of Pages 13
Journal of Energy Storage xxx (2016) xxx–xxx
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Electrochemical impedance spectroscopy based estimation of the state of charge of lithium-ion batteries U. Westerhoff* , T. Kroker, K. Kurbach, M. Kurrat TU Braunschweig, Institute for High Voltage and Electrical Power Systems elenia, Braunschweig, Germany
A R T I C L E I N F O
Article history: Received 6 October 2015 Received in revised form 6 September 2016 Accepted 6 September 2016 Available online xxx Keywords: Electrochemical impedance spectroscopy Lithium ion battery State of charge
A B S T R A C T
The increasing market demand for electric vehicles requires a continuous development and improvement of battery systems. A crucial aspect is the application of analytical methods to characterize the battery systems in the most exact way. At the same time these methods should remain as simple as possible. The current analysis procedures use essentially the battery system- and battery cellcharacteristic of the voltage curve in relaxation- and operation-time. These approaches alone are not conclusive enough due to the influences of relaxation time and varying load currents. In recent years, methods based on electrochemical impedance spectroscopy (EIS) have found application for accurate analysis of occurring electrochemical processes and diagnosis of lithium ion batteries. This publication aims to show how the state of charge can be predicted with the use of EIS and a simplified equivalent circuit for redundant supplementing the OCV-method (open circuit voltage) and the current- counting method. Therefore film batteries with a graphite anode and a Ni1/3 Mn1/3 Co1/3 cathode are charged and discharged according to a specified procedure. The battery is (dis)charged with steps of 10% followed by an EIS measurement. The measured data is used to determine the elements of the simplified equivalent circuit. These elements are analyzed for their different values at various states of charge. From these measurements can be concluded that EIS can be applied for the estimation of state of charge (in the middle range) as redundant method to other estimation methods. It therefore provides an additionally methods by which statements about the battery conditions can be made. ã 2016 Elsevier Ltd. All rights reserved.
1. Introduction Electrochemical impedance spectroscopy (EIS) has been implemented through several decades to analyze and understand electrochemical processes. This method also has found application in the battery diagnosis of Lead-acid batteries [1], nickel-cadmium batteries [2] and nickel-metal-hydrid batteries [3]. EIS has been applied for some years to decipher the electrochemical processes which take place in a lithium ion battery (LIB). An equivalent circuit model (ECM) can be developed from the EIS data and the knowledge of the chemical and physical processes. The measured data are presented regularly as NyquistPlots (NYP). The measured impedance is decomposed with the help of a phase angle in a real part (x axis) and an imaginary part (y axis) which are plotted against each other. The real part is
* Corresponding author. E-mail address: [email protected] (U. Westerhoff).
designated by Z’ and the imaginary part as Z” in the Nyquist representation. Fig. 1 shows a possible equivalent circuit, which is regularly employed [2]. Additionally to the ECM shown in Fig. 1 a wide array of other suggestions exist for the interpretation of the impedance spectra of LIBs [5–8]. In different publications, the graphite electrode was examined through EIS [9–15]. The cell chemistry has a strong effect on the curve of the impedance spectrum. In [4] impedance spectra were recorded of material combination of graphite anodes and various cathode materials. The differences in the impedance spectra can be clearly seen. Both RC-members of the ECM shown in Fig. 1 thus sum up the processes at the cathode and the anode. The origin of the measurable capacitances lies in the solid electrolyte interfaces (SEI), which are formed on the anode (especially by graphite) as well as on the cathode. Both SEI are dielectric and function as an isolator. The SEI on the MO2-electrode is much thinner, than that on the anode (graphite) and dominates therefore the impedance spectrum. Since both SEI layers have
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Please cite this article in press as: U. Westerhoff, et al., Electrochemical impedance spectroscopy based estimation of the state of charge of lithium-ion batteries, J. Energy Storage (2016), http://dx.doi.org/10.1016/j.est.2016.09.001
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R(Sol)
R(Film )
R(CT)*
C(Film)
C(DL)*
W(SSD)
C(IC)*
Fig. 1. Typical equivalent circuit to interpret measured spectra of impedance. It comprises a pre-resistance, two (partly up to four) RC members (film diffusion and double layer), a Warburg+ element (solid processes and diffusion) and an interphase element (intercalation). The “*” marks the circuit components that are highly dependent on potential.
similar dielectric constants, it is hard to separate them through EIS, which leads to a blurring of the impedance spectra of both electrodes. Excluded from the SEI formation is a cell structure with LTO (lithium titanate oxid) anodes because no SEI is formed on LTO anodes [33,34]. The resistance connected in parallel to the capacitances is based on the capability of the lithium ions to penetrate this layer, which can be described by a purely ohmic resistance. Through the specification of an equivalent circuit and different mathematical adaptation methods it is intended to predict different characteristics and conditions of a LIB. This includes particularly the state of charge (SOC) as well as the state of health (SOH) [5,6,16,17,32] and the internal cell temperature [18,19]. These state variables are very hard to predict due to the complex processes in a LIB. Other possibilities to predict the state of charge are: open-circuit voltage measurement [14,19], current-counting method [14,20,21], adaptive systems such as neural networks [14,22–24], Fuzzy-Logic [14] and Kalman filter [14,24–26,30] or hybrid-systems of any methods [14,24]. Additionally, the most methods are based on very complex mathematical models. The equivalent circuit presented in Fig. 1 is too complex to be developed into applications, for example, for battery diagnosis in electric vehicles, and then built into the trip computer of an electric car. Additionally, the analysis of solid diffusion (Warburg, second to last element) and of the intercalation process (ICP, last element) requires work with very low frequencies (50 mHz). The measurement time is therefore too long. This would cause measurement periods of time that are not applicable for the automobile sector. Further problems can arise at higher frequencies because the induction effects influences the abscissa zero crossing in the Nyquist plot. Whereas lower frequencies do not satisfy the requirements of a short measurement time and contains no
important information for SOC estimation. This work aims to show, that a much simpler equivalent circuit and a relatively small frequency band are sufficient to estimate the SOC of a LIB. Just for the practical implementation is the application of small memory footprint and short measurement time an important indicator for the advantageousness. However, a prerequisite is the permanent detecting of the temperature and the progressive aging because they have the biggest factors influencing the curve of the impedance spectrum, in addition to the SOC. Most of the ECMs investigated by other authors use complex equivalent circuits with Warburg impedances and constant-phase elements [2,13,17,18,27,31]. However, there are other sources which show that the simple thevenin equivalent circuit in Fig. 3 is already showing very good results [35–37]. In a review of different equivalent circuits for state of charge estimation has already been seen that a simple equivalent circuit gives good results. The model parameters are not determined on a measured impedance spectrum. They were identified with a Hybrid Pulse Power Characterization (HPPC) [15]. Another paper compares the equivalent circuit from this paper with an equivalent circuit with more RC elements. The results show that the thevenin equivalent circuit provides a similar good SOC estimation than the other models. The model parameters were determined with an adaptive gain sliding mode observers (AGSMO) for the SOC estimation [28]. In a recent publication there is a SOC-estimation with a dual neural network fusion battery model. For the linear neural network battery model based on the structure of thevenin battery model, the average error of SOC estimation is 1%. The average error is slightly less with more RC-elements. [22] Fig. 2 shows a typical NYP, which results from a measurement between 100 mHz and 100 kHz, for the batteries used herein. An approximately half-circular structure results through reduction of the frequency range from 1 Hz to 15,000 Hz. From this structure, a very simple equivalent circuit can be deducted. This circuit is shown in Fig. 3 and is from now on referred as R-RCECM. Three significant advantages arise through the specification of a simple R-RC-ECM and through the measurement in a relative small frequency range: 1 The measurement can be performed in far less time (=5 s), because frequencies smaller than 1 Hz are omitted. 2 In the case of bigger batteries and battery systems, the cables only produce minimal induction effects because the maximal frequency is capped at 15,000 Hz.
Fig. 2. Nyquist-Plot resulting from an impedance measurement between 100 mHz and 100 kHz of the batteries examined herein. The powers of ten are shown as red areas respectively. The potential E of the film battery shown herein is 3.68 V, which corresponds to a state of charge of 50%. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 3. Most simple equivalent circuit to describe the chemical processes of a lithium ion battery. In the Nyquist-Plost, a simple half-circle results with an additional purely ohmic resistance, that is, a half-circle displaced to the “right”.
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3 The SOC can be estimated with only three parameters: R0, RCt (abbreviated below as Rc) and Cdl (abbreviated below as C). This reduces the data volume considerably. These three significant advantages, the simple method is better than a model with higher complexity to use it as a redundant method to existing SOC estimation methods. 2. Experimental research 2.1. Film battery The experiments were performed on self-made film batteries (FB). The active areas, which are made of graphite (anode) and Ni1/3 Mn1/3 Co1/3 (cathode) are sealed in a composite film (Fig. 4). These are high-capacity electrodes with a thick active material layer. The current collectors are made of aluminum (cathode) and nickel (anode). The active area is square and has a lateral longitude of approximately 50 mm. The nominal capacity of the investigated LIBs is approx. 50 mAh. 2.2. Measurement procedure The impedance measurements (IM) were performed with a VersaSTAT 3 Potentiostat from the company Princeton Applied Research in a climate chamber from the company Vötsch Umwelttechnik with a constant temperature of 20 C 0.5 K. There were used a cell holder to minimize the influence of the contact resistance and the 4-wire sensing to eliminate the lead resistance. To guarantee constant measuring conditions and thus comparable data, the state of charge of 0% and 100% are defined as follows (see Table 2): The FB was charged to SOC 100% previous to the IM. To achieve this, the FB was first charged with a constant current step (CC) at 50 mA (1C), until 4.2 V were reached. Next, a constant voltage step (CV) was performed at 4.2 V, until a charging current of 1 mA was reached. After this procedure the FB was put to rest for 10 min. After a 10 min break, no electrochemical balance is established at a battery cell. Measurement studies have shown that the change in the impedance spectrum after 10 min have no serious effect on the SOC estimation as compared to 90 min. The deviation of the charge transfer resistance between RC,10min and RC,90min is less than 2.5%.
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Thus, the influence on the SOC estimation is less than 1%. It should be noted that an electrochemical balance state is only reached after some hours of rest. The result is an almost constant cell voltage through the IM. This state of charge of the FB (including the 10 min pause) was defined as SOC = 100% for all measurements (see Table 2). After reaching SOC 100%, the first IM was performed in a frequency range of 100 mHz to 100 kHz 10 measurement values were registered pro power of ten, wherein each value was measured thrice and averaged in the apparatus. Such a measurement takes about 15 min to complete (see Figs. 5 and 6). Next, the discharge procedure was performed in 10% SOC-steps. To achieve this, a discharge current of 50 mA was set and maintained for 6 min. This represents a discharge step of 5 mAh. The FB was subsequently put to rest again (see Table 2 or Figs. 5 and 6) and the aforementioned measurement was performed again. To preserve the FB, an interruption voltage of 3.0 V was set up, so that the last discharge step is >5 mAh. The SOC step between 0% and 10% was deducted from the measurement log through the integration of the current flow over time. SOC 0% was defined with a final CV step at 3.0 V, until a current of 1 mA was reached. A rest time of 10 min was also taken after this step to guarantee a constant voltage during the measurement. The IM was subsequently performed and defined as SOC 0% (see Table 2). 12 IM result from the discharge procedure. After reaching SOC 0% the charging procedure follows, which is also performed in 10% steps (360 s at 50 mA). An interruption voltage of 4.2 V was set up for the charging process. Due to this, an additional charging step (analogue to discharge) results between SOC 90% and 100%. The FB is charged to the SOC 100%, defined previously, through a last CV step at 4.2 V, until 1 mA is reached. A 10 min rest pause also took place and finally, the last IM was performed (SOC = 100%). 11 IM result from the charging procedure, with a total of 23 IM for the charge and discharge procedures. The complete measurement takes 12 h and is represented graphically in Fig. 5. The black line shows the course of the voltage, whereas the green line represents the intensity of the supplied current. Every voltage level represents a 10 min pause with subsequent IM (about 15 min) (see Fig. 5). The discharge step from SOC = 20% to 10% is presented again in detail in Fig. 6 to show the processes of every charge and discharge step more clearly. Between the measurement processes of the state of charge function, the cells were not cycled or exposed to stress due to high temperatures or pressure during storage. Thus the influences of the aging effects on the measured impedance spectra are negligible. 3. Results and discussion 3.1. General observations
Fig. 4. Self-made film battery in a cell holder and climate chamber Material: C/ NMC, Nominal capacity 50 mAh, Voltage range: 3.0–4.2 V.
The voltage of the charge and discharge steps after a 10 min rest phase in relation to SOC were presented as a way of example in Fig. 7. The voltages shown on Fig. 7 also represent the voltages, at which the IM were performed. The voltages of the IM during the charging procedure are shown as green circles; the blue squares represent the voltages of the IM during the discharge procedure. The IM of the sates of charge 10%, 30%, 50% and 90% (Discharge) are presented in a NYP in Fig. 8. It can be clearly seen from Fig. 8, that the IM result in a compressed half-circle at higher SOC (>50%). At SOC < 50%, a second half-circle becomes visible, which grows with sinking states of charge and becomes dominant at SOC < 10%. Through this measurement, it is possible to show, that the influence of the second RC component (Fig. 1, Table 1), namely the
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Fig. 5. Measurement log of a charge and discharge procedure. The black line represents the course of the voltage. In every voltage plateau a 10 min rest time and an impedance measurement (about 15 min) occur. The green line represents the course of the supplied current. Every current plateau is a 10% charge or discharge step (6 min). Such a measurement cycle comprises a discharge from 100% to 0% and a subsequent charging to 100%. A measurement procedure comprises 23 impedance measurements in total. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 6. Sectional close-up of the discharge procedure from SOC 20% to 10%, wherein the word “rest” represents the 10 min pause.
capacitance of the double layer CDL and the charge transfer resistance greatly increases at low SOC. 3.2. Numerical adjustments (NA) The numerical adjustment was performed with the program ZViewTM from Scribner Associates Inc. A R-RC-ECM was given (see Fig. 3) and fitted for the sum of the least error squares [29]. The measured frequency range was limited for the NA, for impedances measured from 1 Hz to 15,000 Hz (see Section 1). The impedances are decomposed in real and imaginary parts using the phase angle, and are presented in Fig. 9 as black circles in NYP. The graph presented in green is the numerical solution, which results from the specification of an R-RC-ECM.
At very low SOC, the second RC component (double layer) becomes dominant (see Fig. 8). The numerical fitting of the measurement values of SOC 10% is shown in Fig. 10 as a green graph. The error resulting from the numerical fitting should thus be greater at low SOC than at high SOC. The margins of error are listed as a way of example for SOC 0%, 10%, 50% and 90% in Table 3. 3.3. Discussion of the results At this point, the results of the measurements are to be presented and discussed. For this purpose, the frequency range was reduced to those data points, which result from frequencies between 1 and 15,000 Hz (see Chapter 1). Beginning with the RC
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Table 2 Summary of the charge, discharge and measurement procedure.
Fig. 7. SOC vs. Potential: Discharge is shown in blue; charge is shown in green.
Fig. 8. Comparison between four different impedance measurements during the discharge procedure. SOC: 10% (3.46 V), 30% (3.57 V), 50% (3.68 V) and 90% (4.04 V).
results from the ECM presented in Fig. 3, the results from the NA of a single measurement are presented first. The reproducibility of the measurements is discussed subsequently. 23 IM were performed for each FB according to the measurement procedure of 2.3 (Fig. 5, Fig. 6 and Table 2). 12 IM result from the discharge and 11 additional IM result from the charging. The last discharge value is SOC 0%. The capacity of the FB results from the sum of the current flow through time during the charge and
Procedure
Constant Current (CC)
Constant Voltage (CV)
SOC = 100% SOC = 0% 10% Steps Measurement steps at 0% Measurement steps at 100%
50 mA to 4.2 V 50 mA to 3.0 V 360 s + or 50 mA
4.2 V to 1 mA 3.0 V to 1 mA 3.0 V to 1 mA 4.2 V to 1 mA
discharge procedures. The calculated capacity of FB-1 is 50.7 mAh. Because these are hand-made test batteries, there are light discrepancies (see Table 4). The SOC was deducted based upon this and plotted against the determined values RC (Fig. 11), C (Fig. 13) and R0 (Fig. 15). The values determined in the charging process were shown in green in the next figures; the blue values represent the data determined for the discharge process. An exponential fitting was performed subsequently, which is shown as a red line in the following figures. The exponential fitting was selected at random and must be understood as an example for the relation between the SOC and the determined components. The mean value for the circuit components R0, RC and C of three FB was determined next and plotted against the SOC. Three graphs result from this: Fig. 12 for RC, Fig. 14 for C and Fig. 16 for R0. The values were also exponentially fitted in this case. 3.3.1. Determination and interpretation of RC RC comprises, with the fitting to a RC-component, the resistance, which the lithium ions experience upon passage through the SEI and the resistance, which occurs through friction of the solvated lithium ions and the double layers. RC in relation to SOC is shown in Fig. 11. A numerical value between 0.3 V and 0.9 V results for RC. Therein, the resistance of the double layer (second RC-component of Fig. 1) has a growing influence on the NA at low SOC ( < 20%). Due to the adjustment, the largest errors occur for the fitting of low SOC (see Table 3). The correlation coefficient of 0.98 shows, that the resistance can be adequately described by the given exponential graph. Since RC and C grow lightly from SOC 90% to 100%, RC and C reach their smallest values by SOC 90%. After the single measurement of FB-1, two additional FB were measured (Table 4) and the mean value for RC was determined. The RC values can be easily reproduced, as is shown with the help of Fig. 12. The standard deviations for different SOC are listed in Table 5. 3.3.2. Determination and interpretation of C Given the fact that the thickness of the SEI and the areas of the electrodes are constant throughout the measurement processes, the capacitance of the first RC component from Fig. 1 can also be
Table 1 Electrochemical origin of the electrical components from Fig. 1.Circuit element. Circuit element
Electrochemical origin
R(Sol) R(Film) C(Film) R(CT)* C(DL)* W(SSD) C(IC)*
Resistance of the lithium ions in electrolyte Resistance of the lithium ions in the SEI layer (film) Film capacitance Resistance of the lithium ions with penetration of the double layer (Charge Transfer Resistance) Capacitance of the double layer Diffusion of the lithium ions in the solid Capacitance of the intercalation
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Fig. 9. Nyquist-Plot representation of the measured impedances after separation in real and imaginary parts, and the corresponding fitting to a R-RC-circuit. Black ! Measured values; Green ! Fit.
Fig. 10. Numerical fitting (green graph) of the data points resulting from the measurement of SOC 10% (black graph). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
taken as constant. However, due to film capacitance and double layer capacitance being strongly coupled, different values result for C. The double layer capacitance dominates specially for low SOC. This is made clearer by Fig. 10. From Fig. 8 it can be deducted that,
for very low SOC, a second half-circle appears, which is not taken into account through the use of a R-RC-ECM; the NA is thereby heavily influenced, which leads to the generation of very high values for RC and C. R0 also grows rapidly, because this values is
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U. Westerhoff et al. / Journal of Energy Storage xxx (2016) xxx–xxx Table 3 Margins of error at SOC 0%, 10%, 50% and 90% during discharge. SOC [%]
R0 [V]
RC [V]
C [mF]
90 50 10 0
0.365 0.007 0.389 0.007 0.422 0.014 0.480 0.019
0.334 0.012 0.323 0.012 0.417 0.022 0.958 0.097
2.95 0.25 3.11 0.28 9.80 1.36 26.70 3.80
Table 4 Capacities of film batteries. Film battery
Capacity
FB-1 FB-2 FB-3 Mean value
50.7 mAh 49.8 mAh 51.4 mAh 50.6 0.9 mAh
displaced to the right by the NA at low SOC. The capacitances determined for FB-1 are plotted against the state of charge in Fig. 13 and were lastly subjected to exponential fitting (red line). In here, it can also be seen, that the greatest errors occur at low states of charge (analogue to the values for RC in Table 5). The numerical value for capacitance is 0.99, and shows that the collected data are well-matched to this course. It can also be observed, that the value for C reaches its minimum at a SOC of approximately 90%. The mean capacitances, which result from the values of FB-1 to FB-3 are plotted against the state of charge in Fig. 14. The standard deviations are exemplary listed for the states of charge 0%, 10%, 50% and 90% in Table 6 as a way of example. The correlation coefficient is 0.996 and shows that an exponential relation exists between the state of charge and the capacitance (Table 7).
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3.3.3. Determination and interpretation of R0 If the lithium ions move through the electrolytes, these experience a resistance. This resistance can be understood as friction of the ions and the electrolytes, and has a purely ohmic behavior. Generally this resistance is represented with the Rsol in Fig. 1. The resistance R0 (see Fig. 3) is not the same as the RSol, since R0 does not represent the value of the abscissa zero crossing. R0 is the abscissa zero crossing of the numerical fitting result and is not inhibited or fixed in the parameter variation. Only thus will generate the minimal square error between model and measurement results. Figs. 8 and 10 illustrate, that the ohmic resistance, which is experienced by the solvated lithium ions during diffusion through the electrolytes, is practically constant for all SOC. The resistance is approximately 0.38 V. Due to the focusing in the numerical fitting this is not true at R0. This assumption is based upon the fact, that the number of solvate molecules and the number of lithium ions in the electrolyte are approximately constant. The electrolyte resistance R0 is influenced rather by the temperature of the battery. Temperature was held constant throughout the measurements (20 C). Through the specification of a R-RC-circuit, the fitting program can only construct a half-circle, which has its origin on the x-axis (real resistance value). This origin results from the NA of the measured values, so that R0 is displaced to large values especially for low SOC. R0 has a value in the range of approximately 370 mV to 500 mV and is represented in relation to SOC in Fig. 15. For the NA of the R-RC-circuit the error of R0 assumes larger values also for low SOC. The correlation of the determined values is 0.988. In Fig. 16, the mean values of R0 are plotted against SOC. The low standard deviations of R0 show that the starting point for the resistance determination of RC can easily be reproduced. 3.4. Summary of determined data The results of each circuit component are to be observed more closely herein. Two of the three circuit components (RC and C) are
Fig. 11. RC in relation to the state of charge. Green represents charging and blue represents discharging. The red line is a randomly chosen exponential fit. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 12. Mean value of RC in relation to the state of charge. Green represents charging and blue represents discharging. The red line is a randomly chosen exponential fit. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 13. Capacitance in relation to the state of charge of FB-1. Green represents charging and blue represents discharging. The red line is a randomly chosen exponential fit. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
used for predicting the state of charge in a battery. R0 is strongly affected by errors (see Fig. 16). From Fig. 12 (Mean value for RC) and 14 (Mean value for C) result two critical sectors. For very low SOC ( < 20%) large errors occur from NA, which cause the estimation of the SOC through the circuit to be very inexact. If too high SOC are reached, the values for RC and C grow lightly (minimum occurs at about. 90%), which can lead to a wrong interpretation of the SOC. For practical applications, for example in electric vehicles, there is no aim for too low or too high
SOC which is positive for this method. This would certainly lead to accelerated aging of the LIB. These disadvantages can therefore be seen as non-critical. Additionally, the voltage graph is very steep for very high and very low SOC (see. Fig. 7), which means, that the voltage graph can be easily used as an interruption criterion for the charging or discharging. Through the determination of RC and C with impedance spectroscopy, the SOC in the middle can be defined very accurately. Figs. 17 and 18 are magnified sections of Fig. 12 and 14 respectively, and represent the graph of the
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Fig. 14. Mean value of C in relation to the state of charge. Green represents the charging and blue the discharging. The red line is a randomly chosen exponential fit. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 15. R0 in relation to the state of charge. Green represents charging and blue represents discharging. The red line is a randomly chosen exponential fit. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
respective circuit components in the SOC 20–80%. Looking only at the SOC-range of 20–80% the fit with an exponential function give better accuracy as the fit of the complete SOC-range. The operation of a LIB in extreme voltage situations, this is, near 100% or 0% SOC (in the range defined herein) is to be generally avoided, since it greatly accelerates the aging process. Specially in the automobile industry, where batteries with particularly long lives are required, the LIB are operated in the middle range of voltage. Figs. 17 and 18 illustrate, that the method provides reasonable results in the middle SOC range.
In Fig. 19, the maximum error between the adjusted real SOC and from the impedance data estimated SOC are applied. The mean value of the error is 2.7% and the maximum error is 4.8%. The approach to derive the SOC from the fitted parameters is shown schematically in Fig. 20. In this example is assumed that a value of 0.33 ohm for RC and 3.5 mF for C were determined from impedance spectra subsequent to a charging process. The intersections of the values RC and C with the envelope curve of the mean value are used to determine the SOC-range of each parameter. The estimated SOC is within the overlapping area of
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Fig. 16. Mean value of R0 in relation to the state of charge. Green represents the charging and blue the discharging. The red line is a randomly chosen exponential fit. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Table 5 Mean value errors of RC for three film batteries. SOC [%]
Mean Value RC [V]
Standard deviation [V]
90 50 10 0
0.318 0.343 0.524 0.929
0.025 0.018 0.014 0.036
Table 6 Standard deviations of the mean values of C for three film batteries. SOC [%]
Mean Value of C [mF]
Standard deviation [mF]
90 50 10 0
2.90 3.14 10.40 26.36
0.17 0.27 2.16 0.80
Table 7 Standard deviations of mean values of R0 for three film batteries. SOC [%]
Mean value R0 [V]
Standard deviation [V]
90 50 10 0
0.361 0.372 0.423 0.498
0.0082 0.0079 0.0197 0.0481
both SOC ranges and is calculated from the average of the limits of this area. In this example the estimated SOC is 48% whereas the real SOC is 49%. The maximum error provides information about the overlapping SOC range. 4. Conclusion In this paper impedance spectra of self-made film batteries (=50 mAh) were performed in a voltage range from 3.0 to 4.2 V by a
constant temperature of 20 C. The voltages represent a state of charge from 0%-100%. To achieve reproducible results, the framework conditions were exactly defined for all SOC and kept for every measurement. Lastly, the data were represented in a Nyquist-Plot and numerically fitted to a R-RC equivalent circuit. It was possible to show, that a relation exists between SOC and the circuit components RC and C through a simple R-RC equivalent circuit. The method described with only one RC network shows that not the optimal reproduction of the course
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Fig. 17. Graph of the mean values of RC in the SOC 20–80% range.
Fig. 18. Graph of the mean values of C in the SOC 20–80% range.
of an impedance spectrum is essential for estimating the SOC, but already the parameters of a simple numerical adjustment are adequate to derive SOC. Three film batteries of the same construction were used in total, which sufficiently demonstrates reproducibility. The SOC in the middle range (20%-80%) can be estimated especially accurately with this method. The maximum error of estimated SOC to real SOC is less than 5% in the middle range of SOC. The accuracy is therefore sufficiently precise to apply this method in some
applications. This fact is especially advantageous for automotive applications, given that the extreme SOC or voltage ranges are not generally used therein, due to the lithium ion batteries experiencing accelerated aging or irreparable damage. A special advantage of this method is the coupling of the process based on impedance described herein, and the already established method based on the open circuit voltage (OCV). The combination of both methods reduces the deviation of the SOC estimation and thus increases the accuracy. In this way, a lot of information can be obtained about the
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actual state of the battery system and each of the lithium ion batteries. The next step is to apply the possibilities shown herein on batteries with another cathode-material and mechanically produced batteries. Furthermore, the method will be applied for pouch cells, which are used in the automotive industry, with capacities > 35Ah. It must also be examined, if it is possible to develop a standard procedure through this method, and apply it in the automotive field, for example, in charging stations or battery management systems. Further investigation is the effect of temperature on the SOC estimation method. Another advantageous application can be the estimation of the state of health of the battery. The changes in the values of the circuit components throughout the age of the battery must therefore be examined. Fig. 19. Maximum error of estimated to real SOC in the middle SOC range.
Fig. 20. Schematical representation of a SOC estimation from the estimated parameters RC and C.
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Acknowledgment We thank the team of the Battery LabFactory Braunschweig (BLB), which was founded in the context of the Automotive Research Centre Niedersachsen (NFF), for the friendly support and the financial sponsorship from the European Regional Development Fund. References [1] K.J. Euler, Electrochim. Acta 17 (1972) 619–634. [2] S. Rodrigues, N. Munichandraiah, A.K. Shukla, J. Power Sources 87 (2000) 12– 20. [3] K. Bundy, M. Karlsson, G. Lindbergh, A. Lundqvist, J. Power Sources 72 (1998) 118–125. [4] D. Aurbach, B. Markovsky, M.D. Levi, E. Levi, A. Schechter, M. Moshkovich, Y. Cohen, J. Power Sources 81–82 (1999) 95–111. [5] D. Zhang, B.S. Haran, A. Durairajan, R.E. White, Y. Podrazhansky, B.N. Popov, J. Power Sources 91 (2000) 122–129. [6] G. Ning, B. Haran, B.N. Popov, J. Power Sources 117 (2003) 160–169. [7] Y. Zhang, C.Y. Wang, J. Electrochem. Soc. 156 (7) (2009) A527–A535. [8] E. Karden, S. Buller, R.W. De Doncker, J. Power Sources 85 (2000) 72–78. [9] T. Piao, S.-M. Park, C.-H. Doh, S.-I. Moon, J. Electrochem. Soc. 146 (8) (1999) 2794–2798. [10] D. Aurbach, B. Markovsky, I. Weissman, E. Levi, Y. Ein-Eli, Electrochim. Acta 45 (1999) 67–86. [11] C. Wang, A.J. Appleby, F.E. Little, Electrochim. Acta 45 (2001) 1793–1813. [12] M.D. Levi, D. Aurbach, J. Phys. Chem. B 101 (1997) 4630–4640. [13] X. Jun, C. Chunting, C. Binggang, C. Junyi, J. Power Sources 233 (2013) 277–284. [14] W.-Y. Chang, ISRN Appl. Math. (2013) 7. [15] H. He, R. Xiong, J. Fan, Energies 4 (2011) 582–598. [16] H. Min-Hsuan, L. Chang-Hua, L. Liang-Cheng, W. Chien-Ming, J. Power Sources 233 (2014) 861–873. [17] F. Huet, J. Power Sources 70 (1998) 59–69. [18] H. Jing, Y. Huimei, IEEE Ind. Electron. Appl. (ICIEA) (2015) 794–799. [19] Y. Xing, W. He, M. Pecht, K. Leung Tsui, Appl. Energ. 113 (2014) 106–115. [20] H. Zhang, L. Zhao, Y. Chen, Energies 8 (2015) 13811–13828. [21] Z. Yuejiu, O. Minggao, L. Languang, L. Jianqiu, Z. Zhendong, L. Xiangjun, J. Power Sources 289 (2015) 81–90. [22] X. Danga, L. Yana, K. Xua, X. Wua, H. Jianga, H. Sun, Electrochim. Acta 188 (2016) 356–366. [23] Y. Zhou, Y. Zhang, P. Zhao, C. Han, IEEE Strateg. Technol. (IFOST) 1 (2011) 287– 290. [24] M. Charkhgard, M. Farrokhi, IEEE Trans. Ind. Electron. 57 (12) (2010) 4178– 4187. [25] W. He, N. Williard, C. Chen, M. Pecht, Microelectron. Reliab. 53 (2013) 840–847. [26] J. Li, J.K. Barillas, C. Guenther, M.A. Danzer, J. Power Sources 230 (2013) 244– 250. [27] L. Ran, W. Junfeng, W. Haiying, L. Gechen, IEEE Ind. Electron. Appl. (ICIEA) (2010) 684–688. [28] N. Koirala, F. He, W. Shen, IEEE Ind. Electron. Appl. (ICIEA) (2015) 17–22. [29] G. Spinolo, G. Chiodelli, A. Magistris, U.A. Tamburini, J. Electrochem. Soc. 135 (6) (1988) 1419–1424. [30] J. Xu, M. Gao, Z. He, J. Yao, H. Xu, IEEE Comput. Soc. (2009) 316–320. [31] R. Mingant, J. Bernard, V. Sauvant-Moynot, A. Delaille, S. Mailley, J.-L. Hognon, F. Huet, ECS Trans. 33 (39) (2011) 41–53. [32] U. Troltzsch, O. Kanoun, H.R. Trankler, Electrochim. Acta 51 (2006) 1664. [33] I. Belharouak, G.M. Koenig Jr., K. Amine, J. Power Sources 196 (2011) 10344– 10350.
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[34] X. Han, M. Ouyang, L. Lu, J. Li, J. Energies 7 (2014) 4895–4909. [35] G.L. Plett, J. Power Sources 134 (2004) 252–261. [36] H. He, R. Xiong, X. Zhang, F. Sun, J.X. Fan, IEEE Trans. Veh. Technol. 60 (4) (2011) 1461–1469. [37] A. Al-Haj Hussein, I. Batarseh, Proc. IEEE Power Energy Soc. Gen. Meet. (2011) 1–6. Uwe Westerhoff M. Sc. (’83) is a scientific assistant at the Institute for High Voltage Technology and Electrical Power Systems. After his apprenticeship as an electrician he received the B. Eng. at the University of Hannover. Then he graduated his M. Sc. with honors from the Technical University of Braunschweig.
Dr. rer. nat. Thorsten Kroker (’75) is a former research assistant at the Institute for High Voltage Technology and Electrical Power Systems. As a post-doc he researched within an interdisciplinary research project the ageing mechanisms of lithium-ion batteries. Now he works at Volkswagen AG in the development department for battery systems.
Kerstin Kurbach M.Sc. (’88) is a scientific assistant at the Institute for High Voltage Technology and Electrical Power Systems. She made the B. Eng. at the University of Hannover. Then she graduated her M. Sc. from the Technical University of Braunschweig.
Prof. Dr.-Ing. Michael Kurrat (‘63) is university professor in the field High Voltage and Components of Energy Supply” and head of the Institute of High Voltage and Electrical Power Systems (elenia) of the Technical University of Braunschweig.
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Journal of Energy Storage xxx (2016) xxx–xxx
Contents lists available at ScienceDirect
Journal of Energy Storage journal homepage: www.elsevier.com/locate/est
Electrochemical impedance spectroscopy based estimation of the state of charge of lithium-ion batteries U. Westerhoff* , T. Kroker, K. Kurbach, M. Kurrat TU Braunschweig, Institute for High Voltage and Electrical Power Systems elenia, Braunschweig, Germany
A R T I C L E I N F O
Article history: Received 6 October 2015 Received in revised form 6 September 2016 Accepted 6 September 2016 Available online xxx Keywords: Electrochemical impedance spectroscopy Lithium ion battery State of charge
A B S T R A C T
The increasing market demand for electric vehicles requires a continuous development and improvement of battery systems. A crucial aspect is the application of analytical methods to characterize the battery systems in the most exact way. At the same time these methods should remain as simple as possible. The current analysis procedures use essentially the battery system- and battery cellcharacteristic of the voltage curve in relaxation- and operation-time. These approaches alone are not conclusive enough due to the influences of relaxation time and varying load currents. In recent years, methods based on electrochemical impedance spectroscopy (EIS) have found application for accurate analysis of occurring electrochemical processes and diagnosis of lithium ion batteries. This publication aims to show how the state of charge can be predicted with the use of EIS and a simplified equivalent circuit for redundant supplementing the OCV-method (open circuit voltage) and the current- counting method. Therefore film batteries with a graphite anode and a Ni1/3 Mn1/3 Co1/3 cathode are charged and discharged according to a specified procedure. The battery is (dis)charged with steps of 10% followed by an EIS measurement. The measured data is used to determine the elements of the simplified equivalent circuit. These elements are analyzed for their different values at various states of charge. From these measurements can be concluded that EIS can be applied for the estimation of state of charge (in the middle range) as redundant method to other estimation methods. It therefore provides an additionally methods by which statements about the battery conditions can be made. ã 2016 Elsevier Ltd. All rights reserved.
1. Introduction Electrochemical impedance spectroscopy (EIS) has been implemented through several decades to analyze and understand electrochemical processes. This method also has found application in the battery diagnosis of Lead-acid batteries [1], nickel-cadmium batteries [2] and nickel-metal-hydrid batteries [3]. EIS has been applied for some years to decipher the electrochemical processes which take place in a lithium ion battery (LIB). An equivalent circuit model (ECM) can be developed from the EIS data and the knowledge of the chemical and physical processes. The measured data are presented regularly as NyquistPlots (NYP). The measured impedance is decomposed with the help of a phase angle in a real part (x axis) and an imaginary part (y axis) which are plotted against each other. The real part is
* Corresponding author. E-mail address: [email protected] (U. Westerhoff).
designated by Z’ and the imaginary part as Z” in the Nyquist representation. Fig. 1 shows a possible equivalent circuit, which is regularly employed [2]. Additionally to the ECM shown in Fig. 1 a wide array of other suggestions exist for the interpretation of the impedance spectra of LIBs [5–8]. In different publications, the graphite electrode was examined through EIS [9–15]. The cell chemistry has a strong effect on the curve of the impedance spectrum. In [4] impedance spectra were recorded of material combination of graphite anodes and various cathode materials. The differences in the impedance spectra can be clearly seen. Both RC-members of the ECM shown in Fig. 1 thus sum up the processes at the cathode and the anode. The origin of the measurable capacitances lies in the solid electrolyte interfaces (SEI), which are formed on the anode (especially by graphite) as well as on the cathode. Both SEI are dielectric and function as an isolator. The SEI on the MO2-electrode is much thinner, than that on the anode (graphite) and dominates therefore the impedance spectrum. Since both SEI layers have
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R(Sol)
R(Film )
R(CT)*
C(Film)
C(DL)*
W(SSD)
C(IC)*
Fig. 1. Typical equivalent circuit to interpret measured spectra of impedance. It comprises a pre-resistance, two (partly up to four) RC members (film diffusion and double layer), a Warburg+ element (solid processes and diffusion) and an interphase element (intercalation). The “*” marks the circuit components that are highly dependent on potential.
similar dielectric constants, it is hard to separate them through EIS, which leads to a blurring of the impedance spectra of both electrodes. Excluded from the SEI formation is a cell structure with LTO (lithium titanate oxid) anodes because no SEI is formed on LTO anodes [33,34]. The resistance connected in parallel to the capacitances is based on the capability of the lithium ions to penetrate this layer, which can be described by a purely ohmic resistance. Through the specification of an equivalent circuit and different mathematical adaptation methods it is intended to predict different characteristics and conditions of a LIB. This includes particularly the state of charge (SOC) as well as the state of health (SOH) [5,6,16,17,32] and the internal cell temperature [18,19]. These state variables are very hard to predict due to the complex processes in a LIB. Other possibilities to predict the state of charge are: open-circuit voltage measurement [14,19], current-counting method [14,20,21], adaptive systems such as neural networks [14,22–24], Fuzzy-Logic [14] and Kalman filter [14,24–26,30] or hybrid-systems of any methods [14,24]. Additionally, the most methods are based on very complex mathematical models. The equivalent circuit presented in Fig. 1 is too complex to be developed into applications, for example, for battery diagnosis in electric vehicles, and then built into the trip computer of an electric car. Additionally, the analysis of solid diffusion (Warburg, second to last element) and of the intercalation process (ICP, last element) requires work with very low frequencies (50 mHz). The measurement time is therefore too long. This would cause measurement periods of time that are not applicable for the automobile sector. Further problems can arise at higher frequencies because the induction effects influences the abscissa zero crossing in the Nyquist plot. Whereas lower frequencies do not satisfy the requirements of a short measurement time and contains no
important information for SOC estimation. This work aims to show, that a much simpler equivalent circuit and a relatively small frequency band are sufficient to estimate the SOC of a LIB. Just for the practical implementation is the application of small memory footprint and short measurement time an important indicator for the advantageousness. However, a prerequisite is the permanent detecting of the temperature and the progressive aging because they have the biggest factors influencing the curve of the impedance spectrum, in addition to the SOC. Most of the ECMs investigated by other authors use complex equivalent circuits with Warburg impedances and constant-phase elements [2,13,17,18,27,31]. However, there are other sources which show that the simple thevenin equivalent circuit in Fig. 3 is already showing very good results [35–37]. In a review of different equivalent circuits for state of charge estimation has already been seen that a simple equivalent circuit gives good results. The model parameters are not determined on a measured impedance spectrum. They were identified with a Hybrid Pulse Power Characterization (HPPC) [15]. Another paper compares the equivalent circuit from this paper with an equivalent circuit with more RC elements. The results show that the thevenin equivalent circuit provides a similar good SOC estimation than the other models. The model parameters were determined with an adaptive gain sliding mode observers (AGSMO) for the SOC estimation [28]. In a recent publication there is a SOC-estimation with a dual neural network fusion battery model. For the linear neural network battery model based on the structure of thevenin battery model, the average error of SOC estimation is 1%. The average error is slightly less with more RC-elements. [22] Fig. 2 shows a typical NYP, which results from a measurement between 100 mHz and 100 kHz, for the batteries used herein. An approximately half-circular structure results through reduction of the frequency range from 1 Hz to 15,000 Hz. From this structure, a very simple equivalent circuit can be deducted. This circuit is shown in Fig. 3 and is from now on referred as R-RCECM. Three significant advantages arise through the specification of a simple R-RC-ECM and through the measurement in a relative small frequency range: 1 The measurement can be performed in far less time (=5 s), because frequencies smaller than 1 Hz are omitted. 2 In the case of bigger batteries and battery systems, the cables only produce minimal induction effects because the maximal frequency is capped at 15,000 Hz.
Fig. 2. Nyquist-Plot resulting from an impedance measurement between 100 mHz and 100 kHz of the batteries examined herein. The powers of ten are shown as red areas respectively. The potential E of the film battery shown herein is 3.68 V, which corresponds to a state of charge of 50%. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 3. Most simple equivalent circuit to describe the chemical processes of a lithium ion battery. In the Nyquist-Plost, a simple half-circle results with an additional purely ohmic resistance, that is, a half-circle displaced to the “right”.
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3 The SOC can be estimated with only three parameters: R0, RCt (abbreviated below as Rc) and Cdl (abbreviated below as C). This reduces the data volume considerably. These three significant advantages, the simple method is better than a model with higher complexity to use it as a redundant method to existing SOC estimation methods. 2. Experimental research 2.1. Film battery The experiments were performed on self-made film batteries (FB). The active areas, which are made of graphite (anode) and Ni1/3 Mn1/3 Co1/3 (cathode) are sealed in a composite film (Fig. 4). These are high-capacity electrodes with a thick active material layer. The current collectors are made of aluminum (cathode) and nickel (anode). The active area is square and has a lateral longitude of approximately 50 mm. The nominal capacity of the investigated LIBs is approx. 50 mAh. 2.2. Measurement procedure The impedance measurements (IM) were performed with a VersaSTAT 3 Potentiostat from the company Princeton Applied Research in a climate chamber from the company Vötsch Umwelttechnik with a constant temperature of 20 C 0.5 K. There were used a cell holder to minimize the influence of the contact resistance and the 4-wire sensing to eliminate the lead resistance. To guarantee constant measuring conditions and thus comparable data, the state of charge of 0% and 100% are defined as follows (see Table 2): The FB was charged to SOC 100% previous to the IM. To achieve this, the FB was first charged with a constant current step (CC) at 50 mA (1C), until 4.2 V were reached. Next, a constant voltage step (CV) was performed at 4.2 V, until a charging current of 1 mA was reached. After this procedure the FB was put to rest for 10 min. After a 10 min break, no electrochemical balance is established at a battery cell. Measurement studies have shown that the change in the impedance spectrum after 10 min have no serious effect on the SOC estimation as compared to 90 min. The deviation of the charge transfer resistance between RC,10min and RC,90min is less than 2.5%.
3
Thus, the influence on the SOC estimation is less than 1%. It should be noted that an electrochemical balance state is only reached after some hours of rest. The result is an almost constant cell voltage through the IM. This state of charge of the FB (including the 10 min pause) was defined as SOC = 100% for all measurements (see Table 2). After reaching SOC 100%, the first IM was performed in a frequency range of 100 mHz to 100 kHz 10 measurement values were registered pro power of ten, wherein each value was measured thrice and averaged in the apparatus. Such a measurement takes about 15 min to complete (see Figs. 5 and 6). Next, the discharge procedure was performed in 10% SOC-steps. To achieve this, a discharge current of 50 mA was set and maintained for 6 min. This represents a discharge step of 5 mAh. The FB was subsequently put to rest again (see Table 2 or Figs. 5 and 6) and the aforementioned measurement was performed again. To preserve the FB, an interruption voltage of 3.0 V was set up, so that the last discharge step is >5 mAh. The SOC step between 0% and 10% was deducted from the measurement log through the integration of the current flow over time. SOC 0% was defined with a final CV step at 3.0 V, until a current of 1 mA was reached. A rest time of 10 min was also taken after this step to guarantee a constant voltage during the measurement. The IM was subsequently performed and defined as SOC 0% (see Table 2). 12 IM result from the discharge procedure. After reaching SOC 0% the charging procedure follows, which is also performed in 10% steps (360 s at 50 mA). An interruption voltage of 4.2 V was set up for the charging process. Due to this, an additional charging step (analogue to discharge) results between SOC 90% and 100%. The FB is charged to the SOC 100%, defined previously, through a last CV step at 4.2 V, until 1 mA is reached. A 10 min rest pause also took place and finally, the last IM was performed (SOC = 100%). 11 IM result from the charging procedure, with a total of 23 IM for the charge and discharge procedures. The complete measurement takes 12 h and is represented graphically in Fig. 5. The black line shows the course of the voltage, whereas the green line represents the intensity of the supplied current. Every voltage level represents a 10 min pause with subsequent IM (about 15 min) (see Fig. 5). The discharge step from SOC = 20% to 10% is presented again in detail in Fig. 6 to show the processes of every charge and discharge step more clearly. Between the measurement processes of the state of charge function, the cells were not cycled or exposed to stress due to high temperatures or pressure during storage. Thus the influences of the aging effects on the measured impedance spectra are negligible. 3. Results and discussion 3.1. General observations
Fig. 4. Self-made film battery in a cell holder and climate chamber Material: C/ NMC, Nominal capacity 50 mAh, Voltage range: 3.0–4.2 V.
The voltage of the charge and discharge steps after a 10 min rest phase in relation to SOC were presented as a way of example in Fig. 7. The voltages shown on Fig. 7 also represent the voltages, at which the IM were performed. The voltages of the IM during the charging procedure are shown as green circles; the blue squares represent the voltages of the IM during the discharge procedure. The IM of the sates of charge 10%, 30%, 50% and 90% (Discharge) are presented in a NYP in Fig. 8. It can be clearly seen from Fig. 8, that the IM result in a compressed half-circle at higher SOC (>50%). At SOC < 50%, a second half-circle becomes visible, which grows with sinking states of charge and becomes dominant at SOC < 10%. Through this measurement, it is possible to show, that the influence of the second RC component (Fig. 1, Table 1), namely the
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Fig. 5. Measurement log of a charge and discharge procedure. The black line represents the course of the voltage. In every voltage plateau a 10 min rest time and an impedance measurement (about 15 min) occur. The green line represents the course of the supplied current. Every current plateau is a 10% charge or discharge step (6 min). Such a measurement cycle comprises a discharge from 100% to 0% and a subsequent charging to 100%. A measurement procedure comprises 23 impedance measurements in total. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 6. Sectional close-up of the discharge procedure from SOC 20% to 10%, wherein the word “rest” represents the 10 min pause.
capacitance of the double layer CDL and the charge transfer resistance greatly increases at low SOC. 3.2. Numerical adjustments (NA) The numerical adjustment was performed with the program ZViewTM from Scribner Associates Inc. A R-RC-ECM was given (see Fig. 3) and fitted for the sum of the least error squares [29]. The measured frequency range was limited for the NA, for impedances measured from 1 Hz to 15,000 Hz (see Section 1). The impedances are decomposed in real and imaginary parts using the phase angle, and are presented in Fig. 9 as black circles in NYP. The graph presented in green is the numerical solution, which results from the specification of an R-RC-ECM.
At very low SOC, the second RC component (double layer) becomes dominant (see Fig. 8). The numerical fitting of the measurement values of SOC 10% is shown in Fig. 10 as a green graph. The error resulting from the numerical fitting should thus be greater at low SOC than at high SOC. The margins of error are listed as a way of example for SOC 0%, 10%, 50% and 90% in Table 3. 3.3. Discussion of the results At this point, the results of the measurements are to be presented and discussed. For this purpose, the frequency range was reduced to those data points, which result from frequencies between 1 and 15,000 Hz (see Chapter 1). Beginning with the RC
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Table 2 Summary of the charge, discharge and measurement procedure.
Fig. 7. SOC vs. Potential: Discharge is shown in blue; charge is shown in green.
Fig. 8. Comparison between four different impedance measurements during the discharge procedure. SOC: 10% (3.46 V), 30% (3.57 V), 50% (3.68 V) and 90% (4.04 V).
results from the ECM presented in Fig. 3, the results from the NA of a single measurement are presented first. The reproducibility of the measurements is discussed subsequently. 23 IM were performed for each FB according to the measurement procedure of 2.3 (Fig. 5, Fig. 6 and Table 2). 12 IM result from the discharge and 11 additional IM result from the charging. The last discharge value is SOC 0%. The capacity of the FB results from the sum of the current flow through time during the charge and
Procedure
Constant Current (CC)
Constant Voltage (CV)
SOC = 100% SOC = 0% 10% Steps Measurement steps at 0% Measurement steps at 100%
50 mA to 4.2 V 50 mA to 3.0 V 360 s + or 50 mA
4.2 V to 1 mA 3.0 V to 1 mA 3.0 V to 1 mA 4.2 V to 1 mA
discharge procedures. The calculated capacity of FB-1 is 50.7 mAh. Because these are hand-made test batteries, there are light discrepancies (see Table 4). The SOC was deducted based upon this and plotted against the determined values RC (Fig. 11), C (Fig. 13) and R0 (Fig. 15). The values determined in the charging process were shown in green in the next figures; the blue values represent the data determined for the discharge process. An exponential fitting was performed subsequently, which is shown as a red line in the following figures. The exponential fitting was selected at random and must be understood as an example for the relation between the SOC and the determined components. The mean value for the circuit components R0, RC and C of three FB was determined next and plotted against the SOC. Three graphs result from this: Fig. 12 for RC, Fig. 14 for C and Fig. 16 for R0. The values were also exponentially fitted in this case. 3.3.1. Determination and interpretation of RC RC comprises, with the fitting to a RC-component, the resistance, which the lithium ions experience upon passage through the SEI and the resistance, which occurs through friction of the solvated lithium ions and the double layers. RC in relation to SOC is shown in Fig. 11. A numerical value between 0.3 V and 0.9 V results for RC. Therein, the resistance of the double layer (second RC-component of Fig. 1) has a growing influence on the NA at low SOC ( < 20%). Due to the adjustment, the largest errors occur for the fitting of low SOC (see Table 3). The correlation coefficient of 0.98 shows, that the resistance can be adequately described by the given exponential graph. Since RC and C grow lightly from SOC 90% to 100%, RC and C reach their smallest values by SOC 90%. After the single measurement of FB-1, two additional FB were measured (Table 4) and the mean value for RC was determined. The RC values can be easily reproduced, as is shown with the help of Fig. 12. The standard deviations for different SOC are listed in Table 5. 3.3.2. Determination and interpretation of C Given the fact that the thickness of the SEI and the areas of the electrodes are constant throughout the measurement processes, the capacitance of the first RC component from Fig. 1 can also be
Table 1 Electrochemical origin of the electrical components from Fig. 1.Circuit element. Circuit element
Electrochemical origin
R(Sol) R(Film) C(Film) R(CT)* C(DL)* W(SSD) C(IC)*
Resistance of the lithium ions in electrolyte Resistance of the lithium ions in the SEI layer (film) Film capacitance Resistance of the lithium ions with penetration of the double layer (Charge Transfer Resistance) Capacitance of the double layer Diffusion of the lithium ions in the solid Capacitance of the intercalation
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Fig. 9. Nyquist-Plot representation of the measured impedances after separation in real and imaginary parts, and the corresponding fitting to a R-RC-circuit. Black ! Measured values; Green ! Fit.
Fig. 10. Numerical fitting (green graph) of the data points resulting from the measurement of SOC 10% (black graph). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
taken as constant. However, due to film capacitance and double layer capacitance being strongly coupled, different values result for C. The double layer capacitance dominates specially for low SOC. This is made clearer by Fig. 10. From Fig. 8 it can be deducted that,
for very low SOC, a second half-circle appears, which is not taken into account through the use of a R-RC-ECM; the NA is thereby heavily influenced, which leads to the generation of very high values for RC and C. R0 also grows rapidly, because this values is
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U. Westerhoff et al. / Journal of Energy Storage xxx (2016) xxx–xxx Table 3 Margins of error at SOC 0%, 10%, 50% and 90% during discharge. SOC [%]
R0 [V]
RC [V]
C [mF]
90 50 10 0
0.365 0.007 0.389 0.007 0.422 0.014 0.480 0.019
0.334 0.012 0.323 0.012 0.417 0.022 0.958 0.097
2.95 0.25 3.11 0.28 9.80 1.36 26.70 3.80
Table 4 Capacities of film batteries. Film battery
Capacity
FB-1 FB-2 FB-3 Mean value
50.7 mAh 49.8 mAh 51.4 mAh 50.6 0.9 mAh
displaced to the right by the NA at low SOC. The capacitances determined for FB-1 are plotted against the state of charge in Fig. 13 and were lastly subjected to exponential fitting (red line). In here, it can also be seen, that the greatest errors occur at low states of charge (analogue to the values for RC in Table 5). The numerical value for capacitance is 0.99, and shows that the collected data are well-matched to this course. It can also be observed, that the value for C reaches its minimum at a SOC of approximately 90%. The mean capacitances, which result from the values of FB-1 to FB-3 are plotted against the state of charge in Fig. 14. The standard deviations are exemplary listed for the states of charge 0%, 10%, 50% and 90% in Table 6 as a way of example. The correlation coefficient is 0.996 and shows that an exponential relation exists between the state of charge and the capacitance (Table 7).
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3.3.3. Determination and interpretation of R0 If the lithium ions move through the electrolytes, these experience a resistance. This resistance can be understood as friction of the ions and the electrolytes, and has a purely ohmic behavior. Generally this resistance is represented with the Rsol in Fig. 1. The resistance R0 (see Fig. 3) is not the same as the RSol, since R0 does not represent the value of the abscissa zero crossing. R0 is the abscissa zero crossing of the numerical fitting result and is not inhibited or fixed in the parameter variation. Only thus will generate the minimal square error between model and measurement results. Figs. 8 and 10 illustrate, that the ohmic resistance, which is experienced by the solvated lithium ions during diffusion through the electrolytes, is practically constant for all SOC. The resistance is approximately 0.38 V. Due to the focusing in the numerical fitting this is not true at R0. This assumption is based upon the fact, that the number of solvate molecules and the number of lithium ions in the electrolyte are approximately constant. The electrolyte resistance R0 is influenced rather by the temperature of the battery. Temperature was held constant throughout the measurements (20 C). Through the specification of a R-RC-circuit, the fitting program can only construct a half-circle, which has its origin on the x-axis (real resistance value). This origin results from the NA of the measured values, so that R0 is displaced to large values especially for low SOC. R0 has a value in the range of approximately 370 mV to 500 mV and is represented in relation to SOC in Fig. 15. For the NA of the R-RC-circuit the error of R0 assumes larger values also for low SOC. The correlation of the determined values is 0.988. In Fig. 16, the mean values of R0 are plotted against SOC. The low standard deviations of R0 show that the starting point for the resistance determination of RC can easily be reproduced. 3.4. Summary of determined data The results of each circuit component are to be observed more closely herein. Two of the three circuit components (RC and C) are
Fig. 11. RC in relation to the state of charge. Green represents charging and blue represents discharging. The red line is a randomly chosen exponential fit. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 12. Mean value of RC in relation to the state of charge. Green represents charging and blue represents discharging. The red line is a randomly chosen exponential fit. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 13. Capacitance in relation to the state of charge of FB-1. Green represents charging and blue represents discharging. The red line is a randomly chosen exponential fit. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
used for predicting the state of charge in a battery. R0 is strongly affected by errors (see Fig. 16). From Fig. 12 (Mean value for RC) and 14 (Mean value for C) result two critical sectors. For very low SOC ( < 20%) large errors occur from NA, which cause the estimation of the SOC through the circuit to be very inexact. If too high SOC are reached, the values for RC and C grow lightly (minimum occurs at about. 90%), which can lead to a wrong interpretation of the SOC. For practical applications, for example in electric vehicles, there is no aim for too low or too high
SOC which is positive for this method. This would certainly lead to accelerated aging of the LIB. These disadvantages can therefore be seen as non-critical. Additionally, the voltage graph is very steep for very high and very low SOC (see. Fig. 7), which means, that the voltage graph can be easily used as an interruption criterion for the charging or discharging. Through the determination of RC and C with impedance spectroscopy, the SOC in the middle can be defined very accurately. Figs. 17 and 18 are magnified sections of Fig. 12 and 14 respectively, and represent the graph of the
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Fig. 14. Mean value of C in relation to the state of charge. Green represents the charging and blue the discharging. The red line is a randomly chosen exponential fit. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 15. R0 in relation to the state of charge. Green represents charging and blue represents discharging. The red line is a randomly chosen exponential fit. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
respective circuit components in the SOC 20–80%. Looking only at the SOC-range of 20–80% the fit with an exponential function give better accuracy as the fit of the complete SOC-range. The operation of a LIB in extreme voltage situations, this is, near 100% or 0% SOC (in the range defined herein) is to be generally avoided, since it greatly accelerates the aging process. Specially in the automobile industry, where batteries with particularly long lives are required, the LIB are operated in the middle range of voltage. Figs. 17 and 18 illustrate, that the method provides reasonable results in the middle SOC range.
In Fig. 19, the maximum error between the adjusted real SOC and from the impedance data estimated SOC are applied. The mean value of the error is 2.7% and the maximum error is 4.8%. The approach to derive the SOC from the fitted parameters is shown schematically in Fig. 20. In this example is assumed that a value of 0.33 ohm for RC and 3.5 mF for C were determined from impedance spectra subsequent to a charging process. The intersections of the values RC and C with the envelope curve of the mean value are used to determine the SOC-range of each parameter. The estimated SOC is within the overlapping area of
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Fig. 16. Mean value of R0 in relation to the state of charge. Green represents the charging and blue the discharging. The red line is a randomly chosen exponential fit. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Table 5 Mean value errors of RC for three film batteries. SOC [%]
Mean Value RC [V]
Standard deviation [V]
90 50 10 0
0.318 0.343 0.524 0.929
0.025 0.018 0.014 0.036
Table 6 Standard deviations of the mean values of C for three film batteries. SOC [%]
Mean Value of C [mF]
Standard deviation [mF]
90 50 10 0
2.90 3.14 10.40 26.36
0.17 0.27 2.16 0.80
Table 7 Standard deviations of mean values of R0 for three film batteries. SOC [%]
Mean value R0 [V]
Standard deviation [V]
90 50 10 0
0.361 0.372 0.423 0.498
0.0082 0.0079 0.0197 0.0481
both SOC ranges and is calculated from the average of the limits of this area. In this example the estimated SOC is 48% whereas the real SOC is 49%. The maximum error provides information about the overlapping SOC range. 4. Conclusion In this paper impedance spectra of self-made film batteries (=50 mAh) were performed in a voltage range from 3.0 to 4.2 V by a
constant temperature of 20 C. The voltages represent a state of charge from 0%-100%. To achieve reproducible results, the framework conditions were exactly defined for all SOC and kept for every measurement. Lastly, the data were represented in a Nyquist-Plot and numerically fitted to a R-RC equivalent circuit. It was possible to show, that a relation exists between SOC and the circuit components RC and C through a simple R-RC equivalent circuit. The method described with only one RC network shows that not the optimal reproduction of the course
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Fig. 17. Graph of the mean values of RC in the SOC 20–80% range.
Fig. 18. Graph of the mean values of C in the SOC 20–80% range.
of an impedance spectrum is essential for estimating the SOC, but already the parameters of a simple numerical adjustment are adequate to derive SOC. Three film batteries of the same construction were used in total, which sufficiently demonstrates reproducibility. The SOC in the middle range (20%-80%) can be estimated especially accurately with this method. The maximum error of estimated SOC to real SOC is less than 5% in the middle range of SOC. The accuracy is therefore sufficiently precise to apply this method in some
applications. This fact is especially advantageous for automotive applications, given that the extreme SOC or voltage ranges are not generally used therein, due to the lithium ion batteries experiencing accelerated aging or irreparable damage. A special advantage of this method is the coupling of the process based on impedance described herein, and the already established method based on the open circuit voltage (OCV). The combination of both methods reduces the deviation of the SOC estimation and thus increases the accuracy. In this way, a lot of information can be obtained about the
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actual state of the battery system and each of the lithium ion batteries. The next step is to apply the possibilities shown herein on batteries with another cathode-material and mechanically produced batteries. Furthermore, the method will be applied for pouch cells, which are used in the automotive industry, with capacities > 35Ah. It must also be examined, if it is possible to develop a standard procedure through this method, and apply it in the automotive field, for example, in charging stations or battery management systems. Further investigation is the effect of temperature on the SOC estimation method. Another advantageous application can be the estimation of the state of health of the battery. The changes in the values of the circuit components throughout the age of the battery must therefore be examined. Fig. 19. Maximum error of estimated to real SOC in the middle SOC range.
Fig. 20. Schematical representation of a SOC estimation from the estimated parameters RC and C.
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[34] X. Han, M. Ouyang, L. Lu, J. Li, J. Energies 7 (2014) 4895–4909. [35] G.L. Plett, J. Power Sources 134 (2004) 252–261. [36] H. He, R. Xiong, X. Zhang, F. Sun, J.X. Fan, IEEE Trans. Veh. Technol. 60 (4) (2011) 1461–1469. [37] A. Al-Haj Hussein, I. Batarseh, Proc. IEEE Power Energy Soc. Gen. Meet. (2011) 1–6. Uwe Westerhoff M. Sc. (’83) is a scientific assistant at the Institute for High Voltage Technology and Electrical Power Systems. After his apprenticeship as an electrician he received the B. Eng. at the University of Hannover. Then he graduated his M. Sc. with honors from the Technical University of Braunschweig.
Dr. rer. nat. Thorsten Kroker (’75) is a former research assistant at the Institute for High Voltage Technology and Electrical Power Systems. As a post-doc he researched within an interdisciplinary research project the ageing mechanisms of lithium-ion batteries. Now he works at Volkswagen AG in the development department for battery systems.
Kerstin Kurbach M.Sc. (’88) is a scientific assistant at the Institute for High Voltage Technology and Electrical Power Systems. She made the B. Eng. at the University of Hannover. Then she graduated her M. Sc. from the Technical University of Braunschweig.
Prof. Dr.-Ing. Michael Kurrat (‘63) is university professor in the field High Voltage and Components of Energy Supply” and head of the Institute of High Voltage and Electrical Power Systems (elenia) of the Technical University of Braunschweig.
Please cite this article in press as: U. Westerhoff, et al., Electrochemical impedance spectroscopy based estimation of the state of charge of lithium-ion batteries, J. Energy Storage (2016), http://dx.doi.org/10.1016/j.est.2016.09.001