Validation and benchmark methods for battery management system functionalities: State of charge estimation algorithms

Journal of Energy Storage 7 (2016) 38–51

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Journal of Energy Storage journal homepage: www.elsevier.com/locate/est

Validation and benchmark methods for battery management system functionalities: State of charge estimation algorithms Christian Campestrini *, Max F. Horsche, Ilya Zilberman, Thomas Heil, Thomas Zimmermann, Andreas Jossen Chair of Electrical Energy Storage Technology, Technical University of Munich (TUM), Arcisstr. 21, 80333 Munich, Germany

A R T I C L E I N F O

A B S T R A C T

Article history: Received 2 March 2016 Received in revised form 21 April 2016 Accepted 12 May 2016 Available online

Several state of charge estimation algorithms have been developed and validated in the past. However, due to varying validation methods, the results cannot be compared. This paper presents an approach for a generalised validation and benchmark method for state of charge estimation algorithms. The independence of standardised driving cycles is obtained by developing a synthetic load cycle. To do so, a frequency analysis is performed for 149 different driving cycles and the five major time constants are identified at 55.8 s, 9 s, 5.1 s, 3.8 s and 1 s. Using the synthetic load profile, three validation profiles are created. In addition to low- and high-dynamic behaviour, long-term stability is considered at five different temperatures (10 8C, 0 8C, 10 8C, 25 8C and 40 8C). During the long-term test, the temperature varies between 10 8C and 40 8C. To ensure comparability, a quantitative rating technique is introduced for estimation accuracy, transient behaviour, drift, failure stability, temperature stability and residual charge estimation to evaluate the performance of different state estimation algorithms. Furthermore, the benchmark can be used to optimise the state estimator, such as a linear and an extended Kalman filter examined within this study. ß 2016 Elsevier Ltd. All rights reserved.

Keywords: Battery management system State of charge Kalman filter Lithium-ion battery

1. Introduction With the necessity of high-energy and high-power battery packs for different applications, such as stationary energy storage systems (SESS) or electric vehicles (EV), cells must be connected in series and parallel. Due to safety reasons (e.g. over and under voltage), cell balancing and ageing issues, supervision of each cell is indispensable. For this purpose, the battery management system (BMS) is used. The BMS supervises single-cell voltages, current and temperatures in a battery pack to guarantee compliance with cell limits. When a cell exceeds the so-called safe operating area (SOA), the BMS limits the power, or shuts down the system completely before an uncontrollable state is obtained. Beside safety management and cell balancing, other required functions including thermal management, communication with a higher-level control unit, state of charge (SOC) estimation, state of health (SOH) estimation and state of available power prediction are important features of a BMS. All these functions are currently being investigated and reported in the literature [1–3]. Due to different

* Corresponding author. E-mail address: [email protected] (C. Campestrini). URL: http://www.ees.ei.tum.de http://dx.doi.org/10.1016/j.est.2016.05.007 2352-152X/ß 2016 Elsevier Ltd. All rights reserved.

applications and purposes of these functions, their validation and test procedures differ, which not allows a comparison of the algorithms or functionalities. Therefore, we introduce the first proposal for the validation of BMS functionalities. The developed methods are open for discussion and are available on our homepage for open usage.1 As the first part, a method for the validation and evaluation of SOC estimation algorithms is presented. Within the literature, various algorithms for SOC estimation are validated by different methods without further benchmarking. However, a comparison of these algorithms is not possible. Since the area of application is multilateral, shortcomings of the estimators are often not considered in the validation process. An important issue in the validation is the determination of a reference SOC to compare the estimated SOC with a reliable value. A common method to measure the reference SOC is the coulomb counter (Eq. (1)). In this study the resulting SOC is defined as

SOCðtÞ ¼ SOC 0 þ

1 C act

Z

t

iðt Þdt

(1)

t¼0

1 Manual, benchmark calculation script and example data are available at www. ees.ei.tum.de/en/media/downloads/validation/.

C. Campestrini et al. / Journal of Energy Storage 7 (2016) 38–51

Acronyms BMS CC CCCV CV DC DFT ECM EKF EV FFT KF LFP LIB NCA OCV SESS SLC SOA SOC SOH

battery management system constant-current constant-current constant-voltage constant-voltage direct current digital Fourier transformation equivalent circuit model extended Kalman filter electric vehicle fast Fourier transformation Kalman filter lithium-iron-phosphate lithium-ion battery nickel-cobalt-aluminium open circuit voltage stationary energy storage system synthetic load cycle safe operating area state of charge state of health

where SOC0 corresponds to the initial SOC, Cact to the actual measured capacity of the cell, i(t) to the load current and t to the time of operation. One issue is that, mostly, the same current signal is used to calculate the reference SOC and to estimate the SOC with the algorithm [4–8]. An offset-afflicted measurement causes a drift in the reference, calculated by Eq. (1). When the algorithm is not able to correct this drift, the estimation follows the offsetinfluenced reference. Other algorithms, for example, open circuit voltage (OCV)-based algorithms, may correct the error, but when using only one current sensor, it is not possible to distinguish between the correct and incorrect SOC (Fig. 1a). This shortcoming can be addressed by using two different sensors for the reference and for the algorithm [9–12]. Thereby, the current sensor for the reference must be more accurate than the sensor for the algorithm. In Fig. 1b, this concept is depicted schematically. The estimation based on the BMS current measurement (Fig. 1b, sensor 1) drifts apart, while the algorithm partly compensates for the error. By determination of the reference SOC using a coulomb counter, the finite sample rate causes an error during dynamic loads. In Fig. 1c the real current (dashed blue line) and the discrete current measurement (red line) is shown. The green area symbolises the resulting error, caused by the discrete measurement. Furthermore, temperature changes and high currents can cause temporary capacity (Cact) variations, which can affect the SOC calculation (Eq. (1)). A possibly more accurate way to define a reference SOC is a residual charge determination at the end of each test. Due to the constant-current (CC) discharge, the accumulated error caused by the finite sample rate and other influences can be minimised. This approach is mandatory for long-term tests [12]. The behaviour of a battery is dependent on temperature, SOC and current rate. Furthermore, the OCV changes with temperature, depending on chemistry and SOC [13,14]. This is especially important for OCV-based algorithms. Xing et al. [9] show the influence of the temperature-dependent OCV of a lithium-ironphosphate (LFP) cell during state estimation with a Kalman filter (KF). They showed high errors resulting from an incorrect OCV– SOC relationship. To resolve this problem, different OCVs at

39

a) SOC Sensor 1 (estimation) Estimation

∆SOC = 5%

t b) SOC Sensor 1 (estimation) Sensor 2 (reference) Estimation

∆SOC = 2% ∆SOC = 5% t c) Current Real current Measurement Error

t Fig. 1. Validation issues: (a) validation with one current sensor; (b) validation with an additional, more accurate, current sensor; (c) shortcomings of discretising and resulting error.

different temperatures were implemented in the battery model. Consequently, due to possible temperature variations during operation, the validation has to be performed at different and varying temperatures. Otherwise, a reliable and accurate function cannot be guaranteed [12]. The algorithms present in the literature are rarely validated during the charging process. In common applications, the discharge current is highly dynamic, while in the charge direction, the current is comparably constant. As an example for neural networks, this also leads to the need for separate training data for the charge period. Other algorithms such as the dual KF [15–17] or the sliding mode observer [18] also behave differently without any dynamics [12,19]. These behaviours are often neglected. Due to the wide measurement range of current sensors, the measurement accuracy of small currents can be disturbed by noise or by an offset of the sensor. These errors can affect the SOC estimation. To address these issues, pauses and long-term tests [20] are necessary. During these tests, the SOC based on the coulomb counter increases due to the current sensor offset, while the SOC estimation of the algorithm follows the reference SOC [12]. Further investigations showed the estimation accuracy and stability concerning variable ambient temperatures as well as ageing effects. Additionally, the influence of initialisation and parameter errors is mandatory for a proper validation [8]. The rest of the paper is organised as follows. To show the necessity of validation under different conditions battery parameters and their dependency on temperature, current rate and SOC are shown in Section 2. The independence of standardised driving cycles is obtained by developing a synthetic load cycle (SLC) for the validation scenarios in Section 3. All three scenarios are performed at five different temperatures. Furthermore, an evaluation system

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is presented for a good comparability. In Section 4, the measurement set-up and two Kalman filters (KF) for SOC estimation are introduced. Finally, the estimation and benchmark results of these commonly used algorithms are presented and compared in Section 5. The conclusion in Section 6 summarises the paper. 2. Behaviour of lithium-ion batteries As many electrochemical systems, batteries exhibit highly nonlinear behaviour [21]. The dynamic behaviour depends on the impedance of the battery, which is influenced by many parameters such as temperature, SOC, current rate and history [22,23]. In a real application, all these dependencies can occur; hence, it is not sufficient to evaluate a state estimator only under one specific condition in the laboratory. In this section, some of the mentioned dependencies are explained to emphasise the importance of a detailed evaluation. To determine the battery parameters shown in this section, current pulses with different amplitudes are applied to a nickel– cobalt–aluminium (NCA) cell (Panasonic NCR18650PD) over the entire SOC range in steps of 15% of the nominal capacity (CNom = 2.75 A h). The voltage response of every current pulse is then fitted by a least square method to optimise the parameters for an equivalent circuit model (ECM) consisting of one ohmic resistance and two RC terms (Fig. 2). The ohmic resistance contains the resistance of the current collectors, the electrolyte and additional contact resistances [24]. The first RC term represents the charge transfer processes that consists of the double-layer capacitance and the charge transfer resistance. The second RC term represents diffusion effects that consists of the diffusion capacitance and the diffusion resistance [25].

C1

C2 I

Ri OCV(SOC)

R1 U1

R2 U2

U

Fig. 2. ECM consisting of one ohmic resistance (Ri), two RC terms (R1, C1 and R2, C2) and the SOC-dependent OCV.

Fig. 3 shows the most important parameters of the investigated cell. As mentioned in [23,26], ohmic resistances exhibit a low dependency on SOC in comparison to the temperature (Fig. 3a). The increasing resistance with a decreasing temperature arises from the strong temperature-dependent conductivity of the electrolyte. Fig. 3b and c show the charge and discharge current rate dependency at 0 8C and 40 8C, respectively. It is observed that the current dependency decreases with increasing temperature. Similar results are described in [27]. In Fig. 3d, the dependency of battery capacity on temperature is shown. To determine the capacity, the cell is fully charged with a CC of 0.5 C and a constantvoltage (CV) of the maximum allowed voltage Umax (for the tested cell 4.2 V), until the current drops below 0.02 C. This corresponds to SOC = 100%. After that, the cell is discharged with a CC of 1 C to the minimum allowed voltage Umin (for the tested cell 2.5 V), followed by a CV period with a cut-off current of 0.02 C [28]. This corresponds to SOC = 0$. Especially at low temperatures, the usable capacity drops and follows a non-linear characteristic. A similar behaviour is evaluated in [14,29]. In the literature, common estimation algorithms use the OCV as a reference [30,31,16,4,32,33]. In these studies, the SOC derives

Fig. 3. Parameters of NCR18650PD: (a) ohmic resistance Ri at different temperatures; (b) charge transfer resistance Rct at different current rates at 0 8C; (c) charge transfer resistance Rct at different current rates at 40 8C; (d) temperature dependency of the cell capacity Cact; (e) OCV (left axis) and temperature influence at the corresponding SOC (right axis); (f) normalised charge transfer resistance Rct of the used cell (NCA), compared to cells with different cathode materials (normalised to their maximum value) at 25 8C.

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3. Development of validation profiles and benchmark methods To consider different operational conditions, three validation scenarios are created based on standardised driving cycles. For this purpose, existing driving cycles are analysed to identify dominant time constants (Section 3.1). With this information, a SLC is generated (Section 3.2), which is used for the three validation profiles (Section 3.3). In Section 3.4 a benchmark method for performance evaluations is presented. 3.1. Analysis of driving profiles It is already stated that the dynamical response of lithium-ion batterys (LIBs) strongly depend on temperature, SOC and load current. The quality of the state estimator is determined by its ability to provide accurate results under different operating conditions. The comparability can be achieved by applying an identical dynamical stimulus. The driving cycle analysis, which gives the foundation for the derivation of such a solely dynamical stimulus, is described in the following. Any signal in the time domain can be represented by a power distribution in the frequency domain. If the signal is periodic, then the power distribution will be dominated by the corresponding frequency components. In case of vehicle driving cycles, these periodic processes might be related to repeatedly accelerating or braking while driving. Staying at traffic lights, as well as other frequent interruptions of vehicle movement, belong to periodic processes as well. Dynamic components of load profiles in stationary storage applications are of less interest, since very low time constants are dominant. Therefore, only driving cycles are considered in the dynamic profile analysis. In total, 149 reference velocity profiles from [38] are transformed using the common vehicle model presented in [39, p. 77] to extract power profiles. The power requirements are derived from the velocity profile based on this vehicle model, with the parameters summarised in Table 1. Due to the diverse origin and purpose of these driving cycles, all profiles are normalised according to their maximum power. Since not all power profiles are neutral in terms of acceleration and recuperation power, the direct component is eliminated by subtracting the profile average value from itself. Such adjustments are assumed to be valid since only the dynamic information is of particular interest.

Table 1 Parameters of the general vehicle model. Parameter

Value

Gravitation Density of air Ambient temperature Relative ambient humidity Vehicle mass (excluding battery) Battery pack mass Additional mass Air drag coefficient Vehicle frontal area Tire roll resistance factor Rotational mass factor Additional consumption Motor efficiency Inverter efficiency Efficiency factor transmission Recuperation efficiency

9.81 m/s2 1.225 kg/m3 25 8C 0.6 RH 1200 kg 500 kg 150 kg 0.31 2.24 m2 0.013 1.05 0.4 W 0.94% 0.97% 0.95% 0.5%

Adapted profiles are subsequently transformed to the frequency domain using a fast Fourier transformation (FFT) algorithm. The first four dominating frequencies are determined for each profile. A sample result, based on the Artemis HighMot urbdense total driving cycle (distance: 3086 m; duration: 787 s; average speed: 14.1 km/ h1) [38], is shown in Fig. 4. It has to be mentioned that the major frequencies-finding algorithm does not simply take the first highest values in the power spectrum. Such an algorithm would result in closely lying major frequencies, which owe their existence to the leakage effect of digital Fourier transformation (DFT). The actual algorithm replaces the initial spectrum by linear interpolation of local maximas, which is shown in Fig. 4. The process is iterated until the interpolated spectrum has only the desired amount of peaks. For driving cycle frequency analysis, this number is set to four. 3.2. Generation of an application-independent test profile Table 2 holds the averaged major time constants of all adjusted power profiles sorted in descending order of corresponding power magnitudes. The major time constants, which could be extracted by analysing the driving cycles as described in Section 3.1, provide the basis for the dynamic validation profiles. Additionally, the most commonly used sample rate ts = 1.0 s within the analysed driving cycles is appended [38]. So, the Nyquist theorem is guaranteed, according to which the sample rate fs has to be twice the highest frequency fmax to reconstruct the signal (fs = 2  fmax). Using the four time constants and the appended sample time ts, a dynamic load profile A(t) is generated by the sum of sine waves

1 Actual spectrum Relevant spectrum Major frequencies

0.8

Relative power

from the OCV, based on the OCV–SOC correlation [34]. However, the OCV has a non-negligible temperature dependency, as shown in Fig. 3e as well as in [14,31,9]. Thereby, DSOC is the difference between the OCV-based SOC at 25 8C and the OCV-based SOC at the same voltage but at different temperatures. SOC calculations based on the OCV at 25 8C can provoke errors up to DSOC = 4% at low temperatures (T  0 8C) (for clarity reasons only the OCV at 25 8C is shown, the deviation is represented by DSOC). In Fig. 3f, the normalised charge transfer resistances of different cell chemistries at 25 8C are compared with those of the NCR18650PD cell and show a similar behaviour (normalised to their maximum value). For the depicted cell chemistries, at low and high SOC levels, the charge transfer resistance increases or decreases with a strong non-linear behaviour, while in the midrange, a quite constant charge transfer resistance is observed. In addition to these short-term dependencies, all parameters depend on calendar and cyclic ageing [23,35–37]. As the focus of this paper lies on validation methods, we neglect the effect of possible ageing effects within the study. Longer test scenarios are necessary to prove the accuracy and stability of state estimators under ageing. For this purpose, a model-based validation is recommended.

41

0.6 0.4 0.2 0 0

0.05

0.1

0.15

Frequency / Hz Fig. 4. Creating an application-independent test profile: dominant frequencies after a local peak search of the Artemis HighMot urbdense total driving cycle.

C. Campestrini et al. / Journal of Energy Storage 7 (2016) 38–51

42

Table 2 Major time constants and sample rates for discretisation. Number of periods

Sample and hold time (s)

tdc

N

tsh

55.82 9.023 5.144 3.860

1 6 10 14

55.82 9.014 5.140 3.859

ts = 1.0

55

1.015

Relative power

Time constant (s)

1

with ascending sample and hold times tsh, i and its corresponding power distribution ai: AðtÞ ¼

  5  X 2p ai sin t

t sh; i

i¼1

(2)

0.5 0 -0.5 -1 0

100

200

300

400

500

Time / s Fig. 5. Creating an application-independent test profile: the discrete profile with the corresponding sample rates (Eq. (3)).

with kW ½AðtÞ ¼ kWpeak Depending on the application, and hence, different measurement possibilities, the sampling rate of the system varies between seconds and minutes. To validate the algorithm or model for different sampling rates, the sample and hold time tsh is modulated. Therefore, the number of periods N with a constant sample and hold time tsh is rounded to its next integer value (see Table 2). To generate the quantised signal with different step sizes, the dynamic load profile is repeated five times. Both half cycles for each sample and hold time define one time step Dtj = tj+1  tj wherein the average load is calculated. Combining all time steps generates a quantised signal with a decreasing step size, which is equal to the sample and hold time: 0 1 R tjþ1 2N 5 i 1 X X t j AðtÞ dt @ A (3) Sðt j Þ ¼ t sh; i i¼1

j¼0

2

where tj ½Sðt j Þ

¼ j

t sh; i

2 kW ¼ kWpeak

To equalise the different load quantities in charge and discharge directions, without interfering with the frequency spectrum, the profile is extended by the vertically and horizontally mirrored profile. Another advantage is the additional behaviour of the prehistory, whether the battery is stressed high dynamically or quite steady. In conclusion, the generated profile is repeated 10 times to validate the full bandwidth of the load scenarios with all five sample and hold times in ascending and descending orders (see Fig. 5). This Coulomb neutral SLC is used as a subset for the different validation scenarios. To achieve a cell-independent profile, the relative power profile is divided by the nominal voltage of the used battery and scaled to the maximum current of the cell. 3.3. Validation scenarios With the SLC and the information about battery behaviour, the validation profiles can be developed. To validate the stability of the state estimators during low-dynamic (profile A), high-dynamic (profile B) and long-term tests (profile C), three independent validation profiles are created.

To guarantee a reproducible validation, at the beginning of every profile, a complete constant-current constant-voltage (CCCV) charge and discharge is performed to determine the actual capacity, as described in Section 2. The process is shown in Fig. 6 phase 1. Based on the measured capacity, the required initial SOC can be set. At the end of each validation profile A, B, or C (Fig. 6 phase 2), a residual charge determination is performed by a CCCV discharge (Fig. 6 phase 3) with the same constraints as that of the capacity determination. In order to calculate the final SOC based on the residual charge and to consider a capacity fade during long-term tests (profile C), the capacity is measured again (Fig. 6 phase 4). 3.3.1. Profile A Profile A (Fig. 7) aims to validate the low-dynamic behaviour of a state estimator. Several CC charges and discharges are performed. Relaxation times and the coulomb neutral SLC are placed between single CC periods. While the SOC swing during the SLC is negligible, the voltage changes due to the over-potentials of the ohmic resistances, charge transfer and diffusion effects. To investigate the behaviour of the state estimator with strongly changing parameters over the SOC range, this profile is performed at SOC levels where the parameters differ the most (compare Section 2). The distinctive parameter values of most of the LIBs can be found at about 10%, 50% and 90% SOC. At the beginning, the cell is charged from 50% to 90%. After a relaxation period of 30 min, SLC is performed. Subsequent to a second rest period of 30 min, the cell is discharged to the next SOC level of 50% or 10%. This procedure is repeated at 10 8C, 0 8C, 10 8C, 25 8C and 40 8C to investigate the temperature behaviour of the state estimator for low-dynamic profiles. As the temperature decreases, measurable self-heating of the cell increases, due to the increasing resistances (higher resistances at lower SOC, Fig. 3a–c). Thereby, only the CC periods provoke an observable increase in temperature on the cell surface. For the Panasonic NCR18650PD, the measured surface temperature increases by 12 K during profile A performed at 10 8C at lower SOC levels. For proper state estimation, the algorithm should consider these variances in the battery parameters. 3.3.2. Profile B While validation profile A needs a Coulomb neutral profile to ensure a steady state, validation profile B (Fig. 8) comes with an additional direct current (DC) offset. The amount of continuous discharge depends on the recuperation rate of the driving cycles analysed in Section 3.1. Therefore, all driving profiles are normalised in power and time. Afterwards, all load levels are rearranged in descending order of their magnitudes, resulting in a common load duration curve. Cumulatively, for the recuperation levels of the

C. Campestrini et al. / Journal of Energy Storage 7 (2016) 38–51

2

3

Analogous to profile A, the same ambient temperatures of 10 8C, 0 8C, 10 8C, 25 8C and 40 8C are performed for profile B to investigate the temperature behaviour of the state estimator for high-dynamic profiles. At 10 8C, the temperature on the cell surface increases up to 3 K at lower SOC levels.

4

U/V

4.2 3.7

100

3.3.3. Profile C The purpose of validation profile C is to investigate the longterm stability and accuracy during varying temperatures in the range from 10 8C to 40 8C. Validation of profile C uses the Coulomb neutral SLC as in profile A. SOC is maintained constant at 50% and SLC continually repeats itself for seven days. Fig. 9 shows one out of the seven cycles. The temperature cycling starts (tS) and ends (tE) at 25 8C. In between, the five temperature levels (10 8C, 0 8C, 10 8C, 25 8C and 40 8C) are kept constant for 2 h, while the incline or decline to the next temperature level takes one hour. In total, the complete temperature range is cycled in 24 h and repeated for seven days. The resistances of the investigated cell are low at 50% SOC (Fig. 3). Hence, the self-heating even at 10 8C is lower compared with the temperature increase during profile B. The increase of 0.2 K is negligible.

80

3.4. Benchmark of state of charge estimation algorithms

Profile A B C

2.5 0

2

4

6

x

x+6

Time / h

4.4 U SOC

U/V

4

SLC

60 3.6 40 3.2

SOC / %

Fig. 6. Validation profiles for a NCA cell: sequence of the validation process for each profile (1: capacity measurement and initial SOC conditioning; 2: profile A, B or C; 3: residual charge measurement; 4: capacity measurement). The variable x depends on the duration of the profiles.

20

2.8

0 0

1

2

3

4

5

6

Time / h Fig. 7. Validation profiles for a NCA cell: profile A for low-dynamic.

100

4.4 U SOC

U/V

60 3.6 40 3.2

SOC / %

80

4

To guarantee the comparability between state estimators, a standardised evaluation system needs to be defined. In this section, such a system is proposed. A detailed measurement description and the corresponding MATLAB function for calculating the benchmark are available on our homepage in the Media section and are open for discussion. Similar to [8], a scoring system from 0 (worst) to 5 (best) points is applied. In this section, the six categories of the evaluation system are explained: estimation accuracy Kest, drift Kdrift, residual charge determination Kres, transient behaviour Ktrans and failure stability Kfail. For the evaluation, several error boundaries e are defined. Each of them corresponds to an evaluation score P(e). Eq. (4) shows the score depending on the defined error boundaries. In every category the same values are used. 8 5 > > > > 4 > > < 3 PðeÞ ¼ 2 > > > > > 1 > : 0

20

2.8

for for for for for for

0% 0:5% 1% 2% 4%

jej < jej < jej < jej < jej jej >

0:5% 1% 2% 4% 8% 8%

(4)

4 40

0 0

0.5

1

1.5

2

2.5

3

3.8

Time / h

average load duration curve, around 11.35% of the discharged energy is recuperated. The discrete SLC is shifted towards its discharge direction until the recuperation satisfies this requirement. Dividing the power profile by the nominal voltage results in the current profile. While profile A validates the behaviour of estimation algorithms during rest and CC periods, profile B investigates the dynamic behaviour within the SOC range of 10% to 90%. The charging period from 50% to 90% between phase 1 and phase 2 (Fig. 6) is not considered.

U/V

Fig. 8. Validation profiles for a NCA cell: profile B for high-dynamic.

25 3.6 10 3.4

0

U T

tS

T / °C

1

43

tE

-10

3.2 0

4

8

12

16

20

24

28

32

Time / h Fig. 9. Validation profiles for a NCA cell: one out of the seven cycles of profile C for the long-term test (temperature cycle start: tS; temperature cycle end: tE).

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To calculate the average drift score Kdrift, the gradient a of the regression line y is multiplied with the time t1 h: y

e1 h K drift

¼ at þ n ¼ at 1 h ¼ Pðje1 h jÞ

(7)

with ½e1 h  ¼

Fig. 10. Validation principle: evaluation of the estimation accuracy (example with profile B and error boundary e = 0.5%, not all boundaries shown).

3.4.1. Estimation accuracy Kest Here the overall accuracy during cycling is evaluated. The estimation accuracy depends on the total time within a certain P error boundary ( Dt d 2 ei ) in relation to the total measured time tend (see Fig. 10). Thereby, d describes the absolute difference between the reference SOCref and the estimated SOCest:

d ¼ SOC ref SOC est

(5)

The resulting percentage part of the total time is then multiplied with the corresponding point P(ei). This is calculated for all error boundaries and summed for Kest: K est ¼

6 X

P Pðei Þ

i¼1

Dtd 2 ei

! (6)

t end

3.4.2. Drift Kdrift A repeating discharge profile results in an overall linear SOC trend with a certain gradient. In short validation profiles, a difference between the reference and estimation gradient generates a negligible error. However, in long validation tests or in real applications, this differing gradient can provoke an accumulating error and the estimation drifts. When the estimation has the same gradient, despite error-afflicted measurements, as the reference, the state estimator can correct any current offset or other shortcomings. On this account, an investigation of the estimation drift is essential (Fig. 11). Due to possible small transients at the beginning, or a not linear estimation the regression line of the estimation error is calculated.

% h

For profile A, the drift corresponds to the mean of the drift scores during the CC charge and discharge periods. Due to the long duration of profile C the error per hour results in a negligible error, even when the error increases to several percent per week. To consider such drift in the evaluation, the error for long-term tests is related to one week: ½e7 d  ¼

% 7d

The drift score correlates with the estimation score. A low drift score results in a low estimation score, because the estimation is drifting apart. This has a high influence during long-term investigations (profile C). However, if the drift score is high and the estimation score is low, the estimation is not drifting but has a parallel offset. For coulomb counter based algorithms, for example KF, this can be provoked by incorrect parameters or voltage measurement errors. When the estimation is oscillating, the linear regression could result in a falsified drift value. So a long transient oscillation around the correct SOC value can result in a high estimation score but a low drift score. This context is summarised in Table 3. This correlation can determine the reason for low estimation performance. 3.4.3. Residual charge determination Kres During cycling, the reference is influenced by accumulated errors due to the limited sample time and measurement errors. Furthermore, the reference SOC is related to the cell capacity, which may change due to a varying temperature during testing. Hence, the available capacity differs and the reference is falsified as a consequence. The residual charge at the end of a cycle related to the actual capacity represents the true SOCres. The resulting error bound yields the evaluation points for this category: K res ¼ PðeÞ

(8)

with

a)

SOC

±0.5% error ±1% error ±2% error Reference Estimation Regression

tend = t100% b)

t

ε=SOCref - SOCest ε1h t1h

e ¼ SOC est;end 

C res ¼ SOC est;end SOC res C act

where Cres is the remaining capacity determined by a CCCV discharge at the end of the validation profile (Fig. 6, phase 3) and Cact is the cell capacity measured after the validation profiles (Fig. 6, phase 4). 3.4.4. Transient behaviour Ktrans Common state estimation algorithms can compensate for incorrect initial values, measurement errors and changes in parameters, temperature, etc. The investigation of the transient behaviour is performed by the initialisation with incorrect values. Table 3 Possible relationship between Kest and Kdrift.

t

Fig. 11. Validation principle: (a) estimation with drift (example with profile B, not all boundaries shown); (b) linear regression of the estimation error gives the average drift error P(e1 h).

(9)

C. Campestrini et al. / Journal of Energy Storage 7 (2016) 38–51

SOC

ε ≤ ±0.5%

tth=t10%

3.4.6. Temperature stability Ktemp Most algorithms are based on battery models, which use temperature-sensitive parameters. In real applications, the battery temperature varies depending on the ambient temperature or due to high loads. Hence, a state estimator has to demonstrate proper functionality at different temperatures. Here the performance change due to a different temperature in each test is observed. To achieve an independent score for the overall estimation performance, the standard deviation is used to rate the temperature stability Ktemp,x (Eq. (14)). Thereby, x represents the benchmark category. This test uses the results of the estimation, residual charge, drift and transient category.

±0.5% error ±1% error ±2% error Reference Estimation

tend = t100%

t

Fig. 12. Validation principle: evaluation of the transient behaviour (example with profile B, not all boundaries shown).

In Fig. 12, the evaluation of the transient behaviour is depicted. Here it is examined in which error bound the estimator is after 10% of the total time (t10%) after an incorrect initial SOC. The percent specification allows higher requirements to the SOC estimator for shorter profiles and lower requirements for long-term tests. The resulting point is scaled with the initial error mismatch (Eq. (10)). So the maximum points are only reachable when the reference SOC is 100% while the initial estimation SOC is 0% at the beginning. The minimal mismatch must be higher than 8%, which corresponds to the highest error band. K trans

jSOC ref;t0% SOC est;t0% j ¼ PðeÞ SOC ref;t0%

I

U

(11)

(12)

R

The mean value of Kfail,x is the final value for failure stability: K fail ¼

1X K 3 x fail;x

with x 2 fest; drift; resg

(14)

(15)

where K x is the mean of the scores of profile A or B over the temperature range in each category and n is the number of tested temperatures. The mean value Ktemp,x is the final value for temperature stability: 1X K temp;x 3 x

(16)

with

3.4.5. Failure stability Kfail Several errors, such as an offset in the current and voltage measurement as well as incorrect or varying (ageing) parameters, can provoke unstable and inaccurate behaviour in the state estimation algorithm. For a reliable functionality, these error cases should be tested and validated. To do so, a current, voltage or parameter offset is set and scores are compared to the normal operation. From the intensity of the score change, the failure stability score Kfail,x is calculated. Thereby, x represents the benchmark category. This test uses the results of the estimation, residual charge and drift category. For evaluating the state estimator in an error case, a current offset (rI) of 0.1% of the 1 C current and a voltage offset (rU) of 2% of the voltage range of the cell are used. For the parameter error (rR), the algorithm is initialised with 10% of the correct parameter. For a detailed investigation, each error can be considered separately for each category. In the experimental part, for clarity, Kfail,x is the mean of all error influences: X   1 Pðe ¼ 0ÞjK x K x;r j 3 r 2 fr ; r ; r g

with vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n u1 X 2 ðK K x Þ s¼t n i¼1 x;i

(10)

State estimation algorithms can behave differently during lowdynamic loads, high-dynamic loads or rest periods. To validate the transient behaviour correctly, the test should be performed with a low-dynamic load, a high dynamic load and a rest period at the beginning. The mean of these test results is the final evaluation value.

K fail;x ¼

K temp;x ¼ Pðe ¼ 0Þ2s

K temp ¼

with

e ¼ SOC ref;t10% SOC est;t10%

45

(13)

x 2 fest; drift; trans; resg 3.4.7. Overview In Table 4 the categories and their test requirements are summarised. 4. Experimental To give an example of the presented validation method, the procedure is performed with a KF and an extended Kalman filter (EKF). KF algorithms are commonly used for SOC estimation. 4.1. Introduction to the Kalman filter The KF is a set of equations that predicts the state of a physical process. In detail, it minimises the error of the states related to the measured and predicted output of a linear system [15,16,40]. For batteries it is common to use an ECM and a coulomb counter to calculate the predicted output. In this example, the ECM is a firstorder RC model consisting of the SOC-dependent OCV, a serial resistance Rdc1s, referring to the voltage drop caused by the sum of the ohmic and charge transfer resistances and a RC term representing diffusion processes. The Rdc1s is used, because the algorithm is calculated every second (tstep = 1 s). Table 4 Benchmark categories and their requirements. Category

Reference value

Requirements

Kest Kdrift Kres Ktrans Kfail Ktemp

SOCref SOCref SOCres SOCref SOCref SOCref

Profiles A, B, and C Profiles A, B, and C Profiles A, B, and C Profiles A and B with wrong SOC initialisation Kest, Kres and Kdrift with offsets of profiles A, B, and C Kest, Kdrift, Kres, Ktrans of profiles A and B

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The estimated states are SOC and the voltage drop over the RC term (URC). In the first step, the states are calculated with the coulomb counter and the embedded ECM. Based on the states and the ECM, the battery voltage is estimated. In the second step, the filter corrects the states based on the calculated and measured battery voltage by minimising the error to zero. This is performed with the Kalman gain. The Kalman gain also takes account of the model and measurement inaccuracies. The EKF is developed for non-linear systems and linearises the system as well as the measurement matrix. [17,12,41,10,19,42–44] Both filters are compared with the proposed validation method in the next section. The performance of the filters is set by the covariance and process noise matrix and the measurement noise. To guarantee reproducibility, these parameters should be published in each publication about KFs. The tuning parameters of the used filters are determined experimentally and summarised in Table 5. For comparability, both filters use the same fixed set of tuning parameters. The ECM used for both KFs is parametrised at 25 8C and kept constant for the experiments at other temperatures (Table 5). So the temperature influence on the used algorithms can be shown. The parameters are measured by separate experiments. For temperatures different from 25 8C, ECM-based algorithms have to adapt the parameters to each temperature to obtain an optimal estimation of the SOC. Non parameter-adapting algorithms, as both used KFs in this paper, may result in inaccurate estimation results.

Table 6 Accuracies of voltage and current measurement.

Voltage Current Voltage Current

resolution resolution accuracy accuracy

BaSyTec

BMS

a

0.3 mV 0.2 mA 0.016% 0.02%

1.5 mV 10 mA 0.25% 0.25%

– – 15.6 12.5

the BMS. To guarantee the functionality of the used algorithm in real applications, cell voltages, temperatures and current should be measured by the less-accurate BMS. The BMS used in this paper was a self-developed prototype. The accuracies and resolutions of the used sensors are summarised in Table 6. Thereby, the device which provides the reference value must have a higher accuracy and resolution than the device which provides the measurement data for the algorithm. The accuracy factor a describes the quotient between both devices (Table 6). Higher values result in a more accurate validation. To realise the measurements of all three validation profiles (A, B and C) at the defined temperatures, the cell is located in a temperature chamber. 5. Results and discussion In this section, the EKF results are discussed in detail. In the end, these results are summarised and compared with the linear KF.

4.2. Experimental setup

5.1. Estimation behaviour

In Fig. 13, the experimental set-up is shown. The validation profile was performed on the cell using a BaSyTec test system. As in an EV or SESS, the state estimator uses the measurement data of

In Figs. 14a, 14b and 14c, the three profiles are shown with reference and error bounds. Fig. 14c also shows the coulomb counter of the BMS (CC BMS). This coulomb counter gets the same current input as the algorithm. For profiles A and B, the coulomb counter shows the same results as the reference, due to the short duration of the test (Fig. 14a and 14b). The EKF shows good agreement with the reference in profiles A and B. At the beginning of profile C, the algorithm shows an oscillating behaviour. Due to noisy measurement data, the SOC increases, while the reference shows a decreasing behaviour. The development of the SOC based on the coulomb counter of the BMS is different compared with the reference (Ah BMS in Fig. 14c). Here also noise and the limited sample rate are responsible. The noticeable steps in SOC estimation are due to the temperature decrease to 10 8C. At temperatures below 10 8C, the algorithm does not work properly. The reasons for this behaviour are a non-adapting filter tuning and ECM parameters for the temperature. While the SOC based on the residual charge at the end of both short profiles A and B is identical with the last value of the reference, SOCres differs from the reference in profile C (DSOC = 1.7%). Due to the changing cell capacity caused by the varying temperature and accumulated errors in the current measurement, the reference drifts apart. This shows the importance of the residual charge test at the end of long validation profiles. Fig. 14d and e shows the behaviour of the EKF at 0 8C for profiles A and B. For both profiles an estimation offset due to the incorrect parameter at 0 8C is observable. The shortcomings of the ECM at low temperatures are also visible in Fig. 14f. The voltage difference between estimation and measurement at 0 8C and 40 8C is shown. The error increases with decreasing temperature, especially at low SOC levels and during constant charge periods. At high temperatures, the EKF has problems estimating the correct voltage at medium- and low-SOC levels. This result can also be used to optimise the battery model parameters in the mentioned fields. Fig. 15a depicts the results (first t10% = 0.25 h) with an incorrect initial value of the high dynamical profile B at 25 8C. In this case, the correct SOC is 90%, but the filter is initialised with a SOC value of 10%. The remaining offset between the estimation and the

Table 5 Tuning and ECM parameters. Covariance URC Covariance SOC Process noise URC Process noise SOC Measurement noise Rdc1s R1 C1 Cact URC,0

1e-2 1e4 1e-10 1e-15 1e-4 38 mV 16.5 mV 1189 F 2.89 A h 0V

BaSyTec (BST)

A

BMS

A

Power Voltage measurement Current measurement Current sensor Temperature sensor Temperature chamber Fig. 13. Measurement set-up.

A

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Fig. 14. Results of the EKF with correct initialisation: (a) profile A at 40 8C; (b) profile B at 40 8C; (c) profile C; (d) profile A at 0 8C; (e) profile B at 0 8C; (f) voltage error of profile A at 0 8C and 40 8C.

reference is caused by not exact ECM parameters. Similar behaviour is observed with a constant discharge and rest period start of profile A. In each case, the filter can correct the wrong initialisation within the first 10% of the test duration. The fastest transient behaviour shows the filter in the rest period case. In this case, the EKF minimises the difference between the measured and calculated voltage without any changes in the battery voltage. So the EKF adapts the SOC only based on the OCV and is not influenced by the coulomb counter. In Fig. 15b, the influence of a 0.001 C current offset is presented with profile C. Here also the coulomb counter based on the measurement data of the BMS is shown. Because the EKF uses not only the BMS coulomb counter (Ah BMS in Fig. 15b) but also the measured voltage, the algorithm can compensate the drift in parts. But still, the correction based on the voltage is too low for this current offset. This behaviour could not be detected using only one current sensor (see Fig. 1). A voltage offset (2% of the voltage range, for the used cell rU = (4.2 V  2.5 V)  2 % =34 mV) and an incorrect parameter (10% of the correct parameter value, for the used cell Rdc1s = 3.8 mV) cause an estimation offset. In Fig. 15c the result with a parameter offset is shown, the voltage offset provokes a similar estimation behaviour. Thereby, the voltage error corresponds to a parallel shift towards higher values, while the decreased parameter value provokes a parallel shift towards lower values. In fact, both errors have the same origin: the voltage in the ECM is modified and behaves like an offset of the OCV. A dual EKF, which can also adapt the parameters of an ECM, would be able to correct the incorrect parameter, so the influence of this error could be minimised [45].

5.2.1. Estimation accuracy Kest In Fig. 16 the error and error boundaries of profile A at 0 8C are shown. The error lies between the 2% and 8% boundary. With Eq. (6), the corresponding score results to 1.4 points. This calculation is repeated for all temperatures. The estimation results Kest in Table 7 clarify that the temperature is a highly influencing factor. The scores are in the range from 1.7 to 4.8 and 0 to 4.1 for profiles A and B, respectively, whereby the best estimation results are at higher temperatures. Due to the non-adapting parameters, the estimation accuracy at low temperatures is poor. The estimation fails for profile B at 10 8C and 0 8C. Here the estimation is outside of the highest error bound (Fig. 14e). At high SOC levels, the difference between parameter values at 25 8C and at 10 8C or 0 8C is higher than at medium-SOC levels (Fig. 3b and c). So the estimation fails for profile B (SOC t0 % = 90%), but not for profile A (SOC t0% ¼ 50%). During rest periods in profile A, where the incorrect parameters have no influence, the algorithm can compensate the error. The spread of these results yields in a temperature stability of 2.5 and 1.6 for profiles A and B, respectively. Profile C does not allow different evaluations because of the varying temperature. The estimation score results to 4.7. K fail;est shows the mean influence on Kest due to the offset errors (see Section 3.4). Here all profiles have major changes. The error influence increases with temperature for profile A. An evaluation where the estimations fail (for profile B at 10 8C and 0 8C) is not possible. A detailed examination shows that the voltage and resistance offset provoke most changes for profile A and B; for profile C, the current offset causes the highest influence.

5.2. Evaluation All results and the corresponding evaluations, based on Section 3.4, are summarised in Tables 7–10.

5.2.2. Drift Kdrift In Fig. 17a the error between SOCref and SOCest of profile B at 0 8C (Fig. 14b) is shown. After a short transient behaviour the error

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48

Ref

Ah BMS

± 2% error

a)

SOC res

Est

± 4% error

± 8% error

Table 8 Scores of drift Kdrift and failure stability K fail;drift .

100

SOC / %

80 60 40 20 0 0

0.05

0.1

0.15

0.2

0.25

Time / h b)

Table 9 Scores for residual charge accuracy Kres and failure stability K fail;res .

70

SOC / %

65 60 55 50 45 Table 10 Scores for transient behaviour Ktrans.

40 0

25

50

75

100

125

150

175

Time / h c) 100

SOC / %

80 60 40 20 0 0

0.5

1

1.5

2

2.5

Time / h Fig. 15. Results of the EKF with incorrect initialisation: (a) transient behaviour during high-dynamic discharge (first 10% of time of profile B at 25 8C); (b) influence of a current offset (profile C); (c) influence of an incorrect parameter (ohmic resistance, profile B at 25 8C). Table 7 Scores of estimation accuracy Kest and failure stability K fail;est .

increases with time. The linear regression line depicts the gradient of the drifting error. Based on the gradient in profile B (1.8% h1), the score for this example is calculated with Eq. (7) to 3 points. Fig. 17b shows the drift behaviour of profile C (Fig. 14c). The gradient is 0.35%/7d, which results to 5 points.

Fig. 16. Error and error boundaries of profile A at 0 8C.

The results for all temperatures and profiles are summarised in Table 8. The results for Kdrift show a score between 0.3 and 3.3 for profile A and a score between 1 and 5 for profile B. Thereby, the drift score of profile A is calculated by the mean value of the gradients during CC periods. The reason for the low drift score at low temperatures is the incorrect capacity value (Fig. 3d). The estimated SOC based on the coulomb counter is calculated incorrectly (Eq. (1)) and the filter is not able to correct the error. As one can see, the drift is also influenced by errors in the measurement or parametrisation of the battery model. These influences are low compared with the changes in the estimation accuracies, because the tested errors result in a parallel offset (Fig. 15c). Only the current offset provokes changes in the drift behaviour (K drift;err ), but they are low during profiles A and B

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Fig. 17. Error with error boundaries and the linear regression line of (a) profile B at 0 8C and (b) profile C. For purpose of presentation the error is mirrored and shifted by the y-axis interception n (Equation (7)).

because of their short duration. For profile C, only the current offset has an influence for K fail;drift . The gradient of the drift is 6.45%/7 d, which result to 1 point. 5.2.3. Residual charge determination Kres Similar to the estimation score Kest and the drift score Kdrift, Kres also increases with temperature. Here a better performance in profile A is observable. This is related to the rest period in the end, where the algorithm has time to correct the SOC based on the OCV. The changes of K fail;res due to errors are observable in each profile. The error influence is caused by a parallel shift relayed to the voltage and parameter offset. 5.2.4. Transient behaviour Ktrans The score Ktrans is summarised in Table 10 for all temperatures and profiles. To achieve the same starting SOC for the lowdynamic, high-dynamic (see Fig. 15a) and rest scenario, the start time of profile A is shifted. Profile A starts with the charging period to test the low-dynamic behaviour. For testing the rest behaviour, the start is shifted to the rest period. For example at 25 8C, t10% is 0.5 h and 0.25 h for profile A and profile B, respectively. All tests show a high dependency on temperature; the best stability is noticeable when the battery is relaxed and has no current flow. Here the algorithm can correct the error based on the OCV without changes to the coulomb counter. At 10 8C and 0 8C, the transient behaviour fails for the dynamic and low-dynamic tests. The latter also fails at 10 8C. 5.3. Comparison of the Kalman Filter and the extended Kalman filter From the results, a final evaluation of the EKF is presented in Fig. 18. To show the comparability of this validation method, the

Fig. 18. Net diagram with the final scores of the KF and EKF: (a) low-dynamic test (profile A); (b) high-dynamic test (profile B); (c) long-term test (profile C).

EKF is compared with a linear KF. The results of the performed tests are averaged and depicted in a net diagram. For example, K est is the mean of all Kest at each temperature. For K fail (profiles A, B and C) and K temp (profiles A and B), all values from Tables 7–10 are considered. The transient behaviour Ktrans of the algorithm in profile A is calculated by the mean of the score during the lowdynamic and rest periods (K trans ).

50

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Fig. 18a shows the better behaviour of an EKF in low-dynamic applications (profile A). Specifically, the transient and residual charge score outperforms a linear KF. A detailed description of the differences in both filters is beyond the scope of this study. In Fig. 18b, both filters are compared during high-dynamic applications (profile B). Here both algorithms show similar results. The advantage of the EKF is, as with the low-dynamic profile, the drift behaviour. During the long-term test (profile C, Fig. 18c), the EKF shows a better drift behaviour, than the KF. Due to the long duration time, the algorithm can compensate the poor estimation performance at temperatures lower than 10 8C. Both algorithms show the same performance regarding the error stability and estimation accuracy in all profiles. The better performance of the EKF in the remaining categories relies on the linearisation of the non-linear system and measurement matrix. An optimised or adaptive filter tuning could increase the overall performance of the estimation, especially at different temperatures.

6. Conclusion This paper introduces the first proposal for a generalised validation and benchmark method for SOC estimation algorithms. The method can be used to not only compare different algorithms, but also to optimise a state estimator for specific needs. The validation consists of three profiles, where low-dynamic, highdynamic and long-term scenarios are tested. This is repeated for different temperatures in the range from 10 8C to 40 8C. The independence of standardised driving cycles is obtained by developing a synthetic load cycle. To do so, a frequency analysis is performed for 149 different driving cycles and the major time constants are identified. In the end, a benchmark provides information about the weaknesses and strengths of the studied algorithms and enables a comparison between different algorithms. The benchmark has six categories for the short-term validation and four categories for the long-term test. The categories are estimation accuracy, transient behaviour, drift, failure stability, temperature stability and the estimation accuracy related to the residual charge at the end of each test. These categories and the relationship of some benchmark scores allow the detection of shortcomings of the investigated algorithms. As an example for the presented method, the benchmark process is discussed with the EKF. The results are compared with a linear KF. With our developed benchmark process, it is observable that the EKF shows a better performance compared to the linear KF regarding the low-dynamic behaviour. The drift behaviour of the EKF is better than for the KF during all profiles. Using the benchmark results to optimise the algorithm could improve the usage in real applications. Acknowledgements Fundings from the Bayrische Forschungsstiftung (BFS) within the FORELMO project and from the Bayerische Staatsministerium fu¨r Wirtschaft und Medien, Energie und Technologie within the EEBatt project are gratefully acknowledged. The responsibility of this publication stays with the authors.

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