**5.1 SystemC**

In the design of complex digital systems, obtaining a high-level executable specification of the project in early stages of the design process is useful for detecting errors or validate functionality prior to implementation. This is one of the main advantages of SystemC, a C++ class library for hardware design at various abstraction levels - from system level to Register Transfer Level (RTL). **Figure 3** shows the typical design flow for SystemC projects [14].

The SystemC library contains elements that facilitates representation of hardware systems parallelism. Hardware models in SystemC are represented by modules that may run in parallel interconnected by ports and channels (**Figure 4**). In this way, the initial model may contain a few modules representing system level

**Figure 3.** *SystemC hardware design flow [14].*

*System Level Design and Conception of a System-on-a-Chip (SoC) for Cognitive Robotics DOI: http://dx.doi.org/10.5772/intechopen.98643*

functionality and, as the model gets refined, those initial high-level modules are further divided into more specific interconnected modules, until the RTL is reached [14].


**1. Introduction**

The use of energy storage systems is essential for the transition to renewable energies. Due to the unsteady energy supply from renewable energies such as wind power and photovoltaics, energy storage devices are required to compensate for fluctuations in output and to reliably provide energy at all times. For the electrification of the transport sector, energy storage systems are required in order to move vehicles independently of an external energy supply and without burning fossil fuels. In battery electric vehicles in particular, LIBs are by far the most frequently used battery technology due to their high energy and power density.

Large batteries are required in electric vehicles (EVs) and stationary energy storage devices, which are therefore the main cost factor in these applications. Accordingly, the requirements for the service life of the LIBs are high and a high degree of reliability is a prerequisite.

Therefore, non-invasive investigation methods are used to achieve a comprehensive understanding of the underlying degradation mechanisms of LIBs to enable system optimizations with regard to the service life. In addition, the non-invasive methods are required for the online diagnosis of LIBs and to identify potential risks during operation in order to ensure safe operation.

In current studies, the continous determination of the changes in kinetic parameters of LIBs made it possible to draw conclusions about progressive aging and degradation

**Citation:** Goldammer, E.; Kowal, J. Determination of the Distribution of Relaxation Times by Means of Pulse Evaluation for Offline and Online Diagnosis of Lithium-Ion Batteries. *Batteries* **2021**, *7*, 36. https://doi.org/ 10.3390/batteries7020036

Academic Editor: Kai Peter Birke

Received: 26 February 2021 Accepted: 2 April 2021 Published: 1 June 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

mechanisms [1–5]. Compared to recording of the open-circuit-voltage (OCV) or to directly determining the capacity, measuring the dynamic behavior of LIBs is usually less timeconsuming [1].

EIS as a non-invasive technique is widely used for aging studies in order to measure the impedance directly and thus to determine the kinetic parameters of the LIBs [6–9]. Aging processes such as lithium plating [3] and the formation of the solid electrolyte interface (SEI) [4] could be investigated using EIS.

The derivation of the DRT on the basis of the EIS measurement data as well as the further DRT analysis is a common method for the investigation of LIBs and other batteries. In [10–15] methods are investigated and described to obtain the DRT from impedance data. In several publications, the number of dominant electrochemical processes of LIB as well as their time constants and polarization contributions could be quantified by analyzing the DRT of the measured spectra [14–17]. Changes in the time constants and polarization contributions during the aging of the LIBs under investigation can also be determined using the DRT, as recently shown by Sabet et al. [5].

The main disadvantage of EIS is the long measurement time, especially for low frequencies. The measurement time ranges from several hours for frequencies in the millihertz range to several days for frequencies in the microhertz range. Therefore the bandwidth and resolution of the impedance measurement data available for the DRT is limited [15]. Additionally, only small signal amplitudes are permitted to ensure that the steady state condition is not violated during the EIS. The long measuring times and low signal amplitudes cannot be implemented under operating conditions and with commercially available measuring electronics [18], which is why DRT analyzes have so far been limited to laboratory tests. But even under laboratory conditions, when measuring lower frequencies, maintaining the steady state and current drift are becoming increasingly critical [19].

Due to the general availability in online applications, the characterization of cell impedance based on pulse data is of great interest and the subject of some current studies (e.g., [20,21]). The time domain data of current and voltage curves can be evaluated in the event of pulse excitations in order to determine the impedance of the LIB and other battery types. The calculation on the basis of time domain data is generally faster than the direct measurement of the impedance, since several frequencies are excited simultaneously with excitations in the time domain [19]. Thus, on the basis of time domain data, a higher frequency resolution and wider bandwidth of the impedance measurements can be achieved, which is of particular interest with regard to the DRT.

An overview of the options for calculating the impedance using time domain data is given in [22]. In [19,23], the time domain data resulting from pulse measurements were brought into the frequency domain using a fast Fourier transform (FFT) in order to calculate the low frequency impedance. However, the excitation of a pulse is nonperiodic. A window function must therefore be used for the transformations, which in turn generates an offset of the signal [18]. To avoid additional sources of error, as an alternative to the FFT or Laplace transformation, a pre-selected equivalent circuit model (ECM) can be parameterized using the time domain data [19]. The impedance is obtained by transforming the ECM into the frequency domain. The ECM is chosen in a manner that the impedance behavior of the battery can be reproduced. Therefore, the model must be selected individually for each battery type, cell chemistry and the electrochemical processes to be expected [24]. In addition, the impedance of the batteries can change significantly with aging, state of charge (SOC) as well as temperature and thus also the dynamic behavior in the time domain. For this reason, prior knowledge of the electrochemical processes involved and of the aging behavior and further dependencies is required in order to select a suitable model.

The DRT can be derived from the calculated impedance. If the selected ECM consists only of RC elements (parallel connection of resistance and capacitor) and an internal resistance (Thévenin model), the DRT is given directly by the model in the time domain and a transformation to frequency domain is not necessary. Analytical methods have already

been proposed for the online parameterization of a Thévenin model [20,25] but the number of RC elements is limited and too small to be able to derive a DRT with adequate resolution. The sufficient number of RC elements can be characterized by iterative numerical optimization methods such as genetic algorithms and method of least squares. Compared to the analytical methods, however, the computationally intensive iterative calculations are disadvantageous for online applications [25] and the number of RC elements is limited again due to the computing power available [26]. The initial values to be determined also require prior knowledge of the electrochemical processes and their approximate time constants and polarization contributions.

In summary, it can be stated that based on the analysis of the DRT, aging mechanisms have already been examined in numerous investigations. The DRT is determined according to the state of the art on the basis of the impedance. The direct measurement of the impedance by means of EIS cannot be implemented in current online applications without adaptations and at low frequencies, even under laboratory conditions, it is time-consuming and subject to inaccuracies. The indirect determination of the impedance based on the evaluation of time domain data leads to additional inaccuracies or requires an individual definition of a model for different cell chemistries and types. A direct derivation of the DRT based on time domain data, which can also be used online, would therefore be desirable.

In this study a method is proposed and described to derive the DRT directly from the measured voltage course during cell relaxation. The method is validated experimentally by comparing the results with a DRT obtained from EIS measurements. In an aging study, the introduced method and a subsequent DRT analysis are used to identify the time constants and polarization contributions of the electrochemical processes of LIBs. The method is shown to be sufficiently sensitive to quantify the changes in these parameters during aging without the need for EIS equipment or other devices not available in online applications. The study demonstrates that the DRT derived from time domain data offers significantly more insights into processes with large time constants respectively low-frequency impedance with less expenditure of time than a DRT derived from EIS measurements. In addition, a correlation between a polarization contribution of one of the processes with a large time constant and a degradation mechanism could be established. Thus, the proposed method offers a time-effective estimate of the kinetic parameters of a LIB, provides insights into battery degradation and is offline and online applicable.


**4. Discussion**

In the present work, we investigated the effect of SwE application on yields and young shoot quality features of five *L. siceraria* landraces. Irrespective of the genotype, SwE supply improved plant height and the number of leaves. These results are coherent with those of Rouphael et al. [38] who, investigating the influence of *Ecklonia maxima* SwE on production, quality and physiological traits of zucchini squash cultivated under saline conditions, found that, regardless of the salinity treatments, SwE enhances plant aerial weight. Findings are also in line with those of La Bella et al. [23] who, examining the influence of the SwE of *E. maxima* and molybdenum enrichment on yield, quality and NUE in spinach plants, highlighted that SwE application boosts growth plant features. Without regard to the SwE treatments, the G4 and G5 landraces performed better than the other tested genotypes, while the G3 landrace had the lowest plant growth features. As reported by Weiner [39], this was probably because plants may grow efficiently until they achieve the threshold size for reproduction. Once they accomplish this size, a certain fraction of sources is assigned to reproduction. Indeed, the G3 landrace revealed the earliest female flower emission. On the other hand, when averaged over genotype, SwE application delayed first female flower emission, in accordance with the aforesaid vegetative vs. reproductive competitive activity.

There are researches on the favourable effect of diverse plant biostimulants on the marketable yield of various vegetables [22,28]. In this respect, the results of the present study are in agreement with those reported by Ali et al. [40], who underlined that *Ascophyllum nodosum*-based SwE improved tomato yield in a soilless system by 54% compared with the control. These results were related to the *A. nodosum* SwE polysaccharides content which in turn enhances yield promoting endogenous hormone homeostasis [41]. Outcomes agree with those of Colla et al. [28] who, studying the effect of different classes of biostimulants on yield and fruit quality of tomato cultivated under greenhouse, found that SwE 'Kelpak' increase marketable yield compared with the control. Furthermore, the results are sustained by Hussain et al. [42] who found that SwE of *Durvillaea potatorum* and *A. nodosum* augment tomato marketable yield. Data are also consistent with those of Hassan et al. [43] and La Bella et al. [23]. In this study, the marketable fruit increase prompted by the SwE

application was due to a higher fruit mean mass rather than to the higher number of marketable fruits. These results are in contrast with those of Colla et al. [28], who reported that SwE treatment improves the number of fruits per plant but did not affect fruit mean mass. Thus, we may hypothesise that the plant yield response to SwE application is genotype-dependent. G4 and G5 landraces revealed the lowest fruit yields. Averaged over genotype, SwE supply elicited young shoot production, both in terms of yield and number. In this respect, there are reports that brown seaweed extracts comprise phytohormones (IAA, cytokinin, GA, polyamines and ABA) [25,44,45]. Consequently, we may assume that the growth eliciting effects of SwE are linked to their effect. Wally et al. [46] stated that the SwE phytohormone-like action might also be triggered by chemical compounds included in the extract rather than by the phytohormones themselves. On the other hand, irrespective of the SwE application, G4 and G5 landraces had the highest young shoot yield traits. Thus, it seems that young shoot production is a genotype-associated trait and is negatively related to fruit production. Results showed that SwE treatment increased NUEys. These findings are coherent with those of Di Mola et al. [46] who investigated the effect of plant-based biostimulants on nitrogen use and uptake efficiency, yield and quality of leafy vegetables cultivated under different nitrogen regimes, found that treated plants had a higher NUE than untreated ones. Moreover, the results are in agreement with previous studies concerning the influence of *E. maxima* SwE application and molybdenum supply on yield, quality and NUE of spinach [23]. Outcomes showed that the SwE application enhanced fruit firmness. Overall, this is consistent with previous research on the influence of plant-based biostimulants on different tomato cultivars [47]. As reported by Basile et al. [47] and Cozzolino et al. [48] the SwE effect on fruit firmness is related to the higher Ca uptake and accumulation of SwE treated plants compared with the control. Indeed, as pointed out by Hocking et al. [49], calcium-pectin cross-links play an imperative function in defining the resistance of cell walls and, thus, the characteristics of the physical and structural fruit. Furthermore, since it is assumed that auxins partake in Ca transport and fruit uptake [49], the present study suggested that the SwE may have an auxin-like action in *L. siceraria*, improving calcium nutrition. Regardless of the SwE application, statistics showed a significant influence of the genotype on fruit firmness. Findings showed that SwE did not significantly affect young shoot SSC. In this respect, the results concur with those stated by Colla et al. [28] and La Bella et al. [23] who found no significant effect of the SwE on SSC on tomato and spinach, respectively. ANOVA displayed a significant effect of the genotype on young shoot SSC values. A similar response was previously reported for zucchini squash by Rouphael et al. [50] and Rouphael et al. [51], and it was related to a reduction in water accumulation in the fruit without influence on the biosynthesis and accumulation of organic solutes. Thus, since G2, G4 and G5 landraces gave the highest SSC young shoot yield and considering that G2, G4 and G5 were more productive than the other genotypes in terms of young shoots, but less performing in terms of fruit yields, it seems that the aforesaid landraces had a resource translocation mainly toward to the shoots rather than to the fruits compared to the G1 and G3 landraces.

The results displayed that the SwE application reduced N concentration in young shoots. In this respect, there are contrasting reports. Krouk et al. [52] and Castaings et al. [53] state that different *A. nodosum*-based SwE upregulated the expression of a nitrate transporter gene NRT1.1. which enhance nitrogen sensing and auxin transport. On the contrary, Rouphael et al. [38], found that SwE application does not significantly influence N concentration in tomato leaves. Thus, we may hypothesise that the plant N uptake and accumulation response to SwE supply, is significantly related to genotype and plant site. Results on minerals revealed that SwE treatment augmented P, K, Ca and Mg concentrations. These findings are partially coherent with those of Rouphael et al. [12], who found that *E. maxima* SwE application improve K and Mg concentrations in spinach plants. Furthermore, the outcomes concur with those of La Bella et al. [23], who evidenced that SwE treatment increase P, K and Mg concentration in spinach. As highlighted by Battacharyya et al. [29], this improved minerals uptake and build-up could be linked to a modification of the root

architecture, resulting in an enhanced plant mineral uptake. Moreover, Soppelsa et al. [54] pointed out that commercial SwE includes a compound named kahydrin, which modifies plasma membrane proton pumps and elicit the H+ ions excretion into the apoplast determining rhizosphere acidification, resulting in a higher metal ions plant availability [52,53].

Among plant secondary metabolites, ascorbic acid and polyphenols provide benefits to human health and, furthermore, play a crucial role in numerous plant life aspects [55]. The current study showed that SwE application upgraded ascorbic acid and polyphenols concentrations in young shoots of bottle gourd. These results sustained the outcomes of Rouphael et al. [12] and La Bella et al. [23] on spinach and those of Abbas et al. [56] on onion. As reported by Ertani et al. [57] and Rouphael et al. [58], the enhancement of bioactive components, such as ascorbic acid and phenols, could be related to the chalcone isomerase activity, which is a key enzyme in phytochemical homeostasis [59].