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Hybrid characterization procedure of Li-ion battery packs for wide frequency range dynamics applications
Electric Power Systems Research 166 (2019) 9–17
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Hybrid characterization procedure of Li-ion battery packs for wide frequency range dynamics applications
T
Sandra Castano-Solis , Daniel Serrano-Jimenez, Jesus Fraile-Ardanuy, Javier Sanz-Feito ⁎
Universidad Politécnica de Madrid, Madrid 28012, Spain
ARTICLE INFO
ABSTRACT
Keywords: Li-ion battery packs modeling Wide frequency range Battery packs dynamic performance Time–frequency tests
This paper presents a hybrid characterization procedure of battery packs capable of reproducing their behavior under different dynamic operation conditions. During the experimental procedure, both time and frequency tests are performed. These tests have been carried out on a commercial battery pack, instead of a single cell, in order to include packaging effects as well as performance of battery pack devices in real electrical applications. As a result of this procedure the battery pack model has been experimentally validated for four cases based on real electrified transportation and grid applications. Additionally, the model response has been compared with the widely used Partnership for a New Generation of Vehicles (PNGV) model. The validation tests show that the proposed battery pack model reproduces the dynamic battery response with better accuracy than the PNGV for all analyzed cases.
1. Introduction Energy storage devices are becoming key elements for the developing of electrical mobility and smart grids. Advancements in new materials with competitive energy and power densities fostered the increase of commercial storage devices [1]. Lithium based batteries are the most promising energy storage technology because of their high specific power and energy, and long lifetime [2,3]. Large-scale applications such as electrical vehicles (EVs) or supporting electrical systems during voltage dips, require the setting up multi-cell battery devices composed by several individual Li-ion cells in a combination of series and parallel connections, to provide the required nominal voltage and capacity [4–6]. In practice, each of these individual cells are slightly different among them (due to manufacturing process), which can jeopardize the overall operation. Battery packs require a battery management system (BMS) [7,8] to control their dynamic behavior, monitoring and assuring a safe operation (preventing that voltage, temperature and charging/discharging current from exceeding their strict limits) and maximizing the battery performance using different cell-balancing algorithms. These factors, along with the non-linearity of the electrochemical processes that occurs inside Li-ion batteries, make the modeling of battery packs a difficult task. Li-ion battery packs are forced to work under a variety of load cycles. Depending on the duration of these cycles, battery modules may operate over a wide range of dynamic regimes. For highly demanding
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dynamical applications such as EVs, electrical grids support, or frequency control in microgrids [9–11], battery packs performance is specially affected by the different processes that occurs inside the battery module. These electrochemical processes take place with different time constants which determine the transient response of the Li-ion battery module [12]. In electrified transportation and grid applications, there are three frequency ranges of special interest. The first one is related to the fast dynamic processes ranging from millisecond to second, which are relevant for the control and protection of the battery pack. The second refers to the operational regime associated to chargedischarge cycles, within a time horizon from minutes to some hours. Finally, aging effects due to chemical and mechanical degradation [3] that produce modification of the internal structure of the battery components and losses of active materials affect the state of charge (SOC) estimation (these phenomena take place during months or years). Because these processes occurs simultaneously during module operation, battery packs models should explicitly reflect these different time constants in order to accurately reproduce the dynamic behavior of the battery module. Battery simulations are commonly used to predict the battery behavior and to optimize the required storage capacity, reducing development time and cost. Battery models are also used by the BMS to estimate the SOC. Different battery models have been proposed depending on the different applications. The most common battery models for simulation of power applications are based on electrical
Corresponding author. E-mail address: [email protected] (S. Castano-Solis).
https://doi.org/10.1016/j.epsr.2018.09.017 Received 15 January 2018; Received in revised form 24 July 2018; Accepted 18 September 2018 0378-7796/ © 2018 Elsevier B.V. All rights reserved.
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equivalent circuits [13,14], because they directly represent the terminal voltage and current of the battery. There are two main strategies in the literature to determine the parameters of the equivalent circuit models, one based on time domain experimental tests and the other based on the frequency domain techniques. 1.1. Time domain modeling Time domain models are obtained from the analysis of the battery voltage and current evolution during tests, predicting its dynamic behavior as a function of time [15–17]. Some examples of these kind of models are the RC model, the Thevenin model, the PNGV model or Dual polarization (DP) model, among others [18,19]. These models are relatively easy to obtain, but their validity is usually limited to some specific dynamic profile applications [20]. Probably the most popular time-domain test to perform the battery modeling procedure is the current interruption test [20,21]. In this time-domain test, a series of charge/discharge pulses of constant current is applied to the battery, usually starting from 100% SOC to 0% SOC. The subsequent analysis of the variations of terminal voltage vs. output current allows supposedly determining the parameters of the battery equivalent circuit. With this method, however, it is difficult to achieve a very precise model, because it relies, to a great extent, upon the exact determination of some singular points on the terminal voltage record. In the first proposed circuits, only a first-order model (RC model), as it is presented in Ref. [22], can be fitted with reasonable accuracy. In spite of this model is able to reproduce the voltage behavior of the battery in steady-state conditions, it fails to reproduce the dynamical behavior of battery voltage when a pulsed or dynamical current profile is applied [17]. To improve battery model accuracy a second RC network (DP model) or other electrical elements such as capacitors, controlled current or voltage sources can be added (PNGV model). In this case the electrical circuit parameters are determined using advanced simulation tools and could be on-line updated using estimation algorithms like Kalman filter, sliding-mode observer or so on [19,23–25]. These estimation algorithms predict battery behavior as a function of time, based on battery voltage evolution during specific charge–discharge tests and previous measurements. Internal battery behavior is not considered, and therefore their validity is usually limited to a narrow bandwidth. In Ref. [23] a comparison of different electrical battery models has been done. This study reveals that computational times to find optimized parameters as a function of SOC increases by about four times when a second RC network is added. A similar analysis was performed by Refs. [17,19]. In these works, up to five different models of Li-ion batteries were used to simulate the voltage response of a battery in EVs. According to these comparative studies, equivalent circuit models that include two RC network or another electrical elements, improve simulation results in comparison with first-order models. These authors conclude that it is necessary to consider all internal processes of the battery in order to properly reproduce its dynamic performance. These studies show that it is necessary to use advanced algorithms to obtain an accurate model, thus involving even more computational time. Also, dynamical characteristics associated to electrochemical processes inside the battery can be taken into account in order to improve battery modules modeling.
Fig. 1. Li-ion battery characteristic discharge curve.
electrochemical system [26–28]. This excitation signal will cause the system to react, generating an AC voltage (if the excitation signal was initially a current) or AC current (if the excitation signal was initially a voltage). The AC excitation signal is usually applied as a variable frequency sweep. To keep linearity during the tests, the amplitude of the AC excitation signal applied to the battery cell is kept small enough (e.g. 5–10% of the rated voltage/current), as it is depicted in Fig. 1. In addition, this ripple is kept constant during the tests. The complex impedance is calculated as the ratio of the complex voltage and current (Z(ω) = Uac(ω)/Iac(ω)). The subsequent impedance calculation and model fitting is time consuming and complex, so it is recommendable to use an impedance analyzer, which generates the excitation signal and evaluates the complex impedance. To study the influence of SOC variations in impedance parameters, EIS tests are done at different operating points. Furthermore, these tests can also be carried out at different temperatures to analyze other behaviors like thermal runaway or aging effects. Although this procedure provides good simulation results, it presents some drawbacks. One of them is that the AC ripple used in most of commercial EIS analyzers are suitable for testing single battery cells of small capacity (maximum 100 mA), but it is too small to test full-size industrial battery devices. Also, some impedance elements (CPE or Warburg elements) [28] used to describe the electrochemical processes are only valid in the frequency domain and, for this reason, they must be approximated by real electrical elements in order to implement them in the standard simulation platforms. According to the above analysis, battery pack model accuracy can be improved if the internal behavior that occurs inside the cells is considered. Also, the modeling procedure must be applied to battery packs in order to reproduce realistic operation conditions. However, most of the work available in literature only presents individual cell testing and modeling, neglecting the interactions between elements within the battery pack, which is the final assembly needed for a largescale application, despite some recent investigations have revealed that considering BMS and packaging effects in Li-ion battery packs modeling, improves the model accuracy [29,30]. Moreover, only a few studies consider cells parameters variation. To accomplish these objectives, in this work, a battery pack modeling procedure based on time and frequency tests is proposed. The main contribution of this work is to develop a hybrid experimental procedure based on both time and frequency tests to reproduce the dynamic behavior of a battery pack under different dynamic requirements and realistic scenarios. In this way the processes that occur inside the cells are taking into account to obtain the model parameters of the battery pack. Also, the interactions of all components of the module are considered because the characterization process is performed upon the whole pack. As a result of this procedure an electrical circuit of the battery pack is validated applying requirements for two
1.2. Frequency domain modeling The other way to evaluate the model parameters is performing a frequency domain analysis by Electrochemical Impedance Spectroscopy Tests (EIS). Li-ion battery cells present a nonlinear discharging characteristic curve, as it is shown in Fig. 1. If the battery cell is operating around a specific operating point, it is possible to obtain a simple linear model, linearizing the non-linear characteristic curve. During EIS tests, a small AC excitation signal (either current or voltage) is applied to the 10
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Fig. 3. Battery pack model.
2.1. Frequency domain tests The typical EIS procedure has been modified to testing the battery pack. To do so, the frequency sweep signal generated by a commercial impedance analyzer is amplified using the experimental architecture setup proposed in Ref. [31]. To analyze the battery behavior as a function of SOC, it is crucial to maintain this state as constant as possible during the test, in order to determine the impedance parameters at each specific test point. When an AC ripple current is superimposed to a DC offset current component (Icc), the AC battery voltage presents an additional downward trend, because de battery discharges, so the initial SOC cannot be kept constant, as it can be seen in Fig. 4. For this reason, in the proposed experimental procedure no DC offset current component (Icc) is applied. The battery pack has been tested at frequencies ranging from 1 mHz to 5 kHz, with an AC ripple of 5 A (10% Inom) and it has been evaluated under five different SOC values (20%, 40%, 60%, 80% and 90%). Fig. 5 shows the EIS test result at a specific SOC (40%) plotted in a Nyquist
Fig. 2. Squematic battery layout.
main real scenarios: electrified transportation and electric grid applications. To compare the accuracy of this battery pack model, its response is compared with the simulation results of the PNGV model. The paper is organized as follows: Section 2 presents the time–frequency battery characterization procedure, according to the previous section analysis. Section 3 describes the experimental model validation using an experimental setup and shows the comparison of the battery model response with both the battery pack experimental measurements and the PNGV model. Finally, the conclusions are presented in Section 4. 2. Battery pack characterization The Li-ion battery pack tested in this work is a commercial device composed of four parallel-connected strings and a battery management system (BMS) which controls cell voltage, temperature and current of each series connection, cell balancing function, protection functions and charging and discharge processes. A schematic battery pack layout is shown in Fig. 2 and the main battery pack characteristics are shown in Table 1. In this work, a model composed by an electrical circuit and a SOC estimator has been used to reproduce the battery pack response, whose structure is shown in Fig. 3. In this model the dynamic electrochemical processes that occur inside the module are represented by a variable complex impedance, Zpack. The electrical elements of this impedance have been calculated by means of frequency domain analysis. To emulate the active behavior of the battery pack, a voltage source has been used, whose control law has been defined by the relationship between the state of charge (SOC) and the open circuit voltage (OCV). This relationship has been determined from time domain tests. The estimation of the SOC has been obtained by means of a current integration method. The input of the model is the current across of battery (i) and the output is the simulated voltage at battery terminals (umod1).
Fig. 4. Variation of SOC when a DC offset is imposed.
Table 1 Battery pack characteristics. Cells reference Pack rated voltage Pack maximum voltage Pack minimum cut-off voltage Pack capacity, Cn Pack maximum current Range of temperature (charge) Range of temperature (discharge)
MP 176065 Int 25.9 V 29.4 V (4.2 V/cell) 20.3 V (2.9 V/cell) 50 Ah 50 A −20 °C to 60 °C −30 °C to 55 °C
Fig. 5. EIS test result at 40% SOC. 11
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Table 3 OCV–SOC relationship. Disharge results
Charge results
OCV
SOC (%)
OCV
SOC (%)
29.40 28.77 28.23 27.79 27.40 26.89 26.65 26.49 26.33
100 90 80 70 60 50 40 30 20
29.28 29.06 28.65 28.09 27.62 27.08 26.76 26.57 26.33
90.27 87.64 80 70 60 50 40 30 20
2.2. Time domain tests The ideal voltage source that represents the active behavior of the battery pack has been defined by its OCV–SOC characteristic. This relationship has been calculated according to the following procedure: firstly, the battery pack is charged to 100% by using CC/CV charging method: a constant current of 25 A–0.5 C is applied until the voltage reach 29.4 V (pack maximum voltage). Next, the battery is discharged in pulses of 10 A (constant current) during 30 min followed by 90 min of relaxation time. Each pulse corresponds therefore to a SOC variation of 0.1 Cn (5 Ah). The OCV is measured at the end of each relaxation period. After the discharge test has concluded, the battery is charged again in pulses of 10 A (constant current) during 30 min each, followed by 90 min of relaxation time. The upper voltage level in the charging process is imposed at 29.4 V. Table 3 shows the values of discharge and charge tests. In Fig. 7 OCV–SOC characteristic is presented. In the case of charge results, it is not possible to reach 100% of SOC because the BMS limits the current during two last steps to protect the battery pack against over-voltage. This situation is represented by an almost flat line from 90% SOC. This behavior is different to that of a single cell testing because charge and discharge tests of the cell can be carried out from 100% to 0% of SOC as the BMS protection is not required. Results of discharge and charge tests do not show a representative deviation because Li-ion cells have low hysteresis. For this reason average values have been used to calculate the OCV–SOC relationship [33].
Fig. 6. Comparison of EIS tests results.
graph, in which the real part of the complex impedance, Z′, is represented along the x-axis and the imaginary part, Z″, along the downward-directed y-axis. The complex impedance of the battery pack changes as the frequency increases. Four frequency zones can be identified, low frequency, medium-low frequency, medium frequency and high frequency. These zones can be related with different electrochemical processes that occurs inside the battery pack, such as charge transfer, diffusion process, cycling process or inductive reactance effects, etc. [28,32]. The transition from medium frequency to high frequency is produced when the reactance of the complex impedance changes from negative values (capacitive behavior) to positive values (inductive behavior) in a specific point, called resonant frequency (fres) in the figure. Focusing on dynamic performance of the battery pack, only frequencies from 1 mHz to fres (316 Hz) are the most relevant for power applications, because, as explained above, control processes and operational regime occur in this frequency range. In these frequency ranges the pack impedance presents capacitive semi-circles that determine the different time constants. These capacitive behaviors can be represented by means of several RC networks connected in series. EIS tests results at different SOCs are presented in Fig. 6. These plots show that variation of SOC values affect the capacitive behavior of the battery pack at low and medium-low frequencies. Above medium frequencies, battery impedance parameters are not affected by changes in SOC. Table 2 presents the battery pack parameters calculated from EIS tests results. Ro represents the equivalent resistance of the battery pack, τ1, τ2 and τ3 corresponds to the time constants associated to low, medium-low and medium frequency ranges, respectively. Table 2 Battery pack impedance parameters. Element
20%SOC
40%SOC
60%SOC
80%SOC
90%SOC
Ro (Ω) τ1(R1//C1) (s) τ2(R2//C2) (s) τ3(R3//C3) (s)
0.039 23.40 0.295 0.0028
0.039 18.43 0.188 0.0030
0.039 15.71 0.136 0.0030
0.039 11.39 0.116 0.0029
0.039 10.92 0.106 0.0028
Fig. 7. OCV–SOC curve.
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Fig. 8. Proposed battery pack model.
Fig. 9. Experimental test bench.
2.3. Battery pack model
has been carried out for high SOCs (80–70%) and for medium SOCs (40–60%) values to analyze the dynamic pack behavior at different SOCs conditions. Two different scenarios for stationary applications were initially analyzed. The first one is the simulation of a load frequency control (LFC) application. This simulation reproduces fastchanging behavior (typically time steps ranging from 0.2 ms to 10 s) in case of grid frequency control or fault detection. This application involves high dynamic transients so it is determined by the behavior at medium frequencies (τ3). The current profile associated to the LFC application is based on the experimental results presented in Ref. [34] where a hybrid ac/dc micro-grid is analyzed. The second one is a battery based UPS (uninterruptible power supply) operation. The UPS works as an energy support for electrical users (time duration less than 30 min). In this case the dynamic behavior corresponds to low and medium-low frequencies. In the same way, to evaluate electrical vehicles (EVs) dynamics, two different driving cycles were analyzed. The first one is a standardized New York City cycle (NYCC) which reproduces a driving route in New York City during 598 s, with a total distance of 1902.8 m and average speed of 11.5 km/h. The second one is a real driving condition, defined by the recording of real GPS traces measurements during an extra-urban route (EUR). These data was obtained by authors when driving on a Madrid highway. It has duration of 900 s, a maximum speed of 120 km/ h and an average speed above 50 km/h. In these applications the dynamic requirements cover all the different time constants of the battery pack impedance. The current profiles of the applications simulated that represent these cases are shown in Fig. 10. The signals associated to the current profiles previously recorded, have been used as the input of the proposed battery pack model (Fig. 8) defined in Matlab/Simulink®. The voltage response of the battery pack model has been compared to the output of the PNGV model and to the real voltage measurements at pack terminals. The PNGV is a widely used model proposed by the Partnership for a New Generation of Vehicles to simulate the battery behavior in electrical vehicles. In this model the first-order circuit topology is improved by the introduction of a constant capacitor C that simulates the variation of the battery capacity under variation in the SOC. In this work the PNGV model has been implemented in Matlab/Simulink® according to the circuit presented in Fig. 11. The circuit parameters were calculated from time-domain tests following the procedure described in Refs. [35,36]. Figs. 12 and 13 show the comparison between the voltage response of the models and the experimental voltage measurements for the grid and EV applications. In these graphs, upack is the real battery pack voltage, umod1 corresponds to the voltage simulated by the proposed model and umod2 corresponds to the response obtained according to the PNGV model. The simulations results are listed in Table 4.
The model determined from time–frequency tests results is shown in Fig. 8. The voltage at battery pack terminals (umod1) is simulated by Eq. (1). SOC0 represents the initial value of SOC and Cn the rated capacity of the battery module. The impedance Zpack (as explained in Section 2.1) is composed by Ro, τ1 (associated to low frequency), τ2 (for lowmedium frequencies) and τ3 (medium frequency range). Because these parameters depend on SOC the parameters calculation function is added to guarantee that the model reproduces the dynamic behavior of the battery pack for different SOC conditions.
umod1 (SOC , t ) = OCV (SOC , t )
uRo (SOC , t )
uC 2 (SOC , t )
uC1 (SOC , t )
uC 3 (SOC , t )
(1)
where: (2)
uRo (SOC , t ) = Ro (SOC )·i (t ) uC1 (SOC , t ) =
1 · i (t ) C1 (SOC )
uC1 (SOC ) · dt RC1 (SOC )
(3)
uC 2 (SOC , t ) =
1 · i (t ) C2 (SOC )
uC 2 (SOC ) · dt RC 2 (SOC )
(4)
uC 3 (SOC , t ) =
1 · i (t ) C3 (SOC )
uC3 (SOC ) · dt RC3 (SOC )
(5)
3. Experimental model validation The resulting battery pack model accuracy has been tested by means of four different experimental tests. Each test is characterized by a set of different dynamic requirements, in order to check the ability of the model to reproduce the behavior of the battery pack. The test bench, thoroughly described in Ref. [31], is composed by a programmable DC power source in parallel with a programmable DC electronic load (hardware emulation) that represents a two-quadrant active (regenerative) load. The different dynamic requirements are reproduced by means of four load profiles implemented in a Matlab/Simulink® environment (software simulation), the resulting output current of each profile is applied to the real battery pack. The dSpace-based control system generates the current references for the electronic load (during battery discharge) and the source (during energy regeneration) where applicable, and manages the whole data acquisition process. Fig. 9 shows a picture of the experimental test bench. As a result of this experimental simulation, the current profile and the voltage response at pack terminals are recorded. Each simulation 13
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Fig. 10. Current profiles analyzed.
behavior of these batteries over a wide frequency range. The experimental procedure is based upon two types of measurements: the modeling of the internal voltage source is made in the time domain, by means of pulsed current test, whilst the modeling of the internal impedance is performed in the frequency domain, by impedance spectroscopy methods. With this approach, the electrochemical behavior that affects the dynamic response of the battery pack has been represented by means of three RC networks associated to three different frequency bands (low-, medium- and high frequencies). These six parameters along with the ohmic resistance and the internal voltage source are also dependent of the battery state-of-charge, and have been calculated from experimental measurements made on the battery pack instead of single cell measurements. This topology keeps the computational burden of the model under reasonable limits. Also, the model based on an electrical circuit is easily integrated in simulation platforms such as Matlab/Simulink®. The proposed experimental procedure can be used to model any Li-ion battery pack regardless its configuration (series or parallel connections), the limitation is imposed by the maximum power of the experimental test bench, 9 kW in this case. The model response was experimentally validated using an experimental platform which allows reproducing real operating conditions of multi-cells battery packs. Four cases representing real applications of battery packs to electrical grids and electrified transportation have been analyzed, considering also different SOC conditions. Besides, an additional comparison with the response of the PNGV model has been done.
Fig. 11. PNGV circuit.
As it can be observed, the time-based model is not able to reproduce properly the behavior of the battery pack for applications that include high dynamics transients such as LFC NYCC and EUR. Only in the UPS application that presents low frequency transients the PNGV model has a similar accuracy that the proposed model. According to the results obatined, the proposed model reproduces the voltage measured at battery pack terminals with high accuracy for all the applications analyzed. The maximum and the root-mean-square errors are always lower than the ones obtained following the PNGV model. This results indicate that the hybrid time–frequency procedure proposed in this work is able to reproduce the voltage response with better accuracy than the pure time-based approaches. 4. Conclusions In this paper, a hybrid characterization procedure for Li-ion battery packs has been presented with the aim of reproduce the dynamic 14
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Fig. 12. Simulations of grid applications.
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Fig. 13. Simulations of EV applications.
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Table 4 Comparison of models response. Application
SOC test (%)
Max. error (%) mod1
RMSE error (%) mod1
Max. error (%) mod2
RMSE error (%) mod2
LFC (grid) LFC (grid) UPS (grid) UPS (grid) NYCC (EV) NYCC (EV) EUR (EV) EUR (EV)
72 48 78 53 78 47 79 58
0.16 0.28 0.15 0.23 0.68 0.70 0.51 0.43
0.12 0.23 0.13 0.19 0.55 0.54 0.45 0.35
2.11 2.63 0.21 1.81 3.12 3.77 1.32 2.16
1.94 2.25 0.16 1.45 2.45 2.65 0.98 1.95
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According to the experimental simulations results, the hybrid approach presents better accuracy than the PNGV model, used as benchmarking reference in all simulated cases. In the case of applications with high dynamics requirements such as load frequency control and EVs the proposed model shows an excellent fitting of the real battery pack voltage compared with the PNGV model. This fact demonstrates that considering the different time constants associated to inside behavior of battery packs improves modeling results. Thus, the proposed procedure improves the model accuracy and applicability, and reproduces the dynamic behavior of Li-ion battery packs under different application’s requirements. References [1] A. Ajanovic, The future of electric vehicles: prospects and impediments, Wiley Interdiscip. Rev. Energy Environ. 4 (6) (2015) 236–521. [2] M.D. Galus, et al., The role of electric vehicles in smart grids, Wiley Interdiscip. Rev. Energy Environ. 2 (4) (2013) 384–400. [3] A. Barré, et al., A review on lithium-ion battery ageing mechanisms and estimations for automotive applications, J. Power Sources 241 (2013) 680–689. [4] Y. Shang, et al., An automatic equalizer based on forward–flyback converter for series-connected battery strings, IEEE Trans. Ind. Electron. (2017) (in press). [5] J.V. Barreras, et al., Evaluation of a novel BEV concept based on fixed and swappable Li-ion battery packs, IEEE Trans. Ind. Appl. 52 (6) (2016) 5073–5085. [6] K. Takei, et al., Series-connected multi-cell operation of lithium-ion cells by floating method, J. Power Sources 68 (2) (1997) 427–431. [7] L. Ungurean, G. Carstoiu, M.V. Micea, V. Groza, Battery state of health estimation: a structured review of models, methods and commercial devices, Int. J. Energy Res. 41 (2017) 151–181. [8] X. Lin, A.G. Stefanopoulou, Y. Li, R.D. Anderson, State of charge imbalance estimation for battery strings under reduced voltage sensing, IEEE Trans. Control Syst. Technol. 23 (3) (2015) 1052–1062. [9] H. Rahimi-Eichi, F. Baronti, M.Y. Chow, Online adaptive parameter identification and state-of-charge coestimation for lithium-polymer battery cells, IEEE Trans. Ind. Electron. 61 (4) (2014) 2053–2061. [10] R.C. Dugan, J.A. Taylor, D. Montenegro, Energy storage modeling for distribution planning, IEEE Trans. Ind. Appl. 53 (2) (2017) 954–962. [11] Q. Xu, et al., A decentralized dynamic power sharing strategy for hybrid energy storage system in autonomous DC microgrid, IEEE Trans. Ind. Electron. 64 (7) (2017) 5930–5941. [12] A. Jossen, Fundamentals of battery dynamics, J. Power Sources 154 (2006) 530–538. [13] A. Shafiei, A. Momeni, S. Williamson, Battery modeling approaches and management techniques for plug-in hybrid electric vehicles, Vehicle Power and Propulsion
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Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
Hybrid characterization procedure of Li-ion battery packs for wide frequency range dynamics applications
T
Sandra Castano-Solis , Daniel Serrano-Jimenez, Jesus Fraile-Ardanuy, Javier Sanz-Feito ⁎
Universidad Politécnica de Madrid, Madrid 28012, Spain
ARTICLE INFO
ABSTRACT
Keywords: Li-ion battery packs modeling Wide frequency range Battery packs dynamic performance Time–frequency tests
This paper presents a hybrid characterization procedure of battery packs capable of reproducing their behavior under different dynamic operation conditions. During the experimental procedure, both time and frequency tests are performed. These tests have been carried out on a commercial battery pack, instead of a single cell, in order to include packaging effects as well as performance of battery pack devices in real electrical applications. As a result of this procedure the battery pack model has been experimentally validated for four cases based on real electrified transportation and grid applications. Additionally, the model response has been compared with the widely used Partnership for a New Generation of Vehicles (PNGV) model. The validation tests show that the proposed battery pack model reproduces the dynamic battery response with better accuracy than the PNGV for all analyzed cases.
1. Introduction Energy storage devices are becoming key elements for the developing of electrical mobility and smart grids. Advancements in new materials with competitive energy and power densities fostered the increase of commercial storage devices [1]. Lithium based batteries are the most promising energy storage technology because of their high specific power and energy, and long lifetime [2,3]. Large-scale applications such as electrical vehicles (EVs) or supporting electrical systems during voltage dips, require the setting up multi-cell battery devices composed by several individual Li-ion cells in a combination of series and parallel connections, to provide the required nominal voltage and capacity [4–6]. In practice, each of these individual cells are slightly different among them (due to manufacturing process), which can jeopardize the overall operation. Battery packs require a battery management system (BMS) [7,8] to control their dynamic behavior, monitoring and assuring a safe operation (preventing that voltage, temperature and charging/discharging current from exceeding their strict limits) and maximizing the battery performance using different cell-balancing algorithms. These factors, along with the non-linearity of the electrochemical processes that occurs inside Li-ion batteries, make the modeling of battery packs a difficult task. Li-ion battery packs are forced to work under a variety of load cycles. Depending on the duration of these cycles, battery modules may operate over a wide range of dynamic regimes. For highly demanding
⁎
dynamical applications such as EVs, electrical grids support, or frequency control in microgrids [9–11], battery packs performance is specially affected by the different processes that occurs inside the battery module. These electrochemical processes take place with different time constants which determine the transient response of the Li-ion battery module [12]. In electrified transportation and grid applications, there are three frequency ranges of special interest. The first one is related to the fast dynamic processes ranging from millisecond to second, which are relevant for the control and protection of the battery pack. The second refers to the operational regime associated to chargedischarge cycles, within a time horizon from minutes to some hours. Finally, aging effects due to chemical and mechanical degradation [3] that produce modification of the internal structure of the battery components and losses of active materials affect the state of charge (SOC) estimation (these phenomena take place during months or years). Because these processes occurs simultaneously during module operation, battery packs models should explicitly reflect these different time constants in order to accurately reproduce the dynamic behavior of the battery module. Battery simulations are commonly used to predict the battery behavior and to optimize the required storage capacity, reducing development time and cost. Battery models are also used by the BMS to estimate the SOC. Different battery models have been proposed depending on the different applications. The most common battery models for simulation of power applications are based on electrical
Corresponding author. E-mail address: [email protected] (S. Castano-Solis).
https://doi.org/10.1016/j.epsr.2018.09.017 Received 15 January 2018; Received in revised form 24 July 2018; Accepted 18 September 2018 0378-7796/ © 2018 Elsevier B.V. All rights reserved.
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equivalent circuits [13,14], because they directly represent the terminal voltage and current of the battery. There are two main strategies in the literature to determine the parameters of the equivalent circuit models, one based on time domain experimental tests and the other based on the frequency domain techniques. 1.1. Time domain modeling Time domain models are obtained from the analysis of the battery voltage and current evolution during tests, predicting its dynamic behavior as a function of time [15–17]. Some examples of these kind of models are the RC model, the Thevenin model, the PNGV model or Dual polarization (DP) model, among others [18,19]. These models are relatively easy to obtain, but their validity is usually limited to some specific dynamic profile applications [20]. Probably the most popular time-domain test to perform the battery modeling procedure is the current interruption test [20,21]. In this time-domain test, a series of charge/discharge pulses of constant current is applied to the battery, usually starting from 100% SOC to 0% SOC. The subsequent analysis of the variations of terminal voltage vs. output current allows supposedly determining the parameters of the battery equivalent circuit. With this method, however, it is difficult to achieve a very precise model, because it relies, to a great extent, upon the exact determination of some singular points on the terminal voltage record. In the first proposed circuits, only a first-order model (RC model), as it is presented in Ref. [22], can be fitted with reasonable accuracy. In spite of this model is able to reproduce the voltage behavior of the battery in steady-state conditions, it fails to reproduce the dynamical behavior of battery voltage when a pulsed or dynamical current profile is applied [17]. To improve battery model accuracy a second RC network (DP model) or other electrical elements such as capacitors, controlled current or voltage sources can be added (PNGV model). In this case the electrical circuit parameters are determined using advanced simulation tools and could be on-line updated using estimation algorithms like Kalman filter, sliding-mode observer or so on [19,23–25]. These estimation algorithms predict battery behavior as a function of time, based on battery voltage evolution during specific charge–discharge tests and previous measurements. Internal battery behavior is not considered, and therefore their validity is usually limited to a narrow bandwidth. In Ref. [23] a comparison of different electrical battery models has been done. This study reveals that computational times to find optimized parameters as a function of SOC increases by about four times when a second RC network is added. A similar analysis was performed by Refs. [17,19]. In these works, up to five different models of Li-ion batteries were used to simulate the voltage response of a battery in EVs. According to these comparative studies, equivalent circuit models that include two RC network or another electrical elements, improve simulation results in comparison with first-order models. These authors conclude that it is necessary to consider all internal processes of the battery in order to properly reproduce its dynamic performance. These studies show that it is necessary to use advanced algorithms to obtain an accurate model, thus involving even more computational time. Also, dynamical characteristics associated to electrochemical processes inside the battery can be taken into account in order to improve battery modules modeling.
Fig. 1. Li-ion battery characteristic discharge curve.
electrochemical system [26–28]. This excitation signal will cause the system to react, generating an AC voltage (if the excitation signal was initially a current) or AC current (if the excitation signal was initially a voltage). The AC excitation signal is usually applied as a variable frequency sweep. To keep linearity during the tests, the amplitude of the AC excitation signal applied to the battery cell is kept small enough (e.g. 5–10% of the rated voltage/current), as it is depicted in Fig. 1. In addition, this ripple is kept constant during the tests. The complex impedance is calculated as the ratio of the complex voltage and current (Z(ω) = Uac(ω)/Iac(ω)). The subsequent impedance calculation and model fitting is time consuming and complex, so it is recommendable to use an impedance analyzer, which generates the excitation signal and evaluates the complex impedance. To study the influence of SOC variations in impedance parameters, EIS tests are done at different operating points. Furthermore, these tests can also be carried out at different temperatures to analyze other behaviors like thermal runaway or aging effects. Although this procedure provides good simulation results, it presents some drawbacks. One of them is that the AC ripple used in most of commercial EIS analyzers are suitable for testing single battery cells of small capacity (maximum 100 mA), but it is too small to test full-size industrial battery devices. Also, some impedance elements (CPE or Warburg elements) [28] used to describe the electrochemical processes are only valid in the frequency domain and, for this reason, they must be approximated by real electrical elements in order to implement them in the standard simulation platforms. According to the above analysis, battery pack model accuracy can be improved if the internal behavior that occurs inside the cells is considered. Also, the modeling procedure must be applied to battery packs in order to reproduce realistic operation conditions. However, most of the work available in literature only presents individual cell testing and modeling, neglecting the interactions between elements within the battery pack, which is the final assembly needed for a largescale application, despite some recent investigations have revealed that considering BMS and packaging effects in Li-ion battery packs modeling, improves the model accuracy [29,30]. Moreover, only a few studies consider cells parameters variation. To accomplish these objectives, in this work, a battery pack modeling procedure based on time and frequency tests is proposed. The main contribution of this work is to develop a hybrid experimental procedure based on both time and frequency tests to reproduce the dynamic behavior of a battery pack under different dynamic requirements and realistic scenarios. In this way the processes that occur inside the cells are taking into account to obtain the model parameters of the battery pack. Also, the interactions of all components of the module are considered because the characterization process is performed upon the whole pack. As a result of this procedure an electrical circuit of the battery pack is validated applying requirements for two
1.2. Frequency domain modeling The other way to evaluate the model parameters is performing a frequency domain analysis by Electrochemical Impedance Spectroscopy Tests (EIS). Li-ion battery cells present a nonlinear discharging characteristic curve, as it is shown in Fig. 1. If the battery cell is operating around a specific operating point, it is possible to obtain a simple linear model, linearizing the non-linear characteristic curve. During EIS tests, a small AC excitation signal (either current or voltage) is applied to the 10
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Fig. 3. Battery pack model.
2.1. Frequency domain tests The typical EIS procedure has been modified to testing the battery pack. To do so, the frequency sweep signal generated by a commercial impedance analyzer is amplified using the experimental architecture setup proposed in Ref. [31]. To analyze the battery behavior as a function of SOC, it is crucial to maintain this state as constant as possible during the test, in order to determine the impedance parameters at each specific test point. When an AC ripple current is superimposed to a DC offset current component (Icc), the AC battery voltage presents an additional downward trend, because de battery discharges, so the initial SOC cannot be kept constant, as it can be seen in Fig. 4. For this reason, in the proposed experimental procedure no DC offset current component (Icc) is applied. The battery pack has been tested at frequencies ranging from 1 mHz to 5 kHz, with an AC ripple of 5 A (10% Inom) and it has been evaluated under five different SOC values (20%, 40%, 60%, 80% and 90%). Fig. 5 shows the EIS test result at a specific SOC (40%) plotted in a Nyquist
Fig. 2. Squematic battery layout.
main real scenarios: electrified transportation and electric grid applications. To compare the accuracy of this battery pack model, its response is compared with the simulation results of the PNGV model. The paper is organized as follows: Section 2 presents the time–frequency battery characterization procedure, according to the previous section analysis. Section 3 describes the experimental model validation using an experimental setup and shows the comparison of the battery model response with both the battery pack experimental measurements and the PNGV model. Finally, the conclusions are presented in Section 4. 2. Battery pack characterization The Li-ion battery pack tested in this work is a commercial device composed of four parallel-connected strings and a battery management system (BMS) which controls cell voltage, temperature and current of each series connection, cell balancing function, protection functions and charging and discharge processes. A schematic battery pack layout is shown in Fig. 2 and the main battery pack characteristics are shown in Table 1. In this work, a model composed by an electrical circuit and a SOC estimator has been used to reproduce the battery pack response, whose structure is shown in Fig. 3. In this model the dynamic electrochemical processes that occur inside the module are represented by a variable complex impedance, Zpack. The electrical elements of this impedance have been calculated by means of frequency domain analysis. To emulate the active behavior of the battery pack, a voltage source has been used, whose control law has been defined by the relationship between the state of charge (SOC) and the open circuit voltage (OCV). This relationship has been determined from time domain tests. The estimation of the SOC has been obtained by means of a current integration method. The input of the model is the current across of battery (i) and the output is the simulated voltage at battery terminals (umod1).
Fig. 4. Variation of SOC when a DC offset is imposed.
Table 1 Battery pack characteristics. Cells reference Pack rated voltage Pack maximum voltage Pack minimum cut-off voltage Pack capacity, Cn Pack maximum current Range of temperature (charge) Range of temperature (discharge)
MP 176065 Int 25.9 V 29.4 V (4.2 V/cell) 20.3 V (2.9 V/cell) 50 Ah 50 A −20 °C to 60 °C −30 °C to 55 °C
Fig. 5. EIS test result at 40% SOC. 11
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Table 3 OCV–SOC relationship. Disharge results
Charge results
OCV
SOC (%)
OCV
SOC (%)
29.40 28.77 28.23 27.79 27.40 26.89 26.65 26.49 26.33
100 90 80 70 60 50 40 30 20
29.28 29.06 28.65 28.09 27.62 27.08 26.76 26.57 26.33
90.27 87.64 80 70 60 50 40 30 20
2.2. Time domain tests The ideal voltage source that represents the active behavior of the battery pack has been defined by its OCV–SOC characteristic. This relationship has been calculated according to the following procedure: firstly, the battery pack is charged to 100% by using CC/CV charging method: a constant current of 25 A–0.5 C is applied until the voltage reach 29.4 V (pack maximum voltage). Next, the battery is discharged in pulses of 10 A (constant current) during 30 min followed by 90 min of relaxation time. Each pulse corresponds therefore to a SOC variation of 0.1 Cn (5 Ah). The OCV is measured at the end of each relaxation period. After the discharge test has concluded, the battery is charged again in pulses of 10 A (constant current) during 30 min each, followed by 90 min of relaxation time. The upper voltage level in the charging process is imposed at 29.4 V. Table 3 shows the values of discharge and charge tests. In Fig. 7 OCV–SOC characteristic is presented. In the case of charge results, it is not possible to reach 100% of SOC because the BMS limits the current during two last steps to protect the battery pack against over-voltage. This situation is represented by an almost flat line from 90% SOC. This behavior is different to that of a single cell testing because charge and discharge tests of the cell can be carried out from 100% to 0% of SOC as the BMS protection is not required. Results of discharge and charge tests do not show a representative deviation because Li-ion cells have low hysteresis. For this reason average values have been used to calculate the OCV–SOC relationship [33].
Fig. 6. Comparison of EIS tests results.
graph, in which the real part of the complex impedance, Z′, is represented along the x-axis and the imaginary part, Z″, along the downward-directed y-axis. The complex impedance of the battery pack changes as the frequency increases. Four frequency zones can be identified, low frequency, medium-low frequency, medium frequency and high frequency. These zones can be related with different electrochemical processes that occurs inside the battery pack, such as charge transfer, diffusion process, cycling process or inductive reactance effects, etc. [28,32]. The transition from medium frequency to high frequency is produced when the reactance of the complex impedance changes from negative values (capacitive behavior) to positive values (inductive behavior) in a specific point, called resonant frequency (fres) in the figure. Focusing on dynamic performance of the battery pack, only frequencies from 1 mHz to fres (316 Hz) are the most relevant for power applications, because, as explained above, control processes and operational regime occur in this frequency range. In these frequency ranges the pack impedance presents capacitive semi-circles that determine the different time constants. These capacitive behaviors can be represented by means of several RC networks connected in series. EIS tests results at different SOCs are presented in Fig. 6. These plots show that variation of SOC values affect the capacitive behavior of the battery pack at low and medium-low frequencies. Above medium frequencies, battery impedance parameters are not affected by changes in SOC. Table 2 presents the battery pack parameters calculated from EIS tests results. Ro represents the equivalent resistance of the battery pack, τ1, τ2 and τ3 corresponds to the time constants associated to low, medium-low and medium frequency ranges, respectively. Table 2 Battery pack impedance parameters. Element
20%SOC
40%SOC
60%SOC
80%SOC
90%SOC
Ro (Ω) τ1(R1//C1) (s) τ2(R2//C2) (s) τ3(R3//C3) (s)
0.039 23.40 0.295 0.0028
0.039 18.43 0.188 0.0030
0.039 15.71 0.136 0.0030
0.039 11.39 0.116 0.0029
0.039 10.92 0.106 0.0028
Fig. 7. OCV–SOC curve.
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Fig. 8. Proposed battery pack model.
Fig. 9. Experimental test bench.
2.3. Battery pack model
has been carried out for high SOCs (80–70%) and for medium SOCs (40–60%) values to analyze the dynamic pack behavior at different SOCs conditions. Two different scenarios for stationary applications were initially analyzed. The first one is the simulation of a load frequency control (LFC) application. This simulation reproduces fastchanging behavior (typically time steps ranging from 0.2 ms to 10 s) in case of grid frequency control or fault detection. This application involves high dynamic transients so it is determined by the behavior at medium frequencies (τ3). The current profile associated to the LFC application is based on the experimental results presented in Ref. [34] where a hybrid ac/dc micro-grid is analyzed. The second one is a battery based UPS (uninterruptible power supply) operation. The UPS works as an energy support for electrical users (time duration less than 30 min). In this case the dynamic behavior corresponds to low and medium-low frequencies. In the same way, to evaluate electrical vehicles (EVs) dynamics, two different driving cycles were analyzed. The first one is a standardized New York City cycle (NYCC) which reproduces a driving route in New York City during 598 s, with a total distance of 1902.8 m and average speed of 11.5 km/h. The second one is a real driving condition, defined by the recording of real GPS traces measurements during an extra-urban route (EUR). These data was obtained by authors when driving on a Madrid highway. It has duration of 900 s, a maximum speed of 120 km/ h and an average speed above 50 km/h. In these applications the dynamic requirements cover all the different time constants of the battery pack impedance. The current profiles of the applications simulated that represent these cases are shown in Fig. 10. The signals associated to the current profiles previously recorded, have been used as the input of the proposed battery pack model (Fig. 8) defined in Matlab/Simulink®. The voltage response of the battery pack model has been compared to the output of the PNGV model and to the real voltage measurements at pack terminals. The PNGV is a widely used model proposed by the Partnership for a New Generation of Vehicles to simulate the battery behavior in electrical vehicles. In this model the first-order circuit topology is improved by the introduction of a constant capacitor C that simulates the variation of the battery capacity under variation in the SOC. In this work the PNGV model has been implemented in Matlab/Simulink® according to the circuit presented in Fig. 11. The circuit parameters were calculated from time-domain tests following the procedure described in Refs. [35,36]. Figs. 12 and 13 show the comparison between the voltage response of the models and the experimental voltage measurements for the grid and EV applications. In these graphs, upack is the real battery pack voltage, umod1 corresponds to the voltage simulated by the proposed model and umod2 corresponds to the response obtained according to the PNGV model. The simulations results are listed in Table 4.
The model determined from time–frequency tests results is shown in Fig. 8. The voltage at battery pack terminals (umod1) is simulated by Eq. (1). SOC0 represents the initial value of SOC and Cn the rated capacity of the battery module. The impedance Zpack (as explained in Section 2.1) is composed by Ro, τ1 (associated to low frequency), τ2 (for lowmedium frequencies) and τ3 (medium frequency range). Because these parameters depend on SOC the parameters calculation function is added to guarantee that the model reproduces the dynamic behavior of the battery pack for different SOC conditions.
umod1 (SOC , t ) = OCV (SOC , t )
uRo (SOC , t )
uC 2 (SOC , t )
uC1 (SOC , t )
uC 3 (SOC , t )
(1)
where: (2)
uRo (SOC , t ) = Ro (SOC )·i (t ) uC1 (SOC , t ) =
1 · i (t ) C1 (SOC )
uC1 (SOC ) · dt RC1 (SOC )
(3)
uC 2 (SOC , t ) =
1 · i (t ) C2 (SOC )
uC 2 (SOC ) · dt RC 2 (SOC )
(4)
uC 3 (SOC , t ) =
1 · i (t ) C3 (SOC )
uC3 (SOC ) · dt RC3 (SOC )
(5)
3. Experimental model validation The resulting battery pack model accuracy has been tested by means of four different experimental tests. Each test is characterized by a set of different dynamic requirements, in order to check the ability of the model to reproduce the behavior of the battery pack. The test bench, thoroughly described in Ref. [31], is composed by a programmable DC power source in parallel with a programmable DC electronic load (hardware emulation) that represents a two-quadrant active (regenerative) load. The different dynamic requirements are reproduced by means of four load profiles implemented in a Matlab/Simulink® environment (software simulation), the resulting output current of each profile is applied to the real battery pack. The dSpace-based control system generates the current references for the electronic load (during battery discharge) and the source (during energy regeneration) where applicable, and manages the whole data acquisition process. Fig. 9 shows a picture of the experimental test bench. As a result of this experimental simulation, the current profile and the voltage response at pack terminals are recorded. Each simulation 13
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Fig. 10. Current profiles analyzed.
behavior of these batteries over a wide frequency range. The experimental procedure is based upon two types of measurements: the modeling of the internal voltage source is made in the time domain, by means of pulsed current test, whilst the modeling of the internal impedance is performed in the frequency domain, by impedance spectroscopy methods. With this approach, the electrochemical behavior that affects the dynamic response of the battery pack has been represented by means of three RC networks associated to three different frequency bands (low-, medium- and high frequencies). These six parameters along with the ohmic resistance and the internal voltage source are also dependent of the battery state-of-charge, and have been calculated from experimental measurements made on the battery pack instead of single cell measurements. This topology keeps the computational burden of the model under reasonable limits. Also, the model based on an electrical circuit is easily integrated in simulation platforms such as Matlab/Simulink®. The proposed experimental procedure can be used to model any Li-ion battery pack regardless its configuration (series or parallel connections), the limitation is imposed by the maximum power of the experimental test bench, 9 kW in this case. The model response was experimentally validated using an experimental platform which allows reproducing real operating conditions of multi-cells battery packs. Four cases representing real applications of battery packs to electrical grids and electrified transportation have been analyzed, considering also different SOC conditions. Besides, an additional comparison with the response of the PNGV model has been done.
Fig. 11. PNGV circuit.
As it can be observed, the time-based model is not able to reproduce properly the behavior of the battery pack for applications that include high dynamics transients such as LFC NYCC and EUR. Only in the UPS application that presents low frequency transients the PNGV model has a similar accuracy that the proposed model. According to the results obatined, the proposed model reproduces the voltage measured at battery pack terminals with high accuracy for all the applications analyzed. The maximum and the root-mean-square errors are always lower than the ones obtained following the PNGV model. This results indicate that the hybrid time–frequency procedure proposed in this work is able to reproduce the voltage response with better accuracy than the pure time-based approaches. 4. Conclusions In this paper, a hybrid characterization procedure for Li-ion battery packs has been presented with the aim of reproduce the dynamic 14
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Fig. 12. Simulations of grid applications.
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Fig. 13. Simulations of EV applications.
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Table 4 Comparison of models response. Application
SOC test (%)
Max. error (%) mod1
RMSE error (%) mod1
Max. error (%) mod2
RMSE error (%) mod2
LFC (grid) LFC (grid) UPS (grid) UPS (grid) NYCC (EV) NYCC (EV) EUR (EV) EUR (EV)
72 48 78 53 78 47 79 58
0.16 0.28 0.15 0.23 0.68 0.70 0.51 0.43
0.12 0.23 0.13 0.19 0.55 0.54 0.45 0.35
2.11 2.63 0.21 1.81 3.12 3.77 1.32 2.16
1.94 2.25 0.16 1.45 2.45 2.65 0.98 1.95
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