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(a) Equivalent Circuit Model; (b) Schematic of four cells connected in parallel; (c) Mesh junction for cell n; (d) Mesh Loop for cell n.
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Variations in cell properties are unavoidable and can be caused by manufacturing tolerances and usage conditions. As a result of this, cells connected in series may have different voltages and states of charge that limit the energy and power capability of the complete battery pack. Methods of removing this energy imbalance have been extensively rep...
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Context 1
... single cell ECM consists of several elements, as shown in Fig. 1a: the open circuit voltage v OC , internal resistance R D and a resistor-capacitor (RC) pair, which is a resistor R p and capacitor C p in parallel. Multiple RC pairs in series can be used depending on the bandwidth and fidelity of the response required. Eq. (1) shows that for a given current i cell , the terminal voltage v t is ...Context 2
... ECM in Section 2.1 can be expanded to incorporate any number of cells in parallel. For this derivation, four cells with one RC pair each is used, but the methodology is generic and can be extended to any number of cells or RC pairs. Fig. 1b presents a schematic of four cells in parallel with an interconnection resis- tance (R c ) between each terminal. Each cell is represented by its own ECM as in Fig. ...Context 3
... number of cells in parallel. For this derivation, four cells with one RC pair each is used, but the methodology is generic and can be extended to any number of cells or RC pairs. Fig. 1b presents a schematic of four cells in parallel with an interconnection resis- tance (R c ) between each terminal. Each cell is represented by its own ECM as in Fig. ...Context 4
... addition to the state equations for the single cell, there are also algebraic constraints on the parallel cell system. These are based on Kirchoff's laws for current and voltage. The currents at a junction must sum to zero, which for the parallel cell system occurs at the cell connections, as shown Fig. 1c. For N cells, Eq. (7) de- scribes the relationship between loop currents i 1 to i N and cell currents i cell 1 to i cell N . The two cases arise due to there being no i nþ1 for the final ...Context 5
... the voltages around a loop must sum to zero. A typical loop for cell n is shown in Fig. 1d. There are N-1 loops to solve, as the first loop current is the current source and is therefore trivial. The voltage loop equation is given by (8), and can be expanded to (9) by defining the cell voltage through its constituent components ac- cording to ...Context 6
... presented, it has been assumed that there is no addi- tional resistance between each cell. For the experimental work, the wires from each cell were all connected to a common pair of ter- minals, so there was no unique connection between adjacent cells. However, often cells in parallel are connected in a 'ladder' format, such as that presented in Fig. 1b, in which the first cell is connected to the terminals, and the other cells are connected to each other. Ideally, the connection resistance (R c in the Fig. 1b) would be zero, or at least negligible relative to cell impedance. However, if there is a poor connection it can have a significant impact on the pack as a whole [15]. The ...Context 7
... to a common pair of ter- minals, so there was no unique connection between adjacent cells. However, often cells in parallel are connected in a 'ladder' format, such as that presented in Fig. 1b, in which the first cell is connected to the terminals, and the other cells are connected to each other. Ideally, the connection resistance (R c in the Fig. 1b) would be zero, or at least negligible relative to cell impedance. However, if there is a poor connection it can have a significant impact on the pack as a whole [15]. The simulation study presented in Section 5.2 was repeated with R c set to 5 mU, and the results are show in Table 6. The overall effect of this inclusion is to decrease ...Similar publications
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Citations
... Despite this, variations in the characteristics of single cells are possible [7]. Manufacturing-related cell-to-cell variations could be in the form of internal resistance [8-10], capacity [11,12], their combination [13][14][15] and open circuit voltage Open Circuit ...
... The existing literature presents divergent views on this matter. While some researchers [13,14,42,43] affirmed that there exists a convergence and self-balancing attitude among parallel connected cells over time, others' [15,[44][45][46][47] findings oppose this theory. So far, most of the research focus has been on individual cells' behaviour, with some experimental assessment of module connections resumed in [5,18]. ...
... Previous studies have predominantly utilised shunts or Hall-Effect sensors. The former affects current distribution by changing branch resistance [59], whereas the latter is less precise [13]. Fill's study [19] examined branch current measurement using a contact cable with varying resistance and acknowledged the G. Piombo et al. necessity of cable sizing trade-offs. ...
... Due to limited sensor inputs contributing to models, the BMS can only approximate State of Charge (SoC) and pack performance; these approximations are likely to worsen as the pack ages (observations made at a smaller, e.g. individual cell level, do not always scale when used at a system level) [25]. ...
Instrumented battery cells (i.e., those containing sensors) and smart cells (with integrated control and communication circuitry) are essential for the development of the next-generation battery technologies, such as Sodium-ion Batteries (SIBs). The mapping and monitoring of parameters, for example the quantification of temperature gradients, helps improve cell designs and optimise management systems. Integrated sensors must be protected against the harsh cell electrolytic environment. State-of-the-art coatings include the use of Parylene polymer (our reference case).
We applied three new types of coatings (acrylic, polyurethane and epoxy based) to thermistor arrays mounted on flexible printed circuit board (PCBs). We systematically analyse the coatings: (i) PCB submersion within electrolyte vials (8-weeks); (ii) analysis of sample inserted into coin cell; (iii) analysis of sensor and cell performance data for 1Ah pouch SIBs. Sodium-based liquid electrolyte was selected, consisting of a 1M solution of sodium hexafluorophosphate (NaPF6) dissolved in a mixture of ethylene carbonate (EC) and diethylene carbonate (DEC) in a ratio of 3:7 (v/v%). Our novel experiments revealed that the epoxy based coated sensors offered reliable temperature measurements; superior performance observed compared to the Parylene sensors (erroneous results from one sample were reported, under 5 days submersed in electrolyte).
Nuclear magnetic resonance (NMR) spectroscopy revealed in the case of most coatings tested, formation of additional species occurred during exposure to the different coatings applied to the PCBs. The epoxy-based coating demonstrated resilience to the electrolytic-environment, as well as minimal effect on cell performance (capacity degradation compared to unmodified-reference, within 2% for the coin cell, and within 3.4% for pouch cell). The unique methodology detailed in this work allows sensor coatings to be trialled in a realistic and repeatable cell environment. This study demonstrated for the first time that this epoxy-based coating enables scalable, affordable, and resilient sensors to be integrated towards next-generation Smart SIBs.
... These effects are caused by variability between cells, thermal gradients, and uneven potential drops caused by interconnection resistances causing heterogeneous current distributions and state-of-charge (SOC) imbalances between cells. In recent years, researchers have published a range of studies detailing the effects of operating conditions 4 , cell-to-cell capacity and impedance variations [5][6][7][8] , topology 9,10 and thermal gradients 6,10-13 on parallel string current distributions and the instantaneous performance of cells and packs. However, there is limited work addressing the lifetime implications of such heterogeneous conditions, and thus a lack of underpinning understanding of the interplay between pack design factors and degradation modes; motivating this work. ...
Practical lithium-ion battery systems require parallelisation of tens to hundreds of cells, however understanding of how pack-level thermal gradients influence lifetime performance remains a research gap. Here we present an experimental study of surface cooled parallel-string battery packs (temperature range 20-45°C), and identify two main operational modes; convergent degradation with homogeneous temperatures, and (the more detrimental) divergent degradation driven by thermal gradients. We attribute the divergent case to the, often overlooked, cathode impedance growth. This was negatively correlated with temperature and can cause positive feedback where the impedance of cells in parallel diverge over time; increasing heterogeneous current and state-of-charge distributions. These conclusions are supported by current distribution measurements, decoupled impedance measurements and degradation mode analysis. From this, mechanistic explanations are proposed, alongside a publicly available aging dataset, which highlights the critical role of capturing cathode degradation in parallel-connected batteries; a key insight for battery pack developers.
... For this purpose, mismatches between cells regarding capacity and impedance, resulting from manufacturing tolerances [1][2][3][4] and different shipping or storage conditions [5], must be avoided. The reason for this is, that the differences further increase during operation due to varying current [1,2,6] and temperature [1,7,8] distributions, ultimately leading to accelerated [5,[9][10][11][12] or inhomogeneous [5,13] aging. Developing rapid and reliable standard tests to evaluate cell performance, devising robust quality control procedures for production monitoring, and developing factory acceptance testing are just some of the challenges facing cell manufacturers and product integrators that underscore the importance of gaining a comprehensive understanding of cell-to-cell variations (CtCv). ...
... In particular, numerous studies have been conducted in the parallel topology [1,6,23,24]. The cells experience different currents depending on impedance and capacitance [6,13], which may be even higher than the final operating current [13]. Gogoana et al. [10] studied cycle life as a function of internal resistance mismatch and concluded that the mismatch has a larger impact than single-cell resistance alone. ...
... In particular, numerous studies have been conducted in the parallel topology [1,6,23,24]. The cells experience different currents depending on impedance and capacitance [6,13], which may be even higher than the final operating current [13]. Gogoana et al. [10] studied cycle life as a function of internal resistance mismatch and concluded that the mismatch has a larger impact than single-cell resistance alone. ...
Cell-to-cell variations inside a battery pack can result in inhomogeneities, leading to an accelerated, uneven aging. Until today these variations are solely quantified by parameter-based studies, which only offer a limited interpretability. To tackle this inconclusiveness, cell-to-cell variations and their effects on the electrode processes of lithium-ion batteries are investigated in this work. For this purpose 92 cells are characterized by impedance, pulse, and pseudo open-circuit voltage measurements, and the data obtained is compiled as publicly available data set. The data is examined by a holistic distribution of relaxation times analysis, comprising complementary distribution of relaxation times approaches. This enables a reliable identification of process variations between cells. First, the confidence intervals of both the raw data and the distribution of relaxation times are examined. subsequently, the individual processes, their characteristic time constants, and their polarization are determined. The analysis reveals that a normal distribution only applies in one of the examined cases and can even be excluded in four cases. Finally, a correlation analysis is conducted, allowing the categorization of the identified processes into cell winding, electrochemical interface processes, and solid-state diffusion. The potential physicochemical reasons behind are discussed and the work thus contributes to a deeper understanding of cell-to-cell variations.
... The key point lies in the precise fitting relationship between SOC and OCV. Typical battery equivalent circuit models include the Rint model [9], Thevenin model, PNGV model [10], and the most widely used RC network model [11]. GuoF compared different RC models and found that the second-order RC model can better simulate battery dynamics while maintaining low computational complexity. ...
In response to the inaccurate estimation of State of Charge (SOC) in current power battery management systems, and considering that SOC may be subject to offset constraints from State of Health (SOH) when estimated separately. A method combining adaptive robust Kalman filtering with multiple innovation theories and online identification of dual Kalman filtering parameters is proposed. This control method is based on adaptive robust Kalman control. It corrects the estimated values using multiple innovation values and Kalman gains at different times. Dual Kalman filtering is used for online parameter identification and joint estimation of battery health status, which increases the amount of error information and provides an optimized method for accurate estimation of SOC and SOH. To verify the rationality of the algorithm, a second-order RC equivalent circuit model is used to characterize the dynamic characteristics of the battery, and experimental verification is carried out under different operating conditions. The experimental results show that the average error of SOC under three operating conditions: UDDS, FUDS, and US06 is 0.56%, 0.31%, and 1.23%, respectively. The estimated error of SOH after stabilization is less than 1.73%. The estimation error is the lowest among the five estimation algorithms. The proposed algorithm has been verified to have good accuracy and convergence. The multi-innovation adaptive robust dual Kalman filtering algorithm provides a theoretical basis for accurate state estimation and widespread application of lithium batteries.
... These experiments have shown that large current imbalances can persist during parallel-connected system operation [18]. The current-sharing behavior of parallel-connected cells has since been reproduced in simulation using a variety of battery models ranging from equivalent circuit models [19,17,20,21] to physics-based models [22]. These experimental and simulation-based approaches have enabled accurate quantification of the imbalance dynamics, especially in the context of evaluating the impact of temperature gradients [23,20,24]. ...
... where α, β > 0. α is the characteristic slope of the OCV function and β defines the minimum voltage. We note that this is the same starting point as previous works [19,31,30,20]. Section 2.4 later lifts this restriction and studies the model error introduced by this assumption. ...
This paper proposes an analytical framework describing how initial capacity and resistance variability in parallel-connected battery cells may inflict additional variability or reduce variability while the cells age. We derive closed-form equations for current and SOC imbalance dynamics within any given charge or discharge cycle. These dynamics are represented by a first-order equivalent circuit model with a linear open circuit voltage behavior and validated against experimental data. To demonstrate how current and SOC imbalance leads to cell degradation, we developed a simplified, incremental degradation update scheme based on the solid electrolyte interphase growth mechanism. We propose a scheme in which the inter-cycle imbalance dynamics update the intra-cycle degradation dynamics, and vice versa. Using this framework, we demonstrate that current imbalance can cause convergent degradation trajectories, consistent with previous reports. However, we also demonstrate that different degradation assumptions, such as those associated with SOC imbalance, may cause divergent degradation in some cases. We finally highlight the role of different cell chemistries, including different OCV function nonlinearities, on system behavior, and derive analytical bounds on the SOC imbalance using Lyapunov analysis.
... In the model equations of HM, γ denotes the decay rate of the hysteresis voltage. It is assumed that the models of cells in a PCM are identical and generally age together [29]. For modeling a PCM having M cells in parallel, the charge capacity, Q c , is multiplied by M, and internal resistance, R 0 , is divided by M. The complete battery pack or module can be modeled by adding the terminal voltages of all PCMs in series and subtracting the potential drops across the junction resistances (R w ). ...
This paper presents the effect of modeling uncertainty of a lithium ion battery pack on the accuracies of state of charge (SOC) and state of power (SOP) estimates. The battery pack SOC is derived from the SOCs of all parallel cell modules in the pack, which is computed using a sequential estimation process. SOC and SOP estimates are essential for optimizing the energy management of hybrid electric vehicles (HEV). Two model types, an average model (AM) and a hysteresis model (HM), are considered here. The HM captures the hysteresis phenomenon, prominently observed in lithium ferro-phosphate cells commonly used in HEVs. This paper first demonstrates the accuracies of SOC and SOP estimates for AM and HM for laboratory experimental data. The feasibility of on-board implementation of the scheme is demonstrated through a closed-loop vehicle-level hardware-in-the-loop simulation. It is shown that estimates obtained using the HM result in an improved overall energy economy, as well as improved operational limits for batteries, and the underlying reasons, are revealed from the improved choice of operating points enabled by the improved estimates.
... LIBs are placed in series and parallel to make the battery packs for EVs. The battery management system (BMS) controls and monitors SOC, SOH, SOT, etc., for each and every cell of the battery pack; hence, BMS becomes more complicated [10][11][12]. ...
... SOC can be calculated by utilizing adaptive filters based on battery model and observers and physically measured properties. These techniques include Kalman filters, the least squares, particle traditional filter, adaptive Luenberger observer, and black-box models based on machine learning in which measured data including voltage, current, temperature, and charge status are used to train machine learning models [7][8][9][10][11][12][13][14]. ...
The world is advancing toward an era with infrastructure that has been updated with more modern inventions. At the same time, pollution is increasing, causing constant harm to all living creatures. The problems associated with environmental contamination are currently the most concerning topic for the researchers. Internal combustion engines (ICEs) in conventional vehicles have a significant impact on this problem, causing the greenhouse effect and having a noteworthy emission rate. Because EVs use electrical energy to drive their motors efficiently, environmental researchers are paying close attention to the development of electric vehicles. As battery is one of the most important parts of electric vehicle, we need to pay extra attention on different types of battery management strategy, issues related to battery and its impact on environment.
... A Lithium-Iron-Phosphate (LiFePO4) battery model is proposed in this subsectio LiFePO4 battery technology presents a good compromise of the cost and required en getic performances [15][16][17][18][19][20][21]. The proposed model of the batteries is extracted from the LF 100 Ah/3.2 V battery's cell characterization using the method described in [16,21]. ...
... A Lithium-Iron-Phosphate (LiFePO4) battery model is proposed in this subsec LiFePO4 battery technology presents a good compromise of the cost and required e getic performances [15][16][17][18][19][20][21]. The proposed model of the batteries is extracted from the 100 Ah/3.2 V battery's cell characterization using the method described in [16,21]. ...
... A Lithium-Iron-Phosphate (LiFePO4) battery model is proposed in this subsection. LiFePO4 battery technology presents a good compromise of the cost and required energetic performances [15][16][17][18][19][20][21]. The proposed model of the batteries is extracted from the LFP-100 Ah/3.2 V battery's cell characterization using the method described in [16,21]. ...
A Hybrid Electric Ship (HES) is investigated in this work to improve its dynamic response to sudden power demand changes. The HES system is based on a Variable-Speed Diesel Generator (VSDG) used for long-term energy supply, with Two Energy Storage Systems (TESSs) using Batteries and supercapacitors for transient power supply. The TESS mitigates the power demand fluctuations and reduces its impact on VSDG, which is linked to a DC-bus through a controlled rectifier. Batteries and Supercapacitors (SCs) are connected in a DC-bus using the bidirectional DC/DC converters to manage the transient and fluctuating components. Two thrusters (one in the front and the second in the back of the Ship) are considered for the propulsion system. The HES power demand includes the requirement of the thrusters and embedded power consumers (elevator, package lifting, air conditioning, onboard electronics devices, etc.). The highlight of this paper is based on the HES fast response improvement in sudden power demand situations via TESS-based batteries and supercapacitors. The other highlight concerns the SCs’ electrothermal modeling using an extension of the SCs’ current ripples’ frequency range (0 to 1 kHz), considering parameter evolution according to using the temperature and current waveform. This energy management-based dynamic power component separation method is tested via simulations using a variable operating temperature scenario.
... The key point lies in the precise fitting relationship between SOC and OCV. Typical battery equivalent circuit models include the Rint model [11], the Thevenin model, the PNGV model [12], and the most widely used RC network model [13]. The accuracy and complexity of this model are balanced by setting the number of a series of RC cycles. ...
In response to the inaccurate estimation of State of Charge (SOC) in current power battery management systems, and considering that SOC may be subject to offset constraints from State of Health (SOH) when estimated separately. A method combining adaptive robust Kalman filtering with multiple innovation theories and online identification of dual Kalman filtering parameters is proposed. This control method is based on adaptive robust Kalman control. It corrects the estimated values using multiple innovation values and Kalman gains at different times. Dual Kalman filtering is used for online parameter identification and joint estimation of battery health status, which increases the amount of error information and provides an optimized method for accurate estimation of SOC and SOH. To verify the rationality of the algorithm, a second-order RC equivalent circuit model is used to characterize the dynamic characteristics of the battery, and experimental verification is carried out under different operating conditions. The experimental results show that the average error of SOC under three operating conditions: UDDS, FUDS, and US06 is 0.56\%, 0.31\%, and 1.23\%, respectively. The estimated error of SOH after stabilization is less than 1.73\%. The estimation error is the lowest among the five estimation algorithms. The proposed algorithm has been verified to have good accuracy and convergence. The multi-innovation adaptive robust dual Kalman filtering algorithm provides a theoretical basis for accurate state estimation and widespread application of lithium batteries.
