MULTICELL battery is a widely adopted energy source

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1 IEEE TRANSATIONS ON ENERGY ONVERSION, VOL. 25, NO. 4, DEEMBER Modeling Discharge Behavior of Multicell Battery Jiucai Zhang, Student Member, IEEE, Song i, Senior Member, IEEE, Hamid Sharif, Senior Member, IEEE, and Mahmoud Alahmad, Member, IEEE Abstract Multicell battery has been widely used in various electrical and electronics devices. To achieve the optimal multicell battery design, accurately modeling battery discharge behavior of multicell battery is crucial. However, modeling discharge behavior of multicell battery is very challenging due to the nonlinear battery effects, nonuniform cell quality, and various cell connections. In this paper, we develop a circuit-based multicell battery model to accurately model the multicell battery discharge behavior in terms of available capacity, output voltage, and internal resistance with consideration of nonlinear battery effect and nonuniform cell quality. It also characterizes the cell discharge current distribution of cell strings in parallel connection. The proposed multicell battery model has been validated by extensive simulation and experimental results under various load conditions. Index Terms Battery modeling, circuit-based modeling, energy conversion, energy storage, multicell battery. i L i S I B Ii L R i Ri L Ri S Ri T t e t s V B Vi V F Vi o α A α B αi α f α P α S NOMENLATURE Long-transient capacitance of the ith cell. Short-transient capacitance of the ith cell. Discharge current rate of the multicell battery. Discharge current rate of the ith cell. Total operating time of batttery. Serial resistance of the ith cell. Long-transient resistance of the ith cell. Short-transient resistance of the ith cell. Self-discharge resistance of the ith cell. End time for cell string discharging. Start time for cell string discharging. Output voltage of the multicell battery. Output voltage of the ith cell. utoff voltage of the single-cell battery. Open-circuit voltage of the ith single-cell battery. onsumed capacity of a single-cell battery. Remaining capacity of multicell battery. apacity of the ith cell. Full capacity of a single cell. Remaining capacity of cell string in parallel connection. Remaining capacity of cell string in serial connection. Manuscript received October 16, 2009; revised February 17, 2010; accepted March 23, Date of publication June 14, 2010; date of current version November 19, This work was supported in part by the National Science Foundation under Grant Paper no. TE J. Zhang, S. i, and H. Sharif are with the Department of omputer and Electronics Engineering, University of Nebraska-Lincoln, Omaha, NE USA ( jczhang@husker.unl.edu; sci2@unl.edu; hsharif@unl.edu). M. Alahmad is with the Department of Architectural Engineering, University of Nebraska-Lincoln, Omaha, NE USA ( malahmad2@unl.edu). olor versions of one or more of the figures in this paper are available online at Digital Object Identifier /TE μ ϕ i ϕ B i ϕ P i ϕ S i ω Unavailable capacity of the sing-cell battery. State of charge (SO) of the ith single battery. SO of the multicell battery. SO of the cell string in parallel connection. SO of the cell string in series connection. Frequency of discharge current. I. INTRODUTION MULTIELL battery is a widely adopted energy source for various power electronics. Although the battery technologies have been significantly advanced in recent years, current multicell battery still cannot meet the progressive energy demands and size limitation of the today s power electronics devices [1]. In general, the performance of multicell battery in terms of capacity, output voltage, and internal resistance is sensitive to many factors, including cell connections, discharge current rate, and cell status variations, which are discussed in details in the following. First, the multicell battery performance varies with different cell connections. For example, the study in [2] has shown that cell string in parallel connection may provide higher discharge current rate, longer operation time, smoother voltage drop, and higher discharge efficiency than cell string in series connection. This issue becomes more important to recent research on dynamically reconfigured multicell battery [3] [5]. Second, the battery performance will change with the discharge current rate. Higher discharge current rate will lead to the lower available capacity and output voltage as well as larger internal resistance. Third, the reduced available capacity at a high discharge current rate will be recovered after multicell battery having been rested for a while. Fourth, due to the quality variation of manufacturing, fresh battery cells demonstrates performance variation. Therefore, multicell battery design and optimization require a thorough understanding of multicell battery discharge behavior under various operation conditions, making a theoretical battery model highly desirable. So far, a wide variety of single-cell battery models have been developed to capture the battery performance for various purposes such as battery design, performance estimation, and circuit simulation. In general, the existing single-cell battery model can be classified into three categories: electrochemical models, analytical model, and electrical model. Among them, electrochemical models capture fundamental mechanisms of power generation and can be used to optimize physical battery parameters [6]. However, this model is difficult to use, since it may require detailed specifications on battery parameters such as battery structure, chemical composition, capacity, temperature, and other physical characteristics. In addition, their computational complexity is very high due to solving independent partial /$ IEEE

2 1134 IEEE TRANSATIONS ON ENERGY ONVERSION, VOL. 25, NO. 4, DEEMBER 2010 different equations. On the other hand, analytical models employ an equivalent expression of battery circuits for battery modeling [7]. However, they cannot provide battery circuit features in terms of internal resistance, open-circuit voltage, and output voltage. Thus, electrical models take a combination of voltage source, resistors, and capacitors for battery modeling and circuit simulation [8]. However, these models cannot estimate the impact of nonlinear behaviors on battery available capacity. Therefore, a mathematic model with integrated advantages of both analytical model and electrical model has been developed in [9] to capture nonlinear capacity effects and various battery circuit features for single-cell battery. Although existing battery models can characterize the performance of single-cell battery, they are not directly applicable for multicell battery due to the fact that they did not consider the cell connections and cell status variations in multicell battery. In [1], both linear and nonlinear models of a cell string in parallel connection have been presented to describe its charge and discharge efficiency. However, the linear model will not suffice due to ignoring various nonlinearities in battery design, and the nonlinear model is not capable of modeling the battery for the full frequency range due to high complexity of parameter identification. In [10], a computer model of a cell string in parallel connection has been developed to determine the sensitivity of system parameters such as cell resistance, cell capacity, and cell self-discharge. However, this model has not quantitatively described the effect of cell status variations. In [11], a simulation method was proposed to simulate the discharge performance of cell strings in both parallel and series connections. However, this method employed a complicated algorithm to calculate the cell current distribution of cell strings in parallel connection. The high computational complexity of this model limits its application only on multicell battery design with a small number of battery cells. In summary, there is little research done on multicell battery modeling, and no qualitative and comprehensive multicell battery models have been reported in the literature. In this paper, we propose a circuit-based multicell battery model to understand and quantify the multicell battery discharge behavior under various cell connections, discharge current rates, and cell status variations. The major contribution of this paper is two folds: 1) a new multicell battery model has been proposed to quantify the battery discharge behavior under various cell connections and load conditions, providing a theoretical foundation for future multicell battery design and optimization and 2) the proposed multicell battery model can accurately derive the current distribution of cell string in parallel connection with linear computational complexity, which ensures that the proposed multicell battery model can be used for large-scale multicell battery performance modeling. This paper is organized as follows. Section II introduces the multicell battery model. Section III describes the proposed model for cell string in both series and parallel connections. The validation of the proposed models through both extensive simulations and experiments is discussed in Section IV, and Section V concludes the paper. Fig. 1. Multicell battery decomposition. Arbitrary multicell battery can be decomposed into two kinds of subsystems: cell strings in series connection and cell strings in parallel connection. II. PROPOSED MULTIELL BATTERY MODEL Theoretically, an arbitrary multicell connection can be abstracted as either a series system or a parallel system, where each element is a group of cells in series, parallel, or hybrid series and parallel connection. An hybrid series and parallel connection can be further decomposed into either series or parallel connection [12] [14]. In other words, any given cell connection in multicell battery can be characterized by two basic cell connections: cell strings in series connection and cell strings in parallel connection, as shown in Fig. 1. Let f be the model of cell strings in series connection and g be the model of cell strings in parallel connection. Then, the multicell battery as shown in Fig. 1(a) can be modeled as p p = f ( g [( I1,ϕ ) ( 1, I 2,ϕ ) ( 2, I 3,ϕ )] [( 3,s I 4,ϕ )] 4, g [( I5,ϕ ) ( 5, I 6,ϕ )]) 6 (1) where I1 I6 and ϕ 1 ϕ 6 refer to discharge current rates and SOs of battery cells B 1 B 6, respectively. s is denoted as a single-cell battery model [9]. Similarly, the multicell battery as shown in Fig. 1(b) can be modeled as p p = g ( f [( I1,ϕ ) ( 1, I 2,ϕ ) ( 2, I 3,ϕ )] 3, f [( I4,ϕ ) ( 4, I 5,ϕ ) ( 5, I 6,ϕ )]) 6. (2) Recall that arbitrary multicell battery modeling can be decomposed into two kinds of subsystem modeling: the modeling of cell strings in series connection and cell strings in parallel connection. For a cell string in series connection, the discharge current rates of all battery cells are same and determined by the load. Thus, modeling a given cell string in series connection is straightforward. However, for a cell string in parallel connection, the voltage of each cell is always equal to the voltage of the cell string in parallel connection. Due to cell status variations, the load current will be unevenly distributed across the cells of the cell string to keep each cell output at the same voltage. Thus, modeling the performance of a cell string in parallel connection is challenging. In the following sections, we will develop performance models for cell strings in both series and parallel connections in details.

3 ZHANG et al.: MODELING DISHARGE BEHAVIOR OF MULTIELL BATTERY 1135 Fig. 4. Model of single-cell battery [9]. Fig. 2. urrent effect, where the battery capacity varies with the discharge current rate [5]. On the other hand, higher temperature leads to lower internal resistance, thereby accelerating the self-discharge and reducing the available capacity. Fifth, side reactions such as electrolyte decomposition, active material dissolution, and passive film formation results in battery capacity fading [6]. In addition to the aforementioned characteristics, some kinds of batteries such as Nid batteries are known to have memory effect. All these nonlinear effects cause cell status variations in the multicell battery. B. Model of Single-ell Battery A circuit-based model as shown in Fig. 4 has been adopted in this paper. Assuming that the single-cell battery is healthy, the single-cell battery model can capture both battery circuit features and nonlinear battery capacity effects, and the model could be denoted as [9] α A (I,β,L,t s,t e )=I [(t s t e )+F(L, t s,t e,β)] F (L, t s,t e,β)=2 m =1 e β 2 m 2 ( L t s ) e β 2 m 2 ( L t e ) β 2 m 2 ϕ =1 α A α f V o (ϕ )=a 1 e a 2 ϕ + a 3 ϕ a 4 ϕ 2 + a 5 ϕ 3 + a 6 Fig. 3. Recovery effect, where the battery has limited recovery effect at a high discharge current rate. III. MODEL OF ELL STRING IN PARALLEL ONNETION AND SERIES ONNETION A. Background Modeling battery performance is fairly complex due to various nonlinear behaviors such as current effect, recovery effect, temperature effect, aging effect, and memory effect, which will be discussed in details in the following. First, the battery terminal voltage is not constant and drops nonlinearly with various discharge rates, as shown in Fig. 3. Second, the battery capacity varies with the discharge rate; the higher the discharge rate is, the lower the battery capacity is, as shown in Fig. 2 [5]. Third, battery has recovery effect at a high discharge current rate as shown in Fig. 3 [6]. The recovery process takes place when the battery can be rested. The battery recovery capability depends on the SO of the battery and the duration of the rest time. Fourth, temperature also affects internal resistance and full available capacity [15]. The lower the temperature is, the higher the internal resistance is, and lower available capacity will be. R(ϕ )=b 1 e b 2 ϕ + b 3 ϕ b 4 ϕ 2 + b 5 ϕ 3 + b 6 R S (ϕ )=d 1 e d 2 ϕ + d 3 S (ϕ )=f 1 e f 2 ϕ + f 3 R L (ϕ )=g 1 e g 2 ϕ + g 3 L (ϕ )=l 1 e l 2 ϕ + l 3 V (ϕ )=V o i (ϕ ) R(ϕ )I R S (ϕ ) R S (ϕ )jω(ϕ )+1 I R L (ϕ ) R L (ϕ )jω L (ϕ )+1 I (3) where α A is the accumulated capacity during time period [t s,t e ] at rate of I. The first term I (t s t e ) is the consumed capacity by the load I during the load period [t s,t e ]. The second term I F (L, t s,t e,β)] is the amount of discharging loss due to the current effect, which is the maximum recoverable battery capacity at t e. β 2 is a constant related to the diffusion rate within battery. The larger the β 2 is, the faster the battery diffusion rate is, thus, the less the discharging loss. L is the total operating time of the battery. m determines the computational complexity and accuracy of the model. R, V o, α f, and ϕ are battery internal resistance, open-circuit voltage, the full capacity, and SO, respectively. R S, R L, S, and L are resistances and

4 1136 IEEE TRANSATIONS ON ENERGY ONVERSION, VOL. 25, NO. 4, DEEMBER 2010 Fig. 5. Model of the cell string in parallel connection. capacitors to capture the transient response of battery voltage. a 1 a 6, b 1 b 6, d 1 d 3, f 1 f 3, g 1 g 3, and l 1 l 3 are coefficients of the model, which can be achieved by using the standard leastsquare estimator [16] [19].. Model of ell String in Parallel onnection A circuit-based model of cell string in parallel connection can be described in Fig. 5. Each unit could be a single physical cell or an equivalent physical cell string in arbitrary cell connection. Model of cell string in parallel connection can be described as αi A (I i,β,l,t s,t e )=Ii [(t s t e )+F(L, t s,t e,β)] ϕ i V i =1 α A i α f (ϕ i )=V i o(ϕ i ) R i(ϕ i )I i R i S (ϕ i ) R i S (ϕ )jω i S (ϕ i )+1 I R i i L (ϕ i ) R i L (ϕ i )jω i L (ϕ i )+1 I i i (4) V1 (ϕ 1 )=V2 (ϕ 2 )= = VN (ϕ N )=VB Vi o(ϕ i ) V B, i {1, 2,...,N} ϕ B = 1 N N α i (I i ) I B = N I i, Ii 0,i {1, 2,...,N} where α f is the full cell capacity. αi (I i ) is the available capacity of the ith cell. ϕ i is the SO of the ith cell, which is defined as a ratio between the available capacity and the theoretical full capacity. ϕ B is the SO of the whole multicell battery. Vi (ϕ i ) is the output voltage of the ith cell. 1) Internal Resistance: Internal resistance of the ith battery cell can be denoted as Z i (ϕ i )=R(ϕ Ri S i )+ (ϕ i ) Ri S (ϕ i )jωcs i (ϕ i )+1 Ri L + (ϕ i ) Ri L (5) (ϕ i )jωcl i (ϕ i )+1. Based on the model of cell string in parallel connection, the internal resistance of the cell string can be denoted as Z B = N 1 1 Z i (ϕ i ). (6) 2) Available apacity: The available capacity of a cell string in parallel connection (α P ) can be defined as the sum of the consumed capacities on all cells until the weakest cell of a multicell battery reaches its cutoff voltage, which can be expressed α P (I B,β,L,t s,t e )= N αi (Ii,β,L i,t s,t e ), Ii 0. (7) 3) ell Output Voltage and urrent Distribution in a ell String in Parallel onnection: Because of cell status variations, the discharge current rate of each cell in the cell string in parallel connection cannot be simply derived by the ideal current distribution equation Ii = IB (8) N where Ii is the discharge current rate of the ith cell, I B is the discharge current rate of the cell string in parallel connection, and N is the total number of battery cells in the cell string in parallel connection. Instead, battery cells should be discharged unevenly to keep the output voltage of each cell same as the voltage of cell string in parallel connection. An iteration algorithm has been proposed to approximate the discharge current rate of each cell, and then the derived cell discharge current rate is used to calculate the voltage of the cell string [11]. However, the approximation process in the iteration algorithm is very complex and time consuming. Moreover, the computational complexity of the iteration algorithm is significantly increased with the number of battery cells, limiting its application only to small-scale multicell battery design. To model the cell current distribution accurately and efficiently, a new algorithm has been proposed in this study as shown in Fig. 6. Instead of directly calculating the current distribution, the proposed algorithm will first assign the output voltage of cell string. Then, the assigned output voltage and the corresponding cell internal resistance will be used to characterize the cell current distribution. That is, the discharge current rate of the cell string in parallel connection will be characterized by the output voltage. For given cell SOs, the lower the battery output voltage, the larger the battery discharge current rate, as shown in Fig. 7. The discharge current rate of the cell string in parallel connection is a decreasing function of the output voltage, which can be written as N N I B = Ii = V o i V B Z i (9)

5 ZHANG et al.: MODELING DISHARGE BEHAVIOR OF MULTIELL BATTERY 1137 proposed current distribution algorithm can be used in cell string in parallel connection at any scale. D. Model of ell String in Series onnection Model of cell string in series connection is described in Fig. 8. For a N cell string, the output voltage of the cell string can be expressed as αi A (I i,β,l,t s,t e )=Ii [(t s t e )+F(L, t s,t e,β)] Fig. 6. Proposed algorithm to calculate the cell current distribution and the output voltage of the cell string in parallel connection. ϕ i V i =1 α A i c f (ϕ i )= V o i (ϕ i ) S R i (ϕ i )I i R i S (ϕ i ) R i S (ϕ )jω i i S (ϕ )+1 I R i i L (ϕ i ) R i i L (ϕ )jω i i L (ϕ )+1 I i i I 1 (ϕ 1 )=I 2 (ϕ 2 )= = I N (ϕ N )=IB Vi (ϕ i ) V F, i {1, 2,...,N} ϕ B = min N ϕ i V B = N V i, Vi 0,i {1, 2,...,N}. (11) Fig. 7. urve of discharge current rate versus voltage of two-cell string in parallel connection. Here, the discharge current rate of the cell string in parallel connection is a decreasing function of its output voltage. where V B and I B are the assigned output voltage and the corresponding discharge current rate of cell string in parallel connection, respectively. Vi o and Z i are the open-circuit voltage and the internal resistance of the ith cell. Therefore, in the proposed algorithm, when the output voltage of a cell string is gradually decreased from the minimum open-circuit cell voltage to a voltage V B, the discharge current rate of the cell string is increased to the desired discharge current rate I B. The voltage V B corresponding to the discharge current rate of I B is the battery output voltage. When the output voltage is obtained, the discharge current rate of each cell in the cell string will be I i = V i o V B Z i. (10) From (9), we can conclude that the computational complexity of the proposed model is linear to the number of battery cells N in a cell string. With the low computational complexity, the 1) Internal Resistance: The equivalent resistance of cell string in series connection is the sum of internal resistance of each cell Z B. N N Z B = R(ϕ Ri S i )+ (ϕ i ) Ri S (ϕ i )jωcs i (ϕ i )+1 + N R L i (ϕ i ) R L i (ϕ i )jωcl i (ϕ i )+1 (12) 2) Available apacity: For cell string in series connection, all battery cells are equally treated and discharged at the same discharge current rate and time. Therefore, the consumed capacities of all cells during the discharging process are the same. Even though discharged current rate is the same, different battery cells behave differently. Once the weakest cell reaches cutoff voltage, it exhibits a high internal resistance, causing other cells in the cell string in series connection unable to deliver the stored energy. Therefore, the available battery capacity of a cell string in series connection is determined by the weakest cell, which is the cell capacity of the weakest cell. Thus, the available battery capacity of a cell string in series connection is α S (I B,β,L,t s,t e )=Min{α1 (I B,β,L 1,t s,t e ), α2 (I B,β,L 2,t s,t e ),...,αn (I B,β,L N,t s,t e )} (13) 3) Output Voltage of ell String: The output voltage of a cell string in series connection is the sum of the voltage of all cells, which can be denoted as follows: V S = N V i (ϕ i ). (14) Since a cell string in series connection is only as good as the weakest cell in the cell string, the cutoff voltage of the cell string is determined by the weakest cell. As a result, the cell string is discharged to cutoff voltage before all cells in the cell

6 1138 IEEE TRANSATIONS ON ENERGY ONVERSION, VOL. 25, NO. 4, DEEMBER 2010 Fig. 8. Multicell battery model in series connection. TABLE I BATTERY MODEL PARAMETERS string in series connection reaches their cutoff voltages. The actual cutoff voltage of the multicell battery is much higher than nominal cutoff voltage. IV. MODEL VALIDATION A. Experimental Setup All simulations and experiments are conducted on HE18650 battery cells whose full capacity, nominal voltage, and cutoff voltage are 2600 mah, 3.7 V, and 3 V, respectively [20]. The battery model parameters of HE18650 are listed in Table II [9]. The high variation in the battery parameter is used to capture rapid incensement of values of R, R S, and R L, sharp voltage drop at low SO values, as well as transient voltage response. Battery cells are first charged to its full capacity through the method of constant current constant voltage [21]. Then, the multicell battery is discharged at desired configurations. We present experimental and simulation results for multicell battery at both constant load and variable load. The simulation results are derived by using the proposed mathematical model, while the experimental results are collected through the ARBIN battery testing instrument BT2000 [22], as shown in Fig. 9. The proposed multicell battery model has been validated through extensive simulations and experiments. Fig. 9. Multicell battery testing environment. B. Validation of Model of ell String in Parallel onnection To validate the proposed model of the cell string in parallel connection, two different load profiles including continuous and periodic four-phase discharge current rate levels were used to discharge the two-cell string in parallel connection. In the first case, the two-cell string is discharged at 1 A continuously. The relationship between the cell voltages in two-cell string in parallel connection under a continuous load is shown in Fig. 10. Fig. 10. Voltage versus operating time of two-cell string in parallel connection at a constant load (discharge current rate = 1 A). We can observe that experimental results well match with the simulation results, meaning that the cell voltage of cell string in parallel connection can be accurately modeled. We can get the same conclusion in the case of using a periodic four-phase load

7 ZHANG et al.: MODELING DISHARGE BEHAVIOR OF MULTIELL BATTERY 1139 Fig. 11. Voltage versus operating time of two-cell string in parallel connection in a periodic four-phase load profile at discharge current rate of 0.8, 0.4, 1, and 0.6 A. Fig. 13. ell voltage versus operating time of the cell string in series connection. Here, each cell shows different performance due to cell status variations. Fig. 12. urrent distribution of two-cell string in parallel connection at discharge current rate of 1 A. Due to cell status variations of a cell string in parallel connection, each cell has difference discharge current rate. profile at discharge current rate of 0.8, 0.4, 1, and 0.6 A for cell string in parallel, as shown in Fig. 11. Note that near the end of discharge, there is a discrepancy between experimental and simulation results due to the fact that the adopted single-cell battery model in [9] has slightly different from experiment data due to the inadequate data for data fitting of single-cell battery model parameters. In this paper, we also study how the load currents are shared among cells, as shown in Fig. 12. Without losing generality, the experiment and simulation are conducted on two-cell string in parallel connection, where each cell has different capacity. Even though the cell string in parallel connection is discharged at a constant discharge current rate (1 A), the current flow through each battery cell will not be proportionally divided by the capacity ratio due to the time-varying nature of internal resistance raised by electrolyte and electrode, solid-electrolyte interface, charge transfer, and mass transfer. The discharge current rate of each battery cell will dynamically change during the discharge process. When the cell string is connected on the load, both battery cells show a trend to reduce the discharge current rate Fig. 14. Voltage of the cell string in series connection versus operating time. Here, the operating time of a cell string in series connection is determined by the weakest cell string. difference between two cells; when closing to the end of the discharge process, the discharge current rate difference between two cells will significantly increase. The discharge current rate difference between two cells is the result of dominating masstransfer resistance at low SO or large discharge current rate. Therefore, based on the good match between simulation and experiment results, the proposed cell current distribution algorithm has been validated.. Validation of Model of ell String in Series onnection In this study, without losing generality, a three-cell string in series connection is discharged at the discharge current rate of 1 A. Fig. 13 shows the discharge voltage curves of each cell. Due to the cell status variations, each cell has different cell output voltage. When one of the battery cells reaches the cutoff voltage, the cell string in series connection will reach its full discharged states. Fig. 14 indicates the discharge voltage curve of the cell string in series connection. The cutoff voltage of cell string in series connection is 9.5 V, which is much higher than

8 1140 IEEE TRANSATIONS ON ENERGY ONVERSION, VOL. 25, NO. 4, DEEMBER 2010 Fig. 15. ell current distribution of multicell battery in Fig. 1(a). Fig. 17. Experiment and simulation result comparison of multicell battery based on cell connection in Fig. 1(a). The performance of the multicell battery is determined by the weakest cell string. The cutoff voltage of multicell battery is much higher than the nominal cutoff voltage (9 V). The simulation results match well with the experiment results. multicell battery. The close agreement between simulation and experimental results for multicell battery indicates the correctness of the proposed circuit-based battery model. Fig. 16. ell current distribution in multicell battery in Fig. 1(a). its theoretical cutoff voltage 9 V. The close agreement between simulation and experiment results as shown in Figs. 13 and 14 indicates the accuracy of the proposed model of cell string in series connection. D. Validation of Multicell Battery Model To validate the multicell battery model, a continuous discharge is applied to the multicell battery in Fig. 1(a). The multicell battery in Fig. 1(a) can be decomposed into three cell strings in parallel connection, and these three cell strings in parallel connection are further connected in series. The cell current distributions of the first and last cell strings in parallel connection are shown in Figs. 15 and 16, respectively. The strongest cell shares the largest portion of discharge current rate in each cell string. The successful congruence between experiment results and simulation results of cell strings has proved that the proposed multicell battery model is very accurate. Fig. 17 shows the discharge voltage curve of multicell battery in Fig. 1(a) at discharge current rate of 1 A. Failure of the single-cell battery results in a high cutoff voltage of the V. ONLUSION A circuit-based multicell battery model has been proposed to characterize the multicell battery discharge behavior in terms of available capacity, output voltage, discharging current distribution, and internal resistance. The close agreement between simulations and experiments shows that the proposed model can accurately capture and derive the discharging behavior of multicell battery. In addition, the computational complexity of the proposed algorithm of cell current distribution is a linear function of the number of battery cells, making the proposed multicell battery model more applicable for large-scale multicell battery design. The proposed model also offers the capability for engineers to accurately design and derive the battery operating time and optimize the performance of battery power management. Furthermore, with an additional modification of the single-cell battery, the modeling approaches could be used to model supercapacitors and fuel cells. REFERENES [1] M. de Koning, A. Veltman, and P. van den Bosch, Modeling battery efficiency with parallel branches, in Proc. IEEE 35th Annu. Power Electron. Spec. onf., Jun. 2004, vol. 1, pp [2]. Brandolese, W. Fornaciari, L. Pomante, F. Salice, and D. Sciuto, A multi-level strategy for software power estimation, in Proc. 13th Int. Symp. Synth., 2000, pp [3] H. Visairo and P. Kumar, A reconfigurable battery pack for improving power conversion efficiency in portable devices, in Proc. 7th Int. aribbean onf. Devices, ircuits Syst., Apr. 2008, pp [4] M. Alahmad and H. Hess, Reconfigurable topology for JPLs rechargeable micro-scale batteries, in Proc. 12th NASA Symp. VLSI Des., oeur dalene, ID, 2005, pp [5] S. i, J. Zhang, H. Sharif, and M. Alahmad, A novel design of adaptive reconfigurable multicell battery for power-aware embedded networked sensing systems, in Proc. IEEE Global Telecommun. onf., Nov. 2007, pp

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Available: Song i (SM 06) received the B.S. degree from Shandong University, Jinan, hina, in 1992, the M.S. degree from the hinese Academy of Sciences, Beijing, hina, in 1998, and the Ph.D. degree from the University of Nebraska-Lincoln, in 2002, all in electrical engineering. urrently, he is an Associate Professor of computer and electronics engineering at the University of Nebraska-Lincoln. His research interests include dynamic complex system modeling and optimization, green computing and power management, energy storage design and optimization, and dynamically reconfigurable embedded system. Dr. i has been in the Editorial Boards of several international journals, including the Guest Editor of IEEE TRANSATIONS ON MULTIMEDIA,the Guest Editor of IEEE NETWORK MAGAZINE, and the Associate Editor of IEEE TRANS- ATIONS ON VEHIULAR TEHNOLOGY. He is also the Technical Program ommittee (TP) o-hair and the TP Member for numerous international conferences. He is the recipient of the 2009 Faculty Research and reative Activity Award at the ollege of Engineering, University of Nebraska-Lincoln. He is a member of Association for omputing Machinery. Hamid Sharif (SM 06) received the B.Sc. degree from the University of Iowa, Iowa ity, the M.Sc. degree from the University of Missouri, olumbia, and the Ph.D. degree from the University of Nebraska Lincoln, all in Electrical Engineering. He is the Paul and Betty Henson Professor of omputer and Electronics Engineering Department, University of Nebraska Lincoln (UNL). He is also the Director of Advanced Telecommunications Engineering Laboratory (TEL) at UNL. His research interests include wireless communication protocols, wireless sensor networks, communication system performance modeling, and communication and network security. He has authored or coauthored a large number of journal and conference papers. He is serving as an editor for several journals including the co-editor-in-hief of the Wiley s Security and ommunication Networks journal. Dr. Sharif has contributed to the IEEE in many roles including hair of the Nebraska Section, hair of the Nebraska omputer and ommunication hapters and currently, he is the hapter oordinator for the IEEE Region 4. Jiucai Zhang (S 09) received the B.S. degree from the North University of hina, Taiyuan, hina, in 2001, and the M.S. degree from the University of Electronic Science and Technology of hina, hengdu, hina, in 2006, both in electrical engineering. He is currently working toward the Ph.D. degree in the Department of omputer and Electronics Engineering, University of Nebraska-Lincoln, Omaha. He was a Lecturer in the School of Information and ommunication Engineering, North University of hina, in His research interests include battery modeling, power management, green computing, and energy storage design and optimization. Mahmoud Alahmad (M 08) received the B.Sc., M.Sc., and Ph.D. degrees in electrical engineering from the University of Idaho, Moscow. He is currently an Assistant Professor of architectural engineering at the University of Nebraska- Lincoln, Omaha. He has published several papers in power management and microbattery testing and system design implementation. He has been involved in electrical distribution system infrastructure planning and design for new and renovated facilities of various industries. His research interests include battery power management and renewable energy alternatives. Dr. Alahmad has been a Professional Engineer, since 1996.

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