- Email: [email protected]
A study on parameter variation effects on battery packs for electric vehicles
Journal of Power Sources 364 (2017) 242e252
Contents lists available at ScienceDirect
Journal of Power Sources journal homepage: www.elsevier.com/locate/jpowsour
A study on parameter variation effects on battery packs for electric vehicles Long Zhou a, Yuejiu Zheng a, b, *, Minggao Ouyang b, Languang Lu b a b
College of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai 200093, PR China State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, PR China
h i g h l i g h t s A battery pack model with 96 cells in series is proposed for the consistency of battery pack. The capacity loss composition of the battery pack is obtained by simulation and experiment. Use the battery pack available capacity as the inconsistency physical quantity. The battery pack screening and management scheme is proposed.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 May 2017 Received in revised form 20 July 2017 Accepted 10 August 2017
As one single cell cannot meet power and driving range requirement in an electric vehicle, the battery packs with hundreds of single cells connected in parallel and series should be constructed. The most significant difference between a single cell and a battery pack is cell variation. Not only does cell variation affect pack energy density and power density, but also it causes early degradation of battery and potential safety issues. The cell variation effects on battery packs are studied, which are of great significant to battery pack screening and management scheme. In this study, the description for the consistency characteristics of battery packs was first proposed and a pack model with 96 cells connected in series was established. A set of parameters are introduced to study the cell variation and their impacts on battery packs are analyzed through the battery pack capacity loss simulation and experiments. Meanwhile, the capacity loss composition of the battery pack is obtained and verified by the temperature variation experiment. The results from this research can demonstrate that the temperature, selfdischarge rate and coulombic efficiency are the major affecting parameters of cell variation and indicate the dissipative cell equalization is sufficient for the battery pack. © 2017 Elsevier B.V. All rights reserved.
Keywords: Electric vehicle Battery pack Cell variation Battery parameters Cell equalization Capacity loss
1. Introduction Due to the commercialization of pure electric vehicle, the mileage range and the lifespan of electric vehicle have gained increasing interests to the researchers. Hence, a lot of studies have primarily focused on the single cell and new materials [1e4], power density and cycle life of the single cell. However, single cell is unable to meet the power and energy requirements for electric vehicles. Hundreds of the single cells need to be connected in series and parallel to each other to construct battery packs [5e8] so as to
* Corresponding author. College of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai 200093, PR China. E-mail address: [email protected] (Y. Zheng). http://dx.doi.org/10.1016/j.jpowsour.2017.08.033 0378-7753/© 2017 Elsevier B.V. All rights reserved.
provide enough power and energy for electric vehicles to meet the requirements of its accelerated climbing and mileage. Unfortunately, due to the inconsistency of the manufacturing process and use of the process environment, the cell variations always exist [9e11] and are unable to eliminate. The energy density, durability and safety performances of the battery pack are affected by every single cell in group because of cell variation [5]. Therefore, the battery pack is usually equalized to reduce the inconsistency. There are two general equalization methods: one is the dissipative cell equalization, and the other is the non-dissipative cell equalization (energy transfer). The dissipative cell equalization method usually adopts resistance discharge equalization, and the non-dissipative cell equalization adopts topology diversity. The topology of nondissipative cell equalization method is summarized in previous studies [12e13].
L. Zhou et al. / Journal of Power Sources 364 (2017) 242e252
In practical application, the poor uniformity of the battery cells will influence the performance of the whole battery pack. First, because of the inconsistent initial capacity and initial state of charge (SOC), the actual available energy of the battery pack is lower than any single cell; it will directly cause the loss of the energy density in group. Second, due to the non-uniformity of internal resistance, the maximum current of the series battery pack is limited by the worst power density of the single cell. So the power density of the battery decreases in the battery pack. Third, compared to the single cell, the actual available power of the battery pack is not only limited by the capacity fade, but also affected by the self-discharge and coulombic efficiency. So its life is shorter than any single cell. As the consistency of the battery cells is an important factor influencing the above three aspects which are adopted to evaluate the performance of the battery pack, the studies on the battery consistency have attracted greater attention recently. Some studies indicate that the cycle life of the battery pack is much less than the single cell. Even the single cells have a cycle life more than 1000 cycles in group, without a balancing technology, the battery pack actual cycle life could be less than 200 cycles. The causes of this phenomenon is not that one cell cycle life is shortened to 200 cycles [14], but the capacity of the battery pack is limited by the minimum residual and rechargeable capacity of the single cells. The lifespan of the battery pack could be decreased when the cell inconsistency is increased. Significant efforts have been made from single cell models to pack-level models, taking into account cell variability [15e18]. However, the current studies [19e21] on the evolution mechanism of battery pack inconsistency are still in the stage of qualitative description. For example, Mathew et al. [19] investigated the simulation framework of cell replacement in a battery pack. Baronti et al. [22] compared five topologies for balancing series connected lithium-ion batteries by the statistical simulations. They showed that the cell to cell topology was the quickest and most efficient one. Dubarry et al. [23] investigated cells balancing behavior in parallel, and an equivalent circuit model was developed to simulate the spontaneous transient balancing currents in a battery system. In order to deeply analyze the inconsistencies evolution mechanism of battery packs, the basic features and description method of the consistency performance in battery packs for pure electric vehicles are investigated in this paper. The battery pack model with 96 cells in series is established. The influence factors of the consistency on battery pack are studied by simulation and experiment. The capacity loss composition of the battery pack is obtained and verified by the temperature variation experiment. Finally, the battery pack screening and management scheme regarding the consistency of the battery pack is proposed. 2. Description for the consistency characteristics of a battery pack 2.1. Consistency characteristics and the influence factors of battery packs Practice shows that the consistency of the battery pack will experience a gradual deterioration process. In general, the inconsistencies damage to the battery pack life is more serious than that of the durability of the single cell. Most of the literature suggests that the inconsistencies between cells reflect in the voltage, SOC, capacity, internal resistance and temperature. In fact, the inconsistency of these parameters is only reflected in the current state, so it is not complete. Considering the variation of the time, the inconsistency between the cells also includes the inconsistency of the self-discharge rate, the inconsistency of the coulomb
243
efficiency, the inconsistency of the capacity degradation and the aging of the internal resistance etc. The inconsistencies of these parameters in the process will be directly reflected in the inconsistency of state. Fig. 1 demonstrates the mutual relations among various parameters of cells. We divide them into three classes, the initial states, the current states, and the time accumulations. Their mutual influence cell parameters are shown in Fig. 1. Generally, we use the current states to express inconsistency of the battery pack. The current states include the capacity, voltage, SOC, internal resistance and temperature. Specifically, direct impacts on the practical battery energy output are the capacity and SOC, while the internal resistance decisively affects the practical power output. Moreover, the voltage and temperature are relatively easy to measure. Therefore, these current states are popularly adopted in the battery pack consistency analysis for practice applications. But in fact the influence factors of battery consistency are the initial states and the time accumulations. The initial states are the states when the cells are just constructed, and the parameters of the initial states have great influence on the short term consistency of the battery pack. And since their measurement and control difficulty is relatively low, the initial state becomes the main factors in the screening process for battery cells. The time accumulations affect the longterm consistency of the battery pack, and the influences are greater than the initial states. So screening process for the time accumulative factors is more important. However, due to the difficulty of screening the time accumulations, these parameters are less likely to be screened in practice. The above analysis and practice show that the consistency of the battery pack has the following basic characteristics: 2.1.1. Coupling property Parameter inconsistencies of the cells are coupled together, forming a complex association network. In particular, temperature inconsistency affects almost all other cell parameters. Some parameters are coupled to form a positive feedback to accelerate the inconsistency of the battery pack, such as coupling temperature and internal resistance results in greater inconsistency of the temperature and internal resistance. Due to the presence of coupling, the battery pack inconsistency behave complex. The evolution mechanism of cell inconsistencies is difficult to reveal. 2.1.2. Statistical property The consistency of the battery pack is reflected by the statistic characteristics of the single battery cell. The battery pack is usually made in parallel and series by thousands of cells, and all parameters of the battery cells meet certain statistical behavior. 2.1.3. Weight property The worse performance of the cell will have worse effects on the
Time accumulations Capacity fading rate
The current states
The initial states Initial capacity
Capacity Voltage
The resistance rate of growth
Coulomb efficiency
Initial SOC
SOC Internal resistance
Initial resistance
Temperature
Initial temperature
Fig. 1. Influence relationship of cell parameters.
244
L. Zhou et al. / Journal of Power Sources 364 (2017) 242e252
inconsistency of the battery pack. However, the average performance of the battery in the battery pack does not affect the inconsistency. So when using the statistics to describe the parameters of the battery pack, the weight of battery cells should be taken into account for the battery inconsistency analysis. In statistics, the weights of various samples are generally the same, such as the standard deviation, variance and so on, while the range statistics is extreme weight. 2.1.4. Irreversibility In the absence of external effects (such as a balanced, or replace part of the battery cells), the consistency of the battery pack always tends to be worse. Due to the initial states, there could be a certain inconsistency in the battery pack. And generally with the cell screening process, initial inconsistency could be relatively small. The inconsistency of the battery pack is mainly caused by the inconsistency of the time accumulative factors. The inconsistency of the battery pack caused by the time accumulative factors is not reversible, and the inconsistency always tends to increase. 2.1.5. Graduality The change of the battery pack consistency is a gradual process. Even if the consistency is very poor, it will not produce a very rapid decline. This is because the differences of time accumulative factors between cells are very small in the short term. Therefore, the time scale used to measure the consistency change of the battery pack is commonly counted not in days but in months. If a large consistency change of the battery pack was found, it usually means battery malfunction, or the consistency of judgment error might happen.
minimum chargeable capacity of cells. We use the following equation to calculate the pack capacity [11].
CPack ¼ minðSOC$CÞ þ minðð1 SOCÞ$CÞ
(1)
Where CPack is the battery pack capacity, SOC is a vector consisting of all the cells SOC in the battery pack. C is a vector consisting of all the single cell capacity of the battery pack. Operator min () represents the minimum value of the elements in the vector. Operator represents the corresponding elements of the vector multiplication. It can be seen from formula (1) that the capacity of the battery pack is usually smaller than the minimum cell. The capacity loss of the battery pack is mainly composed of three parts. First, the capacity of the single cell cannot be fully utilized, resulting in inconsistencies capacity loss of the battery pack (marked as DCI), which can be compensated through a conventional equalization method. Its maximum potential capacity of the battery pack is the minimum capacity of the cell. Second, the capacity loss for the battery pack (marked as DCII) is caused by the inconsistency capacity of the cells, which is resulted from the inconsistencies of the capacity fade and the initial capacity. This part of the capacity loss can be compensated by a more complex, real time, non-dissipative balancing approach, which has the greatest potential to recover the average capacity of all the cells in the battery pack. Finally, the inevitable cell capacity loss leads to the capacity loss of the battery pack, and this part of capacity loss for a battery pack (marked as DCIII) depends entirely on the cell durability. The influence factors of the consistency for the battery pack will be studied from the above three aspects of capacity loss in the following sections.
2.2. Methods for describing consistency of battery pack 3. Battery pack modeling According to the consistency characteristics of the battery pack, the standard deviation and the range statistics are often used to describe the inconsistency of the battery. These described methods are relatively easy to implement, thus have a much wider application. But these statistics do not directly reflect the decrease in the energy density of the battery pack due to the inconsistency. In this paper, we use the battery pack available capacity as the inconsistency physical quantity which can directly describe the shortened life of the battery pack. The definition of battery pack capacity is similar to the single cell. That is, under 25 C environment, the battery pack starts to discharge in 1/3C rate when one of the cells in the battery pack is in the fully charged state, until one cell has completely released its capacity. Since the charge capacity and the discharge capacity of the lithium-ion battery difference is small [6], the charge capacity can also be approximated as the battery capacity. In the absence of a balancing technology, due to inconsistencies of the battery pack, when some of the cells have no remaining capacity and power (noted as Cell A), other batteries could still have surplus capacity. But the battery pack cannot continue to be discharged, otherwise it will result in a large reduction in battery life, and even safety problems due to over-discharge of Cell A. Similarly, when some of the cells achieve the cut-off voltage (noted as Cell B, Cell B also may be Cell A), other cells still have rechargeable capacities, but the battery pack cannot continue charging. The battery pack available capacity should be the capacity charged from the empty Cell A to fully charged Cell B. When Cell A and B are the same, the available capacity of the battery pack is the same as Cell A. For the series connected battery pack that is not completely emptied, the amount of electricity that can be charged and released is determined by the minimum remaining charging and discharging cells respectively. Therefore, the battery pack capacity is considered as the sum of the minimum remaining available capacity and the
3.1. The overall modeling scheme of battery pack Battery pack model is mainly used for consistency simulation analysis. The 70 Ah LiFePO4 battery parameters are used from the single cell experiment as a reference, and battery model is built up using Matlab Simulink®. The basic structure of the model is shown in Fig. 2. Battery pack system model includes a battery pack model, power management and output gauges. The main function of power management is to control the battery charge and discharge, the purpose is to prevent any cell voltage form exceeding a cut-off voltage. In order to accelerate the speed of cell cycle, we use 1C rate to charge and discharge. After charging to the charge cut-off voltage, the power management module discharges the battery pack directly to the discharge cut-off voltage, and completes a cycle. The function of the output gauges is to observe the state of the battery, and record the battery data. The battery pack model is composed of 96 cells in series. Each
Fig. 2. Battery pack model.
L. Zhou et al. / Journal of Power Sources 364 (2017) 242e252
cell model has a basic circuit model and also contains five sub models, including internal resistance model, coulombic efficiency model, capacity fading model, self-discharge model and thermal model. These models are the most important part of the whole battery pack system. These models are discussed in the following sections respectively.
245
is the mass; Cmi is the specific heat capacity of the battery. The essence of the simple thermal model is the thermal balance process between the cell internal resistance heat release and convection heat dissipation. For the currently selected 70 Ah battery, these parameters are set to qi ¼ 20 W/K$m2, Ai ¼ 0.12 m2, mi ¼ 2 kg, Cmi ¼ 1000 K/W$kg$s.
3.2. Single cell model 3.2.1. Basic circuit model The simple Rint model is used as the cell equivalent circuit model of the battery pack. The Rint model proposed by G.L. Plett et al. [24] considers the cell as an ideal voltage source and a resistance in series. The open circuit voltage and resistance vary with time, and the model is as follows.
U ¼ OCVðSOCÞ þ IRi
(2)
U is the battery terminal voltage, which is measurable. OCV (SOC) is the open circuit voltage and the SOC curve of the battery, which is measured by the basic performance experiment. I is the current, positive when charged and vice versa. Ri is the internal resistance of the battery, which is given by the resistance model. The calculation of SOC is determined by the relationship between the remaining electric quantity and the capacity. Its model is as follows.
Z Cri ¼ SOC0i $C0i
zi ðtÞdt þ
Z
hi ðtÞIðtÞdt
(3)
Cri is the remaining electric quantity of battery i. SOC0i and C0i are the initial SOC and capacity of the battery i. The first integral term is the capacity of self-discharge loss, and the value is given by the selfdischarge model. The second integral is the Ampere-Hour integral, where hi(t) is the coulombic efficiency, charging, hi(t) < 1, discharging, hi(t) ¼ 1, which is given by the coulombic efficiency model. Here we do not consider the influence of balancing current, so the equilibrium current is zero. The calculation of SOC, as shown in formula (4).
3.2.3. Capacity fading model Capacity fading model is based on the work of John Wang et al. [25]. They summarized the capacity fade model based on lots of experiments. The capacity fade model of LiFePO4 battery concludes that capacity loss is primarily affected by three factors, namely temperature, the total Ah amount of charge and discharge and charging (discharging) rate CRate. The final mode formula is as follows
31700 þ 370:3 CRate ,B,ðAhÞ0:55 Qloss ¼ exp RT
Where Qloss is battery capacity fading losses, and B is function of discharge rate CRate, Ah is the total charging (discharging) ampere number and the ratio of battery capacity. The paper is based on the conditions of the constant current and temperature. However, the fact is that the current and temperature of the battery are constantly changing. Therefore, this formula cannot be directly used in this model. But we still think that this model is applicable after a certain modification. First of all, according to the results of the paper, Ref. [25] did not give the value of B under 1C rate, so we have the following approximate fitting for the coefficient B.
B ¼ 20000
15 CRate
1 3
(4)
Ci is the current total capacity of the cell. SOC is the ratio of the remaining battery capacity to the nominal capacity, and we should consider the influence of durability, where the Ci value is given by the capacity fading model.
3.2.2. Thermal model Thermal model is the basic model for other sub models. Many models are related to the temperature, so the thermal model is introduced first. A simple model for heat source transfer is used here:
Ti ¼
Z
I 2 Ri qi ðTi T0i ÞAi
. mi Cmi dt þ T0i
(5)
Where Ti is the temperature of the battery i, qi is the heat transfer coefficient, T0i is the ambient temperature, Ai is the cooling area, mi
(7)
We believe that the battery can be approximately deemed at a constant current and temperature conditions in a short time, while the total capacity of the capacity losses can be achieved by capacity loss integration in each time period. Under this assumption, we introduce the capacity fading loss rate dQloss/dt.
2 1 dQloss 31700 þ 370:3 CRate 3 ¼ exp ,11000,153 ,ðAhÞ0:45 ,CRate dt RT
SOCi ¼ Cri =Ci
(6)
(8)
By integrating the capacity loss rate, the capacity loss can be obtained within a certain period of time. At the same time, a parameter FadeDif is introduced to characterize the change law of different cell capacity decay loss rate. If the battery is fully consistent with the above model, then the FadeDif ¼ 1. For the battery i, the loss rate of the capacity loss is as follows. FadeDif can be provided by normal distribution and other statistical methods. dQloss,i/dt ¼ FadeDifi$dQloss/dt
(9)
3.2.4. Self-discharge model The basic law of the self-discharge model is based on the paper of Takashi Utsunomiya et al. [26]. In this paper, the self-discharge characteristics of different carbon anode materials are studied, and the results of self-discharge are given under the static
246
L. Zhou et al. / Journal of Power Sources 364 (2017) 242e252
condition of battery. The self-discharge of the battery is gradually improved due to the passivation of the surface of the active material. But in the charging and discharging cycles, the battery is constantly in the process of chemical reaction. Therefore, selfdischarge may not have similar behavior under charging and discharging. However, because no literature has reported the selfdischarge behavior under charging or discharging, it is difficult for us to analyze the actual self-discharge of the battery during charging and discharging process. So we use the assumption of constant self-discharge rate to study the self-discharge of the battery. Using the hard carbon as reference, the fitting formula (10) is as follows.
Qselfdch ¼ kt 23800 k ¼ 0:5 exp RT
(10)
Where Qsefldch is the Ah amount of battery self-discharge and the square root of time linear relationship, parameter k as temperature coefficient, similarly, we introduce a self-discharge loss rate dQsefldch/dt. The formula for self-discharge loss rate is as follows.
dQselfdch 23800 ¼ k ¼ 0:5 exp RT dt
(11)
The self-discharge loss in a certain time is obtained by the integral of the self-discharge loss rate dQsefldch/dt.
3.2.5. Coulombic efficiency model Due to the high coulombic efficiency of lithium batteries, it is very difficult to accurately determine the coulombic efficiency [27], and there is no relevant research about the effect of temperature on the coulombic efficiency in the current literature. But it can be inferred that in the general temperature environment, with the increase of temperature, the coulombic efficiency is decreased due to high temperature side reactions. And we have the experience that the SOC of LiFePO4 battery has little effect on the coulombic efficiency [28]. So we simply fit the following formula.
h ¼ 1 þ k,ðT 298Þ
(12)
Where k is the temperature coefficient, its value is negative, here taken as 0.00002, namely 10 change based on 25 cause the 0.02% coulombic efficiency change which is a relatively small value.
3.2.6. Internal resistance model There is no formula described the internal resistance regarding SOC and temperature and also the resistance increase with the time and temperature are not formulated in literature, so we use the map between SOC, temperature and internal resistance to determine the initial resistance value. Accordingly, we use temperature and time to determine the resistance increase caused by durability. The internal resistance model is as follows.
R ¼ f ðSOC; TÞ,gðT; tÞ
dR=dt ¼ kR $expð Ea=RTÞ
(14)
Here takekR ¼ 0.05 U/s, Ea ¼ 30000 J/mol. 4. Battery pack consistency simulation 4.1. Simulation experimental scheme The consistency of the battery pack is gradual, so it requires a very long time to the actual experiment. In addition, because of the statistical of the battery pack consistency, more cells are needed to experiment in group. The control and measurement of the single cell parameters will affect the experiment of battery pack. The complexity of the experimental study is not operational. Therefore, the study on the inconsistency mechanism of the battery pack is mainly based on the simulation experiment. Based on the simulation study to the basic behavior of the consistency of the battery pack, a simplified experimental study is carried out in this article. In practice, there are many factors affecting the inconsistency of the battery pack, and there is a complex coupling relationship, which is difficult to distinguish the influence factors of the inconsistency of the battery pack. But we can get the ideal battery pack by simulation experiment, which is obtained only one inconsistent factor in the early stage in group and the other factors are completely consistent. The consistency influence factors of the battery pack are obtained by the consistency simulation of the ideal battery pack. It can provide a theoretical guidance for the screening and equalization methods of the battery pack. Taking into account the consistency of the battery manufacturing, some parameters themselves are relatively good, and the consistency of the other parameters is relatively difficult to guarantee. Battery cells are commonly screened before they are in group. According to different screening conditions, inconsistency parameters in group necessarily vary. We assume that the parameter after the screening process will comply with a normal distribution of small standard deviation. Without screening, the parameter distribution is still normal distribution, but the standard deviation will be larger than the screened parameters. Table 1 gives the simulation experimental parameter matrix. Three different scenarios, namely, good consistency, general consistency and poor consistency, are given for four initial state parameters and four other parameters in Fig. 1. The expectations of the three scenarios are the same, and the difference lies in the standard deviation. Among them, the situation 1 (S1) standard deviation is the smallest, that is, the consistency is the best, and the scenario3 (S3) standard deviation is the biggest, corresponding to the worst consistency. The criteria for selection of the standard deviation are as close as possible and include all possible actual consistency of the battery packs. The simulation experiment is carried out in 24 groups, each group has 1000 standard cycles, and the results are compared and analyzed. 4.2. Simulation analysis and results
(13)
Wheref ðSOC; TÞis the initial resistance, gðT; tÞis the resistance increase caused by durability. Toshio Matsushima [29] gives a 400 Ah lithium battery internal resistance change curve. According to this curve, we approximate that at constant temperature the resistance growth is linear with the time. Similarly the resistance rate of growth dR/dt is introduced, and resistance under the temperature varies is obtained by the internal resistance growth rate dR/dt integral.
We take the battery pack capacity as the main indicator of the consistency of the pure electric vehicle battery pack. 24 groups of simulation experimental results for 8 kinds of single factor parameter are analyzed. Because of so many results, this paper gives the simulation results analysis of four typical single factor parameters. That is coulombic efficiency inconsistency analysis, self-discharge rate Inconsistency analysis, capacity fading inconsistency analysis and temperature inconsistency analysis. The authors have made the same analysis to the other four parameters,
L. Zhou et al. / Journal of Power Sources 364 (2017) 242e252
247
Table 1 Simulation parameter settings. Single factor
Initial capacity (Ah) Initial SOC (%) Initial resistance Initial temperature ( C) Capacity decay Internal resistance growth Self-discharge rate Coulombic efficiency
Expectations
70 50 1 25 1 1 1 0.9995
Standard deviation Scenario 1(S1)
Scenario 2(S2)
Scenario 3(S3)
0.07 0.1 0.05 0.5 0.05 0.05 0.05 1e-5
0.35 0.5 0.1 1 0.1 0.1 0.1 3e-5
0.7 1 0.15 1.5 0.15 0.15 0.15 5e-5
Fig. 3. Battery pack capacity, capacity loss composition and the comparison equalization recoverable capacity under different coulombic efficiency inconsistency scenarios.
and the results show that the other four factors have little effect on the inconsistency, so they are no more discussed in this paper. Inconsistency analysis results are mainly used to guide the design of the battery pack and the equalization. Our previous research [30] shows that the battery pack could be balanced by the dissipative cell equalization, and the maximum potential of the dissipative cell equalization is to make the battery pack to reach the smallest cell capacity. Therefore, comparing the capacity of the battery pack and the smallest cell can indicate that the battery pack capacity can be recovered after the equalization. 4.2.1. Coulombic efficiency The solid line in Fig. 3(A) is the battery pack capacity obtained with the number of cycles as the horizontal coordinate, and the dashed line shows the maximum battery pack capacity that be achieved by the dissipative cell equalization (the smallest capacity of cell in the battery pack). Capacity of the battery pack is calculated by formula (1). Here initial battery rated capacity is uniformly used as the rated capacity and the nominal capacity of the battery pack. S1, S2 and S3, respectively, represent three scenarios in Table 1 that coulombic efficiency inconsistency from low to high. From Fig. 3(A), we can see that the capacity of the battery pack is equal to that of the single cell at the beginning. With the ongoing cycles, battery
capacity fade is greater than the single cell of the minimum capacity, and the higher the coulombic efficiency standard deviation is, the faster the capacity decay of the battery pack. Since only the coulombic efficiency is not consistent, the capacity decay curves of the single cells basically overlap. We can see that the capacity of the battery pack is very sensitive to the coulombic efficiency. Within 1000 cycles, the capacity loss is only about 10%. However, the battery pack capacity loss under the minimal standard deviation simulation scenarios S1 has reached 16%, namely, coulombic efficiency inconsistency contributed about 6% capacity loss. For the simulation scenarios S2 and S3 with larger coulombic efficiency inconsistency, and the battery capacity of the battery pack has reached the end of life in about 900 and 500 cycles, that is, 80% of the initial capacity. For the coulombic efficiency inconsistency simulation S2, the capacity loss caused by the coulombic efficiency inconsistency is almost equal to that by durability. Fig. 3(B) gives the composition of the capacity loss of the battery pack under simulation scenarios S2. The red part of DCIII is the capacity loss of battery pack, which cannot be balanced. It is caused by the capacity loss of the single cell itself. The yellow and narrow part DCII which cannot be clearly seen in this figure is the capacity of battery pack that the real time non-dissipative cell equalization will additionally gain compared to the dissipative cell
248
L. Zhou et al. / Journal of Power Sources 364 (2017) 242e252
equalization. The green part DCI is the restore capacity can be restored by the dissipative cell equalization and the blue part is the capacity of the battery pack under S2. We can see the recovery capacity DCI and the loss capacity DCIII is almost equal. For the worst inconsistency under the S3, the dissipative cell equalization needs to recover 21% capacity within 1000 cycles, with each cycle of only 0.21‰. If battery pack has 1 h for the balancing in a cycle, with the current which is 1‰ of the pack capacity, the battery pack would be well balanced. It means for the 100 Ah battery pack, the current needed for the dissipative cell equalization is only 100 mA. So even if the coulombic efficiency is not consistent under the worst S3, the dissipative cell equalization is completely adequate. Fig. 3(C) gives the recoverable capacity of the dissipative cell equalization. Fig. 3(D) shows the real time non-dissipative cell equalization can recover additional capacity compared to the dissipative cell equalization. It can be seen that with the increase of coulomb efficiency inconsistency, the real time non-dissipative cell equalization additional recovery capacity is increased. The inconsistency of the coulomb efficiency affects the durability inconsistency, and the two are positively correlated, and both are positively related, namely the increase of coulomb efficiency inconsistency will raise the inconsistency of durability. However, considering the specific impact, after 1000 cycles, the real time non-dissipative cell equalization additional recovery capacity less than 0.1%, so this effect can be ignored. The above analysis shows that the dissipative cell equalization can meet the requirements of the battery pack due to the inconsistency of coulomb efficiency, and the difference between the recovery capacity and the real time non-dissipative cell equalization is very small, so it is not necessary to carry out the real time non-dissipative cell equalization. 4.2.2. Self-discharge rate The same result can be seen by the analysis of the inconsistency
effect of self-discharge rate in a similar way. Due to the inconsistency of self-discharge rate, the capacity decay of the battery pack is larger than that of the smallest cell, and the higher the selfdischarge rate standard deviation is, the faster the capacity decay of the battery pack. The effect of self-discharge rate on the capacity of the battery pack is slightly less than that of the coulombic efficiency. But for the S3 of the larger self-discharge rate inconsistency, which can also account for about 5% of the capacity loss. This 5% loss can also be recovered by the dissipative cell equalization. 4.2.3. Capacity fade In Fig. 4(A), the capacity of the battery pack under the inconsistency of capacity fading is presented. The solid line in Fig. 4(A) is the battery pack capacity. The dashed lines expressed the maximum battery pack capacity CI by using the dissipative cell equalization and they are completely overlapped. So the dissipative cell equalization cannot restore the capacity of the battery pack in this case. In addition, the small capacity decay inconsistency of the battery pack under the S1 compared to that under the S3 has a larger capacity. Because the capacity of battery pack is completely determined by the minimum cell capacity of the battery pack. And the minimum single cell capacity of the battery pack with large capacity fading inconsistency has a fast capacity loss. But the capacity loss caused by capacity fade inconsistencies proportion is not big. In Fig. 4(A), the capacity of the battery pack is still about 85% after 1000 cycles under the S3 which is the maximum capacity fade inconsistency. Fig. 4(B) gives the composition of the capacity loss of the battery pack under simulation scenarios S2. The red part of DCIII is the capacity loss of battery pack, which cannot be balanced. It is caused by the average capacity loss of the single cells. The yellow part DCII is the capacity of battery pack that the real time non-dissipative cell equalization can restore. The green part DCI is the restored capacity of the dissipative cell equalization and its value is essentially zero.
Fig. 4. Battery pack capacity, capacity loss composition and the comparison of equalization recoverable capacity under different capacity fade inconsistency scenarios.
L. Zhou et al. / Journal of Power Sources 364 (2017) 242e252
The blue part is the capacity of the battery pack under S2. The recovery capacity DCI by the dissipative cell equalization is very small, but the recovery capacity DCII is a major part of the battery pack recoverable capacity. Fig. 4(C) and (D) show the comparison of the dissipative cell equalization and the real time non-dissipative cell equalization recovery capacity. It can be found that the dissipative cell equalization has no capacity to recover under capacity fade inconsistency scenarios. But in the worst capacity fade inconsistency scenario, the real time non-dissipative cell equalization additional recoverable capacity can only reach about 4% of the battery pack capacity. While in reality, the real time non-dissipative cell equalization can only achieve good results by ensuring that all the cells are fully charged and discharged. In this process, the non-dissipative cell equalization must work in real time. The charge of the larger capacity cell is transferred to the smaller capacity cell when discharging, and charging is on the contrary. Therefore, the equalization algorithm becomes complicated. 4.2.4. Temperature Fig. 5(A) shows that the temperature inconsistency has great influence on the capacity of the battery pack. The consistency of the single cell is influenced by the temperature inconsistency, so the minimum single cell capacity curve is not consistent in the three scenarios. The battery pack capacity fade is relatively small in temperature difference S1 (2.2 C)). The temperature difference of the S3 is 8.8 C, and the battery pack reached the end of life after about 750 cycles. The capacity loss caused by the temperature inconsistency is almost equal to that caused by durability. Fig. 5(B) gives the composition of the capacity loss of the battery pack under simulation scenarios S2. At this scene, the green DCI and yellow DCII can be obviously observed. In the case of temperature is
249
not consistent, the recoverable capacity DCI of energy consumption has great value. Compared with the dissipative cell equalization, the recovery capacity DCII by the complicated real time nondissipative cell equalization is relatively small. From Fig. 5(C), the battery pack recovery capacity of the dissipative cell equalization after the 1000 cycles is only about 3% under the smallest temperature difference S1. While under the maximum temperature difference scenario S3 (8.8 C) the recoverable capacity of the dissipative cell equalization reaches 11% after the 1000 cycles. In contrast, from Fig. 5(D), the real time non-dissipative cell equalization additional recovery capacity is only about 2% under maximum temperature difference scenario S3. Therefore, we believe that in temperature inconsistency situation, the dissipative cell equalization of the battery pack is sufficient to meet the requirements. 4.2.5. Other parameters and capacity loss rate The other parameters inconsistency simulation includes the initial SOC, the initial capacity, internal resistance growth and the internal resistance. The inconsistency of the initial SOC and the initial capacity does not increase the battery capacity loss, and it was screened before in group, so it can be considered that the inconsistency has little effect on the inconsistency of the battery pack. Fig. 6 shows the capacity loss rate of the battery pack after 1000 cycles. From Fig. 6, the coulombic efficiency, temperature, internal resistance growth and self-discharge rate are the main factors that affect the consistency of the battery pack. The factors that directly affect the inconsistency of the battery pack are the coulomb efficiency and the self-discharge rate. Temperature difference is caused by the internal resistance inconsistency, and the temperature difference leads to the inconsistency of coulomb efficiency and self-discharge rate.
Fig. 5. Battery pack capacity, capacity loss composition and the comparison of equalization recoverable capacity under different temperature inconsistency scenarios.
250
L. Zhou et al. / Journal of Power Sources 364 (2017) 242e252
Fig. 6. Battery pack capacity loss rate under different inconsistency scenarios.
4.3. Conclusion of simulation results We conclude the following main conclusions from the simulation results: (1) Coulombic efficiency, temperature and self-discharge rate are the main factors that affect the consistency of the battery pack. Because of coulombic efficiency and the self-discharge rate is generally difficult for screening, it has a great influence on the consistency of the battery pack. This problem requires special attention when the battery is in group. (2) The temperature has a great effect on the consistency of the battery pack, although the temperature does not directly affect the consistency of the battery and also has little effect on the inconsistency of battery capacity. But the temperature will affect the coulombic efficiency and self-discharge rate, which leads to the inconsistency of SOC. So it has a great influence on the battery pack inconsistency. In the simulation experiment, the temperature difference is less than 5 C, the inconsistency is reluctantly accepted. And when temperature difference reached more than 8 C, the capacity of the battery pack decreased quickly. So it is very important to ensure good temperature uniformity for the batteries in group. We suggest that the temperature difference in the thermal management of the battery pack should be controlled within 5 C. (3) The dissipative cell equalization is enough to online equalization for battery packs. There is no need to use the complicated real time non-dissipative cell equalization for on line application. It is suggested that the non-dissipative cell equalization can be used for the maintenance of the battery pack, while the on-board vehicle battery can be balanced by the dissipative cell equalization.
influence of temperature inconsistency on the battery pack. Commercial 12 Ah cells with the anode of graphite and the cathode of LiFePO4 are chosen for the experiment. The experiment by changing the two cells temperature difference is to verify the composition of capacity loss of battery pack. Under the condition of no manufacturing defects, two cells are considered to have little differences. The two cells are respectively placed in two different temperature incubators. A larger temperature difference between cells I and II is chosen to get the obvious results and accelerate the experimental process. Cell I is in a 30 C environment and cell II is placed in a constant temperature chamber of 45 C. The experiment procedure is described in Table 2, which has three stages. In the first stage, capacities of the cell I and II are tested at two different environmental temperatures respectively. The cells capacity test procedure: the cell is discharged at a constant current of 4 A which is the normal discharge rate of 1/3C. After standing for 1 h, the cell is charged to the charge cutoff voltage at a constant current of 1/3C, and then the cell is rested for 10 s and is continued to be charged at a constant current of 1/20C (0.6 A) to the charge cutoff voltage again. The cell completes a full cycle. There are four cycles. After completing the cell basic performance experiments in the first stage, the battery pack experiment is carried out in the second stage. The battery pack is cycled 200 times at a 1C charge and discharge and a 10 day rest which should also consider calendar aging. Battery pack capacity is tested once every 20 cycles and after a standing for 10 day. The schematic diagram of the battery pack testing procedure in the second stage is shown in Fig. 7. Pack capacity is measured using the same scheme as the cells. The charge and discharge end voltage of the battery pack is at the cutoff voltage of any cells. In the third stage, the battery pack is disassembled into cell I and cell II. Capacity test is carried out at the original temperature, and the testing process is the same as the first stage.
5. Preliminarily experimental verification 5.2. Measured results 5.1. Experiment setup Two cells are connected in series in the experiment to verify the
Cell capacity test results in the first stage and third stage are shown in Table 3. The charging capacity and discharge capacity are
L. Zhou et al. / Journal of Power Sources 364 (2017) 242e252
251
Table 2 Three stages in the experiment. Stage number
stage 1
Experiment subject
Cell I, Cell II Battery pack
stage 2
stage 3 Cell I, Cell II
Experiment environment
Cell I 30 C Cell I 30 C, Cell II 45 C Cell II 45 C Cell I and cell II connected in series
Cell I 30 C Cell II 45 C
Experiment contents
Capacity tests
20 cycles at 1C and a pack capacity test as a large cycle. A total of 10 large cycles and the pack is rested for 10 days after the Capacity third large cycle tests
Fig. 7. A schematic diagram of the battery pack testing procedure in the second stage.
Table 3 Cell capacities in the first and third stage. Stage number
Cell I (30 C)
Charge capacity (Ah) Discharge capacity (Ah) Charge capacity (Ah) Discharge capacity (Ah)
Cell II (45 C)
Stage 1
Stage 3
11.8233 11.7919 11.8157 11.7946
11.5780 11.5379 11.3304 11.3075
Table 4 Battery pack capacity in the second stage. Cycle
0
20
40
60A
60B
80
Charge capacity (Ah) Discharge capacity (Ah)
11.7909 11.7617
11.7065 11.6734
11.6460 11.6117
11.5891 11.5568
11.4254 11.3963
11.3972 11.3643
Cycle
100
120
140
160
180
200
Charge capacity (Ah) Discharge capacity (Ah)
11.3532 11.3207
11.3074 11.2752
11.2373 11.2053
11.1902 11.1542
11.1395 11.1108
11.0726 11.0387
Fig. 8. Battery pack capacity and capacity loss composition in the experiment.
252
L. Zhou et al. / Journal of Power Sources 364 (2017) 242e252
very close. Accordingly, the discharge capacity is selected as the capacity of the single cell. Single cell capacity can only be measured in the first and third stages, namely 0 and 200 cycle capacity. The cell capacity in other cycle stages is estimated by linear interpolation. This linear estimation is acceptable for the cell in 200 cycles. Pack capacities in the specific cycles during the second stage are also obtained from the experiment, and the results are shown in Table 4. The difference of the charge and discharge pack capacity is also significantly small so the discharge capacity is selected as the capacity of battery pack. The label of 60A is the result of the capacity test before 10 days settling time, and 60B is the result after 10 day settling time. Fig. 8(A) shows a comparison of the cell capacity by linear estimation and measured pack capacity. The cell temperature difference has great influence on the capacity of the battery pack. Fig. 8(B) demonstrates the normalized capacity loss composition of the battery pack from the experiment. The experimental capacity loss composition results are consistent with the simulation. The green DCI and yellow DCII can be obviously observed. In order to more obvious experimental results, the cell temperature difference is set to 15 C. If the experimental temperature difference is set to the same simulated temperature difference (5 C), the experimental results may be closer to the simulation results. The recoverable capacity DCI of energy consumption has great value from the experiment results. Compared with the dissipative cell equalization, the recovery capacity DCII by the complicated real time nondissipative cell equalization is relatively small. 6. Conclusion In this study a battery pack model with 96 cells in series model was proposed and used for describing the consistency of the battery pack. The basic consistency performance characteristics of the coupling, statistical, weight, irreversibility and graduality of the battery pack for pure electric vehicle were analyzed. We use the actual physical quantity (battery pack capacity) to describe the consistency of the battery pack. The factors that affect the consistency of the battery pack were studied. According to the simulation and experiment, the capacity loss composition of the battery pack was obtained and verified, which is mainly composed of three parts. Based on our results, we can choose the optimal equilibrium strategy of the battery pack in electric vehicles. This study offers a comprehensive understanding of the parameter variation effects on battery packs for electric vehicles. The results show that the consistency of the battery pack is mainly affected by coulombic efficiency, temperature and self-discharge rate. Coulombic efficiency and self-discharge rate are difficult to be screened, and therefore it is important to control the differences among the battery cells in manufacturing process to improve the consistency of the battery pack. The control of temperature difference needs to have a good battery thermal management. The consistency of the battery pack in the temperature difference is acceptable when it is less than 5 C. On the other hand, when the temperature difference is greater than 8 C, the consistency of the
battery pack will be considered poor. The simulation and experimental results also show that the dissipative cell equalization is enough for the online equilibrium of the battery pack. The equilibrium current required by the dissipative cell equalization channels can be as less as 1‰ of the 1 C charge and discharge current of the battery pack. Acknowledgment This research is supported by the National Natural Science Foundation of China (NSFC) under the Grant number of 51507102, “Chenguang Program” supported by Shanghai Education Development Foundation and Shanghai Municipal Education Commission under the grant number of 16CG52, and the State Key Laboratory of Automotive Safety and Energy under Project No. KF16022. References [1] V. Etacheri, R. Marom, E. Ran, G. Salitra, D. Aurbach, Energy Environ. Sci. 4 (2011) 3243e3262. [2] L.X. Yuan, Z.H. Wang, W.X. Zhang, X.L. Hu, J.T. Chen, Y.H. Huang, J.B. Goodenough, Energy Environ. Sci. 4 (2010) 269e284. [3] B. Scrosati, J. Hassoun, Y.K. Sun, Energy & Environ. Sci. 4 (2011) 3287e3295. [4] G. Jeong, Y.U. Kim, H. Kim, Y.J. Kim, H.J. Sohn, Energy Environ. Sci. 4 (2011) 1986e2002. [5] Y. Zheng, X. Han, L. Lu, J. Li, M. Ouyang, J. Power Sources 223 (2013) 136e146. [6] S. Castano, L. Gauchia, E. Voncila, J. Sanz, Energy Convers. Manag. 92 (2015) 396e405. [7] L.H. Saw, Y. Ye, A.A.O. Tay, W.T. Chong, H.K. Seng, C.Y. Ming, Appl. Energy 177 (2016) 783e792. [8] M. Berecibar, M. Garmendia, I. Gandiaga, J. Crego, I. Villarreal, Energy 103 (2016) 784e796. [9] B. Kenney, K. Darcovich, D.D. Macneil, I.J. Davidson, J. Power Sources 213 (2012) 391e401. [10] Y. Wang, C. Zhang, Z. Chen, J. Xie, X. Zhang, Appl. Energy 145 (2015) 36e42. [11] L. Lu, X. Han, J. Li, J. Hua, M. Ouyang, J. Power Sources 226 (2013) 272e288. [12] M. Daowd, N. Omar, P.V.D. Bossche, J.V. Mierlo, in: 26 th Hybrid and Fuel Cell Electric Vehicle Symposium (EVS-26) 26th Hybrid and Fuel Cell Electric Vehicle Symposium (EVS-26), 2012, pp. 1e9. [13] J. Gallardo-Lozano, E. Romero-Cadaval, M.I. Milanes-Montero, M.A. GuerreroMartinez, J. Power Sources 246 (2014) 934e949. [14] Z.P. Wang, F.C. Sun, L. Chen, Beijing Ligong Daxue Xuebao/Trans. Beijing Inst. Technol. 26 (2006) 577e580. [15] M. Guo, R.E. White, J. Electrochem. Soc. 158 (2011) A1166eA1176. [16] M. Dubarry, N. Vuillaume, B.Y. Liaw, J. Power Sources 186 (2009) 500e507. [17] J. Li, M.S. Mazzola, J. Power Sources 237 (2013) 215e228. [18] M. Dubarry, N. Vuillaume, B.Y. Liaw, Int. J. Energ. Res. 34 (2010) 216e231. [19] M. Mathew, Q.H. Kong, J. Mcgrory, M. Fowler, J. Power Sources 349 (2017) 94e104. [20] X. Zhang, Y. Wang, D. Yang, Z. Chen, Energy 115 (2016) 219e229. [21] P. Liu, H.H. Zhu, J. Chen, G.Y. Li, in: Chinese Control and Decision Conference, 2016, pp. 6228e6231. [22] F. Baronti, R. Roncella, R. Saletti, J. Power Sources 267 (2014) 603e609. [23] M. Dubarry, A. Devie, B.Y. Liaw, J. Power Sources 321 (2016) 36e46. [24] G.L. Plett, J. Power Sources 134 (2004) 262e276. [25] J. Wang, P. Liu, J. Hicks-Garner, E. Sherman, S. Soukiazian, M. Verbrugge, H. Tataria, J. Musser, P. Finamore, J. Power Sources 196 (2011) 3942e3948. [26] T. Utsunomiya, O. Hatozaki, N. Yoshimoto, M. Egashira, M. Morita, J. Power Sources 196 (2011) 8598e8603. [27] J. Wang, B. Cao, Q. Chen, F. Wang, Control Eng. Pract. 15 (2007) 1569e1576. [28] Y. Zheng, M. Ouyang, L. Lu, J. Li, Z. Zhang, X. Li, J. Power Sources 289 (2015) 81e90. [29] T. Matsushima, J. Power Sources 189 (2009) 847e854. [30] Y. Zheng, M. Ouyang, L. Lu, J. Li, X. Han, L. Xu, J. Power Sources 247 (2014) 676e686.
Contents lists available at ScienceDirect
Journal of Power Sources journal homepage: www.elsevier.com/locate/jpowsour
A study on parameter variation effects on battery packs for electric vehicles Long Zhou a, Yuejiu Zheng a, b, *, Minggao Ouyang b, Languang Lu b a b
College of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai 200093, PR China State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, PR China
h i g h l i g h t s A battery pack model with 96 cells in series is proposed for the consistency of battery pack. The capacity loss composition of the battery pack is obtained by simulation and experiment. Use the battery pack available capacity as the inconsistency physical quantity. The battery pack screening and management scheme is proposed.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 May 2017 Received in revised form 20 July 2017 Accepted 10 August 2017
As one single cell cannot meet power and driving range requirement in an electric vehicle, the battery packs with hundreds of single cells connected in parallel and series should be constructed. The most significant difference between a single cell and a battery pack is cell variation. Not only does cell variation affect pack energy density and power density, but also it causes early degradation of battery and potential safety issues. The cell variation effects on battery packs are studied, which are of great significant to battery pack screening and management scheme. In this study, the description for the consistency characteristics of battery packs was first proposed and a pack model with 96 cells connected in series was established. A set of parameters are introduced to study the cell variation and their impacts on battery packs are analyzed through the battery pack capacity loss simulation and experiments. Meanwhile, the capacity loss composition of the battery pack is obtained and verified by the temperature variation experiment. The results from this research can demonstrate that the temperature, selfdischarge rate and coulombic efficiency are the major affecting parameters of cell variation and indicate the dissipative cell equalization is sufficient for the battery pack. © 2017 Elsevier B.V. All rights reserved.
Keywords: Electric vehicle Battery pack Cell variation Battery parameters Cell equalization Capacity loss
1. Introduction Due to the commercialization of pure electric vehicle, the mileage range and the lifespan of electric vehicle have gained increasing interests to the researchers. Hence, a lot of studies have primarily focused on the single cell and new materials [1e4], power density and cycle life of the single cell. However, single cell is unable to meet the power and energy requirements for electric vehicles. Hundreds of the single cells need to be connected in series and parallel to each other to construct battery packs [5e8] so as to
* Corresponding author. College of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai 200093, PR China. E-mail address: [email protected] (Y. Zheng). http://dx.doi.org/10.1016/j.jpowsour.2017.08.033 0378-7753/© 2017 Elsevier B.V. All rights reserved.
provide enough power and energy for electric vehicles to meet the requirements of its accelerated climbing and mileage. Unfortunately, due to the inconsistency of the manufacturing process and use of the process environment, the cell variations always exist [9e11] and are unable to eliminate. The energy density, durability and safety performances of the battery pack are affected by every single cell in group because of cell variation [5]. Therefore, the battery pack is usually equalized to reduce the inconsistency. There are two general equalization methods: one is the dissipative cell equalization, and the other is the non-dissipative cell equalization (energy transfer). The dissipative cell equalization method usually adopts resistance discharge equalization, and the non-dissipative cell equalization adopts topology diversity. The topology of nondissipative cell equalization method is summarized in previous studies [12e13].
L. Zhou et al. / Journal of Power Sources 364 (2017) 242e252
In practical application, the poor uniformity of the battery cells will influence the performance of the whole battery pack. First, because of the inconsistent initial capacity and initial state of charge (SOC), the actual available energy of the battery pack is lower than any single cell; it will directly cause the loss of the energy density in group. Second, due to the non-uniformity of internal resistance, the maximum current of the series battery pack is limited by the worst power density of the single cell. So the power density of the battery decreases in the battery pack. Third, compared to the single cell, the actual available power of the battery pack is not only limited by the capacity fade, but also affected by the self-discharge and coulombic efficiency. So its life is shorter than any single cell. As the consistency of the battery cells is an important factor influencing the above three aspects which are adopted to evaluate the performance of the battery pack, the studies on the battery consistency have attracted greater attention recently. Some studies indicate that the cycle life of the battery pack is much less than the single cell. Even the single cells have a cycle life more than 1000 cycles in group, without a balancing technology, the battery pack actual cycle life could be less than 200 cycles. The causes of this phenomenon is not that one cell cycle life is shortened to 200 cycles [14], but the capacity of the battery pack is limited by the minimum residual and rechargeable capacity of the single cells. The lifespan of the battery pack could be decreased when the cell inconsistency is increased. Significant efforts have been made from single cell models to pack-level models, taking into account cell variability [15e18]. However, the current studies [19e21] on the evolution mechanism of battery pack inconsistency are still in the stage of qualitative description. For example, Mathew et al. [19] investigated the simulation framework of cell replacement in a battery pack. Baronti et al. [22] compared five topologies for balancing series connected lithium-ion batteries by the statistical simulations. They showed that the cell to cell topology was the quickest and most efficient one. Dubarry et al. [23] investigated cells balancing behavior in parallel, and an equivalent circuit model was developed to simulate the spontaneous transient balancing currents in a battery system. In order to deeply analyze the inconsistencies evolution mechanism of battery packs, the basic features and description method of the consistency performance in battery packs for pure electric vehicles are investigated in this paper. The battery pack model with 96 cells in series is established. The influence factors of the consistency on battery pack are studied by simulation and experiment. The capacity loss composition of the battery pack is obtained and verified by the temperature variation experiment. Finally, the battery pack screening and management scheme regarding the consistency of the battery pack is proposed. 2. Description for the consistency characteristics of a battery pack 2.1. Consistency characteristics and the influence factors of battery packs Practice shows that the consistency of the battery pack will experience a gradual deterioration process. In general, the inconsistencies damage to the battery pack life is more serious than that of the durability of the single cell. Most of the literature suggests that the inconsistencies between cells reflect in the voltage, SOC, capacity, internal resistance and temperature. In fact, the inconsistency of these parameters is only reflected in the current state, so it is not complete. Considering the variation of the time, the inconsistency between the cells also includes the inconsistency of the self-discharge rate, the inconsistency of the coulomb
243
efficiency, the inconsistency of the capacity degradation and the aging of the internal resistance etc. The inconsistencies of these parameters in the process will be directly reflected in the inconsistency of state. Fig. 1 demonstrates the mutual relations among various parameters of cells. We divide them into three classes, the initial states, the current states, and the time accumulations. Their mutual influence cell parameters are shown in Fig. 1. Generally, we use the current states to express inconsistency of the battery pack. The current states include the capacity, voltage, SOC, internal resistance and temperature. Specifically, direct impacts on the practical battery energy output are the capacity and SOC, while the internal resistance decisively affects the practical power output. Moreover, the voltage and temperature are relatively easy to measure. Therefore, these current states are popularly adopted in the battery pack consistency analysis for practice applications. But in fact the influence factors of battery consistency are the initial states and the time accumulations. The initial states are the states when the cells are just constructed, and the parameters of the initial states have great influence on the short term consistency of the battery pack. And since their measurement and control difficulty is relatively low, the initial state becomes the main factors in the screening process for battery cells. The time accumulations affect the longterm consistency of the battery pack, and the influences are greater than the initial states. So screening process for the time accumulative factors is more important. However, due to the difficulty of screening the time accumulations, these parameters are less likely to be screened in practice. The above analysis and practice show that the consistency of the battery pack has the following basic characteristics: 2.1.1. Coupling property Parameter inconsistencies of the cells are coupled together, forming a complex association network. In particular, temperature inconsistency affects almost all other cell parameters. Some parameters are coupled to form a positive feedback to accelerate the inconsistency of the battery pack, such as coupling temperature and internal resistance results in greater inconsistency of the temperature and internal resistance. Due to the presence of coupling, the battery pack inconsistency behave complex. The evolution mechanism of cell inconsistencies is difficult to reveal. 2.1.2. Statistical property The consistency of the battery pack is reflected by the statistic characteristics of the single battery cell. The battery pack is usually made in parallel and series by thousands of cells, and all parameters of the battery cells meet certain statistical behavior. 2.1.3. Weight property The worse performance of the cell will have worse effects on the
Time accumulations Capacity fading rate
The current states
The initial states Initial capacity
Capacity Voltage
The resistance rate of growth
Coulomb efficiency
Initial SOC
SOC Internal resistance
Initial resistance
Temperature
Initial temperature
Fig. 1. Influence relationship of cell parameters.
244
L. Zhou et al. / Journal of Power Sources 364 (2017) 242e252
inconsistency of the battery pack. However, the average performance of the battery in the battery pack does not affect the inconsistency. So when using the statistics to describe the parameters of the battery pack, the weight of battery cells should be taken into account for the battery inconsistency analysis. In statistics, the weights of various samples are generally the same, such as the standard deviation, variance and so on, while the range statistics is extreme weight. 2.1.4. Irreversibility In the absence of external effects (such as a balanced, or replace part of the battery cells), the consistency of the battery pack always tends to be worse. Due to the initial states, there could be a certain inconsistency in the battery pack. And generally with the cell screening process, initial inconsistency could be relatively small. The inconsistency of the battery pack is mainly caused by the inconsistency of the time accumulative factors. The inconsistency of the battery pack caused by the time accumulative factors is not reversible, and the inconsistency always tends to increase. 2.1.5. Graduality The change of the battery pack consistency is a gradual process. Even if the consistency is very poor, it will not produce a very rapid decline. This is because the differences of time accumulative factors between cells are very small in the short term. Therefore, the time scale used to measure the consistency change of the battery pack is commonly counted not in days but in months. If a large consistency change of the battery pack was found, it usually means battery malfunction, or the consistency of judgment error might happen.
minimum chargeable capacity of cells. We use the following equation to calculate the pack capacity [11].
CPack ¼ minðSOC$CÞ þ minðð1 SOCÞ$CÞ
(1)
Where CPack is the battery pack capacity, SOC is a vector consisting of all the cells SOC in the battery pack. C is a vector consisting of all the single cell capacity of the battery pack. Operator min () represents the minimum value of the elements in the vector. Operator represents the corresponding elements of the vector multiplication. It can be seen from formula (1) that the capacity of the battery pack is usually smaller than the minimum cell. The capacity loss of the battery pack is mainly composed of three parts. First, the capacity of the single cell cannot be fully utilized, resulting in inconsistencies capacity loss of the battery pack (marked as DCI), which can be compensated through a conventional equalization method. Its maximum potential capacity of the battery pack is the minimum capacity of the cell. Second, the capacity loss for the battery pack (marked as DCII) is caused by the inconsistency capacity of the cells, which is resulted from the inconsistencies of the capacity fade and the initial capacity. This part of the capacity loss can be compensated by a more complex, real time, non-dissipative balancing approach, which has the greatest potential to recover the average capacity of all the cells in the battery pack. Finally, the inevitable cell capacity loss leads to the capacity loss of the battery pack, and this part of capacity loss for a battery pack (marked as DCIII) depends entirely on the cell durability. The influence factors of the consistency for the battery pack will be studied from the above three aspects of capacity loss in the following sections.
2.2. Methods for describing consistency of battery pack 3. Battery pack modeling According to the consistency characteristics of the battery pack, the standard deviation and the range statistics are often used to describe the inconsistency of the battery. These described methods are relatively easy to implement, thus have a much wider application. But these statistics do not directly reflect the decrease in the energy density of the battery pack due to the inconsistency. In this paper, we use the battery pack available capacity as the inconsistency physical quantity which can directly describe the shortened life of the battery pack. The definition of battery pack capacity is similar to the single cell. That is, under 25 C environment, the battery pack starts to discharge in 1/3C rate when one of the cells in the battery pack is in the fully charged state, until one cell has completely released its capacity. Since the charge capacity and the discharge capacity of the lithium-ion battery difference is small [6], the charge capacity can also be approximated as the battery capacity. In the absence of a balancing technology, due to inconsistencies of the battery pack, when some of the cells have no remaining capacity and power (noted as Cell A), other batteries could still have surplus capacity. But the battery pack cannot continue to be discharged, otherwise it will result in a large reduction in battery life, and even safety problems due to over-discharge of Cell A. Similarly, when some of the cells achieve the cut-off voltage (noted as Cell B, Cell B also may be Cell A), other cells still have rechargeable capacities, but the battery pack cannot continue charging. The battery pack available capacity should be the capacity charged from the empty Cell A to fully charged Cell B. When Cell A and B are the same, the available capacity of the battery pack is the same as Cell A. For the series connected battery pack that is not completely emptied, the amount of electricity that can be charged and released is determined by the minimum remaining charging and discharging cells respectively. Therefore, the battery pack capacity is considered as the sum of the minimum remaining available capacity and the
3.1. The overall modeling scheme of battery pack Battery pack model is mainly used for consistency simulation analysis. The 70 Ah LiFePO4 battery parameters are used from the single cell experiment as a reference, and battery model is built up using Matlab Simulink®. The basic structure of the model is shown in Fig. 2. Battery pack system model includes a battery pack model, power management and output gauges. The main function of power management is to control the battery charge and discharge, the purpose is to prevent any cell voltage form exceeding a cut-off voltage. In order to accelerate the speed of cell cycle, we use 1C rate to charge and discharge. After charging to the charge cut-off voltage, the power management module discharges the battery pack directly to the discharge cut-off voltage, and completes a cycle. The function of the output gauges is to observe the state of the battery, and record the battery data. The battery pack model is composed of 96 cells in series. Each
Fig. 2. Battery pack model.
L. Zhou et al. / Journal of Power Sources 364 (2017) 242e252
cell model has a basic circuit model and also contains five sub models, including internal resistance model, coulombic efficiency model, capacity fading model, self-discharge model and thermal model. These models are the most important part of the whole battery pack system. These models are discussed in the following sections respectively.
245
is the mass; Cmi is the specific heat capacity of the battery. The essence of the simple thermal model is the thermal balance process between the cell internal resistance heat release and convection heat dissipation. For the currently selected 70 Ah battery, these parameters are set to qi ¼ 20 W/K$m2, Ai ¼ 0.12 m2, mi ¼ 2 kg, Cmi ¼ 1000 K/W$kg$s.
3.2. Single cell model 3.2.1. Basic circuit model The simple Rint model is used as the cell equivalent circuit model of the battery pack. The Rint model proposed by G.L. Plett et al. [24] considers the cell as an ideal voltage source and a resistance in series. The open circuit voltage and resistance vary with time, and the model is as follows.
U ¼ OCVðSOCÞ þ IRi
(2)
U is the battery terminal voltage, which is measurable. OCV (SOC) is the open circuit voltage and the SOC curve of the battery, which is measured by the basic performance experiment. I is the current, positive when charged and vice versa. Ri is the internal resistance of the battery, which is given by the resistance model. The calculation of SOC is determined by the relationship between the remaining electric quantity and the capacity. Its model is as follows.
Z Cri ¼ SOC0i $C0i
zi ðtÞdt þ
Z
hi ðtÞIðtÞdt
(3)
Cri is the remaining electric quantity of battery i. SOC0i and C0i are the initial SOC and capacity of the battery i. The first integral term is the capacity of self-discharge loss, and the value is given by the selfdischarge model. The second integral is the Ampere-Hour integral, where hi(t) is the coulombic efficiency, charging, hi(t) < 1, discharging, hi(t) ¼ 1, which is given by the coulombic efficiency model. Here we do not consider the influence of balancing current, so the equilibrium current is zero. The calculation of SOC, as shown in formula (4).
3.2.3. Capacity fading model Capacity fading model is based on the work of John Wang et al. [25]. They summarized the capacity fade model based on lots of experiments. The capacity fade model of LiFePO4 battery concludes that capacity loss is primarily affected by three factors, namely temperature, the total Ah amount of charge and discharge and charging (discharging) rate CRate. The final mode formula is as follows
31700 þ 370:3 CRate ,B,ðAhÞ0:55 Qloss ¼ exp RT
Where Qloss is battery capacity fading losses, and B is function of discharge rate CRate, Ah is the total charging (discharging) ampere number and the ratio of battery capacity. The paper is based on the conditions of the constant current and temperature. However, the fact is that the current and temperature of the battery are constantly changing. Therefore, this formula cannot be directly used in this model. But we still think that this model is applicable after a certain modification. First of all, according to the results of the paper, Ref. [25] did not give the value of B under 1C rate, so we have the following approximate fitting for the coefficient B.
B ¼ 20000
15 CRate
1 3
(4)
Ci is the current total capacity of the cell. SOC is the ratio of the remaining battery capacity to the nominal capacity, and we should consider the influence of durability, where the Ci value is given by the capacity fading model.
3.2.2. Thermal model Thermal model is the basic model for other sub models. Many models are related to the temperature, so the thermal model is introduced first. A simple model for heat source transfer is used here:
Ti ¼
Z
I 2 Ri qi ðTi T0i ÞAi
. mi Cmi dt þ T0i
(5)
Where Ti is the temperature of the battery i, qi is the heat transfer coefficient, T0i is the ambient temperature, Ai is the cooling area, mi
(7)
We believe that the battery can be approximately deemed at a constant current and temperature conditions in a short time, while the total capacity of the capacity losses can be achieved by capacity loss integration in each time period. Under this assumption, we introduce the capacity fading loss rate dQloss/dt.
2 1 dQloss 31700 þ 370:3 CRate 3 ¼ exp ,11000,153 ,ðAhÞ0:45 ,CRate dt RT
SOCi ¼ Cri =Ci
(6)
(8)
By integrating the capacity loss rate, the capacity loss can be obtained within a certain period of time. At the same time, a parameter FadeDif is introduced to characterize the change law of different cell capacity decay loss rate. If the battery is fully consistent with the above model, then the FadeDif ¼ 1. For the battery i, the loss rate of the capacity loss is as follows. FadeDif can be provided by normal distribution and other statistical methods. dQloss,i/dt ¼ FadeDifi$dQloss/dt
(9)
3.2.4. Self-discharge model The basic law of the self-discharge model is based on the paper of Takashi Utsunomiya et al. [26]. In this paper, the self-discharge characteristics of different carbon anode materials are studied, and the results of self-discharge are given under the static
246
L. Zhou et al. / Journal of Power Sources 364 (2017) 242e252
condition of battery. The self-discharge of the battery is gradually improved due to the passivation of the surface of the active material. But in the charging and discharging cycles, the battery is constantly in the process of chemical reaction. Therefore, selfdischarge may not have similar behavior under charging and discharging. However, because no literature has reported the selfdischarge behavior under charging or discharging, it is difficult for us to analyze the actual self-discharge of the battery during charging and discharging process. So we use the assumption of constant self-discharge rate to study the self-discharge of the battery. Using the hard carbon as reference, the fitting formula (10) is as follows.
Qselfdch ¼ kt 23800 k ¼ 0:5 exp RT
(10)
Where Qsefldch is the Ah amount of battery self-discharge and the square root of time linear relationship, parameter k as temperature coefficient, similarly, we introduce a self-discharge loss rate dQsefldch/dt. The formula for self-discharge loss rate is as follows.
dQselfdch 23800 ¼ k ¼ 0:5 exp RT dt
(11)
The self-discharge loss in a certain time is obtained by the integral of the self-discharge loss rate dQsefldch/dt.
3.2.5. Coulombic efficiency model Due to the high coulombic efficiency of lithium batteries, it is very difficult to accurately determine the coulombic efficiency [27], and there is no relevant research about the effect of temperature on the coulombic efficiency in the current literature. But it can be inferred that in the general temperature environment, with the increase of temperature, the coulombic efficiency is decreased due to high temperature side reactions. And we have the experience that the SOC of LiFePO4 battery has little effect on the coulombic efficiency [28]. So we simply fit the following formula.
h ¼ 1 þ k,ðT 298Þ
(12)
Where k is the temperature coefficient, its value is negative, here taken as 0.00002, namely 10 change based on 25 cause the 0.02% coulombic efficiency change which is a relatively small value.
3.2.6. Internal resistance model There is no formula described the internal resistance regarding SOC and temperature and also the resistance increase with the time and temperature are not formulated in literature, so we use the map between SOC, temperature and internal resistance to determine the initial resistance value. Accordingly, we use temperature and time to determine the resistance increase caused by durability. The internal resistance model is as follows.
R ¼ f ðSOC; TÞ,gðT; tÞ
dR=dt ¼ kR $expð Ea=RTÞ
(14)
Here takekR ¼ 0.05 U/s, Ea ¼ 30000 J/mol. 4. Battery pack consistency simulation 4.1. Simulation experimental scheme The consistency of the battery pack is gradual, so it requires a very long time to the actual experiment. In addition, because of the statistical of the battery pack consistency, more cells are needed to experiment in group. The control and measurement of the single cell parameters will affect the experiment of battery pack. The complexity of the experimental study is not operational. Therefore, the study on the inconsistency mechanism of the battery pack is mainly based on the simulation experiment. Based on the simulation study to the basic behavior of the consistency of the battery pack, a simplified experimental study is carried out in this article. In practice, there are many factors affecting the inconsistency of the battery pack, and there is a complex coupling relationship, which is difficult to distinguish the influence factors of the inconsistency of the battery pack. But we can get the ideal battery pack by simulation experiment, which is obtained only one inconsistent factor in the early stage in group and the other factors are completely consistent. The consistency influence factors of the battery pack are obtained by the consistency simulation of the ideal battery pack. It can provide a theoretical guidance for the screening and equalization methods of the battery pack. Taking into account the consistency of the battery manufacturing, some parameters themselves are relatively good, and the consistency of the other parameters is relatively difficult to guarantee. Battery cells are commonly screened before they are in group. According to different screening conditions, inconsistency parameters in group necessarily vary. We assume that the parameter after the screening process will comply with a normal distribution of small standard deviation. Without screening, the parameter distribution is still normal distribution, but the standard deviation will be larger than the screened parameters. Table 1 gives the simulation experimental parameter matrix. Three different scenarios, namely, good consistency, general consistency and poor consistency, are given for four initial state parameters and four other parameters in Fig. 1. The expectations of the three scenarios are the same, and the difference lies in the standard deviation. Among them, the situation 1 (S1) standard deviation is the smallest, that is, the consistency is the best, and the scenario3 (S3) standard deviation is the biggest, corresponding to the worst consistency. The criteria for selection of the standard deviation are as close as possible and include all possible actual consistency of the battery packs. The simulation experiment is carried out in 24 groups, each group has 1000 standard cycles, and the results are compared and analyzed. 4.2. Simulation analysis and results
(13)
Wheref ðSOC; TÞis the initial resistance, gðT; tÞis the resistance increase caused by durability. Toshio Matsushima [29] gives a 400 Ah lithium battery internal resistance change curve. According to this curve, we approximate that at constant temperature the resistance growth is linear with the time. Similarly the resistance rate of growth dR/dt is introduced, and resistance under the temperature varies is obtained by the internal resistance growth rate dR/dt integral.
We take the battery pack capacity as the main indicator of the consistency of the pure electric vehicle battery pack. 24 groups of simulation experimental results for 8 kinds of single factor parameter are analyzed. Because of so many results, this paper gives the simulation results analysis of four typical single factor parameters. That is coulombic efficiency inconsistency analysis, self-discharge rate Inconsistency analysis, capacity fading inconsistency analysis and temperature inconsistency analysis. The authors have made the same analysis to the other four parameters,
L. Zhou et al. / Journal of Power Sources 364 (2017) 242e252
247
Table 1 Simulation parameter settings. Single factor
Initial capacity (Ah) Initial SOC (%) Initial resistance Initial temperature ( C) Capacity decay Internal resistance growth Self-discharge rate Coulombic efficiency
Expectations
70 50 1 25 1 1 1 0.9995
Standard deviation Scenario 1(S1)
Scenario 2(S2)
Scenario 3(S3)
0.07 0.1 0.05 0.5 0.05 0.05 0.05 1e-5
0.35 0.5 0.1 1 0.1 0.1 0.1 3e-5
0.7 1 0.15 1.5 0.15 0.15 0.15 5e-5
Fig. 3. Battery pack capacity, capacity loss composition and the comparison equalization recoverable capacity under different coulombic efficiency inconsistency scenarios.
and the results show that the other four factors have little effect on the inconsistency, so they are no more discussed in this paper. Inconsistency analysis results are mainly used to guide the design of the battery pack and the equalization. Our previous research [30] shows that the battery pack could be balanced by the dissipative cell equalization, and the maximum potential of the dissipative cell equalization is to make the battery pack to reach the smallest cell capacity. Therefore, comparing the capacity of the battery pack and the smallest cell can indicate that the battery pack capacity can be recovered after the equalization. 4.2.1. Coulombic efficiency The solid line in Fig. 3(A) is the battery pack capacity obtained with the number of cycles as the horizontal coordinate, and the dashed line shows the maximum battery pack capacity that be achieved by the dissipative cell equalization (the smallest capacity of cell in the battery pack). Capacity of the battery pack is calculated by formula (1). Here initial battery rated capacity is uniformly used as the rated capacity and the nominal capacity of the battery pack. S1, S2 and S3, respectively, represent three scenarios in Table 1 that coulombic efficiency inconsistency from low to high. From Fig. 3(A), we can see that the capacity of the battery pack is equal to that of the single cell at the beginning. With the ongoing cycles, battery
capacity fade is greater than the single cell of the minimum capacity, and the higher the coulombic efficiency standard deviation is, the faster the capacity decay of the battery pack. Since only the coulombic efficiency is not consistent, the capacity decay curves of the single cells basically overlap. We can see that the capacity of the battery pack is very sensitive to the coulombic efficiency. Within 1000 cycles, the capacity loss is only about 10%. However, the battery pack capacity loss under the minimal standard deviation simulation scenarios S1 has reached 16%, namely, coulombic efficiency inconsistency contributed about 6% capacity loss. For the simulation scenarios S2 and S3 with larger coulombic efficiency inconsistency, and the battery capacity of the battery pack has reached the end of life in about 900 and 500 cycles, that is, 80% of the initial capacity. For the coulombic efficiency inconsistency simulation S2, the capacity loss caused by the coulombic efficiency inconsistency is almost equal to that by durability. Fig. 3(B) gives the composition of the capacity loss of the battery pack under simulation scenarios S2. The red part of DCIII is the capacity loss of battery pack, which cannot be balanced. It is caused by the capacity loss of the single cell itself. The yellow and narrow part DCII which cannot be clearly seen in this figure is the capacity of battery pack that the real time non-dissipative cell equalization will additionally gain compared to the dissipative cell
248
L. Zhou et al. / Journal of Power Sources 364 (2017) 242e252
equalization. The green part DCI is the restore capacity can be restored by the dissipative cell equalization and the blue part is the capacity of the battery pack under S2. We can see the recovery capacity DCI and the loss capacity DCIII is almost equal. For the worst inconsistency under the S3, the dissipative cell equalization needs to recover 21% capacity within 1000 cycles, with each cycle of only 0.21‰. If battery pack has 1 h for the balancing in a cycle, with the current which is 1‰ of the pack capacity, the battery pack would be well balanced. It means for the 100 Ah battery pack, the current needed for the dissipative cell equalization is only 100 mA. So even if the coulombic efficiency is not consistent under the worst S3, the dissipative cell equalization is completely adequate. Fig. 3(C) gives the recoverable capacity of the dissipative cell equalization. Fig. 3(D) shows the real time non-dissipative cell equalization can recover additional capacity compared to the dissipative cell equalization. It can be seen that with the increase of coulomb efficiency inconsistency, the real time non-dissipative cell equalization additional recovery capacity is increased. The inconsistency of the coulomb efficiency affects the durability inconsistency, and the two are positively correlated, and both are positively related, namely the increase of coulomb efficiency inconsistency will raise the inconsistency of durability. However, considering the specific impact, after 1000 cycles, the real time non-dissipative cell equalization additional recovery capacity less than 0.1%, so this effect can be ignored. The above analysis shows that the dissipative cell equalization can meet the requirements of the battery pack due to the inconsistency of coulomb efficiency, and the difference between the recovery capacity and the real time non-dissipative cell equalization is very small, so it is not necessary to carry out the real time non-dissipative cell equalization. 4.2.2. Self-discharge rate The same result can be seen by the analysis of the inconsistency
effect of self-discharge rate in a similar way. Due to the inconsistency of self-discharge rate, the capacity decay of the battery pack is larger than that of the smallest cell, and the higher the selfdischarge rate standard deviation is, the faster the capacity decay of the battery pack. The effect of self-discharge rate on the capacity of the battery pack is slightly less than that of the coulombic efficiency. But for the S3 of the larger self-discharge rate inconsistency, which can also account for about 5% of the capacity loss. This 5% loss can also be recovered by the dissipative cell equalization. 4.2.3. Capacity fade In Fig. 4(A), the capacity of the battery pack under the inconsistency of capacity fading is presented. The solid line in Fig. 4(A) is the battery pack capacity. The dashed lines expressed the maximum battery pack capacity CI by using the dissipative cell equalization and they are completely overlapped. So the dissipative cell equalization cannot restore the capacity of the battery pack in this case. In addition, the small capacity decay inconsistency of the battery pack under the S1 compared to that under the S3 has a larger capacity. Because the capacity of battery pack is completely determined by the minimum cell capacity of the battery pack. And the minimum single cell capacity of the battery pack with large capacity fading inconsistency has a fast capacity loss. But the capacity loss caused by capacity fade inconsistencies proportion is not big. In Fig. 4(A), the capacity of the battery pack is still about 85% after 1000 cycles under the S3 which is the maximum capacity fade inconsistency. Fig. 4(B) gives the composition of the capacity loss of the battery pack under simulation scenarios S2. The red part of DCIII is the capacity loss of battery pack, which cannot be balanced. It is caused by the average capacity loss of the single cells. The yellow part DCII is the capacity of battery pack that the real time non-dissipative cell equalization can restore. The green part DCI is the restored capacity of the dissipative cell equalization and its value is essentially zero.
Fig. 4. Battery pack capacity, capacity loss composition and the comparison of equalization recoverable capacity under different capacity fade inconsistency scenarios.
L. Zhou et al. / Journal of Power Sources 364 (2017) 242e252
The blue part is the capacity of the battery pack under S2. The recovery capacity DCI by the dissipative cell equalization is very small, but the recovery capacity DCII is a major part of the battery pack recoverable capacity. Fig. 4(C) and (D) show the comparison of the dissipative cell equalization and the real time non-dissipative cell equalization recovery capacity. It can be found that the dissipative cell equalization has no capacity to recover under capacity fade inconsistency scenarios. But in the worst capacity fade inconsistency scenario, the real time non-dissipative cell equalization additional recoverable capacity can only reach about 4% of the battery pack capacity. While in reality, the real time non-dissipative cell equalization can only achieve good results by ensuring that all the cells are fully charged and discharged. In this process, the non-dissipative cell equalization must work in real time. The charge of the larger capacity cell is transferred to the smaller capacity cell when discharging, and charging is on the contrary. Therefore, the equalization algorithm becomes complicated. 4.2.4. Temperature Fig. 5(A) shows that the temperature inconsistency has great influence on the capacity of the battery pack. The consistency of the single cell is influenced by the temperature inconsistency, so the minimum single cell capacity curve is not consistent in the three scenarios. The battery pack capacity fade is relatively small in temperature difference S1 (2.2 C)). The temperature difference of the S3 is 8.8 C, and the battery pack reached the end of life after about 750 cycles. The capacity loss caused by the temperature inconsistency is almost equal to that caused by durability. Fig. 5(B) gives the composition of the capacity loss of the battery pack under simulation scenarios S2. At this scene, the green DCI and yellow DCII can be obviously observed. In the case of temperature is
249
not consistent, the recoverable capacity DCI of energy consumption has great value. Compared with the dissipative cell equalization, the recovery capacity DCII by the complicated real time nondissipative cell equalization is relatively small. From Fig. 5(C), the battery pack recovery capacity of the dissipative cell equalization after the 1000 cycles is only about 3% under the smallest temperature difference S1. While under the maximum temperature difference scenario S3 (8.8 C) the recoverable capacity of the dissipative cell equalization reaches 11% after the 1000 cycles. In contrast, from Fig. 5(D), the real time non-dissipative cell equalization additional recovery capacity is only about 2% under maximum temperature difference scenario S3. Therefore, we believe that in temperature inconsistency situation, the dissipative cell equalization of the battery pack is sufficient to meet the requirements. 4.2.5. Other parameters and capacity loss rate The other parameters inconsistency simulation includes the initial SOC, the initial capacity, internal resistance growth and the internal resistance. The inconsistency of the initial SOC and the initial capacity does not increase the battery capacity loss, and it was screened before in group, so it can be considered that the inconsistency has little effect on the inconsistency of the battery pack. Fig. 6 shows the capacity loss rate of the battery pack after 1000 cycles. From Fig. 6, the coulombic efficiency, temperature, internal resistance growth and self-discharge rate are the main factors that affect the consistency of the battery pack. The factors that directly affect the inconsistency of the battery pack are the coulomb efficiency and the self-discharge rate. Temperature difference is caused by the internal resistance inconsistency, and the temperature difference leads to the inconsistency of coulomb efficiency and self-discharge rate.
Fig. 5. Battery pack capacity, capacity loss composition and the comparison of equalization recoverable capacity under different temperature inconsistency scenarios.
250
L. Zhou et al. / Journal of Power Sources 364 (2017) 242e252
Fig. 6. Battery pack capacity loss rate under different inconsistency scenarios.
4.3. Conclusion of simulation results We conclude the following main conclusions from the simulation results: (1) Coulombic efficiency, temperature and self-discharge rate are the main factors that affect the consistency of the battery pack. Because of coulombic efficiency and the self-discharge rate is generally difficult for screening, it has a great influence on the consistency of the battery pack. This problem requires special attention when the battery is in group. (2) The temperature has a great effect on the consistency of the battery pack, although the temperature does not directly affect the consistency of the battery and also has little effect on the inconsistency of battery capacity. But the temperature will affect the coulombic efficiency and self-discharge rate, which leads to the inconsistency of SOC. So it has a great influence on the battery pack inconsistency. In the simulation experiment, the temperature difference is less than 5 C, the inconsistency is reluctantly accepted. And when temperature difference reached more than 8 C, the capacity of the battery pack decreased quickly. So it is very important to ensure good temperature uniformity for the batteries in group. We suggest that the temperature difference in the thermal management of the battery pack should be controlled within 5 C. (3) The dissipative cell equalization is enough to online equalization for battery packs. There is no need to use the complicated real time non-dissipative cell equalization for on line application. It is suggested that the non-dissipative cell equalization can be used for the maintenance of the battery pack, while the on-board vehicle battery can be balanced by the dissipative cell equalization.
influence of temperature inconsistency on the battery pack. Commercial 12 Ah cells with the anode of graphite and the cathode of LiFePO4 are chosen for the experiment. The experiment by changing the two cells temperature difference is to verify the composition of capacity loss of battery pack. Under the condition of no manufacturing defects, two cells are considered to have little differences. The two cells are respectively placed in two different temperature incubators. A larger temperature difference between cells I and II is chosen to get the obvious results and accelerate the experimental process. Cell I is in a 30 C environment and cell II is placed in a constant temperature chamber of 45 C. The experiment procedure is described in Table 2, which has three stages. In the first stage, capacities of the cell I and II are tested at two different environmental temperatures respectively. The cells capacity test procedure: the cell is discharged at a constant current of 4 A which is the normal discharge rate of 1/3C. After standing for 1 h, the cell is charged to the charge cutoff voltage at a constant current of 1/3C, and then the cell is rested for 10 s and is continued to be charged at a constant current of 1/20C (0.6 A) to the charge cutoff voltage again. The cell completes a full cycle. There are four cycles. After completing the cell basic performance experiments in the first stage, the battery pack experiment is carried out in the second stage. The battery pack is cycled 200 times at a 1C charge and discharge and a 10 day rest which should also consider calendar aging. Battery pack capacity is tested once every 20 cycles and after a standing for 10 day. The schematic diagram of the battery pack testing procedure in the second stage is shown in Fig. 7. Pack capacity is measured using the same scheme as the cells. The charge and discharge end voltage of the battery pack is at the cutoff voltage of any cells. In the third stage, the battery pack is disassembled into cell I and cell II. Capacity test is carried out at the original temperature, and the testing process is the same as the first stage.
5. Preliminarily experimental verification 5.2. Measured results 5.1. Experiment setup Two cells are connected in series in the experiment to verify the
Cell capacity test results in the first stage and third stage are shown in Table 3. The charging capacity and discharge capacity are
L. Zhou et al. / Journal of Power Sources 364 (2017) 242e252
251
Table 2 Three stages in the experiment. Stage number
stage 1
Experiment subject
Cell I, Cell II Battery pack
stage 2
stage 3 Cell I, Cell II
Experiment environment
Cell I 30 C Cell I 30 C, Cell II 45 C Cell II 45 C Cell I and cell II connected in series
Cell I 30 C Cell II 45 C
Experiment contents
Capacity tests
20 cycles at 1C and a pack capacity test as a large cycle. A total of 10 large cycles and the pack is rested for 10 days after the Capacity third large cycle tests
Fig. 7. A schematic diagram of the battery pack testing procedure in the second stage.
Table 3 Cell capacities in the first and third stage. Stage number
Cell I (30 C)
Charge capacity (Ah) Discharge capacity (Ah) Charge capacity (Ah) Discharge capacity (Ah)
Cell II (45 C)
Stage 1
Stage 3
11.8233 11.7919 11.8157 11.7946
11.5780 11.5379 11.3304 11.3075
Table 4 Battery pack capacity in the second stage. Cycle
0
20
40
60A
60B
80
Charge capacity (Ah) Discharge capacity (Ah)
11.7909 11.7617
11.7065 11.6734
11.6460 11.6117
11.5891 11.5568
11.4254 11.3963
11.3972 11.3643
Cycle
100
120
140
160
180
200
Charge capacity (Ah) Discharge capacity (Ah)
11.3532 11.3207
11.3074 11.2752
11.2373 11.2053
11.1902 11.1542
11.1395 11.1108
11.0726 11.0387
Fig. 8. Battery pack capacity and capacity loss composition in the experiment.
252
L. Zhou et al. / Journal of Power Sources 364 (2017) 242e252
very close. Accordingly, the discharge capacity is selected as the capacity of the single cell. Single cell capacity can only be measured in the first and third stages, namely 0 and 200 cycle capacity. The cell capacity in other cycle stages is estimated by linear interpolation. This linear estimation is acceptable for the cell in 200 cycles. Pack capacities in the specific cycles during the second stage are also obtained from the experiment, and the results are shown in Table 4. The difference of the charge and discharge pack capacity is also significantly small so the discharge capacity is selected as the capacity of battery pack. The label of 60A is the result of the capacity test before 10 days settling time, and 60B is the result after 10 day settling time. Fig. 8(A) shows a comparison of the cell capacity by linear estimation and measured pack capacity. The cell temperature difference has great influence on the capacity of the battery pack. Fig. 8(B) demonstrates the normalized capacity loss composition of the battery pack from the experiment. The experimental capacity loss composition results are consistent with the simulation. The green DCI and yellow DCII can be obviously observed. In order to more obvious experimental results, the cell temperature difference is set to 15 C. If the experimental temperature difference is set to the same simulated temperature difference (5 C), the experimental results may be closer to the simulation results. The recoverable capacity DCI of energy consumption has great value from the experiment results. Compared with the dissipative cell equalization, the recovery capacity DCII by the complicated real time nondissipative cell equalization is relatively small. 6. Conclusion In this study a battery pack model with 96 cells in series model was proposed and used for describing the consistency of the battery pack. The basic consistency performance characteristics of the coupling, statistical, weight, irreversibility and graduality of the battery pack for pure electric vehicle were analyzed. We use the actual physical quantity (battery pack capacity) to describe the consistency of the battery pack. The factors that affect the consistency of the battery pack were studied. According to the simulation and experiment, the capacity loss composition of the battery pack was obtained and verified, which is mainly composed of three parts. Based on our results, we can choose the optimal equilibrium strategy of the battery pack in electric vehicles. This study offers a comprehensive understanding of the parameter variation effects on battery packs for electric vehicles. The results show that the consistency of the battery pack is mainly affected by coulombic efficiency, temperature and self-discharge rate. Coulombic efficiency and self-discharge rate are difficult to be screened, and therefore it is important to control the differences among the battery cells in manufacturing process to improve the consistency of the battery pack. The control of temperature difference needs to have a good battery thermal management. The consistency of the battery pack in the temperature difference is acceptable when it is less than 5 C. On the other hand, when the temperature difference is greater than 8 C, the consistency of the
battery pack will be considered poor. The simulation and experimental results also show that the dissipative cell equalization is enough for the online equilibrium of the battery pack. The equilibrium current required by the dissipative cell equalization channels can be as less as 1‰ of the 1 C charge and discharge current of the battery pack. Acknowledgment This research is supported by the National Natural Science Foundation of China (NSFC) under the Grant number of 51507102, “Chenguang Program” supported by Shanghai Education Development Foundation and Shanghai Municipal Education Commission under the grant number of 16CG52, and the State Key Laboratory of Automotive Safety and Energy under Project No. KF16022. References [1] V. Etacheri, R. Marom, E. Ran, G. Salitra, D. Aurbach, Energy Environ. Sci. 4 (2011) 3243e3262. [2] L.X. Yuan, Z.H. Wang, W.X. Zhang, X.L. Hu, J.T. Chen, Y.H. Huang, J.B. Goodenough, Energy Environ. Sci. 4 (2010) 269e284. [3] B. Scrosati, J. Hassoun, Y.K. Sun, Energy & Environ. Sci. 4 (2011) 3287e3295. [4] G. Jeong, Y.U. Kim, H. Kim, Y.J. Kim, H.J. Sohn, Energy Environ. Sci. 4 (2011) 1986e2002. [5] Y. Zheng, X. Han, L. Lu, J. Li, M. Ouyang, J. Power Sources 223 (2013) 136e146. [6] S. Castano, L. Gauchia, E. Voncila, J. Sanz, Energy Convers. Manag. 92 (2015) 396e405. [7] L.H. Saw, Y. Ye, A.A.O. Tay, W.T. Chong, H.K. Seng, C.Y. Ming, Appl. Energy 177 (2016) 783e792. [8] M. Berecibar, M. Garmendia, I. Gandiaga, J. Crego, I. Villarreal, Energy 103 (2016) 784e796. [9] B. Kenney, K. Darcovich, D.D. Macneil, I.J. Davidson, J. Power Sources 213 (2012) 391e401. [10] Y. Wang, C. Zhang, Z. Chen, J. Xie, X. Zhang, Appl. Energy 145 (2015) 36e42. [11] L. Lu, X. Han, J. Li, J. Hua, M. Ouyang, J. Power Sources 226 (2013) 272e288. [12] M. Daowd, N. Omar, P.V.D. Bossche, J.V. Mierlo, in: 26 th Hybrid and Fuel Cell Electric Vehicle Symposium (EVS-26) 26th Hybrid and Fuel Cell Electric Vehicle Symposium (EVS-26), 2012, pp. 1e9. [13] J. Gallardo-Lozano, E. Romero-Cadaval, M.I. Milanes-Montero, M.A. GuerreroMartinez, J. Power Sources 246 (2014) 934e949. [14] Z.P. Wang, F.C. Sun, L. Chen, Beijing Ligong Daxue Xuebao/Trans. Beijing Inst. Technol. 26 (2006) 577e580. [15] M. Guo, R.E. White, J. Electrochem. Soc. 158 (2011) A1166eA1176. [16] M. Dubarry, N. Vuillaume, B.Y. Liaw, J. Power Sources 186 (2009) 500e507. [17] J. Li, M.S. Mazzola, J. Power Sources 237 (2013) 215e228. [18] M. Dubarry, N. Vuillaume, B.Y. Liaw, Int. J. Energ. Res. 34 (2010) 216e231. [19] M. Mathew, Q.H. Kong, J. Mcgrory, M. Fowler, J. Power Sources 349 (2017) 94e104. [20] X. Zhang, Y. Wang, D. Yang, Z. Chen, Energy 115 (2016) 219e229. [21] P. Liu, H.H. Zhu, J. Chen, G.Y. Li, in: Chinese Control and Decision Conference, 2016, pp. 6228e6231. [22] F. Baronti, R. Roncella, R. Saletti, J. Power Sources 267 (2014) 603e609. [23] M. Dubarry, A. Devie, B.Y. Liaw, J. Power Sources 321 (2016) 36e46. [24] G.L. Plett, J. Power Sources 134 (2004) 262e276. [25] J. Wang, P. Liu, J. Hicks-Garner, E. Sherman, S. Soukiazian, M. Verbrugge, H. Tataria, J. Musser, P. Finamore, J. Power Sources 196 (2011) 3942e3948. [26] T. Utsunomiya, O. Hatozaki, N. Yoshimoto, M. Egashira, M. Morita, J. Power Sources 196 (2011) 8598e8603. [27] J. Wang, B. Cao, Q. Chen, F. Wang, Control Eng. Pract. 15 (2007) 1569e1576. [28] Y. Zheng, M. Ouyang, L. Lu, J. Li, Z. Zhang, X. Li, J. Power Sources 289 (2015) 81e90. [29] T. Matsushima, J. Power Sources 189 (2009) 847e854. [30] Y. Zheng, M. Ouyang, L. Lu, J. Li, X. Han, L. Xu, J. Power Sources 247 (2014) 676e686.