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Lithium-ion battery pack equalization based on charging voltage curves
Electrical Power and Energy Systems 115 (2020) 105516
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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Lithium-ion battery pack equalization based on charging voltage curves a
a
b
Lingjun Song , Tongyi Liang , Languang Lu , Minggao Ouyang a b
b,⁎
T
School of Transportation Science and Engineering, Beihang University, Beijing 100191, PR China State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, PR China
A R T I C LE I N FO
A B S T R A C T
Keywords: Electric vehicle Battery management system Battery pack equalization SOC consistency Voltage consistency
Lithium-ion battery pack capacity directly determines the driving range and dynamic ability of electric vehicles (EVs). However, inconsistency issues occur and decrease the pack capacity due to internal and external reasons. In this paper, an equalization strategy is proposed to solve the inconsistency issues. The difference of inconsistency for lithium-ion battery pack equalization is determined based on the uniform charging cell voltage curves hypothesis. Stability of the sampling voltage interval and convergence of equalization are analyzed experimentally. Finally, the results of simulation and experiment both show that the equalization strategy not only maximizes pack capacity, but also adapts to different consistency scenarios. Pack capacity and consistency in the fresh or aged state are significantly improved after battery equalization. In the real battery module experiment, the maximum absolute errors of open circuit voltage (OCV) and state of charge (SOC) are 21.9 mV and 1.86%, and the capacity is improved by 13.03%. Importantly, the equalization strategy has high precision and competitive simplicity with low computation, making it suitable for on-line equalization in EVs.
1. Introduction The energy revolution has ravaged the world to solve the escalating energy consumption and environmental pollution. With excellent merits of high power density, high energy density, low self-discharge rate, and long cycle life, lithium-ion batteries have drawn worldwide attraction in the field of energy storage [1]. Lithium-ion battery, the power source of electric vehicles (EVs), is one of the key factors of electrification and zero emission transportation [2]. However, the driving range is one of the main issues that hinders the popularization of EVs. Because a single cell provides insufficient voltage and capacity, hundreds and thousands of single cells are connected in parallel and in series to supply sufficient power and energy output to EVs [3]. However, cells in a pack tend to age in different degrees after a period of usage. The power and capacity performance of a battery pack degrades faster than a single cell because of the inconsistency issue among cells [4]. Two major reasons are identified, namely, internal issues, such as physical volume, internal impedance, and self-discharge rate, and external reasons, such as the difference of temperature distribution across the pack [5]. Although the cells are carefully screened by manufactures, minor differences or matters will gradually enlarge after a long time of usage and finally cause inconsistency problems and even safety issues [6,7]. To deal with cell inconsistency, a proper equalization strategy is necessary.
⁎
Pack equalization is commonly divided into two parts. The first part is the equalization strategy (ES). The purpose is to determine the amount of charge of each cell that needs to be dissipated or transferred. The second part is the equalization circuit (EC), which makes the cells convert the extra energy in a specific way. According to different studies, ES can be divided into three categories, namely, voltage-based [8], state of charge (SOC)-based [9,10], and pack capacity-based [11]. Voltage-based ESs, which aim to minimize the differences of the cells’ terminal voltages, are the most feasible methods because cell terminal voltages are measured directly. Thus, they are extensively applied in practical engineering. An accurate SOC estimation is the foundation of SOC-based ESs, but an ideally accurate SOC estimation is difficult to obtain [12,13]. Capacity-based ESs take the maximum available capacity of the battery pack, which is based on accurate cell SOC and capacity estimation, as an objective [14,15]. However, at present, the accuracy of SOC and capacity estimation cannot be guaranteed at a high precision level simultaneously, which exerts great difficulty in online application for EVs [16,17]. ESs are divided into two main groups: passive (dissipative) ECs [18,19] and active (non-dissipative) ECs [20–22]. Conventional passive ECs employ shunting resistors to bypass current because they dissipate the extra energy of battery cells with high voltage or SOC to achieve cell consistency. Their simplicity has resulted in their wide online application in real BMS. In contrast, active ECs are more complicated. They
Corresponding author. E-mail addresses: [email protected] (L. Song), [email protected] (M. Ouyang).
https://doi.org/10.1016/j.ijepes.2019.105516 Received 19 January 2019; Received in revised form 30 June 2019; Accepted 23 August 2019 0142-0615/ © 2019 Elsevier Ltd. All rights reserved.
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minimum remaining capacity and the minimum charging capacity, then i is equal to j, and the capacity of cell i (or j) determines the battery pack capacity. Practically, with the presence of cell degradation and inconsistency issue, the cell with the minimum remaining capacity is usually not the same cell that has the minimum charging capacity, thus the pack capacity is usually less than each cell capacity in the pack. The capacity and power of the battery pack tend to decrease seriously as inconsistency escalates gradually. To solve this issue, battery equalization is necessary. Theoretically and ideally, dissipative equalization fully charges and discharges the cell with the minimum cell capacity. This means that the minimum cell capacity is the pack capacity, which can be expressed as
require various electronic devices, such as capacitors and converters, to transfer charge and energy among different cells [23,24]. Although active ECs have the advantage that pack energy can be fully used without dissipation, passive ECs are superior for their simplicity and economy [24]. Zheng et al. [25] compared active and passive ECs and suggested that active ECs cost higher and their hardware is difficult to realize, but increased capacity attributed by active ECs is quite small if the cells are properly screened. Passive ECs are suitable for on-line battery pack equalization in EVs. From the aforementioned methods, we can be aware of that the voltage-based ESs have significant simplicity and feasibility that other ESs, no matter applied in passive or active ECs. However, the terminal voltage is influence by many factors, for example, capacity and internal resistance. A proper voltage difference is usually difficult to define. As a result, over-equalization occurs, and the energy of the battery pack is wasted. It is obvious that the capacity of the battery pack fails to be maximized. In order to solve inconsistency issues, we proposed an ES based on the cell voltage curves. By employing charging cell voltage curve (CCVC) hypothesis to evaluate the inconsistence of the cells in the module/pack, the drawbacks of the voltage-based method are eliminated successfully. Hence, the maximization of the capacity of the battery module/pack is realized. Analysis of stability and the convergence of the proposed method are presented. Furthermore, the proposed method is validated in the simulation and real BMS platform in different scenarios.
Cp = min (Ci )
In an active equalization, extra energy is transferred from cell to cell all the time, and the maximum pack capacity of the battery pack is the mean value of all cell capacities. This is expressed by Eq. (3) below.
Cp = mean (Ci)
(3)
2.2. Uniform charging cell voltage curves hypothesis Open circuit voltage (OCV) is cell’s electrical characterization when the internal electrochemical reaction of the cell is in equilibrium. For a specific battery manufactured in the same batch, it is generally assumed that all cells have a similar OCV curve. It is also noted that a slight change of OCV may have a significant influence on the accuracy of SOC estimation [27]. This change’s influence on the terminal voltage, however, can be ignored compared with the influence from the capacity or internal resistance differences. The uniform charging cell voltage curves (UCCVC) hypothesis is used to describe the relationship among the differences of cell’s capacity, resistance, and SOC. The UCCVC hypothesis is described as follows: batteries fabricated in the same batch and possess identical internal resistances, SOCs, and capacities have the same charging curves if they are charged in a constant current rate. Even if batteries of the same batches have different internal resistances, SOCs, and capacities, their charging cell voltage curves can also coincide after curve translations. The charging cell voltage curves (CCVCs) have a similar regular shape as the OCV curve. The analytical and proving process is illustrated in [28]. The difference in internal resistances can be eliminated by CCVC vertical translations ΔU calculated by Eq. (4) as shown in Fig. 2(a). Using Eq. (5), the difference of the initial SOC in the cell is compensated by CCVC horizontal translations ΔAh and Fig. 2(b) is achieved. In addition, horizontal scaling can eliminate the difference in cell capacities of CCVCs, as expressed in Eq. (6) and Fig. 2(c). Finally, they coincide as depicted in Fig. 2(d).
2. Theory 2.1. Battery pack capacity Cell capacity is commonly defined as the total available electricity that cell discharges from the upper cutoff voltage to the lower cutoff voltage under a designated circumstance formulated by manufacturers. However, the battery pack capacity in a series-connected module is also charged/discharged in the limitation of each single cell’s terminal voltage for the safety issue of a single cell [26]. Thus, each cell capacity has great influence on battery pack capacity. As shown in Fig. 1(a), cell 1 has the minimum available discharging capacity, whereas cell 3 has the minimum available charging capacity. In the charge/discharge cycling process, the battery pack is not allowed to discharge when cell 1 is fully discharged but other cells are not fully discharged. Similarly, the battery pack cannot charge if cell 3 is fully charged. Overall, pack capacity can be formulated as
CP = min (SOCi·Ci ) + min [(1 − SOCj )·Cj]
(2)
(1)
where CP is the pack capacity, SOCi , SOCj are the current state of charge, and Ci , Cj are the capacity of cell i or j. If one cell has the
Fig. 1. Schematic diagram of pack capacity without (a) or with (b) passive/active equalization. 2
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connected module, the CCVCs of different cells are translated from an identical CCVC by vertical movement. Here, only SOC inconsistency is considered. Internal resistance and capacity inconsistency are analyzed in Section 3.3. In Fig. 3, 4 cells are series-connected with different initial SOCs. When they are charged, the possible CCVCs of each cell are noted as cell 1 (red line), cell 2 (black dashed), cell 3 (green dashed), and cell 4 (blue dashed). Cell 1 will always have the highest voltage and reach the upper cutoff voltage, but the others cannot. The terminal voltages of each cell are respectively marked as A, B, C, and D as the module is fully charged. However, if the module has a good consistency, more electricity can be charged and the module capacity could increase significantly. The ideal result is that all cells reach the upper cutoff voltage at the same time. To achieve module capacity maximization, we propose an ES based on the UCCVC. First, the sampling start and end points of the highest cell voltage in the module or system are set in advance. This voltage curve is regarded as the reference to evaluate the difference of cells. The ES is divided into two steps as illustrated in Fig. 4. Step 1. Initial condition judgment and data recording. The purpose is to judge whether the equalization starts or not. Specific procedures are conducted as follows:
Fig. 2. Schematic diagram of uniform charging cell voltage curves hypothesis.
ri = r0 +
ΔU I
SOCi = SOC0 +
(4)
ΔAh C0
a. Calculation of the Ampere-hour that has to be charged (noted as ΔAh ) when the module is charging, if the highest cell voltage below the sampling interval. b. Recording of the ΔAh and the highest voltage with a voltage interval of 1 mV (noted as dV = 1 mV ) from the lower sampling voltage to upper sampling voltage and the ending voltage of all cells (noted as V_endi) when the highest voltage reaches upper sampling voltage.
(5) (6)
Ci = k i C0
Wherein, the parameters r0 , C0 and SOC0 are initial internal resistance, capacity and SOC of cell 0, respectively. The parameters ri , Ci and SOCi are initial internal resistance, capacity and SOC of cell i, respectively. In a series-connected module, all cells fabricated in the same batch are charged in the same constant current rate, and thus the UCCVC hypothesis is applicable. Though OCV is one of the most precise methods for parameter calibration, difficulties in obtaining OCV restrict its further application in practical engineering. The UCCVC hypothesis provides another way of comparing the differences among cells. Thereby, it can be used to evaluate the inconsistency of cells in a seriesconnected module or pack.
Step 2. Dynamic look-up table establishment and table look up. In this step, a voltage curve with respect to charged electricity can be established. It is used as a dynamic table to determine the difference among cells. c. Establishment of a dynamic look-up table using the sampled voltage as the y-axis and the corresponding ΔAh as the x-axis. d. Use V_endi of each cell to look up the established dynamic look-up table, and then obtain the corresponding ΔAhi of cell i. e. Calculate the difference (noted as dAh i ) between ΔAh i and the minimum one using the equation
3. Methodology
dAh i = ΔAh i − min (ΔAh)
3.1. Equalization strategy
(7)
dAh i is the electricity that cell i needs for equalization. Then, equalization would be completed by EC. In the ES, we choose [4.000 V, 4.100 V] as the sampling interval. The reason that why the entire charging curve is used is that we think part of the charging curve is capable enough for a practical condition. Since the inconsistency issue caused by battery aging is a slow process, the inconsistency of 10%SOC among cells is almost impossible to occur in this short time [29,30]. Specifically, the maximum amount of equalized electricity in equalization is approximately 10% of the SOC (SOC at 4.000 V is 80.5% and 4.100 V is 91% of the SOC), and has adequate electricity that a cell needs for equalization, even if the equalization condition is reached after several months. Besides, the length of the sampling voltage interval is 100 mV, which is short, thus requiring less memory and calculation. It should be emphasized that this sampling interval is not a fixed setting, but an example to implement the proposed method.
Based on the UCCVC hypothesis, the cells in a series-connected module fulfill their requirements. As shown in Fig. 3, all cells (cells 1–4) theoretically have the same CCVC, but the initial SOCs are different. According to Section 2.2, when SOC inconsistency occurs in a series-
3.2. Stability analysis of the sampling voltage interval Guaranteeing the stability of sampling voltage interval is an essential premise of accurate equalization. In practical usage, EVs are likely to be charged in any initial SOC. If the starting voltage of the charging process is close to sampling voltage interval, stability of this interval
Fig. 3. Schematic diagram of the equalization strategy. 3
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Fig. 4. Schematic diagram of pack/module equalization.
may be influenced by charging polarization. In this case, an opening threshold of equalization, which avoids charging polarization, and keeps the sampling interval stable, should be set. We adopt the electricity charged from the beginning as the threshold and conduct the following experiments to determine the value of this threshold. Three different scenes are considered where the cell is charged switching from the rest state (0C) and high current rate charging (1C and 2C) to constant current rate (0.5C, standard charging rate for a module). The test results are shown in Fig. 5, where three starting points are chosen as the beginning of the 0.5C charging. They are at approximately 70% SOC, 75% SOC and 78.5% SOC, respectively. The distances from the switching points to the sampling beginning point (80.5% SOC) are 10.5%, 5.5%, and 2% SOCs, respectively. The black line is a reference line charged from 60% SOC to 4.12 V in a constant current rate of 1/2C. To eliminate the effect of polarization phenomenon, a specific period is needed before cell charges switching from a current rate (0C, 1C and so on) to another rate (1/2C in this paper). Compared with others, charging at 0C costs more time for a cell to be in a stable state (see arrows 1 and 3 in Fig. 5). Moreover, when switching from a high rate, the terminal voltage may already reach 4.000 V as indicated by arrow 2. Under this circumstance, the terminal voltage is sampled in the high rate, which would be sampled again in the 1/2C charging process. Thus, the distance of 2% SOC is insufficient. Currently, stable sampling voltage curves are maintained in the fresh cell, as the charged electricity is 5.5% SOC. However, polarization deteriorates gradually as the cell ages. More time is required for the cell to be in a stable state, as indicated by arrows 1 and 3, and it may be still unstable when the terminal voltage reaches 4.000 V. Furthermore, terminal voltage, as pointed by arrow 4, maybe already reach 4.000 V before the current rate switches. Thus, the charged electricity of 5.5% SOC is insufficient, but 10.5% is sufficient. For calculation convenience, the equalization threshold is set to 10% of the nominal capacity.
Fig. 5. Results of stability test of different scenes.
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remaining electricity of cell 1 needed for equalization isΔAh2 . According to Eq. (12),
ΔAh2 < 0.625%SOC
(13)
The Ahthreshold is the threshold on value analyzed in Section 3.3.3, and Ahthreshold is 0.5% of nominal capacity. Accordingly, ΔAh2 can be reformulated as
ΔAh2 ≈ Ahthreshold
The convergence of equalization is obviously obtained after the second equalization. If C2 < C1, the extreme range of k is 1 > k > 0.8. After the first equalization, the remaining electricity of cell 1 needed for equalization, ΔAB1, is expressed as Eq. (9). The ending terminal voltage of cell 2 should rise to point D if cell 1 reaches the upper cutoff voltage, which is impossible. Now, the remaining electricity needed for equalization is given as
Fig. 6. Cell equalization with capacity inconsistency.
ΔAh1 = |ΔAB1 − ΔAA*| = (1 − k )ΔAA*
3.3. Convergence analysis of equalization
1 1 ΔAh2 = ΔAB − ΔAh1 = ⎛ − 1⎞ ΔAh1 = ⎛ − 1⎞ (1 − k )ΔAB∗ ⎝k ⎠ ⎝k ⎠
ΔAh2 ≈ 0.5%SOC = Ahthreshold
3.3.2. Internal resistance inconsistency The difference of internal resistance inconsistency has a significant influence on terminal voltage. For two same cells with different internal resistances, the cell with a higher internal resistance reaches the upper/ lower voltage in advance, which determines the pack capacity if the cells are series-connected. Under this circumstance, equalization does not improve the pack capacity but improves the pack’ voltage consistency. This is also illustrated by Fig. 3. If cell 1 has the highest internal resistance, then the difference of CCVCs only results from internal resistance inconsistency when the initial SOC of all cells are equal. After using the proposed method to equalize the module, the consistent terminal voltage is achieved in the charging or discharging process. Furthermore, the pack capacity power increases, although the pack capacity does not change. Terminal voltage and SOC consistency cannot be realized at the same time for a pack with internal resistance inconsistency. Apparently, terminal voltage consistency is more important than SOC consistency in this situation.
where k is the coefficient between C1 and C2. As depicted in Fig. 6, cell 1 has a higher initial SOC, thus reaching the upper cutoff voltage ahead of cell 2. Cell 2 is not fully charged and point A is the ending terminal voltage. By applying the proposed ES, the electricity of cell 1 for equalization is ΔAA*. However, because of the uncertainty of C2, it may be larger, equal, or smaller than C1, and the corresponding CCVCs are plotted in Fig. 6. The amount of electricity of cell 1 needed for equalization is ΔABi (i = 0, 1, 2), which is easy to deduce from Eq. (8). (9)
If k = 1, C2 = C1 and ΔAB0 = ΔAA*, the difference of SOC is eliminated after one equalization. Meanwhile, if k > 1, C2 > C1, the maximum value is 1.25 in the extreme scene where the capacity degradation rate of cell 1 is 20% and that of cell 2 is 0%. Thus, the range of k is 1.25 > k > 1. After the first equalization, the ending terminal voltage of cell 2 rises to point C, and the remaining electricity of cell 1 needed for equalization can be derived by Eq. (10).
3.3.3. Equalization threshold analysis Here, we analyze the sampling error resulting from the voltage and current sensor. If we directly set the threshold on value (noted as Ahthreshold ) to zero, over-equalization may occur. Unfortunately, equalization begins when the equalization condition is maintained in charging, whether the pack needs it or not. Consequently, the workload of BMS increases and energy dissipates. An appropriate threshold on value should be set according to the sensor sampling accuracy. In this paper, the BMS we used is provided by Beijing KeyPower Technologies Co., Ltd. (shown in Fig. 7(b)). The voltage measurement range is −5 V to 5 V with the sampling of ± 1.5 mV. The current sensor measurement is 0.5% (> 30 A) and ± 0.1 A (< 30 A). The current sampling error results in a wrong ΔAh value in the xaxis, making the CCVC move horizontally. In a series-connected
(10)
After n times equalization, the remaining electricity of cell 1 needed for equalization is formulated as
ΔAh n = (k − 1) nΔAA*
(11)
ΔAA∗
Given that 1.25 > k > 1 and the maximum value of is about 10% SOC, Eq. (11) can be modified by using the equation expressed as
1 n 1 n ΔAhi < ⎛ ⎞ ΔAA* ≈ ⎛ ⎞ × 10%SOC ⎝4⎠ ⎝4⎠
(17)
Convergence of equalization is also achieved after the second equalization. Consequently, capacity inconsistency would be eliminated after two equalizations.
(8)
ΔAh1 = ΔAB2 − ΔAA* = (k − 1)ΔAA*
(16)
As ΔAA* ≈ 10% SOC, Eq. (16) can be rearranged modified as
3.3.1. Capacity inconsistency The equalization between cells 1 and 2 is used as an example. According to Eq. (6), the relationship between the capacities of cell 2 (note as C2) and cell 1 (noted as C1) is expressed as
ΔABi = k ΔAA∗
(15)
In the second equalization, cell 2 has the higher voltage. Therefore, the second equalization of k < 1 is the same as the first equalization of k > 1. ΔAh1 is the remaining electricity of cell 2 needed for equalization. After the second equalization, the remaining electricity needed for equalization, ΔAh2, is given by
The convergence of the proposed ES is defined as the event when all cells in the module reach the upper cutoff voltage at the same time. As battery ages, capacity degradation, uneven temperature distribution, and internal resistance increase are critical factors causing cells inconsistency. In the charging process, the cells are in a relatively stable condition, the difference among cells is less than 5 °C, the influence of which to pack consistency is negligible [25]. We provide an analysis of the convergence of equalization when the battery pack has aged.
C2 = kC1
(14)
(12)
When equalization has been performed twice, that is, n = 2, the 5
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Fig. 7. Schematic diagram of simulation and experiment platform.
ECMs include the Rint model and one or multi-order RC model et al. In this paper, the second order RC model is adopted. As shown in Fig. 7(a), this model consists of OCV, ohmic resistance R0, and two RC components. The R1C1 and R2C2 circuits describe the polarization phenomenon of the battery caused by transfer, diffusion, and other factors. The equations that describe the electrical characteristics are respectively given by
module, the current errors of all cells are unanimous because the current is measured by one current sensor. Thusthe current measurement has no effect on the equalization result. Meanwhile, cell voltage is sampled individually. Thus, CCVC has an inconsistent vertical movement. In other words, voltage sensor with high accuracy ( ± 1.5 mV in this paper) promises good equalization result in the practical implementation, because the equalization threshold is defined by the voltage error. The maximum absolute error among CCVCs is 3.0 mV, and thus we can calculate the maximum SOC error based on the OCVSOC curve. The maximum SOC error caused by the voltage sensor is 0.370% SOC. Accordingly, Ah threshold is 0.370%SOC. For the convenience of calculation, the constant value is set to 0.5% of the nominal capacity. Ah threshold guarantees that over-equalization will not occur. To obtain a highly accurate result, the threshold off is set to 0.2% of the nominal capacity, whereas the sampling error cannot always be the maximum value.
U1 = IR1 [1 − exp (−t / τ1)]
(18)
U2 = IR2 [1 − exp (−t / τ2)]
(19)
Ut = fOCV (SOC ) − IR 0 − U1 − U2
(20)
where I is the current, Ut is the terminal voltage, and U1 and U2 are the voltages across R1C1 and R2C2, respectively. In addition, τ1 and τ2 are the time constants that satisfy equations τ1 = R1 C1 and τ2 = R2 C2 . fOCV (SOC ) is the function between SOC and OCV. A commercial lithium-ion battery with an NMC/graphite electrode is employed in the tests. It has a nominal capacity of 37 Ah and upper/ lower cut-off voltages of 4.2/2.8 V. The standard capacity test at 25 °C and the hybrid pulse power characteristic (HPPC) tests at various temperatures are conducted successively, and then the genetic algorithm is applied to identify the model parameters.
4. Simulation and experiment platform To validate the effectiveness and precision, we simulate the equalization in a cell module in fresh and aged states and embed the proposed strategy into a real BMS. 4.1. Single cell model
4.2. Cell module model with equalization circuit Among battery models, such as equivalent circuit model (ECM), pseudo two-dimensional model (P2D), and single particle model [31,32], ECM can precisely describe battery electrical characteristics and has low calculation requirements, and thus widely applied [33].
Fig. 7(a) presents the schematic diagram of the battery module with a passive equalization circuit. The cell module is series-connected by 12 cells in which every cell is simulated using a second-order RC model. 6
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The passive equalization circuit consists of several 24 Ω and 4 Ω resistances and switches. Hence, the equalization current of each cell can be solved according to Ohm’s law and Kirchhoff’s rules. As shown in Fig. 4, switching is controlled by the equalization state. Equalization starts (switching on) if the equalized electricity is less than the electricity amount needed for equalization. Otherwise, equalization stops (switching off).
respectively. Meanwhile, the module capacity successfully increases from 32.03 Ah to 35.92 Ah, 95.13% of the theoretical capacity that is 37.76 Ah.
5.1.2. Aged cell module equalization Cell degradation occurs in different degrees due to both internal and external reasons. The parameters of the aged cell pack are presented in Table 1, where capacity degradation has no significant correlation with internal resistance increase [34,35]. Fig. 8(b) shows that a serious inconsistency phenomenon occurs in the aged cell module, especially for cell 2, which has the maximum SOC, and cell 4 with the minimum SOC. If no equalization is performed, the performance of the pack will deteriorate, and the driving range of EV and the cycle life of the pack might decrease greatly. Faced with the severe inconsistency problem, the module is equalized according to the proposed strategy. Fig. 8(b) shows significant optimization in the performance of the module. An excellent consistency is obtained, and the equalization accuracy is calculated and presented in Table 2. The module capacity efficiently increases from 25.57 Ah to 29.26 Ah, accounting for approximately 14.43% of the initial capacity without equalization. Compared with the theoretical capacity, namely the minimum cell’s capacity, which is 31 Ah, the proposed method could realize 94.39% of the theoretical capacity. The analysis indicates that the proposed equalization strategy is successfully validated in the simulation platform. The consistency issue is solved, while the capacity increases 12.14% and 14.43% in fresh and aged module, respectively.
4.3. Experiment platform To validate the practicality of the proposed method, we embed it into a real BMS. The hardware system is shown in Fig. 7(b), which consists of a current meter, a cell module, a sampling board, a BMS controller, a test bench, and a monitoring computer. In the experiment, the cell module is charged/discharged by the test bench at room temperature (25 °C ± 5 °C). The equalization strategy is running in BMS based on the voltage sampled by the sampling board and the current sampled by the current meter. The equalization states, including voltages and the temperature of the cell, are displayed on the monitoring computer. 5. Results and discussion A series of simulations and experiments are designed and carried out, the results of which are described and discussed in this section. 5.1. Results of simulations 5.1.1. Fresh cell module equalization The proposed ES is firstly simulated in a fresh state cell module, which can be used for comparison with the result of the real BMS test. The parameters among cells in the cell module are assumed to be in normal distribution [34]. The fresh cells have good consistency, and the initial normal distribution values of capacity, SOC, internal resistance, and temperature are provided in Table 1. In the simulation, the resistance coefficient is a gain that multiplies the resistance values to simulate the resistance inconsistency among cells in the module. To simulate an inconsistent cell module situation, the initial SOC of cell 1 is modified to 20% SOC. The cell is charged in a two-step charging profile. The first step is to charge the cell until 4.12 V reaches in a constant current of ½ C, then charged in 1/10 C to 4.12 V again. Equalization starts when the conditions meet. After two charging processes, equalization is complete. The comparison of different states before and after equalization in fully-charged mode is showed in Fig. 8(a). The red dotted and solid curves represent the SOC of cells in the module before and after equalization; the blue dotted and solid curves stand for the terminal voltage of cells in the module before and after equalization. The initial SOC and terminal voltage of cell 1 are obviously lower than those of the others, but they eventually converge to the same value after the equalization is completed. The results of parameters comparison are presented in Table 2. The maximum absolute errors of OCV and SOC are 135 mV and 12.04% SOC before equalization, respectively. After equalization, they significantly decrease to 11.4 mV and 0.68% SOC,
5.2. Results of real BMS experiment The proposed strategy was then embedded into a real BMS controller to further verify its applicability. Cell aging takes too long, and thus only fresh cells were utilized in this experiment. To acquire an inconsistent situation in the module, cell 1 is previously discharged to a low SOC. The charging profile adopted in the simulation is used to charge the module. Fig. 8(c) presents the CCVCs of all cells in which the CCVC of cell 1 is obviously apart from others and much lower. This means that cell 1 cannot be fully charged, but reaching the lower cutoff voltage first, which then leads to a low module capacity. The discharge profile is similar to the charge profile shown in Fig. 8(d). The discharge capacity is calculated as 32.54 Ah. The charging profiles of cells after equalization are presented in Fig. 8(e), which shows consistent CCVCs and no distinct distance among the curves, implying that more electricity can be charged in the module than before. After equalization, cells discharge in a consistent path as depicted in Fig. 8(f). The capacity has risen by 13.03% to 36.78 Ah. The maximum absolute errors of OCV and SOC are greatly optimized from 145.2 mV, 13.00% SOC to 21.9 mV, 1.86% SOC, respectively. Compared with different methods listed in Table 3, the proposed method has a good performance of equalization, even though it is applied with a passive EC. Over equalization is avoided successfully, reducing energy cost. Importantly, the equalization strategy has high precision competitive simplicity with low computation. On the other hand, the limitation of the proposed method is that specific charging condition must be reached as discussed in Section 3.3.3, making it challenging to be applied in various charging scenes. In other word, only charging profiles must fulfill the requirement, can the equalization strategy works. Overall, the proposed equalization method is validated in the real BMS with excellent performance. The capacity increases by 12.14% in the fresh module and by 14.43% in the aged state. The result of the real BMS test also indicates the remarkable applicability of this method. Therefore, the proposed ES can deal with the inconsistency problem in fresh or aged modules, extending the driving distance or time from that of the battery pack without equalization.
Table 1 Parameters in simulations of fresh and aged module. State
Capacity (Ah)
SOC
Resistance coefficient
Temperature (°C)
Fresh Aged
(38, 0.2, 12, 1) (33, 1.0, 12, 1)
(0.3, 0.01, 12, 1) (0.3, 0.05, 12, 1)
(1.0, 0.05, 12, 1) (1.5, 0.20, 12, 1)
(25, 0.5, 12, 1) (25, 0.8, 12, 1)
Note: normal distribution is expressed as (a, b, c, d), where a, b, c, and d are the parameters in the normal distribution; a is the mean, b is the standard deviation, c is the array length, and d is the array dimension. 7
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Fig. 8. Results of simulation and real BMS experiment.
obtaining the electricity required by cells for equalization is obtained. The proposed ES is based on the terminal voltages that are directly sampled by the voltage sensor, and thus applicable in practical engineering. To keep the sampled voltage interval stable, an equalization opening threshold of 10% nominal capacity, which is the prerequisite of equalization, is set according to a series of stability tests. We demonstrate the convergence of the ES in different scenes with SOC inconsistency and internal resistance for fresh or aged packs. Moreover, the effectiveness and precision are preliminarily validated in a simulation platform where the inconsistency in fresh and aged modules are simulated. The SOC consistency and module capacity are significantly improved, and the maximum absolute errors of OCV and SOC are 11.4 mV and 0.68% SOC in the fresh state and 42.0 mV and 3.54% SOC in the aged state, respectively. Meanwhile, the proposed strategy is embedded in a real BMS controller. The results of the real BMS further verify its applicability with an accuracy of 21.9 mV and 1.86% SOC, and the capacity is improved by 13.03%. The results above prove that the proposed method could
Table 2 Comparison of parameters before and after equalization. Experiment
Fresh module
Aged module
Real module
State
Before
After
Before
After
Before
After
Capacity (Ah) R_OCV (mV) R_SOC (%)
32.03 135 12.04
35.92 11.4 0.68
25.57 180 16.44
29.26 42 3.54
32.54 145.2 13.00
36.78 21.9 1.86
Note: R_OCV is the maximum absolute error of OCV, and R_SOC is the maximum absolute error of SOC.
6. Conclusion This paper proposeed an ES method to solve the inconsistency issue in battery modules/packs. Based on the UCCVC hypothesis, a dynamic look-up table is established using the voltages of the cell with the highest voltage. Then, we look up the table by the ending voltages of each cell and identify the difference with the minimum one, thereby 8
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Table 3 Performance comparison of different methods. References
ES
EC
Validation
Errors
Merits
Drawbacks
[36] [37] [38] [39]
SOC and capacity-based Voltage-based SOC-based SOC-based
active passive active active
simulation experiments simulation experiments
19.1 mV/12.2 mV 7 mV 0.5% SOC 20 mV/2% SOC
Avoid over equalization High precise Low SOC difference high balancing efficiency
High computational cost Over-equalization may occur Require precise SOC; over-equalization may occur High computational cost
extend the driving distance or time and guarantee a better battery pack performance than that of the battery pack without equalization.
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Declaration of Competing Interest We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted. Acknowledgement This work is supported by National Key R&D Program of China (2018YFB0104100). References [1] Betzin C, Wolfschmidt H, Luther M. Electrical operation behavior and energy efficiency of battery systems in a virtual storage power plant for primary control reserve. Int J Electr Power Energy Syst 2018;97:138–45. [2] Xiong R, Cao JY, Yu QQ. Reinforcement learning-based real-time power management for hybrid energy storage system in the plug-in hybrid electric vehicle. Appl Energy 2018;211:538–48. [3] Zhang CP, Jiang Y, Jiang JC, Cheng G, Diao WP, Zhang WG. Study on battery pack consistency evolutions and equilibrium diagnosis for serial- connected lithium-ion batteries. Appl Energy 2017;207:510–9. [4] Zheng YJ, Ouyang MG, Lu LG, Li JQ. Understanding aging mechanisms in lithiumion battery packs: from cell capacity loss to pack capacity evolution. J Power Sources 2015;278:287–95. [5] Zhou L, Zheng YJ, Ouyang MG, Lu LG. A study on parameter variation effects on battery packs for electric vehicles. J Power Sources 2017;364:242–52. [6] Ren D, Liu X, Feng X, Lu L, Ouyang M, Li J, et al. Model-based thermal runaway prediction of lithium-ion batteries from kinetics analysis of cell components. Appl Energy 2018;228:633–44. [7] Feng X, Ouyang M, Liu X, Lu L, Xia Y, He X. Thermal runaway mechanism of lithium ion battery for electric vehicles: a review. Energy Storage Mater 2018;10:246–67. [8] Zheng Y, Ouyang M, Lu L, Li J, Han X, Xu L. On-line equalization for lithium-ion battery packs based on charging cell voltages: Part 2. Fuzzy logic equalization. J Power Sources 2014;247:460–6. [9] Wang Y, Zhang C, Chen Z, Xie J, Zhang X. A novel active equalization method for lithium-ion batteries in electric vehicles. Appl Energy 2015;145:36–42. [10] Zhang S, Yang L, Zhao X, Qiang J. A GA optimization for lithium–ion battery equalization based on SOC estimation by NN and FLC. Int J Electr Power Energy Syst 2015;73:318–28. [11] Cui X, Shen W, Zhang Y, Hu C, Zheng J. Novel active LiFePO4 battery balancing method based on chargeable and dischargeable capacity. Comput Chem Eng 2017;97:27–35. [12] Zheng Y, Gao W, Ouyang M, Lu L, Zhou L, Han X. State-of-charge inconsistency estimation of lithium-ion battery pack using mean-difference model and extended Kalman filter. J Power Sources 2018;383:50–8. [13] Zheng Y, Ouyang M, Han X, Lu L, Li J. Investigating the error sources of the online state of charge estimation methods for lithium-ion batteries in electric vehicles. J Power Sources 2018;377:161–88. [14] Diao W, Xue N, Bhattacharjee V, Jiang J, Karabasoglu O, Pecht M. Active battery cell equalization based on residual available energy maximization. Appl Energy 2018;210:690–8. [15] Wu Z, Ling R, Tang R. Dynamic battery equalization with energy and time efficiency for electric vehicles. Energy. 2017;141:937–48. [16] Xiong R, Yu Q, Wang LY, Lin C. A novel method to obtain the open circuit voltage for the state of charge of lithium ion batteries in electric vehicles by using H infinity filter. Appl Energy 2017;207:346–53.
9
Contents lists available at ScienceDirect
Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Lithium-ion battery pack equalization based on charging voltage curves a
a
b
Lingjun Song , Tongyi Liang , Languang Lu , Minggao Ouyang a b
b,⁎
T
School of Transportation Science and Engineering, Beihang University, Beijing 100191, PR China State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, PR China
A R T I C LE I N FO
A B S T R A C T
Keywords: Electric vehicle Battery management system Battery pack equalization SOC consistency Voltage consistency
Lithium-ion battery pack capacity directly determines the driving range and dynamic ability of electric vehicles (EVs). However, inconsistency issues occur and decrease the pack capacity due to internal and external reasons. In this paper, an equalization strategy is proposed to solve the inconsistency issues. The difference of inconsistency for lithium-ion battery pack equalization is determined based on the uniform charging cell voltage curves hypothesis. Stability of the sampling voltage interval and convergence of equalization are analyzed experimentally. Finally, the results of simulation and experiment both show that the equalization strategy not only maximizes pack capacity, but also adapts to different consistency scenarios. Pack capacity and consistency in the fresh or aged state are significantly improved after battery equalization. In the real battery module experiment, the maximum absolute errors of open circuit voltage (OCV) and state of charge (SOC) are 21.9 mV and 1.86%, and the capacity is improved by 13.03%. Importantly, the equalization strategy has high precision and competitive simplicity with low computation, making it suitable for on-line equalization in EVs.
1. Introduction The energy revolution has ravaged the world to solve the escalating energy consumption and environmental pollution. With excellent merits of high power density, high energy density, low self-discharge rate, and long cycle life, lithium-ion batteries have drawn worldwide attraction in the field of energy storage [1]. Lithium-ion battery, the power source of electric vehicles (EVs), is one of the key factors of electrification and zero emission transportation [2]. However, the driving range is one of the main issues that hinders the popularization of EVs. Because a single cell provides insufficient voltage and capacity, hundreds and thousands of single cells are connected in parallel and in series to supply sufficient power and energy output to EVs [3]. However, cells in a pack tend to age in different degrees after a period of usage. The power and capacity performance of a battery pack degrades faster than a single cell because of the inconsistency issue among cells [4]. Two major reasons are identified, namely, internal issues, such as physical volume, internal impedance, and self-discharge rate, and external reasons, such as the difference of temperature distribution across the pack [5]. Although the cells are carefully screened by manufactures, minor differences or matters will gradually enlarge after a long time of usage and finally cause inconsistency problems and even safety issues [6,7]. To deal with cell inconsistency, a proper equalization strategy is necessary.
⁎
Pack equalization is commonly divided into two parts. The first part is the equalization strategy (ES). The purpose is to determine the amount of charge of each cell that needs to be dissipated or transferred. The second part is the equalization circuit (EC), which makes the cells convert the extra energy in a specific way. According to different studies, ES can be divided into three categories, namely, voltage-based [8], state of charge (SOC)-based [9,10], and pack capacity-based [11]. Voltage-based ESs, which aim to minimize the differences of the cells’ terminal voltages, are the most feasible methods because cell terminal voltages are measured directly. Thus, they are extensively applied in practical engineering. An accurate SOC estimation is the foundation of SOC-based ESs, but an ideally accurate SOC estimation is difficult to obtain [12,13]. Capacity-based ESs take the maximum available capacity of the battery pack, which is based on accurate cell SOC and capacity estimation, as an objective [14,15]. However, at present, the accuracy of SOC and capacity estimation cannot be guaranteed at a high precision level simultaneously, which exerts great difficulty in online application for EVs [16,17]. ESs are divided into two main groups: passive (dissipative) ECs [18,19] and active (non-dissipative) ECs [20–22]. Conventional passive ECs employ shunting resistors to bypass current because they dissipate the extra energy of battery cells with high voltage or SOC to achieve cell consistency. Their simplicity has resulted in their wide online application in real BMS. In contrast, active ECs are more complicated. They
Corresponding author. E-mail addresses: [email protected] (L. Song), [email protected] (M. Ouyang).
https://doi.org/10.1016/j.ijepes.2019.105516 Received 19 January 2019; Received in revised form 30 June 2019; Accepted 23 August 2019 0142-0615/ © 2019 Elsevier Ltd. All rights reserved.
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minimum remaining capacity and the minimum charging capacity, then i is equal to j, and the capacity of cell i (or j) determines the battery pack capacity. Practically, with the presence of cell degradation and inconsistency issue, the cell with the minimum remaining capacity is usually not the same cell that has the minimum charging capacity, thus the pack capacity is usually less than each cell capacity in the pack. The capacity and power of the battery pack tend to decrease seriously as inconsistency escalates gradually. To solve this issue, battery equalization is necessary. Theoretically and ideally, dissipative equalization fully charges and discharges the cell with the minimum cell capacity. This means that the minimum cell capacity is the pack capacity, which can be expressed as
require various electronic devices, such as capacitors and converters, to transfer charge and energy among different cells [23,24]. Although active ECs have the advantage that pack energy can be fully used without dissipation, passive ECs are superior for their simplicity and economy [24]. Zheng et al. [25] compared active and passive ECs and suggested that active ECs cost higher and their hardware is difficult to realize, but increased capacity attributed by active ECs is quite small if the cells are properly screened. Passive ECs are suitable for on-line battery pack equalization in EVs. From the aforementioned methods, we can be aware of that the voltage-based ESs have significant simplicity and feasibility that other ESs, no matter applied in passive or active ECs. However, the terminal voltage is influence by many factors, for example, capacity and internal resistance. A proper voltage difference is usually difficult to define. As a result, over-equalization occurs, and the energy of the battery pack is wasted. It is obvious that the capacity of the battery pack fails to be maximized. In order to solve inconsistency issues, we proposed an ES based on the cell voltage curves. By employing charging cell voltage curve (CCVC) hypothesis to evaluate the inconsistence of the cells in the module/pack, the drawbacks of the voltage-based method are eliminated successfully. Hence, the maximization of the capacity of the battery module/pack is realized. Analysis of stability and the convergence of the proposed method are presented. Furthermore, the proposed method is validated in the simulation and real BMS platform in different scenarios.
Cp = min (Ci )
In an active equalization, extra energy is transferred from cell to cell all the time, and the maximum pack capacity of the battery pack is the mean value of all cell capacities. This is expressed by Eq. (3) below.
Cp = mean (Ci)
(3)
2.2. Uniform charging cell voltage curves hypothesis Open circuit voltage (OCV) is cell’s electrical characterization when the internal electrochemical reaction of the cell is in equilibrium. For a specific battery manufactured in the same batch, it is generally assumed that all cells have a similar OCV curve. It is also noted that a slight change of OCV may have a significant influence on the accuracy of SOC estimation [27]. This change’s influence on the terminal voltage, however, can be ignored compared with the influence from the capacity or internal resistance differences. The uniform charging cell voltage curves (UCCVC) hypothesis is used to describe the relationship among the differences of cell’s capacity, resistance, and SOC. The UCCVC hypothesis is described as follows: batteries fabricated in the same batch and possess identical internal resistances, SOCs, and capacities have the same charging curves if they are charged in a constant current rate. Even if batteries of the same batches have different internal resistances, SOCs, and capacities, their charging cell voltage curves can also coincide after curve translations. The charging cell voltage curves (CCVCs) have a similar regular shape as the OCV curve. The analytical and proving process is illustrated in [28]. The difference in internal resistances can be eliminated by CCVC vertical translations ΔU calculated by Eq. (4) as shown in Fig. 2(a). Using Eq. (5), the difference of the initial SOC in the cell is compensated by CCVC horizontal translations ΔAh and Fig. 2(b) is achieved. In addition, horizontal scaling can eliminate the difference in cell capacities of CCVCs, as expressed in Eq. (6) and Fig. 2(c). Finally, they coincide as depicted in Fig. 2(d).
2. Theory 2.1. Battery pack capacity Cell capacity is commonly defined as the total available electricity that cell discharges from the upper cutoff voltage to the lower cutoff voltage under a designated circumstance formulated by manufacturers. However, the battery pack capacity in a series-connected module is also charged/discharged in the limitation of each single cell’s terminal voltage for the safety issue of a single cell [26]. Thus, each cell capacity has great influence on battery pack capacity. As shown in Fig. 1(a), cell 1 has the minimum available discharging capacity, whereas cell 3 has the minimum available charging capacity. In the charge/discharge cycling process, the battery pack is not allowed to discharge when cell 1 is fully discharged but other cells are not fully discharged. Similarly, the battery pack cannot charge if cell 3 is fully charged. Overall, pack capacity can be formulated as
CP = min (SOCi·Ci ) + min [(1 − SOCj )·Cj]
(2)
(1)
where CP is the pack capacity, SOCi , SOCj are the current state of charge, and Ci , Cj are the capacity of cell i or j. If one cell has the
Fig. 1. Schematic diagram of pack capacity without (a) or with (b) passive/active equalization. 2
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connected module, the CCVCs of different cells are translated from an identical CCVC by vertical movement. Here, only SOC inconsistency is considered. Internal resistance and capacity inconsistency are analyzed in Section 3.3. In Fig. 3, 4 cells are series-connected with different initial SOCs. When they are charged, the possible CCVCs of each cell are noted as cell 1 (red line), cell 2 (black dashed), cell 3 (green dashed), and cell 4 (blue dashed). Cell 1 will always have the highest voltage and reach the upper cutoff voltage, but the others cannot. The terminal voltages of each cell are respectively marked as A, B, C, and D as the module is fully charged. However, if the module has a good consistency, more electricity can be charged and the module capacity could increase significantly. The ideal result is that all cells reach the upper cutoff voltage at the same time. To achieve module capacity maximization, we propose an ES based on the UCCVC. First, the sampling start and end points of the highest cell voltage in the module or system are set in advance. This voltage curve is regarded as the reference to evaluate the difference of cells. The ES is divided into two steps as illustrated in Fig. 4. Step 1. Initial condition judgment and data recording. The purpose is to judge whether the equalization starts or not. Specific procedures are conducted as follows:
Fig. 2. Schematic diagram of uniform charging cell voltage curves hypothesis.
ri = r0 +
ΔU I
SOCi = SOC0 +
(4)
ΔAh C0
a. Calculation of the Ampere-hour that has to be charged (noted as ΔAh ) when the module is charging, if the highest cell voltage below the sampling interval. b. Recording of the ΔAh and the highest voltage with a voltage interval of 1 mV (noted as dV = 1 mV ) from the lower sampling voltage to upper sampling voltage and the ending voltage of all cells (noted as V_endi) when the highest voltage reaches upper sampling voltage.
(5) (6)
Ci = k i C0
Wherein, the parameters r0 , C0 and SOC0 are initial internal resistance, capacity and SOC of cell 0, respectively. The parameters ri , Ci and SOCi are initial internal resistance, capacity and SOC of cell i, respectively. In a series-connected module, all cells fabricated in the same batch are charged in the same constant current rate, and thus the UCCVC hypothesis is applicable. Though OCV is one of the most precise methods for parameter calibration, difficulties in obtaining OCV restrict its further application in practical engineering. The UCCVC hypothesis provides another way of comparing the differences among cells. Thereby, it can be used to evaluate the inconsistency of cells in a seriesconnected module or pack.
Step 2. Dynamic look-up table establishment and table look up. In this step, a voltage curve with respect to charged electricity can be established. It is used as a dynamic table to determine the difference among cells. c. Establishment of a dynamic look-up table using the sampled voltage as the y-axis and the corresponding ΔAh as the x-axis. d. Use V_endi of each cell to look up the established dynamic look-up table, and then obtain the corresponding ΔAhi of cell i. e. Calculate the difference (noted as dAh i ) between ΔAh i and the minimum one using the equation
3. Methodology
dAh i = ΔAh i − min (ΔAh)
3.1. Equalization strategy
(7)
dAh i is the electricity that cell i needs for equalization. Then, equalization would be completed by EC. In the ES, we choose [4.000 V, 4.100 V] as the sampling interval. The reason that why the entire charging curve is used is that we think part of the charging curve is capable enough for a practical condition. Since the inconsistency issue caused by battery aging is a slow process, the inconsistency of 10%SOC among cells is almost impossible to occur in this short time [29,30]. Specifically, the maximum amount of equalized electricity in equalization is approximately 10% of the SOC (SOC at 4.000 V is 80.5% and 4.100 V is 91% of the SOC), and has adequate electricity that a cell needs for equalization, even if the equalization condition is reached after several months. Besides, the length of the sampling voltage interval is 100 mV, which is short, thus requiring less memory and calculation. It should be emphasized that this sampling interval is not a fixed setting, but an example to implement the proposed method.
Based on the UCCVC hypothesis, the cells in a series-connected module fulfill their requirements. As shown in Fig. 3, all cells (cells 1–4) theoretically have the same CCVC, but the initial SOCs are different. According to Section 2.2, when SOC inconsistency occurs in a series-
3.2. Stability analysis of the sampling voltage interval Guaranteeing the stability of sampling voltage interval is an essential premise of accurate equalization. In practical usage, EVs are likely to be charged in any initial SOC. If the starting voltage of the charging process is close to sampling voltage interval, stability of this interval
Fig. 3. Schematic diagram of the equalization strategy. 3
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Fig. 4. Schematic diagram of pack/module equalization.
may be influenced by charging polarization. In this case, an opening threshold of equalization, which avoids charging polarization, and keeps the sampling interval stable, should be set. We adopt the electricity charged from the beginning as the threshold and conduct the following experiments to determine the value of this threshold. Three different scenes are considered where the cell is charged switching from the rest state (0C) and high current rate charging (1C and 2C) to constant current rate (0.5C, standard charging rate for a module). The test results are shown in Fig. 5, where three starting points are chosen as the beginning of the 0.5C charging. They are at approximately 70% SOC, 75% SOC and 78.5% SOC, respectively. The distances from the switching points to the sampling beginning point (80.5% SOC) are 10.5%, 5.5%, and 2% SOCs, respectively. The black line is a reference line charged from 60% SOC to 4.12 V in a constant current rate of 1/2C. To eliminate the effect of polarization phenomenon, a specific period is needed before cell charges switching from a current rate (0C, 1C and so on) to another rate (1/2C in this paper). Compared with others, charging at 0C costs more time for a cell to be in a stable state (see arrows 1 and 3 in Fig. 5). Moreover, when switching from a high rate, the terminal voltage may already reach 4.000 V as indicated by arrow 2. Under this circumstance, the terminal voltage is sampled in the high rate, which would be sampled again in the 1/2C charging process. Thus, the distance of 2% SOC is insufficient. Currently, stable sampling voltage curves are maintained in the fresh cell, as the charged electricity is 5.5% SOC. However, polarization deteriorates gradually as the cell ages. More time is required for the cell to be in a stable state, as indicated by arrows 1 and 3, and it may be still unstable when the terminal voltage reaches 4.000 V. Furthermore, terminal voltage, as pointed by arrow 4, maybe already reach 4.000 V before the current rate switches. Thus, the charged electricity of 5.5% SOC is insufficient, but 10.5% is sufficient. For calculation convenience, the equalization threshold is set to 10% of the nominal capacity.
Fig. 5. Results of stability test of different scenes.
4
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remaining electricity of cell 1 needed for equalization isΔAh2 . According to Eq. (12),
ΔAh2 < 0.625%SOC
(13)
The Ahthreshold is the threshold on value analyzed in Section 3.3.3, and Ahthreshold is 0.5% of nominal capacity. Accordingly, ΔAh2 can be reformulated as
ΔAh2 ≈ Ahthreshold
The convergence of equalization is obviously obtained after the second equalization. If C2 < C1, the extreme range of k is 1 > k > 0.8. After the first equalization, the remaining electricity of cell 1 needed for equalization, ΔAB1, is expressed as Eq. (9). The ending terminal voltage of cell 2 should rise to point D if cell 1 reaches the upper cutoff voltage, which is impossible. Now, the remaining electricity needed for equalization is given as
Fig. 6. Cell equalization with capacity inconsistency.
ΔAh1 = |ΔAB1 − ΔAA*| = (1 − k )ΔAA*
3.3. Convergence analysis of equalization
1 1 ΔAh2 = ΔAB − ΔAh1 = ⎛ − 1⎞ ΔAh1 = ⎛ − 1⎞ (1 − k )ΔAB∗ ⎝k ⎠ ⎝k ⎠
ΔAh2 ≈ 0.5%SOC = Ahthreshold
3.3.2. Internal resistance inconsistency The difference of internal resistance inconsistency has a significant influence on terminal voltage. For two same cells with different internal resistances, the cell with a higher internal resistance reaches the upper/ lower voltage in advance, which determines the pack capacity if the cells are series-connected. Under this circumstance, equalization does not improve the pack capacity but improves the pack’ voltage consistency. This is also illustrated by Fig. 3. If cell 1 has the highest internal resistance, then the difference of CCVCs only results from internal resistance inconsistency when the initial SOC of all cells are equal. After using the proposed method to equalize the module, the consistent terminal voltage is achieved in the charging or discharging process. Furthermore, the pack capacity power increases, although the pack capacity does not change. Terminal voltage and SOC consistency cannot be realized at the same time for a pack with internal resistance inconsistency. Apparently, terminal voltage consistency is more important than SOC consistency in this situation.
where k is the coefficient between C1 and C2. As depicted in Fig. 6, cell 1 has a higher initial SOC, thus reaching the upper cutoff voltage ahead of cell 2. Cell 2 is not fully charged and point A is the ending terminal voltage. By applying the proposed ES, the electricity of cell 1 for equalization is ΔAA*. However, because of the uncertainty of C2, it may be larger, equal, or smaller than C1, and the corresponding CCVCs are plotted in Fig. 6. The amount of electricity of cell 1 needed for equalization is ΔABi (i = 0, 1, 2), which is easy to deduce from Eq. (8). (9)
If k = 1, C2 = C1 and ΔAB0 = ΔAA*, the difference of SOC is eliminated after one equalization. Meanwhile, if k > 1, C2 > C1, the maximum value is 1.25 in the extreme scene where the capacity degradation rate of cell 1 is 20% and that of cell 2 is 0%. Thus, the range of k is 1.25 > k > 1. After the first equalization, the ending terminal voltage of cell 2 rises to point C, and the remaining electricity of cell 1 needed for equalization can be derived by Eq. (10).
3.3.3. Equalization threshold analysis Here, we analyze the sampling error resulting from the voltage and current sensor. If we directly set the threshold on value (noted as Ahthreshold ) to zero, over-equalization may occur. Unfortunately, equalization begins when the equalization condition is maintained in charging, whether the pack needs it or not. Consequently, the workload of BMS increases and energy dissipates. An appropriate threshold on value should be set according to the sensor sampling accuracy. In this paper, the BMS we used is provided by Beijing KeyPower Technologies Co., Ltd. (shown in Fig. 7(b)). The voltage measurement range is −5 V to 5 V with the sampling of ± 1.5 mV. The current sensor measurement is 0.5% (> 30 A) and ± 0.1 A (< 30 A). The current sampling error results in a wrong ΔAh value in the xaxis, making the CCVC move horizontally. In a series-connected
(10)
After n times equalization, the remaining electricity of cell 1 needed for equalization is formulated as
ΔAh n = (k − 1) nΔAA*
(11)
ΔAA∗
Given that 1.25 > k > 1 and the maximum value of is about 10% SOC, Eq. (11) can be modified by using the equation expressed as
1 n 1 n ΔAhi < ⎛ ⎞ ΔAA* ≈ ⎛ ⎞ × 10%SOC ⎝4⎠ ⎝4⎠
(17)
Convergence of equalization is also achieved after the second equalization. Consequently, capacity inconsistency would be eliminated after two equalizations.
(8)
ΔAh1 = ΔAB2 − ΔAA* = (k − 1)ΔAA*
(16)
As ΔAA* ≈ 10% SOC, Eq. (16) can be rearranged modified as
3.3.1. Capacity inconsistency The equalization between cells 1 and 2 is used as an example. According to Eq. (6), the relationship between the capacities of cell 2 (note as C2) and cell 1 (noted as C1) is expressed as
ΔABi = k ΔAA∗
(15)
In the second equalization, cell 2 has the higher voltage. Therefore, the second equalization of k < 1 is the same as the first equalization of k > 1. ΔAh1 is the remaining electricity of cell 2 needed for equalization. After the second equalization, the remaining electricity needed for equalization, ΔAh2, is given by
The convergence of the proposed ES is defined as the event when all cells in the module reach the upper cutoff voltage at the same time. As battery ages, capacity degradation, uneven temperature distribution, and internal resistance increase are critical factors causing cells inconsistency. In the charging process, the cells are in a relatively stable condition, the difference among cells is less than 5 °C, the influence of which to pack consistency is negligible [25]. We provide an analysis of the convergence of equalization when the battery pack has aged.
C2 = kC1
(14)
(12)
When equalization has been performed twice, that is, n = 2, the 5
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Fig. 7. Schematic diagram of simulation and experiment platform.
ECMs include the Rint model and one or multi-order RC model et al. In this paper, the second order RC model is adopted. As shown in Fig. 7(a), this model consists of OCV, ohmic resistance R0, and two RC components. The R1C1 and R2C2 circuits describe the polarization phenomenon of the battery caused by transfer, diffusion, and other factors. The equations that describe the electrical characteristics are respectively given by
module, the current errors of all cells are unanimous because the current is measured by one current sensor. Thusthe current measurement has no effect on the equalization result. Meanwhile, cell voltage is sampled individually. Thus, CCVC has an inconsistent vertical movement. In other words, voltage sensor with high accuracy ( ± 1.5 mV in this paper) promises good equalization result in the practical implementation, because the equalization threshold is defined by the voltage error. The maximum absolute error among CCVCs is 3.0 mV, and thus we can calculate the maximum SOC error based on the OCVSOC curve. The maximum SOC error caused by the voltage sensor is 0.370% SOC. Accordingly, Ah threshold is 0.370%SOC. For the convenience of calculation, the constant value is set to 0.5% of the nominal capacity. Ah threshold guarantees that over-equalization will not occur. To obtain a highly accurate result, the threshold off is set to 0.2% of the nominal capacity, whereas the sampling error cannot always be the maximum value.
U1 = IR1 [1 − exp (−t / τ1)]
(18)
U2 = IR2 [1 − exp (−t / τ2)]
(19)
Ut = fOCV (SOC ) − IR 0 − U1 − U2
(20)
where I is the current, Ut is the terminal voltage, and U1 and U2 are the voltages across R1C1 and R2C2, respectively. In addition, τ1 and τ2 are the time constants that satisfy equations τ1 = R1 C1 and τ2 = R2 C2 . fOCV (SOC ) is the function between SOC and OCV. A commercial lithium-ion battery with an NMC/graphite electrode is employed in the tests. It has a nominal capacity of 37 Ah and upper/ lower cut-off voltages of 4.2/2.8 V. The standard capacity test at 25 °C and the hybrid pulse power characteristic (HPPC) tests at various temperatures are conducted successively, and then the genetic algorithm is applied to identify the model parameters.
4. Simulation and experiment platform To validate the effectiveness and precision, we simulate the equalization in a cell module in fresh and aged states and embed the proposed strategy into a real BMS. 4.1. Single cell model
4.2. Cell module model with equalization circuit Among battery models, such as equivalent circuit model (ECM), pseudo two-dimensional model (P2D), and single particle model [31,32], ECM can precisely describe battery electrical characteristics and has low calculation requirements, and thus widely applied [33].
Fig. 7(a) presents the schematic diagram of the battery module with a passive equalization circuit. The cell module is series-connected by 12 cells in which every cell is simulated using a second-order RC model. 6
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The passive equalization circuit consists of several 24 Ω and 4 Ω resistances and switches. Hence, the equalization current of each cell can be solved according to Ohm’s law and Kirchhoff’s rules. As shown in Fig. 4, switching is controlled by the equalization state. Equalization starts (switching on) if the equalized electricity is less than the electricity amount needed for equalization. Otherwise, equalization stops (switching off).
respectively. Meanwhile, the module capacity successfully increases from 32.03 Ah to 35.92 Ah, 95.13% of the theoretical capacity that is 37.76 Ah.
5.1.2. Aged cell module equalization Cell degradation occurs in different degrees due to both internal and external reasons. The parameters of the aged cell pack are presented in Table 1, where capacity degradation has no significant correlation with internal resistance increase [34,35]. Fig. 8(b) shows that a serious inconsistency phenomenon occurs in the aged cell module, especially for cell 2, which has the maximum SOC, and cell 4 with the minimum SOC. If no equalization is performed, the performance of the pack will deteriorate, and the driving range of EV and the cycle life of the pack might decrease greatly. Faced with the severe inconsistency problem, the module is equalized according to the proposed strategy. Fig. 8(b) shows significant optimization in the performance of the module. An excellent consistency is obtained, and the equalization accuracy is calculated and presented in Table 2. The module capacity efficiently increases from 25.57 Ah to 29.26 Ah, accounting for approximately 14.43% of the initial capacity without equalization. Compared with the theoretical capacity, namely the minimum cell’s capacity, which is 31 Ah, the proposed method could realize 94.39% of the theoretical capacity. The analysis indicates that the proposed equalization strategy is successfully validated in the simulation platform. The consistency issue is solved, while the capacity increases 12.14% and 14.43% in fresh and aged module, respectively.
4.3. Experiment platform To validate the practicality of the proposed method, we embed it into a real BMS. The hardware system is shown in Fig. 7(b), which consists of a current meter, a cell module, a sampling board, a BMS controller, a test bench, and a monitoring computer. In the experiment, the cell module is charged/discharged by the test bench at room temperature (25 °C ± 5 °C). The equalization strategy is running in BMS based on the voltage sampled by the sampling board and the current sampled by the current meter. The equalization states, including voltages and the temperature of the cell, are displayed on the monitoring computer. 5. Results and discussion A series of simulations and experiments are designed and carried out, the results of which are described and discussed in this section. 5.1. Results of simulations 5.1.1. Fresh cell module equalization The proposed ES is firstly simulated in a fresh state cell module, which can be used for comparison with the result of the real BMS test. The parameters among cells in the cell module are assumed to be in normal distribution [34]. The fresh cells have good consistency, and the initial normal distribution values of capacity, SOC, internal resistance, and temperature are provided in Table 1. In the simulation, the resistance coefficient is a gain that multiplies the resistance values to simulate the resistance inconsistency among cells in the module. To simulate an inconsistent cell module situation, the initial SOC of cell 1 is modified to 20% SOC. The cell is charged in a two-step charging profile. The first step is to charge the cell until 4.12 V reaches in a constant current of ½ C, then charged in 1/10 C to 4.12 V again. Equalization starts when the conditions meet. After two charging processes, equalization is complete. The comparison of different states before and after equalization in fully-charged mode is showed in Fig. 8(a). The red dotted and solid curves represent the SOC of cells in the module before and after equalization; the blue dotted and solid curves stand for the terminal voltage of cells in the module before and after equalization. The initial SOC and terminal voltage of cell 1 are obviously lower than those of the others, but they eventually converge to the same value after the equalization is completed. The results of parameters comparison are presented in Table 2. The maximum absolute errors of OCV and SOC are 135 mV and 12.04% SOC before equalization, respectively. After equalization, they significantly decrease to 11.4 mV and 0.68% SOC,
5.2. Results of real BMS experiment The proposed strategy was then embedded into a real BMS controller to further verify its applicability. Cell aging takes too long, and thus only fresh cells were utilized in this experiment. To acquire an inconsistent situation in the module, cell 1 is previously discharged to a low SOC. The charging profile adopted in the simulation is used to charge the module. Fig. 8(c) presents the CCVCs of all cells in which the CCVC of cell 1 is obviously apart from others and much lower. This means that cell 1 cannot be fully charged, but reaching the lower cutoff voltage first, which then leads to a low module capacity. The discharge profile is similar to the charge profile shown in Fig. 8(d). The discharge capacity is calculated as 32.54 Ah. The charging profiles of cells after equalization are presented in Fig. 8(e), which shows consistent CCVCs and no distinct distance among the curves, implying that more electricity can be charged in the module than before. After equalization, cells discharge in a consistent path as depicted in Fig. 8(f). The capacity has risen by 13.03% to 36.78 Ah. The maximum absolute errors of OCV and SOC are greatly optimized from 145.2 mV, 13.00% SOC to 21.9 mV, 1.86% SOC, respectively. Compared with different methods listed in Table 3, the proposed method has a good performance of equalization, even though it is applied with a passive EC. Over equalization is avoided successfully, reducing energy cost. Importantly, the equalization strategy has high precision competitive simplicity with low computation. On the other hand, the limitation of the proposed method is that specific charging condition must be reached as discussed in Section 3.3.3, making it challenging to be applied in various charging scenes. In other word, only charging profiles must fulfill the requirement, can the equalization strategy works. Overall, the proposed equalization method is validated in the real BMS with excellent performance. The capacity increases by 12.14% in the fresh module and by 14.43% in the aged state. The result of the real BMS test also indicates the remarkable applicability of this method. Therefore, the proposed ES can deal with the inconsistency problem in fresh or aged modules, extending the driving distance or time from that of the battery pack without equalization.
Table 1 Parameters in simulations of fresh and aged module. State
Capacity (Ah)
SOC
Resistance coefficient
Temperature (°C)
Fresh Aged
(38, 0.2, 12, 1) (33, 1.0, 12, 1)
(0.3, 0.01, 12, 1) (0.3, 0.05, 12, 1)
(1.0, 0.05, 12, 1) (1.5, 0.20, 12, 1)
(25, 0.5, 12, 1) (25, 0.8, 12, 1)
Note: normal distribution is expressed as (a, b, c, d), where a, b, c, and d are the parameters in the normal distribution; a is the mean, b is the standard deviation, c is the array length, and d is the array dimension. 7
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Fig. 8. Results of simulation and real BMS experiment.
obtaining the electricity required by cells for equalization is obtained. The proposed ES is based on the terminal voltages that are directly sampled by the voltage sensor, and thus applicable in practical engineering. To keep the sampled voltage interval stable, an equalization opening threshold of 10% nominal capacity, which is the prerequisite of equalization, is set according to a series of stability tests. We demonstrate the convergence of the ES in different scenes with SOC inconsistency and internal resistance for fresh or aged packs. Moreover, the effectiveness and precision are preliminarily validated in a simulation platform where the inconsistency in fresh and aged modules are simulated. The SOC consistency and module capacity are significantly improved, and the maximum absolute errors of OCV and SOC are 11.4 mV and 0.68% SOC in the fresh state and 42.0 mV and 3.54% SOC in the aged state, respectively. Meanwhile, the proposed strategy is embedded in a real BMS controller. The results of the real BMS further verify its applicability with an accuracy of 21.9 mV and 1.86% SOC, and the capacity is improved by 13.03%. The results above prove that the proposed method could
Table 2 Comparison of parameters before and after equalization. Experiment
Fresh module
Aged module
Real module
State
Before
After
Before
After
Before
After
Capacity (Ah) R_OCV (mV) R_SOC (%)
32.03 135 12.04
35.92 11.4 0.68
25.57 180 16.44
29.26 42 3.54
32.54 145.2 13.00
36.78 21.9 1.86
Note: R_OCV is the maximum absolute error of OCV, and R_SOC is the maximum absolute error of SOC.
6. Conclusion This paper proposeed an ES method to solve the inconsistency issue in battery modules/packs. Based on the UCCVC hypothesis, a dynamic look-up table is established using the voltages of the cell with the highest voltage. Then, we look up the table by the ending voltages of each cell and identify the difference with the minimum one, thereby 8
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Table 3 Performance comparison of different methods. References
ES
EC
Validation
Errors
Merits
Drawbacks
[36] [37] [38] [39]
SOC and capacity-based Voltage-based SOC-based SOC-based
active passive active active
simulation experiments simulation experiments
19.1 mV/12.2 mV 7 mV 0.5% SOC 20 mV/2% SOC
Avoid over equalization High precise Low SOC difference high balancing efficiency
High computational cost Over-equalization may occur Require precise SOC; over-equalization may occur High computational cost
extend the driving distance or time and guarantee a better battery pack performance than that of the battery pack without equalization.
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