Modeling and Control Problems in Sustainable Transportation and Power Systems
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Multistage CCCV Charge Method for LiIon Battery
Abstract
Charging the Liion battery with constant current and constant voltage (CCCV) strategy at −10°C can only reach 48.47% of the normal capacity. To improve the poor charging characteristic at low temperature, the working principle of charging battery at low temperature is analyzed using electrochemical model and firstorder RC equivalent circuit model; moreover, the multistage CCCV strategy is proposed. In the proposed multistage CCCV strategy, the charging current is decreased to extend the charging process when terminal voltage reaches the charging cutoff voltage. The charging results of multistage CCCV strategy are obtained at 25°C, 0°C, and −10°C, compared with the results of CCCV and twostage CCCC strategies. The comparison results show that, at the target temperatures, the charging capacities are increased with multistage CCCV strategy and it is notable that the charging capacity can reach 85.32% of the nominal capacity at −10°C; also, the charging time is decreased.
1. Introduction
With the advantages of zero pollution, high energy efficiency, and pluralistic energy sources, electric vehicle (EV) has been the new development point of motor industry [1–3]. Liion battery has been widely used in EV for its high energy density, long cycle life, and high safety level [4]. But the battery technology still cannot meet the EV demand of long travel distance, fast capacity recovery, and low temperature utilization [5]. At low temperature, battery chemical activity decreases, resistance increases, and capacity is decreased. Charging process is more difficult than the discharging process at low temperature [6, 7].
Much work has been done on charging strategies in recent years. In [8] a threestep charging method for Ni/MH battery was proposed to obtain the rapid charge. In [9], an optimum current charging strategy based on the boundary charging current curves was proposed. The boundary charging current curves were obtained by analysis of temperature rise and polarization voltage in charging process. The charging period was decreased and capacity was increased with the strategy. Reference [10] proposed a dutyvaried voltage charging strategy that can detect and dynamically track the suitable duty of the charging pulse. Compared with conventional CCCV strategy, the charging speed was increased by 14%, and charging efficiency was increased by 3.4%. Reference [11] constructed a SOC estimation model and the CCCV charging process was controlled by battery SOC. The charging capacity can be monitored to gain a higher level charging degree and avoid being overcharged. In [12], an Ant Colony System algorithm was used to select the optimum charging current among five charging states and the charging time was decreased and battery cycle life was extended by 25%. In [13], a Taguchibased algorithm was used to obtain rapid charge. With the charging strategy, the battery capacity could reach to 75% in 40 min. In [14], a constantpolarizationbased fuzzycontrol charging method was proposed to adapt charging current acceptance with battery SOC stages. The charging strategy could shorten charging time with no obvious temperature rise. Ruan et al. and Zhao et al. [15, 16] studied the temperature characteristic of charging and discharging process. The temperature increased more in discharging process compared to the temperature increase in charging process. The pulse charging/discharging process was added before charging process so the battery could be preheated. The battery could start charging process at relatively high temperature and charging capacity was increased at low temperature.
All the charging strategies increase the battery charging characteristic at different degrees proposed in [8–14]. But the charging performance at low temperature is not considered. Although the preheating charging strategy at low temperature proposed in [15, 16] can increase the charging capacity, the selfpreheating process costs too much time and cannot work at low SOC condition. This paper analyzes the charging characteristic of a Liion battery at different temperature, uses electrochemical model and firstorder equivalent circuit model to analyze the bad low temperature characteristic of Liion battery in theory, and proposes a multistage CCCV strategy. The multistage CCCV strategy is compared with CCCV and twostage CCCV strategies at 25°C, 0°C, and −10°C.
2. Experimental
2.1. Battery and Equipment
The battery used is 18650 cylindrical Liion battery with normal capacity of 1.37 Ah, a normal voltage of 3.2 V, and a cutoff voltage of 3.6 V. The maximum charging and discharging rates are 1 C and 2 C, respectively. The positive electrode material is LiFePO_{4}, and negative electrode material is LiC_{6}. The battery tester is LD battery tester with 8 test channels and the test process can be programmed and monitored by computer. The battery was tested in a temperature chamber to ensure the temperature parameter to be constant. The detailed parameters of battery tester and temperature chamber are shown in Table 1. The experimental setup can be described as in Figure 1.

2.2. Experimental Process
The battery charging strategies tested in experiments were CCCV, twostage CCCV, and multistage CCCV. The test temperature points were 25°C, 0°C, and −10°C. The charging strategies are explained as follows.
For the CCCV strategy, the constant current process was charging at 0.3 C to the cutoff voltage of 3.6 V and the constant voltage process was charging at 3.6 V for 5 min.
For the twostage CCCV strategy, the first constant current process was charging at 1 C to the cutoff voltage of 3.6 V. Then in the second constant current process, the charging current was decreased to 0.5 C. Since the charging current was decreased, the terminal voltage was decreased below 3.6 V allowing the constant current process to be extended, until the terminal voltage reached the cutoff voltage once again. The constant voltage process was charging at 3.6 V for 5 min [17].
For the multistage CCCV strategy, the constant current process was divided into ten stages. The maximum and minimum rates were 1 C and 0.1 C, respectively, and the charging current was decreased by 0.1 C when terminal voltage reached the cutoff voltage. The constant voltage process was charging at 3.6 V for 5 min.
3. Charging Characteristic of Battery at Low Temperature
3.1. Charging Capacity Characteristic at Different Temperature
The selected battery was charged by CCCV strategy at 25°C, 0°C, and −10°C to obtain the charging capacity characteristic at low temperature. Before every charging process at different temperature, the battery was discharged empty at 25°C and kept for six hours to ensure the whole battery temperature to be uniform. As shown in Figure 2, the charging capacities at 25°C, 0°C, and −10°C are 1.309 Ah, 1.196 Ah, and 0.664 Ah, respectively. The charging capacity is decreased by 8.6% at 0°C and 49.3% at −10°C compared with that at 25°C. The charging capacity has a great decrease at −10°C.
3.2. OCV Characteristic at Different Temperature
The battery was tested by hybrid pulse power characteristic (HPPC) rule that is detailed in “Freedom CAR Battery Test Manual” [18] to obtain OCV, ohmic resistance (), and polarization resistance (). SOC can be calculated by the following formula: where is the initial SOC of the battery, AHC is the normal capacity of the battery at 25°C, and is the discharge (positive ) or charge (negative ) current. As the OCV curves shown in Figure 3, the OCV reflects increasing tendency with temperature decreasing and the difference of OCV at different temperature is relatively more obvious at low SOC.
3.3. and Characteristic at Different Temperature
As shown in Figures 4 and 5, both and increase with temperature decreasing. remains steady with SOC increasing, and the increase is nearly 258% at −10°C. increases with SOC increasing and temperature decreasing, and the maximum increase in is nearly 257% at −10°C with 90% of SOC.
4. Electrochemical and FirstOrder Equivalent Circuit Model
4.1. Electrochemical LiIon Battery Model
Doyle et al. have proposed the porous electrode theory for the analysis of electrochemical process of Liion battery [19]. The onedimensional geometry consists of negative/positive current collector, negative/positive electrodes, and separator. The negative current collector material is copper, and positive current collector material is aluminum. The positive electrode active material is LiFePO_{4}, and negative electrode active material is LiC_{6}. The separator is polyolefin porous membrane. The electrolyte is lithium salt dissolved in 1 : 1 or 2 : 1 liquid mixture of ethylene carbonate (EC) and dimethyl carbonate (DMC). The onedimensional geometry example of charging process is shown in Figure 6 [20] and the charging chemical equation is
In the charging process, the electrons move from the positive electrode to the negative electrode through the external circuit, and Li^{+} moves from the positive electrode to the negative electrode through the separator in electrolyte. As the charging process is a chemical reaction, the reaction characteristic is influenced by concentration and Li^{+} diffusion. The Liion concentration in electrolyte phase changes with time and can be described by Fick’s second law along the coordinate shown in Figure 6 [21]:where is the concentration of Liion in electrolyte phase, is Li^{+} diffusion coefficient in electrolyte phase, is the transference number of lithium ions with respect to the velocity of the solvent, is Faraday constant, and is charging transfer current density.
The distribution of Liion in solid state phase is also described by Fick’s second law of diffusion in polar coordinates [21]:where is the concentration of Liion in solid, is the Li^{+} diffusion coefficient in solid state phase, and is radius of spherical particle.
The Arrhenius formula shows the Li^{+} diffusion coefficient in solid state phase as shown below [21]:where is the activation energy for diffusion. is the universal gas constant, is the reference diffusion coefficient at , is the reference temperature, and is the temperature. Formula (5) shows that the diffusion coefficient decreases with the temperature decreasing. Reference [14] indicates that the solid state phase diffusion polarization dominates the total polarization and the solid state phase polarization is increased with diffusion coefficient decreasing. The increase of polarization results in higher polarization voltage compared with that of normal temperature, the terminal voltage increasing space during constant current charging process is decreased, and the charging capacity will be decreased.
The charging transfer current density can be obtained using the following ButlerVolmer formula [20]:where is the exchange current density, and are the transfer coefficients of anode and cathode, and is the surface over potential, which can be obtained using the following formula [20]:where is the solid phase potential, is the electrolyte phase potential, and is the open circuit voltage.
can be described as shown below [20]: where is the reaction rate coefficient, is the maximum Liion concentration in the electrodes, and is the Liion concentration on the active particles surface.
can be obtained using the following formula [20]:where is the reaction activation energy and is the reaction rate coefficient at . With the temperature decreasing, reaction rate coefficient is decreased. As formula (7) shows, is decreased with temperature decreasing. The charging reaction is impeded for the reaction rate coefficient decreasing. As the parameter is timeinvariant, the charging obstruction can be considered as a resistive process. The increase of impedance also results in the terminal voltage increase and the decrease of charging capacity.
The electrochemistry model analysis of the charging process at low temperature shows that the main obstruction consists of polarization and impedance increase. This increase can be analyzed by the equivalent circuit model, the polarization can be modeled by capacitance and resistance in parallel, and the impedance can be modeled by resistance. A firstorder equivalent circuit model is used in the next part.
4.2. FirstOrder Equivalent Circuit Model
The firstorder equivalent circuit model is used to analyze the charging process [21, 22]. As shown in Figure 7, represents the ohmic resistance, is the voltage on , and , respectively, represent the polarization capacity and polarization resistance, is the voltage on and , OCV is the open circuit voltage, is the terminal voltage, and is the charging current. The following formulas can be obtained:
With assumption of and , the following can be obtained:where .
It can be seen from formulas (10)(11) that is determined by OCV, , , and . As is mentioned above, OCV changes little with temperature decreasing, while and increase significantly with temperature decreasing. The increase of can be explained by the slow kinetics of electrochemical reaction influenced by temperature. The constant current process of CCCV strategy is limited by cutoff voltage and the charging capacity mainly depends on the constant current process. At low temperature, and increase making and increase, and is higher than that at normal temperature. The cutoff voltage is reached earlier and the constant current process is stopped earlier [23]. The increasing of and depends on the battery design parameters and cannot be controlled during the charging process. The only parameter which can be controlled is the charging current. As proposed in [17], for a twostage CCCV strategy, the constant current charging process was divided into two stages. The first stage is charging battery with the maximum charging rate until the cutoff voltage is reached. The second stage charging current was decreased to half of the maximum charging rate, and the terminal voltage can be decreased to extend the constant current charging process to increase capacity. According to the current decrease process of the twostage CCCV strategy, a multistage CCCV strategy with more detailed current rates is proposed in this paper. Once the cutoff voltage is rapidly reached at a low temperature, the terminal voltage can be decreased with charging current decreasing, and the constant current charging process can be repeatedly extended to increase charging capacity. Meanwhile, the charging current is decreased from the maximum rate, and the multistage can automatically and degressively select the optimal charging current to use high charging rate as far as possible and shorten the charging period.
5. Result and Discussion
5.1. Different Charging Strategy Analysis at 25°C
Figures 8–10 show the terminal voltage curves with different charging strategies at 25°C. The terminal voltage of CCCV strategy increases to 3.25 V at the low SOC range of 0%–10%, while the terminal voltages of twostage CCCV and multistage CCCV strategies increase to near 3.4 V. The terminal voltage of CCCV strategy increases to 3.4 V with SOC reaching 90% and has a huge increase to 3.6 V at the end of charging. The terminal voltages of twostage CCCV and multistage CCCV strategies increase to 3.6 V with SOC of 85%. With current decreasing, the terminal voltage of twostage CCCV strategy decreases to 3.49 V and increases to 3.6 V again with SOC increasing of 7%. Unlike twostage CCCV strategy, the terminal voltage of multistage CCCV strategy has more decreasing times to extend the charging SOC to a higher level.
Figure 11 shows the SOC curves of different charging strategies at 25°C. The charging capacities of CCCV, twostage CCCV, and multistage CCCV charging strategies are 1.309 Ah, 1.299 Ah, and 1.368 Ah, respectively. The capacities of twostage CCCV and multiCCCV strategies are higher than that of CCCV strategy for current decreasing process. The multiCCCV has the highest charging capacity because the current decrease process of multistage CCCV strategy has more gradients than twostage CCCV strategy. The charging periods of CCCV, twostage CCCV, and multistage CCCV charging strategies are 223 min, 67.4 min, and 94.7 min, respectively. It is obvious that the CCCV charging strategy has the longest charging period for a low constant charging rate. Although the whole charging period of twostage CCCV is shorter than that of the multistage CCCV, multistage CCCV charging strategy has a larger charging capacity. The charging period of multistage CCCV strategy is shorter than that of twostage CCCV strategy at the same charging SOC point 94.8%.
5.2. Different Charging Strategy Analysis at 0°C
As shown in Figure 12, unlike the terminal voltage at 25°C, the terminal voltage of CCCV strategy increases to 3.35 V at low SOC range of 0%–10%. The terminal voltage increase slope during SOC range of 10%–80% is enhanced. The terminal voltage increase towards the cutoff voltage and sharp increase at 25°C with SOC range beyond 80% are vanished. The increase in terminal voltage indicates that the normal CCCV charging process has been changed by the increase in internal resistance at low temperature.
As shown in Figures 1314, the first charging stage of twostage CCCV strategy does not last long before the cutoff voltage is reached for the increase in internal resistance and the high charging rate. The second charging stage decreases the charging current rate by 0.5 C, and the terminal voltage decreases by 0.23 V and keeps on increasing until the cutoff voltage is reached. Unlike the twostage CCCV strategy, the current decreases by 0.1 C of the multistage CCCV strategy. The terminal voltages of 1 C–0.7 C constant current charging stages increase rapidly with SOC below 22%. Terminal voltages of 0.6 C–0.4 C constant current charging stages increase slower with SOC between 22% and 73.4%. Terminal voltages of 0.3 C–0.1 C constant current charging stages increase rapidly again with SOC beyond 73.4%. The terminal voltage curve of multistage CCCV indicates that multistage CCCV strategy can automatically select the optimal charging current by cutoff voltage limiting and current decreasing.
The charging result at 0°C shows that the capacities of CCCV, twostage CCCV, and multistage CCCV charging strategies are 1.196 Ah, 0.758 Ah, and 1.246 Ah, respectively. Compared with the charging result at 25°C, the charging capacities of CCCV, twostage CCCV, and multistage CCCV charging strategies decrease by 8.2%, 39.5%, and 8.9%, respectively. As the main charging rate of twostage CCCV strategy is 0.5 C higher than 0.3 C of CCCV strategy and the charging rate does not decrease further, the twostage CCCV strategy has the largest decrease in charging capacity decrease at 0°C. As multistage CCCV strategy has 0.2 C and 0.1 C charging rate lower than 0.3 C of CCCV strategy, the charging capacity of multistage CCCV strategy is higher than that of CCCV strategy.
Figure 15 shows the SOC curves of different charging strategies at 0°C. The charging periods of CCCV, twostage CCCV, and multistage CCCV charging strategies are 183.4 min, 68.7 min, and 148 min. The curve tendency of multistage CCCV charging strategy shows the obvious capacity increasing speed, although the speed is slowed down for the current decrease at later period. As the dotted line shows, the charging period of multistage CCCV is shorter than that of twostage CCCV strategy with the same charging SOC of 55.32%. The multistage CCCV still has the maximum charging capacity and minimum charging period at 0°C.
5.3. Different Charging Strategy Analysis at −10°C
Figures 16–18 show the terminal voltage curves with different charging strategies at −10°C. The terminal voltage of CCCV strategy reaches cutoff voltage at SOC point of 48.67%. The terminal voltage of the first stage of twostage CCCV strategy increases straightly towards the cutoff voltage and the second stage only extends the SOC to 32.26%. All the terminal voltages of charging current at 1 C–0.6 C of multistage CCCV strategy increase rapidly to the cutoff voltage with SOC growth less than 10%. The terminal voltages of charging current at 0.5 C–0.1 C increase slower with near 75% of SOC growth. All the terminal voltage curves indicate that the voltage increases faster at the lower temperature and higher charging current rate.
The charging result at −10°C shows that the capacities of CCCV, twostage CCCV, and multistage CCCV charging strategies are 0.664 Ah, 0.442 Ah, and 1.169 Ah, respectively. Compared with the charging result at 25°C, the charging capacities of CCCV, twostage CCCV, and multistage CCCV charging strategies decrease by 47.08%, 62.56%, and 14.53%, respectively. It can be indicated that the charging capacity of CCCV decreases badly and the first stage of twostage CCCV strategy oppositely becomes the capacity limit. The multistage CCCV strategy can keep the charging capacity beyond 80% even at −10°C.
Figure 19 shows SOC curves of different charging strategies at −10°C, and the charging periods of CCCV, twostage CCCV, and multistage CCCV charging strategies are 101.7 min, 39.38 min, and 197.1 min, respectively. The curve of twostage CCCV charging strategy shows the obvious difficulty of capacity increasing at such temperature. Although the terminal voltage increasing slope of twostage CCCV strategy is close to that of multistage CCCV strategy, the charging capacity is significantly different. The comparison of the SOC curves shows that the charging period of multistage CCCV strategy is still the shortest at the same SOC point. The multistage CCCV still has maximum charging capacity at −10°C.
5.4. Analysis of Multistage CCCV Strategy
Figure 20 shows the capacity curves of different charging current rates of multistage CCCV strategy at different temperature, and the high charging capacity corresponding charging current rate decreases with temperature decreasing. The charging capacity of 1 C is 1.162 Ah, beyond 80% of battery capacity, and the other charging rates only need to recover the rest of capacity at 25°C. While the high charging rate does not work well with temperature decreasing, the charging current rate with the maximum charging capacity of 0.28 Ah is 0.5 C at 0°C. The charging current rate with the maximum charging capacity of 0.266 Ah is 0.3 C at −10°C. The main capacity is charged with a range of charging current rates at low temperature. The multistage CCCV can automatically select the optimal charging current rate for two reasons. The cutoff voltage limit can stop the charging stage of the not optimal charging current rate. The multistage has ten charging current rates from the maximum 1 C to the minimum 0.1 C ensuring the charging demands at different temperature points. The multistage CCCV strategy is a wide temperature range charging strategy that keeps high charging capacity and low charging period.
6. Conclusion
It can be seen from the presentation above that the charging capacity of the CCCV strategy can be only 48.47% of the normal capacity at −10°C. The charging process is analyzed by electrochemical Liion battery model and firstorder equivalent circuit model. The increase in internal resistance is the main limitation of charging capacity at low temperature. The proposed multistage CCCV strategy can extend the constant current charging process to obtain a larger capacity by decreasing the charging rate when the terminal voltage reaches the cutoff voltage. Experimental results indicate that the charging capacities with multistage CCCV strategy at 25°C, 0°C, and −10°C are 1.368 Ah, 1.246 Ah, and 1.169 Ah, respectively. Compared with CCCV and twostage CCCV strategies, the multistage CCCV strategy has the largest charging capacities and the shortest charging periods at the target temperatures.
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
Acknowledgment
This work is supported by National Natural Science Foundation (NNSF) of China (Grant no. 51105220).
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Copyright © 2015 Xiaogang Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.