Multistage CC-CV Charge Method for Li-Ion Battery

Charging the Li-ion battery with constant current and constant voltage (CC-CV) strategy at −10C 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 first-order RC equivalent circuit model; moreover, the multistage CCCV strategy is proposed. In the proposed multistage CC-CV strategy, the charging current is decreased to extend the charging process when terminal voltage reaches the charging cut-off voltage.The charging results of multistage CC-CV strategy are obtained at 25C, 0C, and −10C, compared with the results of CC-CV and two-stage CC-CC strategies. The comparison results show that, at the target temperatures, the charging capacities are increased with multistage CC-CV strategy and it is notable that the charging capacity can reach 85.32% of the nominal capacity at −10C; also, the charging time is decreased.


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][2][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 three-step 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 duty-varied voltage charging strategy that can detect and dynamically track the suitable duty of the charging pulse.Compared with conventional CC-CV 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 CC-CV 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 Taguchi-based algorithm was used to obtain rapid charge.With the charging strategy, the battery capacity could reach to 75% in 40 min.In [14], a constantpolarization-based fuzzy-control 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][9][10][11][12][13][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 self-preheating process costs too much time and cannot work at low SOC condition.This paper analyzes the charging characteristic of a Li-ion battery at different temperature, uses electrochemical model and first-order  equivalent circuit model to analyze the bad low temperature characteristic of Li-ion battery in theory, and proposes a multistage CC-CV strategy.The multistage CC-CV strategy is compared with CC-CV and two-stage CC-CV strategies at 25 ∘ C, 0 ∘ C, and −10 ∘ C.

Battery and Equipment.
The battery used is 18650 cylindrical Li-ion battery with normal capacity of 1.37 Ah, a normal voltage of 3.2 V, and a cut-off 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.For the CC-CV strategy, the constant current process was charging at 0.3 C to the cut-off voltage of 3.6 V and the constant voltage process was charging at 3.6 V for 5 min.

Experimental
For the two-stage CC-CV strategy, the first constant current process was charging at 1 C to the cut-off 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 cut-off voltage once again.The constant voltage process was charging at 3.6 V for 5 min [17].
For the multistage CC-CV 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 cut-off voltage.The constant voltage process was charging at 3.6 V for 5 min.

Charging Characteristic of Battery at
Low Temperature  resistance (  ).SOC can be calculated by the following formula: where SOC 0 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.  of charging process is shown in Figure 6 [20] and the charging chemical equation is

𝑅
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 Li-ion 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 Li-ion in electrolyte phase,   is Li + diffusion coefficient in electrolyte phase,  0 + is the transference number of lithium ions with respect to the velocity of the solvent,  is Faraday constant, and  Li is charging transfer current density.
The distribution of Li-ion in solid state phase is also described by Fick's second law of diffusion in polar coordinates [21]: where   is the concentration of Li-ion 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,  ref is the reference diffusion coefficient at  ref ,  ref 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 Butler-Volmer formula [20]: where  0 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  ocv is the open circuit voltage. 0 can be described as shown below [20]: where  0 is the reaction rate coefficient,  ,max is the maximum Li-ion concentration in the electrodes, and  ,surf is the Li-ion concentration on the active particles surface. 0 can be obtained using the following formula [20]: where   is the reaction activation energy and  ,ref is the reaction rate coefficient at  ref .
With the temperature decreasing, reaction rate coefficient is decreased.As formula (7) shows,  0 is decreased with temperature decreasing.The charging reaction is impeded for the reaction rate coefficient decreasing.As the parameter is time-invariant, 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 first-order  equivalent circuit model is used in the next part.
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 CC-CV strategy is limited by cut-off voltage and the charging capacity mainly depends on the constant current process.At low temperature,   and   increase making   and   increase, and  0 is higher than that at normal temperature.The cut-off 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 two-stage CC-CV strategy, the constant current charging process was divided into two stages.The first stage is charging battery with the maximum charging rate until the cut-off 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 two-stage CC-CV strategy, a multistage CC-CV strategy with more detailed current rates is proposed in this paper.Once the cut-off 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.Figure 11 shows the SOC curves of different charging strategies at 25 ∘ C. The charging capacities of CC-CV, twostage CC-CV, and multistage CC-CV charging strategies are 1.309 Ah, 1.299 Ah, and 1.368 Ah, respectively.The capacities of two-stage CC-CV and multi-CC-CV strategies are higher than that of CC-CV strategy for current decreasing process.The multi-CC-CV has the highest charging capacity because the current decrease process of multistage CC-CV strategy The charging result at 0 ∘ C shows that the capacities of CC-CV, two-stage CC-CV, and multistage CC-CV 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 CC-CV, two-stage CC-CV, and multistage CC-CV charging strategies decrease by 8.2%, 39.5%, and 8.9%, respectively.As the main charging rate of two-stage CC-CV strategy is 0.5 C higher than 0.3 C of CC-CV strategy and the charging rate does not decrease further, the two-stage CC-CV strategy has the largest decrease in charging capacity decrease at 0 ∘ C. As multistage CC-CV strategy has 0.2 C and 0.1 C charging rate lower than 0.3 C of CC-CV strategy, the charging capacity of multistage CC-CV strategy is higher than that of CC-CV strategy.

Result and Discussion
Figure 15 shows the SOC curves of different charging strategies at 0 ∘ C. The charging periods of CC-CV, twostage CC-CV, and multistage CC-CV charging strategies The charging result at −10 ∘ C shows that the capacities of CC-CV, two-stage CC-CV, and multistage CC-CV 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 CC-CV, two-stage CC-CV, and multistage CC-CV charging strategies decrease by 47.08%, 62.56%, and 14.53%, respectively.It can be indicated that the charging capacity of CC-CV decreases badly and the first stage of two-stage CC-CV strategy oppositely becomes the capacity limit.The multistage CC-CV 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 CC-CV, two-stage  The multistage CC-CV can automatically select the optimal charging current rate for two reasons.
(1) The cut-off voltage limit can stop the charging stage of the not optimal charging current rate.
(2) 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 CC-CV strategy is a wide temperature range charging strategy that keeps high charging capacity and low charging period.

Conclusion
It can be seen from the presentation above that the charging capacity of the CC-CV strategy can be only 48.47% of the Process.The battery charging strategies tested in experiments were CC-CV, two-stage CC-CV, and multistage CC-CV.The test temperature points were 25 ∘ C, 0 ∘ C, and −10 ∘ C. The charging strategies are explained as follows.

Figure 2 :
Figure 2: CC-CV strategy charging capacities at different temperature.

Figure 6 :
Figure 6: One-dimensional geometry example of charging process.

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 CC-CV strategy increases to 3.25 V at the low SOC range of 0%-10%, while the terminal voltages of two-stage CC-CV and multistage CC-CV strategies increase to near 3.4 V.The terminal voltage of CC-CV 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 two-stage CC-CV and multistage CC-CV strategies increase to 3.6 V with SOC of 85%.With current decreasing, the terminal voltage of two-stage CC-CV strategy decreases to 3.49 V and increases to 3.6 V again with SOC increasing of 7%.Unlike two-stage CC-CV strategy, the terminal voltage of multistage CC-CV strategy has more decreasing times to extend the charging SOC to a higher level.

Figure 20 :
Figure 20: Capacity curves of different charging current rates of multistage CC-CV strategy at different temperature.
[21,22]st-Order Equivalent Circuit Model.The first-order  equivalent circuit model is used to analyze the charging process[21,22].As shown in Figure7,   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: CC-CV, and multistage CC-CV charging strategies are 101.7 min, 39.38 min, and 197.1 min, respectively.The curve of two-stage CC-CV charging strategy shows the obvious difficulty of capacity increasing at such temperature.Although the terminal voltage increasing slope of two-stage CC-CV strategy is close to that of multistage CC-CV strategy, the charging capacity is significantly different.The comparison of the SOC curves shows that the charging period of multistage CC-CV strategy is still the shortest at the same SOC point.The multistage CC-CV still has maximum charging capacity at −10 ∘ C. Figure20shows the capacity curves of different charging current rates of multistage CC-CV 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.