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Ambient temperature is a significant factor that influences the characteristics of lithiumion batteries, which can produce adverse effects on state of charge (SOC) estimation. In this paper, an integrated SOC algorithm that combines an advanced amperehour counting (Adv Ah) method and multistate opencircuit voltage (multi OCV) method, denoted as “Adv Ah + multi OCV”, is proposed. Ah counting is a simple and general method for estimating SOC. However, the available capacity and coulombic efficiency in this method are influenced by the operating states of batteries, such as temperature and current, thereby causing SOC estimation errors. To address this problem, an enhanced Ah counting method that can alter the available capacity and coulombic efficiency according to temperature is proposed during the SOC calculation. Moreover, the battery SOCs between different temperatures can be mutually converted in accordance with the capacity loss. To compensate for the accumulating errors in Ah counting caused by the low precision of current sensors and lack of accurate initial SOC, the OCV method is used for calibration and as a complement. Given the variation of available capacities at different temperatures, rated/nonrated OCV–SOCs are established to estimate the initial SOCs in accordance with the Ah counting SOCs. Two dynamic tests, namely, constant and alternatedtemperature tests, are employed to verify the combined method at different temperatures. The results indicate that our method can provide effective and accurate SOC estimation at different ambient temperatures.
Temperatures in many cities around the world, such as Salt Lake City in the US, Harbin in China, Moscow in Russia, and Vancouver in Canada, can reach below 0 °C in winter. In highlatitude and cold regions, temperatures can even reach −30 °C to −40 °C. To enable electric vehicles (pure electric vehicle (EV), plugin hybrid electric vehicle (PHEV), and hybrid electric vehicle (HEV), which are collectively called xEVs) to work normally in these areas, the temperaturedependent parameters of energy storage systems should be suitable. Lithiumion batteries are characterized by high specific energy, high efficiency, and long life. These unique properties have made lithiumion batteries feasible power sources for xEVs. However, lithiumion battery technology for xEV applications still has many disadvantages, such as its narrow operational temperature range [
The state of charge (SOC) of a battery is an important parameter in xEV applications. Battery SOC is provided to the drivers to show remaining mileage. SOC indicates how to improve a battery's reliability, extend its lifespan, and optimize the power distribution strategy of vehicles. Various techniques have been proposed to estimate SOC. Lu
Given the high complexity of advanced algorithms, the reliability and robustness of these methods are challenged. In practice, the basic algorithms are more feasible. For batteries in pure EVs, the working conditions (driving, rest, and charging) are simple. With vehicle movement and little braking regeneration, the battery SOC may fluctuate but mostly decreases; this phenomenon is defined as the chargedepleting mode. By contrast, the battery SOC increases with the accumulation of charge when the vehicles are charged. The cells are monotonously discharged or charged, so OCV moves along with the OCV boundary curves. The hysteresis of the OCV is easy to eliminate [
However, several existing problems of Ah counting and OCV methods, such as the available capacity decrease at low temperature, which directly influences the accuracy of SOC estimation, are seldom addressed [
The current study proposes a correctionintegrated algorithm that mainly includes an enhanced Ah counting method calibrated with the use of a multistate OCV method. In the Ah counting method, the available capacity and coulombic efficiency at different conditions are the primary factors. In Section 2, a testing method of available capacity and capacity loss at different temperatures are presented. We then discuss the current factor that influences the available capacity. In Section 3, given the variable energy losses at different conditions, the coulombic efficiency and equivalent coulombic efficiency are considered. In addition, the testing method of coulombic efficiency is introduced, and the calculation process of equivalent coulombic efficiency based on the coulombic efficiency is illustrated. The influence of current and temperature on the coulombic efficiency is also discussed. In Section 4, we provide the definition of the rated/nonrated SOC, which is applied to the batteries with/without a thermal management system (TMS). The Ah counting calculation of the rated/nonrated SOC is developed to satisfy the requirement for the applications at different temperatures. For the OCV method (Section 5) corresponding to the rated/nonrated SOC, the rated/nonrated OCV–SOCs are established to estimate the rated/nonrated initial SOC. To estimate the nonrated initial SOC under different temperature paths, we establish the
Battery capacity is sensitive to current and temperature. Therefore, current and temperature values must be specified in the capacity definition. For example, the capacity, which is discharged at rated current
The test bench setup (
Given the temperature dependence of the capacity, the test is conducted from −20 to 20 °C at 10 °C intervals. The test procedures designed by many battery test manuals [
The purpose of the above test procedures is to verify the sustainable performance of capacities at different temperatures. Among these procedures, step (1) is implemented at room temperature, which is different from the ambient temperature in real vehicle applications. The operation temperature of the batteries without TMS in real vehicles varies along the ambient temperature.
Therefore, the test procedures of available capacity at each temperature are redesigned as follows: (1) the cell ambient temperature is decreased to the target temperature
Although the battery is charged/discharged until the voltage reaches the same upper/bottom cutoff voltage at different ambient temperatures, the releasable capacity at each temperature varies. The capacity loss test is used to measure the difference of releasable capacities between two different temperatures. The difference between releasable capacities with fully charged battery at
The test procedures of capacity loss at each temperature are as follows: (1) the cell is fully charged using a constant current of 1/3C until the voltage reaches the upper cutoff voltage of 3.65 V at
The results of
Current also influences capacity. A capacity test with different currents is conducted at
Compared with the temperature effect, the influence of current on capacity is relatively small. Moreover, in real vehicle applications, the battery pack is charged with a suitable current, as recommended by the manufacturer. Although a sophisticated dynamic current profile is run on the battery pack when the vehicle is working, the large current is limited by BMS within a reasonable range. To satisfy the requirement of power and energy for xEVs, a suitable battery pack size is selected during the design phase. Thus, the battery pack is mainly operated in the highefficiency area and the large current does not last for a long time. In addition, the influence of current on capacity is temporarily neglected in SOC estimation.
Coulombic efficiency is another important parameter of SOC estimation. Battery coulombic efficiency, like capacity, is sensitive to current and temperature. Therefore, current and temperature must also be specified in the definition of coulombic efficiency. In the last section, capacity losses at different currents and temperatures mainly involve changes in the thermodynamic and in the kinetic aspects of a battery [
Coulombic efficiency is the ratio of the Ah removed from a battery during discharging to the Ah required to restore the battery to the SOC before discharging [
Energy loss also depends on current and temperature. Therefore, the same number of charge that enters/exits the battery during charging/discharging at different currents and temperatures need different amounts of energy. The equivalent charge/discharge coulombic efficiency is defined as the ratio of the charged/discharged capacity at the nonrated condition to the charged/discharged capacity at the rated condition. The equivalent charge coulombic efficiency is given as:
The equivalent discharge coulombic efficiency is given as:
According to the different currents and temperatures running
For example, the charge capacity at rated condition
According to the definition of equivalent charge/discharge coulombic efficiency, we can extend it to a more comprehensive equivalent charge/discharge coulombic efficiency, which is not only between nonrated condition and rated condition but also between different conditions. According to the different currents and temperatures running
For example, the charge capacity at nonrated condition
On the basis of the analysis in Section 2, the available capacity is influenced by current and temperature. Therefore, with regard to the variation in available capacity, SOC should be redefined. In this section, we provide the definition of the rated/nonrated SOC according to the available capacity at the rated and nonrated condition. The calculation of the rated/nonrated SOC is then developed to meet the applications at different conditions.
The rated capacity
The rated SOC is based on the rated capacity that is unaffected by current and temperature. On the basis of the analysis in Section 2, the influence of current on available capacity is neglected. Therefore, the rated SOC is applied to the batteries with TMS, which can maintain the temperature of batteries in the rated temperature range.
The nonrated capacity
Compared with the rated SOC, the nonrated SOC is based on the nonrated capacity influenced by current and temperature. Therefore, the nonrated SOC is applied to the batteries without TMS. In this case, the temperature of batteries changes with the ambient temperature.
The rated SOC is based on the rated capacity
When the rated SOC is calculated using
On the basis of the analysis in Section 3.4, the influence of current on coulombic efficiency is neglected. Therefore, the calculation of coulombic efficiency η
Compared with the rated SOC, the nonrated SOC is based on the nonrated capacity
When the nonrated SOC is calculated using
On the basis of the analysis in Section 2.2, the influence of current on capacity is negligible. Therefore, the nonrated SOC is based on
In addition to the influence of temperature on coulombic efficiency, the variation in available capacity at different temperatures should be considered in calculating the nonrated SOC. Although the battery has the same releasable capacities, SOCs are different at different temperatures. Therefore, SOCs between different temperatures should be converted depending on the available capacity and capacity loss. According to
The battery soaked in the temperature of
At temperature
Given that the releasable capacities are the same at
When the battery is cooled from
When the battery is warmed from
SOC is related to the embedding quantity of lithiumion in the active material and with static thermodynamics. Therefore, the OCV after adequate resting can be considered to reach balanced potential because onetoone correspondence exists between OCV and SOC and bear little relation to the service life of batteries; it is also an effective method to estimate SOC of lithiumion batteries [
Corresponding to the rated/nonrated SOC in the last section, the rated/nonrated OCV–SOCs are established to estimate the initial SOC. To estimate the nonrated initial SOC under different temperature paths, we further establish the R–L nonrated OCV–SOCs and the L–L nonrated OCV–SOCs. SOC estimation by the above OCV–SOCs at different conditions is defined as multistate OCV method.
The rated OCV–SOCs are established to estimate the rated initial SOC. The relationship between SOC and OCV should be based on the rated capacity
The rated SOC is generally applied to batteries with TMS. Although TMS exist in battery packs, vehicles also experience cold cranking in winter. In the cold cranking process, the TMS cannot warm the battery on time, which causes a low internal temperature of the battery. Given the OCV thermosensitivity, gaps exist in the OCV–SOCs at different temperatures. In addition, OCV exhibits pronounced hysteresis phenomena, resulting in the nonoverlapped charged and discharged OCV–SOC [
The rated OCV–SOC test procedures are as follows: (1) the cell is fully discharged using a constant current of 1/3C rate until the voltage reaches the cutoff voltage of 2.5 V at 20 °C; (2) After a suitable period of rest (generally more than 3 h), the measured OCV is at SOC = 0%, which is denoted as
Five charged and discharged OCV–SOCs are obtained from −20 °C to 20 °C at an interval of 10 °C.
The rated OCV–SOCs can be obtained using the rated OCV–SOC at different temperatures with the fitting method:
As shown in
Compared with the rated OCV–SOCs, the nonrated OCV–SOCs are established to estimate the nonrated initial SOC. The nonrated SOC is based on
The nonrated SOC is generally applied to the batteries without TMS. In real vehicle applications, the battery pack without TMS experiences the following two cases of temperature variation: (1) the vehicle works at room temperature during daytime and rests in the evening. Given the large temperature difference during the day, the temperature sharply decreases in the evening. The next morning, the vehicle is restarted at low temperature; (2) The vehicle is operated at low temperature all the time. We define the above two cases as the different temperature paths: (1) From room temperature to low temperature (
OCV is affected by the different temperature paths that cause errors in SOC estimation.
As shown in
The R–L nonrated OCV–SOCs are converted using the rated OCV–SOCs according to the available capacity and capacity loss at different temperatures. Considering the rated OCV–SOC at
The R–L nonrated OCV–SOCs can be obtained using the R–L nonrated OCV–SOC at different temperatures with the use of the fitting method:
Considering
The L–L nonrated OCV–SOCs can be obtained using the L–L nonrated OCV–SOC at different temperatures with the fitting method:
According to whether the battery pack is with/without TMS, we calculate the rated SOC/nonrated SOC, respectively. The calculation procedures of the rated SOC are as follows. When the vehicle is started, the BMS measures the temperature of the battery pack. According to the measured temperature, we propose the application of the rated OCV–SOCs instead of the conventional OCV–SOC, which is often established at room temperature, to estimate the rated initial SOC. The other parameters in the rated SOC algorithm, such as η
A validation test with a sophisticated dynamic current profile, the federal urban driving schedule (FUDS) is conducted to verify the SOC estimation algorithm. In the laboratory test, a dynamic current sequence is transferred from the FUDS time–velocity profile. The current sequence is then scaled to fit the specification of the test battery. A completed FUDS current profile over 1372 s is emphasized in
The constant temperature test is used to validate the performance of the SOC by Ah counting (
The pretest is conducted before the constant temperature test. The cell is charged using the constant current of C/3 rate at
Under the condition of known
As shown in
The alternated temperature test is used to validate the performance of the Ah counting (
In the alternated temperature test, voltage, temperature, and SOC are depicted in
Ambient temperature significantly influences the characteristics of lithiumion batteries, such as capacity, coulombic efficiency, and OCV. Such temperature effects cause direct errors in SOC estimation. In this paper, we propose a combined SOC algorithm to address the temperature dependence of battery characteristics. First, our method simply and effectively improves the accuracy of the estimated SOC for lithiumion batteries at different ambient temperatures. With minimal calculations this method can be used in BMS for onboard estimation. Second, the data of battery characteristics are obtained using the uncomplicated battery test from −20 to 20 °C, with a temperature interval of 10 °C. If the method is flexible in a wider temperature range or higher temperature resolution, the tests are only implemented under the corresponding temperature. Finally, two dynamic loading tests are conducted on the battery under constant and alternated temperatures to assess the SOC estimation performance using the proposed approach. The results indicate that the rated/nonrated initial SOC estimation based on the rated/nonrated OCV–SOCs in different temperature paths provides accurate values to calibrate the SOC estimated by Ah counting. In addition, the conversion of SOC between different temperatures exhibits high accuracy. The two SOC algorithms at different ambient temperatures have good consistency. Thus, this approach could be used in actual vehicle applications. Further studies on the following two aspects are recommended. First, advanced algorithms with the battery model under different temperatures can be applied to estimate online, realtime, and closedloop SOC. Second, if this method is to be developed for SOC estimation of battery packs, other problems, such as the variation of cells, should be considered.
This research was supported by the National High Technology Research and Development Program of China (grant No. 2012AA111003) in part and the National Energy Technology Research and Application of Engineering Demonstrative Project of China (grant No. NY201107031) in part. The author would also like to thank the reviewers for their corrections and helpful suggestions.
The authors declare no conflict of interest.
Schematic of the battery test bench.
Discharge voltage curves at different temperatures.
Temperature of Harbin (China) one day in winter.
Test process of capacity loss at different temperatures.
The percentage of
Discharged curves at different current rates.
Influence of current and temperature on coulombic efficiency.
The coulombic efficiency η
The coulombic efficiency
The conversion of SOC between different temperatures.
Rated charged and discharged OCV–SOCs at different temperatures.
Charged and discharged OCV–SOCs in different temperature paths.
Process of conversion from the rated OCV–SOCs to the R–L nonrated OCV–SOCs.
Charged and discharge R–L nonrated OCV–SOCs at different temperatures.
Charged and discharged L–L nonrated OCV–SOCs with respect to capacity.
Charged and discharged L–L nonrated OCV–SOCs with respect to SOC.
Chart of battery SOC estimation at different ambient temperatures.
Current profile of FUDS.
FUDS cycle test at constantly varying temperatures. (
FUDS cycle test during alternated temperature. (
Available capacity at different temperatures.
20  100  100  99  100 
10  98  98  98  98 
0  83  82  82  82 
−10  67  66  65  66 
−20  32  32  32  32 
20  0  100  0 
10  1  98  1 
0  11  82  7 
−10  22  66  12 
−20  47  32  21 
Coulombic efficiency at different conditions.
 




 




















Equivalent charge coulombic efficiency at different conditions.
 




 




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Equivalent discharge coulombic efficiency at different conditions.
 




 




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The RL nonrated initial SOC and SOC error at 20, 0, and −10 °C (point 1).
20  70  3.319  71.9  1.9 
0  71.9  3.316  69.4  −2.5 
−10  72.7  3.306  70.4  −2.3 
The nonrated SOC, LL nonrated initial SOC, and SOC error at 20, 0, and −10 °C (point 2).
20  33.4  3.270  32.1  −1.3  34.3  0.9 
0  25.8  3.269  26.6  0.8  27.0  1.2 
−10  20.6  3.267  19.4  −1.2  19.9  −0.7 