A Mixed SOC Estimation Algorithm with High Accuracy in Various Driving Patterns of EVs

Abstract

In this paper, a mixed algorithm is proposed to overcome the limitations of the conventional algorithms, which cannot be applied in various driving patterns of drivers. The proposed algorithm based on the coulomb counting method is mixed with reset algorithms that consist of the enhanced OCV reset method and the DCIR iterative calculation method. It has many advantages, such as a simple model structure, low computational overload in various profiles, and a low accumulated SOC error through the frequent SOC reset. In addition, the enhanced parameter based on a mathematical analysis of the second-order RC ladder model is calculated and is then applied to all of the methods. The proposed algorithm is verified by experimental results based on a 27-Ah LiPB. It is observed that the SOC RMSE of the proposed algorithm decreases by about 9.16% compared to the coulomb counting method.

I. INTRODUCTION

A battery management system (BMS) is considered to be a key technology for safe and efficient operation of electric vehicles (EVs) [1]-[3]. Among the various factors managed by a BMS, the state of charge (SOC) is the most important because it is used as an indicator to protect the battery against over-charge and over-discharge. Moreover, through an accurate estimation of the SOC, the usable range of the battery can be extended, i.e., EVs can be driven longer.

A coulomb counting method (CCM) is generally used to estimate the SOC because of its ease of implementation and robustness to noise [4]-[6]. The CCM estimates the SOC by accumulating charges based on the initial value of a battery charge. However, the CCM has an error due to the current measurements made by current sensors to sense current through physical sensors. Even though the current sensor of a BMS has a high accuracy, it also has a small error. In case of the CCM, the battery current is continuously accumulated, which further results in an inevitable accumulation of a small error into a large error. As the time advances, this problem of an accumulated error of the battery current in the CCM is aggravated.

Therefore, various algorithms have been recently developed to solve the problem of an accumulated error in the CCM. Among the various algorithms, the extended Kalman filter (EKF) [7]-[12] is an intelligent mathematical tool for estimating the present state of a non-linear dynamic system. Because the battery has non-linear properties, the EKF is an effective solution for SOC estimation. Meanwhile, neural networks (NNs) [13]-[15] are a family of statistical learning models inspired by biological neural networks. They can solve complex, uncertain, and non-linear problems like SOC estimation. Since the EKF and NNs only use the present values of the current and voltage without accumulated operations of the battery current when compared to the CCM, these algorithms do not generate the accumulated error. In the SOC reset method [16], [17], the accumulated SOC error occurring in the CCM can be actively reduced by resetting the initial SOC of a battery. This means that the accumulated current error is also initialized to zero.

Previously described algorithms have only been verified for a specific profile. However, in EVs, such verification cannot insure estimation accuracy because the actual current profiles of the batteries for EVs are very diverse depend on the driver’s driving pattern. For example, in the case of highway driving at a constant speed, the current profile may be monotonous. However, if a vehicle is operated at various speeds with frequent stop as in urban driving, its current profile is more dynamic. Thus, without considering the various current profiles of EVs, a highly reliable and accurate SOC estimation algorithm cannot be achieved. In other words, the SOC algorithm for an EV needs to achieve high reliability for all current profiles.

However, the above-mentioned algorithms [7]-[17] are insufficient to meet this requirement. Especially, the mathematical approaches such as EKF and NNs have to be exponentially complex to cover various profiles. This complexity cause a computational overload of the arithmetic unit which has a physical limitation. Meanwhile, in the case of SOC reset algorithms, which are only effective in specific current conditions, the reliability of their estimation performance can be seriously decreased in other profiles where they do not meet any reset conditions. In summary, the conventional SOC estimation algorithms cannot provide a high reliability in terms of their performance for the various profiles.

In this paper, a mixed SOC reset algorithm, which has a low computational burden and high reliability in various current profiles, is proposed. The large coverage of the SOC reset is the most important factor for selecting the algorithm pair to be mixed. Thus, two representative algorithms, which operate independently in the driving or stop sections, are selected in order to cover various driving patterns. Moreover, to maximize the estimation performance, the key parameter for the reset is rationally redefined based on a detail analysis of each algorithm. As a result, the proposed algorithm is able to perform the SOC reset even at a low computational load and for various profiles. The proposed algorithm is verified with the help of experimental results by using a Kokam 27-Ah LiPB in four driving patterns, which consist of the urban dynamometer-driving schedule (UDDS) profile and the highway fuel economy test (HWFET) profile.

 

II. COMPARATIVE ANALYSIS OF CONVENTIONAL SOC RESET ALGORITHMS

A. Principle of the Enhanced OCV Reset Algorithm

The conventional open circuit voltage (OCV) reset method has the advantage of high accuracy. However, it has the disadvantage in that it requires a long rest time. An enhanced OCV reset method is proposed in order to overcome this disadvantage [16]. In the rest-time curve, as shown in Figs. 1(a) and 1(b), there are two parts of short term effect and long term effect. The short term effect of the first part is a precipitous voltage drop of the battery, and the long term effect of the second part is a gradual voltage change which is slowly stabilized. At this time, the battery terminal voltage after the end of the short term effect is similar to the OCV in a short time. In the case of a reset using this terminal voltage, the enhanced OCV reset method has some error. However, the enhanced OCV reset algorithm has a high accuracy in the total range through frequent reset.

Fig. 1.Operation principle of the SOC reset algorithms.

The reset condition of the enhanced OCV method is similar to urban driving situations, which have many stop events, in the enhanced OCV reset algorithm of Table I. Therefore, the enhanced OCV reset method has an advantage in terms of the UDDS profile since the current during rest time does not flow through the battery and the enhanced OCV reset method can operate. However, it does not operate in the various profiles of constant speed driving such as highway driving.

TABLE IRESETTABLE REGIONS OF VARIOUS ALGORITHMS

B. Principle of the DCIR Iterative Calculation Algorithm

As shown in Fig. 1(c), the SOC estimation algorithm by using the direct current internal resistance (DCIR) is conducted by averaging the DCIR, the terminal voltage, and the current of battery. The DCIR iterative calculation algorithm is represented in the terminal voltage that is expressed by the sum of the OCV and the products of the DCIR and the battery current [17]. This algorithm is estimated through iterative calculations of the DCIR and OCV. It is possible to estimate an accurate value of the DCIR during the DCIR calculation process by including the direct current and terminal voltage in the constant current region. Therefore, the reset algorithm using the DCIR is able to reduce the SOC error because the algorithm conducts the reset operation in the constant current region [17]. However, the SOC accuracy, which is estimated through the DCIR algorithm, is low when the direct current is not flowing. In addition, the DCIR algorithm has a disadvantage in terms of not being able to operate in the rest regions.

The reset condition of the DCIR iterative calculation reset method is similar to the HWFET profile. This profile has many static current regions by constant speed of EVs on the highway. Therefore, the DCIR iterative calculation reset method has an advantage since it is possible to frequently reset the reference SOC through the DCIR reset. However, the DCIR iterative calculation reset method does not operate in the UDDS profile because of the rest-time region and the dynamic current of the battery. The reset conditions for these algorithms in the rest and static current regions are summarized in Table I.

 

III. PRINCIPLE OF THE PROPOSED ALGORITHM

A. Possibility of Mixing the Two Algorithms

As shown in Figs. 2(a) to 2(c), the accumulated SOC error is represented according to the reset region of each SOC estimation method. First, in the case of the CCM, the accumulated SOC error continuously increases because of no specific reset method, as shown in Fig. 2(a). As discussed previously, the two reset methods, i.e., the enhanced OCV reset and the DCIR reset have a reset point in a specific region, as shown in Figs. 2(b) and 2(c), respectively. The reset point of the enhanced OCV reset method is in the region where the battery current does not flow such as in urban driving patterns. Moreover, the reset point of the DCIR iterative calculation reset method is in the region where the battery current constantly flows such as in highway-driving patterns. Therefore, the two-reset methods have completely different characteristics with respect to the reset region. Thus, the principles of operation for the two-reset methods are independent.

Fig. 2.SOC reset region and frequency of various algorithms.

It is possible to mix the two independent reset methods and the result is shown in Fig. 2(d). The profile of the reset point, as shown in Fig. 2(d), is a composition of the urban driving pattern in the front part and the highway driving pattern in the back part. Using the enhanced OCV reset method and the DCIR iterative calculation reset method for resetting in this profile, it is possible to reset only once. However, the proposed algorithm, which is a mix of the two-reset methods, is able to the reset the SOC twice.

B. Advantage of a mixed algorithm

According to the composition of the profile, each reset method has different magnitude of the SOC error. In the case of specific profiles such as the UDDS and HWFET, both the enhanced OCV reset method and the DCIR iterative calculation reset method result in large SOC errors. For example, in the case of the enhanced OCV reset method, the profile in the regions of waiting for a traffic signal occurs frequently and has many SOC reset points. However, if the profile has a few regions of waiting for a traffic signal such as the HWFET, the enhanced OCV reset does not occur. Therefore, the accumulated SOC error of the enhanced OCV reset method is equal to the conventional CCM. In contrast to the enhanced OCV reset method, the DCIR iterative calculation reset method shows opposite results in the two profiles. Thus, the proposed reset algorithm is able to obtain a smaller SOC error when compared to the conventional reset methods without specific profiles from mixture of two independent reset algorithms.

 

IV. VARIOUS DRIVING PATTERNS OF EVS

As mentioned in the introduction, algorithm accuracy depends on the driving pattern. In order to evaluate the driving patterns of various EVs, the proposed algorithm is compared with the conventional reset methods through a combination of conventional profiles. In general, the United States environmental protection agency (USEPA) provides a profile that is used to evaluate the fuel efficiency of EVs. The USEPA provides the UDDS profile, which imitates the urban dynamic driving pattern, and the HWFET profile, which imitates the static driving patterns on the highway. Thus, four profiles are evaluated to represent the real driving patterns of EVs.

Each individual profile of the UDDS and HWFET consumes 80% of the SOC in the same battery. However, the four driving patterns have different ratios of the UDDS and HWFET. A-profile has a SOC consumption of 8% of the UDDS profile and 72% of the HWFET profile. The change from A-profile to D-profile is that the ratio of the UDDS profile is increased, while the HWFET ratio is decreased. The performance of the algorithms is evaluated for a combination of these four profiles.

A. Conversion from Velocity Profile to the Current Profile

Both the UDDS and HWFET profiles, which are provided by USEPA, are applied to the enhanced OCV reset and DCIR reset methods. As mentioned earlier, the UDDS profile, which imitates urban driving patterns, includes many short waiting times at traffic signals. Considering the waiting time at traffic signals, the UDDS profile adds about 160 seconds of waiting time after the end of the UDDS profile in order to equal the total time of the validation profile. Fig. 3 shows the velocity profiles of the UDDS and HWFET as provided by USEPA. The current profile of a real battery is decided by the specifications of the EV hardware. Hence, the profile has to be recreated to consider the system specifications.

Fig. 3.UDDS and HWFET velocity profiles of the USEPA.

In this paper, the current profile is determined based on the velocity profile by using the specifications of the AVANTE HYBRID and the other parameters, as shown in Table II of the reference. The 80% efficiency (η) of the 80-kW three phase inverter and interior permanent magnet synchronous motor of the AVANTE HYBRID is considered to be a very low and bad condition for EVs. As shown in Fig. 4, for driving a vehicle, the running resistance (R) should be as much as the sum of three resistances, which are the rolling resistance (Rr), the air resistance (Ra), and the acceleration resistance (Ri), as in the following equations [18] :

where ur is rolling resistance coefficient, and w is weight of the vehicle,

where ua is the air resistance coefficient, A is the frontal projected area, and v is the velocity of the vehicle,

where w’ is the equivalent weight of rotation, a is the acceleration of the vehicle, and g is the gravitational acceleration,

The interaction formula between the power of the mechanical system (Pm) and that of the electrical system (Pe) is expressed by:

where η is conversion efficiency from the mechanical system to the electrical system. Finally, the current profile can be derived from the velocity profile of the vehicle, as indicated by:

TABLE IIAVANTE HYBRID SPECIFICATIONS [18]

Fig. 4.Running resistance of the general vehicle [18].

The current profiles are illustrated with the UDDS and HWFET as shown Figs. 5(a) and 5(b), respectively. In the current profile of the UDDS, there is the deceleration range, as shown in Fig. 5(a). It is generated from regenerative breaking, in which the battery is charged by negative current. In the current profile of the HWFET, the largest deceleration range exists at the last region of the profile, as shown in Fig. 5(b).

Fig. 5.Current profiles converted from velocity profiles.

B. Combination of each of the Reference Profile

The combination of each current profile shown in Fig. 5 is used to create composite profiles A, B, C, and D that have different ratios of dynamic and static properties. Fig. 6(a) shows a profile that includes a lot of highway driving. This profile includes a dynamic current profile that consumes 8% of the SOC and a static current profile that consumes 72% of the SOC. It implies that the A profile discharges from a 100% SOC battery to a 20% SOC battery. A waiting time of 160 seconds for a traffic signal is inserted after the dynamic profile of the UDDS. The enhanced OCV reset is applied and the SOC is reset after the UDDS profile.

Fig. 6.Four driving profiles generated by various ratios of the UDDS and HWFET profiles.

In order to apply the equal integrating error of the CCM to the A, B, C, and D profiles, each profile should have the same consumption of time and SOC. Since the experimental conditions cannot exceed the limits of the test equipment, the current scale of the UDDS profile is multiplied by a factor of 0.437, and the current scale of the HWFET profile is multiplied by a factor of 0.123. A single cycle in the UDDS consumes 4% of the SOC and has a duration of about 26 minutes, while a cycle of the HWFET consumes 2% of the SOC and has a duration of about 13 minutes. The ratio of the dynamic and static SOC consumption for profile B, which represents the mid-level driving pattern, is 32% and 48%, respectively; for profile C, which is also a mid-level driving pattern, the SOC consumption ratio is 48% dynamic and 32% static; and for profile D, which is closest to the highway driving pattern, the ratio is 72% dynamic and 8% static SOC consumption, as shown in Fig. 6.

 

V. THEORETICAL CONSIDERATIONS FOR MIXING

A. Effects of the Weighted Current Value IDC

In order to improve the performance of the enhanced OCV reset method and the DCIR reset method, the second-order RC ladder model is mathematically analyzed to estimate the SOC of a battery as shown Fig. 7 [19]-[20]. If the voltage of the RC network inside the battery is estimated exactly, the accuracy of the SOC estimation can be improved. Therefore, a mathematical analysis of the internal impedance inside the battery is important.

Fig. 7.Second-order RC ladder model of LiPB [19], [20].

The second-RC ladder model of the battery is analyzed for the characteristic of a step response for the current of certain magnitude as shown in the left figure of Fig. 8(b). The terminal voltage, which is deduced as a result of the Laplace transform, is given by (7). The terminal voltage is the sum of six terms. The first term is the result of the OCV change that is influenced by the current flow of the battery. The second term is a part of a series voltage drop in the series resistance Rs. The third and fourth terms are parts of an exponential variation from the RC network. The fifth and sixth terms are parts of the initial voltage applied to the RC network inside the battery. The initial voltage V1(t0) and V2(t0) of the RC network can be calculated by the capacitance (C1 and C2) and the current of the capacitance (iC1(t) and iC2(t)) in (8). Therefore, the initial voltage V1(t0) and V2(t0) of the RC network are complicated to calculate [21].

Fig. 8.Reset method for increasing the accuracy of conventional methods and the proposed algorithm.

After the capacitance of the RC Ladder is fully charged (saturation), the internal voltage of the RC-ladder can be simply calculated by multiplying the battery terminal current and internal resistance [17]. In order to simplify the actual dynamic situation such as 3, this is the main concern when the RC-ladder is fully charged (or saturated). Therefore, the average time constant (TA) of the two time constants (T1 and T2) is useful for the detection of the RC-ladder saturation. This is because the TA can represent both of the effects of the battery dynamics: short term (T1) effect and long term (T2) effect.

T1 and T2 are dependent on the R and C parameters resulting from the voltage curve fitting with T1 being shorter than T2. The LiPB, which is used in this experiment, has T1 and T2 values of 55 seconds and 870 seconds, respectively in (9). Therefore, the value of TA is 463 seconds and value of the 3τ (95.02%) is used in the area factor as shown in Fig. 8 (b). In addition, by using this factor, the representative current (IDC), which is matched with the constant battery current of the step response condition, can be deduced by (10) despite its actual dynamic current profile. This can facilitate the RC ladder voltage calculation. Therefore, TA and IDC are helpful for the calculation of the battery component voltage. As a result, they can make the each SOC reset algorithm more accurate.

The value of the average current that is used in the conventional reset method cannot accurately represent the voltage characteristic of the battery, as shown in Fig. 8(a). Thus, according to Fig. 8 (b), the green line dynamic current profile is multiplied by an area factor calculated from (10) when the profile is applied to the battery. The calculated IDC, shown as a red line in Fig. 8 (b), is applied to the two methods. In the enhanced OCV reset method, IDC is the index of the static current in the battery, and it makes voltage estimation possible during the expected rest time. The conventional enhanced OCV reset method uses the weighted current value IDC during 18 minutes of the average charge and discharge rate (C-rate). In this case, the estimation does not include an increase in the voltages V1 and V2 during full charging of the capacitance with the second-order RC ladder model. This results in an incorrect current estimation. Therefore, the area factor reflects the current influence before the rest time. The calculated IDC is also applied to the DCIR reset method. The difference between these two methods is that in the DCIR reset method, the method begins only when the instantaneous current achieves an error lower than 5% with respect to the calculated current value after 3τ. If not, the conventional CCM begins.

Applying the weighted current value IDC to each method gives an improvement over the conventional method, and the SOC estimation accuracy is increased. In this paper, a flow chart of the proposed algorithm is presented as shown in Fig. 9. The weighted current value and expected error of the CCM are calculated and separated from the OCV reset method by the terminal current value. After that, the algorithm operates as the CCM and SOC reset occurs when the condition of each method is satisfied.

Fig. 9.Flowchart of the proposed algorithm.

 

VI. SIMULATION RESULTS

A. Simulation Platform and Evaluation Method

The Simulation platform is configured using PLECS, as shown in Fig. 10. The test profile shown in Fig. 11(a) is given as the input to the PLECS. The simulation is configured by entering the error value, which is obtained through experiments and a reference SOC. The conventional CCM, the two reset methods, and the proposed reset algorithm, which is presented in this paper, are configured in the software block and the simulations are performed through the PLECS program.

Fig. 10.PLECS simulation platform.

Fig. 11.Simulation results of the test profile.

The test profiles are simulated by four methods (coulomb counting method, enhanced OCV reset method, DCIR reset method, and the proposed algorithm). In order to verify that the proposed algorithm effectively removes the accumulated error of the CCM, the results of the proposed algorithm are compared with the those of the SOC estimations for the CCM and the two reset algorithms (the enhanced OCV reset algorithm and the DCIR iterative calculation reset algorithm). The root mean square error (RMSE) of the estimated SOC result is used to verify the SOC error during battery usage. As shown in Fig. 11(b) and 11(c), the proposed algorithm has frequent reset events. As a result, its estimated SOC is closer to the reference SOC than the other methods. The total period of the test profile is 8 hours and 30 minutes and the RMSE of the estimated SOC during this period is calculated by (11). The RMSEs of the SOC for the CCM and the proposed algorithm are 6.59% and 1.48%, respectively, as shown in Fig 11. The RMSE of the SOC for the test profile using the simulation when compared to the CCM is reduced by 5.11%. As a result, it is confirmed that the proposed algorithm is more accurate than each of the reset methods.

Using the same method, simulations were conducted for the four types of profiles mentioned in the previous paragraph. As a result, the average SOC RMSE of the proposed method is 1.44%, which is reduced by 9.09% when compared to the 10.52% of the CCM results as shown in Fig. 12. In addition, the SOC RMSEs of the four profiles are always under 1.69% in the proposed method.

Fig. 12.Simulation results of SOC RMSE for each profile.

 

VII. EXPERIMENTAL RESULTS

In this paper, the experimental set is a BMS test bed as shown in Fig. 13(a). It consists of a microcontroller (TI’s DSP TMS320F28335), a current sensor (LEM’s HAS 500-P), and a circuit breaker. A 4-channel single cell charging and discharging machine with a rating up to 50-A is used for charging and discharging the battery. The charging and discharging machine is shown in Fig. 13(b). Additionally, an emulator (RealSYS’s RealDSP-UT) is used to connect to the computer for communication. In addition, the UDDS and HWFET profiles, which are provided by the USEPA, are applied to the battery in the experiment using the exclusive program of charging and discharging.

Fig. 13.Configuration of BMS hardware.

The experiments are performed using a Kokam 27-Ah LiPB and a charging and discharging device of 50-A rating at 25 ºC. The experimental results show an improved value of the weighted current value IDC with respect to the target current for the A, B, C, and D profiles as shown in Fig. 14. In the experiment, the reset points of the proposed reset algorithm can be improperly generated due to inaccuracy in the model parameter and the sensing noise of the battery current and/or voltage. Therefore, the accuracy of the experimental results can be lower than that of the simulation results which do not consider sensing noise and model inaccuracy. The SOC RMSE of the proposed algorithm is lower than that of the conventional CCM, the enhanced OCV reset method, and the DCIR reset method, regardless of the driving pattern type. As a result, the average SOC RMSE of the proposed method is 1.36%, which is reduced by 9.16% compared to the 10.52% of the CCM results as shown in Fig. 15. In addition, the SOC RMSEs of the four profiles are always under 1.72% in the proposed method, which is significantly accurate compared to the existing method results (CCM: 12.73%, DCIR: 11.27%, OCV: 6.58%). Thus, it is confirmed that the proposed mixed algorithm is more accurate than the reset methods.

Fig. 14.Experimental results of the estimated SOC for each profile.

Fig. 15.Experimental results of SOC RMSE for each profile.

 

VIII. CONCLUSION

In this paper, an SOC estimation algorithm is proposed to reduce the accumulated SOC error of the CCM. The proposed algorithm mixes the enhanced OCV reset method and the DCIR reset method through an increase of the reset frequency in the driving pattern. In addition, the two conventional methods are verified by the converted and applied weighted current value IDC. It can be seen from the experimental results that the SOC RMSE of the A, B, C, and D profiles are reduced by 6.65%, 8.86%, 10.13%, and 11.01%, respectively, in comparison to the CCM. As a result, the average RMSE of the SOC is reduced by 9.16%. Although the proposed SOC estimation algorithm is tested in a long driving pattern with a duration of 8 hours and 30 minutes, the average RMSE of the four profiles is under 1.72% which is always lower than the conventional methods. Therefore, the proposed algorithm has a high accuracy for the various driving patterns of drivers which further increases the maintenance and management performance of the battery management system.