1. Introduction
In recent years, due to the impact of the energy crisis and environmental problems, electric vehicles (EVs) have developed rapidly [
1,
2]. As a key issue in the development of EVs, there is a lot of research on the life of lithium-ion batteries. Battery life is mainly determined by the cycles of the battery, the Depth of Discharge (DOD), the temperature, and the c-rate [
3,
4,
5]. In addition, the battery life is also affected by the change in the battery current. In [
6], the battery life with random or constant discharge current was compared experimentally. According to the comparison, although the average discharge current of the battery with random discharge current is smaller, the capacity degradation is greater in the later period with the increase in cycle numbers. In [
7], the researchers conducted a variable cycling discharge current experiment on lithium-ion batteries. Through comparison, it was found that the degradation rate of the batteries would be faster than the constant cycling current condition due to the change in the cycling current.
As an energy storage device, ultracapacitors (UCs) have the advantages of a high-power density and a long life cycle, which are complementary with the characteristics of lithium-ion batteries. Therefore, a hybrid energy storage system (HESS) composed of a lithium-ion battery and UC has become a research hotspot [
8,
9]. Compared with battery-only configuration, it is essential to establishing a reasonable strategy to distribute power to different energy storage devices in HESSs, which can efficiently prolong the battery lifetime, reduce the energy losses of HESSs, and improve the economy of EVs.
In terms of the power distribution strategies of HESSs, the studies can be divided into two types: rule-based and optimization-based [
10]. The rule-based strategies are subdivided into strategies of logic thresholds [
11], fuzzy logic-based strategies [
12], filter-based strategies [
13], etc. Rule-based strategies are very simple and have low application costs, so they are mostly widely used. However, they do not consider actual driving conditions, and their robustness cannot be guaranteed.
In order to improve the economy of EVs, researchers have made a lot of progress in the field of optimization-based strategies in the past decade, which mainly involve offline optimization and online optimization. Offline optimization algorithms include dynamic programming (DP) [
14], particle swarm optimization (PSO) [
15], etc. Theoretically, these algorithms can obtain the global optimization for HESS. However, they are difficult in practical applications because the whole driving data must be obtained in advance. Several rules are extracted from the DP results to control the HESS online, which is expected to solve the real-time problem of the DP algorithm [
16]. However, due to the unclear energy distribution law corresponding to the DP results and the difficulty in predicting future driving information, the actual effect of the extracted rule-based strategy is limited. In order to obtain more realistic strategies, some researchers have attempted to design power distribution strategies through model predictive control (MPC) [
17,
18], which can be directly applied online. In [
19], the adaptive model predictive control (AMPC) is employed to the power distribution strategy, where the control strategy of each step is obtained by minimizing the cost function. However, this method requires a high-precision model and tremendous memory, and the calculation process is time consuming.
With the development of computers and artificial intelligence, data-driven algorithms are widely used in various fields because of their simple online application and good ability to handle nonlinear problems. Neural networks are often used to learn the control rules or to predict the future driving patterns [
20,
21]. In [
22], a neural network was applied to predict the vehicle speed to reduce the calculation burden of MPC. Moreover, to reduce the online calculation cost, Pontryagin’s Minimum Principle is used to solve the optimization problem in a rolling horizon. The simulation results show that the proposed method exhibits better performance in terms of battery lifetimes, energy consumption, and computational efficiency. However, the demands of computing and memory are still high.
To balance performance of HESS and computational requirements, this paper presents a novel power distribution strategy combining offline optimization and online driving condition recognition based on a neural network. On the one hand, the optimization process is completed offline, which can greatly reduce the calculation amount and hardware cost compared with the MPC strategy. On the other hand, the online recognition of driving conditions based on a neural network can greatly improve the adaptability of the strategy without apparently increasing the computational complexity. In general, the power distribution strategy proposed in this paper can not only reduce the computational requirement but achieve good results in different operations. The basic idea of this paper is that, firstly, a new power distribution model is proposed through the analyses of the HESS. Then, PSO is employed to determine the unknown parameters in the power distribution model. By establishing a typical driving cycles library, optimal parameters calculated by PSO are combined with driving condition recognition to realize the online application of the control strategy. The major contributions of this paper are as follows.
(1) To prolong the battery lifetime and improve the UC utilization, a novel and simple power distribution model for HESSs is proposed, and the PSO algorithm is employed to optimize the unknown parameters in the model.
(2) By establishing a driving cycles library and combining offline global optimization with online identification, the online application of the strategy is realized, and the adaptability of the strategy is improved.
The rest of this paper is as follows. In
Section 2, the model and parameters of the HESS are mainly described. In
Section 3, a bilinear power distribution model of the HESS is proposed, and the optimal model parameters are obtained by the PSO algorithm. In
Section 4, a driving condition recognizer based on a neural network is proposed. In
Section 5, we compare the strategy proposed with the battery-only configuration, the rule-based strategy, and the strategy based on offline PSO.
2. HESS Model
Generally, topologies of HESS are divided into three types: passive parallel topology, fully active topology, and semi-active topology [
23]. In this paper, the UC semi-active topology of the HESS shown in
Figure 1 is used, which has advantages in terms of efficiency and cost. In addition, the semi-active topology has a wide UC voltage range in order to reach its full potential.
The DC bus voltage of a typical EV is 360 V. Therefore, we use 112 series-connected 3.2 V LiFePO4 battery cells, and the terminal voltage of the battery is 358.4 V.
In this paper, a typical EV is selected as an example, whose specific dynamic parameters are shown in
Table 1. According to the vehicle force balance, the longitudinal force
Ft of the vehicle is as follows [
24]:
where
vr is the speed of the vehicle relative to the wind (m/s), and the wind speed is 0.
P is the total power demanded for the vehicle powertrain and is equal to the output power of HESS, which is as follows:
where
v is the vehicle speed (m/s),
ηt represents the efficiency of the mechanical transmission system, which is set to 0.9, and
ηm represents the efficiency of the inverter and motor, which is set to 0.85.
According to the target that the vehicle can travel 300 km at a constant velocity of 100 km/h, the number of parallel groups of lithium-ion battery cells is calculated as 3.36 and set to 3, and, therefore, the total battery energy is 64 kWh. Considering the capacity, cost, and volume of UCs comprehensively, the parameters of the UC are set as shown in
Table 2, where the maximum energy storage of the UC is only 131 220 J (about 0.03645 kWh).
In order to calculate the battery current, the equivalent circuit model is employed (as shown in
Figure 2). According to
Figure 2, we can obtain the following equation.
Then, the battery current formula can be obtained as follows.
where
E = 358.4 V, which is the ideal battery voltage,
R = 40 mΩ, which is the equivalent series internal resistance of the battery, and
PBAT represents the battery output power.
To display the available energy of the UC clearly, the state of energy of the UC (
SOEUC) is defined, which is the ratio of the current available energy of the UC to the maximum energy storage of the UC [
25]:
where
UUC is the current voltage,
is the maximum voltage, which is equal to 216 V, and
is the minimum voltage of the UC, which is set to 0.2 ×
.
4. Online Application of the PSO-Based Strategy
The strategy based on the PSO algorithm proposed in
Section 3 has a strong dependence on driving conditions, while the global driving conditions are always unknown in practical applications. In order to realize the online application of the strategy, this section proposes a driving condition recognizer based on a neural network. When the vehicle is running, the recognizer can judge the current driving condition type online according to the historical data of the vehicle. By combining the strategy based on the PSO algorithm with the online recognizer, a new power distribution strategy is proposed. Compared with the strategy based on PSO, the new strategy in this section can be applied without knowing the working condition information in advance, and the model parameters can be adjusted according to the actual driving conditions, thus greatly improving the adaptability of the power distribution. The detailed flow of the strategy based on driving condition identification is shown in
Figure 4. In the offline part, first, a library of
n typical driving cycles is established, and PSO is carried out to obtain the lookup table (LUT) of the optimized model parameters corresponding to the driving cycles. At the same time, driving segments are obtained from the typical driving cycles library, and the characteristic parameters (
vmean,
vstd,
amax, …; the meanings of these will be introduced in the next section) are extracted from the segments. Next, a neural network that can recognize driving conditions online has been trained. During online application, the system will record the vehicle driving information in real time. Then, the characteristic parameters are extracted from the historical driving information, and the current driving condition is identified by the neural network to obtain the corresponding optimal model parameters. Finally, the optimal model parameters are substituted into (8) to calculate the UC output power, and then the battery output power is calculated by (14).
4.1. Selection of Characteristic Parameters
In this paper, 9 of the 11 driving cycles of passenger cars and light trucks issued by the EPA are used as typical driving cycles [
30,
31], and the parameters of the 9 driving cycles are shown in
Table 3. Basically, the characteristics of driving cycles can be observed through speed parameters. Ericsson proposed 62 parameters to describe the driving mode, including parameters regarding speed, acceleration, and the engine [
32]. In [
31], the number of the above-mentioned parameters shrinks to 40; in addition, 7 new parameters are supplemented, including trip time, trip distance, maximum speed, maximum acceleration, maximum deceleration, number of stops, and idle time. Finally, 47 characteristic parameters are adopted. If there are too many parameters, there is a lot of time to extract and analyze all existing parameters online. Therefore, in order to recognize the driving condition in real time, the number of characteristic parameters must be reduced. In [
33], the number of characteristic parameters is set to shrink from 47 to 14. In order to balance the accuracy and real-time performance of driving condition recognition, after comparing and analyzing the above studies, 11 characteristic parameters are selected in this paper, as shown in
Table 4.
Furthermore, to recognize the driving condition at time
t, the characteristic parameters are extracted from the driving speed in the segment [
t − Δ
T,
t]. Here, Δ
T is the window size of the segment used for carrying out the driving condition identification. The research shows that, under urban traffic, the typical start and stop cycle is about 3 min [
34]. By comparing the recognition results with Δ
T = 90 s, 120 s, 150 s, and 180 s, respectively, Δ
T is finally set to 120 s. In order to obtain the segments of each typical driving cycle more comprehensively, the staggered method is adopted, as shown in
Figure 5, which means that the identification time interval of the typical cycles is set to Δ
T/2.
In order to further verify the difference significance of these characteristic parameters, we conducted analysis of variance (ANOVA) on the 11 characteristic parameters, as shown in
Table 5.
F is the ratio of the mean square deviation of the characteristic parameters under different driving conditions to the mean square deviation under one driving condition, which reflects the difference in the characteristic parameters between driving conditions. The larger
F is, the more significant the difference in the characteristic parameters under different driving conditions is.
PANOVA is the test probability. When
PANOVA is less than 0.05, it can be considered that the characteristic parameter has significant differences in different typical driving conditions. It can be seen from
Table 5 that the
PANOVA of each characteristic parameter is less than 0.05, which indicates that the selection of characteristic parameters is reasonable.
4.2. Driving Condition Recognition Based on a Neural Network
At present, the common recognition algorithms include neural networks, extreme learning machines, support vector machines, and so on. Among them, the BP (back propagation) neural network, which is widely used in pattern recognition and linear and nonlinear fitting and exhibits good robustness and real-time performance, is the most widely used algorithm in neural networks. Therefore, the BP neural network is utilized to establish the recognizer of driving conditions in this section.
The recognition results based on the BP neural network for nine typical driving cycles are represented in
Table 6, where the first line is the time of driving segments in each cycle and the left side is the real classes of driving segments. The circled numbers in the table indicate that the results are mismatched compared with the real classes. Actually, most driving segments can be accurately recognized by the neural network with an accuracy rate of 94.03%. At the same time, it should be pointed out that these mismatched segments are likely caused by the similarity of adjacent typical driving cycles. For example, some segments in C1 are classified as C2, and C1 and C2 are highly similar in terms of average speed, maximum speed, etc.
UDDS, NEDC, WLTC, and US06, shown in
Figure 6, are selected for identification examples next. The window size Δ
T is still 120 s, and the identification time interval is set to 10 s for more accurate results. Moreover, the window size is set to the driving time of the vehicle when the operating time of the vehicle is less than Δ
T. The results of the identification are shown in
Figure 7. We can see that the neural network can distinguish the operating conditions well in this figure. It should be noted that, due to the lack of historical driving data during the start-up state of the vehicle, identification becomes very difficult. Therefore, in practical applications, the start-up state is classified as C9 by default in the first 30 s, because C9 has the characteristics of a low speed and a long idle time, which are consistent with the characteristics of the vehicle starting.
5. Results and Comparisons
To verify the effectiveness of the proposed strategy, the other three control strategies, namely, the battery-only configuration, rule-based strategy, and offline PSO-based strategy, are compared in this section.
In this paper, UDDS, NEDC, WLTC, and US06, shown in
Figure 6, are used as the test driving cycles. UDDS is a typical urban test cycle whose speed is relatively low. NEDC is composed of four small cycles of urban conditions and one cycle of suburban conditions. WLTC includes four categories of low-speed, medium-speed, high-speed, and ultra-high-speed conditions. US06 includes a long-term high-speed condition. The four driving cycles cover various road types, which can test the adaptability of strategies.
5.1. Results under UDDS
Figure 8 shows the UC output power and the total power demanded under UDDS using the strategy proposed.
Figure 9 shows the battery output power and the total power demanded under UDDS.
Next, the simulation results are analyzed with
Figure 8 and
Figure 9 simultaneously. From the figures, we can find that the overall trend of the UC output power is consistent with the total power. When the total power is greater than zero, the battery and UC provide energy together. When the total power is less than 0, that is, when the EV brakes, the UC absorbs most of the braking regenerative energy. Moreover, it can be seen that when
P > 0, if the total power is small and changes violently, such as area ①, the amplitude of the battery output power is significantly reduced, and the waveform of the battery output power is relatively flat. If the vehicle runs at a high speed, that is, when the total power is at a high level continuously, such as area ②, due to the small capacity of the UC, the UC cannot output large power for a long time, so the total power demanded is mainly provided by the battery. When
P ≤ 0, that is, when the vehicle is braking, as shown in area ③, we can find that the regenerative braking energy is absorbed by the UC first. However, the UC can no longer absorb energy when the capacity of the UC reaches its maximum value. Therefore, the remaining regenerative energy is absorbed by the battery in turn. In another braking area ④, it can be seen that the UC absorbs the energy from the battery and vehicle regenerative braking at the same time, which is conducive for the UC to store energy as soon as possible for the subsequent acceleration process.
Overall, the strategy proposed in this paper can significantly reduce the fluctuation of the battery power and reduce the amplitude of the battery power at medium and low speeds so as to improve the battery life and reduce energy losses effectively.
5.2. Comparisons of Different Methods
To further study the impact of the strategy on battery lifetime and energy losses, we compare the strategy proposed in this paper with other methods. The final power distribution strategy proposed in this paper is improved on the basis of the offline PSO-based strategy proposed in
Section 3. Compared with the offline PSO-based strategy, the proposed strategy does not need to know the global driving condition data in advance and can adjust the parameters of the power distribution model according to the actual conditions. By comparing the two strategies, it can be further explained that it is reasonable to use the combination of the condition identification method and offline optimization to realize online application.
In addition, in order to verify the superiority of the strategy proposed, we also tested the battery-only configuration and the traditional rule-based strategy [
13]. The schematic diagram of the rule-based strategy is shown in
Figure 10, where
Pth is set as 20 kW. It can be found that, in the rule-based strategy, the goal of the UC is mainly to control the battery power at 0~
Pth, so UC only plays a role when the demand power is greater than
Pth or less than 0. We can also find that, in the rule-based strategy,
SOEUC is used as the safety threshold in the application process. Therefore, the purpose of
SOEUC is only to avoid the overcharge and over-discharge of the UC. In addition, the threshold parameter
Pth in the strategy is set according to experience, and it is a fixed value under various working conditions which cannot be adjusted for the actual driving conditions. In contrast, in the strategy proposed in this paper, the UC can play a role at any time and can adjust the output power according to its own capacity and driving conditions, which is more adaptive.
Finally, the four driving cycles of UDDS, NEDC, WLTC, and US06 with the battery-only configuration, the rule-based method, the PSO method, and the strategy proposed are simulated. In order to compare the results obtained by different methods under different driving cycles clearly, the results of the battery-only configuration under each driving cycle are set to 1 for normalization. Finally, ∑
f1, reflecting the battery current fluctuation, and ∑
f2, reflecting the battery current amplitude, are obtained, as shown in
Figure 11.
By comparing the three strategies in
Figure 10 with the battery-only configuration, it can be seen that the application of the UC can reduce the fluctuation and amplitude of the battery current significantly.
- (1)
Comparisons with the rule-based strategy
Comparing the strategy proposed with the rule-based method, under UDDS, NEDC, WLTC, and US06, the ∑f1 of the strategy proposed in this paper is reduced by 68.05%, 65.54%, 41.35%, and 33.99%, respectively, and ∑f2 is decreased by 29.34%, 8.51%, 5.16%, and 2.96%, respectively. Overall, compared with the rule-based strategy, the strategy proposed can significantly reduce the battery current fluctuations and is superior to the rule-based method in terms of reducing the battery current.
- (2)
Comparisons with the strategy based on offline PSO
Comparing the strategy proposed with the offline PSO-based strategy, the strategy proposed is more effective in reducing the battery current fluctuation ∑f1. In terms of reducing the battery current amplitude ∑f2, the effect of the strategy proposed is basically the same as the offline PSO-based strategy.
The results of the strategy proposed are basically the same as those of the offline PSO-based strategy. Moreover, the strategy proposed has obvious advantages in reducing the fluctuations of the battery current, which further proves that it is feasible to combine the PSO algorithm and driving condition identification based on a neural network for online application. Overall, the strategy proposed in this paper can obtain good results under various driving cycles.
6. Conclusions
In this paper, first, a novel power distribution model for HESSs is proposed, and the PSO algorithm is used to optimize the unknown parameters in the model. Then, in order to enable the strategy based on the PSO algorithm to be applied online, this paper establishes a typical driving cycles library. Through the PSO of each typical driving cycle in turn, the corresponding relationships between the driving conditions and the optimal parameters of the model are established. In addition, according to the data of the typical driving cycles library, the neural network, which can be used for online driving condition recognition, has been trained. Finally, the online application of the strategy proposed is realized by combining offline global optimization and online identification.
To measure the impact of the proposed strategy, this paper takes the battery-only configuration, the rule-based strategy, and the PSO based strategy as control groups. Under the four test cycles, compared with the battery-only configuration, the strategy proposed reduces∑f1 by 60.74% and ∑f2 by 23.61%, on average. Compared with the rule-based method, the average ∑f1 of the strategy proposed is reduced by 52.23%, and the average ∑f2 is reduced by 11.51%. By comparison, the strategy in this paper is significantly better than the traditional rule-based strategy in prolonging the battery lifetime and reducing the battery energy losses. At the same time, compared with the strategy based on the off-line PSO, the ∑f1 of the strategy proposed is reduced by 15.96%, on average, and the deviation of ∑f2 under each driving cycle is no more than 1%, which further shows that the strategy proposed exhibits excellent performance and good adaptability.
In this paper, we only discuss the problem of power distribution during vehicle operation. In fact, the charging strategy of electric vehicles is also noteworthy because it not only involves the balance between the charging speed and battery life but also has a great impact on the grid load. Therefore, we will conduct further research on the charging strategy of lithium-ion batteries.