A Novel Power Distribution Strategy and Its Online Implementation for Hybrid Energy Storage Systems of Electric Vehicles

Abstract

Hybrid energy storage systems (HESS) composed of a battery and ultracapacitor (UC) provide a feasible solution to the economy of electric vehicles (EVs). To fully exploit the potential of HESSs, a power distribution strategy that can split power between the battery and UC in HESSs plays an important role. Therefore, a novel power distribution strategy and its online application are proposed in this paper. First, a new and simple power distribution model of HESSs is proposed, and the model parameters are optimized offline through particle swarm optimization (PSO). Then, a driving condition recognizer based on a neural network is introduced, and the online application of the strategy is realized by combining offline global optimization and online recognition. Compared with the traditional rule-based strategy, the strategy proposed reduces the average fluctuation of the battery current by 52.53% and the average amplitude of the battery current by 11.51%. Meanwhile, it can be seen from the results that the strategy proposed is very close to the offline PSO-based strategy proposed and exhibits good performance under all driving cycles.

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. Parameters of the vehicles.

Parameter	Value
m, Vehicle mass (kg)	1500
g, Gravitation acceleration (m/s2)	9.8
f, Rolling resistance coefficient	0.015
α, Grade of the road	0
ρ, Density of air (kg/m3)	1.2258
CD, Coefficient of air resistance	0.4
A, Windward area (m2)	2.34
δ, Correction coefficient of the rotation mass	1.08

. According to the vehicle force balance, the longitudinal force F_t of the vehicle is as follows [24]:

$$F_t=mg\cdot \sin \alpha +fmg\cdot \cos \alpha +0.5\rho C_{D}A\cdot v_r+\delta m\cdot d{v}_r/dt$$

(1)

where v_r 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:

$$P=\{\begin{array}{c}{F}_t\cdot v/\left({\eta }_t\cdot {\eta }_m\right), F_t\ge 0\\ F_t\cdot v\cdot \left({\eta }_t\cdot {\eta }_m\right), F_t<0\end{array}$$

(2)

where v is the vehicle speed (m/s), η_t represents the efficiency of the mechanical transmission system, which is set to 0.9, and η_m 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. Parameters of the battery and UC.

Parameters of the Battery	Value	Parameters of the UC	Value
Cell nominal voltage (V)	3.2	Cell maximum voltage (V)	2.7
Cell capacity (Ah)	60	Cell rated capacitance (F)	10
Number of series	112	Number of series	80
Number of parallels	3	Number of parallels	45

, 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.

$$u_{BAT}=E-i_{BAT}\cdot R$$

(3)

$$P_{BAT}=u_{BAT}\cdot i_{BAT}$$

(4)

Then, the battery current formula can be obtained as follows.

$$i_{BAT}=\frac{E-{(E^2-4R\cdot P_{BAT})}^{1/2}}{2R}$$

(5)

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 P_BAT represents the battery output power.

To display the available energy of the UC clearly, the state of energy of the UC (SOE_UC) is defined, which is the ratio of the current available energy of the UC to the maximum energy storage of the UC [25]:

$$SO{E}_{\mathrm{UC}}=\frac{{(U_{\mathrm{UC}})}^2-{(U_{\mathrm{UC}}^{\min })}^2}{{(U_{\mathrm{UC}}^{\max })}^2-{(U_{\mathrm{UC}}^{\min })}^2}$$

(6)

where U_UC is the current voltage, $U_{\mathrm{U}\mathrm{C}}^{\mathrm{m}\mathrm{a}\mathrm{x}}$ is the maximum voltage, which is equal to 216 V, and $U_{\mathrm{U}\mathrm{C}}^{\mathrm{m}\mathrm{i}\mathrm{n}}$ is the minimum voltage of the UC, which is set to 0.2 × $U_{\mathrm{U}\mathrm{C}}^{\mathrm{m}\mathrm{a}\mathrm{x}}$.

3. A Novel Power Distribution Strategy

3.1. Power Distribution Model of the UC

In HESS, the main purpose of utilizing UCs is usually to reduce the battery current and thereby prolong the battery lifetime. When the strategy distributes power, in order to utilize UC more safely and efficiently, the UC input/output power distributed should also be adjusted according to SOE_UC. Next, we analyze the principles of power distribution in two cases of P ≥ 0 and P < 0, respectively.

(1)

P ≥ 0 (the vehicle is powered by HESS)

When the total power P demanded for the vehicle powertrain is equal to or more than 0, to reduce the battery current, the greater P is, the greater the UC output power P_UC is. In addition, when SOE_UC is high, it indicates that the UC has a lot of available energy and not enough room to absorb energy. Therefore, the UC output power should be increased to ensure that there is enough room to absorb energy during vehicle braking. When the SOE_UC is low, the UC output power should be reduced to reserve energy for possible acceleration in the future. Overall, the UC output power P_UC is simultaneously and positively correlated with the total power P and the state of energy of the UC SOE_UC in the HESS.

Based on the above analyses, P_UC may be calculated by P and SOE_UC. Assuming that the UC output power P_UC is linear with P and SOE_UC, a bilinear model of P_UC is defined as:

$$P_{\mathrm{U}\mathrm{C}}=k_1\cdot P+k_2\cdot SO{E}_{\mathrm{U}\mathrm{C}}$$

(7)

where k₁ and k₂ are coefficients greater than zero, k₁ is dimensionless, and the dimension of k₂ is power.

According to (7), if the vehicle stands still and the total power is 0, the UC output power is k₂·SOE_UC, which means that the UC will discharge continuously at this time, which is obviously unreasonable. Generally, we hope that the UC is charged up to full capacity before startup such that it is ready to provide power during acceleration. Therefore, corrective term −P₀ (P₀ > k₂·SOE_UC) is added to (7) to ensure that the UC supplements energy as much as possible before the vehicle starts. Finally, the UC output power is as follows:

$$P_{\mathrm{U}\mathrm{C}}=k_1\cdot P+k_2\cdot SO{E}_{\mathrm{U}\mathrm{C}}-P_0$$

(8)

(2)

P < 0 (the vehicle regenerates energy to the HESS)

For the convenience of analysis, the regenerative power is defined as P′ (P′ = −P). When the regenerative power P is increased, the UC input power $P_{\mathrm{U}\mathrm{C}}^{\prime }$ should also increase to reduce the battery current, so $P_{\mathrm{U}\mathrm{C}}^{\prime }$ is positively correlated with P′. When SOE_UC is high, the UC input power should be reduced in order to avoid the UC overcharge. When SOE_UC is low, the UC input power should increase to store energy for acceleration. Therefore, $P_{\mathrm{U}\mathrm{C}}^{\prime }$ has a negative correlation with SOE_UC. According to the above analyses, it can also be assumed that $P_{\mathrm{U}\mathrm{C}}^{\prime }$ is linearly related to P′ and SOE_UC, and the UC input power $P_{\mathrm{U}\mathrm{C}}^{\prime }$ during vehicle regenerative braking is determined as follows:

$$P_{\mathrm{U}\mathrm{C}}^{\prime }=k_1^{\prime }\cdot P^{\prime }-k_2^{\prime }\cdot SO{E}_{\mathrm{U}\mathrm{C}}$$

(9)

where $k_1^{\prime }$ and $k_2^{\prime }$ are coefficients and are greater than zero, $k_1^{\prime }$ is dimensionless, and the dimension of $k_2^{\prime }$ is power.

According to (9), the first term $k_1^{\prime }$·P′ is greater than zero, and the second term $k_2^{\prime }$·SOE_UC is also greater than zero. So, the UC input power obtained by subtracting the second term from the first term may be greater than or less than zero. If the UC input power is less than zero, it means that the battery will absorb the energy from both the UC and the vehicle, which will increase the battery current amplitude and reduce the battery lifetime. Moreover, during the whole regeneration braking process, we often hope that the UC can absorb regenerative braking energy as much as possible to supplement energy for future acceleration. Meanwhile, it can also avoid the frequent switching of the battery between charging and discharging. Therefore, a correction term $P_0^{\prime }$ ($P_0^{\prime }$ > $k_2^{\prime }$·SOE_UC) is added to (9), so the UC will always maintain the charging state during vehicle braking. Finally, the UC input power during vehicle braking is defined as:

$$P_{\mathrm{U}\mathrm{C}}^{\prime }=k_1^{\prime }\cdot P^{\prime }-k_2^{\prime }\cdot SO{E}_{\mathrm{U}\mathrm{C}}+P_0^{\prime }$$

(10)

In fact, the UC input power is equivalent to the negative output power of the UC, that is, $P_{\mathrm{U}\mathrm{C}}^{\prime }$ = −P_UC. Therefore, (10) can be written as follows:

$$\begin{gathered} -P_{\mathrm{UC}}=k_1^{\prime }\cdot (-P)-k_2^{\prime }\cdot SO{E}_{\mathrm{U}\mathrm{C}}+P_0^{\prime } \\ \text{⇒}{P}_{\mathrm{UC}}=k_1^{\prime }\cdot P+k_2^{\prime }\cdot SO{E}_{\mathrm{U}\mathrm{C}}-P_0^{\prime } \end{gathered}$$

(11)

It can be found that the forms of (8) and (11) are completely consistent, so (8) is set as the UC power distribution model during the whole vehicle operations.

3.2. Optimization of the Model Parameters

The three parameters in (8), k₁, k₂, and P₀, are unknown and need to be determined. The PSO algorithm has the advantages of its ease of use and its fast convergence, and it exhibits a good search performance when solving some optimization problems with non-linear, non-convex, or non-differentiable objective functions [26]. Therefore, the PSO algorithm is adopted to optimize these three parameters in this section.

In order to improve the economy of HESS, on the one hand, it is necessary to extend the service life of the system as much as possible when the hardware cost has been determined; on the other hand, it is necessary to improve the efficiency of the system to improve energy utilization and save energy costs. Research [16] adopted the semi-empirical battery life formula as the optimization objective and compared the cost per kilometer under different super capacitor sizes. Research [27] set the fluctuation of the battery current and the total power loss in the HESS as the optimization objective. Research [28] designed a strategy based on online optimization, taking the square of the battery power and the square of the power difference, as well as the square of the difference between the battery and the super capacitor SOC and the reference value, as the optimization objectives. In Research [13,29], the battery life and energy loss were taken as the optimization objectives, and the influence of the battery current amplitude and fluctuation was mainly considered in battery life. In addition, energy losses in HESSs occur mainly in the battery, the UC, and the bi-directional DC-DC converter. The energy storage of the UC is small, and the power losses of the semi-active topology are significantly lower than those of the fully active topology. Therefore, the energy losses of the battery, which are related to the internal resistance and the square of the battery current, are only considered in this section. Since the internal resistance of the battery rarely changes in one driving cycle, the square value of the battery current must be reduced as much as possible to improve the efficiency. In summary, we take the fluctuation of the battery current and the amplitude of the battery current as optimization objectives, as shown below.

$$\begin{gathered} \text{Minimize}: \\ {\displaystyle {\sum }_{k=1}^{k=N}\left[\epsilon \cdot f_1(k)+\left(1-\epsilon \right)\cdot f_2(k)\right]} \end{gathered}$$

(12)

where

$$\begin{array}{l}{f}_1(k)=\{\begin{array}{ll}{\left[i(k)\right]}^2& k=1\\ {\left[i(k)-i(k-1)\right]}^2& k=2,\cdots ,N\end{array}\\ f_2(k)={\left[i(k)\right]}^2 k=1,\cdots ,N\end{array}$$

where i(k) is the battery current of the kth sample, N is the number of samples in a driving cycle, ε is a constant weight coefficient. The first and second terms of (12) are used to minimize the fluctuations of the battery current and the energy losses of the battery, respectively. Since the battery current magnitude affects not only the energy losses of the battery but also the battery lifetime, ε is set to 0.3, which means that f₂ is weighted more than f₁.

For safety reasons, the state of charge of the battery (SOC_BAT), the battery output power P_BAT, and the UC voltage U_UC should be ensured within a certain range, as shown in (13).

Subject to:

$$\begin{array}{c}SO{C}_{\mathrm{BAT}}^{\min }\le SO{C}_{\mathrm{BAT}}\le SO{C}_{\mathrm{BAT}}^{\max }\\ P_{\mathrm{BAT}}^{\min }\le P_{\mathrm{BAT}}\le P_{\mathrm{BAT}}^{\max }\\ U_{\mathrm{UC}}^{\min }\le U_{\mathrm{UC}}\le U_{\mathrm{UC}}^{\max }\end{array}$$

(13)

where ${SOC}_{\mathrm{B}\mathrm{A}\mathrm{T}}^{\mathrm{m}\mathrm{i}\mathrm{n}}$ is the minimum value of SOC_BAT, ${SOC}_{\mathrm{B}\mathrm{A}\mathrm{T}}^{\mathrm{m}\mathrm{a}\mathrm{x}}$ is the maximum value of SOC_BAT, $P_{BAT}^{min}$ is the minimum value of P_BAT, and $P_{BAT}^{max}$ is the maximum value of P_BAT.

To ensure that the UC voltage is within the range in (13), the UC protection module is shown in Figure 3. The input parameters of the module are P_UC and SOE_UC, where P_UC is calculated by (8) and SOE_UC represents the current state of energy of the UC. When SOE_UC = 0, if P_UC > 0, P_UC = 0; otherwise, P_UC remains unchanged. When SOE_UC = 1, if P_UC < 0, P_UC = 0; otherwise, P_UC remains unchanged. When SOE_UC is between 0 and 1, P_UC remains unchanged. After obtaining the UC power, the battery output power is as follows:

$$P_{\mathrm{B}\mathrm{A}\mathrm{T}}=\{\begin{array}{c}P-P_{\mathrm{U}\mathrm{C}}\cdot {\eta }_{\mathrm{D}\mathrm{C}-\mathrm{D}\mathrm{C}},P_{\mathrm{U}\mathrm{C}}\ge 0\\ P-P_{\mathrm{U}\mathrm{C}}/{\eta }_{\mathrm{D}\mathrm{C}-\mathrm{D}\mathrm{C}},P_{\mathrm{U}\mathrm{C}}<0\end{array}$$

(14)

where η_DC-DC is the efficiency of the bi-directional DC-DC converter connected with the UC, which is set to 0.9.

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 (v_mean, v_std, a_max, …; 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. Statistics of the 11 Facility-Specific Driving Cycles.

Driving Cycle	vmean (km/h)	vmax (km/h)	Mileage (km)	Time (s)
Freeway High Speed	101.71	119.74	17.25	610
Freeway LOS A-C	96.08	117.64	13.76	516
Freeway LOS D	85.13	113.62	9.59	406
Freeway LOS E	49.08	101.39	6.21	456
Freeway LOS F	29.93	80.31	3.69	442
Freeway LOS “G”	21.08	57.45	2.29	390
Freeway Ramp	55.68	96.88	4.12	266
Arterial/Collectors LOS A-B	39.91	94.79	8.16	737
Arterial/Collectors LOS C-D	30.90	79.66	5.41	629
Arterial/Collectors LOS E-F	18.67	64.21	2.61	504
Local Roadways	20.76	61.64	3.01	525

. 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. 11 Characteristic Parameters.

Parameter	Description
vmax	Maximum Speed (km/h)
vmean	Mean Speed (km/h)
vstd	Speed Standard Deviation (km/h)
amax	Maximum Acceleration (m/s2)
amean	Mean Acceleration (m/s2)
rmean	Mean Deceleration (m/s2)
rmax	Maximum Deceleration (m/s2)
Rstop	Proportion of time when speed is equal to 0
v0–15	Proportion of time in the speed interval 0–15 km/h
v15–30	Proportion of time in the speed interval 15–30 km/h
v90–110	Proportion of time in the speed interval 90–110 km/h

.

Furthermore, to recognize the driving condition at time t, the characteristic parameters are extracted from the driving speed in the segment [t − ΔT, t]. Here, ΔT 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 ΔT = 90 s, 120 s, 150 s, and 180 s, respectively, ΔT 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 ΔT/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. Results of the ANOVA of the 11 characteristic parameters.

	vmax	vmean	vstd	amax	amean	rmean	rmax	Rstop	v0–15	v15–30	v90–100
F	38.44	106.03	18.06	2.58	22.18	6.46	21.59	12.62	23.56	20.47	23.59
PANOVA	0	0	0	0.017	0	0	0	0	0	0	0

. 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. P_ANOVA is the test probability. When P_ANOVA 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 P_ANOVA 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. Classification results of the network.

	Class	0~120 s	60~180 s	120~240 s	180~300 s	240~360 s	300~420 s	360~480 s	420~540 s	480~600 s	540~660 s	600~720 s
Time
C1		1	1	②	②	1	1	1	1	1	N/A	N/A
C2		2	2	2	2	2	2	2	N/A	N/A	N/A	N/A
C3		3	3	3	②	3	N/A	N/A	N/A	N/A	N/A	N/A
C4		4	4	4	4	4	4	N/A	N/A	N/A	N/A	N/A
C5		5	5	5	5	5	5	N/A	N/A	N/A	N/A	N/A
C6		6	6	6	6	6	6	6	6	6	6	6
C7		7	7	7	7	7	7	7	7	7	N/A	N/A
C8		8	8	8	8	8	8	8	N/A	N/A	N/A	N/A
C9		9	9	9	⑧	9	9	9	N/A	N/A	N/A	N/A

, 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 ΔT 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 ΔT. 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 P_th 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~P_th, so UC only plays a role when the demand power is greater than P_th or less than 0. We can also find that, in the rule-based strategy, SOE_UC is used as the safety threshold in the application process. Therefore, the purpose of SOE_UC is only to avoid the overcharge and over-discharge of the UC. In addition, the threshold parameter P_th 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.