1. Introduction
In recent years, new energy vehicles have developed rapidly due to the demand for energy conservation and environmental protection. Plug-in hybrid electric vehicles (PHEVs) have attracted much attention due to their combination of the advantages of pure electric vehicles and fueled vehicles [
1,
2,
3]. The powertrain of PHEVs is usually composed of motors, engines, and other power sources, which are coordinated to form a variety of working modes through the clutch or the planetary gear. Over the past few years, PHEVs with different configurations have been applied to various fields [
4], whereas in the public transport areas, the single-shaft parallel configuration equipped with automated mechanical transmission (AMT) has become very popular owing to its compact architecture and efficient operating modes [
5]. The performance of the PHEV is closely related to the energy management strategy (EMS). A reasonable EMS can allocate the power flow efficiently, give full play to the advantages of the engine and motor, and achieve the best performance of the vehicle.
Generally speaking, the EMS of PHEVs can be divided into two categories: the rule-based EMS and the optimization-based EMS. The rule-based strategies have shorter computation times and reliable application, and the rules can be set by drawing on practical engineering experience, with reference to engine optimal operating points and offline optimization strategy extraction [
6]. The rule-based control strategies include deterministic rule-based methods and fuzzy logic rule-based methods [
7]. For example, some researchers proposed a classical rule-based energy management strategy for PHEVs, which exhibited good reliability and stability in test driving cycles [
8,
9,
10]. At the same time, many scholars have proposed fuzzy logic rules [
11,
12,
13]. Although the rule-based EMS is easy to formulate, its rules need to be determined by a large number of experiments or practical calibrations. Once the working conditions change, it is necessary to set new rules, otherwise the fuel economy may get worse. Compared with the rule-based control strategy, the optimal control strategy can provide better energy allocation.
The optimization-based approaches can be further divided into global optimization and real-time optimization. As global optimization algorithms, dynamic programming (DP), particle swarm optimization (PSO) and genetic algorithm (GA), are widely applied in the solution process of the energy management problem of PHEVs [
14,
15]. Since the use of DP algorithm might be an effective way to design a theoretically global optimal EMS [
16,
17], a lot of studies on the DP-based strategy for PHEVs have been carried out. Peng [
18] used the DP algorithm to optimize the fixed condition and obtained an improved control regulation. However, this method is only beneficial to the vehicles running on a fixed route. Once the route changes or the working conditions are unknown, it is not applicable. To solve the above problem, references [
19,
20,
21] employed a driving pattern recognition technique of switching among the control rule sets extracted from DP results of each representative driving pattern, and the generality of the rules was realized. Besides, considering the time consuming of DP, it is difficult for a DP-based algorithm to be realized in practice from an engineering perspective. Chen [
22] used quadratic programming and simulated annealing method together to obtain the optimal result. Compared with the DP algorithm, computation time was saved without affecting the calculation accuracy. In [
23,
24], a novel pseudo-spectral power management algorithm was presented, and the results showed that this algorithm was numerically more efficient than DP and was able to achieve a solution very close to that of DP.
For real-time optimization control, the equivalent consumption minimization strategy (ECMS) and model predictive control (MPC) are the two most representative methods. On the basis of real-time information provided by historical driving data, mathematical models or intelligent transportation systems, MPC can predict the torque requirements of vehicles and optimize the energy allocation ratio to achieve low fuel consumption and emission [
25,
26]. However, the MPC control effect depends on the future driving information prediction accuracy, which remained to be an open question for now [
27,
28,
29]. Based on Pontryagin’s minimum principle, the ECMS simplifies the dynamic optimization problem into an equivalent instantaneous optimization problem, which reduces the computational complexity of the optimal algorithm and is suitable for real-time controllers. In ECMS, energy conversion coefficient, i.e.,
s(
t) is a key dynamic variable, which determines the real-time performance [
30]. In order to obtain accurate
s(
t), many scholars have presented improved methods. Reference [
31] obtained
s(
t) by predicting the future road speed, but this method needs a lot of accurate prediction. Kessels [
32] used fuzzy control-based ECMS to deal with the complex relation between fuel economy and the state of charge (
SOC). However, the
s(
t) accuracy of this method depends on the knowledge and experience of the expert. In [
33,
34], feedback control was used to adjust the
s(
t). However, due to the discharge characteristics of large capacity batteries, this method cannot be directly applied to PHEBs. Based on these valuable research works, using optimization methods may be a fruitful direction in ECMS to obtain an optimized
s(
t).
However, the EMS mentioned above mainly concentrate on the fuel economy and the emissions without considering the drivability and the ride comfort. For the PHEB, the switching between different working modes often brings a sudden change of the torque and the speed of different power sources, which leads to the instability of the power output and affects the driving performance and ride comfort. At the same time, the frequent gear-shifting will also affect the drivability of vehicles. Therefore, it is worthwhile to study the improvement of the drivability and ride comfort on the premise of ensuring fuel economy. In [
35,
36], an insightful method that simultaneously optimizes the power split and the gear-shifting is proposed. However, due to the closely interactive relationship between power split and gear-shifting, it would break the optimal decisions and worsen the vehicle fuel economy considerably if any changes happen to the optimal gear-shifting to obtain good drivability. Moreover, the simultaneous optimization would highly increase the calculation burden [
37]. Therefore, it is necessary to decouple the gear-shifting logic from the whole optimization.
In this paper, considering the improvement of the drivability and economic performance of the PHEB, a real-time EMS is proposed. The proposed strategy includes an offline part and an online part. The offline optimization consists of two parts: the first part is to obtain the energy conversion factor s(t). First, the driving cycles are divided into segments based on actual bus stops, then the s(t) of each segment is optimized by linear weight particle swarm optimization algorithm (LinWPSO). The optimization results of s(t) can be used to make real-time adjustments to online control strategy. The second part is that the corresponding control parameters that affect the vehicle drivability and riding comfort are extracted by DP algorithm, which includes AMT gear-shifting strategy and mode switching boundary parameters. In the online part, combining with the s(t), AMT gear-shifting correction and mode switching boundary parameters which are obtained through offline optimization, the real-time EMS is proposed to solve the trade-off problem between minimizing the fuel consumption and improving the drivability and ride comfort.
The organization of this paper is as follows:
Section 2 illustrates the compositions and mathematical models of the plug-in hybrid powertrain.
Section 3 describes the problem formulation and the optimal strategy. The AMT gear-shifting correction and mode switching boundary parameters are extracted in
Section 4. Then, the optimization results and the comprehensive performance analysis are presented in
Section 5. The conclusions are presented in
Section 6.
3. The Energy Management Optimization for REEBs
PHEB energy management strategy is the core function of the vehicle controller, which has a great impact on vehicle performance. For the single axis parallel hybrid city bus with AMT, the frequent gear-shifting and mode switching process will be accompanied by power interruptions, which affects the riding comfort and driving stability. Therefore, it is necessary to consider the drivability of the vehicle. To improve this situation, a novel algorithm is brought forward to improve the fuel economy and the drivability of the PHEB in any given city-bus driving cycle. The diagram of the algorithm is shown in
Figure 6. As shown in
Figure 6, the proposed strategy includes two parts, i.e., the offline part and the online part.
To clearly show the proposed strategy, the detailed procedure can be divided into three parts. Part one: s(t) is obtained through offline optimization. First, the driving cycles are divided into segments according to the actual positions of the bus stops. Then, the s(t) of each segment is optimized by LinWPSO. Last, the optimization results of s(t) are converted into a 2-dimensional look-up table, which can be used to make real-time adjustments to online control strategy. Part two: the AMT gear-shifting correction and mode switching boundary parameters that have obvious influence on the drivability of the vehicle are obtained by an offline DP algorithm. Part three: combined with the parameters of offline optimization, a real-time optimal EMS can be developed to solve the instantaneous optimization problem for the studied PHEB. Finally, the proposed strategy was verified in a real-world driving cycle in simulation.
3.1. Real-Time Optimal Energy Management Strategy
The ECMSis used more in the PHEV energy management strategy. It makes the electrical consumption of the motor equivalent to fuel consumption, and it also makes the overall equivalent fuel consumption of each moment of the system minimum to achieve local optimal. The ECMS-based PHEV energy management strategy can be described like this: at a certain time
t, there is an optimal control vector
, which minimizes the system cost function
JECMS(
t) at this moment. Their expressions are shown as follows:
where
is the engine fuel consumption rate,
s(
t) is the energy conversion coefficient, which canbe attained by the following offline optimization.
is the equivalent fuel consumption rate of the motor,
is the control variable.
The standard ECMS only considers the energy distribution. However, while concerning the energy distribution, this paper also considers the driving performance of the vehicle. Therefore, based on ECMC, this paper proposes a new real-time management strategy. The optimal control problem is to find the control input
to minimize the following cost function:
where
δ is the mode switching boundary parameters, which can be attained by the next offline optimization. When
δ = 1 the engine and EM work together to drive the vehicle, when
δ = 0, the EM drives the vehicle alone.
The EM equivalent fuel consumption rate
can be obtained:
where
Qlhv is the low calorific value of fuel,
ηm,req(Tm,req(t), ωm(t)) is the EM efficiency,
Tm,req(t) the EM demand torque,
ωm(t) is the EM speed.
For a single-axis parallel PHEB, when the clutch is closed, the engine speed is equal to the motor speed, so the energy distribution ratio is replaced by the torque distribution ratio. The best control vector is shown as follows:
where
is the engine torque,
is the EM torque,
is the AMT gear-shifting rules, which can be attained by the following offline optimization.
Considering the actual operating performance of the PHEB, the operating state of the engine, EM and battery should be limited by the following constraints:
where
ωm,min,
ωm,max are the EM speed lower limit and upper limit,
Te,min(ωe(t)),
Te,max(ωe(t)) are the engine torque lower limit and upper limit,
Tm,min(ωe(t),SOC(t)),
Tm,max(ωe(t),SOC(t)) are the EM torque lower limit and upper limit,
SOCmin,
SOCmax are the battery
SOC lower limit and upper limit.
rATM(t) is the gear of the AMT,
rATM,min,
rATM,max are the maximum gear and minimum gear.
3.2. s(t) Optimization
In order to get better economic performance with the ECMS control strategy, the choice of s(t) is especially critical. If the value of s(t) is large, the engine fuel consumption will increase. On the contrary, the power consumption will increase and the battery SOC will drop at a faster rate. Moreover, the s(t) should not be set to a static coefficient or a fixed value, which will affect the performance of the vehicle. Therefore, it is necessary to optimize s(t) in the real time according to the information of vehicle driving conditions and battery SOC.
As repeated operations on the same routine route are characteristic of urban buses, the total daily running mileage of the vehicle is known, and the distance between the vehicle stops is also fixed, so the equivalent coefficient
s(
t) can be optimized under known conditions. Yang [
38] provided a new method to optimize
s(
t), which has achieved good results. The specific implementation process is shown in the
Figure 7. There are in total four steps.
In step 1, the driving conditions were divided into several parts based on actual bus stations, then, the bus station and the vehicle speed are selected as input variables for subsequent optimization.
In step 2, historical data collected from different parts are used to design the reference
SOC. Therefore, the reference
SOCr can be obtained as follows:
where
SOCi is the initial
SOC of the battery,
SOCl is the minimum value of the battery
SOC,
n is the number of the bus station,
j is the total number of the bus stations,
fi is the coefficient of
SOC changing rate,
li is the distance between stations,
D is the driving distance of the vehicle,
is the average demand torque.
In step 3, based on the reference
SOC, the
s(
t) of each part is optimized by LinWPSO. For LinWPSO, the inertia weight factor can be written as:
where
T,
Tmax are the current iteration number and the maximum iteration number, respectively.
Xmax is the initial weight factor,
Xmin is the final weight factor.
The objective function
JP can be shown in the following equation:
where
ti,
tj are the start and end time, respectively.
Pb is the power of the battery,
Hf is the low heat value of the gas,
s is the energy conversion coefficient.
Then, the
s(
t) can be obtained as:
where
si is the initial
s(
t),
k is the coordination variable,
SOCn is the current
SOC.
In step 4, the
s(
t) of each part can be displayed in the form of the 2-dimensional look-up tables. For the specific calculation process, please refer to [
37].
5. Verification and Discussion
Through the off-line optimization, the parameters that affect the vehicle’s economic performance and the drivability are obtained. These parameters are combined together to form the PHEV real-time optimization energy management strategy.
In this section, the proposed EMS is verified by a simulation. To verify the proposed strategy, the Beijing typical city bus driving cycle is chosen as the test driving cycle, as shown in
Figure 12. This working condition is extracted from the actual driving conditions of several Beijing buses. The mileage of a single driving cycle is 6.81 km, with 10 stops, 21 acceleration sections and 10 traffic lights. According to the vehicle’s full-day driving range of 200 km, an average of 30 selected driving cycles are required for one day. Therefore, in the simulation, 30 driving cycles were taken as input conditions.
Table 2 shows the statistics of Beijing typical citybus driving cycle.
In order to show the advantages of the proposed strategy, the control performance, the fuel consumption and the comparison result of the drivability with different strategies are given in the following part, in which the effectiveness, the fuel economy improvement, and the drivability are verified.
5.1. Control Performance of Proposed Control Strategy
To verify the control performance of the proposed strategy, the simulation works are carried out under Beijing typical city bus driving cycle. The initial
SOC is set as 100%, and the terminal
SOC is set as 30%. The results are shown in
Figure 13,
Figure 14 and
Figure 15.
Figure 13 show the basic simulation results, including battery
SOC of hybrid powertrain, engine output power, and EM output power, which can reflect the control performance of the proposed strategy. It can be seen from
Figure 13 that
SOC has decreased steadily during the entire mileage and remains at 0.3 by the end of the journey. When the
SOC is higher, the motor’s braking energy recovery is less, and when the
SOC is lower, the motor’s braking energy recovery is more.
Since the overall operating data is too large, it is not suitable for observation, so the condition that the battery
SOC is 0.7 is utilized for our explanation. As shown in
Figure 14, the simulated vehicle speed is the same as the actual vehicle speed. In addition, the battery
SOC continues to decrease with the operation conditions, the
SOC of the initial state is 0.7, and the
SOC of the terminal state is 0.678, which conform to the trend of the energy consumption.
As shown in
Figure 15a, the
s(
t) adopted in the proposed method would change with the variation of the driving condition along the whole bus routine. Under the selected driving cycle conditions, the EM and engine torque are shown in
Figure 15b, the output torque of engine and EM could satisfy the demand torque of hybrid powertrain to ensure the drivability of PHEB. To avoid the low-efficiency working area of engine, the EM is controlled to drive the vehicle in most of time, engine will start to provide the driving torque when the demand torque exceeds the max torque of motor or the battery
SOC is lower than the threshold. When the PHEB is operating under the braking conditions, the demand torque is negative. As shown in
Figure 15b, the large amount of braking torque occurs in the driving cycle, because some emergent braking situations would occur occasionally in the actual driving condition, and when that situation happens, the mechanical braking system is controlled to compensate for the insufficient braking torque provided by motor to ensure the safety of the vehicle.
Figure 15c,d show the engine state and AMT gear position information under single cycle conditions. When the Engine State = 1, the engine is on, when the Engine State = 0, the engine is off. The engine starts only when the motor’s max torque cannot satisfy the required torque from the driving cycle. Owing to the high power of the motor and the existence of AMT, the bus in most parts of the trip can be operated in pure electric mode.
After the above simulation verification, it can be determined that the designed PHEB real-time energy management strategy meets the needs of adapting to the changing driving conditions of the vehicle. Therefore, the proposed strategy is proved to be effective.
5.2. Energy Consumption
In this part, in order to evaluate the performance of the proposed real-time optimized control strategy, the rule-based control strategy and standard ECMS were taken as the benchmark. The simulation results are shown in
Figure 16 and
Table 3. As shown in
Figure 16, for the three control strategies, the electricity energy stored in the battery is consumed to the expected lower limit in the end. Therefore, the electric consumption of the above strategies are similar with each other. However, the rule-based control strategy tends to deplete the battery energy in advance, the ECMS can consume the battery evenly throughout the routine, and the proposed methods have similar trends as the ECMS.
Furthermore, as shown in
Table 3, under the similar electric consumption, the energy consumption produced by the proposed strategy is slightly higher than that produced by the standard ECMS but significantly lower than that of the rule-based control strategy. It is understandable from the results that the rule-based control strategy have the worst fuel economy by using experience to set rules, the ECMS takes advantage of local optimization about this driving cycle to achieve better fuel economy, whereas the adopted method considers the drivability of the vehicle to improve driving comfort at the expense of fuel consumption.
On the one hand, the optimization results of
s(
t) reflect the advantages of the proposed strategy, the vehicle controller would perform the more reasonable torque distribution combined with the optimized
s(
t), and then significantly reduce the fuel consumption. By the reasonable energy distribution of the proposed strategy, the working efficiency of the two power sources is high. As shown in
Figure 17, most of the operating points of the engine are close to the engine optimal operating line, and the motor mainly runs in the high efficiency area. On the other hand the adopted method considers the drivability of the vehicle to improve driving comfort at the expense of fuel consumption.
5.3. Drivability
To highlight the advantages of the proposed strategy compared with the standard ECMS and the rule-based control strategy, some comparisons are carried out during the drivability of the PHEB in this part. According to the parameters extracted in
Section 4.2 that affect the drivability of the vehicle, the comparison curve about shifting rules and engine start-stop status in the given driving cycle are shown in
Figure 18 and
Figure 19.
As shown in
Figure 18, the proposed method has fewer gear-shifts than the other two strategies. At the same time, the number of engine starts-stops is less than with the other two strategies, as shown in
Figure 19. Therefore, the energy management strategy proposed in this paper can improve the drivability of the vehicle and improve driving comfort.
Next, from the perspective of the overall performance, a quantitative comparative analysis of the three strategies is carried out. This paper introduces the overall performance index
Jmulti to evaluate the control effect about fuel economy and the drivability in the form of weighted calculation of each indicator. The
Jmulti can be written as:
where
Mf is the fuel consumption per 100 km, the unit is m
3/100 km,
shift is the average number of shifts per kilometer,
is the average number of start-stop per kilometer of engine.
Table 4 shows the simulation results of the three control methods under Beijing typical citybus driving cycle conditions. As shown in
Table 4, compared with the rule-based control strategy, the ECMS has reduced fuel consumption, but since the ECMS does not consider the drivability, the gear-shifting frequency and engine start-stop times are as the same as the rule-based control strategy, the overall performance is only 6.61% improvement. However, though the EMS proposed in this paper has an increase in fuel consumption compared with ECMS, due to the influence of the drivability, the gear-shifting frequency and engine start-stop times are significantly reduced, so the overall performance is 18.54% improvement compared with the rule-based control strategy. Therefore, it can be concluded that the PHEB with the proposed strategy can reduce fuel consumption and improve the vehicle drivability simultaneously.