Abstract
This paper proposes an adaptive real-time energy management strategy for a parallel plug-in hybrid electric vehicle (PHEV). Three efforts have been made. First, a novel driving pattern recognition method based on statistical analysis has been proposed. This method classified driving cycles into three driving patterns: low speed cycle, middle speed cycle, and high speed cycle, and then carried statistical analysis on these three driving patterns to obtain rules; the types of real-time driving cycles can be identified according to these rules. Second, particle swarm optimization (PSO) algorithm is applied to optimize equivalent factor (EF) and then the EF MAPs, indexed vertically by battery’s State of Charge (SOC) and horizontally by driving distance, under the above three driving cycles, are obtained. Finally, an adaptive real-time energy management strategy based on Simplified-ECMS and the novel driving pattern recognition method has been proposed. Simulation on a test driving cycle is performed. The simulation results show that the adaptive energy management strategy can decrease fuel consumption of PHEV by 17.63% under the testing driving cycle, compared to CD-CS-based strategy. The calculation time of the proposed adaptive strategy is obviously shorter than the time of ECMS-based strategy and close to the time of CD-CS-based strategy, which is a real-time control strategy.
1. Introduction
The energy crisis and environmental pollution problem have become a serious concern in the recent years [1]. Plug-in hybrid electric vehicles (PHEVs) assume an essential role in decreasing fuel consumption and pollutant emissions [2]. Indeed, the fuel economy and emissions performance of PHEVs is strongly influenced by many optimization tasks, that is, mechanical construction optimization [3], the powertrain parameters optimization [4], and the energy management strategy (EMS) optimization. The optimization of mechanical construction and the powertrain parameters is currently a well-proved technology. Nevertheless, the optimization-based energy management strategies (also called blended strategies) still have some implementation issues, such as high computation effort caused by algorithm complexity, robustness, and sensitivity to drive cycle information.
The optimization-based EMSs are classified into global optimization-based EMSs and instantaneous optimization-based EMSs [5]. The global optimization-based EMSs mainly encompass dynamic programming- (DP-) based EMS [6–8], simulated annealing- (SA-) based EMS [9], and genetic algorithm- (GA-) based EMS [10]. DP-based EMS is able to compute global optimal solutions for PHEVs. Nonetheless, this EMS usually engenders “curse of dimensionality;” its computational burden increases exponentially with the number of states and control variables [11]. As a result, DP-based EMS is widely utilized in offline analysis to benchmark alternative EMSs [12], inspire RB strategies design [13], and serve as training data for machine learning algorithms [14]. SA and GA provide good performance even when dealing with complex problems [15]. They often combine with other algorithms to develop the EMS; that is, Chen et al. [9] derived an EMS based on combining SA with PMP for a PHEV; Chen et al. [10] combined GA with quadratic programming (QP) to optimize the engine power and battery current in a power-split PHEV. SA-based EMS and GA-based EMS can obtain satisfactory results, but the calculation time is too long, making its online implementation difficult.
The instantaneous optimization-based-EMSs mainly encompass convex programming- (CP-) based-EMS [16–18], Pontryagin’s minimum principle- (PMP-) based-EMS [19–21], and equivalent consumption minimization- (ECMS-) based-EMS [22–24]. CP-based-EMS to PHEV has been reported in the recent literature. Zhang et al. [16] dealt with an analytical solution for the power management of a PHEV, where the vehicle model is simplified using quadratic equations. Hu et al. [17] designed two EMSs based on convex optimization in a series plug-in hybrid electric bus. Beck et al. [18] presented two approaches for an adaptive EMS with CP optimization, and both solutions were simulated; simulation results demonstrated that these solutions obtained near-optimal results with a significant decrease in computational time. CP-based-EMS simplifies the complexity of vehicle models and can attain near-optimal results in reduced time. Nevertheless, CP-based-EMS can only be applicable when the problem is strictly expressed in convex terms, which requires both cost function and inequality constraints expressed in convex form, and affine equality constraints [25, 26]. Consequently, the application of such EMS is limited, owing to strong assumptions over the vehicle models. PMP-based-EMS transformed the global optimization problem to an instantaneous Hamiltonian optimization problem, which makes its real-time control possible. However, it is still a challenge for optimizing the Hamiltonian real-time due to the massive computational load required [27]. ECMS-based-EMS is a more promising option for energy management strategy of PHEV [28]. It was first introduced by Paganelli et al. in [22]. Sciarretta et al. [29] demonstrated that this EMS outperforms rule based EMS in a simulation environment. This EMS has also proved to be more computationally efficient than DP-based-EMS. However, the real-time application of ECMS-based-EMS requires further reduction of the calculation time [30].
To reduce the calculation time of the ECMS-based-EMS, we proposed a Simplified-ECMS-based EMS for a parallel plug-in hybrid electric vehicle in our previous article [31]. In that paper, the models of engine’s fuel rate and battery’s equivalent fuel consumption rate were approximately fitted by the piecewise function. Then, the total equivalent fuel rate was expressed by a convex piecewise function. According to the properties of convex functions, the ECMS problem was simplified to calculate and compare total equivalent fuel rate of only five candidates to identify the optimal torque distribution, instead of calculating and comparing the total equivalent fuel rate of huge candidates, who cover all over the control domain. In Simplified-ECMS-based EMS, the battery’s electricity consumption is converted to an equivalent amount of fuel consumption using the equivalent factor (EF). EF is a key dynamic variable, which determines the practical implementation of Simplified-ECMS-based EMS. In our previous article [31], to get the suitable EF, we used extreme learning machine (ELM) for driving pattern recognition. ELM is a single layer feedforward neural network. As we all know, this neural network has high computational cost and is hard to be implemented to real-time control.
To solve the above problem and obtain an adaptive real-time energy management strategy for plug-in hybrid electric vehicle, a novel driving pattern recognition method with low computational cost was first proposed. This method classified driving cycles into three driving patterns: low speed cycle, middle speed cycle, and high speed cycle, carried statistical analysis on these three driving patterns to obtain rules, and identified the types of real-time driving cycles according to these obtained rules. Second, particle swarm optimization (PSO) algorithm is applied to optimize EF, and the EF MAPs under the above three driving cycles are obtained. Finally, an adaptive real-time energy management strategy based on Simplified-ECMS and the novel driving pattern recognition method was proposed. Simulation on a test driving cycle is performed to verify the proposed adaptive strategy.
This paper is outlined as follows. The structure and parameters of parallel CVT-based PHEV powertrain are described in Section 2, Simplified-ECMS-based EMS is introduced in Section 3, the adaptive real-time energy management strategy based on Simplified-ECMS and the novel driving pattern recognition method is presented in Section 4, and simulation results and discussions are provided in Section 5; this paper is ended with conclusion in Section 6.
2. The Structure and Parameters of the Powertrain System
This study focused on a single-shaft parallel CVT-based PHEV. Figure 1 shows the powertrain of this vehicle. The powertrain includes the internal combustion engine (ICE), the integrated starter and generator motor (ISG motor), the battery, the clutch, the continuously variable transmission (CVT), and final drive (FD). The vehicle runs in different operating modes by controlling the state of the engine and motor and the separation and combination of the clutch. According to the state of engine, the working mode of vehicle can be divided into two modes: engine on mode and engine off mode. During the engine on mode, the clutch is closed, the engine provides positive power, and the output power of the motor can be positive (driving), negative (generating), or zero (idle). During the engine off mode, only motor runs, and this mode can be subdivided into motor driving mode and braking mode. The basic parameters of the PHEV are shown in Table 1.
3. Simplified-ECMS-Based EMS
Simplified-ECMS-based EMS is derived from ECMS-based EMS. The detailed derivation process can be found in our previous article [31]. A brief description of the derivation process is given as follows:
Firstly, the engine’s fuel rate and battery’s equivalent fuel consumption rate are approximately fitted by the piecewise function. And the fitted result of the engine’s fuel rate is expressed as follows [31]:where is the engine’s fuel rate, are constants, is the required torque needed to be distributed between engine and motor, is the output torque of engine, is the output torque of motor, is the engine’s torque corresponding to the best efficiency point at a certain engine speed, is the engine’s minimum output torque, is the engine’s maximum output torque, and and are the minimum and maximum output torque of motor, respectively.
The fitted result of the battery’s equivalent fuel consumption rate is expressed as follows [31]:where is the battery’s equivalent fuel consumption rate, and are constants, and is the equivalent factor (EF).
Then, the total equivalent fuel rate can be expressed by a convex piecewise function [31]:
(1) If , thenwhere , , , , , , , , .
(2) If , thenwhere , , .
According to Eqs. (3) and (4), the total equivalent fuel rate is a piecewise function, which is composed of four continuous convex quadratic functions. Based on the property of convex function, the total equivalent fuel rate is also a convex function. Therefore, the minimum value of the total equivalent fuel rate can only be obtained at points of demarcation of the convex piecewise function [31]. As shown in Eqs. (3) and (4), the demarcation points of the piecewise function are , , , , and . Thus, the optimal control variable can only be obtained from above five points. The optimal solution can be determined by comparing the values of the total equivalent fuel rate of the five points.
Consequently, the concept of the Simplified-ECMS-based EMS is achieving the optimal solution by calculating and comparing the total equivalent fuel rate of the above five points for each time instant, instead of calculating and comparing the total equivalent fuel rate of huge candidates, who cover all over the control domain [31]. Therefore, the Simplified-ECMS-based EMS can greatly reduce the amount of calculation and shorten the time of calculation. The procedure flow chart of the Simplified-ECMS-based EMS is shown in Figure 2. , , , , and are the five demarcation points, , , , , and are the corresponding total equivalent fuel rates of above five points. The operating principle of this EMS is as follows:
(1) Calculate the required torque according to the driver's pedal. And, if , then the vehicle runs in braking energy recovery mode.
(2) If , then calculate five demarcation points.
(3) Obtain the equivalent factor (EF) by a certain algorithm and then calculate the total equivalent fuel rate of above five points according to Eqs. (3) and (4).
(4) Obtain the optimal control variable after comparing the total equivalent fuel rates of above five points, and output the optimal torque distribution to power system.
4. The Adaptive Real-Time Energy Management Strategy Based on Simplified-ECMS and the Novel Driving Pattern Recognition Method
The detailed development process of the adaptive real-time energy management for the plug-in HEV based on simplified-ECMS and the novel driving pattern recognition method is illustrated in Figure 3. It mainly consists of two parts, that is, the offline part and the online part. The offline part has three modules, three typical driving cycles, probability density function of two driving features under three typical driving cycles, and global offline optimizer based on PSO algorithm, while the online part mainly includes four modules, driving pattern recognition, look-up MAPs of EF, simplified-ECMS-based EMS, and powertrain system.
The logic flow is also shown in Figure 3. To clearly show the proposed strategy, the detailed procedure is shown in Table 2. There are a total of 8 steps.
In step 1, three typical driving cycles (low speed cycle, middle speed cycle, and high speed cycle) are constructed after driving data gathering, driving features selection, and driving segments clustering. The profiles of three typical driving cycles are shown in Figure 4.
(a) Low speed cycle
(b) Middle speed cycle
(c) High speed cycle
In step 2 and step 3, mean velocity () and cruise percentage () are chosen for driving pattern recognition, and the probability density functions of these two driving features under the above typical driving cycles are obtained by statistical analysis. These probability density functions are shown in Figure 5. , , and are the probability of low speed cycle, middle speed cycle, and high speed cycle, respectively. is the mean velocity corresponding to the A point, is the mean velocity corresponding to the B point, is the cruise percentage corresponding to the C point, and is the cruise percentage corresponding to the D point. In this study, the previous 100 s duration of historical information has been determined to identify a real-time driving pattern. is the mean velocity of the past 100 s. is the cruise percentage of the past 100 s. Then, we can obtain the following deduction according to Figure 5.(1)If , then , and the current driving cycle is inclined to low speed cycle, and this state is expressed as .(2)If , then , and the current driving cycle is inclined to middle speed cycle, and this state is expressed as .(3)If , then , and the current driving cycle is inclined to high speed cycle, and this state is expressed as .(4)If , then , and the current driving cycle is inclined to low speed cycle, and this state is expressed as .(5)If , then , and the current driving cycle is inclined to middle speed cycle, and this state is expressed as .(6)If , then , and the current driving cycle is inclined to high speed cycle, and this state is expressed as .
(a) Probability density function of mean velocity under different types of driving cycles
(b) Probability density function of cruise percentage under different types of driving cycles
Based on the above deduction, the rules for driving cycle recognition are determined, and these rules are shown in Table 3. In this table, Low stands for the low speed cycle, Middle stands for the middle speed cycle, and High stands for the high speed cycle.
In Step 4, particle swarm optimization (PSO) algorithm is applied to optimize equivalent factor (EF) of the simplified-ECMS-based EMS under each typical driving cycle, driving distance, and SOC. The fitness function is expressed as
The flow chart of EF optimization is shown in Figure 6, the simulation is performed under high speed cycle, the driving distance is 66.02 km, and the SOC is 0.95. These parameters of PSO are set as follows: the size of particle swarm is 100, the maximum number of iterations is 100, the initial inertia weight is 0.9, and the final inertia weight is 0.4.
The optimization result is shown in Figure 7, the optimal value of EF is 2.277, and the optimal fuel consumption is 2.675L.
EF is mainly affected by driving distance and SOC in certain driving cycle, the above EF optimization is based on given driving distance and SOC; next, under high speed cycle, the EF optimization is implemented one by one in different driving distances and SOC through offline optimization, and the MAP figure of EF under high speed cycle, as shown in Figure 8, is obtained. In the same way, the MAPs figure of EF under middle speed cycle and low speed cycle are also obtained, and they are shown in Figures 9 and 10, respectively. As shown in Figures 8, 9, and 10, when the driving distance is less than the pure electric mileage, EF is a constant, and its value is minimum; the reason is that electrical energy is enough in this condition; a small EF makes driving using battery power as much as possible; when the driving distance is larger than the pure electric mileage, EF increases with the increasing driving distance in certain SOC, which can blend electric energy with the trip distance adding. EF reduces with the increasing SOC in certain driving distance; then, the opportunity of motor participation increases in this way.
In Step 5, the real-time driving pattern is identified according to the driving cycle recognition rules. In this step, the time window of data sampling is set to 100 s. Once the vehicle is running, the vehicle controller will monitor the vehicle speed. When the operating time exceeds 100s, the driving cycle recognition module will calculate mean velocity and cruise percentage for the previous driving block, and then these data will be used to identify the driving pattern according to the driving cycle recognition rules. It is noted that in the above recognition process, the initial driving pattern is set to the middle speed cycle.
In Step 6, the driving distance is got by navigation system and vehicle’s velocity. The total distance can be obtained by navigation system. The completed distance can be calculated by the vehicle’s velocity. Then driving distance is obtained by subtracting the completed distance from the total distance.
In Step 7, based on the aforementioned work, the EF can be obtained by looking up EF Maps through the type of driving cycle, driving distance, and SOC.
In Step 8, simplified-ECMS-based EMS is employed to solve the energy distribution optimization problem, and the optimal torque distribution between engine and motor can be obtained.
5. Results and Discussions
In this section, the proposed adaptive energy management strategy is verified in simulation. To evaluate the control performance of the proposed adaptive energy management strategy, the CD-CS-based strategy and the proposed strategy were simulated in MATLAB/Simulink, and the CD-CS-based strategy was taken as the benchmark.
The simulation works are carried out under a test driving cycle. The driving cycle is shown in Figure 11. It is made of different representative driving cycles, such as NYGTC, CSHVR, UDDS, NewYorkBus, US06_HWY, WVUCITY, and HWFET. The speed profiles of these driving cycles are obtained from advanced vehicle simulator (Advisor), which is developed by the National Renewable Energy Laboratory of America. The simulation results are shown in Figures 12, 13, 14, 15, and 16. And the comparison of calculation time under different strategies is shown in Table 4.
The driving pattern recognition result is shown in Figure 12. On the y-axis, 1 stands for low speed cycle, 2 stands for middle speed cycle, and 3 stands for high speed cycle. The results indicate that the driving cycle recognition algorithm in Step 5 of Section 4 can accurately and effectively identify the driving pattern.
The basic results, including the required torque of plug-in hybrid powertrain (), engine torque (), motor torque (), and EF, are shown in Figure 13. The output torque of engine and motor could satisfy the required torque of plug-in hybrid powertrain to ensure the drivability of plug-in hybrid electric vehicle. The results of EF reflect that the proposed adaptive real-time strategy can adjust the EF according to the type of cycle, driving distance, and SOC, so the proposed adaptive real-time strategy executed the reasonable torque distribution combined with the optimized EF.
SOC curves of these two strategies on the test driving cycle were shown in Figure 14. As shown in this figure, the driving cycle has a relatively long distance and the battery energy alone is not enough to cover the entire driving cycle, so the battery of these two strategies are almost depleted. And the SOC under the CD-CS-based strategy decreased faster than the proposed adaptive strategy.
Engine working points of these two strategies on the test driving cycle are shown in Figure 15. As shown in this figure, most of the engine’s working points under the proposed adaptive real-time strategy are distributed in the engine’s economic zone. While lots of engine’s working points under CD-CS-based strategy are away from this zone, the proposed adaptive strategy can effectively improve the engine’s operation efficiency.
Fuel consumption curves of these two strategies on the test driving cycle are shown in Figure 16. From the figure, the fuel consumption under the CD-CS-based strategy is 2.581 L. The fuel consumption under the proposed adaptive strategy is 2.125L; this strategy helps to reduce the fuel consumption significantly. Compared to CD-CS-based strategy, the proposed adaptive strategy reduces the fuel consumption by 17.63% under the testing driving cycle. Therefore, the proposed adaptive strategy has a good fuel economy performance.
The calculation time of different control strategies under the test driving cycle is shown in Table 4. The calculation time of the proposed adaptive strategy is slightly longer than the time of Simplified-ECMS-based strategy. The calculation time of the above two strategies is obviously shorter than the time of ECMS-based strategy, and they are close to the time of CD-CS-based strategy, which is a real-time control strategy. Therefore, we can conclude that it is very likely to apply the proposed adaptive energy management strategy for real-time control.
6. Conclusions
In this paper, an adaptive real-time energy management strategy based on simplified-ECMS and a novel driving pattern recognition method for PHEV is proposed. The findings of this paper can be shown as follows:
(1) A novel driving pattern recognition method based on statistical analysis has been proposed. This method classifies driving cycles into three driving patterns: low speed cycle, middle speed cycle, and high speed cycle, and then statistical analysis on these three driving patterns is carried to obtain rules. Simulation results show that the types of real-time driving cycles can be effectively identified according to these rules.
(2) Particle swarm optimization (PSO) algorithm is applied to optimize equivalent factor (EF) and then the EF MAPs, indexed vertically by battery’s SOC and horizontally by driving distance, under the above three driving cycles are obtained.
(4) An adaptive real-time energy management strategy based on Simplified-ECMS and a novel driving pattern recognition has been proposed. Simulation on a test driving cycle is performed. The simulation results show that the adaptive energy management strategy can decrease fuel consumption of PHEV by 17.63% under the testing driving cycle, compared to CD-CS-based strategy. The calculation time of the proposed adaptive strategies is obviously shorter than the time of ECMS-based strategy and close to the time of CD-CS-based strategy, which is a real-time control strategy.
Currently, the proposed adaptive strategy is only verified through simulations. The next step is to perform hardware-in-the-loop test or experimental validations.
Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that they have no competing interests.
Acknowledgments
The work presented in this paper is supported by the National Natural Science Foundation of China (Grant no. 51665020) and the State Key Laboratory of Mechanical Transmission’s open fund (Grant no. SKLMT-KFKT-201617).