Modeling and energy management strategy research of a power-split hybrid electric vehicle

Abstract

A power-split hybrid electric vehicle with a dual-planetary gearset is researched in this paper. Based on the lever analogy method of planetary gearsets, the power-split device is theoretically modeled, and the driveline simulation model is built by using vehicle modeling and simulation toolboxes in MATLAB. Six operation modes of the vehicle are discussed in detail, and the kinematic constraint behavior of power sources are analyzed. To verify the rationality of the modeling, a rule-based control strategy (RB) and an adaptive equivalent consumption minimization strategy (A-ECMS) are designed based on the finite state machine and MATLAB language respectively. In order to demonstrate the superiority of A-ECMS in fuel-saving and to explore the impact of different energy management strategies on emission, fuel economy and emission performance of the vehicle are simulated and analyzed under UDDS driving cycle. The simulation results of the two strategies are compared in the end, shows that the modeling is rational, and compared with RB strategy, A-ECMS ensures charge sustaining better, enables power sources to work in more efficient areas, and improves fuel economy by 8.65%, but significantly increases NO_x emissions, which will be the focus of the next research work.

Introduction

In order to alleviate the dual pressure of oil shortage and environmental pollution, new energy vehicles have become the mainstream tendency of the development of the automobile industry. Hybrid electric vehicles (HEVs) integrate the internal combustion engine, electrical machine and battery effectively, which can not only take full advantage of the long driving distance of internal combustion engine vehicles and the high efficiency and energy saving of pure electric vehicles, but also avoid the disadvantages of these two kinds of vehicles, making it the most promising solution of new energy vehicles in the short term. ¹ According to the configuration of powertrain, HEVs can be divided into three types: parallel, series, and power-split. ² With the advanced power-split device and efficient energy management strategy, the power-split HEVs can make the vehicle work in series, parallel or both of them with the change of road load, therefore, maximize the potential of improving fuel economy.

The power-split device is the core component of power-split powertrain system, the task of it is to make the part power output of the engine drive the vehicle directly through the mechanical path, and the other part through the electric path to charge the battery in driving. ³ Meanwhile, the use of the power-split device can make the engine speed and torque decouple from vehicle speed and road load, implementing the function of continuously variable speed, which makes it easier to control the engine and keep it in the high-efficiency area. ⁴ At present, the relatively mature power-split systems are Toyota Hybrid System (THS) of Toyota and America Hybrid System (AHS) of GM.^5,6 The power-split devices are designed with planetary gearsets, which are used in conjunction with clutches (or brakes) to couple the engine and electrical machine, so as to realize the switch between different operation modes of the vehicle. ⁷

Energy management strategies have always been the core technology of HEVs. Only by controlling the power-split device through efficient energy management strategies can the advantages of HEVs be fully exerted. ⁸ The energy management strategies of HEVs are mainly divided into rule-based control strategies and optimization-based control strategies. ⁹ Rule-based control strategies include logic threshold and fuzzy logic, which are mainly to divide multiple operation modes for the vehicle clearly and to switch between different modes by setting multiple control rules as switching conditions. ¹⁰ As the most basic online control strategy, the rule-based control strategy was first applied to HEVs, such as Toyota Prius. ¹¹ The optimization-based control strategies mainly include dynamic programming (DP), equivalent fuel consumption minimization strategy (ECMS), model predictive control (MPC), and deep reinforcement learning algorithm that have emerged with artificial intelligence in recent years.^12–15 Compared with the rule-based control strategies, the optimization-based control strategies don’t need to divide the operation modes for the vehicle, the optimal or sub-optimal solution of the control can be obtained. Therefore, the fuel-saving effect is more obvious. The disadvantages are that the algorithm principle based on optimization is more complex and the calculation amount is much larger. Although the principle of each algorithm is different, the optimization-based control strategies are essentially to reasonably distribute the torque between the engine, generator and motor according to the current driving status, so that the distribution effect is better when it meets the driving demand.

The performance verification of the power-split device and energy management strategies depends on the vehicle simulation experiment. The premise of simulation analysis is to conduct accurate and reasonable modeling of the research object. ¹⁶ In the same type of published papers, the commonly used modeling methods mainly include Advisor, AVL Cruise and MATLAB-Simscape Driveline. Karaoglan et al. built a parallel HEV model in Advisor, and studied the influence of transmission ratio of transmission components on fuel economy and emission in MATLAB-Simulink simulation environment. ¹⁷ Prathibha et al. studied the fuel economy of pure electric vehicles, parallel hybrid electric vehicles and fuel cell vehicles of different driving cycles by using Advisor and MATLAB-Simulink co-simulation, and obtained the optimal vehicle type under specific driving cycles. ¹⁸ Fu et al. matched the parameters of parallel HEV powertrain based on multi-objective optimization, and studied the dynamic performance, fuel economy and emission performance by using AVL Cruise and MATLAB-Simulink co-simulation. ¹⁹ Yin et al. used co-simulation of AVL Cruise and MATLAB-Simulink to study the economic improvement effect of particle swarm optimization algorithm relative to the engine mechanical point control strategy, but did not study the emission performance. ²⁰ Ahmed et al. built a parallel hybrid vehicle model with MATLAB-Simscape Driveline, and studied the influence of different types of engines on the dynamic performance and fuel economy of the same vehicle. ²¹ Anbaran et al. simulated the power-split hybrid bus model in MATLAB-Simscape Driveline environment, and verified the rationality of the designed logic threshold control strategy. ²² As far as modeling is concerned, before using Advisor or AVL Cruise to co-simulate with Simulink, the co-simulation environment needs to be configured with a file in feature format, which is error-prone, and AVL Cruise is not open source. ²³ MATLAB-Simscape Driveline does not need co-simulation, but the model is not intuitive enough and the topology is complex. Since MATLAB2017a, Simulink has successively launched two toolboxes for vehicle modeling and simulation: Powertrain Blockset and Vehicle Dynamics Blockset, which contain various modules required for vehicle modeling. Based on the modeling idea of modular packaging, it is easy to operate with the high level of visualization, and the simulation process is entirely open-source, which can obviously shorten the modeling time and improve the simulation efficiency.

In summary, papers that analyze both fuel economy and emission performance is currently mainly for parallel HEVs, there are few papers deal with the emission performance of power-split HEVs, and papers on vehicle modeling and simulation with vehicle modeling and simulation toolboxes in MATLAB have not been published. This paper focuses on two key technologies of power-split HEVs: the power-split device and energy management strategy. Based on MATLAB-Simulink, the vehicle modeling and simulation toolboxes in MATLAB are used to build the simulation model. Choose a typical control strategy from rule-based control strategies and optimization-based control strategies respectively: the logic threshold control strategy and the equivalent consumption minimization strategy to study the fuel economy and explore the emission performance. Comparing the simulation results of the two control strategies not only verifies the rationality of the modeling, but also improves fuel economy and explores the impact of different types of control strategies on emission performance.

Powertrain system modeling

As a technologic change, the power-split device of 2010 Toyota Prius is designed with the double planetary gearset, the torque of the engine, motor and generator can be coupled without using clutches or brakes, and the vehicle can operate in multiple modes, so that the effect of oil saving is obvious. The power-split configuration of 2010 Toyota Prius is often used to develop efficient energy management strategies.^24,25 The power distribution device adopted in this paper is similar to 2010 Toyota Prius, but the ring gear of the rear planetary gearset is fixed, and in result torque is output by carrier, which is different from 2010 Toyota Prius. Therefore, the effect of reducing rotating speed and increasing torque is more obvious, and electrical machines with small torque can be used to reduce the volume, at the same time the speed range is wider, which makes it work in the efficient area. The powertrain system configuration of the power-split vehicle in this paper is shown in Figure 1.

Figure 1.

Powertrain system configuration.

As shown in Figure 1, MG1 and MG2 represent the two electrical machines respectively. MG1 is usually used as a generator and MG2 as a motor. PG1 is a 2-DOF planetary gearset, which is used to split the power of the engine. PG2 is a planetary gearset as well, but its ring gear is locked, so it only has one DOF, it is used to reduce the rotating speed and increase the torque of MG2. Engine and MG1 are connected to the carrier and sun gear of PG1 respectively, and MG2 is connected to the sun gear of PG2.

Based on the lever analogy method, the powertrain shown in Figure 1 is theoretically modeled. ²⁶ According to the rotational speed and torque relationship among the planetary gearsets, the free-body diagram is drawn as shown in Figure 2.

Figure 2.

Free-body diagram of the powertrain.

As shown in Figure 2, the arrow’s direction indicates the direction of the torque and rotational speed, while left is defined to be the positive direction. PG1 and PG2 are highlighted in dashed boxes. $J$ , $T$ , and $\omega$ represent inertia, torque and rotational speed, respectively. $R$ and $S$ represent the radius of ring gear and sun gear, respectively. $F$ represents internal force between the planetary gears. Subscript e, mg1, mg2, s, c and r, represent engine, MG1, MG2, sun gear, carrier and ring gear, respectively. Subscript 1 and 2 represent PG1 and PG2, respectively. $T_{\mathrm{out}}$ represents the output torque of the power-split device. $T_{\mathrm{f}}$ represents the torque of resistance. $i_0$ is the gear ratio of the final drive, and $m$ is the vehicle mass.

The viscosity loss and friction loss in the process of planetary gear meshing are ignored. According to Euler’s law, the internal force relationship satisfies equation (1)

$$\{\begin{array}{c}{J}_{\mathrm{s}1}{\stackrel{·}{\omega }}_{\mathrm{s}1}=F_1{S}_1-T_{\mathrm{s}1}\hfill \\ \multicolumn{1}{c}{J_{\mathrm{c}1}{\stackrel{·}{\omega }}_{\mathrm{c}1}=T_{\mathrm{s}1}-F_1{S}_1-F_1{R}_1}\\ \multicolumn{1}{c}{J_{\mathrm{r}1}{\stackrel{·}{\omega }}_{\mathrm{r}1}=F_1{R}_1-T_{\mathrm{r}1}}\end{array}$$ (1)

The sun gear and carrier of PG1 are connected to MG1 and engine respectively, so equation (2) can be obtained as follows

$$\{\begin{array}{c}{J}_{\mathrm{mg}1}{\stackrel{·}{\omega }}_{\mathrm{mg}1}=T_{\mathrm{s}1}-T_{\mathrm{mg}1}\hfill \\ \multicolumn{1}{c}{J_{\mathrm{e}}{\stackrel{·}{\omega }}_{\mathrm{e}}=T_{\mathrm{e}}-T_{\mathrm{c}1}}\end{array}$$ (2)

By equation (1) and (2), equation (3) can be obtained as follows

$$\{\begin{array}{c}(J_{\mathrm{s}1}+J_{\mathrm{mg}1}){\stackrel{·}{\omega }}_{\mathrm{mg}1}=F_1{S}_1-T_{\mathrm{mg}1}\hfill \\ \multicolumn{1}{c}{(J_{\mathrm{c}1}+J_{\mathrm{e}}){\stackrel{·}{\omega }}_{\mathrm{e}}=T_{\mathrm{e}}-F_1{R}_1-F_1{S}_1}\end{array}$$ (3)

The speed relation of single planetary gearset is given as follows

$${\omega }_{\mathrm{mg}1}{S}_1+{\omega }_{\mathrm{r}1}{R}_1-{\omega }_{\mathrm{e}}(S_1+R_1)=0$$ (4)

$k_1$ is used to represent the characteristic parameter of PG1 (i.e. $k_1=R_1/S_1$ ), so equation (3) can be transformed into

$${\omega }_{\mathrm{mg}1}+k_1{\omega }_{\mathrm{r}1}=(k_1+1){\omega }_{\mathrm{e}}$$ (5)

According to the above equations, the relation between output torque $T_{\mathrm{r}1}$ and input torque $T_{\mathrm{e}}$ of PG1 can be obtained as follows

$$T_{\mathrm{r}1}=\frac{k_1}{k_1+1}{T}_{\mathrm{e}}-\frac{k_1}{k_1+1}(J_{\mathrm{c}1}+J_{\mathrm{e}}){\stackrel{·}{\omega }}_{\mathrm{e}}-J_{\mathrm{r}1}{\stackrel{·}{\omega }}_{\mathrm{r}1}$$ (6)

The above equations can be combined into a matrix equation to describe the dynamic behavior of PG1

$$\begin{array}{c}\left[\begin{array}{cccc}-(J_{\mathrm{s}1}+J_{\mathrm{mg}1})\hfill & 0\hfill & 0\hfill & S_1\hfill \\ \multicolumn{1}{c}{0}& J_{\mathrm{c}1}+J_{\mathrm{e}}\hfill & 0\hfill & S_1+R_1\hfill \\ \multicolumn{1}{c}{0}& \frac{k_1}{k_1+1}(J_{\mathrm{c}1}+J_{\mathrm{e}})\hfill & J_{\mathrm{r}1}\hfill & 0\hfill \\ \multicolumn{1}{c}{S_1}& -(S_1+R_1)\hfill & R_1\hfill & 0\hfill \end{array}\right]\hfill \\ \left[\begin{array}{c}{\stackrel{·}{\omega }}_{\mathrm{mg}1}\hfill \\ \multicolumn{1}{c}{{\stackrel{·}{\omega }}_{\mathrm{e}}}\\ \multicolumn{1}{c}{{\stackrel{·}{\omega }}_{\mathrm{r}1}}\\ \multicolumn{1}{c}{F_1}\end{array}\right]=\left[\begin{array}{c}{T}_{\mathrm{mg}1}\hfill \\ \multicolumn{1}{c}{T_{\mathrm{e}}}\\ \multicolumn{1}{c}{\frac{k_1}{k_1+1}{T}_{\mathrm{e}}-T_{\mathrm{r}1}}\\ \multicolumn{1}{c}{0}\end{array}\right]\hfill \end{array}$$ (7)

In the same way, the relationship between the internal forces of MG2 satisfies equation (8)

$$\{\begin{array}{c}{J}_{\mathrm{s}2}{\stackrel{·}{\omega }}_{\mathrm{s}2}=T_{\mathrm{s}2}-F_2{S}_2\hfill \\ J_{\mathrm{c}2}{\stackrel{·}{\omega }}_{\mathrm{c}2}=F_2{S}_2+F_2{R}_2-T_{\mathrm{c}2}\hfill \end{array}$$ (8)

MG2 is connected to the sun gear of PG2, so equation (2) can be obtained as follows

$$J_{\mathrm{mg}2}{\stackrel{·}{\omega }}_{\mathrm{mg}2}=T_{\mathrm{mg}2}-T_{\mathrm{s}2}$$ (9)

By equation (8) and (9), equation (10) can be obtained as follows

$$(J_{\mathrm{mg}2}+J_{\mathrm{s}2}){\stackrel{·}{\omega }}_{\mathrm{mg}2}=T_{\mathrm{mg}2}-F_2{S}_2$$ (10)

Since the ring gear of MG2 is fixed, its speed is always 0, and the speed relation of MG2 is

$${\omega }_{\mathrm{mg}2}{S}_2-{\omega }_{\mathrm{c}2}(S_2+R_2)=0$$ (11)

$k_2$ is used to represent the characteristic parameter of PG2 (i.e. $k_2=R_2/S_2$ ), so equation (11) can be transformed into

$${\omega }_{\mathrm{mg}2}=(k_2+1){\omega }_{\mathrm{c}2}$$ (12)

According to the above equations, the relation between output torque $T_{\mathrm{c}2}$ and input torque $T_{\mathrm{mg}2}$ of PG2 can be obtained as follows

$$T_{\mathrm{c}2}=(1+k_2)T_{\mathrm{mg}2}-[(J_{\mathrm{mg}2}+J_{\mathrm{s}2})(1+k_2{)}^2+J_{\mathrm{c}2}]{\stackrel{·}{\omega }}_{\mathrm{c}2}$$ (13)

The above equations from (8) to (13) can be combined into a matrix equation to describe the dynamic behavior of PG2

$$\begin{array}{c}\left[\begin{array}{ccc}{J}_{\mathrm{s}2}+J_{\mathrm{mg}2}\hfill & 0\hfill & S_2\hfill \\ \multicolumn{1}{c}{0}& -J_{\mathrm{c}2}\hfill & S_2+R_2\hfill \\ \multicolumn{1}{c}{0}& (J_{\mathrm{s}2}+J_{\mathrm{mg}2})(1+k_2^2)-J_{\mathrm{c}2}\hfill & 0\hfill \\ \multicolumn{1}{c}{S_2}& -(S_2+R_2)\hfill & 0\hfill \end{array}\right]\hfill \\ \left[\begin{array}{c}{\stackrel{·}{\omega }}_{\mathrm{mg}2}\hfill \\ \multicolumn{1}{c}{{\stackrel{·}{\omega }}_{\mathrm{c}2}}\\ \multicolumn{1}{c}{F_2}\end{array}\right]=\left[\begin{array}{c}{T}_{\mathrm{mg}2}\hfill \\ \multicolumn{1}{c}{T_{\mathrm{c}2}}\\ \multicolumn{1}{c}{(k_2+1)T_{\mathrm{mg}2}-T_{\mathrm{c}2}}\\ \multicolumn{1}{c}{0}\end{array}\right]\hfill \end{array}$$ (14)

At the torque output end of the power-split device, there is a torque relation as follows

$$T_{\mathrm{out}}=T_{\mathrm{r}1}+T_{\mathrm{c}2}$$ (15)

By equation (5), (6), (12), (13) and neglect all the inertia, the speed and torque relation among power sources and the torque output end is derived as follows

$$\{\begin{array}{c}\multicolumn{1}{c}{{\omega }_{\mathrm{e}}=\frac{1}{1+k_1}{\omega }_{\mathrm{mg}1}+\frac{k_1}{(1+k_1)(1+k_2)}{\omega }_{\mathrm{mg}2}}\\ \multicolumn{1}{c}{T_{\mathrm{e}}=(1+\frac{1}{k_1})T_{\mathrm{out}}-\frac{(1+k_1)(1+k_2)}{k_1}{T}_{\mathrm{mg}2}}\end{array}$$ (16)

Equation (16) explains the principle of “double decoupling” of speed and torque of power-split device: since ${\omega }_{\mathrm{mg}2}$ and $T_{\mathrm{out}}$ directly depend on vehicle speed and road load respectively, the engine speed and torque can be adjusted by changing the values of ${\omega }_{\mathrm{mg}2}$ and $T_{\mathrm{out}}$ . Therefore, MG1 and MG2 are used as a “speed regulator” and a “torque regulator” of the engine respectively, so that the working condition of the engine is not affected by vehicle speed and road load, the engine can always work in the efficient area in result.

According to the torque balance relationship at the output end of the power-split device, equation (17) can be obtained as follows

$$\{\begin{array}{c}{\stackrel{·}{\omega }}_{\mathrm{c}2}(m\frac{r^2}{i_0}+J_{\mathrm{c}2}{i}_0)=T_{\mathrm{out}}{i}_0-T_{\mathrm{f}}\hfill \\ T_{\mathrm{f}}=T_{\mathrm{fb}}+\mathrm{mgfr}\cos \alpha +\mathrm{mgr}\sin \alpha +\frac{C_{\mathrm{d}}A{v}^{2}r}{21.15}\hfill \\ v=\frac{{\omega }_{\mathrm{c}2}r}{i_0}\hfill \end{array}$$ (17)

Where $r$ is the wheel radius, $T_{\mathrm{fb}}$ represents the total braking torque, $f$ is the rolling resistance coefficient, A represents vehicle frontal area, $C_{\mathrm{d}}$ is the drag coefficient of air, $g$ is acceleration of gravity, $\alpha$ represents the road gradient, $v$ is vehicle speed.

Based on equation (7), (14), and (17), the driveline simulation model shown in Figure 3 is built using Powertrain Blockset and Vehicle Dynamics Blockset in MATLAB-Simulink (the power-split device is highlighted in the dashed box).

Figure 3.

Driveline simulation model.

The key parameters of the dual-planetary power-split HEV are shown in Table 1.

Table 1.

Key parameters of the dual-planetary power-split HEV.

Parameter	Description	Value	Parameter	Description	Value
$m$	Vehicle mass	1700 kg	$P_{\mathrm{mg}1\mathrm{\_}\mathrm{rat}}$	MG1 rated power	12.5 kW
$r$	Wheel radius	0.302 m	$T_{\mathrm{mg}1\mathrm{\_}\max }$	MG1 maximum torque	80 Nm
$f$	Coefficient of rolling resistance	0.012	${\omega }_{\mathrm{mg}1\mathrm{\_}\max }$	MG1 maximum speed	12,000 rpm
$C_{\mathrm{d}}$	Drag coefficient of air	0.32	$P_{\mathrm{mg}2\mathrm{\_}\max }$	MG2 maximum power	50 kW
$A$	Front area	2.35 m2	$P_{\mathrm{mg}2\mathrm{\_}\mathrm{rat}}$	MG2 rated power	30 kW
$i_0$	Final drive ratio	3.2	$T_{\mathrm{mg}2\mathrm{\_}\max }$	MG2 maximum torque	160 Nm
$k_1$	Characteristic parameter of PG1	2.8	${\omega }_{\mathrm{mg}2\mathrm{\_}\max }$	MG2 maximum speed	20,000 rpm
$k_2$	Characteristic parameter of PG2	2.8	$J_{\mathrm{e}}$	Engine inertia	0.075 kg·m2
$P_{\mathrm{e}\mathrm{\_}\max }$	Engine maximum power	70 kW	$J_{\mathrm{mg}1}$	MG1 inertia	0.022 kg·m2
$T_{\mathrm{e}\mathrm{\_}\max }$	Engine maximum torque	150 Nm	$J_{\mathrm{mg}2}$	MG2 inertia	0.032 kg·m2
${\omega }_{\mathrm{e}\mathrm{\_}\max }$	Engine maximum speed	5000 rpm	$C_{\max }$	Battery capacity	18.5 Ah
$P_{\mathrm{mg}1\mathrm{\_}\max }$	MG1 maximum power	25 kW	$V_{\mathrm{oc}}$	Battery voltage	300 V

Based on the bench test data of the engine, MG1 and MG2, efficiency maps of the power sources are drawn as shown in Figure 4.

Figure 4.

Efficiency maps of the power sources: (a) fuel consumption map of the engine, (b) efficiency map of MG1, and (c) efficiency map of MG2.

Rule-based control strategy

Operation modes analysis

Before the logic threshold control strategy is designed, multiple operation modes are designed for the vehicle. The more detailed the modes are, and the more precise the control rules are, the better the control effect is. In order to better adapt to urban driving conditions, six basic operation modes are designed: pure electric mode (OpMode = 1), driving-charging mode (OpMode = 2), motor-powering mode (OpMode = 3), braking mode (OpMode = 4), parking-charging mode (OpMode = 5), and parking mode (OpMode = 6). Meanwhile, one operation mode may be composed of several operating states: the pure electric mode includes vehicle starting state (OpMode = 1A) and engine starting state (OpMode = 1B), the driving-charging mode includes low-speed cruising state (OpMode = 2A) and high-speed cruising state (OpMode = 2B), the motor-powering mode includes acceleration state (OpMode = 3A) and the maximum speed driving state (OpMode = 3B). Since both fuel economy and emission simulations are implemented under forward operation conditions, the astern mode is not considered in this paper. The operating states of each power source and energy source under different modes are shown in Table 2.

Table 2.

Operating states of each power source and energy source.

OpMode		Engine	MG1	MG2	Battery
1	1A	Off	Off	Motor	Discharge
	1B	Off	Motor	Motor	Discharge
2	2A	On	Generator	Motor	Charge
	2B	On	Motor	Generator	Charge
3	3A	On	Generator	Motor	Discharge
	3B	On	Generator	Motor	Discharge
4		Off	Off	Generator	Charge
5		On	Generator	Off	Charge
6		Off	Off	Off	Off

When the vehicle just started, the speed is low, and if battery power is sufficient, the vehicle can be driven solely by MG2, which is powered by the battery. After the vehicle starts, when the speed is higher than a certain set value, MG1 is used to be a motor to start the engine, at this point, both MG1 and MG2 are powered by the battery. When the vehicle is cruising at a low speed, the power output of the engine is partly to drive the vehicle directly, and partly to make MG1 charge the battery, while MG2 provides the auxiliary driving force. When the vehicle is cruising at a high speed, the engine speed is high and the output power is large. Part of the power directly drives the vehicle, and the other part is used to drive the MG2 to charge the battery. Thus, the battery SOC is kept stable during high-speed driving. When the vehicle is accelerating or operating at the highest speed, the output power of the engine is not enough to drive the vehicle, then MG2 is needed to provide the auxiliary driving force. At the same time, in order to avoid the rapid decline of SOC, MG1 is used as a generator to charge the battery. The speed constraint lever diagram of power sources corresponding to each operation mode is shown in Figure 5.

Figure 5.

Speed constraint lever diagram of power sources: (a) OpMode = 1A, (b) OpMode = 1B, (c) OpMode = 2A, (d) OpMode = 2B, (e) OpMode = 3A, (f) OpMode = 3B, (g) OpMode = 4, (h) OpMode = 5, and (i) OpMode = 6.

Figure 5 illustrates the working state of each power source corresponding to each mode. Take Figure 5(c) as an example, both the engine and MG2 are positive rotation, and the value of output power is positive as well. MG2 is used as a motor at this time. MG1 is driven to be positive rotation, since the torque of MG1 is all negative when operating, the output power is negative, which is used as a generator. At this time, the electrical energy provided by MG1 for the battery is more than that consumed by MG2, so SOC increases slightly, and the battery is in charge on the whole. Figure 6 shows the powertrain energy flow direction corresponding to Figure 5(c).

Figure 6.

Energy flow direction of the powertrain (OpMode = 2A).

Design of RB strategy

In this paper, the logic threshold control strategy is based on the idea of “power flow.” The power demand while driving is calculated using the driver model. According to the current operation mode and SOC, to calculate the power that should be provided by each power source to meet the demand of driving, then the engine output speed and torque are controlled based on the optimal operation curve. ²⁷ Meanwhile, the serial regenerative braking control strategy is adopted to reduce fuel consumption to the greatest extent when braking (to simplify the simulation, engine braking is not considered in this paper).

The research object of this paper is a gasoline electric hybrid vehicle, the main power source is still the engine. It is necessary to set multiple starting conditions for the engine to control SOC within a small range of fluctuation. Starting conditions of the engine are designed as follows

$$\{\begin{array}{c}(\mathrm{SOC}<\mathrm{SO}{C}_{\mathrm{tar}})\mathrm{\&}(\mathrm{Dec}=0)\hfill \\ \multicolumn{1}{c}{(v>v_{\mathrm{e}\mathrm{\_}\max })\&(\mathrm{Dec}=0)}\\ \multicolumn{1}{c}{\mathrm{Acc}>0.5}\\ \multicolumn{1}{c}{\mathrm{OpMode}=5}\end{array}$$ (18)

The logic of the above conditions are “or”, that is, as long as any one of them is satisfied, the engine starts. $\mathrm{SOC}$ represents the current state of charge, $\mathrm{SO}{C}_{\mathrm{tar}}$ represents the target value of SOC, $v_{\mathrm{e}\mathrm{\_}\max }$ represents the maximum speed of pure electric driving. $\mathrm{Acc}$ and $\mathrm{Dec}$ represent the opening of the accelerator pedal and braking pedal, respectively.

The transfer conditions and power distribution of each mode are shown in Table 3.

Table 3.

The transfer conditions and power distribution of each mode.

OpMode		Transfer conditions	$P_{\mathrm{e}}$	$P_{\mathrm{mg}1}$	$P_{\mathrm{mg}2}$
1	1A	$(\mathrm{EngOn}=0)\&(v<v_{\mathrm{e}\mathrm{\_}max})$	0	0	$P_{\mathrm{cmd}}$
	1B	$(\mathrm{EngOn}=0)\&(v=v_{\mathrm{e}\mathrm{\_}max})$	0	$P_{\mathrm{est}}$	$P_{\mathrm{cmd}}$
2	2A	$(\mathrm{EngOn}=1)\&(0<P_{\mathrm{cmd}}<P_{\mathrm{me}})\&(v<=v_{\mathrm{c}\mathrm{\_}\mathrm{low}})$	$P_{\mathrm{cmd}}+P_{\mathrm{ch}}$	$-(P_{\mathrm{e}}-P_{\mathrm{me}})$	$P_{\mathrm{cmd}}-P_{\mathrm{e}}$
	2B	$(\mathrm{EngOn}=1)\&(0<P_{\mathrm{cmd}}<P_{\mathrm{me}})\&(v_{\mathrm{c}\mathrm{\_}\mathrm{low}}<v<v_{\mathrm{c}\mathrm{\_}\mathrm{high}})$		$-P_{\mathrm{mg}2}-P_{\mathrm{ch}}$	$-P_{\mathrm{mg}1}-P_{\mathrm{ch}}$
3	3A	$(\mathrm{EngOn}=1)\&(P_{\mathrm{cmd}}>=P_{\mathrm{me}})\&(\mathrm{Acc}>0)$	$P_{\mathrm{emax}}$	$-(P_{\mathrm{e}}-P_{\mathrm{me}})$	$P_{\mathrm{mg}1}+P_{\mathrm{dis}}$
	3B	$(\mathrm{EngOn}=1)\&(P_{\mathrm{cmd}}>=P_{\mathrm{me}})\&(v>=v_{max})$
4		$\mathrm{Dec}>0$	0	0	$P_{\mathrm{cmd}}$
5		$(v=0)\&(\mathrm{SOC}<\mathrm{SO}{C}_{\mathrm{tar}})$	$P_{\mathrm{ch}}$	$-P_{\mathrm{ch}}$	0
6		$(v=0)\&(\mathrm{SOC}>=\mathrm{SO}{C}_{\mathrm{tar}})$	0	0	0

$P_{\mathrm{e}}$ , $P_{\mathrm{mg}1}$ , and $P_{\mathrm{mg}2}$ represent the power of the engine, MG1 and MG2, respectively. $\mathrm{EngOn}=1$ represents the engine is in operation. $v_{\mathrm{c}\mathrm{\_}\mathrm{low}}$ , $v_{\mathrm{c}\mathrm{\_}\mathrm{high}}$ , and $v_{\max }$ represent low-speed cruising speed, high-speed cruising speed and the maximum speed of the vehicle, respectively. $P_{\mathrm{cmd}}$ , $P_{\mathrm{est}}$ , $P_{\mathrm{me}}$ , and $P_{\mathrm{emax}}$ represent the power demand in driving, the power demand to start the engine and the power transferred from the engine to the wheels through the mechanical path, respectively. $P_{\mathrm{ch}}$ and $P_{\mathrm{dis}}$ represent the charging and discharging power of the battery, respectively.

MATLAB-Stateflow is used to design the logic threshold controller as shown in Figure 7.

Figure 7.

Logic threshold controller.

Design of A-ECMS algorithm

For gasoline electric hybrid vehicles, the external power supply is not required to replenish battery energy, so SOC should be maintained while saving fuel. Since SOC varies in a small range during driving, it can be considered that all the energy consumed by driving the vehicle comes from fuel, that is, the battery can be regarded as an “energy buffer”: the electricity consumed by the motor can be replenished by oil through the engine and generator in the future, and when the battery is recharged, the equivalent of the excess mechanical energy of the engine or the energy recovered during braking is returned to the oil tank. Based on the idea of ECMS, the calculation formula of equivalent fuel consumption any instantaneous moment is as follows

$${\stackrel{·}{m}}_{\mathrm{equ}}(t)={\stackrel{·}{m}}_{\mathrm{e}}(t)+s·{\stackrel{·}{m}}_{\mathrm{batt}}(t)$$ (19)

Where ${\stackrel{·}{m}}_{\mathrm{equ}}(t)$ represents the equivalent fuel consumption rate, ${\stackrel{·}{m}}_{\mathrm{e}}(t)$ represents the fuel mass flow rate, and ${\stackrel{·}{m}}_{\mathrm{batt}}(t)$ represents the equivalent fuel consumption rate of the battery. $s$ is the equivalence factor. Since the efficiency of converting electrical energy into mechanical energy is higher than that of the conversion of chemical energy into mechanical energy of fuel, if only the addition of ${\stackrel{·}{m}}_{\mathrm{e}}(t)$ and ${\stackrel{·}{m}}_{\mathrm{batt}}(t)$ is taken as the optimization objective function, the control strategy will tend to use electrical energy only, so it is difficult to guarantee the maintenance effect of SOC. Therefore, by setting the equivalence factor, the control strategy can flexibly decide whether to use electric energy at the next moment, so as to maintain the value of SOC.

From equation (19), if the value of $s$ is too large, the control strategy is more inclined to use fuel, resulting in excessive fuel consumption and continuously rising SOC. On the contrary, if the value of $s$ is too small, SOC will continue to decline. Therefore, the equivalence factor $s$ can be adjusted adaptively as the parameter which should be adapted for online optimization according to the feedback from SOC, then SOC can be maintained around its target value.

In order to design an adaptive optimal supervisory controller, a PI controller is adopted to realize the online adaption of the equivalence factor based on SOC feedback. Equation (20) shows the theoretical formula of the PI controller.

$$\begin{array}{c}\multicolumn{1}{c}{s(t)=s_0+k_{\mathrm{P}}(\mathrm{SO}{C}_{\mathrm{tar}}-\mathrm{SOC}(t))}\\ +k_{\mathrm{I}}{\int }_{t_0}^{t_{\mathrm{f}}}(\mathrm{SO}{C}_{\mathrm{tar}}-\mathrm{SOC}(t))\mathrm{d}t\hfill \end{array}$$ (20)

Where $s_0$ represents the initial value of $s$ , $\mathrm{SOC}(t)$ represents the current value of SOC, $k_{\mathrm{P}}$ and $k_{\mathrm{I}}$ represent proportional gain and integral gain, respectively.

Meanwhile, in order to achieve better control effect, the equivalence factor is modified based on the current SOC. Equation (21) shows the computational formula of the correction factor.

$$f(\mathrm{SOC})=1-{\left(\frac{\mathrm{SOC}(t)-\mathrm{SO}{C}_{\mathrm{tar}}}{0.5(\mathrm{SO}{C}_{\max }-\mathrm{SO}{C}_{\min })}\right)}^3$$ (21)

Where $f(\mathrm{SOC})$ is the correction factor of the equivalence factor, $\mathrm{SO}{C}_{\max }$ and $\mathrm{SO}{C}_{\min }$ represent the upper limit and lower limit of SOC.

Based on the above analysis, using $s(t)$ and the correction factor $f(\mathrm{SOC})$ to replace the equivalence factor $s$ in equation (19), so the equation can be transformed into the objective function of A-ECMS as follows

$$H_{min}=min({\stackrel{·}{m}}_{\mathrm{e}}(t)+f(\mathrm{SOC})·s(t)·{\stackrel{·}{m}}_{\mathrm{batt}}(t))$$ (22)

Where $H_{min}$ represents the minimum value of the objective function. Since ${\stackrel{·}{m}}_{\mathrm{e}}(t)$ depends on the engine speed and torque, equation (23) can be obtained.

$${\stackrel{·}{m}}_{\mathrm{e}}(t)={\stackrel{·}{m}}_{\mathrm{e}}(T_{\mathrm{e}}(t),{\omega }_{\mathrm{e}}(t))$$ (23)

Equation (24) shows the computational formula of ${\stackrel{·}{m}}_{\mathrm{batt}}(t)$ .

$${\stackrel{·}{m}}_{\mathrm{batt}}(t)=\frac{P_{\mathrm{batt}}(T_{\mathrm{mg}1}(t),{\omega }_{\mathrm{mg}1}(t),T_{\mathrm{mg}2}(t),{\omega }_{\mathrm{mg}2}(t))}{Q_{\mathrm{lhv}}}$$ (24)

Where $Q_{\mathrm{lhv}}$ is the lower heating value of gasoline.

From equation (16), the power-split device makes a fixed constraint relationship between the speed and torque of each power source, so $T_{\mathrm{mg}1}(t)$ , $T_{\mathrm{mg}2}(t)$ and ${\omega }_{\mathrm{mg}1}(t)$ at any time can be calculated according to $T_{\mathrm{e}}(t)$ and ${\omega }_{\mathrm{e}}(t)$ . Therefore, equation (22) can be transformed into

$$\begin{array}{c}{H}_{min}=min\hfill \\ ({\stackrel{·}{m}}_{\mathrm{e}}(T_{\mathrm{e}}(t),{\omega }_{\mathrm{e}}(t))+f(\mathrm{SOC})·s(t)·\frac{P_{\mathrm{batt}}(T_{\mathrm{e}}(t),{\omega }_{\mathrm{e}}(t))}{Q_{\mathrm{lhv}}})\hfill \end{array}$$ (25)

The constraint conditions to be satisfied for the optimization problem are as follows

$$\{\begin{array}{c}{T}_{\mathrm{e}\mathrm{\_}min}\le T_{\mathrm{e}}(t)\le T_{\mathrm{e}\mathrm{\_}\max }\hfill \\ \multicolumn{1}{c}{{\omega }_{\mathrm{e}\mathrm{\_}min}\le {\omega }_{\mathrm{e}}(t)\le {\omega }_{\mathrm{e}\mathrm{\_}\max }}\\ \multicolumn{1}{c}{T_{\mathrm{mg}1\mathrm{\_}min}\le T_{\mathrm{mg}1}(t)\le T_{\mathrm{mg}1\mathrm{\_}\max }}\\ \multicolumn{1}{c}{{\omega }_{\mathrm{mg}1\mathrm{\_}min}\le {\omega }_{\mathrm{mg}1}(t)\le {\omega }_{\mathrm{mg}1\mathrm{\_}\max }}\\ \multicolumn{1}{c}{T_{\mathrm{mg}2\mathrm{\_}min}\le T_{\mathrm{mg}2}(t)\le T_{\mathrm{mg}2\mathrm{\_}\max }}\\ \multicolumn{1}{c}{{\omega }_{\mathrm{mg}2\mathrm{\_}min}\le {\omega }_{\mathrm{mg}2}(t)\le {\omega }_{\mathrm{mg}2\mathrm{\_}\max }}\\ \multicolumn{1}{c}{\mathrm{SO}{C}_{min}\le \mathrm{SOC}(t)\le \mathrm{SO}{C}_{\max }}\end{array}$$ (26)

From equation (25), the control variables of the optimization problem in this paper are $T_{\mathrm{e}}$ and ${\omega }_{\mathrm{e}}$ , and the state variable is SOC. ${\stackrel{·}{m}}_{\mathrm{e}}(t)$ can be obtained from the map of fuel mass flow rate by interpolation and ${\stackrel{·}{m}}_{\mathrm{batt}}(t)$ at any time can be calculated. A-ECMS control structure is shown in Figure 8. As shown, according to $T_{\mathrm{d}}$ (torque demand in driving), $v$ and SOC at a given moment, and to discretize $T_{\mathrm{e}}$ and ${\omega }_{\mathrm{e}}$ in their value ranges, the equivalent fuel consumption rate of each set of control variables can be calculated by using the engine fuel consumption rate map and motor efficiency map, then the minimum value can be obtained. Thus, a combination of control variables that minimizes the value of the target function can be obtained. Finally, the optimal speed and torque distribution results of each power source can be obtained. The torque distribution results of the engine and MG2 calculated by A-ECMS can be directly used to control the engine and MG2 as command torque, but the torque distribution results of MG1 are not feasible. Since the engine speed is regulated by MG1, a PI controller can be designed to control the command torque of MG1 by using the command and actual engine speed.

Figure 8.

A-ECMS control structure.

Simulation and analysis

To demonstrate the rationality of the modeling and compare the performance of the two energy management strategies, the simulation is conducted under Urban Dynamometer Driving Schedule (UDDS), which is a test cycle developed by Environmental Protection Agency in 1972 to certify emission performance. As shown in Figure 9, the total simulation time of UDDS is 1369 s, 11.99 km for the total distance, with the maximum speed of 91.25 km/h and an average speed of 31.51 km/h. ²⁸

Figure 9.

UDDS driving cycle.

Parameters associated with control strategies introduced in section “Rule-based control strategy” and section “Design of A-ECMS algorithm” are listed in Table 4.

Table 4.

Parameters associated with control strategies.

Parameter	Value	Parameter	Value
$v_{\mathrm{e}\mathrm{\_}max}$	40 km/h	$\mathrm{SO}{C}_{max}$	0.8
$v_{\mathrm{c}\mathrm{\_}\mathrm{low}}$	70 km/h	$\mathrm{SO}{C}_{min}$	0.6
$v_{\mathrm{c}\mathrm{\_}\mathrm{high}}$	120 km/h	$\mathrm{SO}{C}_{\mathrm{tar}}$	0.7
$v_{max}$	160 km/h	$s_0$	3

The simulation results under UDDS are shown in Figure 10.

Figure 10.

Simulation results for UDDS: (a) velocity tracking results, (b) battery SOC, (c) engine speed, (d) engine torque, (e) MG1 torque, (f) MG1 power, (g) MG2 speed, and (h) MG2 power.

As can be seen from Figure 10(a), the simulation results of the two control strategies are in good agreement with the target speed. It can be seen from Figure 10(b) that SOC corresponding to RB and A-ECMS decreased by 1.43% and 0.59%, respectively, and the SOC curve with A-ECMS is smoother than that of RB, always remained near the target value. From Figure 10(c) and (d), the average engine speed and torque with A-ECMS are higher than RB, so that the engine can operate in a more efficient area. From Figure 10(e), due to the constraint of PG1, the MG1 torque corresponding to the two strategies is always negative or zero and is roughly proportional to the engine torque, satisfying equation (6). Figure 10(g) shows that the MG2 speed curves corresponding to the two strategies are basically coincident and proportional to the vehicle speed. This is because the ring gear of PG2 is fixed and the carrier is directly connected to the final drive. Figure 10(f) and (h) illustrate the power of MG1 and MG2 respectively, it can be seen that the power of MG1 is usually negative, while MG2 is usually positive, indicating that MG1 is often used as a generator and MG2 as a motor. What’s more, the average power of MG1 and MG2 during the simulation with A-ECMS is closer to their rated power than that with RB, thus making MG1 and MG2 more efficient. Through the above analysis, the rationality of modeling is verified.

In order to demonstrate the rationality of RB strategy and the superiority of A-ECMS algorithm, the operating points of each power source are illustrated in maps, as shown in Figure 11.

Figure 11.

Operating points of each power source: (a) engine operating points, (b) MG1 operating points, and (c) MG2 operating points.

Figure 11(a) illustrates the distribution of engine operating points: The operating points with RB centrally distribute along the optimal operation curve. In contrast, the operating points with A-ECMS relatively disperse around the optimal operation curve. However, due to the higher speed and torque with this strategy, more points distribute in the efficient area. From Figure 11(b), the efficiency of MG1 operating points with A-ECMS is obviously higher than that of RB. From Figure 11(c), MG2 operating points of A-ECMS are closer to the rated power curve of MG2 than that of RB, so the efficiency is higher. The above analysis shows that A-ECMS makes the operation efficiency of all power sources significantly improved.

The simulation results of fuel consumption are listed in Table 5, from which it can be seen that compared with RB strategy, A-ECMS improved fuel economy by 8.65% under the UDDS cycle.

Table 5.

Simulation results of fuel consumption (L/100 km).

Strategy	Engine consumption	Electrical equivalent consumption	Total consumption
RB	4.34	0.05	4.39
A-ECMS	3.98	0.03	4.01

In order to evaluate the emission performance, hydrocarbon (HC), carbon monoxide (CO) and nitrogen oxides (NO_x) emissions are calculated using the emission data taken from engine bench test. Figure 12 shows the flow rate maps of HC, CO, and NO_x: the mass flow rate of emissions ( ${\stackrel{·}{m}}_{\mathrm{HC}}$ , ${\stackrel{·}{m}}_{\mathrm{CO}}$ and ${\stackrel{·}{m}}_{\mathrm{NOx}}$ ) calculated from the emission data by using the interpolation method are regarded as functions of engine command torque and speed, and the effect of other factors on emission is not considered in this paper.

Figure 12.

Flow rate maps of exhaust gas: (a) HC flow rate map, (b) CO flow rate map, and (c) NO_x flow rate map.

A calculation model of emission performance is established in Simulink, as shown in Figure 13. The mass flow rate of emissions is evaluated by interpolation through 2D look-up tables. Input parameters are engine speed, engine command torque, and vehicle velocity in the model. Through the integration of each simulation step, exhaust emission results could be calculated as outputs.

Figure 13.

Emission performance calculation model.

Table 6 lists the simulation results of emission performance under UDDS, it can be seen that compared with RB strategy, HC emissions decreased by 25.16%, CO emissions increased by 11.32%, and NO_x emissions increased by 65.78% when A-ECMS is adopted. The variation of NO_x emissions is significantly greater than that of HC and CO, because the engine speed and command torque will increase to ensure the operating points of the engine in a more efficient area when A-ECMS is adopted as shown in Figure 11(a), and according to Figure 12, the mass flow rate of NO_x is much higher than HC and CO, and the production of NO_x is more sensitive to the change of engine command torque than that of HC and CO.

Table 6.

Simulation results of exhaust gas emissions (mg/km).

Strategy	HC	CO	NOx
RB	19.63	11.13	18.06
A-ECMS	14.69	12.39	29.94

Conclusion

A theoretical model of the dual-planetary power-split device is built and matrix equations are derived to describe the dynamic behavior of the powertrain based on the lever analogy method and the free-body diagram of planetary gearsets. Based on the matrix equations, vehicle modeling and simulation toolboxes in MATLAB are used to model the vehicle, especially the driveline.

A logic threshold control strategy based on rules is designed, and the constraint behavior of power sources of six operation modes are analyzed. Based on the concept of “power flow,” MATLAB-Stateflow is used to build a logic threshold energy management controller.

Taking engine speed and torque as control variables and battery SOC as the state variable, A-ECMS energy management strategy is designed and PI controller is used to control the command torque of MG2.

The simulation results of rotational speed and torque of each power source verify the rationality of the modeling. A-ECMS maintains SOC around its target value all the time, ensures charge sustaining better than RB. Compared with RB strategy based on rules, A-ECMS based on optimization enables all power sources to work in more efficient areas, improving fuel economy by 8.65%, but increasing NO_x emissions by 65.78%. In the following research work, it is planned to add the emission constraints in the energy management strategy and carry out the weighted calculation of emissions in the cost function, then to achieve the balance between energy conservation and emission reduction by adjusting the weighting factor.