J. Cent. South Univ. (2012) 19: 962-973

DOI: 10.1007/s11771-012-1098-y

Novel flexible hybrid electric system and adaptive online-optimal energy management controller for plug-in hybrid electric vehicles

HE Jian-hui(何建辉), YANG Lin(杨 林), QIANG Jia-xi(羌嘉曦),CHEN Zi-qiang(陈自强), ZHU Jian-xin(朱建新)

School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

? Central South University Press and Springer-Verlag Berlin Heidelberg 2012

Abstract: In order to achieve the improvement of the driving comfort and energy efficiency, an new e-CVT flexible full hybrid electric system (E2FHS) is proposed, which uses an integrated main drive motor and generator to take the place of the original automatic or manual transmission to realize the functions of continuously variable transmission (e-CVT). The design and prototype realization of the E2FHS system for a plug-in hybrid vehicle (PHEV) is performed. In order to analyze and optimize the parameters and the power flux between different parts of the E2FHS, simulation software is developed. Especially, in order to optimize the performance of the energy economy improvement of the E2FHS, the effect of the different energy management controllers is investigated, and an adaptive online-optimal energy management controller for the E2FHS is built and validated by the prototype PHEV.

Key words: e-CVT flexible full hybrid electric system; adaptive online-optimal controller; plug-in hybrid vehicle

1 Introduction

In recent years, global concern has grown with vehicle-generated air pollution emissions, greenhouse gas emissions and energy consumption. In response, the greatest part of the effort is directed toward the hybridization of automotive power trains, which are combined with more than one power source with significant potential in fuel saving and emissions reduction. It is assumed to be one of the most promising alternatives to engine-only vehicles [1], and an increasing number of hybrid electric vehicles (HEVs) have become available in the market [2].

Generally speaking, HEVs can be classified into three types: series, parallel, and series–parallel hybrid electric vehicles (i.e. full hybrid vehicles) [3]. Among them, the full hybrid system is assumed to have more potential in fuel saving and emission reduction since it is a combination of the advantages of the series type and parallel type [4]. Now, plug-in hybrid electric vehicles (PHEVs) go a step further in reducing fuel consumption, which is essentially a combination of a battery electric vehicle (BEV) and a HEV, having all of the electric capability of a BEV in urban areas and a smaller on-board ICE for the extended range capability of a  HEV, recharging the battery from the local grid and yielding over 45% reduction in fuel consumption [5]. Different hybrid schemes have been proposed, but many of them have not worked out in the real world because of the difficulty of balancing the vehicle’s performance and cost.

It is well known that the energy management technique of a HEV largely influences its competitiveness [6-7]. Over past decades, numerous attempts have been made to develop new controllers in order to better utilize the fuel saving and emission reduction potential of HEVs.

The first type is the rule-based control strategy [8], which is also called the baseline control. This type of control strategy is a static optimization method based on engineering intuition and a simple analysis of the efficiencies of components [9].

The second type is the intelligent-based control strategy for estimation and control algorithm, such as rule based fuzzy logic [10] and an artificial neural network control strategy [11]. In these intelligent control strategies, experts’ knowledge is coded in the form of rules, and decisions are made to split the power requests between the ICE and the electric motor based on engineering intuition. Both the rule-based control techniques and the fuzzy logic controllers need to be predetermined and can only be optimized for a specific drive cycle [12]. These systems do not fully adapt to the driving style of each driver and working conditions.

The third type is the optimal energy management control approach, and in this type of approach, dynamic programming (DP) techniques are investigated in order to obtain global optimal solutions for the power management of various types of HEV relying on certain drive cycles [13]. The DP-based method is ideal for global optimality, i.e. the power distribution can be optimized for the whole trip. However, because the trip model (drive cycle) contains future information for vehicle operation, not all of the DP-based work is applicable for real-time implementation. Therefore, it is claimed that a global optimization result can only be used as a reference for power management design. The stochastic optimal control approaches to power management in conventional HEV and plug-in HEV [14] have been studied in order to optimize the power distribution of many drive cycles using stochastic dynamic programming (SDP). Recently, a trip-based power control scheme has been researched, which applies the information of road and traffic to the future predictive route provided by global position system (GPS) and geographic information system (GIS) on board for HEVs [15]. Particularly, for the energy management control problem, a major drawback of the SDP-based and trip-based control approaches is the existence of the “curse of dimensionality”, i.e. the computation and memory needed by value iteration and policy iteration will increase exponentially with the number of states. This also limits their application for real-time implementation in the design of energy management systems [16].

The goal of this work is to propose an efficient e-CVT flexible hybrid electric system (E2FHS) and the adaptive online-optimal energy management controller, and to develop the prototype for a plug-in hybrid electric transit bus.

2 Operation modes and strategy outline

The architecture of the hybrid system proposed in this work is shown in Fig. 1. It contains an internal combustion engine (ICE), an integrated starter and generator (ISG), an electronically controlled clutch, an integrated main drive motor and generator (dMG), a battery pack, a battery charger and electronic control systems (including the hybrid control unit, HCU, the engine management system, EMS, the integrated motor controller for the ISG and the dMG, and the battery management system, BMS). Obviously, this system is a full hybrid system with electronic CVT characteristics. It should also be noted that the system is a typical PEV system without the assembly composed of ICE, ISG and the clutch, and will be a typical fuel-cell hybrid system if the assembly is replaced by a fuel-cell engine. Simply, it will be a typical series hybrid system if there is no clutch, and it can also be a typical ISG-type parallel hybrid system if the dMG is replaced by a transmission.

Fig. 1 Architecture of E2FHS hybrid system

The E2FHS can be divided into two structural modes, i.e. a series-structural mode (Fig. 2(a)) and a parallel-structural mode (Fig. 2(b)), with 16 operational modes (Table 1).

Fig. 2 Series-structural mode (a) and parallel-structural mode (b) of E2FHS

3 Model for online controller

The control process of the energy management controller for a hybrid electrical system is, in essence, the signal flow between the controller and the components in the system. The driver’s manipulation of the acceleration pedal and brake pedal, reflects the driver’s power demand at the vehicle’s wheels, P_dem. For the purpose of online real-time energy management, rather than focusing on the vehicles’ dynamics, the corresponding models concentrate on fueling characteristics and energy efficiency [17]. As a result, only the dynamic aspects necessary for energy management control are considered.

Table 1 Operation modes and energy-flow path of E2FHS

3.1 ICE

As a real-time control application, the fuel consumption of the ICE is usually expressed as the relationship between the engine speed ω_ICE (rad/s) and the torque T_ICE (N·m) by a non-linear 3-D MAP from the quasi-steady test data.

However, it should be noted that, if the fuel consumption MAP is deliberately presented as an almost linear (affine) relationship exists between the fuel rate and the engine power P_ICE (kW) for different engine speeds ω_ICE.

Therefore, the ICE fuel-rate, f_ICE(P_ICE|ω_ICE), for the power P_ICE at speed ω_ICE, can be approximated as a piecewise affine function:

(1)

where i=1, 2, …, N_f; and with N_f line segments,  f_ICE,i(ω_ICE) is the fuel-rate at the first point of the power segment i with power P_ICE,I; ξ_i(ω_ICE) is the slope of the segment i. It should be noted that all of the parameters f_ICE,i(ω_ICE), ξ_i(ω_ICE) and P_ICE,i depend on ω_ICE, and the larger ξ_i(ω_ICE), the greater f_ICE(P_ICE|ω_ICE).

The affine relationship of the 5.3 L diesel engine used in our prototype is shown in Fig. 3, where, N_f=5 with maximum error less than 1.8%.

Fig. 3 ICE fuel consumption f(P_ICE|ω_ICE)

The control variables of the energy management controller of the ICE include the ICE power at current ICE speed, (P_ICE, ω_ICE), and the start-up and shutdown command, S_ICE. When S_ICE=1, fuel injection and engine is running; S_ICE=0 indicates engine shut down or stop injection. Thus, at any work point, the ICE’s fuel consumption rate can be expressed as f_ICE(P_ICE|ω_ICE)S_ICE.

As a special case, when the E2FHS is controlled to operate in the series-structural mode, for any ICE power request, P_ICE,i, from an efficiency point of view, it will be beneficial to operate the engine along the optimal operating line, which is the set of those operating points with a minimum fuel consumption rate at any speed, ω_ICE. This line is called the opt-line (optimal line), with a minimum fuel consumption rate at the operating point

                 (2)

For the 5.3l L diesel engine used in our prototype:

      (3)

3.2 ISG and dMG

For convenience, the ISG and the dMG will be simply named the MG. The MG efficiency can be expressed as a non-linear MAP function of MG speed, ω_MG (rad/s), and MG torque T_MG (N·m). But, it is not easy to use such a non-linear MAP function for the optimal energy management control problem [18]. So, the conversion shown in Fig. 4 is implemented. In Fig. 4, the electrical power, P_{MG_e} (kW), is a function of the mechanical power, P_MG (kW), at each speed, ω_MG. In this way, the P_{MG_e} can be approximated to a piecewise affine function of P_MG as follows:

          (4)

where i=1, 2, …, N_MG; MG={ISG, dMG}. And with N_MG line segments, P_{MG_e} and P_MG will take a positive value when MG operates in motor mode and a negative value in generator mode. The parameters P_{MG_e,i}(ω_MG) and ξ_MG,i(ω_MG) depend on motor speed ω_MG. For the i-th speed segment, P_{MG_i}(ω_MG) (kW) is the electrical power when P_MG=0 and at speed ω_MG and ξ_MG,i(ω_MG) is the P_{MG_e} rate of change relative to P_MG at speed ω_MG. Thus, the corresponding efficiency of each MG mode can be defined as

Motor mode:

          (5)

Generator mode:

           (6)

The maximum errors of the ISG (a permanent magnet synchronous motor) and the dMG (an AC induction motor) in our prototype with N_MG=2 are 1.12% and 0.91%, respectively.

Fig. 4 Mechanical power versus electrical power of ISG

3.3 Battery

Since the concern of this work is the actual remaining energy of the battery (especially for PHEV), the parameter state of energy, r_SOE, is used, defined as the ratio of energy stored in battery Q_s(J), to some known maximum energy capacity, Q_batt(J).

The battery efficiency MAP expresses the relationship between the power P_batt (W) at the battery terminals and the net internal power P_{batt_S} (W). If P_batt and P_{batt_S} take a positive value when the battery is discharged, and a negative value when it is charged,  then

               (7)

Because of the different effects of current and temperature on battery efficiency at different r_SOE levels during discharging and charging, P_{batt_S} is different from P_batt. Denoting the measured efficiency through parameter η_{batt_c} during charging, and η_{batt_d}  during discharging, respectively, the relationship between P_{batt_S} and P_batt results in

                 (8)

3.4 Clutch

By controlling the speed of the ISG and the dMG, the rotational speed synchronization of the clutch input side and output side can quickly be achieved, which will help to resolve the problem of clutch wear. This means that there are two states of the clutch during E2FHS operation, denoted by parameter S_clutch:

            (9)

3.5 Electrical power net

Since the resistance of the wire system is generally small, its power loss can be disregarded [19]. Denoting the electrical power demand of all auxiliaries presented in the vehicle through parameter P_aux, the expression of the battery power, P_batt, can be obtained.

Therefore, if P_batt is used as one control signal, the electrical power of the ISG, P_ISG, can be uniquely determined under power of dMG,  P_dMG, and with the request P_aux, the formula f₁(·) is derived:

P_ISG=f₁(P_batt, P_dMG|v, P_aux)                                    (10)

3.6 Powertrain and driver power demand

With further reference to Fig. 1, there are five control inputs: P_ICE, P_ISG, P_dMG, S_ICE and S_clutch. Among the control signals P_ICE, P_ISG and P_dMG, any two control signals are necessary to satisfy the driver’s power demand, P_dem. Although the P_dem is real-time calculated from the driver’s operation signals of the acceleration pedal and the brake pedal, based on the vehicle longitudinal dynamics model, P_dem can be also expressed in terms of vehicle speed and vehicle parameters:

P_dem=(F_road+Mv=f₁(v, S_APP, S_BPP)              (11)

where  is the vehicle acceleration, S_APP is the signal of the acceleration pedal, S_BPP is the signal of the brake pedal, F_road is the total road load acting on the ER-PHEV.

In order to satisfy the driver’s power demand, P_dem, taking P_batt and P_dMG as the control variables, the ICE power, P_ICE, can be immediately determined. Therefore, f₂(·) is derived:

P_ICE=f₂(P_batt, P_dMG, S_clutch|P_dem, v, P_aux)            (12)

Next, with reference to the architecture of the ER-PHEV system in Fig. 1, the rotor of the motor dMG is directly connected to the input shaft of the driving axle. Therefore, the speed of the dMG, ω_dMG, is proportional to the vehicle speed.

As mentioned above, the vehicle will be driven only by the dMG when the vehicle speed is lower than a threshold. Especially, when the vehicle is to start up, the torque demand will be determined only by the acceleration pedal signal, since the vehicle speed is zero. The torque at wheels demanded by the driver, T_veh, is expressed by the driver’s power demand P_dem, the tire radius r_tire and the vehicle speed v as follows:

                 (13)

where δ₃ is the threshold of v.

For the series-structural mode:

for S_clutch=0  (14)

For the parallel-structural mode:

       (15)

where I_ICE+ISG represents the sum rotational inertia of ICE and ISG; η_T is the efficiency of the wheel/axle as a function of vehicle velocity.

4 Adaptive online-optimal controller design

4.1 Objective function

As described above, the energy management controller decides upon the four control variables, i.e. the battery power P_batt, the dMG electric machine power P_dMG, the clutch engaging or disengaging signal S_clutch (0, 1), and the engine-running signal S_ICE(0, 1). By controlling these four variables, the controller aims to obtain minimum fuel costs followed by the battery energy depleting depth for a desired trip distance. The optimal energy management controller follows the solution of a standard optimization problem:

              (16)

where J(u) is the objective function, and G(u) is the constraints on the control variable u. The objective function, J(u), represents the cumulative cost of fuel and electrical energy consumption over an arbitrary driving cycle within time length T. At any time instant t, the system cost function is as follows:

(17)

where the coefficient ζ_fuel is used to convert the fuel consumption rate coefficient (g/s) into equivalent electrical energy (kW·h/s), the coefficient ζ_elec is used to convert the electrical power into kW·h/s, factor  is the price ratio of the fuel equivalent to the electrical energy, and η_grid is the efficiency to recharge the battery from the grid. By means of factor  it becomes possible to further optimize energy management based on the change of the fuel price and electricity price. Therefore, with the minimum total cost as the target, the objective function is as follows:

   (18)

4.2 Constraints

In order to extend the life of the battery, in addition to taking its largest charge and discharging power to reasonable restrictions, it also needs to be within a certain range of r_SOE limits to avoid over-charge or over-discharge. To achieve this, the following constraints must first be introduced:

           (19)

where ω_{ICE_ISG_min}=min(ω_{ICE_min}, ω_{ISG_min}), which is set to the engine idle velocity; ω_{ICE_ISG_max}=max(ω_{ICE_max}, ω_{ISG_max}), which is set to the engine’s nominal velocity. For a city bus usage of the prototype developed in this work, the maximum vehicle velocity is set at v_max=25 m/s, ω_{ICE_ISG_min}=260.8 rad/s. r_{SOE_min} and r_{SOE_max} are set to  be 0.15 and 0.9, respectively. It is noted that P_batt is negative during battery charging and positive during discharging, P_{batt_min} is the maximum charging power and P_{batt_max} is the maximum discharging power, and both of P_{batt_min} and P_{batt_max} are respectively the functions of r_SOE and temperature, also constrained by the maximum/ minimum power of the ISG motor and the dMG motor. Constraining the battery in such a way helps to protect it against capacity and power fade due to over-charging or excessive discharging.

Furthermore, due to inertia effects, the speed of the ICE, ISG, dMG and vehicle speed will have its own maximum acceleration and deceleration. The ICE work process, which decides to change its torque, also has a maximum and minimum rate of change. In terms of the ISG and the dMG, in order to prevent the closed-loop control of torque or the speed from appearing too large to overshoot, its torque output is also with a respective maximum rate of change. From the driving comfort point of view, there is also the need for appropriate restrictions on vehicle acceleration. Comprehensive consideration of these factors gives further constraints as follows:

           (20)

where  and  are the possible minimum and maximum accelerations under current vehicle speed, respectively, given by:

    (21)

where T_{disk_brak}(S_BPP) is the friction torque of the brake disk, which is expressed as a function of S_BPP and equals the remainder in addition to the regenerative brake torque.

For each κ={min, max}, the operator is defined as follows:

    (22)

where T_a is the maximum allowable adhesion for the current vehicle speed, obtained by means of experimental data or an empirical formula. T_{ICE_min}(t) and T_{ICE_max}(t) are the maximum torque rates of change for the current engine speed, also obtained by means of experimental data or an empirical formula. This work seeks to avoid drastic changes in the engine operating conditions which will result in the deterioration of fuel consumption and emissions, in the whole ICE speed range to take -100 N·m/s and 100 N·m/s. Also, for the  and  which respectively represent the maximum decreasing rate and the increasing rate of the ISG torque under the current ISG speed, according to test data, this work takes  =-500 N·m/s and =500 N·m/s. For the dMG, the similar constraints on the rate of torque change,   and  take the same value. Using the model in Section 4, the maximum and minimum speed change rate of the ICE, the ISG and the dMG, can be respectively obtained, also the battery r_SOE maximum and minimum rates of change,  and  can be obtained

According to the optimization problem (16), constraints (19)-(20) need to be rewritten in the format G(u)≤0, and the E2FHS vehicle models are used again. Also, for narrative convenience, the inequalities (19)-(20) can be constrained by Ω_g, namely:

For the PHEV, when the r_SOE is reduced to its lower limit, r_{SOE_min}, the battery should be recharged from grid. However, since the technology for fast-charging, the battery is not yet mature, and also in consideration of the grid load, recharging is usually done in the evening. This requires the vehicle recharging time interval T, vehicle mileage driving user’s expectation mileage, S, and in this mileage with the total cost (35) minimum and at the end of this mileage an expected r_SOE level, r_{SOE_ref}. This is achieved by including an end-point constraint on the energy level of the battery:

 (22)

Equation (22) shows that this optimization problem will be a battery depleting drive process when r_SOE>r_{SOE_ref}. When battery r_SOE drops to r_{SOE_ref}, it will automatically translate into r_SOE balance control around the expected r_SOE level, r_{SOE_ref}. This means that the following adaptive online energy management controller described in this section has a universal nature.

4.3 Online controller design

As mentioned earlier, due to the clutch status having only two values, S_clutch(0, 1), the engine status also has only two values, S_ICE(0, 1), so the problem in Section 4.1 can be decomposed into four sub-problems:

Sub-problem 1: S_ICE=1, S_clutch=1

Sub-problem 2: S_ICE=1, S_clutch=0

Sub-problem 3: S_ICE=0, S_clutch=0

Sub-problem 4: S_ICE=0, S_clutch=1

4.3.1 Sub-problem 1

Sub-problem 1 corresponds to a parallel-structural mode (PHD mode). The objective function (18) of the optimization problem (16) can be simplified as follows:

  (23)

where

       (24)

A new optimization problem is defined by the objective function (23) together with an equality constraint (22). For convenience, it is rewritten into a discrete form assuming that the control interval Δt is a constant value, and there are N time steps during the expected mileage, S, i.e.:

(25)

Subjected to:

   (26)

It is justified that the function F(P_batt(k), P_dMG(k)| P_dem(k), v(k), P_aux(k)) is a convex function at each time instant k, by the shape of the ICE fuel consumption combined with the ISG and dMG model and the battery model. This means that the solution for this optimization problem can be found by incorporating the equality constraint into the Lagrangian function using a Lagrange multiplier λ, and the resulting solution will be a global optimal solution. The following Lagrangian L function is defined:

 (27)

Without loss of generality, assuming that Δt=1, then the optimal solution to the optimization problem (25) with constraint (26) can be obtained by resolving the following set of equations:

                                             (28)

(29)

for k=1, 2, …, N, and 

(30)

Resolving the 2N+1 equations in (28), (29) and (30) can produce the unique optimal solution of optimization problems  The solution λ^*, is calculated from information from the entire driving mileage, which appears as a penalty factor for r_SOE level control, and also represents the cost conversion relationship between fuel consumption and electrical energy. However, if λ^* is known, all 2N equations from (28) and (29) are entirely decoupled. This means that calculating  by (28) and (29) can be undertaken with P_dem(k), v(k) and P_aux(k) only being known at time instant k. As a result, the optimal solution  from (25) and (26) is also found by the following policy at time instant k, i.e.:

       (31)

In order to guarantee that the inequality constraints Ω_g are not violated, the model in Section 4 is used to rewrite the inequality constraints Ω_g in terms of (P_batt, P_dMG). By resolving the inequalities of Ω_g, one new constraint on (P_batt, P_dMG) with a lower bound   and an upper bound  is calculated, respectively. Since the ICE speed must not be lower than its idle speed, ω_{ICE_idle}, for effective power output, and not be higher than its maximum speed, ω_{ICE_norm}, at any time, further new constraints should be introduced for this sub-problem 1:

                           (32)

                           (33)

Again, the model in Section 3 is used to rewrite the inequality constraints, (32)(33), in terms of (P_batt, P_dMG). By combining these boundaries with the above  and  the final new boundaries for this sub-problem are produced, i.e.,  and   respectively, and through these final new boundaries, a feasible solution to this sub-problem is obtained:

             (34)

with the corresponding total cost  of  as follows:

     (35)

Since applying the new boundary constraints to F(P_batt, P_dMG|P_dem, v, P_aux) does not change the convexity of this function, the optimal solution  is unique.

4.3.2 Sub-problem 2

Sub-problem 2 corresponds to a series-structural mode (SHD mode). In this mode, since the clutch is disengaged, constraints (32) and (33) are not needed. This means that only constraint Ω_g is necessary for Sub-problem 2, and the ICE will be controlled to operate along its opt-line (defined in Section 3.1). Hence, the cost function (23) in the objective function (24) is transformed as follows:

By a similar method, the corresponding total cost  of  is resolved as follows:

   (36)

4.3.3 Sub-problem 3

Sub-problem 3 corresponds to one PEVD operational mode (PEVD1 mode). In this mode, since the clutch is disengaged (S_clutch=0) and the ICE is turned off (S_ICE=0), in order to satisfy the driver’s power demand P_dem, and the auxiliaries’ power demand P_aux, the following constraints are introduced to activate this mode.

In the sub-problem, the ICE is turned off, so fuel consumption is zero, and the corresponding total cost of  is as follows:

   (37)

4.3.4 Sub-problem 4

Sub-problem 4 corresponds to another PEVD operation mode (PEVD2 mode). In this mode, since the clutch is engaged (S_clutch=1) while the ICE is turned off (S_ICE=0), power loss exists because the ICE will be dragged by the vehicle. As a result, this mode is usually activated only when the PEVD is necessary because of this constraint (32) while the dMG only cannot satisfy the driver’s power demand. The constraints for this Sub- problem 4 are as follows.

The corresponding total cost for  is as follows:

   (38)

4.3.5 Adaptive algorithm of λ^*

As mentioned above, λ^* is for the entire driving cycle. Therefore, different λ^* is required for different driving cycles. To meet the constraints on the battery r_SOE, the value of λ^* which can take r_SOE to r_{SOE_ref} at the end of the driving cycle is unique for this particular driving cycle. This means that, for the solution of an accurate value of λ^*, the entire driving cycle should be known or it should be possible to accurately predict future driving demands.

However, in the real-world driving process, the deiving cycle is uncertain. Therefore, only the past driving cycle and the present information should be used to realize the adaptive estimation of λ^*. From Eqs. (31) and (35), it can be observed that, if the estimate of λ^* is too large, the battery tends to be fully charged at the end of this cycle or desired mileage, that is r_SOE(T)→100%, and this counters the original goals of PHEVs. On the other hand, if the estimate of λ^* is too small, the battery tends to be depleted and is empty at the end, that is r_SOE(T)→0%, and this does not meet the requirements of constraints (19) and (21). From a control point of view, in order to enable r_SOE to reach the desired level r_{SOE_ref} at the end of mileage S, it should correspond to a leveling control problem where r_SOE should be kept near r_{SOE_ref}. A proportional integral (PI) controller can be used to adaptively adjust the value of λ^* for this requirement online. The control period of the PI controller should be generally small, but not too small, and pre-tuned by analyzing the power spectrum of the E2FHS. The block diagram is shown in Fig. 5, with the value of λ^* as follows:

               (39)

where λ(0) is the initial value of  K_p is the proportion action coefficient; K_I is the integral action coefficient.

Fig. 5 Scheme for estimating

4.3.6 Final controller

The final controller for (P_batt, P_dMG) comprises a combination of all four possible sub-problems. This means that only when a Sub-problem and the corresponding constraints are met with the total cost minimum of the above four sub-problems, the solution of this sub-problem can be selected as the solution of the original problem (16). That is, each sub-problem can have selected conditions:

Sub-problem 1:

         (40)

Sub-problem 2:

               (41)

Sub-problem 3:

               (42)

Sub-problem 4:

               (43)

The final control law for (P_batt, P_dMG) is as follows:

       (44)

       (45)

From the control law for (P_batt, P_dMG) from Eqs. (44) and (45), having selected a sub-problem and its solution, the control variables, (S_ICE, S_clutch), are also uniquely determined. This means that, based on Eqs. (44) and (45), the control signals (P_batt, P_dMG, S_ICE, S_clutch) depend only on the current information of the vehicle, (P_dem, v, P_aux), and the Lagrange multiplier, λ^*. Since λ^* is adaptively calculated online during the vehicle driving process, this indicates that the use of the above-mentioned energy management controller is independent of the future information of the driving cycle. Therefore, this energy management controller is adaptive online for different driving cycles and the real-world driving process.

5 Prototype development

In order to test the E2FHS system and the energy management controller, the prototype for a transit bus is developed. Firstly, a rule-based energy management controller for E2FHS is established, which is used to optimize the parameters of E2FHS and to validate the real-time performance of the adaptive online-optimal energy management controller proposed. It has been proven that a fuzzy logic controller (FLC) has a better effect on fuel consumption compared to other rule-based energy management strategies for the r_SOC balance-type HEVs [20]. The FLC designed for E2FHS is shown in Fig. 6, with three fuzzy input variables, namely, the driver demand torque factor,  the dMG speed, ω_dMG, and r_SOE of the battery, and three fuzzy output variables, i.e. the ICE torque factor,  the ISG torque factor,  and the clutch state, S_clutch. There are 160 rules in this FLC. Among them, according to the driving cycle, the range of the driver demand torque is divided into eight segments (-2-6), where negative values indicate braking torque, and 0 indicates that the torque demand is 0. From the driver’s instructions (accelerator pedal or brake pedal signals), the aggregate demand torque is calculated, and in accordance with the eight segments of the torque,  is determined as input. The clutch state S_clutch has only two values, i.e. 1 indicates the engaged state and 0 indicates the disengaged state. In accordance with the efficiency MAPs of the ICE and the ISG, the working range of the ICE, as well as the working range of the ISG, is divided into six segments, respectively, where 0 indicates that the output torque is 0. The final outputs, including the ICE torque, T_ICE, the ISG torque, T_ISG, the dMG torque, T_dMG, are produced by means of the de-fuzzification model.

Fig. 6 Fuzzy controller for E2FHS energy management

Then, in order to obtain an optimal match for the parameters of the E2FHS, the MatLab/SimuLink software is used to write the simulation software, with the optimized parameters as follows. The definitions of major subsystems are also provided in Table 2. The transit bus with this prototype is shown in Fig. 7, with the basic performance as: the maximum speed is 92 km/h, the pure electric driving maximum mileage is 48 km, and the acceleration time for start-up to 50 km/h is 15.3 s.

Table 2 Specification of E2FHS HEV

Fig. 7 Effects of different energy management controllers on improvement in fuel consumption of E2FHS

6 Results and discussion

As mentioned earlier, for a known driving cycle, the DP-based method is generally considered to be the best fuel economy available for HEVs, so in many researches the DP-based method was used to investigate potential fuel-saving [21]. To this end, the DP-based method is also introduced in this work to examine the effect of the adaptive online-optimal energy management controller in Section 5 on the improvement of the fuel economy of the prototype PHEV transit bus.

For a known driving cycle, through careful tuning of  the fuel-saving effect of the adaptive online- optimal energy management controller with this fixed  is very close to the fuel-saving potential of the DP- based method. Under the four driving cycles of CBDC, UDDS, 1015 and ECE, fuel economy improvement is 65.31%-68.5% by using the DP-based method, with an average improvement of 66.98%.

The test results of the prototype by respectively using the following three controllers are also shown in Fig. 7, where it is seen that:

1) Using a manual carefully calibrated and fixed  fuel economy improvement by means of an adaptive online-optimal energy management controller is 65.11%-68.55%, with an average improvement of 66.77%. The mean difference in comparison with the average improvement value by using DP-based method is only 0.2%, indicating that the adaptive online-optimal energy management controller can be used for the energy optimal control of PHEVs.

2) By using an adaptive online-optimal energy management controller, the  online adaptively adjusted by a PI-controller, for the above four driving cycles, the fuel economy improvement is 64.73%- 67.91%, with an average improvement of 66.21%. The mean difference compared with the average improvement value when  is fixed is only 0.56%. However, it should be noted that, in the test analysis, for four driving cycles,  has been calibrated for the same value initialized to the average of the four values of  tuned in the above test 1) for the four driving cycles, respectively. In these tests, pre-driving is done for each driving cycle in order to automatically adjust  to its optimal value. The numbers of the pre-driving cycle are 16 for CBDC, 12 for UDDS, 13 for 1015 and 17 for ECE, with mileages of 102.6, 153.2, 56.7 and 17.6 km, respectively. These results also further prove that the controller does not need to know the future driving profile in advance, or the self-adaptability.

3) For all four driving cycles, by using the adaptive online-optimal energy management controller, the  online is adaptively adjusted by a PI-controller, and the average fuel economy improvement is 8.77% higher than the average improvement when using the FLC, and 12.63% higher than the average improvement when using the baseline strategy.

In addition to fuel consumption, the plug-in hybrid vehicles also consume electrical energy. Therefore, to reduce their operating costs is often the greatest concern of users and the government. According to China’s current diesel prices and the electricity prices charged at night, the ability of E2FHS to reduce the rate of vehicle operating costs is analyzed and the results are shown in Fig. 8. For the four driving cycles, by using the adaptive online-optimal energy management controller, the  online is adaptively adjusted by a PI-controller and the E2FHS, and the operating costs can be reduced by 62.96%-65.99%, with an average of 64.47%. Compared to FLC and the baseline strategy, the average cost reduction is 9.01% and 12.73%, respectively.

Fig. 8 Effects of different energy management controllers on vehicle running cost reduction of E2FHS

The prototype is tested in the real-world driving cycle, as shown in Fig. 9. Since the transit bus mileage for 1 d is 174.4 km, including eight round-trips with  21.8 km for each round-trip, the fuel rate is limited to 10% per 21.8 km to allow for it to drop.

After 1 d of the 174.4 km pre-test, the fuel economy improvement of the prototype under the real-world driving cycle is 69.34%. Compared with the above standard driving cycles, the rate of fuel-saving is further improved, mainly due to the adaptive online-optimal energy management controller. Therefore: 1) Due to the introduction of constraints Ω_g, the components in E2FHS switch operating points to a stable and less intense transient process to ensure driving comfort, and almost all of the operating points of the ICE and the ISG are

Fig. 9 Real-world drive cycle

concentrated in high-efficiency regions. 2) The electricity consumption in PEVD modes is only 43% of the total electricity consumption, indicating that 57% of electricity is involved in the optimization of energy efficiency. 3) Since on the roads in the downtown areas, traffic lights cause more jams, more idling and stopping, its acceleration is with a lower average speed, so the controller automatically adapts to the characteristics of this real-world driving cycle, with the result that the optimal management of energy flow is realized. 4) The r_SOE drop in a cycle is 9.92%, close to control objectives, equivalent to 4.6%/10 km which is more than 4%/10 km limited in the tests, thereby the fuel consumption is reduced.

7 Conclusions

1) Under each of the typical driving cycles of the United States, Europe, Japan and China, the test results of the PHEV with E2FHS proposed in this work show that the E2FHS can result in significantly improved fuel economy, with an average fuel economy improvement of 12.11% over the series hybrid system and the parallel hybrid system. It also has a lower cost and its features are easier to implement.

2) The adaptive online-optimal energy management controller does not depend on the future vehicle power demand profile, and obtains almost the same effect of energy economy improvement as the improvement potential of the DP-based energy optimization method. It also has good self-adaptability for different driving cycles including the real-world driving cycle. For the prototype transit bus with E2FHS and this controller, the fuel economy improvement is 64.73%-67.91%, with an average improvement of 66.21% which is an average of 8.77%-12.63% higher than the improvement by the fuzzy logic controller and the baseline strategy, and with an average of 9.01%-12.73% lower vehicle operating costs. The fuel economy improvement is 17.17% higher than the improvement by using a parallel hybrid electric system and a fuzzy logic controller, and 24.58% higher than the improvement by using a series hybrid electric system and a fuzzy logic controller.

3) As for the prototype in the real-world running test, the battery r_SOE is precisely controlled to expectation. The requirement of recharging battery from the grid at night is met. After running for 1 d, the controller is adaptive to the optimal state with fuel-saving up to 69.34%.

Acknowledgements

The authors acknowledge their colleagues and students at the Institute of Automotive Electronic Technology of Shanghai Jiao Tong University and the SJTU-NEC Joint Laboratory for their help with the prototype development and preparation of the manuscript.

References

[1] DEMIRDOVEN N, DEUTCH J. Hybrid cars now, fuel cell cars later [J]. Science, 2004, 305(5686): 974-976.

[2] XIONG Wei-wei, ZHANG Yong, YIN Cheng-liang. Optimal energy management for a series–parallel hybrid electric bus [J]. Energy Conversion and Management, 2009, 50(7): 1730-1739.

[3] LIU Jin-ming, PENG Hui. Modeling and control of a power-split hybrid vehicle [J]. IEEE Transactions on Control Systems Technology, 2008, 16( 6): 1242-1251.

[4] WHITE ROB, GM DAIMLER CHRYSLER. BMW premiere unprecedented hybrid technology [J]. Automotive Industries AI, 2006, 186(5): 745-765.

[5] ERDINC O, VURAL B, UZUNOGLU M. A wavelet-fuzzy logic based energy management strategy for a fuel cell/battery/ ultra-capacitor hybrid vehicular power system [J]. Journal of Power Sources, 2009, 194(1): 369-378.

[6] CHAN C C. The state of the art of electric and hybrid vehicles [J]. PROC IEEE, 2002, 90(2): 247-275.

[7] WIRASINGHA, SANJAKA G, SCHFIELD NIGEL, EMADI ALI. Plug-in hybrid electric vehicle developments in the US: Trends barriers and economic feasibility [C]// 2008 IEEE Vehicle Power and Propulsion Conference. Harbin: IEEE, 2008: 1-8.

[8] HELLGREN J. A methodology for the design of cost effective hybrid vehicles [D]. Gothenburg, Sweden: Chalmers Univ. Technol, 2004.

[9] BAUMANN B M, WASHINGTON G, GLENN B C, RIZZONI G. Mechatronic design and control of hybrid electric vehicles [J]. IEEE/ASME Trans Mechatronics, 2000, 5(1): 58-72.

[10] EREN Y, ERDINR O, GORGUN H, UZUNOGLU M, VURAL B. A fuzzy logic based supervisory controller for an FC/UC hybrid vehicular power system [J]. International Journal of Hydrogen Energy, 2009, 34(20): 8681-8692.

[11] SCHOUTEN N J, SALMAN M A, KHEIR N A. Fuzzy logic control for parallel hybrid vehicles [J]. IEEE Transactions on Control Systems Technology, 2002, 10(3): 460-468.

[12] MORENO J, ORTUZAR M E, DIXON J W. Energy management system for a hybrid electric vehicle, using ultra-capacitors and neural networks [J]. IEEE Transactions on Industrial Electronics, 2006, 53(2): 614-623.

[13] BRAHMA A, GUEZENNEC Y, RIZZONI G. Optimal energy management in series hybrid electric vehicles [C]// Proceedings of the American Control Conference. Chicago: IEEE, 2000: 60-64.

[14] AO G Q, QIANG J K, ZHONG Hui, MAO Xiao-jiang, LI Yang. Fuel economy and NO_x emission potential investigation and trade-off of a hybrid electric vehicle based on dynamic programming [J]. Journal of Automobile Engineering, 2008, 222(10): 1851-1864.

[15] LIU Jin-ming, HAGENA J, PENG Hui, FILIPI Z S. Engine-in-the-loop study of the stochastic dynamic programming optimal control design for a hybrid electric HMMWV [J]. International Journal of Heavy Vehicle Systems, 2008, 15(24): 309-326.

[16] AOKI K, KURODA S, KAJIWARA S, SATO H, YAMAMOTO Y. Development of integrated motor assist hybrid system [C]// 2000 SAE. Warrendal: SAE International, 2000: 2000-2059.

[17] AIBERT I, KAHRIMANOVIC E, EMADI A. Diesel sport utility vehicles with hybrid electric drive trains [J]. IEEE Transactions of Vehicular Technology, 2004, 53(4): 1247-1256.

[18] ZERAOULIA M, BENBOUZID M, DIALLO D. Electric motor drive selection issues for HEV propulsion systems: A comparative study [J]. IEEE Transactions of Vehicular Technology, 2006, 155(6): 1756-1764.

[19] LIAN Jing, ZHOU Ya-fu, MA Teng, WANG Wei. Design for motor controller in hybrid electric vehicle based on vector frequency conversion technology [J]. Mathematical Problems in Engineering, 2010, 51(3): 1-22.

[20] LARS J, MATTIAS ?, EGARDT B. Assessing the potential of predictive control for hybrid vehicle powertrains using stochastic dynamic programming [J] IEEE Transactions on Intelligent Transportation Systems, 2007, 8(1): 71-83.

[21] ANTONIOU A I, EMADI A. Adaptive control strategy for hybrid electric vehicles [C]// 5TH IEEE Vehicle Power and Propulsion Conference, VPPC, Dearborn: IEEE, 2009: 242-246.

(Edited by HE Yun-bin)

Foundation item: Project(2007CB209707) supported by the National Basic Research Program of China

Received date: 2010-10-27; Accepted date: 2011-04-11

Corresponding author: YANG Lin, Professor, PhD; Tel: +86-21-34206365; E-mail: yanglin@sjtu.edu.cn