European Journal of Control (2005)11:509–524 # 2005 EUCA
A-ECMS: An Adaptive Algorithm for Hybrid Electric Vehicle Energy Management Cristian Musardo1,, Giorgio Rizzoni2,, Yann Guezennec3, and Benedetto Staccia4 1
Research Department at Renault, France; 2Center for Automotive Research; 3Professor of Mechanical Engineering, Ohio State University, OH, USA; 4McKinsey & Co.
Hybrid electric vehicle (HEV) improvements in fuel economy and emissions strongly depend on the energy management strategy. The control of an HEV with minimum fuel consumption and emissions is a global problem and the control action taken at each time instant affects the following. Thus, dynamic programming (DP) is a well-suited technique to find the optimal solution to the control problem. Unfortunately, this approach to solving the optimal control problem requires a priori knowledge of the driving conditions (necessary to implement the DP backward algorithm) and is therefore not suitable for HEV real-time control. It is shown that it is possible to obtain the global optimal control policy using the instantaneous minimization of a ‘‘well-defined’’ cost function dependent only on the system variables at the current time. The definition of such a cost function requires an equivalence factor for comparing the electrical energy with the fuel energy. This approach is known in literature as equivalent consumption minimization strategy (ECMS). The optimal value of the equivalence factor can be found through a systematic optimization only if the driving cycle is known. In this paper a new control strategy called adaptive ECMS (A-ECMS) is presented. This real-time energy management for HEV is obtained adding to the ECMS framework an on-the-fly algorithm for the estimation
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[email protected] Correspondence to: B. Staccia. E-mail: benedetto_staccia@ mckinsey.com
of the equivalence factor according to the driving conditions. The main idea is to periodically refresh the control parameter according to the current road load, so that the battery state of charge is maintained within the boundaries and the fuel consumption is minimized. The results obtained with A-ECMS show that the fuel economy that can be achieved is only slightly suboptimal and the operations are charge-sustaining. Keywords: Automotive; Hybrid Electric Vehicle; Optimal Control; Real-Time Control; Supervisory Control
1. Introduction Hybrid vehicles are vehicles equipped with at least two different sources of energy. A hybrid powertrain combines two modes of propulsion to achieve results that cannot be obtained with a single drivetrain. In the specific case of hybrid electric vehicles (HEVs) that are discussed in this paper, two sources coexist and one of them is electrical. By virtue of their concept, HEV can offer significant benefits compared with conventional vehicles in reducing pollutant emissions and energy consumption. The presence of an additional degree of freedom for satisfying the driver power demand implies that
Received 10 May 2005; Accepted 20 June 2005. Recommended by E.F. Camacho, R. Tempo, S. Yurkovich, P.J. Fleming.
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Fig. 1. Schematic of a pre-transmission parallel hybrid electric powertrain.
the performance of an HEV system strongly depends on the control of the power split. The objective of this paper is to analyze the problem of the HEV control and to propose a new energy management strategy that achieves fuel economy improvement and pollutant emissions reduction. In particular, the results discussed here refer to the OSU BuckHybrid 2004, a prototype of a pretransmission parallel HEV derived from a Ford Explorer 2002 in order to participate in the 2004 FutureTruck Competition. The generic architecture of a pre-transmission parallel hybrid electric powertrain is sketched in Fig. 1. The internal combustion engine (ICE) is a 103 kW, 2.5 l, direct injection diesel engine made by VM motori and the Electric Motor (EM) is a Siemens 18/32 kW induction motor. The EM is coupled to the drivetrain through a Goodyear timing belt that connects sprockets on both the electric motor shaft and the diesel engine crankshaft. The battery box contains a series string of 150 sealed leadacid two-volt Hawker Cyclon E cells (8 Ahr), creating a nominal package of 300 V. The maximum allowed current is 90 A in discharge mode (positive current) and 60 A in recharge mode (negative current).
2. Vehicle Model Two different approaches to the HEV modeling can be adopted: the backward- and forward-facing modeling with respect to the physical causality principles. The former makes the assumption that the vehicle meets the target performance, so that the vehicle speed is supposed known and the power request is calculated using the kinematical relationships imposed by the drivetrain. Forward-facing modeling, on the contrary, takes as inputs the driver commands and, simulating the physical behaviors of each component, generates the vehicle performance as output. The backward-facing approach is beneficial in simplicity and low computational cost, while forwardfacing, requiring the resolution of the differential motion equation of the vehicle, needs more computational time. However, when the vehicle modeling serves as a platform for the implementation of the control strategy of an actual vehicle, the
forward-facing approach seems more appropriate. In this way, the simulator reflects the actual architecture of the vehicle and the control strategy developed in the simulator can directly be implemented in the actual vehicle. In this paper, a forward quasi-static simulator called vehicle performance simulator (VP-SIM) [1] is used as platform for the implementation of the control strategy of the OSU BuckHybrid 2004. The simulator is developed in the MATLAB/Simulink1 environment and it contains three main blocks in its top layer as shown in Fig. 2: the Driver, the Powertrain and the Vehicle Dynamics block. The software implementation of the Powertrain block is structured to directly resemble the layout of the physical system and its top layer is shown in Fig. 3. The ICE and EM are modeled using steady-state maps of the engine and the motor provided by the constructors. The battery is modeled with a Thevenin equivalent circuit. The open-circuit voltage V1 is considered a function of the battery state of charge (SOC), while the internal resistance Rin is function of the SOC but also of the operating mode (charging/ discharging). These functions are available from experimental data published by the constructor. The SOC is obtained integrating the following differential equation: dSOCðtÞ ¼ IðtÞ, Qmax dt where Qmax is the total charge that the battery can hold. The Driver module compares the desired vehicle speed with the actual vehicle velocity and, through a PI controller, calculates the accelerator or brake commands. These signals are sent to the Powertrain to calculate the tractive force at the wheels. The actual vehicle velocity is then calculated by considering the tractive force and the total force needed to overcome the aerodynamic, grade and rolling resistance. After the simulation is completed, vehicle performance, such as fuel economy, vehicle speed trace, SOC, engine and electric machine operating points, can be displayed. A detailed and complex model as VP-SIM is desirable for evaluating the performance achievable
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Fig. 2. Simulink implementation of VP-SIM.
Fig. 3. Simulink implementation of the pre-transmission parallel hybrid powertrain of the OSU BuckHybrid 2004.
by the actual configuration of the vehicle. However, such a model requires excessive computation time for the calculation of the optimal control policy with advanced control techniques, such as dynamic programming (DP) (see Section 4). For this purpose, a simplified quasi-static backward model is more appropriate. Obviously, the results obtained with the two approaches are not directly comparable. In fact, the presence of the driver implies that the road loads are different and even if the vehicle speed traces
are similar, the torque requests calculated backwards and forwards are rather different. Hence, even the same control strategy would lead to different torque splits and the performances measured with the two models would differ. Thus, the simplified model is retained as base for the comparison of the control strategies presented along this paper. However, the new control strategy proposed here (A-ECMS) is also implemented in VP-SIM, in order to be directly implemented in the actual vehicle.
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3. Problem Statement The essence of HEV control is the instantaneous management of the power flow from the ICE and the EM. The HEV control strategy aims at minimizing the vehicle fuel consumption, while also attempting to minimize engine emissions. These objectives are global, in the sense that the quantity to be minimized is the integral over the whole trip, while the control actions are local in time. Furthermore, the control is subject to integral constrains, such as nominally maintaining the SOC, and local constraints, such as meeting the driver demand and respecting the components limitations. Mathematically, the problem can be formulated as follows (here, pollutant emissions are not taken into account): Z Tf m_ ice ðPice ðtÞÞHLHV dt J Tt ¼ 0 opt fPopt ice ðtÞ, Pem ðtÞg ¼ arg
min
fPice ðtÞ;Pem ðtÞg
JTt , t ¼ 0, ..., Tf
8 Preq ðtÞ ¼ Pice ðtÞ þ Pem ðtÞ > > > < SOCmin < SOCðtÞ < SOCmax 8t subject to > 0 Pice ðtÞ Pice;max ðtÞ > > : Pem;min ðtÞ Pem ðtÞ Pem;maxðtÞ where Preq is the driver power demand, Pem is the power of the electric motor, Pice is the power of the engine, m_ ice( ) is the fuel mass flow rate and SOC is the battery state of charge.
4. Optimal Solution to the Control Problem The energy management of HEV is essentially a global optimization problem whose objective is to determine the power split between the ICE and the EM that minimizes fuel consumption and pollutant emissions. The solution can be seen as a sequence of commands at each time instant that achieves this goal. Since a driving cycle usually lasts hundreds or even thousands of seconds and at each instant tens of possible values of ICE and EM power must be evaluated, it is evident that a ‘‘brute force’’ enumeration of the solutions is not conceivable. A more efficient optimization procedure is provided by DP, instead. This technique is in fact well suited to multistage processes requiring a sequence of interrelated decisions [2,3]. The control of an HEV with minimum fuel consumption and emissions is a global problem and the
control action taken at each time instant affects the following. Thus, DP is a well-suited technique to find the optimal solution to the control problem. The vehicle is considered a discrete dynamic system. A simplified model is necessary to reduce the computational burden of DP. The energy stored in the battery (or equivalently its SOC) is the dynamic state and the power output of the EM is the control variable. The power requested by the driver is determined from the vehicle velocity through kinematical relationships and the cost of each allowed torque split at a given time instant is evaluated by the backward DP algorithm. At the end of it, the trajectory from the initial to the final SOC which minimizes fuel consumption gives the optimal solution, i.e., the sequence of values of power that the EM must provide. The SOC constraint is automatically satisfied by the discretization of the state variable, that is set between SOCmin ¼ 0.6 and SOCmax ¼ 0.8. The fuel consumption obtained with DP for the Federal Urban Driving Schedule (FUDS) is 25.7 mpg (miles per gallon gasoline) and for the Federal Highway Driving Schedule (FHDS) is 26.0 mpg. The operating points of the ICE for those cycles are reported in Fig. 4 and Fig. 5 shows the SOC profiles for those cycles. It is worth noting how the ICE operating points are concentrated in the high efficiency region of the ICE, which explains why HEVs can achieve better fuel economy than conventional vehicles. Moreover, the vehicle is charge-sustaining by construction: the final value of SOC is imposed as initial condition of the DP backward algorithm. The DP approach proposed in this section has the great advantage of dealing in a reasonable time with an optimization problem that would be otherwise impossible to handle. It seems then that DP is the perfect tool for optimal control of HEV, in the sense that it solves the problem and it also finds the optimal solution, but there are some obstacles to its effective use in the embedded control systems of a vehicle. The DP algorithm is based on a fundamental hypothesis. Since it is a global approach to a problem that has a certain extent in time, the problem must be known and well formulated for all its duration. In other words, the driving schedule over which the fuel consumption is minimized must be entirely known at the beginning of the trip. In fact, the final state is the initial condition of the recursive rule. In addition to the critical assumption of a problem formulated in a global way, DP also encounters some practical difficulties: its computational requirement. Even if it is very efficient compared with other approaches, the number of operations that must be carried
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(a)
(b)
Fig. 4. Distribution of the ICE operating points for the optimized hybrid mode: (a) FUDS and (b) FHDS.
out and the amount of data that must be kept in memory lead to a simulation time of several hours on a Pentium IV PC. In conclusion, it is imperative to find a more flexible and cheaper approach to determine the best instantaneous torque split achieving good overall performance. The solution will necessarily be suboptimal, and DP will be a powerful validation tool to compare the new solution to the global optimum.
5. Equivalent Consumption Minimization Strategy As illustrated in the previous section, although DP represents a powerful tool for solving the global optimization problem of energy management of HEV, it is not suitable for real-time applications. In this section, a promising approach to the realtime control is presented. The main idea is to reduce
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(a)
(b)
Fig. 5. Optimal SOC trajectory for (a) FUDS and (b) FHDS cycles.
the global criterion to an instantaneous optimization problem, introducing a cost function dependent only on the system variables at the current time. In general terms, the local criterion can be formulated as follows: At time t: Jt ¼ Jt ðPice ðtÞ, Pem ðtÞÞ opt fPopt ice ðtÞ, Pem ðtÞg ¼ arg
min
fPice ðtÞ;Pem ðtÞg
Jt
subject to
8 Preq ðtÞ ¼ Pice ðtÞ þ Pem ðtÞ > > > > > > < SOCmin < SOCðtÞ < SOCmax
8t
> > 0 Pice ðtÞ Pice;max ðtÞ > > > > : Pem;min ðtÞ Pem ðtÞ Pem;max ðtÞ:
Because of the SOC self-sustainability requirement, the cost function has to take into account not only the
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fuel consumption, but also the variations in the stored electrical energy. To deal with such aspects, various approaches have been proposed. In some cases, a tuning parameter, which is adjusted according to the current SOC deviation by means of a PID controller, is introduced into the cost function minimization [4]. In other cases, the cost function is the sum of all losses in the electrical and thermal paths [5]. Another, more promising approach was used in Refs [6,7]. It consists of evaluating the instantaneous cost function as a sum of the fuel consumption and an equivalent fuel consumption related to the SOC variation (equivalent consumption minimization strategy, ECMS). According to this approach, the instantaneous cost function is the sum of the fuel consumption m_ ice( ) and of an equivalent fuel consumption related to the use of the EM: Jt ¼ m_ ice ðPice ðtÞÞ þ ðPem ðtÞÞ, where the function (Pem(t)) represents the fuel equivalent of the electrical energy. It is clearly recognized that the electrical energy and the fuel energy are not directly comparable, but an equivalence factor is needed. The equivalence between electrical energy and fuel energy is basically evaluated by considering average energy paths leading from the fuel to the storage of electrical energy. The assumption behind this approach is that every variation in the state of charge will be compensated in the future by the engine running at the current operating point. With this assumption the equivalent fuel flow rate owing to the use of the EM is ¼
1 þ sinðPem ðtÞÞ 2
&ðPem ðtÞÞ ¼ sdis
1 Pem ðtÞ batt ðPem Þ em ðPem Þ HLHV
þ ð1 Þ schg batt ðPem Þ em ðPem Þ
Pem ðtÞ , HLHV
where sdis and schg represent the equivalence factors when the electrical energy is discharged, respectively recharged, and can be considered as control parameters of the ECMS approach. Thus, the local criterion at each time t is Jt ¼ m_ ice ðPice ðtÞÞ þ m_ em;equ ðPem ðtÞÞ m_ em;equ
1 þ sinðPem Þ 2
opt fPopt ice ðtÞ, Pem ðtÞg ¼ arg
min
fPice ðtÞ;Pem ðtÞg
Jt
if Preq ðtÞ 0 opt fPopt ice ðtÞ ¼ 0, Pem ðtÞ ¼ Preq g
subject to
if Preq ðtÞ < 0 8 Preq ðtÞ ¼ Pice ðtÞ þ Pem ðtÞ > > > > < SOCmin < SOCðtÞ < SOCmax
8t
> 0 Pice ðtÞ Pice;max ðtÞ > > > : Pem;min ðtÞ Pem ðtÞ Pem;max ðtÞ
ECMS strongly depends on the definition of the equivalent cost of the use of the equivalence factors. Unfortunately, those equivalence factors vary with the driving conditions so that a pair of equivalence factors (sdis, schg) that is suitable for a driving cycle will lead to poor performance or even no charge sustaining conditions for others. An interesting exercise in order to assess the potential of the ECMS approach is to find the pair of equivalence factors (sdis, schg) that minimizes the fuel consumption for a given driving cycle. The overall fuel consumption can be considered as a function of the equivalence factors and a systematic optimization can be used in order to find the equivalence factors that minimize the overall fuel consumption constrained to the SOC sustainability, i.e., final SOC equal to initial SOC. It should be noticed that such a control cannot be implemented in real-time, since the equivalence factors cannot be calculated a priori, i.e., the systematic optimization can be applied only if the driving cycle is known. Using the optimal pair of equivalence factors, ECMS gives 25.7 mpg on FUDS and 25.9 mpg on FHDS, comparable with the results given by DP. Although this strategy cannot be implemented in real-time (since the optimum equivalence factors are not known), the results show the ECMS potential for achieving performance very close to the global optimum. Thus, the ECMS principle represents a promising approach for formulating a control strategy for HEV. This aspect will be discussed in more details in the next section.
6. DP versus ECMS
1 Pem ¼ sdis em ðPem Þem ðPem Þ HLHV þ ð1 Þ schg em ðPem Þem ðPem Þ
¼
6.1. Optimal Solution and Local Minimization Pem HLHV
The most significant indicator of the performance of a control strategy for HEV energy management is the
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fuel economy, expressed in miles per gallon of gasoline. Table 1 summarizes the results obtained with DP and optimal ECMS for some standard driving schedules. The performances in terms of fuel economy are practically the same for the local ECMS solution and the optimal DP solution. Thus, it can be asserted that a very slight suboptimal solution can be achieved with a technique much simpler than the one leading to the optimal policy. The assumptions and the limits of this statement will be extensively discussed in the next subsection. Keeping the focus on the comparison of DP and ECMS, a deeper insight is gained when the SOC profile is analyzed. Figure 6 presents the plot of the SOC obtained with DP and ECMS for a FUDS cycle. The similarity of the two profiles is in line with the fuel consumption results.
Table 1. Fuel Economy for Different Driving Cycles: DP versus ECMS. Driving cycle
ECMS opt
DP
FUDS FHDS ECE EUDC NEDC JP1015
25.7 25.9 24.5 24.7 24.5 25.1
25.7 26.0 24.5 24.8 24.5 25.2
The match of the SOC profiles is the consequence of similar control policies adopted by the two strategies. A detailed view of the EM power profile clearly shows till what point it is possible to state that DP and optimal ECMS give the same solution. In the window of 170 s reported in Fig. 7 as an example, only a few decisions made by ECMS do not correspond to the optimal EM power determined by DP and the two profiles are almost always perfectly superposed. Hence, the correct choice of the equivalence factors allows the ECMS, with an instantaneous minimization carried out without any knowledge of the future, to replicate the solution found with a complex algorithm that analyzes the problem in its full extension. 6.2. The Optimality of ECMS The results shown above are very promising, in the sense that a slightly suboptimal solution can be achieved with a straightforward instantaneous minimization. Nevertheless, it must be pointed out that it is still a theoretical approach that cannot be implemented in a real-time vehicle controller. In particular, it lacks the flexibility necessary to attain optimal performance in every situation. The local minimization would return exactly the optimal solution only if the pair of equivalence factors are perfectly tuned. Their values are strictly cycledependent and can be calculated only for a perfectly
Fig. 6. The DP and ECMS SOC profiles for a FUDS cycle present the same features.
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Fig. 7. The EM power profile obtained with ECMS matches the optimal policy from DP.
Table 2. Optimal choice of the equivalence factors for different driving cycle. Driving cycle
sdis
schg
FUDS FHDS ECE EUDC NEDC JP1015
2.59 2.45 2.55 2.37 2.50 2.50
2.63 2.61 2.65 2.71 2.63 2.73
In conclusion, a local minimization can lead to good performance only when the pair (Schg, Sdis) is optimized for a precise driving cycle. Unfortunately, the system is very rigid and slight deviations from these values can jeopardize the vehicle operations. For a real-time energy management a more flexible solution must be investigated, keeping the performance as close as possible to the global optimum. 6.3. A-ECMS: A Real-Time Control Strategy
known driving schedule. Hence, the ECMS leading to the exact optimal solution would have the same weakness of DP. The drawback is that the optimal choice of (Schg, Sdis) is different for each driving schedule, as reported in Table 2. One may observe that all the values look rather close. Nonetheless, the control strategy is so sensitive to them that the pair that is suitable for the FUDS, for instance, will not be optimal for the FHDS. From a practical standpoint, it means that the strategy should be properly tuned every time that the nature of the driving cycle changes. There is no choice of the parameters that can be performed only once as initialization of the control strategy and applied in every situation. The control performance is very sensitive to the variation of the equivalence factors. In fact, small perturbations of the control parameters lead to noncharge sustaining operation (see Fig. 8).
As explained previously, ECMS calculates the torque split at each time based on an instantaneous minimization of a cost function that depends only on the system variables at that precise moment. The main advantage of such a controller is that it is real-time oriented. In fact, it is computationally cheap and readily accounts for unexpected events. Moreover, it leads to a solution only slightly suboptimal with respect to the DP. Unfortunately, this result can be achieved only with a perfect tuning of the equivalence factors according to the current driving cycle. Additionally, the system is very rigid and slight deviations from these values can lead to unacceptable operations of the vehicle outside the allowed SOC boundaries. Thus, the match of the equivalent cost with the current driving schedule is critical. A real-time energy management for HEV is obtained adding to the ECMS framework a device
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Fig. 8. SOC for optimal and non-optimal parameters: in the latter case a wrong evaluation of the equivalent cost leads to a non chargesustaining behavior.
able to relate the control parameters to the current velocity profile. In this paragraph, an on-the-fly algorithm for the estimation of the equivalence factors according to the driving conditions is presented. The main idea is to periodically refresh the control parameters according to the current road load, so that the SOC is maintained within the boundaries and the fuel consumption is minimized. In particular, the algorithm identifies the mission that the vehicle is following and determines the optimal equivalence factors for the current mission. The mission is built combining past and predicted data, so that a trade off between adaptivity and accuracy on the estimation of the equivalence factors is achieved. In the presence of altitude variations, the prediction of the vehicle velocity is not sufficient to identify the road load. In this case, the use of external information, such as GPS, is necessary to provide accurate data about elevation. If the mission is treated as a short cycle and if its length is such that the overall performance is close to the optimum, a systematic optimization can be used for the determination of the equivalence factors to be applied to the current mission. Thus, at each instant when the equivalence factors must be updated, the algorithm first builds the current mission combining past and predicted vehicle speed and GPS data, then determines the control parameters that minimize the fuel consumption, while respecting the charge sustainability constraint. The resulting
strategy is called adaptive ECMS (A-ECMS), with emphasis on the role of the online adaptive algorithm for the estimation of the equivalence factors according to the current driving conditions. A critical point of the control strategy is the refresh rate of the equivalence factors. Although a high frequency of refresh is suitable for the adaptivity of the algorithm, the computational burden could jeopardize the real-time operation. However, if the equivalence factors do not match the driving cycle for a relatively long time, the system could operate outside the prescribed SOC limits. As explained in the previous paragraph, the use of the prediction allows obtaining the desired adaptivity of the algorithm. Thus, a good choice is to estimate the equivalence factors every k seconds, where k is the prediction horizon. The high-level block diagram of the algorithm is sketched in Fig. 9. The control block diagram points out the feedback introduced by the adaptive device added to the ECMS framework. Without such a mechanism for the online estimation of the control parameters, the ECMS controller would operate in open-loop and, consequently, the system could be unstable. The algorithm on which A-ECMS is based gives to the controller more stability and insensitiveness to the equivalence factors, so that the strategy does not need any tuning or a priori knowledge and can be implemented in real-time applications.
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Fig. 9. Control block diagram of the A-ECMS.
Table 3. Fuel economy for different driving cycles: optimal ECMS with two control parameters, optimal ECMS with one control parameter versus DP. ECMS opt 2 par
ECMS opt 1 par
Driving cycle
sdis
schg
mpg
s
mpg
DP
FUDS FHDS ECE EUDC NEDC JP1015
2.59 2.45 2.55 2.37 2.50 2.50
2.63 2.61 2.65 2.71 2.63 2.73
25.7 25.9 24.5 24.7 24.5 25.1
2.61 2.54 2.60 2.48 2.51 2.69
25.7 25.8 24.5 24.7 24.5 25.1
25.7 26.0 24.5 24.8 24.5 25.2
The core of the A-ECMS is the on-the-fly algorithm for the estimation of the equivalence factors according to the driving conditions. The control parameters for the current mission can be determined using a systematic optimization. This approach leads to an exact estimation of the equivalent cost, but requires solving a bi-dimensional minimization problem. For mission of length of 100 s, the computation burden is still heavy for a real-time implementation. To overcome this drawback, the bi-dimensional problem can be reduced to a one-dimensional nonlinear optimization, assuming a unique equivalence factor for the recharging and discharging mode: sdis ðtÞ ¼ schg ðtÞ ¼ sðtÞ In order to assess the validity of this assumption, Table 3 reports the fuel economy obtained applying the systematic optimization procedure to different regulatory driving cycles with a pair and with a unique equivalence factor, respectively. The performances are practically the same for both optimal ECMS and very close to the DP optimal solution. Thus, the assumption of unique equivalence factor for the recharging and discharging mode can be considered valid and maintains the effectiveness of all the conclusions carried out in the previous chapters. It is worth noting that the equivalence factor s is
always between sdis and schg, so that the unique equivalence factor can be interpreted as the result of an averaging of the equivalence factors in recharging and discharging mode.
6.4. Results The A-ECMS must address the issues related to the implementation of a real-time controller for HEV energy management. Recalling the discussions of the previous chapters, they can be summarized as follows: (1) Minimization of fuel consumption and pollutant emissions. (2) Maintain of the battery SOC (charge-sustaining vehicle). (3) Validity in every driving condition. (4) Causality, i.e., no a priori knowledge required. (5) Real-time implementation. A-ECMS meets the last two requirements by construction. In fact, the use of the prediction in the portion of mission that describes the driving cycle ahead replaces any form of a priori knowledge; the power split actually sent to the powertrain is determined at every time instant, so that even unexpected changes in the road load or driver behavior are
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Table 4. Fuel economy in mpg for regulatory cycles with different control strategies. Pure thermal
DP
Driving cycle
mpg
mpg
FUDS FHDS ECE EUDC NEDC JP1015
22.1 24.8 20.8 23.3 22.2 21.0
25.7 26.0 24.5 24.8 24.5 25.2
ECMS opt
A-ECMS
Improv. (%)
mpg
Improv. (%)
mpg
Improv. (%)
16.4 4.9 18.2 6.3 10.7 20.1
25.7 25.8 24.5 24.7 24.5 25.1
16.3 4.1 18.0 6.2 10.7 19.8
25.5 25.8 24.5 24.7 24.4 24.8
15.5 3.9 17.9 6.1 10.1 18.2
The percent age of improvement over the pure thermal mode is also reported. Table 5. A-ECMS: VP-SIM results. Driving cycle
mpg
SOC fin
FUDS FHDS ECE EUDC NEDC JP10-15
26.3 26.1 22.3 23.7 23.8 25.3
0.695 0.655 0.732 0.701 0.733 0.705
immediately taken into account. This subsection presents the main results proving the effectiveness of A-ECMS in fulfilling all the other requirements as well, and the interest of its introduction in HEV energy management strategies. The first indicator of the performance of the control strategy is the gas mileage achieved over a set of regulatory cycles that reproduce common driving situations and are used for official estimates. Table 4 compares the performance of the optimal solution obtained with DP over the full cycle, the solution obtained with a perfectly tuned one-parameter ECMS and the solution from A-ECMS. All the results are obtained on the simplified backward model already used in the previous sections. As pointed out in the previous sections, the ECMS with an optimal estimation of the equivalent cost gives a suboptimal solution. A-ECMS is also affected by a suboptimality owing to the instantaneous minimization and the approach by mission. However, the degradation of the fuel economy is so slight that it is absolutely acceptable. A-ECMS gives an outcome very close to DP, and it is worth insisting again on a relevant point: among the three possible approaches, A-ECMS is the only one that can be implemented in practice and that can be used in every situation. The two others just represent a valuable benchmark to appreciate the effectiveness of the new control strategy proposed herein. Table 5 reports the A-ECMS results obtained with the full vehicle simulator VP-SIM. Also indicated is the final SOC of the battery; when different from the
initial value of 0.7, its equivalent cost is taken into account in a correction of the fuel consumption of the ICE. It can be noted that the final SOC is always included in the boundaries and the strategy is chargesustaining for every cycle. The simulator used to test the A-ECMS, VP-SIM, is more detailed of the simplified backward model adopted in the study of the DP or ECMS solution. The efficiency of the components is variable and a driver simulator is added to reproduce the action on the accelerator and brake pedal. These differences lead to the discrepancy in the final results obtained with the two models. However, since VP-SIM is better suited for modeling the entire vehicle and its actual control strategy, the rest of the section will present results obtained with this simulator. In order to confirm and analyze the results, the case of FUDS and FHDS cycles is investigated in more detail. Figure 10 shows the SOC profiles. In both the cases the SOC trajectory over time stays within the boundaries. The SOC constraints are fulfilled and the vehicle is overall charge-sustaining. This important achievement is a consequence of the definition of equivalent cost for the use of the EM: when correctly estimated, i.e., when the correct value of s is determined, it implicitly compensates the natural tendency to deplete the battery of the consumption minimization. Comparing these plots to the corresponding SOC profiles obtained with DP (Fig. 5), several differences become evident. Solving the problem by mission introduces oscillations. In fact, when significant changes in the cycle patterns occur, the equivalent cost does not reflect the cycle characteristics and for short periods the SOC deviates from the reference value of 0.7. However, the algorithm reacts to the changed situation and adapts the equivalence factor, thus keeping the SOC within the prescribed limits. The distribution of the ICE operating points confirms the validity of A-ECMS. As shown by the clustering of dots in Fig. 11, the EM motor in recharging mode is often used as a variable load for
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(a)
(b)
Fig. 10. A-ECMS SOC trajectory for (a) FUDS and (b) FHDS cycles.
the ICE, so that the latter can work in the highest efficiency regions. Moreover, the bottom area with lower efficiency is almost completely avoided: in these situations, the ICE efficiency would be very poor and the small power request is satisfied by the EM instead. A real vehicle often operates in very diverse driving conditions, such as urban, highway and even off-road for SUVs. The control strategy that manages the hybrid powertrain must be able to recognize the
current situation and to take the most appropriate actions. In the literature, some pattern recognition procedures have been proposed to identify the cycle characteristics [8]. The control parameters are tuned offline in accordance with each pattern and stored in the memory of the vehicle control unit so that they can be adopted when the corresponding pattern is recognized. However, when the real driving schedule traits do not belong to the family of analyzed patterns, and in particular when grade is added even to those
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(a)
(b)
Fig. 11. Distribution of the ICE operating points with A-ECMS: (a) FUDS and (b) FHDS.
patterns, this technique fails in the estimation of the control parameters. A-ECMS has the major advantage of adapting the equivalence factor online, i.e., with calculations carried out frequently enough to follow the evolution of the driving conditions. The absence of static precomputed maps also provides flexibility with respect to the vehicle characteristics. If a component is changed, or if weariness alters its efficiency, there is no need to reinitialize the vehicle controller. Furthermore, the recurring computation of the control parameter implicitly adds a feedback that reduces the
sensitivity of the control strategy to variations of this parameter. As a proof of the effectiveness of A-ECMS, the algorithm was tested on a real driving cycle that does not belong to the regulatory cycles usually taken as reference. Indeed, it was obtained by measured velocity and elevation data collected during a trip on the hills around Zurich, Switzerland. The velocity and elevation profiles are plotted in Fig. 12. Table 6 compares the fuel economy achieved in pure thermal mode and with A-ECMS. An improvement of more than 20% is obtained.
523
Hybrid Electric Vehicle Energy Management
Fig. 12. Measured velocity and elevation for a real driving cycle around Zurich, Switzerland.
Fig. 13. Distribution of ICE operating points with A-ECMS (Zurich cycle).
Even in a cycle that is very different from the ones used to study and initially test the A-ECMS, the results are encouraging, with the control strategy adding 2 mpg and more to the pure thermal fuel economy. The analysis of the ICE in Fig. 13 confirms and explains this performance. Consistently with
Table 6. Fuel economy for the Zurich cycle. Strategy
mpg
Improvement (%)
Pure thermal A-ECMS
14.5 17.7
0.0 21.9
524
what discussed for other cycles, the control strategy manages the two sources of power so that the ICE operating points are confined as often as possible in the high efficiency regions. In contrast with mild cycles, such as FUDS or FHDS, the presence of a grade requires more power in several circumstances and the ICE sometimes operates close to the maximum torque.
C. Musardo et al.
different category of hybrid vehicles is also under study. Heavy-duty vehicles operating in urban environments such as garbage collection trucks may benefit from hybridization. The series architecture is usually preferred in these cases and there are some differences from the passenger car problem. Nonetheless, because of its flexibility and other numerous advantages, it may be worth investigating the adoption of the adaptive approach of A-ECMS in these applications as well.
7. Conclusion This paper presents a new control strategy for the energy management of HEV called A-ECMS. It is the outcome of a detailed analysis of the two most promising theoretical approaches, i.e., DP and the ECMS. The problem of HEV control with the objective of minimizing fuel consumption and pollutant emissions is global in nature, i.e., it is well posed when it accounts for the entire trip of the vehicle. DP deals with the problem in a global perspective and it is thus capable of finding the optimal solution. Unfortunately, the hypothesis of perfect knowledge of the driving conditions clashes with the characteristics of general purpose automotive applications and is not suitable for real-time applications. ECMS on the other hand, relies only on the information at the current time instant to make a single decision at the same time. No a priori knowledge is required, but the evaluation of the equivalent cost of the use of the electric motor represents a theoretical and practical challenge of difficult solution. DP and ECMS solve the HEV energy management in two opposite ways and it is proved that under certain hypotheses they almost give the same results. Since ECMS has some advantages that make it implementable, contrarily to DP, it is the best candidate for a vehicle supervisory controller. The introduction of the idea of mission allows the determination of the equivalent cost for the current driving conditions and introduces nonlocal information that compensates the lacks of ECMS and recalls a major advantage of DP. The resulting algorithm, A-ECMS, exploits an instantaneous ECMS-like minimization of the fuel consumption, where the equivalent cost is evaluated on the basis of past and predicted data on the driving conditions. The results show that the fuel economy that can be achieved is only slightly suboptimal and the operations are charge-sustaining. As an indication for future work, the impact of the A-ECMS control strategy on pollutant emissions is currently evaluated. The extension of A-ECMS to a
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