REDUCING fuel consumption has always been a major

Transcription

1 494 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 15, NO. 3, MAY 2007 Energy Management for the Electric Powernet in Vehicles With a Conventional Drivetrain John T. B. A. Kessels, Student Member, IEEE, Michiel Koot, Bram de Jager, Paul P. J. van den Bosch, Member, IEEE, N. (Edo) P. I. Aneke, and Daniel B. Kok Abstract The electric power demand in road vehicles increases rapidly. Energy management (EM) turns out to be a viable solution for supplying all electric loads efficiently. The EM strategies developed in this paper focus on vehicles with a conventional drivetrain. By exploiting the storage capacity of the battery, the production, and distribution of electric power is rescheduled to more economic moments. In addition, this paper explores the advantages of electric loads with a flexible power demand. Based on optimization techniques, an optimal offline strategy as well as a causal online strategy are presented. Simulations illustrate the benefits of the EM strategies in terms of fuel economy. The online strategy has also been implemented in a series-production vehicle. Real-world experiments on a roller dynamometer test-bench validate the strategy, but also reveal additional fuel benefits due to unexpected side-effects from the engine control unit and the driver. Measured profits in fuel economy are as large as 2.6%, with only minimal changes to the vehicle hardware. Index Terms Energy management, flexible electric loads, fuel optimal control, road vehicle power systems. I. INTRODUCTION REDUCING fuel consumption has always been a major challenge to the automotive industry. Whereas marketing aspects first gave rise to innovative research, environmental regulations now force the industry to look for alternative solutions. Historically, the research concentrated on improvements for the mechanical side of the vehicle. However, due to the growing electric power demand, the electric power supply can no longer be neglected [9], [16]. Moreover, the introduction of hybrid electric vehicles (HEV), where the propulsion power can also be delivered by an electric machine, contributes to even higher electric power demands. As indicated in [20], energy management (EM) becomes more and more important for the electric power net, such that the fuel request and the corresponding emissions remain limited. Manuscript received May 26, 2006; revised October 29, Manuscript received in final form February 23, Recommended by Associate Editor J. Buckland. J. T. B. A. Kessels and P. P. J. van den Bosch are with the Department of Electrical Engineering, Technische Universiteit Eindhoven, 5600 MB Eindhoven, The Netherlands ( j.t.b.a.kessels@tue.nl; p.p.j.v.d.bosch@tue.nl). M. Koot and B. de Jager are with the Department of Mechanical Engineering, Technische Universiteit Eindhoven, 5600 MB Eindhoven, The Netherlands ( m.w.t.koot@tue.nl; a.g.de.jager@tue.nl). N. P. I. Aneke is with the Hybrid Vehicle Technologies Team, Ford Forschungszentrum Aachen GmbH, D Aachen, Germany ( naneke@ford.com). D. B. Kok is with the Micro Hybrid Systems and Energy Management Group, Ford Dunton Technical Center, Basildon, SS15 6EE, Essex, U.K. ( dkok@ford.com). Color versions of Figs. 2, 3, 5, 7, and 8 are available online at ieee.org. Digital Object Identifier /TCST In general, it is expected that EM should be applied only in combination with an HEV. However, a traditional vehicle with a conventional drive-train and a belt-driven alternator also offers freedom for EM. Conceptually, the topology of a parallel HEV looks similar to a traditional vehicle, although the power through the alternator is limited to one direction. Moreover, the size of the electric machine in an HEV is much larger as it provides tractive force to the wheels. In combination with a suitable battery pack, the additional investments for an HEV are currently rated between $3000 and $7000, see [18]. This initiated the following question: What can EM offer in a traditional vehicle, without the need for additional investments in vehicle hardware? With primarily changes in vehicle software, the return on investment is high. Nevertheless, the absolute fuel profits will be limited, because the mechanical power demand is far more dominant than the electric power request in a traditional vehicle. An EM strategy uses the storage capacity of the battery when the power from the alternator does not match the power request of the electric loads. This concept has two disadvantages: first, temporarily storing energy always brings additional losses and, second, the storage device wears out faster. To overcome both problems, this paper also considers electric loads with a flexible power demand. In this way, the power request from the loads can be adapted to the generated power. Loads with a flexible power demand are characterized by the fact that they accept, up to a certain level, more or less power, without significant performance degradation for the driver. Especially heating and cooling functions are suited for this purpose, as shown in [2]. With only minor changes to the vehicle, it is possible to implement an EM strategy that takes into account two degrees-of-freedom: the power from the alternator and the power to the electric loads. The power to the battery is controlled indirectly. For convenience, the alternator power control problem will be called power supply management (PSM), whereas PSM extended with additional freedom for the electric loads is captured by power distribution management (PDM). Earlier publications on PSM and PDM appeared in [14] and [12], respectively. Over the years, much research has been carried out in the field of EM for HEVs (see, e.g., [25] for an extended overview). A technique that has been applied by many researchers is dynamic programming (DP) [4]. This optimization technique provides an optimal control law for EM within the accuracy of the discretized state-space. However, the future driving cycle must be exactly known. Due to the computational demand, a strategy based on DP is generally not suitable for online implementation, but the results are often used as a benchmark for other strategies, /$ IEEE

2 KESSELS et al.: ENERGY MANAGEMENT FOR THE ELECTRIC POWERNET 495 Fig. 1. Overview of powerflow signals in the vehicle. see [15]. Moreover, PDM uses a 2-D state-space, so the required memory resources increase exponentially when a higher accuracy for the discretized state-space is preferred. One can also obtain an optimal control law using alternative optimization techniques such as linear programming (LP) and quadratic programming (QP). Here, the work of Tate and Boyd [21] is an excellent starting point and provides a well-defined LP-problem. Compared to DP, the LP and QP methods avoid excessive memory usage or extreme calculation times while handling a multidimension state-space. Furthermore, these methods are easily incorporated into a model predictive control framework [6]. This way, the added value of additional prediction information can be analyzed using a prediction horizon with variable length. For the research presented here, the QP-method is applied as a benchmark for other strategies. It turns out that an EM strategy becomes very conservative if only limited prediction information is available and if the strategy has to guarantee a preferred energy level in the battery at the end of the prediction horizon. To overcome this problem, EM strategies are developed that introduce an equivalent fuel cost for the energy exchange with the battery, see, e.g., [17] and [19]. The EM strategy developed in this paper follows a similar reasoning, but differs from existing strategies through the equivalent fuel cost parameter that incorporates both a mathematical and a physical explanation. A practical solution is presented to determine this parameter online in the vehicle. Furthermore, the EM strategy can handle loads with a flexible power demand and it includes a tuning mechanism to prevent battery wear. The strategy has been analyzed in a simulation environment and validation is done with vehicle experiments on a roller-dynamometer. This paper is organized as follows. Section II presents the vehicle model that is used for strategy development. The concept behind EM is explained in Section III, whereas a formal control problem is formulated in Section IV. By means of QP, Section V presents an optimal offline control law and Section VI derives an online strategy. The simulation environment and the vehicle implementation is explained in Section VII. An overview of the results is presented in Section VIII. Finally, the strategies are evaluated in Section IX and the conclusions are given in Section X. The drive-train model calculates the mechanical power request W as well as the engine speed [rad/s] from the speed profile of the driving cycle. The ICE converts fuel into mechanical power. This power goes to the drivetrain for vehicle propulsion and a small portion goes to the alternator. The alternator is connected to the powernet, so electric power can go directly to the electric loads or it can be stored in the battery. The battery model consists of an efficiency map followed by an integrator to keep track of the energy level in the battery. The PSM strategy allows freedom in, whereas the PDM strategy allows freedom in both and. The engine model is described by a nonlinear static map which specifies the relation between the fuel massflow, engine power, and engine speed where (1) The notation with the conditional-operator is introduced to emphasize the dependency between and. In literature, fuel maps are often presented as a function of engine torque and engine speed. However, the engine torque can be derived from the engine power if the engine speed is known, so these maps represent identical information. Using a similar approach, the alternator model is captured by a nonlinear static map, expressing the mechanical power as a function of the electric power W where (2) Obtaining an accurate model of the battery is part of ongoing research. In this paper, the battery model consists of two blocks. The first block introduces the energy losses between the power at the battery terminals and the net stored/retrieved power W (3) For simplicity, the losses in the battery depend only on the actual battery power, but it is very well possible to extend this model with additional parameters such as the actual energy level in the battery or its temperature. More details about the function will be given in Section V. The second block in the battery model keeps track of the energy level by means of a simple integrator J (4) Furthermore, it is assumed that the energy capacity of the battery is fixed. Consequently, the relative energy level in the battery can be denoted by the quantity state of energy (SOE) SOE (5) II. VEHICLE CONTROL MODEL The PSM and PDM strategy make use of a power-based vehicle model, see Fig. 1. In this model, the internal combustion engine (ICE) and the alternator rely on quasi-static maps. Because the EM system does not interfere with the vehicle dynamics, these models are sufficiently accurate. III. DIRECTIONS FOR IMPROVING FUEL ECONOMY As indicated in Section I, many energy management concepts are known from the literature. What these concepts have in common, is that they reshape some of the basic properties of the ICE such that the overall energy request is delivered with higher

3 496 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 15, NO. 3, MAY 2007 Fig. 2. Normalized efficiency map of SI-engine: max ( ;!)=1. efficiency. This will be demonstrated in this section, using a suitable representation for the engine s fuel map. By nature, there exists a strong relation between the engine s fuel consumption and its power delivered at the crankshaft. Taking only into account the engine speed and the crankshaft torque, the momentary fuel consumption can be described with a static function, in [grams per second]. The engine efficiency describes the ratio between the mechanical output power and the chemical input power. Given the chemical energy content of fuel [J/g] (typically 44.5 kj/g for gasoline), the efficiency equals - (6) A typical (normalized) efficiency map of a spark ignition (SI) engine is shown in Fig. 2. Although efficiency maps are widely used in EM strategies, directions to improve the fuel economy are hardly visible in this representation. For convenience, consider the efficiency map in Fig. 2 for rad/s r/min. Here, the efficiency increases rapidly in the low torque region, whereas the efficiency remains almost constant at higher torque levels. This suggests that the engine characteristics are rather nonlinear. However, as will be shown next, an ICE has typically piecewise linear behavior and the steep slopes in the efficiency map are due to the fuel-offset at zero torque. To that end, the fuel map is reconsidered but now with respect to engine power, using separate curves for different engine speeds as defined in (1). These new fuel-curves are drawn in Fig. 3, using the same data as used for the efficiency map from Fig. 2. Typically, the slope of these curves remains constant in several areas This quantity expresses the equivalent fuel cost, as it indicates the additional fuel massflow to produce a certain amount J (7) Fig. 3. Fuel consumption matches piecewise linear function. of mechanical power. With help of this definition, the map can be approximated as a piecewise affine function if if if (8) where denotes the fuel cutoff point and indicates a point close to the maximum engine power. Note that all parameters,, and depend on, although its influence on is limited g/j. This immediately puts a limitation on the possible benefits of any EM strategy, as will be explained in the following. The power to the drivetrain, in combination with the power demand of the alternator, determines the operating point of the ICE. The situation where the engine power exactly matches the power demand for the drivetrain plus the electric load request is called baseline (BL). By definition, BL implies that the battery is not used, so. There are two reasons why shifting the engine s operating point away from BL could be economically attractive. First, producing more power with the engine is a valid action as long as the additional fuel request remains small. Second, producing less power is favorable when the fuel use decreases significantly. Both observations follow directly from the actual value of. So discharging of the battery takes place if becomes large and charging should be done when is small. Note that regenerative braking also fits in this framework. Regenerative braking refers to the situation when the vehicle is slowing down while the electric machine recuperates free braking energy and stores it in the battery. This provides electric energy without any fuel costs (i.e., ) and should be applied as much as possible. Different from a traditional vehicle, the friction brakes are only activated if the alternator power is insufficient to achieve the desired vehicle deceleration. During regenerative braking, the engine has moved to its fuel cutoff point so it will be limited to situations where.as a result, the engine drag torque puts a serious limitation on the energy available for regenerative braking, since this torque level determines the location of.

4 KESSELS et al.: ENERGY MANAGEMENT FOR THE ELECTRIC POWERNET 497 IV. PROBLEM DEFINITION In this work, the control objective of an EM system is to improve the vehicle s fuel economy, although the reduction of particular tail-pipe emissions is done in a similar way. The primary energy source in the vehicle is the ICE, whereas the storage capacity of the battery offers freedom to schedule the driver s electric power request over time. Furthermore, the flexible electric loads offer additional freedom to maximize the fuel economy. For developing an EM strategy with optimal performance, the control problem is formulated as an optimization problem subject to (9) The cost function is selected such that it represents the vehicle s fuel use over an arbitrary driving cycle with time length where (10) (11) and defined in (2). Note that the decision variable covers two variables: the internal battery power and the power to the electric loads. The corresponding control variable is calculated afterwards using (2) and (3). The constraints in are due to physical limitations of components as well as the requirement to have a charge sustaining vehicle. The operating range of the engine, the alternator, and the battery is limited in power, so inequality constraints are introduced on the minimum and maximum power flow of these components (12) (13) (14) A charge sustaining strategy claims that the battery satisfies a minimum SOE level at the end of the driving cycle. This can be achieved by including an end-point constraint on the energy level of the battery (15) where is an arbitrarily selected reference value that should be satisfied at, e.g.,. Finally, constraints on are used to characterize the energy and power demand of the electric loads. It is assumed that all individual loads can be aggregated and this results in a separate power and energy constraint (16) (17) V. QUADRATIC PROGRAMMING Finding the optimal solution for the problem defined in the previous section is computationally demanding. To come to a solution close to the global optimal solution, the original problem is approximated with a QP problem. Such a QP-structure is characterized by a quadratic cost function, subject to linear constraints subject to (18) where and are matrices and and are (column) vectors of appropriate dimensions, as defined in the remainder of this section. The decision variable is a column vector. A. Model Reduction To derive a quadratic description for the cost function (10), the models of the individual components need to be reduced. For the engine map, a (piecewise) linear approximation will be used (19) The parameters and are state dependent and are selected such that they represent a local fit of the fuel map in the area. In practical situations, the fuel map of an engine is obtained by measuring its fuel consumption at a finite number of grid points. These grid points cover the entire operating area of the engine. Compared to the power range of the alternator, this is a relatively coarse grid and, therefore, it is acceptable to approximate the fuel consumption by a local linear fit. The efficiency of a conventional alternator varies according to its operating point between 40% and 80%. Similar to the ICE, these large variations are due to friction losses and they have a dominant effect when the alternator generates no electric power. Measurement data shows that the mechanical input power increases almost proportionally with the output power. Only at higher power levels do these losses increase more than proportionally. For that reason, the alternator map is approximated by a quadratic fit (20) The parameters,, and are speed dependent. They approximate the alternator map over its entire power range at a certain engine speed. According to impedance spectra measurements of a lead-acid battery [5], it is known that the losses in the battery increase for higher power flows. Moreover, the impedance changes when charging or discharging the battery. Consequently, a battery model incorporating linear and quadratic losses is used (21) In Fig. 4, the contribution of each individual term is shown. The parameter represents the quadratic losses, whereas

5 498 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 15, NO. 3, MAY 2007 The decision variable all periods for and in (18): covers and yields the following description (25) (26) with (27) and Fig. 4. Parameters in battery efficiency model. and indicate the piecewise linear losses for charging and discharging, respectively. In this work, these parameters are estimated from experimental data. However, they can also serve as a tuning parameter to limit the actual battery usage of the EM strategy. That is, incorporating more losses in the battery model than actually present in reality will discourage the EM strategy from using the battery as an energy storage buffer. Because battery usage is strongly related to battery wear, the parameters,, and turn out to be a tradeoff between battery wear versus performance from EM. B. QP Formulation The battery model described in (21) cannot be directly included in the QP-framework of (18). Fortunately, the restrictions on,, and guarantee that (21) is always a convex function. As shown in [7], it is possible to reformulate the expression with an auxiliary variable subject to (22) After replacing the second term in (21) with (22), this new expression is substituted into (20) with. The substitution of (20) into (19) then results in a fourth-order expression between fuel use and battery power. Because a quadratic relation is needed for a QP-structure, a second-order Taylor approximation has been applied, leaving out the higher order terms. To that end, the decision variable has been changed into the zero-mean variable, representing the deviation from the average load power (23) The cost criterion in (10) is rewritten in discrete time with sampling interval over periods (24) (28) All constraints given in (12) (17) have to be written as linear constraints on the decision variables. Due to the losses in the battery model, the relation between and is nonlinear, see (21). Therefore, one cannot use a linear combination of and to replace the constraint on. To circumvent this problem, the energy losses in the battery model are neglected during constraint handling, so is assumed to be equal to at this point. Now, it is possible to write (12) as a linear constraint on and by using the inverse of (20) and selecting the correct solution. Also, (13) appears as a linear constraint, whereas the implementation of (14) is trivial. Note that these new constraints allow slightly more freedom than the original problem, but differences are very limited. Finally, the three constraints are aggregated into one constraint for each period (29) The end-point constraint in (15) on the energy level in the battery becomes (30) The requirements on the power and energy to the loads are written in terms of. For the constraint in (16), this is rather straight forward and for each period (31) The energy constraint from (17) needs to be evaluated in all periods, resulting in constraints (32) Altogether, a driving cycle with periods leads to decision variables and constraints in the QP-structure from (18).

6 KESSELS et al.: ENERGY MANAGEMENT FOR THE ELECTRIC POWERNET 499 C. Model Predictive Control (MPC) The optimization problem previously formulated requires the entire driving cycle be known in advance. In real-world driving situations, this will be practically impossible. However, the idea that the vehicle speed can be predicted in the near future is certainly realistic. With only minor changes, it is possible to put the QP-problem into an MPC framework, see [3] and [23]. Instead of performing the optimization in (18) over the entire driving cycle, it will be limited to a prediction horizon of periods. Only the first value of the resulting control sequence is implemented, whereas the calculations are repeated each time instant with updated state and prediction information. The implementation of this MPC strategy in a simulation environment shows that a reduced prediction horizon for (24) and (30) puts a serious limitation on its performance, see Section VIII. Particularly, the end-point constraint (30) forces the strategy to keep the battery close to such that it resembles the BL situation. This end-point constraint is only a method to guarantee a charge sustaining solution. Section VI presents an alternative solution by reformulating this constraint. VI. ONLINE STRATEGY This section presents a causal EM strategy, which is again derived from the original problem definition. It does not rely on prediction information through a relaxation of the end-point constraint from (30). A. Strategy Analysis First, consider the problem definition from (9) without the inequality constraints. In the situation of PSM, the electric load cycle is predefined and the optimization problem reduces to one decision variable (33) Now assume that at the end of the trip the energy in the battery matches its initial starting value. This way, the end-point constraint changes into an equality constraint (34) using a Lagrange multiplier,. A similar approach has also been followed by Guzzella in [10], but can be found already in [22]. The following Lagrangian is defined: (36) Physically, this new objective function makes sense because it weighs the energy change of the battery with the actual fuel consumption of the engine. The quantity [g/j] represents the corresponding fuel cost when energy is stored or taken from the battery. It is clear that there exists a strong relation between this quantity and the definition of as given in (7). Nevertheless, only considers the fuel costs from the ICE, whereas the influence from the electric machine and the battery is not included there. The minimum value for is found by putting the derivatives equal to zero (37) (38) In the case where is a strictly convex function, there exists a unique solution for this set of equations. Typically, the solution of is calculated with information about the entire driving cycle. However, if is known, the sequence,, can also be calculated by an optimization at the present moment (39) So far, all calculations have been done with decision variable, but the control variable is the alternator power. Therefore, a description for the battery losses in (3) is required. For convenience, the description from (21) is taken with only linear losses present, so and the overall battery efficiency equals. The inverse battery model satisfies the following description: A new problem definition is formulated for the minimization of (33) in combination with the equality constraint (34). For convenience, it is written in discrete time but the sampling interval has been omitted Using (40), the minimization from (39) is rewritten with the optimization variable (40) as subject to (35) A solution for this optimization problem can be found by incorporating the equality constraint into the Lagrangian function (41) This last minimization procedure is illustrated in Fig. 5. The optimal value for follows from the point where the distance between the curves and is minimal. There are three locations where the minimum can appear:,, or. The situation with becomes more favorable if the battery losses increase.

7 500 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 15, NO. 3, MAY 2007 Fig. 6. Feedback diagram for estimating ^. Fig. 5. Objective function with minimum distance at P. In case or, the exact setpoint for the alternator power is described by and, respectively (42) (43) Altogether, the corresponding battery power is described by the following control law: (44) In this framework it is easy to include the power limitations of the alternator. Given the maximum alternator power, the battery power is restricted to, so (44) is extended to (45) Finally, the situation with PDM is considered, where the power to the electric load offers additional freedom. Similar to the required energy in the battery at the end of the driving cycle, the loads also require a certain amount of energy at the end of the trip. As such, the load power is calculated in a similar manner as (46) The minimum and maximum power to the loads is restricted by (16). Incorporating these constraints leads to the following setpoint for : (47) B. Optimal Performance This online control strategy achieves the highest fuel benefits if is calculated correctly. Moreover, each driving cycle requires a different to obtain a preferred energy level at the end of the driving cycle. Notice that charging is done more frequently for higher values of. On the other hand, discharging the battery is less preferred when increases. As a result, there exists a unique solution for where the energy exchange with the battery is balanced and the SOE at the beginning and end of the driving cycle are equivalent. C. Adaptive Strategy Instead of calculating offline in advance, one could make an online estimation,. The method that has been selected here results in an adaptive strategy as presented in [14]. Although different approaches are known from the literature (e.g., zone control, see [23]), this method enables the online EM strategy to achieve a performance close to the optimal MPC strategy, described in Section V. The basic idea is that the SOE of the battery indicates whether is estimated correctly or not. In case has been selected too small, the battery becomes depleted in the end. Conversely, when is selected too high, the battery becomes fully charged. From a control point of view, this corresponds to a leveling control problem where the SOE should be kept near a nominal value SOE. A proportional integral (PI) controller with a rather small bandwidth fulfills this requirement. The block diagram is shown in Fig. 6, with equal to with an initial guess. A. Simulation Environment VII. EXPERIMENTAL VALIDATION (48) For analyzing the EM-strategies, a simulation environment has been developed that describes the Ford Mondeo vehicle. This is a midsize series-production vehicle with a gasoline engine and a five-speed manual transmission. The simulation model is built around a dynamic forward-facing drive-train model, including a dynamic model for the driver. The main components are listed as follows. Driver: To control the speed of the vehicle, a PI-controlled driver model is applied. The output signals are the three pedal positions: throttle, brake, and clutch. The initial parameter settings for the driver are taken from literature, see [1]. Drivetrain: The drive-train model covers the longitudinal dynamics of the vehicle. It describes the relation from the engine to the wheels and consists of the clutch, transmission, final drive, and chassis. It is based on the ADVISOR model [24], but differs from it by being forward facing. This means that it converts the input torque from the ICE into a rotational speed for the wheels using a dynamic drive-train model. Powernet: The traditional SLI-battery (Start, Light, and Ignition) is replaced by a valve-regulated lead-acid (VRLA) battery, which can handle much more charge/discharge cycles before it wears out. The simulation model

8 KESSELS et al.: ENERGY MANAGEMENT FOR THE ELECTRIC POWERNET 501 makes use of an impedance-based battery model as described by Buller et al. [5]. Furthermore, an advanced alternator (1.6 kw, voltage controlled) replaces the standard alternator. This allows the EM strategy to control the power from the alternator. Finally, the electric loads that are present in the vehicle are represented as one lumped load in the simulation model. All the vehicle components are developed in Matlab Simulink and are structured in separate library blocks. Experimental results from a test vehicle on a roller-dynamometer are used to validate the drive-train model and the exhaust gas emissions. In addition, separate tests are executed to validate the electric power net model. An extended overview of the simulation model and its validation procedure can be found in [11]. TABLE I OVERVIEW OF EVALUATED STRATEGIES follows the setpoints from the EM strategy, whereas the average load remains 250 W through adaptation of the restrictions on in (16) B. Vehicle Implementation The strategy has been implemented in the Mondeo vehicle using a MicroAutoBox from dspace. The alternator has been modified such that its output voltage is not fixed but follows a voltage setpoint. A VRLA battery with a capacity of 60 Ah replaces the original 12-V battery. During the vehicle tests, special attention is given to the interaction between the engine control unit (ECU) and the alternator. In the original vehicle configuration, the alternator sends a status-signal to the ECU about its present electric load. Given this information, the ECU adds a feedforward signal to the engine fueling system, such that it anticipates quick changes in the alternator power. However, this feedforward compensation leads to extra fuel injection during regenerative braking. Therefore, a by-pass of the alternator signal is done when the EM-strategy is implemented in the vehicle. It turns out that the original configuration also benefits from this alternator by-pass in terms of fuel economy. Unfortunately, the vehicle tests with the baseline configuration include this feedforward signal. As presented next, further research is needed on the interaction between the ECU and the fueling system to improve the accuracy of the simulation environment. At the moment, the feedforward signal is not present in this environment. C. Evaluated Strategies The standard driving cycle for vehicle homologation in Europe is the New European Driving Cycle (NEDC). This cycle exactly prescribes the vehicle speed and the gearshifts for a trip of 1180 seconds. Based on this driving cycle, four different EM strategies are evaluated: BL, BL 250 W, PSM, and PDM. The BL configuration refers to the original vehicle configuration with a fixed alternator voltage at 13.7 V. In line with the official NEDC regulations, configuration BL corresponds to the native engine load, which is approximately 220 W. Unfortunately, this load is always present, and to validate the concept of PDM, more flexibility in the power demand is desired. This is achieved with an external electric load connected to the powernet. For the configuration BL 250 W, this extra load adds 250 W to the native engine load along the entire driving cycle. With PDM, this load with if if (49) (50) In the simulation environment, both the offline and the online strategies are evaluated for PSM and PDM. The simulation with the offline MPC strategy is done in two steps. First, the signals and are recorded during a pilot simulation with configuration BL. Next, these signals are used as prediction information in a second simulation with the MPC strategy. It has been verified that differences between the first and second simulation for and are sufficiently small. Otherwise, further iterations would be required. The real-world experiments are executed with the online strategy from Section VI and these experiments are done with a cold and hot engine start. In the simulation environment this is not possible because the engine model is only valid for a hot engine. Table I provides a brief overview of all strategies that are considered in Section VIII. The MPC strategy calculates its control law by solving (18) with the cost criterion (24) and constraints (29) (32). The control law for the online PSM strategy is given in (45), using (42) (43), and the online PDM strategy applies (45) (47). Note that for PSM the value of is predefined by the driving cycle and is not calculated by the EM strategy. VIII. STRATEGY RESULTS A. Influence of Prediction Horizon The influence of the prediction horizon is evaluated with the QP method from Section V in an MPC-framework. Fig. 7(a) shows the reduction in fuel consumption, whereas Fig. 7(b) illustrates the total amount of energy stored in the battery. Both the PSM and PDM strategy are simulated for receding horizons of increasing lengths, and s. When the prediction horizon reaches the end of the driving cycle, the

9 502 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 15, NO. 3, MAY 2007 TABLE II OVERVIEW OF SIMULATION RESULTS (HOT-ENGINE START) TABLE III OVERVIEW OF ROLLER-DYNAMOMETER EXPERIMENTS Fig. 7. Influence of prediction horizon on (a) fuel use and (b) battery use. control law is no longer updated and all remaining control actions are taken directly from that time instant. The results for battery wear in Fig. 7(b) are normalized with respect to - (51) The first observation from Fig. 7(a) is that the achieved fuel reduction with PSM and PDM is ultimately bounded. Moreover, the fuel benefits increase rapidly until and remain almost constant for a higher prediction length. This behavior can be explained as follows. The end-point constraint in (30) becomes very dominant for short predictions. That is, the EM strategy acts conservative when is small, because it has to guarantee the preferred energy level in the battery at the end of the prediction horizon. Moreover, the vehicle speed determines the operating point of the ICE and, consequently, the equivalent fuel cost as defined in (7). As shown in [8], the frequency spectrum of gives insight into the minimum length of the prediction horizon, so the speed profile of the NEDC is closely related to the required prediction length. To obtain a performance close to the optimal situation, an accurate speed prediction of at least s is required, but due to uncertainties these predictions are not readily available. As a result, a different EM concept is preferred that does not rely on lengthy predictions, but still achieves a similar performance. This is achieved with the online strategy, by relaxing the end-point constraint. Finally, one can extend the information in Fig. 7 with an extra parameter for the efficiency of the battery model (3). By including extra losses in the battery model, the EM strategy tends to follow the baseline strategy and hence, decreases. Given the cycle life of the battery, it is up to the designer to optimize the tradeoff between fuel benefits and battery wear. B. Results From Experimental Validation An overview of the simulation results and the results from the roller-dynamometer experiments is given in Tables II and III, respectively. Each strategy has been tested at least two times on the roller-dynamometer, and Table III presents average results. The columns in these tables cover the following information. : Initial SOE of the battery. Each baseline strategy starts with a completely charged battery, so SOE 100%. The PSM and PDM strategies start at SOE SOE 75%. : This column expresses the average measured electric load profile along the NEDC. The electric load request from the vehicle experiments has also been used in the simulation environment. Fuel mass and : Knowledge about the vehicle s fuel economy is shown in these columns. The engine map in the simulation environment denotes the actual fuel massflow of the engine, so the simulation model directly provides the fuel consumption along the driving cycle. This is different with the vehicle experiments, where the tailpipe emissions are measured instead of the injected fuel massflow. A good representation for the vehicle s fuel consumption is the tail-pipe carbon dioxide CO emission. The measured CO emissions are shown in grams per kilometer and the relative reduction in CO emissions will be used to calculate the benefits in fuel economy, see the last column. : The final SOE level reached at the end of the driving cycle is indicated in this column. Fuel eco: The improvement in fuel economy for a particular strategy is calculated here. The values are calculated without taking differences between SOE and SOE into account. The signals of interest from one vehicle measurement (using the PSM strategy) are shown in Fig. 8 over the last 600 [s] of the NEDC driving cycle. In this figure, the following information is shown: the speed of the vehicle, the position of the accelerator pedal, the alternator power, and the SOE of the battery. This figure also includes the corresponding signals from the simulation model. The accelerator pedal reveals that the human driver spends considerable more effort to follow the desired speed profile than the simulation model. The EM strategy makes use of

10 KESSELS et al.: ENERGY MANAGEMENT FOR THE ELECTRIC POWERNET 503 TABLE IV MODEL UNCERTAINTIES AND INFLUENCE ON FUEL ECONOMY (FE) Fig. 8. Control actions with PSM strategy (hot-engine start). the pedal positions to estimate the engine s operating point. This explains why fluctuations in the accelerator pedal show up as variations in the alternator power setpoint during the vehicle measurements. Although the switching profile of the alternator power is much richer in the vehicle tests, its average behavior is similar to the simulation model. This follows from the SOE curves which remain close to each other. IX. EVALUATION AND DISCUSSION The results in Tables II and III provide, among other things, insight in the improvement in fuel economy. All strategies achieve an improvement between 1.1% and 2.6%, whereas SOE is close to SOE. The following three observations are contrary to the expectations and will be clarified in this section. First, the vehicle experiments achieve a better performance than expected from simulations. In simulations, PSM and PDM achieve a fuel reduction of 1.5% and 1.1%, respectively. This is significantly lower than in the vehicle experiments, where the profits for PSM vary between 2.6% and 2.4% (cold and hot engine) and PDM achieves a fuel reduction of 1.4%. Second, the simulation results reveal that the offline and online strategies achieve equal performance, although no predictions are used for the online strategy. Finally, the last observation is that the profits with PDM are lower than with PSM, whereas higher profits are logically expected. A. Differences Between Simulations and Experiments It turns out that the simulation environment suffers from three dominant model inaccuracies: 1) the PI-controlled driver model has a limited complexity, compared to a human driver; 2) the alternator status-signal is not present in the simulation environment; and 3) the engine speed is not compensated for alternator power changes. As will be shown next, these elements prevent the simulation environment from achieving results similar to the vehicle experiments. 1) The PI-controlled driver model follows the desired speed profile perfectly and the accelerator pedal changes smoothly, see Fig. 8. Because the accelerator pedal is related to the engine operating point by means of the ECU, less variation is also recognized in the operation point of the engine. These variations are a necessity for an EM strategy and, hence, the simulation model offers less opportunities for EM. For validation, different parameter values are assigned to the driver model to emulate the overshoot from a human driver. Depending on the tuning-parameters of the PI-controlled driver, the cumulative fuel use changes around. Although this effect is relatively small, it confirms that there is a correlation. 2) As discussed in Section VII, the feedforward signal from the alternator to the ECU is not present in the simulation environment. Only the vehicle tests with the baseline strategy use this signal. Additional simulations have been done with a baseline strategy that includes a tentative feedforward signal. Depending on the bandwidth of the PI-controlled driver, additional fuel consumption is seen. An accurate driver with a high bandwidth experiences only minor influence from the feedforward signal and the fuel consumption of the baseline strategy increases around 0.5%. On the other hand, a driver with a low bandwidth is not able to counteract the feedforward signal at undesired moments (e.g., during vehicle deceleration). Here, the baseline strategy requires additional fuel up to 1.0%. In general, one can draw the conclusion that ignoring the alternator feedforward signal during deceleration phases is not only profitable for the EM strategy, but also for the baseline strategy as well. 3) Another side-effect of increasing the alternator power when there is no feedforward signal present, is that the vehicle decelerates. This can be compensated by the human driver, but especially during braking phases, this extra braking force is often preferred. The vehicle experiments point out that a vehicle with the EM strategy travels at a lower engine speed during the deceleration phases. Although the differences are rather small, the average engine speed over the entire driving cycle reduces approximately 6 [r/min]. Simulations with this reduced engine speed indicate an extra fuel benefit of 0.3%. An overview of the model uncertainties that limit the profits in fuel economy of the simulation results is shown in Table IV. The cumulative uncertainty is of similar size as the improvement in fuel economy shown by PSM or PDM in the simulation environment. Adding the model uncertainties to the simulation results is sufficient to close the gap with the roller-dynamometer experiments. Nevertheless, this large uncertainty indicates that the model for the driver and the ECU have limited validity. Due to accuracy limitations of the roller-dynamometer, more accurate measurement data are currently not available, but further research is needed to obtain adequate models for the driver and the ECU.

11 504 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 15, NO. 3, MAY 2007 B. Similar Performance With Offline and Online Strategies Theoretically, the MPC strategy achieves a better fuel economy than the online strategy because it relies on exact prediction information from the future driving cycle, whereas the online strategy does not use this a priori knowledge. In practical situations, however, the computational power is limited and the offline strategy uses a discrete sampling period of s. On the other hand, the online strategy has a low computational demand and its sampling interval has been selected equal to s. In this way, the online strategy is able to anticipate quick events and achieves a performance close to the MPC strategy. Note that the extra fuel benefits will be small in the simulation environment due to the moderate driver behavior. However, during vehicle experiments, this higher sampling frequency becomes relevant because of more intensive driver behavior. C. Lower Profits With PDM Than With PSM Conceptually, PDM offers more freedom for energy management than PSM, because PDM controls two design variables (the alternator power and the electric load demand), whereas PSM is restricted to only one variable (the alternator power). Therefore, it is expected that PDM achieves better fuel economy. However, the increased electric load demand that has been selected for PDM dominates the results of the experiments. Due to the extra load of 250 W, the alternator reaches its power limitations more often, leading to less freedom for the PDM strategy. Furthermore, the baseline strategy also recovers a fraction of the free kinetic energy during vehicle deceleration and this fraction becomes larger when the electric load increases. This observation is extensively discussed in [13] and points out that the advantage of PDM with respect to the baseline becomes less visible if the electric load increases. D. Discussion Although the online strategies do not enforce a fixed energy level for the battery at the end of the driving cycle, they are able to finish the NEDC driving cycle close to, by means of the PI-controller. From other simulations it is known that the differences between SOE and SOE as indicated in Table III have less than 0.1% effect on the fuel economy. As a result, no correction methods are used when calculating the absolute benefit in fuel economy. So far, no attention has been paid to the vehicle experiments with a cold engine start. Before the EM strategies were tested, vehicles experiments are done with the baseline strategy and a cold engine start. According to the measured relation between fuel use and engine coolant temperature, the assumption was made that temperature only influences the fuel offset, rather than the slope of the fuel curves. Considering the objective function in Fig. 5, it becomes clear that the location of is only affected by the slope from and not by its offset. Hence, the EM strategy requires no modifications for a cold engine start and the PSM and PDM algorithms do not take the temperature of the ICE into account. Remarkably, the results from Table III show that driving the NEDC with a cold engine start offers more potential for EM than starting this trip with a hot engine. This means that the influence from the ICE temperature is not well understood. In future work, temperature aspects have to be considered for further refinement of the EM strategy. X. CONCLUSION EM strategies are developed for the electric powernet in a conventional vehicle. As a benchmark, an offline strategy has been defined that solves a QP optimization problem in an MPC framework. In addition, a causal online strategy has been developed that does not rely on prediction information. Additional freedom for EM is obtained by introducing electric loads with a flexible power demand. Furthermore, all strategies have the opportunity to include extra losses in the battery model. This allows the designer to make a tradeoff between battery wear and fuel economy. To obtain performance that is close to the optimal solution, the offline MPC strategy requires a prediction horizon of more than 100 [s] for a typical driving cycle. On the other hand, the online causal strategy achieves a similar performance without using any prediction information. This strategy is directly suitable for implementation in a vehicle. The causal EM strategy has been implemented in a Ford Mondeo vehicle. A roller-dynamometer test-bench has been used to validate the control actions of the strategy. The tailpipe emissions are measured to obtain insight into the achieved profits in fuel economy. From the vehicle experiments it can be concluded that EM has a positive effect on the vehicle s fuel economy up to 2.6%. This result is better than expected from simulations. In particular, the behavior of the human driver as well as the communication between the alternator and the ECU are not well modeled in the simulation environment and explain the deficiencies currently seen in fuel economy. Further refinement of the simulation model requires more advanced vehicle experiments, gaining more in-depth knowledge of the driver and the ECU and how the EM strategy interacts with them. The present roller-dynamometer experiments also show that typical vehicle aspects (e.g., a cold engine start) require more understanding, in order to utilize the full potential of EM. ACKNOWLEDGMENT The authors would like to thank the people from the Alternative Powertrains and Energy Management Group, Ford Forschungszentrum Aachen (FFA), for their valuable discussions and their technical support. 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Kessels (S 04) received the B.Sc. degree (with honors) in electrical engineering from Fontys Hogescholen, Eindhoven, The Netherlands, in 2000, and the M.Sc. degree (cum laude) in electrical engineering from the Technische Universiteit Eindhoven, Eindhoven, The Netherlands, in 2003, where he is currently pursuing the Ph.D. degree in electrical engineering, Section Control Systems. His research interests include the field of automotive control applications. Michiel Koot received the M.Sc. degree in mechanical engineering and the Ph.D. degree from the Technische Universiteit Eindhoven, Eindhoven, The Netherlands, in 2001 and 2006, respectively. His dissertation was entitled Energy management for vehicular electric power systems. Currently, he is a Research Fellow with the Technische Universiteit Eindhoven in a project focused on hybrid electric trucks. His research interests include control of mechanical systems, optimization, and energy management for hybrid vehicles. Bram de Jager received the M.Sc. degree in mechanical engineering from Delft University of Technology, Delft, The Netherlands, and the Ph.D. degree from the Technische Universiteit Eindhoven, Eindhoven, The Netherlands. Currently, he is with the Technische Universiteit Eindhoven. He was with Delft University of Technology and Stork Boilers BV, Hengelo, The Netherlands. His research interests include robust control of (nonlinear) mechanical systems, integrated control and structural design, control of fluidic systems, control structure design, and application of symbolic computation in nonlinear control. Paul P. J. van den Bosch (M 84) received the M.Sc. degree (cum laude) in electrical engineering and the Ph.D. degree in optimization of electric energy systems from Delft University of Technology, Delft, The Netherlands. After his study, he joined the Control Systems Group, Delft University of Technology, and was appointed Full Professor in control engineering in In 1993, he was appointed Full Professor in the Control Systems Group of Electrical Engineering at the Technische Universiteit Eindhoven, Eindhoven, The Netherlands, and in 2004, a part-time Professor at the Department of Biomedical Engineering. His research interests include modeling, optimization, and control of dynamical systems. In his career, he has created many common research projects with industry, among others automotive applications, large scale electric systems, advanced electromechanical actuators, and recently, embedded systems and biomedical modeling. Dr. van den Bosch was a recipient of several prizes for his educational activities and several patents. He has served in boards of journals (Journal A) and conference committees. N. (Edo) P. I. Aneke was born in Delft, The Netherlands, in He received the M.Sc. degree in applied mathematics from the University of Twente, Twente, The Netherlands, in 1998, and the Ph.D. degree in mechanical engineering with emphasis on system modeling and control system design from Eindhoven University of Technology, Eindhoven, The Netherlands, in In 2003, he joined the Ford Motor Company and the Vehicle Electronics and Controls Group. In 2005, he joined the Hybrid Vehicle Technologies Team and is currently working on the development of hybrid electric vehicles. His main fields of expertise include vehicle dynamics, vehicle electronics and controls, and software design and development. Daniel B. Kok was born in 1968 in Hertogenbosch, The Netherlands. He received the B.Sc. degree from the Hogere Technische School Automotive Engineering, Apeldoorn, The Netherlands, in 1991, the M.Sc. degree in mechanical engineering from the Eindhoven University of Technology, Eindhoven, The Netherlands, in 1994, and the Ph.D. degree in 1999, where his dissertation was entitled Design Optimisation of a Flywheel Hybrid Vehicle. In 2000, he joined the Ford Research Center, Aachen, Germany. From 2001 until June 2005, he was responsible for Research and Advanced Engineering activities on Energy Management and Hybrid Electric Vehicles. Since July 2005, he has been a Technical Leader of Micro-Hybrid Systems and Energy Management at the Ford Dunton Technical Center, U.K. In 1994, he joined the Automotive Engineering Group, Faculty of Mechanical Engineering, Eindhoven University of Technology, as a Research Associate. From 1999 to 2000, he worked as Project Leader at TNO Automotive, Delft, The Netherlands, on a series Hybrid Electric Vehicle.