Fuel reduction potential of energy management for vehicular electric power systems. Michiel Koot,* John Kessels, Bram de Jager and Paul van den Bosch

Transcription

1 112 Int. J. Alternative Propulsion, Vol. 1, No. 1, 26 Fuel reduction potential of energy management for vehicular electric power systems Michiel Koot,* John Kessels, Bram de Jager and Paul van den Bosch Technische Universiteit Eindhoven, P.O. Box 513, 56 MB, Eindhoven, The Netherlands Fax: *Corresponding author Abstract: In the near future a significant increase in electric power consumption in vehicles is to be expected. To limit the associated increase in fuel consumption and exhaust emissions, smart strategies for the generation, storage/retrieval, distribution and consumption of the electric power can be used. This paper considers a vehicle configuration with a conventional drive train. Two energy management strategies that control the alternator power are analysed: a regenerative braking strategy and a more advanced strategy based on optimisation techniques. The potential behind these strategies is analysed by studying the typical characteristics of components that are directly related to the energy flow in the vehicle. It is shown that operating the internal combustion engine at the highest efficiency will not inherently lead to the lowest fuel consumption. Subsequently, engineering rules are presented to evaluate the performance that can be expected for each strategy. The component characteristics are included as input parameters to make the method generally applicable. To show the value of the engineering rules, the potential fuel reduction is computed for a specific vehicle configuration and driving cycle and compared with simulations results. Keywords: vehicular electric power systems; energy management; regenerative braking; mild hybrid electric vehicles; fuel reduction. Reference to this paper should be made as follows: Koot, M., Kessels, J., de Jager, B. and van den Bosch, P. (26) Fuel reduction potential of energy management for vehicular electric power systems, Int. J. Alternative Propulsion, Vol. 1, No. 1, pp Biographical notes: Michiel Koot received an MSc in Mechanical Engineering from Technische Universiteit Eindhoven, Eindhoven, The Netherlands, in 21. Currently, he is a PhD student with the Dynamics and Control Technology group, Department of Mechanical Engineering, Technische Universiteit Eindhoven. His research interests include control of mechanical systems, optimisation and energy management for automotive vehicles. John Kessels received an BSc in Electrical Engineering from Fontys Hogescholen, Eindhoven, The Netherlands in 2, and the MSc in Electrical Engineering from Technische Universiteit Eindhoven in 23. Currently, he is a PhD student in the Control Systems group, Department of Electrical Engineering, Technische Universiteit Eindhoven. His research interests are modelling and control of the electric power supply system in vehicles. Copyright 26 Inderscience Enterprises Ltd.

2 Fuel reduction potential of energy management 113 Bram de Jager received his MSc in Mechanical Engineering from Delft University of Technology, Delft, The Netherlands, and the PhD from Technische Universiteit Eindhoven. He was with Delft University of Technology and Stork Boilers BV, Hengelo, The Netherlands. Currently, he is with Technische Universiteit Eindhoven. His research interests include robust control of (non-linear) mechanical systems, integrated control and structural design, control of fluidic systems, control structure design, application of symbolic computation in non-linear control. Paul van den Bosch received his MSc in Electrical Engineering and the PhD in Optimisation of Electric Energy Systems from Delft University of Technology. After his study he joined the Control Systems group in Delft and was appointed full-time Professor in Control Engineering in In 1993, he was appointed full-time Professor in the Control Systems group, Department of Electrical Engineering, Technische Universiteit Eindhoven and in 24, additionally, a part-time Professor in the Department of Biomedical Engineering. His research interests concern modelling, optimisation and control of dynamical systems. He has served in boards of journals (Journal A) and conference committees. 1 Introduction The vehicular electric power system, or simply power net, usually consists of an alternator that generates electric power, a storage device, such as a battery and the various electric consumers in the vehicle (Emadi et al., 23). In the last two decades, the electric power consumption in automobiles increased significantly, approximately 4% every year, and in the near future, even higher power demands are expected (Kassakian et al., 1996, 2; Nicastri and Huang, 2). Reasons for this trend are: the introduction of the drive-by-wire concept which replaces mechanical and/or hydraulic components by electrical devices customers expect more safety and comfort in new vehicles. For example the features such as active suspension or video entertainment at the back seat. An overview of the total current and expected energy use in various transportation sectors is given by Ortmeyer and Pilay (21). At this moment, the average electric power consumption in modern vehicles ranges between 2 W and 1 kw, depending on the vehicle and its accessories (Kassakian et al., 2). Considering the fact that a belt-driven 14 V alternator typically supplies 1.5 kw at full load, power limitations cannot be neglected in the forthcoming years. In the mid-199s, several automobile manufacturers already realised this problem and started considering new methods to overcome this problem. One of the most promising proposals is to introduce an advanced power net, operating at a higher nominal voltage level. These topologies make use of high-power components and offer new challenges for energy management to improve the overall energy efficiency of the vehicle.

3 114 M. Koot et al. Especially the so-called 42 V PowerNet has been extensively discussed in the literature, (see, e.g. Ehlers et al., 21; Emadi et al., 23; Kassakian et al., 1996, 2; Nicastri and Huang, 2). For this power net, several new topologies are defined, to meet tomorrow s power requirements. Although these advanced power nets will be able to meet tomorrow s power requirements, a problem that now arises is how to control the power net, so as to obtain maximum fuel economy within the vehicle. One way is to improve the efficiency of electric components such as the alternator (Liang et al., 1999). Another way is to extend the power net with alternative components, such as an Ultra Capacitor (Miller and Everett, 24; Sebille, 23). In addition, an energy management strategy can be used which schedules the amount of energy that is stored in the battery, such that fuel consumption and emissions are reduced. Energy management is often applied to Hybrid Electric Vehicles (HEV), where the electric machine is also used for propulsion, (see, e.g. Back et al., 22; Delprat et al., 24; Johnson et al., 2; Lin et al., 23; Schouten et al., 22; Sciarretta et al., 24; Scordia et al., 25). The 42V power net topology considered in this paper can be seen as a scaled version of a conventional 14 V power net. An advanced alternator (i.e. power controlled) is connected to the electric loads and the battery. At its mechanical side, the alternator is connected to the engine s crankshaft with a belt. In this way, the electric power delivered by the alternator influences the operating point of the engine. An energy management strategy can control the alternator power such that all electrical loads receive their requested power and simultaneously the combustion engine runs in more favourable operating areas. Figure 1 shows how the energy management controller interacts with the vehicle. On the basis of information of the current state of the vehicle and the possible prediction of the future vehicle state, the electric power setpoint is provided to the alternator and a feed forward torque compensation is given to the engine. Figure 1 Energy management controller in the vehicle Brakes / Clutch / Gear Driving Cycle Driver Throttle Electr. load + Combustion Engine Crankshaft Drive Train Vehicle speed Fuel Energy storage Vehicle signals Energy Management Controller Trq. compensation Alternator setpoint Alternator Electr. power net Electric Load In Koot et al., (25), this energy management problem is formulated as an optimisation problem and an online implementation strategy has been derived. In addition to that work, this paper presents a physical analysis and, subsequently, a set of engineering rules that estimate what performance can be expected, regarding the typical characteristics of the components. This makes it easy to predict the influence of component sizing when designing a vehicle.

4 Fuel reduction potential of energy management 115 The rest of this paper is structured as follows: the vehicle is modelled in Section 2. The concept of energy management including regenerative braking is handled in Section 3. The engineering rules to predict the performance of an energy management strategy are presented in Section 4. In Section 5, the expected performance is compared with simulation results. Finally, conclusions are given in Section 6. 2 Vehicle model and component characteristics 2.1 Power flow in a vehicle This paper focusses on conventional vehicles with a manual transmission. The structure of such a vehicle is represented as a power-based model in Figure 2. The drive train block contains all drive train components including clutch, gears, wheels and inertia. The alternator is connected to the engine with a fixed gear ratio. Figure 2 fuel Power flow in a conventional vehicle Engine P m P d Drive Train P g Alternator P e P b Battery P s Es Efficiency P l Electric Load The power flow in the vehicle starts with the fuel that goes into the combustion engine. The mechanical power that comes out of the engine splits up into two directions: one part goes to the drive train for vehicle propulsion, whereas the other part goes to the alternator. The alternator provides electric power to the electrical loads, but also takes care of charging the battery. The power flow to the battery can be positive as well as negative. In the end, the power becomes available for vehicle propulsion and for the electrical devices connected to the power net. The goal of energy management is to control the alternator power such that the fuel consumption is reduced, while the drivability remains unaffected, that is, the driver should not experience different vehicle behaviour when the controller is applied. This requirement greatly reduces the problem complexity. It implies that the vehicle speed and thus the drive train torque and engine speed remain unaffected and therefore it is possible to use them as given information. The remaining components of interest are the engine, the alternator and the battery. Using a sampling interval of 1 sec or more, their dynamic behaviour is neglected, so their characteristics are represented by static models. The only remaining dynamics in the model is an integrator for the energy storage in the battery. 2.2 Fuel converter The Internal Combustion Engine (ICE) can be represented by a non-linear static map that describes the fuel rate ṁ as a function of the engine speed ω, and the torque delivered by

5 116 M. Koot et al. the engine τ m. For a given engine speed, the mechanical power delivered by the engine P m can be derived from the engine torque as follows: P m = ωτ m (1) Using this relation, the fuel map can also be written as a function of engine speed and power: ṁ = f(p m,ω) (2) A measured fuel map of a 2. litre Spark Ignition (SI) engine is displayed in Figure 3. In this figure, the fuel consumption curves are drawn for different engine speeds as a function of mechanical power. As can be seen, the fuel map can approximately be represented by a linear relation between the mechanical power and the fuel rate for each engine speed: f(p m,ω) f (ω) + k f P m (3) h f The fuel consumption at zero torque f (ω) is caused by mechanical friction and pumping losses in the engine. It increases with the engine size, the number of cylinders and the engine speed. The dimensionless factor k f has a typical value around 2.5, which corresponds to a combustion efficiency of 4%. Parameter h f is the lower heating value of fuel, that is, the chemical energy content of fuel, with a typical value of 44 kj/g for gasoline and 49 kj/g for diesel. Figure 3 Fuel map of an SI engine 1 Fuel Map Fuel Use [g/s] Mechanical Power [kw] In automotive engineering, several different forms are used to visualise the fuel consumption of an ICE. The absolute fuel consumption can be normalised with respect to the power delivered by the engine. This so-called Brake Specific Fuel Consumption (BSFC) is defined as β ICE = ṁ = ṁ (4) P m ωτ m which is usually expressed in kg/kwh.

6 Fuel reduction potential of energy management 117 The efficiency of the engine is the ratio of the ingoing chemical power to the outgoing mechanical power and is inverse to the BSFC: η ice = P m P f = ωτ m h f ṁ = 1 h f β ice (5) The efficiency is usually visualised as a contour plot of engine speed and torque, as is done in Figure 4. The efficiency at low torques is low, because there the term f (ω) is relatively large. Figure 4 Characteristic efficiency map of an SI engine 2 Efficiency Map [%] Engine Torque [Nm] Engine Speed [rpm] 1 As can be seen in Figure 4, the operating range of the fuel converter is bounded by a drag torque and a maximum torque that are both speed-dependent. Translated to power, this becomes P m min (ω) P m P m max (ω) (6) The drag torque is defined as the engine torque when no fuel is injected: f (ω) + k f h f P m min = P m min (ω) = h f k f f (ω) (7) The fuel map can then also be described as ṁ = k f h f (P m P m min ) (8) The fuel consumption over a driving cycle can be computed by m = te ṁ dt = k f h f te (P m P m min )dt (9)

7 118 M. Koot et al. 2.3 Alternator The alternator can be represented by a static non-linear map that describes the mechanical power as a function of the electrical power and the rotational speed. A measured map of a 42V 5 kw alternator is presented in Figure 5, which shows smooth and almost linear behaviour. Figure 5 Alternator map 7 Alternator Map 6 Mechanical Power [W] Electric Power [W] Similar to the engine, the alternator can be approximated by a linear relation between the electrical power P e and the mechanical power P g with a constant slope k g : P g = g(p e,ω) g (ω) + k g P e (1) The slope k g has a typical value around 1.25, which corresponds to an incremental efficiency of 8%. g (ω) is caused by mechanical friction and increases with the speed. The operating range of the alternator is bounded between: where P e P e max (ω) P g min (ω) P g P g max (ω) (11) P g min (ω) = g (ω) and P g max (ω) = g (ω) + k g P e max (12) 2.4 Battery The battery characteristics can be modelled by P b = P s + P loss (P s,e s,t) (13) where P b represents the power entering or leaving the battery terminals and P s represents the power actually stored in the battery. P loss represents the battery losses that depend on the stored power, the energy level in the battery E s and the temperature T.

8 Fuel reduction potential of energy management 119 In the rest of this paper, the battery losses are ignored, so (13) reduces to P b = P s (14) The energy level in the battery is given by a simple integrator: t E s (t) = E s () + P s (τ) dτ (15) The State Of Charge (SOC) represents the relative energy level in the battery: SOC = E s E s max 1% (16) 2.5 Drive train The drive train consists of clutch, transmission, final drive, wheels and inertia. They need not be modelled in detail, only the relation among vehicle speed, engine speed and drive train torque is of interest. For a given vehicle speed profile v(t), road slope α(t) and selected gear ratio g r (t), the corresponding engine speed and torque needed for propulsion can be calculated using the following formulas: ω(t) = f r w r g r (t) v(t) (17) F d (t) = M v(t) ρc d A d v(t) 2 + MgC r sign(v(t)) + Mg sin(α(t)) (18) τ d (t) = w r 1 f r g r (t) F d(t) (19) P d (t) = ω(t)τ d (t) (2) When the engine speed drops below a certain value, the clutch is opened. Then the drive train torque becomes zero and the engine runs at idle speed. The parameters are explained in Table 1. Table 1 Parameter explanation Symbol M A d C d C r w r f r g ρ Quantity Vehicle mass Frontal area Air friction coefficient Rolling resistance Wheel radius Final drive ratio Gravity Air density

9 12 M. Koot et al. 3 Energy management Energy management strategies shift the operating points of energy converting components, such that the losses are reduced. In the situation considered in this paper, only the alternator power is controlled, thereby shifting the engine torque, which should lead to a lower fuel consumption. This section takes a closer look at the fuel consumption characteristics of an engine and explains how fuel savings can be obtained. 3.1 The difference between efficiency improvement and fuel reduction As can be seen in Figure 4, the efficiency of the combustion engine varies drastically over the operating range. This may give the impression that a large fuel reduction can be obtained by a small shift in engine torque, by manipulating the alternator power. It will be shown here, that this is not the case. It is easy to assume that increasing the efficiency will result in a lower fuel consumption. In some situations this is true, for example, the gear shifting problem where the requested engine power is predefined and freedom exists in the engine speed by selecting the optimal gear shifting pattern. Because the engine power is fixed at each time instant, a higher efficiency corresponds with a lower fuel rate and results in a lower fuel consumption for a driving cycle. However, the energy management problem considered in this paper is not solved by simply bringing the engine to an area with a higher efficiency. In a vehicle with a conventional drive train and manual transmission, the engine speed is controlled by the driver, so only the engine torque can be altered. Figure 6 shows the fuel rate versus power for a particular engine speed. The power required for propulsion, is indicated by P d. Depending on the requested alternator power P e, the engine moves to the operating point P m = P d + P g. The corresponding change in fuel consumption ṁ depends directly on the slope of the fuel map and the alternator map. Figure 6 Explanation of the incremental cost Fuel rate m [g/s] m P d P d +P g Engine power P m [kw]

10 Fuel reduction potential of energy management 121 This leads to the definition of the incremental cost λ: λ = P f ṁ P g = h f (21) P e P m P e Electric energy can be produced cheaply at moments when λ is low. Therefore, an effective strategy should compare the incremental cost at each time instant and store electric energy when λ is low and retrieves it when it is high. This does not correspond to shifting the engine to the high efficiency area. This can be seen in Figure 7, where a linear, a convex and a concave fuel curve and their corresponding efficiency curves are drawn. For all the three cases, the efficiency increases with increasing power because the fuel consumption at zero power f (ω) becomes relatively less. Figure 7 Fuel and efficiency curves 3 Normalised Fuel Use [ ] 4 Efficiency [%] Normalised Power [ ] Normalised Power [ ] By looking at the slope of the fuel map it turns out that for the convex fuel curve, it is cheaper to generate in the low torque area, whereas for the concave fuel curve, it is cheaper to generate in the high torque area. For the linear curve, it does not matter where electricity is generated. For most engines, the fuel map is convex, but the changes in λ are rather smaller over a larger range of operating conditions. This enables the use of the approximation 3, but limits the fuel reduction that can be obtained with an electrical energy management system. When battery losses are taken into account, the differences of the fuel map must be larger than the additional losses of storing and retrieving energy, which further reduces the potential. 3.2 Regenerative braking When a vehicle is decelerating, kinetic energy becomes available, causing a negative drive train torque. As long as the clutch is closed, a part of this energy is absorbed by the engine (which has a negative drag torque). The remaining part can be absorbed by the brakes that convert it into useless heat and wear, but it can also be used by the alternator to convert it into useful electrical energy. When the clutch is engaged, the kinetic energy can no longer be used by the engine or the alternator, so it will all be absorbed by the brakes.

11 122 M. Koot et al. Because regenerative braking delivers electrical power with no extra fuel consumption, it should be used as much as possible. When the clutch is closed, the brakes should only be used if the desired deceleration torque exceeds the maximum negative torque that can be delivered by the engine and the alternator. The potential of regenerative braking can be increased by altering the drive train configuration such that the alternator is connected to the drive train instead of to the engine. In this case, generating can be continued when the clutch is open and the vehicle is still decelerating. A drawback is that no electric power can be generated when the vehicle is standing still, so electricity is drawn from the battery. This configuration is not further investigated in this paper. 3.3 Hybrid electric vehicles The analysis presented in this paper also applies to mild hybrid electric vehicles with an Integrated Starter Generator (ISG) that is mounted directly on the crank shaft of the engine, such as the Honda Insight (Fukuo et al., 21) and the Honda Civic IMA (Integrated Motor Assist). The only difference is that P e min is negative. There, the engine and the ISG are always operating simultaneously and there is no freedom in the engine speed. Fuel reduction is obtained mostly by the fact that a smaller engine can be used, because the ISG can be used for boosting to obtain a similar performance with a larger engine. A smaller engine has smaller friction and pumping losses and thus a smaller drag torque. This results in less fuel consumption during propulsion, and also leaves more energy available for regenerative braking. Furthermore, the engine is turned off during the standstill. Full hybrid electric vehicles, such as the Toyota Prius (Hermance and Sasaki, 1998), have both freedom in the engine speed and torque and the engine and the electric motor can be operated independently. This makes the energy management problem more complex and lies beyond the scope of this paper. 4 Engineering rules This section presents a set of engineering rules to predict how much fuel reduction can be obtained for a given configuration with regenerative braking and with a more advanced energy management strategy compared to a baseline strategy. 4.1 Baseline strategy The baseline strategy is defined such that the alternator always generates exactly what is requested, so the battery is not used P e = P l P g = g (ω) + k g P l (22) For a given speed and gear profile, the corresponding engine speed ω and propulsion power P d can be computed as shown in Section 2. By adding the alternator power, the total mechanical power becomes P p = P d + P g (23)

12 Fuel reduction potential of energy management 123 The power delivered by the engine is then given by P m = max(p p,p m min ) (24) The fuel consumption, using the linear approximation of the fuel map, is given by te m bl = k f P m dt (25) h f It appears that the baseline strategy already uses some of the regenerative braking potential. During the deceleration periods where P d <P m min, some or all of the electrical power is generated without using fuel. This is illustrated in Figure 8, where the mechanical energy that can be obtained freely and is used for generating the electric power is indicated by the solid areas. This amount of free mechanical energy can be calculated as follows: P g regen bl = min(max(p m min P g,p d ), P m min P g min ) (26) +P m min P g min The corresponding electric power is then given by P e regen bl = 1 k g P g regen bl (27) Figure 8 Regenerative braking potential of the baseline strategy 4 3 P d P m min P g min P m min P g Baseline strategy Mechanical Power [kw] Time [s] If the baseline strategy would not exploit the regenerative braking potential at all, the fuel consumption is given by: m bl = k f h f te Pm dt (28) where Pm is defined as Pm = max(p d,p m min ) + P g (29)

13 124 M. Koot et al. The amount of fuel that is saved by exploiting the regenerative braking potential is given by m regen bl = k f h f te P g regen bl dt (3) The amount of electrical energy that is obtained freely increases with P g and thus with the requested load. 4.2 Regenerative braking strategy The regenerative braking strategy as will be considered in this paper is defined as follows. During the normal operation, the alternator generates exactly what is requested. During the deceleration phase, it generates the maximum amount of the electrical power that does not cost fuel. If this is more than what is requested at that moment, the surplus of electrical energy will be stored in the battery. After the braking period, the electric load is supplied by the battery, till it reaches the original SOC level. From that point, the load is again provided by the alternator. During normal operation, the additional fuel consumption is more or less proportional with the electrical energy provided, so the fuel saving that can be obtained with regenerative braking depends on the amount of electrical energy that can be generated freely during the deceleration periods. The mechanical power that can be used freely during braking is the part between the engine drag power minus the alternator drag power, and the engine drag power minus the maximum alternator power. This is illustrated by the solid areas in Figure 9. The amount of power can be calculated as follows: P g regen = min(max(p m min P g max,p d ), P m min P g min ) +P m min P g min (31) Figure 9 Regenerative braking potential of a regenerative braking strategy 4 3 P d P m min P g min P m min P g max Regenerative Braking strategy Mechanical Power [kw] Time [s]

14 Fuel reduction potential of energy management 125 The corresponding electric power is then given by P e regen = 1 k g P g regen (32) The corresponding fuel consumption that can be saved is given by m regen = k f h f te P g regen dt (33) The amount of electrical energy that can be obtained freely with regenerative braking does not depend on the requested electric load, but depends only on the power needed for propulsion and the alternator capacity P e max. How much of the electrical energy is stored for later usage, does depend on the load. The amount of electrical energy that is already obtained freely by the baseline strategy increases with the requested load. This means that for higher electrical loads, the additional improvement of a real regenerative braking strategy will then decrease. 4.3 Advanced energy management strategy On top of the regenerative braking, an additional fuel reduction can be obtained by using a more advanced energy management strategy, that exploits the differences in the incremental cost and only generates when these costs are low, as explained in Section 3.1. Its potential depends on the differences between the non-linear fuel and alternator map and their linear approximations, in other words, the deviation of λ(p m,ω) from the linear approximation λ = k f k g. The fuel reduction also depends on the amount of the requested electrical load and the maximum alternator power. When the amount of the electrical load is smaller compared to the maximum alternator power, most of the electricity can be generated in the cheapest area. Since the load is small, the fuel consumption needed for it is also small and the fuel reduction will also be small. When the load is higher, it causes more fuel consumption, so the fuel that can be saved by generating only at cheaper moments also increases. When the requested load is close to the maximum alternator power, there is not much freedom anymore as and when to generate, so the fuel reduction will decrease again. Suppose the driving cycle is such that the corresponding λ is uniformly distributed between 1 σ f < λ λ < 1 + σ f (34) If the requested electrical load equals the maximum alternator power, it is generated within the interval [1 σ f, 1 + σ f ], with an average of 1. If the requested load is half of the maximum alternator power, it can be generated within the interval [1 σ f, 1], with an average of σ f. If the requested load is a quarter of the maximum alternator power, it can be generated within the interval [1 σ f, σ f], with an average of σ f.

15 126 M. Koot et al. More generally, the load can be generated within the interval [1 σ f, 1 (1 2 α) σ f ], with an average of 1 (1 α) σ f, where α is the ratio between the average requested load over a driving cycle and the maximum alternator power: α = P l P e max (35) The fuel that can be saved on top of regenerative braking is then given by m em = (1 α) σ f λ h f te (P l P e regen ) dt (36) 5 Comparison In this section, the fuel reduction that can be obtained with regenerative braking and advanced electrical energy management for a specific vehicle and driving cycle will be estimated with the rules presented in the previous sections and will be compared with simulations results. The fuel consumption is estimated for the following four strategies: 1 the fictive baseline strategy that does not use regenerative braking according to (28) 2 the realistic baseline strategy according to (3) 3 the regenerative braking strategy according to (33) 4 the advanced energy management strategy according to (36). The simulation results are obtained using the original non-linear fuel and alternator map using the following four strategies: 1 the fictive baseline strategy that does not use regenerative braking 2 the realistic baseline strategy 3 a heuristic regenerative braking strategy 4 advanced energy management using Dynamic Programming. When using the fictive baseline strategy, fuel is injected during the deceleration periods to supply the load, whereas the realistic baseline strategy recuperates part of the kinetic energy from the vehicle. The heuristic regenerative braking strategy operates as described in the beginning of Section 4.2. The Dynamic Programming (Bertsekas, 1995) strategy used for the simulation minimises the fuel consumption over the entire driving cycle with the constraint that the energy level of the battery at the end is the same as at the beginning. This method assumes the entire driving cycle is known and acts as a benchmark for other strategies. The implementation of this method is described in more detail in Koot et al. (25), which also presents the derivation of an online implementable strategy.

16 Fuel reduction potential of energy management Simulation parameters Simulations are done for a conventional vehicle equipped with a 1 kw 2. liter SI engine, as shown in Figure 3, and a manual transmission with five gears. A 42V 5 kw alternator, as shown in Figure 5, and a 36V 3Ah lead-acid battery make up the alternator and storage components of the 42V power net. The battery is modelled without any losses. For the electric power request, constant loads between and 5 W are used. The parameter values for the simulation model are given in Table 2. Table 2 Parameter values for the simulation model Quantity Symbol Value Unit Mass M 14 kg Frontal area A d 2 m 2 Air friction coefficient C d.3 Rolling resistance C r.15 Wheel radius w r.3 m Final drive ratio f r 4. Gear ratio g r Idle speed ω i 7 rpm Air density ρ 1.2 kg/m 3 Gravity g 9.8 m/s 2 Simulations are done for the New European Driving Cycle (NEDC) (European Council, 197), in which the vehicle speed and the corresponding engine speed, torque and power are shown in Figure 1. This cycle consists of four identical urban parts followed by an extra-urban part. This cycle is rather conservative as the engine speed and torque remain far below their maximum allowed values. The distribution of the incremental cost λ for this cycle at P e = is shown as a histogram in Figure 11. It varies roughly between 2.2 and 2.9, although not uniformly, leading to a value of.1 for σ f. 5.2 Results an evaluation The results are presented in Figure 12. The total fuel consumption, the absolute fuel reduction with respect to the fictive baseline and the percentile reduction with respect to the normal baseline are displayed. As could be expected, the total fuel consumption increases more or less proportionally with the requested electrical load. The fuel reduction obtained with the regenerative braking is predicted rather well. The benefits of regenerative braking over a normal baseline strategy are large for low electrical loads and decrease for higher loads because the regeneration potential that is already absorbed by the baseline increases with the load. A load of 2 W can be provided solely by the regenerative braking. For smaller loads, the regenerative braking potential is not completely used because the SOC at the end must equal its initial value. This explains the rapid increase in fuel reduction between and 2 W.

17 128 M. Koot et al. Figure 1 New European Driving Cycle New European Driving Cycle Velocity [km/h] Speed [RPM] Torque [Nm] Power [kw] Time [s] Figure 11 Distribution of λ 4 35 Number of Occurances [ ] Incremental Cost [ ] The additional fuel reduction obtained with the advanced energy management shows larger differences between the analysis and simulation. According to the analysis, the highest additional fuel reduction is obtained with a load that is half of the maximum alternator power. In the simulation, the fuel reduction deviates for loads between 1 and 4 W.

18 Fuel reduction potential of energy management 129 This can be explained because the distribution of λ is not uniform, as illustrated in Figure 11, so the profits depend largely on which operating points of the fuel map are visited. Figure 12 Fuel consumption [g] Results Analysis Fictive Baseline Baseline Regenerative Braking Advanced Simulation Fictive Baseline Baseline Regenerative Braking Dynamic Programming Fuel reduction [g] Fuel reduction [%] Electric Load [W] Electric Load [W] When battery losses are taken into account, the profits of regenerative braking and advanced energy management will be smaller because the baseline strategy does not use the battery. 6 Conclusions A set of engineering rules are applied to estimate the fuel reduction that can be obtained with regenerative braking and with more advanced electrical energy management strategies in conventional vehicles. An explanation is given for this application, where the engine speed is predefined and only the torque can be manipulated, shifting the engine to an operating point with a higher efficiency will not necessarily lead to a lower fuel consumption. For a specific vehicle configuration and driving cycle, the estimated fuel consumption is compared with simulations, with reasonable results, showing the value of the engineering rules. With regenerative braking a fixed amount of electrical energy can be obtained. This amount does not depend on the requested load. The baseline strategy already provides some regenerative braking, where the amount increases with the requested load.

19 13 M. Koot et al. This means that for higher electrical loads, the additional fuel reduction of a real regenerative braking strategy becomes smaller. The additional fuel reduction that can be obtained with an advanced electrical energy management system depends on non-linearities and speed dependency of the fuel map. For the engine and the driving cycle used in this analysis, these deviations are rather small which limits the additional fuel reduction. References Back, M., et al. (22) Predictive control of drivetrains, Proceedings of the IFAC 15th Triennial World Congress, Barcelona, Spain. Bertsekas, D.P. (1995) Dynamic Programming and Optimal Control, Belmont, MA: Athena Scientific. Delprat, S., et al. (24) Control of a parallel hybrid powertrain: optimal control, IEEE Transactions on Vehicular Technology, Vol. 53, No. 3, pp Ehlers, K., et al. (21) 42V - an indication for changing requirements on the vehicle electrical system, Journal of Power Sources, Vol. 95, pp Emadi, A., et al. (23) Vehicular Electric Power Systems: Land, Sea, Air, and Space Vehicles, New York: Marcel Dekker. European Council (197) New European Driving Cycle, Directive 7/22/EEC with amendments. Fukuo, K., et al. (21) Development of the ultra-low-fuel-consumption hybrid car Insight, JSAE Review, Vol. 22, No. 1, pp Hermance, D. and Sasaki, S. (1998) Hybrid electric vehicles take to the streets, IEEE Spectrum, Vol. 35, No. 11, pp Johnson, V.H., et al. (2) HEV control strategy for real-time optimization of fuel economy and emissions, Proceedings of the Future Car Congress, Washington, DC, SAE Paper Kassakian, J.G., et al. (1996) Automotive electrical systems circa 25, IEEE Spectrum, Vol. 33, No. 8, pp Kassakian, J.G., et al. (2) Automotive electronics power up, IEEE Spectrum, Vol. 37, No. 5, pp Koot, M., et al. (25) Energy management strategies for vehicular electric power systems, IEEE Transactions on Vehicular Technology, Vol. 54, No. 3, pp Liang, F., et al. (1999) A vehicle electric power generation system with improved output power and efficiency, IEEE Transactions on Industry Applications, Vol. 35, No. 6, pp Lin, C.C., et al. (23) Power management strategy for a parallel hybrid electric truck, IEEE Transactions on Control Systems Technology, Vol. 11, No. 6, pp Miller, J.M. and Everett, M. (24) Ultra-capacitor augmentation of the vehicle electrical system to reset its power budget, Proceedings of the 8th IEEE Workshop on Power Electronics in Transportation, Detroit, pp Nicastri, P. and Huang, H. (2) 42V PowerNet: providing the vehicle electrical power for the 21st century, Proceedings of the SAE Future Transportation Technology Conference, Costa Mesa, CA, SAE Paper Ortmeyer, T.H. and Pillay, P. (21) Trends in transportation sector technology energy use and greenhouse gas emissions, Proceedings of the IEEE, Vol. 89, No. 12, pp Schouten, N.J., et al. (22) Fuzzy logic control for parallel hybrid vehicles, IEEE Transactions on Control Systems Technology, Vol. 1, No. 3, pp

20 Fuel reduction potential of energy management 131 Sciarretta, A., et al. (24) A real-time optimal control strategy for parallel hybrid vehicles with on-board estimation of the control parameters, Proceedings of the IFAC Symposium on Advances in Automotive Control, Salerno, Italy. Scordia, J., et al. (25) Systematic elaboration of online energy management laws for hybrid vehicles, Proceedings of the EVS 21 Electric Vehcile Symposium, Monte Carlo, Monaco. Sebille, D. (23) Electrical energy management: 42V perspective, MIT 42V meeting, Dearborn, MI.