AVEC 04 1 Vehicle Modeling for Energy Management Strategies J.T.B.A. Kessels, M.W.T. Koot, R.M.L. Ellenbroek, M.F.M. Pesgens, F.E. Veldpaus, P.P.J. van den Bosch Technische Universiteit Eindhoven M. Eifert, D.B. Kok Ford Forschungszentrum Aachen GmbH P.O. Box 513, 5600 MB Eindhoven, The Netherlands Phone: +31 40 247 2300 Fax: +31 40 243 4582 E-mail: j.t.b.a.kessels@tue.nl In modern vehicles, a significant amount of electric power is consumed, and more is to be expected in the future. For that reason, energy management for vehicle power nets gets a lot of attention in the automotive world. This paper describes a complete simulation environment for developing and evaluating energy management strategies. Two different model classes are distinguished: a simulation model to analyze the energy management strategy and a control model as part of the strategy itself. Experimental data from vehicle tests on a roller-dynamometer as well as power net measurements are used for model validation. Topics / A25, B9 1. INTRODUCTION In present vehicles, the electric power demand is already important in the total vehicle power balance. It is expected that electric power demands will increase significantly in the near future. Reasons for this are higher standards on safety and comfort, but also the replacement of pure mechanical or hydraulic systems by electric devices [3]. Clearly, the application of energy management strategies in vehicle power nets becomes more and more important. The main idea behind energy management is that generation, storage/retrieval and distribution of electric power can be done more efficiently than in present vehicles. By taking advantage of the characteristics of the energy converting components such as the internal combustion engine (ICE), the alternator and the battery, energy losses can be minimized and hence, the overall vehicle characteristics will improve (see [4], [6]). Simulation models can be used to develop and evaluate different energy management strategies. However, this is only possible when the models accurately represent the situation in reality. This paper deals with the question which vehicle characteristics are important for energy management. To that end, it presents a simulation environment that is used for developing, testing, and verifying energy management strategies. In Section 2, special attention is given to the structure of the simulation environment. The essential elements of the individual models will be discussed in Section 3 and 4. Section 5 presents the results from model validation and the conclusions are given in Section 6. 2. CLASSES OF MODELS To evaluate the behavior of an energy management strategy, a simulation environment has been developed. Depending on the purpose of the model, two model classes are distinguished: a simulation model and a control model. The simulation model is used to analyze and validate the control actions of an energy management strategy. This is a complex dynamic vehicle model with a flexible interface for connecting the energy management strategy. The control model is incorporated in the energy management strategy itself. By evaluating this model, the strategy determines which control actions should be taken. Typically, the control model runs at a much lower sampling frequency than the simulation model and also its structure will be less complex. In this way, real-time implementation of an energy management strategy can be guaranteed. As can be seen in Fig. 1, both models are directly derived from a real vehicle. By following a modular approach, these models are assembled from the following subsystems: Driving cycle: Represents cycles for evaluating energy management strategies. Driver: Acts as a controller to obtain the correct speed-profile. Engine: Describes engine characteristics such as fuel consumption. Drivetrain: Embodies the longitudinal vehicle dynamics.
AVEC 04 2 Vehicle Driving cycle Engine Alternator Electric loads Driver Drivetrain Energy storage... Simulation model Control model Figure 1: Simulation model and control model derived from a real vehicle Alternator: Energy storage: Electric loads: 3. SIMULATION MODEL Converts mechanical power to electrical power. Describes the medium used for storing electric energy. Comprehends the power demand of all electric devices in the vehicle. The simulation model constructed in this section is derived from a series-production vehicle with a manual transmission. The implementation of energy management in a conventional vehicle requires some modifications of vehicle components. In this case the alternator and electric power net are replaced by more advanced components (power controlled and offering a larger energy capacity). The topology of the drivetrain remains unaffected. A schematic overview of the simulation model is given in Fig. 2, showing the physical connections that are present between subsystems. By including all relevant vehicle dynamics into the model, a simulation model has been derived that can be used to evaluate an energy management strategy and to assess its influence on drivability. The following sections explain each subsystem in more detail. 3.1 Driving cycle Standard driving cycles are used for testing vehicles on a test-bench. The specified quantities are among other things the vehicle speed, the gear shifting points and how the clutch should be engaged. These signals are offered to the driver model. Although the New European Driving Cycle (NEDC) is considered in this paper, the simulation model can also handle other (user-defined) driving cycles. It is not difficult to see that the speed profile of the driving cycle influences the performance of energy management; think for example of profits from regenerative braking that are directly related to periods of vehicle deceleration, [5]. Therefore, a careful selection of the cycle profile contributes to better insight in the control actions from energy management. 3.2 Driver model To control the speed of the vehicle, a driver model has been used. Similar to a real vehicle, this driver model operates the throttle, clutch and brake pedal, such that the speed profile of the driving cycle is followed. In a simulation environment for testing energy management strategies, the driver notices possible control actions as a disturbance on the actual vehicle speed (assuming no feedforward compensation from the strategy itself). To visualize possible effects on driveability, it is important that the dynamic behavior of the driver model corresponds to reality. Basically, the driver model applied here is a feedback proportional integral (PI) controller, taking the actual vehicle speed and the desired vehicle speed as input signals (including a selected gear position as specified in the driving cycle). The output signals are three pedal positions: throttle, brake, and clutch. The initial parameter settings are derived from specific driver characteristics found in literature (see [1] and the references therein). For calculating the position of the brake pedal, this approach works satisfactory. However, the throttle and the clutch signals require further refinement. Depending on the status of the vehicle, a corresponding mode will be selected (stop, launch, shift, or drive), with its own setting for the PI-controller. 3.3 Internal combustion engine Although an ICE is a very complex thermodynamic machine, only two properties are of interest here: the interface from throttle position to operating point and the resulting fuel use. The relation between throttle position θ t and the torque delivered by the engine τ eng can be modeled by a first order response: κ τ eng = γ s + 1 θ t (1) The time constant γ decreases with increasing engine speed. For a warm engine, the instantaneous fuel consumption as a function of the operating point, i.e., engine speed ω and engine torque τ eng can be represented by a static look-up table: f = f(τ eng, ω) (2) Measurements are usually done only at a limited number of operating points, so interpolation is used for values in between. To capture all significant information, the measurement grid needs to be sufficiently dense. The influence of temperature has not yet been incorporated in the simulation model, so the model is only valid for simulations with a hot engine start.
AVEC 04 3 Brakes / Clutch / Gear Driving Cycle Driver Throttle Electr. load Combustion Engine Crankshaft Drivetrain Vehicle speed Vehicle signals Energy Controller Alternator setpoint Alternator Electr. power net Electric loads Energy storage Figure 2: Overview of simulation model 3.4 Drivetrain model The drivetrain model covers the longitudinal dynamics of the vehicle. It describes the relation from the engine torque to the vehicle speed and consists of the clutch, transmission, final drive, wheels, and chassis. It is based on the Advisor model [7], but differs from it by being forward facing. The inputs are the engine torque, braking force, clutch status and gear position. The output is the vehicle speed. A forward facing vehicle model is characterized by the fact that the actual vehicle speed results indirectly from the engine torque, and the engine torque is calculated from the throttle position as requested by the driver. Each component is modeled as a separate dynamic model. They are connected as shown in Fig. 3 (including the engine block). The torque and the cumulative inertia of the preceding components are passed through from left to right. The resulting vehicle speed is calculated in the chassis block. The corresponding rotational speeds of the components are passed through from right to left. The resulting engine speed is calculated in the clutch block. 3.5 Alternator The alternator in a conventional vehicle is equipped with a voltage regulator to keep the vehicle s power net at a constant voltage level. For energy management purposes, this situation is not desired since the strategy should have freedom in deciding how much power is generated by the alternator. Therefore, the alternator has been replaced by an advanced alternator with adjustable voltage setpoint. For this advanced alternator, measurement data is available, covering the relation between alternator speed, required mechanical torque and delivered electric power. By using linear interpolation, this data is translated into a look-up table, covering the complete operating range of the alternator. Important for energy management is that this look-up table offers an accurate description of the conversion from mechanical to electric power, also in the areas where conventional alternators are never used. The electric power limitations have also direct influence on the behavior of an energy management strategy. Variations in the output power of the alternator are assumed to happen much faster than required by the energy management strategy. Therefore, no further dynamics are included in the model, except for its inertia. The alternator is always connected to the engine s crankshaft, which makes it possible to include the inertia in the engine model. 3.6 Energy storage To generate electric power at other times than requested by the load, an energy buffer is required. Conventional vehicles are already equipped with a lead-acid battery, making them suitable for energy management. The lifetime of a battery reduces significantly when its energy throughput increases. Therefore, the traditional SLI-battery (Start, Light, and Ignition) will be replaced by a valve-regulated lead-acid (VRLA) battery. This increases the total energy throughput at least 3 times with respect to the SLI-battery. Obtaining an accurate model of a battery is far from trivial. Especially simulations over a long time horizon put high demands on the fast and slow dynamics of the battery model, in order to obtain accurate results over the entire simulation. An impedance-based non-linear battery model as described by Buller et al. [2] is able to fulfill these requirements. This model is able to simulate the voltage response of a VRLA battery during highly dynamic current profiles over various state of charge (SOC) levels. However, charge acceptance of the battery is not included in the model, so simulation results might be too optimistic about the amount of power that can be accepted by the battery. Also the influence of temperature and battery aging is not taken into account. 3.7 Electric loads The electric loads that are present in the vehicle are represented as one lumped load in the simulation model. It is assumed that this is a power-controlled load, although many electric devices do not meet this assumption at this moment.
AVEC 04 4 2 Brake 3 Gear 4 Clutch 1 Throttle 5 T_gen Throttle T_gen v_veh fuel_use Clutch pedal Clutch Gear Gearbox Brake pedal T_br_rear v_veh T_br_front Brakes Final drive T_br_front v_wheel F_x_wheel Front wheels F_z_wheel v_wheel F_x_wheel v_veh Tyre/road contact T_br_rear F_z_wheel F_x_wheel v_veh Chassis 1 v_veh [km/h] Engine 3 T_eng [Nm] 4 fuel_use [L/s] 2 w_eng [rpm] Figure 3: Drivetrain model 4. CONTROL MODEL The intention of energy management is to improve specific behavior of the vehicle. Typically, this is described in terms of reducing fuel consumption or emissions. As presented in [6], energy management can be established by translating all requirements into an optimization problem and solving this problem on-line in a vehicle. From a computational point of view, it is attractive to use a quadratic programming setting, where a quadratic objective function is minimized subject to linear constraints: min x x T Hx + f T x, sub Ax < b (3) The optimization problem covers all vehicle characteristics that are important for energy management. This means that an implicit description of the control model is present in (3) through matrix H and A and vector f and b. Vector x represents the design variable. Suppose that the net power flow through the battery P s, is selected as design variable x. To construct a control model within the framework of (3), two steps are taken. First, information from the driver about desired vehicle speed and gear ratio is used to estimate how much mechanical power is required. Due to this power demand, the engine and alternator are forced to operate in a restricted operating range. The second step expresses the properties of interest (for example the instantaneous fuel consumption) as a function of the design variable, here P s. Because the operating area of components is known from the first step, a quadratic function describes the interesting behavior sufficiently accurate and fits directly in (3). Both steps are explained in more detail in Section 4.1 and 4.2, respectively. Note that the optimization problem in (3) is not restricted to the present time moment. When there is information available about the future driving cycle, additional profits with energy management can be made by anticipating on upcoming events. Therefore, the design variable P s needs to be evaluated at various time instants along the prediction horizon. This is established in (3) by stacking P s at predefined moments into vector x. After solving the optimization problem, only the first control action will be implemented. At the next sample moment, all calculations are repeated taking an update of the measurement data into account. More details on this model-based predictive control approach are given in [4]. 4.1 Backward facing drivetrain model It is not difficult to see that a complex control model leads to a complex optimization problem and so a realtime implementation of the control strategy requires a balanced trade-off between model accuracy and computational demands. For that reason, only those characteristics that are important for energy management are included in the model. For a given vehicle speed v(t), slope profile α(t) and a selected gear ratio g r (t), the corresponding engine speed and drivetrain torque are calculated using the following formulas: ω(t) = f r w r g r (t) v(t) τ drive (t) = 1 η d w r f r 1 g r (t) F drive(t) F drive (t) = M v(t) + 1 2 ρ C d A d v(t) 2 + M g C r sign(v(t)) + M g sin(α(t)) The parameters are explained in Table 1. When the engine speed drops below a certain value, the clutch is opened. Then the drivetrain torque drops to zero and the engine runs at idle speed. Table 1: Parameter explanation Symbol Quantity Symbol Quantity M Vehicle mass w r Wheel radius A d Frontal area f r Final drive ratio C d Air drag coeff. g Gravity C r Rolling resist. ρ Air density η d Drivetrain eff. The dynamics of the drivetrain and the driver are not taken into account in the control model. Therefore, simulations with energy management in the simulation model are necessary to answer the question if driveability is influenced or not.
AVEC 04 5 140 120 100 Rollerdyno experiment 3000 2500 Rollerdyno experiment Vehicle speed [km/h] 80 60 40 Engine speed [RPM] 2000 1500 20 1000 0 20 0 200 400 600 800 1000 1200 500 20 40 60 80 100 120 140 160 180 200 Figure 4: Validation of vehicle speed Figure 5: Validation of engine speed 4.2 Cost criterion Primarily, profits from energy management originate from energy converting components, operating in a more beneficial working area. For the control model, this means that a description of the combustion engine, the alternator and the battery is indispensable. Given the framework in (3), these models are restricted to a quadratic fit of the relation between the design variable x and a physical quantity y that should be minimized (for example the instantaneous fuel consumption as a function of P s ): y(x, t) = α 2 (t)x 2 + α 1 (t)x + α 0 (t) (4) Engine Torque [Nm] 100 80 60 40 20 0 20 40 20 40 60 80 100 120 140 160 180 200 Figure 6: Validation of engine torque Physical limitations of components are added as linear constraints in (3). In addition, restrictions on the SOC-level of the battery are also translated into linear constraints and will be added to (3). 5. MODEL VALIDATION The simulation model and the control model are validated against data obtained from a real vehicle driving the NEDC driving cycle on a test-bench. The selected vehicle is equipped with a 2.0L SI-engine (100kW) and a 5-speed manual transmission. During the tests, the electric power demand is kept constant and a fixed setpoint for the alternator has been chosen. Because this excludes possible model errors from the electric power net in the validation process, additional experiments will be necessary to validate the actual behavior of the power net, see Section 5.2. 5.1 Roller-dynamometer measurements The signals that are validated are vehicle speed, engine speed, engine torque, instantaneous fuel use and cumulative fuel use. Starting with the vehicle speed, Fig. 4 shows the results from both the measurement at the roller-dynamometer as well as the simulation results. One can see that the measured vehicle speed is sometimes slightly above the simulated profile. It is assumed that these differences are caused by inaccuracies on the roller-dynamometer. The measured engine speed is given in Fig. 5, together with the results from the simulation and control model. This figure does not show the entire driving cycle but is restricted to a small area where also gear-shifting takes place. The gear shifts give rise to large variations in the engine speed, which are modeled well. Furthermore, one can see that the human driver presses the gas pedal just before the vehicle starts moving, whereas the driver in the simulation model waits until vehicle launch. The engine torque is not available in the measurement data. Nevertheless, the engine torque available in the simulation model can be compared to the engine torque from the control model, as shown in Fig. 6. The vehicle dynamics are only included in the simulation model, which explains the smoothness of the curve from the simulation model. The test-bench provides measurements on CO 2 emissions, which are used to estimate the actual fuel use. A fixed conversion factor will be used for calculating CO 2 - mass into grams of fuel. Fig. 7 shows the instantaneous fuel use as output from the models, together with the signal from the CO 2 measurement. To indicate that fluctuations are present in the measured signal, this figure presents only a small part of the driving cycle. It turns out that the oscillating behavior originates from the applied measuring technique. The CO 2 emissions are measured by feeding the exhaust gasses through particle filters. Due to the length of the flow channel and differences in pressure, emissions arrive with a varying time-delay leading
AVEC 04 6 Instantaneous fuel use [g/s] Rollerdyno experiment Voltage [V] 40 39 38 37 36 35 34 25 Voltage profile [V] 0 20 40 60 80 100 120 140 160 180 200 Figure 7: Validation of instantaneous fuel use Current [A] 25 50 Battery current (model) [A] Battery current (measurement) [A] 75 580 600 620 640 660 680 700 720 740 760 780 to oscillating behavior. This explains also why the signals from the simulation model and control model become immediately zero during deceleration phases, whereas the measured signal decreases slowly. Finally, the cumulative fuel use follows from integration of the instantaneous fuel use. It turns out that differences in the instantaneous fuel use average out. The measured fuel use and results from the simulation model show a deviation of less than 2% along the driving cycle. This is reasonable, because the accuracy of measurements on a roller-dynamometer are in the same order of magnitude. 5.2 Power net measurements The battery that is connected to the electric power net introduces a lot of uncertainty in the simulation model, due to its complex dynamic behavior. The experiments here concentrate on the voltage and current profile at the battery terminals. A preliminary control strategy on a 42V power net is used to generate a power profile for the alternator. Depending on the electric load request, this results in a voltage and current profile for the battery. The battery voltage that is measured during the experiment is offered to the simulation model. A fragment of this sequence is shown in the upper graph of Fig. 8. The lower graph compares the current profile from the simulation model with the measurement data. Despite the fact that limitations on charge acceptance are not implemented in the battery model, the simulated current profile corresponds very well to the measured signal. However, there are moments that the battery current from the model is lower than in the measurement. This is different than one would expect. 6. CONCLUSIONS A simulation environment has been developed for testing and validating energy management strategies. Simulation takes place on a simulation model whereas the strategy itself utilizes a control model. Because a modular approach has been taken, new vehicle components can be incorporated easily in the simulation environment. By excluding influences of the electric Figure 8: Validation of battery model power net, the simulation model and the control model have been validated against measurement data from a roller-dynamometer. Additional experiments are done to validate the characteristics of the battery model. REFERENCES [1] R.W. Allen, T.J. Rosenthal, and J.R. Hogue. Modeling and simulation of driver/vehicle interaction. In SAE International Congress & Exposition, Detroit, MI, USA, February 1996. SAE 960177. [2] S. Buller, M. Thele, E. Karden, and R.W. de Doncker. Impedance-based non-linear dynamic battery modeling for automotive applications. Journal of Power Sources, 113(2):422 430, January 2003. [3] J.G. Kassakian, J.M. Miller, and N. Traub. Automotive electronics power up. IEEE Spectrum, 37(5):34 39, May 2000. [4] M. Koot, J. Kessels, B. de Jager, M. Heemels, and P. van den Bosch. Energy management strategies for vehicle power nets. In American Control Conference, Boston, USA, June 2004. [5] M. Koot, J. Kessels, B. de Jager, and P. van den Bosch. Energy management for vehicle power nets. In FISITA World Automotive Conference, Barcelona, Spain, May 2004. [6] E. D. Tate and S. P. Boyd. Finding ultimate limits of performance for hybrid electric vehicles. In SAE Future Transportation Technology Conference and Exposition, Costa Mesa, California, USA, August 2000. SAE 2000-01-3099. [7] K.B. Wipke, M.R. Cuddy, and S.D. Burch. AD- VISOR 2.1: A user-friendly advanced powertrain simulation using a combined backward/foreward approach. IEEE Transactions on Vehicular Technology, 48(6):1751 1761, November 1999.