A-virtual-prototype-for-a-hybrid-electric-vehicle_Gökdere_2002
Content
Mechatronics 12 (2002) 575–593
A virtual prototype for a hybrid electric vehicle
€ Levent U. Gokdere *, Khalid Benlyazid, Roger A. Dougal, Enrico Santi, Charles W. Brice
Electrical Engineering Department, University of South Carolina, Swearingen 3A80, Columbia, SC 29208, USA Received 20 November 1999; accepted 11 October 2000
Abstract A virtual prototype of a hybrid electric vehicle (HEV) is created within the virtual test bed (VTB) environment, which has been developed for modeling, simulation, analysis and virtual prototyping of large-scale multi-technical dynamic systems. Attention is focused on the electric system, which is composed of (i) a fuel cell system as a prime power source, (ii) battery and super capacitor banks as energy storage devices for high and intense power demands, (iii) DCto-DC power converters to control the flow of power, (iv) a three-phase inverter-fed permanent magnet synchronous motor as a drive, and (v) a common DC bus. The simulation of the proposed system is conducted using two types of driving cycles. These are: (i) rapid acceleration and deceleration, and (ii) Federal Urban Driving Schedule (FUDS). The parameter values chosen for the components and the numerical results obtained by simulation are consistent with the practical HEV applications. Ó 2002 Elsevier Science Ltd. All rights reserved.
Keywords: Hybrid electric vehicle; Modeling and simulation; Virtual prototype
1. Introduction Considerable efforts have been expended to develop hybrid electric vehicles (HEVs) as replacements for high-emission cars, buses, and trucks powered by conventional gasoline or diesel engines [1]. The main objective of this paper is to describe a virtual prototype of a HEV by the use of a suitable simulation model. This is an important step in the development of the HEVs due primarily to the following two
Corresponding author. Present address: Rockwell Science Center, 1049 Camino Dos Rios, A18 Thousand Oaks, CA 91360, USA. Tel.: +1-805-373-4087; fax: +1-805-373-4383. E-mail address: [email protected] (L.U. G€kdere). o 0957-4158/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 9 5 7 - 4 1 5 8 ( 0 1 ) 0 0 0 0 9 - 5
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reasons: (i) a good virtual prototype allows for proof testing before hardware is assembled, which means likely reduction in the manufacturing cost and time, and (ii) new design possibilities can be explored; e.g., study of tradeoffs between sizes of components in the HEV is feasible. The National Renewable Energy Laboratory (NREL) has developed ADVISOR, Advanced Vehicle Simulator, which is a very helpful computer simulation tool for analysis of energy use and emissions in both conventional and advanced vehicles [2–4]. The ADVISOR has been developed within the MATLABâ Simulinkâ environment and it allows the user to interchange a variety of components, vehicle configurations, and control strategies [2–4]. Moreover, the ADVISOR has a graphical user interface (GUI) that allows for easy manipulation of input files, test routines, and output plots [2–4]. Further information on ADVISOR and the applications can be found on the web site: www.ctts.nrel.gov/analysis/advisor.html. In this work, the virtual test bed (VTB) is utilized for virtual prototyping of a HEV. The VTB has two important features [5,6]: (i) it has the capability of integrating models that have been created in a variety of languages into a single simulation environment; and (ii) it provides advanced visualization of simulation results, including full-motion animation of mechanical components, and imaginative mappings of computed results onto the system topology. The first feature of the VTB allows each component of a large-scale multi-technical system to be described in the most appropriate language (e.g., SPICE for electronic components, ACSLâ , Advanced Continuous Simulation Language, for dynamic systems, and SABERâ for power electronic circuits) [7]. On the other hand, the second feature enhances user’s comprehension of the simulation results significantly. Unlike any other simulators based on the state variable modeling approach (such as MATLABâ and ACSLâ ), the VTB solver is based on the resistive companion (RC) modeling approach [8]. In this approach, each device (component) is represented as interconnections of resistors and current sources whose values depend on the device parameters and past-history values of the device state variables [8]. In addition, each device is treated as a box with a number of terminals, which provide connections to other devices [8]. A major advantage of the RC modeling approach over the state variable modeling approach is that once the device models are constructed, interconnections of any set of devices can be easily handled [8]. This is especially important for the study of large-scale multi-technical dynamic systems. More information about VTB can be found on the web site http://vtb.engr.sc.edu/ The VTB software and the supporting tools can be also downloaded from the same site for free of charge. The electrical part of the HEV considered in this study is composed of (i) a fuel cell system as the prime source of average electric power (10–15 kW), (ii) battery and super capacitor banks as energy storage devices for high and intense power demands (e.g., 50 and 150 kW, respectively), (iii) boost and Cuk type DC-to-DC power converters to control the flow of power, (iv) a pulse-width modulated (PWM) inverter-fed three-phase permanent magnet synchronous motor (PMSM) with associated vector controller as a drive, and (v) a common DC bus for energy distribution.
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Models for each component of the HEV electrical system were previously developed using ACSLâ , and have been reported in [9,10]. Explanations of the models are given in the next section. Based on the component descriptions, a virtual prototype of the HEV is then built within the VTB. Finally, simulation and animation results are presented to numerically verify the virtual prototype and demonstrate the advanced visualization capabilities of the VTB.
2. Component descriptions for HEV Fig. 1 shows a simplified block diagram for the electrical part of the HEV [9]. The definitions of the fuel cell system, battery bank, super capacitor bank, boost con verter, Cuk converter, PMSM, and the PWM inverter are given in the following subsections. 2.1. Fuel cell system The voltage-current characteristic of a single proton exchange membrane (PEM) hydrogen fuel cell is illustrated in Fig. 2. In this figure, Vfc (vertical axis) is the voltage at the terminals of the fuel cell, and Ifc (horizontal axis) is the current flowing out of the fuel cell. It is seen that there are basically three operation regions. These are, (i) the low current region in which the voltage decreases exponentially as the current increases, (ii) the linear region that covers a large portion of the characteristic, and (iii) the high current region in which there is a sharp drop of the voltage to near-zero [11]. Note also that, the units for Vfc and Ifc are millivolts and milliamperes, respectively. For the values of Ifc which remain in the low current and linear regions, Vfc versus Ifc may be expressed by
Fig. 1. Block diagram for the electrical part of the HEV.
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Fig. 2. The fuel cell voltage in mV versus fuel cell current in mA.
Vfc ¼ Vfco À b logðIfc =Afc Þ À Rfc Ifc ;
ð1Þ
where Vfco is the open-circuit (zero current) voltage of the fuel cell in mV, b is the Tafel slope in mV, Afc is the cross-sectional area of the fuel cell in cm2 , and Rfc is the internal ohmic resistance of the fuel cell in X [11]. A more complete expression, which is valid for the entire current range, is (see [12]) Vfc ¼ Vfco À b logðIfc =Afc Þ À Rfc Ifc À m expðnIfc =Afc Þ: ð2Þ
In (2), the parameters m and n are empirical equation constants and they can be obtained by a nonlinear regression analysis [12]. The total voltage of a fuel cell stack is given by Vfctotal ¼ Nfc Vfc ; ð3Þ
where Nfc is the number of cells in the stack. The numerical values for the fuel cell parameters are listed in Table 1. The values of Vfco , Afc and Nfc were obtained from [4] while the others were chosen to fit the curve in Fig. 2, where the ranges for the low current and linear regions were adapted from [4]. The fuel cell system under consideration produces power up to 18 kW. This is enough to overcome average air drag and other losses at highway speeds. Another consideration is that the output voltage of the fuel cell system is always low when compared with the common DC bus voltage. This calls for an intermediate
L.U. G€kdere et al. / Mechatronics 12 (2002) 575–593 o Table 1 Fuel cell parameters Vfco b Afc Rfc m n Nfc 1000 mV 25 mV 292 cm2 0.000819 X 0.0475 mV 0.0065 cm2 mAÀ1 110
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DC-to-DC power converter which is capable of transferring the energy from one side with lower voltage to another with higher voltage (see Section 2.4). 2.2. Battery bank The battery bank is composed of a series connection of 25 twelve-volt lead-acid batteries, each rated at 26 A h (or 93,600 C). The dynamic equations of each battery are given by Vcharge ¼ Vchargemin þ ðVchargemax À Vchargemin ÞQ=Qmax ; Vterminal ¼ Vcharge À Rinternal Ibattery ; Q¼ Z
0 t
ð4Þ ð5Þ ð6Þ
ðÀIbattery Þdt þ Qð0Þ;
where Vcharge is the battery internal voltage, Q is the state of charge of the battery, Vterminal is the voltage measured at the terminals of the battery, and Ibattery is the current flowing out of the battery. In (4)–(6), Qmax is the maximum value of Q, Rinternal is the equivalent series resistance of the battery, and Qð0Þ is the initial state of charge of the battery. For Qð0Þ ¼ Qmax , the battery model (4)–(6) is exactly the same as the Ford battery model used in [13]. The parameter values are adapted from [4] and are listed in Table 2. In the simulation, Qð0Þ is set to 10.4 A h (40% of Qmax ), which yields a total battery internal voltage of about 308 V. The battery bank together with the fuel cell system supplies power in the amount of 55 kW, which is sufficient for most of the urban and highway driving cycles including hill climbing at certain speeds.
Table 2 Battery parameters Vchargemin Vchargemax Qmax Rinternal 9.5 V 16.5 V 26 A h 0.015 X
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2.3. Super capacitor bank In this work, a single double-layer super capacitor is represented by the circuit in Fig. 3, which consists of an equivalent series resistance Resr and an ideal capacitance Cideal [14]. The equivalent series resistance, also abbreviated as ESR, accounts for the losses in the super capacitor [14]. As shown in Fig. 3, let Vsuper and Isuper denote, respectively, the voltage at the terminals of the super capacitor and current flowing into the super capacitor. The voltage-current relationship of the super capacitor is then expressed by Z t 1 Vsuper ¼ Resr Isuper þ Isuper dt þ Videal ð0Þ; ð7Þ Cideal 0 where Videal ð0Þ is the initial voltage across the ideal capacitance Cideal . Note that Vsuper ð0Þ (the initial value of Vsuper ) is equal to Videal ð0Þ if Isuper ð0Þ (the initial value of Isuper ) is zero. Table 3 lists the parameter ratings of single double-layer super capacitor [14]. To achieve higher voltage rating, the series and parallel connections of the super capacitors are considered in this work. Specifically, a super capacitor network of four parallel branches is utilized, where each branch consists of series connections of 200 super capacitors. This results in a super capacitor bank, the overall voltage rating, capacitance and ESR of which are 460 V, 9.4 F and 0.225 X, respectively. The overall initial voltage of the super capacitor bank is set to 460 V in the simulation. The super capacitor bank contributes to the peak and intense power requirements of the HEV, which might be as high as 160 kW and as brief as few seconds. This is necessary to accelerate the vehicle under consideration to a speed of 50 km/hr (31.1 mph) in 7 s. The super capacitor bank also accepts (transiently) part of the energy released by the drive motor during regenerative braking [9,10].
Fig. 3. The equivalent circuit for the super capacitor.
Table 3 Super capacitor parameters Cideal Resr Rated voltage Maximum current 470 F 4.5 mX 2.3 V 343 A
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The voltage across the super capacitor bank might swing above and below the common DC bus voltage considerably due to the excessive incoming and outgoing currents during rapid braking and acceleration. This necessitates an intermediate bidirectional DC-to-DC power converter, which is capable of operating in both up and down modes (see Section 2.4). 2.4. Power converters for fuel cell system and super capacitor The fuel cell system and super capacitor are connected to the common DC power bus through DC-to-DC power converters of the boost and Cuk topologies. The converter associated with the fuel cell is boost type and commands the energy transfer out of the fuel cell. On the other hand, the converter for the super capacitor is bi-directional and Cuk type. It controls the power flow into and out of the super capacitor. Fig. 4 shows the circuit diagram for the boost converter [15]. The state-space average model of the circuit is given by [16] diL Àð1 À DÞvout þ vin ¼ ; dt L dvC ð1 À DÞiL À iout ¼ ; dt C ð8Þ ð9Þ
where duty ratio D is the fraction of the switching period during which switch S1 is closed and switch S2 is opened. The parameter values are selected as in Table 4. Fig. 5 is the circuit diagram for the bi-directional Cuk converter [15,17]. The corresponding average model is [16] diL1 vin À ð1 À DÞvC ¼ ; dt L1 ð10Þ
Fig. 4. Circuit diagram for the boost converter.
Table 4 Boost converter parameters L C 1 mH 100 lF
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Fig. 5. Circuit diagram for the bi-directional Cuk converter.
diL2 DvC À vout ¼ ; dt L2 dvC ð1 À DÞiL1 À DiL2 ¼ ; dt C
ð11Þ ð12Þ
where duty ratio D is defined in a similar manner. The values of the inductances and the capacitor are given in Table 5. In [10,18], the feedback controllers were designed, and also verified by simulation results, to accomplish the operational objectives of the boost and Cuk converters. The feedback controllers were based on the average models (8), (9) and (10)–(12). 2.5. Three-phase PMSM The d–q model of the three-phase PMSM considered for the HEV is given by dId Vd Rs ¼ À Id þ pxIq ; dt L L dIq Vq Rs 3p xkmax ; ¼ À Iq À pxId À 2L dt L L dx 1 ¼ ðTe À k0 À k1 x2 Þ; dt k2 ð13Þ ð14Þ ð15Þ
where Vd and Vq are the stator d and q voltages, Id and Iq are the stator d and q currents, x is the angular velocity of the rotor, Rs is the resistance of the stator phase winding, L is the inductance of the stator phase winding, p is the number of polepairs and kmax is the flux linkage due to the permanent magnets. The parameters k0 , k1 and k2 are related to the force opposing the motion of the vehicle and are defined as
Table 5 Cuk converter parameters L1 L2 C 1 mH 1 mH 100 lF
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k0 ¼ k1 ¼
D D
D
1 ðmgrw sin hh þ kR mgrw cos hh Þ; ng
3 qCd Af rw ; 2n3 g 2 mrw þ Jw ; n2 g
ð16Þ ð17Þ ð18Þ
k2 ¼ Jm þ
where m is the mass of the vehicle, hh is the angle of vehicle to horizontal, n is the overall gear ratio, g is the transmission efficiency, rw is the wheel radius, kR is the rolling resistance coefficient, g is the acceleration due to gravity, q is the air density, Cd is the drag coefficient, Af is the frontal area, Jm is the moment of inertia of the drive motor (PMSM), and Jw is the moment of inertia of the wheels [19]. In (15), Te is the electrical torque (i.e., the torque produced by the motor) and is computed from Te ¼ pkmax Iq : ð19Þ
The stator d–q voltages Vd and Vq are related to the stator three-phase voltages Va , Vb , and Vc by 2 3 V 3=2 pffiffiffiffiffiffiffiffi 0 0ffiffiffiffiffiffiffiffi 4 a 5 Vd cosðphÞ sinðphÞ p ð20Þ Vb : ¼ 0 3=2 À 3=2 Vq À sinðphÞ cosðphÞ Vc The same relationship is also valid for the stator d–q and three-phase currents. The parameter values for the PMSM and vehicle are listed in Tables 6 and 7, respectively. The parameter values in Table 7 are for a prototype electric vehicle Fiat Cinquecento [19]. To fulfill the acceleration and deceleration requirements of the vehicle, a currentcommand rotor-oriented speed controller (vector controller) is designed, and also verified by simulation results, in [9]. The reader is referred to [20,21] for more information on PMSMs and associated vector controllers. 2.6. PWM inverter for PMSM Over the years, the space vector pulse-width modulation (SVPWM) technique for voltage source inverters has received widespread acceptance due to its implementation simplicity and superior performance characteristics such as low-harmonic loss factor [22–25]. The linear modulation range of SVPWM technique terminates at a
Table 6 PMSM parameters Rs L p kmax Jm 0.39 X 444 lH 3 0.0737 Wb 0.0355 kg m2
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Table 7 Vehicle parameters (from [19]) m hh n g rw kR g q Cd Af Jw 1260 kg 0.0 radians 7.3 0.9 0.256 m 0.009 9.81 m sÀ2 1.225 kg mÀ3 0.315 1.75 m2 0.004 kg m2
pffiffiffi modulation index of 3p=6 ¼ 0:907 [23–25]. In other words, with SVPWM scheme, the maximum value of the fundamental component of the output (phase) ffiffivoltage pffi that can be commanded without introducing low-order harmonics is Vdc = 3 where Vdc is the DC link (bus) voltage [26]. Taking this into account, the stator d–q voltages of the PMSM are limited by (see transformation (20)) [26] qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi 3 Vdc : Vd2 þ Vq2 6 ð21Þ 2 Assuming that the inverter is lossless, the input current Idc into the inverter is calculated by setting Pin ¼ Pout and then solving for Idc where Pin ¼ Vdc Idc is the input power to the inverter and 2 Pout ¼ ðVd Id þ Vq Iq Þ 3 ð23Þ ð22Þ
is the output power delivered by the inverter to the PMSM [26]. The expression for Idc is then obtained as Idc ¼ 2 Vd Id þ Vq Iq : 3 Vdc ð24Þ
The constraint (21) and expression (24) represent an average-value model for the SVPWM inverter [26].
3. A virtual prototype of HEV in VTB In this section, based on the component descriptions in Section 2, a virtual prototype for the electrical part of the HEV is developed and also verified by simulation results within the VTB environment. The virtual prototyping of the HEV is accomplished using VTB native models, which are originally written in C++. Once the source code for each component is created, it is then built into a dynamically linked library (DLL) form that allows the component to be inserted into or removed from
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the system topology at will during an interactive simulation [5,6]. The C++ source code includes the component description based on the RC modeling approach [8]. Fig. 6 illustrates the VTB schematic view for the electric system of the HEV [18]. In the schematic, the user can easily change the values of the component parameters through an editor which pops up by double clicking on the component. The simulation of the proposed HEV system was carried out considering two types of driving cycles. These are: (i) rapid acceleration and deceleration, and (ii) Federal Urban Driving Schedule (FUDS). The following subsections present the simulation results. The parameter values chosen for the components and vehicle are the same as in Section 2, unless indicated otherwise. 3.1. Rapid acceleration and deceleration In this move, the vehicle was first accelerated to a speed of 50 km/h (31.1 mph) in 7 s, then, held constant at that speed for 3 s, and finally, brought down to rest in 7 s. Figs. 7–9 show the results obtained with this move. Fig. 7 displays the speed tracking performance of the vehicle. In this figure, due to the close tracking, the actual and reference speeds are on top of each other. The input current Idc into the PWM inverter and the DC bus voltage Vdc are given in Fig. 8. It is seen that during the acceleration phase (from 0 to 7 s), Vdc drops as Idc increases. On the other hand, in the deceleration phase (from 10 to 17 s), Vdc reaches a peak value. During the deceler-
Fig. 6. The VTB schematic view for the electrical system of the HEV.
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Fig. 7. Actual and reference speeds of HEV (maximum speed 31.1 mph).
Fig. 8. Input current in amperes and bus voltage in volts (for driving cycle in Fig. 7).
ation, the energy supplied by the motor charges the battery bank via the DC bus. As a result, the DC bus voltage, which is floating at the battery bank voltage, increases [9]. Fig. 9 shows the total input power Pin to the inverter and contributions of the fuel cell (Pfc ), battery bank (Pbattery ) and super capacitor (Psuper ) to Pin . During the acceleration, the fuel cell system is commanded to provide power up to the 18 kW (due to the recommendations of manufacturer, the minimum voltage of the fuel cell system is limited to 60 V, which corresponds to a maximum power of 18 kW [4]). On the other hand, the battery bank together with the fuel system provides just about 55 kW (maximum). Finally, the super capacitor supplies the rest of Pin , which goes up to 160 kW during the acceleration. Note here that the super capacitor also accepts a significant fraction of Pin during deceleration to prevent the battery bank from overcharging.
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Fig. 9. Contribution of each energy device to the total input power (for driving cycle in Fig. 7).
In another test, the vehicle was accelerated to the maximum speed of 100 km/h (62.1 mph) in 18 s, then, held constant at that speed for 12 s, and finally, brought down to rest in 18 s. It was observed that the motor torque Te and the total input power required for the steady-state operation at the maximum speed are 14.5 N m and 12.5 kW, respectively. These are consistent with the vehicle specifications mentioned in [19]. Figs. 10 and 11 illustrate the results for this test. 3.2. Federal urban driving schedule (FUDS) Fig. 12 shows the actual and reference vehicle speeds for the FUDS (the two are on top of each other due to close tracking). The total input power and contributions of each energy device are given in Figs. 13–16. The control strategies for the energy
Fig. 10. Motor torque in N m and vehicle speed in mph (maximum speed 62.1 mph).
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Fig. 11. Total input power (for driving cycle in Fig. 10).
Fig. 12. Actual and reference speeds of HEV for FUDS.
devices are as in Section 3.1. From Fig. 16, it is seen that the super capacitor is inactive for the most of the driving cycle. This is due to the fact the total input power remains mostly below 55 kW. Also, it has been observed the bus voltage fluctuates between 250 and 340 V for the entire cycle, while the single battery charge reduces to only 9.8 A h (from 10.4 A h) at the end of the cycle. This implies that, with the control strategies mentioned above, the vehicle sustains enough energy to overcome demanding and lengthy driving cycles. In another test, a new set of vehicle parameters were adapted from [4]. Table 8 lists the new values (the other parameters remain the same). The total input power for this test follows a similar pattern to that of [4]. The result is shown in Fig. 17.
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Fig. 13. Total input power for FUDS.
Fig. 14. Power supplied by fuel cell system for FUDS.
Fig. 15. Power supplied by battery bank for FUDS.
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Fig. 16. Power supplied by super capacitor bank for FUDS.
Table 8 Vehicle parameters (adapted from [4]) m hh n g rw kR g q Cd Af Jw 1191 kg 0.0 rad 9.0 0.9 0.282 m 0.009 9.81 m sÀ2 1.2 kg mÀ3 0.335 2.00 m2 0.004 kg m2
Fig. 17. Total input power for FUDS (with vehicle parameters in Table 8).
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4. Animation of HEV An important feature of the VTB is its advanced visualization system, which allows full motion animation of the mechanical components. The visualization can operate either interactively or off-line. During an interactive session, the simulation output data is streamed to the visualization sub-system [5]. On the other hand, data generated in an off-line simulation is first stored in the form of a text file and then interfaced to the visualization system by a plug-in device [5].
Fig. 18. Animation view of the vehicle body.
Fig. 19. Animation view of the vehicle dashboard.
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This aspect of the VTB has been utilized to achieve the full motion animation of the HEV. Figs. 18 and 19 display the screen snapshots that come from the animation. Fig. 18 is the animation view of the vehicle body while Fig. 19 is the animation view of the vehicle dashboard. During the animation, the vehicle travels on the ground level at varying speeds specified by the driving cycle, while the gauges on the dashboard indicate the instant values of the corresponding variables.
5. Conclusions A virtual prototype for a HEV was developed and also numerically verified by simulation results within the VTB environment. The virtual prototyping was achieved using the VTB native models of the components. Also, based on the simulation results, a full motion animation of the HEV was performed to demonstrate the advanced visualization capabilities of the VTB. One of the unique features of the virtual prototype is that it includes all possible energy devices (fuel cell system, battery bank, and super capacitor bank) for the next generation HEVs. Further, to be consistent with the real world applications, the nonlinear dynamics, ohmic losses, and voltage/current limits of the components are taken into account.
Acknowledgements This work was supported by the Office of Naval Research under Grants N0001496-1-0926 and N00014-00-1-0131.
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[7] G€kdere LU, Brice CW, Dougal RA. An advanced modeling and simulation tool for analysis of o mechatronic systems. In: Proceedings of the Seventh Mechatronics Forum International Conference (Mechatronics 2000), September 6–8, 2000, Atlanta, GA. [8] Meliopoulos APS, Cokkinides GJ. A time domain model for flicker analysis. In: Proceedings of the IPST’97, June 22–26, 1997. Seattle, WA. p. 365–68. [9] G€kdere LU, Benlyazid K, Santi E, Brice CW, Dougal RA. Hybrid electric vehicle with permanent o magnet traction motor: a simulation model. In: Proceedings of IEEE International Electric Machines and Drives Conference (IEMDC ’99), May 9–12, 1999. Seattle, Washington. p. 502–4. [10] Benlyazid K, Dougal RA, Santi E, G€kdere LU, Brice CW. Hybrid electric vehicle: a simulation o study. In: Proceedings of IASTED International Conference on Modeling and Simulation (MS ’99), May 5–8, 1999. Philadelphia, Pennsylvania. p. 462–7. [11] Blomen LJMJ, Mugerwa MN. Fuel cell systems. New York: Plenum Press, 1993. [12] Kim J, Lee SM, Srinivasan S, Chamberlin CE. Modeling of proton exchange membrane fuel cell performance with an emprical equation. J Electrochem Soc 1995;142(8):2670–4. [13] Bumby JR, Spooner E. Compact ‘Torus’ PM generator for hybrid electric vehicle. In: Proceedings of the International Conference on Electrical Machines (ICEM ’98), September 2–4, 1998. Istanbul, Turkey. p. 1779–84. [14] Spyker RL, Nelms, RM. Evaluation of double-layer capacitor technologies for high power and high energy storage applications. In: Proceedings of the 23rd International Conference on Industrial Electronics, Control, and Instrumentation (ICON ’97), November 9–14, 1997. New Orleans, Louisiana. p. 1086–91. [15] Kassakian JG, Schlecht MF, Verghese GC. Principles of power electronics. New York: AddisonWesley, 1991. [16] Middlebrook RD, Cuk S. A general unified approach to modelling switching-converter power stages. In: Proceedings of IEEE Power Electronics Specialists Conference (PESC ’76), June 8–10, 1976. Cleveland, Ohio. p. 18–34. [17] Cuk S, Middlebrook RD. A new optimum topology switching DC-to-DC converter. In: Proceedings of IEEE Power Electronics Specialists Conference (PESC ’77), June 14–16, 1977. Palo Alto, CA. p. 160–79. [18] Benlyazid K, Hybrid electric vehicle: a simulation study. M.S. thesis, University of South Carolina, Columbia, SC, 1999. [19] Harson A, Mellor PH, Howe D. Design considerations for induction machines for electric vehicle drives. In: Proceedings of IEE Seventh International Conference on Electric Machines and Drives, September 11–13, 1995. University of Durham, UK. p. 16–20. [20] Vas P. Vector control of AC machines. Oxford: Clarendon Press, 1990. [21] Leonhard W. Control of electric drives. New York: Springer, 1990. [22] van der Broeck HW, Skudelny H, Stanke G. Analysis and realization of a pulse width modulator based on voltage space vectors. In: Proceedings of the 1986 IEEE IAS Annual Meeting, September 28–October 3, 1986. Denver, Colorado. p. 244–51. [23] Holtz J. Pulsewidth modulation for electronic power conversion. Proc IEEE 1994;82(8):1194–214. [24] Hava AM, Kerkman RJ, Lipo TA. Simple analytical and graphical tools for carrier based PWM methods. In: Proceedings of the 28th IEEE Power Electronics Specialist Conference (PESC97), June 22–27, 1997. St. Louis, Missouri. p. 1462–71. [25] Hava AM. Carrier based PWM–VSI drives in the overmodulation region. Ph.D. Dissertation, University of Wisconsin, Madison, WI, 1998. [26] Kuhn BT, Sudhoff SD, Whitcomb CA. Performance characteristics and average-value modeling of auxiliary resonant commutated pole converter based induction motor drives. IEEE Trans Energy Conver 1999;14(3):493–9.
A virtual prototype for a hybrid electric vehicle
€ Levent U. Gokdere *, Khalid Benlyazid, Roger A. Dougal, Enrico Santi, Charles W. Brice
Electrical Engineering Department, University of South Carolina, Swearingen 3A80, Columbia, SC 29208, USA Received 20 November 1999; accepted 11 October 2000
Abstract A virtual prototype of a hybrid electric vehicle (HEV) is created within the virtual test bed (VTB) environment, which has been developed for modeling, simulation, analysis and virtual prototyping of large-scale multi-technical dynamic systems. Attention is focused on the electric system, which is composed of (i) a fuel cell system as a prime power source, (ii) battery and super capacitor banks as energy storage devices for high and intense power demands, (iii) DCto-DC power converters to control the flow of power, (iv) a three-phase inverter-fed permanent magnet synchronous motor as a drive, and (v) a common DC bus. The simulation of the proposed system is conducted using two types of driving cycles. These are: (i) rapid acceleration and deceleration, and (ii) Federal Urban Driving Schedule (FUDS). The parameter values chosen for the components and the numerical results obtained by simulation are consistent with the practical HEV applications. Ó 2002 Elsevier Science Ltd. All rights reserved.
Keywords: Hybrid electric vehicle; Modeling and simulation; Virtual prototype
1. Introduction Considerable efforts have been expended to develop hybrid electric vehicles (HEVs) as replacements for high-emission cars, buses, and trucks powered by conventional gasoline or diesel engines [1]. The main objective of this paper is to describe a virtual prototype of a HEV by the use of a suitable simulation model. This is an important step in the development of the HEVs due primarily to the following two
Corresponding author. Present address: Rockwell Science Center, 1049 Camino Dos Rios, A18 Thousand Oaks, CA 91360, USA. Tel.: +1-805-373-4087; fax: +1-805-373-4383. E-mail address: [email protected] (L.U. G€kdere). o 0957-4158/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 9 5 7 - 4 1 5 8 ( 0 1 ) 0 0 0 0 9 - 5
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reasons: (i) a good virtual prototype allows for proof testing before hardware is assembled, which means likely reduction in the manufacturing cost and time, and (ii) new design possibilities can be explored; e.g., study of tradeoffs between sizes of components in the HEV is feasible. The National Renewable Energy Laboratory (NREL) has developed ADVISOR, Advanced Vehicle Simulator, which is a very helpful computer simulation tool for analysis of energy use and emissions in both conventional and advanced vehicles [2–4]. The ADVISOR has been developed within the MATLABâ Simulinkâ environment and it allows the user to interchange a variety of components, vehicle configurations, and control strategies [2–4]. Moreover, the ADVISOR has a graphical user interface (GUI) that allows for easy manipulation of input files, test routines, and output plots [2–4]. Further information on ADVISOR and the applications can be found on the web site: www.ctts.nrel.gov/analysis/advisor.html. In this work, the virtual test bed (VTB) is utilized for virtual prototyping of a HEV. The VTB has two important features [5,6]: (i) it has the capability of integrating models that have been created in a variety of languages into a single simulation environment; and (ii) it provides advanced visualization of simulation results, including full-motion animation of mechanical components, and imaginative mappings of computed results onto the system topology. The first feature of the VTB allows each component of a large-scale multi-technical system to be described in the most appropriate language (e.g., SPICE for electronic components, ACSLâ , Advanced Continuous Simulation Language, for dynamic systems, and SABERâ for power electronic circuits) [7]. On the other hand, the second feature enhances user’s comprehension of the simulation results significantly. Unlike any other simulators based on the state variable modeling approach (such as MATLABâ and ACSLâ ), the VTB solver is based on the resistive companion (RC) modeling approach [8]. In this approach, each device (component) is represented as interconnections of resistors and current sources whose values depend on the device parameters and past-history values of the device state variables [8]. In addition, each device is treated as a box with a number of terminals, which provide connections to other devices [8]. A major advantage of the RC modeling approach over the state variable modeling approach is that once the device models are constructed, interconnections of any set of devices can be easily handled [8]. This is especially important for the study of large-scale multi-technical dynamic systems. More information about VTB can be found on the web site http://vtb.engr.sc.edu/ The VTB software and the supporting tools can be also downloaded from the same site for free of charge. The electrical part of the HEV considered in this study is composed of (i) a fuel cell system as the prime source of average electric power (10–15 kW), (ii) battery and super capacitor banks as energy storage devices for high and intense power demands (e.g., 50 and 150 kW, respectively), (iii) boost and Cuk type DC-to-DC power converters to control the flow of power, (iv) a pulse-width modulated (PWM) inverter-fed three-phase permanent magnet synchronous motor (PMSM) with associated vector controller as a drive, and (v) a common DC bus for energy distribution.
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Models for each component of the HEV electrical system were previously developed using ACSLâ , and have been reported in [9,10]. Explanations of the models are given in the next section. Based on the component descriptions, a virtual prototype of the HEV is then built within the VTB. Finally, simulation and animation results are presented to numerically verify the virtual prototype and demonstrate the advanced visualization capabilities of the VTB.
2. Component descriptions for HEV Fig. 1 shows a simplified block diagram for the electrical part of the HEV [9]. The definitions of the fuel cell system, battery bank, super capacitor bank, boost con verter, Cuk converter, PMSM, and the PWM inverter are given in the following subsections. 2.1. Fuel cell system The voltage-current characteristic of a single proton exchange membrane (PEM) hydrogen fuel cell is illustrated in Fig. 2. In this figure, Vfc (vertical axis) is the voltage at the terminals of the fuel cell, and Ifc (horizontal axis) is the current flowing out of the fuel cell. It is seen that there are basically three operation regions. These are, (i) the low current region in which the voltage decreases exponentially as the current increases, (ii) the linear region that covers a large portion of the characteristic, and (iii) the high current region in which there is a sharp drop of the voltage to near-zero [11]. Note also that, the units for Vfc and Ifc are millivolts and milliamperes, respectively. For the values of Ifc which remain in the low current and linear regions, Vfc versus Ifc may be expressed by
Fig. 1. Block diagram for the electrical part of the HEV.
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Fig. 2. The fuel cell voltage in mV versus fuel cell current in mA.
Vfc ¼ Vfco À b logðIfc =Afc Þ À Rfc Ifc ;
ð1Þ
where Vfco is the open-circuit (zero current) voltage of the fuel cell in mV, b is the Tafel slope in mV, Afc is the cross-sectional area of the fuel cell in cm2 , and Rfc is the internal ohmic resistance of the fuel cell in X [11]. A more complete expression, which is valid for the entire current range, is (see [12]) Vfc ¼ Vfco À b logðIfc =Afc Þ À Rfc Ifc À m expðnIfc =Afc Þ: ð2Þ
In (2), the parameters m and n are empirical equation constants and they can be obtained by a nonlinear regression analysis [12]. The total voltage of a fuel cell stack is given by Vfctotal ¼ Nfc Vfc ; ð3Þ
where Nfc is the number of cells in the stack. The numerical values for the fuel cell parameters are listed in Table 1. The values of Vfco , Afc and Nfc were obtained from [4] while the others were chosen to fit the curve in Fig. 2, where the ranges for the low current and linear regions were adapted from [4]. The fuel cell system under consideration produces power up to 18 kW. This is enough to overcome average air drag and other losses at highway speeds. Another consideration is that the output voltage of the fuel cell system is always low when compared with the common DC bus voltage. This calls for an intermediate
L.U. G€kdere et al. / Mechatronics 12 (2002) 575–593 o Table 1 Fuel cell parameters Vfco b Afc Rfc m n Nfc 1000 mV 25 mV 292 cm2 0.000819 X 0.0475 mV 0.0065 cm2 mAÀ1 110
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DC-to-DC power converter which is capable of transferring the energy from one side with lower voltage to another with higher voltage (see Section 2.4). 2.2. Battery bank The battery bank is composed of a series connection of 25 twelve-volt lead-acid batteries, each rated at 26 A h (or 93,600 C). The dynamic equations of each battery are given by Vcharge ¼ Vchargemin þ ðVchargemax À Vchargemin ÞQ=Qmax ; Vterminal ¼ Vcharge À Rinternal Ibattery ; Q¼ Z
0 t
ð4Þ ð5Þ ð6Þ
ðÀIbattery Þdt þ Qð0Þ;
where Vcharge is the battery internal voltage, Q is the state of charge of the battery, Vterminal is the voltage measured at the terminals of the battery, and Ibattery is the current flowing out of the battery. In (4)–(6), Qmax is the maximum value of Q, Rinternal is the equivalent series resistance of the battery, and Qð0Þ is the initial state of charge of the battery. For Qð0Þ ¼ Qmax , the battery model (4)–(6) is exactly the same as the Ford battery model used in [13]. The parameter values are adapted from [4] and are listed in Table 2. In the simulation, Qð0Þ is set to 10.4 A h (40% of Qmax ), which yields a total battery internal voltage of about 308 V. The battery bank together with the fuel cell system supplies power in the amount of 55 kW, which is sufficient for most of the urban and highway driving cycles including hill climbing at certain speeds.
Table 2 Battery parameters Vchargemin Vchargemax Qmax Rinternal 9.5 V 16.5 V 26 A h 0.015 X
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2.3. Super capacitor bank In this work, a single double-layer super capacitor is represented by the circuit in Fig. 3, which consists of an equivalent series resistance Resr and an ideal capacitance Cideal [14]. The equivalent series resistance, also abbreviated as ESR, accounts for the losses in the super capacitor [14]. As shown in Fig. 3, let Vsuper and Isuper denote, respectively, the voltage at the terminals of the super capacitor and current flowing into the super capacitor. The voltage-current relationship of the super capacitor is then expressed by Z t 1 Vsuper ¼ Resr Isuper þ Isuper dt þ Videal ð0Þ; ð7Þ Cideal 0 where Videal ð0Þ is the initial voltage across the ideal capacitance Cideal . Note that Vsuper ð0Þ (the initial value of Vsuper ) is equal to Videal ð0Þ if Isuper ð0Þ (the initial value of Isuper ) is zero. Table 3 lists the parameter ratings of single double-layer super capacitor [14]. To achieve higher voltage rating, the series and parallel connections of the super capacitors are considered in this work. Specifically, a super capacitor network of four parallel branches is utilized, where each branch consists of series connections of 200 super capacitors. This results in a super capacitor bank, the overall voltage rating, capacitance and ESR of which are 460 V, 9.4 F and 0.225 X, respectively. The overall initial voltage of the super capacitor bank is set to 460 V in the simulation. The super capacitor bank contributes to the peak and intense power requirements of the HEV, which might be as high as 160 kW and as brief as few seconds. This is necessary to accelerate the vehicle under consideration to a speed of 50 km/hr (31.1 mph) in 7 s. The super capacitor bank also accepts (transiently) part of the energy released by the drive motor during regenerative braking [9,10].
Fig. 3. The equivalent circuit for the super capacitor.
Table 3 Super capacitor parameters Cideal Resr Rated voltage Maximum current 470 F 4.5 mX 2.3 V 343 A
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The voltage across the super capacitor bank might swing above and below the common DC bus voltage considerably due to the excessive incoming and outgoing currents during rapid braking and acceleration. This necessitates an intermediate bidirectional DC-to-DC power converter, which is capable of operating in both up and down modes (see Section 2.4). 2.4. Power converters for fuel cell system and super capacitor The fuel cell system and super capacitor are connected to the common DC power bus through DC-to-DC power converters of the boost and Cuk topologies. The converter associated with the fuel cell is boost type and commands the energy transfer out of the fuel cell. On the other hand, the converter for the super capacitor is bi-directional and Cuk type. It controls the power flow into and out of the super capacitor. Fig. 4 shows the circuit diagram for the boost converter [15]. The state-space average model of the circuit is given by [16] diL Àð1 À DÞvout þ vin ¼ ; dt L dvC ð1 À DÞiL À iout ¼ ; dt C ð8Þ ð9Þ
where duty ratio D is the fraction of the switching period during which switch S1 is closed and switch S2 is opened. The parameter values are selected as in Table 4. Fig. 5 is the circuit diagram for the bi-directional Cuk converter [15,17]. The corresponding average model is [16] diL1 vin À ð1 À DÞvC ¼ ; dt L1 ð10Þ
Fig. 4. Circuit diagram for the boost converter.
Table 4 Boost converter parameters L C 1 mH 100 lF
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Fig. 5. Circuit diagram for the bi-directional Cuk converter.
diL2 DvC À vout ¼ ; dt L2 dvC ð1 À DÞiL1 À DiL2 ¼ ; dt C
ð11Þ ð12Þ
where duty ratio D is defined in a similar manner. The values of the inductances and the capacitor are given in Table 5. In [10,18], the feedback controllers were designed, and also verified by simulation results, to accomplish the operational objectives of the boost and Cuk converters. The feedback controllers were based on the average models (8), (9) and (10)–(12). 2.5. Three-phase PMSM The d–q model of the three-phase PMSM considered for the HEV is given by dId Vd Rs ¼ À Id þ pxIq ; dt L L dIq Vq Rs 3p xkmax ; ¼ À Iq À pxId À 2L dt L L dx 1 ¼ ðTe À k0 À k1 x2 Þ; dt k2 ð13Þ ð14Þ ð15Þ
where Vd and Vq are the stator d and q voltages, Id and Iq are the stator d and q currents, x is the angular velocity of the rotor, Rs is the resistance of the stator phase winding, L is the inductance of the stator phase winding, p is the number of polepairs and kmax is the flux linkage due to the permanent magnets. The parameters k0 , k1 and k2 are related to the force opposing the motion of the vehicle and are defined as
Table 5 Cuk converter parameters L1 L2 C 1 mH 1 mH 100 lF
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k0 ¼ k1 ¼
D D
D
1 ðmgrw sin hh þ kR mgrw cos hh Þ; ng
3 qCd Af rw ; 2n3 g 2 mrw þ Jw ; n2 g
ð16Þ ð17Þ ð18Þ
k2 ¼ Jm þ
where m is the mass of the vehicle, hh is the angle of vehicle to horizontal, n is the overall gear ratio, g is the transmission efficiency, rw is the wheel radius, kR is the rolling resistance coefficient, g is the acceleration due to gravity, q is the air density, Cd is the drag coefficient, Af is the frontal area, Jm is the moment of inertia of the drive motor (PMSM), and Jw is the moment of inertia of the wheels [19]. In (15), Te is the electrical torque (i.e., the torque produced by the motor) and is computed from Te ¼ pkmax Iq : ð19Þ
The stator d–q voltages Vd and Vq are related to the stator three-phase voltages Va , Vb , and Vc by 2 3 V 3=2 pffiffiffiffiffiffiffiffi 0 0ffiffiffiffiffiffiffiffi 4 a 5 Vd cosðphÞ sinðphÞ p ð20Þ Vb : ¼ 0 3=2 À 3=2 Vq À sinðphÞ cosðphÞ Vc The same relationship is also valid for the stator d–q and three-phase currents. The parameter values for the PMSM and vehicle are listed in Tables 6 and 7, respectively. The parameter values in Table 7 are for a prototype electric vehicle Fiat Cinquecento [19]. To fulfill the acceleration and deceleration requirements of the vehicle, a currentcommand rotor-oriented speed controller (vector controller) is designed, and also verified by simulation results, in [9]. The reader is referred to [20,21] for more information on PMSMs and associated vector controllers. 2.6. PWM inverter for PMSM Over the years, the space vector pulse-width modulation (SVPWM) technique for voltage source inverters has received widespread acceptance due to its implementation simplicity and superior performance characteristics such as low-harmonic loss factor [22–25]. The linear modulation range of SVPWM technique terminates at a
Table 6 PMSM parameters Rs L p kmax Jm 0.39 X 444 lH 3 0.0737 Wb 0.0355 kg m2
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Table 7 Vehicle parameters (from [19]) m hh n g rw kR g q Cd Af Jw 1260 kg 0.0 radians 7.3 0.9 0.256 m 0.009 9.81 m sÀ2 1.225 kg mÀ3 0.315 1.75 m2 0.004 kg m2
pffiffiffi modulation index of 3p=6 ¼ 0:907 [23–25]. In other words, with SVPWM scheme, the maximum value of the fundamental component of the output (phase) ffiffivoltage pffi that can be commanded without introducing low-order harmonics is Vdc = 3 where Vdc is the DC link (bus) voltage [26]. Taking this into account, the stator d–q voltages of the PMSM are limited by (see transformation (20)) [26] qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi 3 Vdc : Vd2 þ Vq2 6 ð21Þ 2 Assuming that the inverter is lossless, the input current Idc into the inverter is calculated by setting Pin ¼ Pout and then solving for Idc where Pin ¼ Vdc Idc is the input power to the inverter and 2 Pout ¼ ðVd Id þ Vq Iq Þ 3 ð23Þ ð22Þ
is the output power delivered by the inverter to the PMSM [26]. The expression for Idc is then obtained as Idc ¼ 2 Vd Id þ Vq Iq : 3 Vdc ð24Þ
The constraint (21) and expression (24) represent an average-value model for the SVPWM inverter [26].
3. A virtual prototype of HEV in VTB In this section, based on the component descriptions in Section 2, a virtual prototype for the electrical part of the HEV is developed and also verified by simulation results within the VTB environment. The virtual prototyping of the HEV is accomplished using VTB native models, which are originally written in C++. Once the source code for each component is created, it is then built into a dynamically linked library (DLL) form that allows the component to be inserted into or removed from
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the system topology at will during an interactive simulation [5,6]. The C++ source code includes the component description based on the RC modeling approach [8]. Fig. 6 illustrates the VTB schematic view for the electric system of the HEV [18]. In the schematic, the user can easily change the values of the component parameters through an editor which pops up by double clicking on the component. The simulation of the proposed HEV system was carried out considering two types of driving cycles. These are: (i) rapid acceleration and deceleration, and (ii) Federal Urban Driving Schedule (FUDS). The following subsections present the simulation results. The parameter values chosen for the components and vehicle are the same as in Section 2, unless indicated otherwise. 3.1. Rapid acceleration and deceleration In this move, the vehicle was first accelerated to a speed of 50 km/h (31.1 mph) in 7 s, then, held constant at that speed for 3 s, and finally, brought down to rest in 7 s. Figs. 7–9 show the results obtained with this move. Fig. 7 displays the speed tracking performance of the vehicle. In this figure, due to the close tracking, the actual and reference speeds are on top of each other. The input current Idc into the PWM inverter and the DC bus voltage Vdc are given in Fig. 8. It is seen that during the acceleration phase (from 0 to 7 s), Vdc drops as Idc increases. On the other hand, in the deceleration phase (from 10 to 17 s), Vdc reaches a peak value. During the deceler-
Fig. 6. The VTB schematic view for the electrical system of the HEV.
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Fig. 7. Actual and reference speeds of HEV (maximum speed 31.1 mph).
Fig. 8. Input current in amperes and bus voltage in volts (for driving cycle in Fig. 7).
ation, the energy supplied by the motor charges the battery bank via the DC bus. As a result, the DC bus voltage, which is floating at the battery bank voltage, increases [9]. Fig. 9 shows the total input power Pin to the inverter and contributions of the fuel cell (Pfc ), battery bank (Pbattery ) and super capacitor (Psuper ) to Pin . During the acceleration, the fuel cell system is commanded to provide power up to the 18 kW (due to the recommendations of manufacturer, the minimum voltage of the fuel cell system is limited to 60 V, which corresponds to a maximum power of 18 kW [4]). On the other hand, the battery bank together with the fuel system provides just about 55 kW (maximum). Finally, the super capacitor supplies the rest of Pin , which goes up to 160 kW during the acceleration. Note here that the super capacitor also accepts a significant fraction of Pin during deceleration to prevent the battery bank from overcharging.
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Fig. 9. Contribution of each energy device to the total input power (for driving cycle in Fig. 7).
In another test, the vehicle was accelerated to the maximum speed of 100 km/h (62.1 mph) in 18 s, then, held constant at that speed for 12 s, and finally, brought down to rest in 18 s. It was observed that the motor torque Te and the total input power required for the steady-state operation at the maximum speed are 14.5 N m and 12.5 kW, respectively. These are consistent with the vehicle specifications mentioned in [19]. Figs. 10 and 11 illustrate the results for this test. 3.2. Federal urban driving schedule (FUDS) Fig. 12 shows the actual and reference vehicle speeds for the FUDS (the two are on top of each other due to close tracking). The total input power and contributions of each energy device are given in Figs. 13–16. The control strategies for the energy
Fig. 10. Motor torque in N m and vehicle speed in mph (maximum speed 62.1 mph).
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Fig. 11. Total input power (for driving cycle in Fig. 10).
Fig. 12. Actual and reference speeds of HEV for FUDS.
devices are as in Section 3.1. From Fig. 16, it is seen that the super capacitor is inactive for the most of the driving cycle. This is due to the fact the total input power remains mostly below 55 kW. Also, it has been observed the bus voltage fluctuates between 250 and 340 V for the entire cycle, while the single battery charge reduces to only 9.8 A h (from 10.4 A h) at the end of the cycle. This implies that, with the control strategies mentioned above, the vehicle sustains enough energy to overcome demanding and lengthy driving cycles. In another test, a new set of vehicle parameters were adapted from [4]. Table 8 lists the new values (the other parameters remain the same). The total input power for this test follows a similar pattern to that of [4]. The result is shown in Fig. 17.
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Fig. 13. Total input power for FUDS.
Fig. 14. Power supplied by fuel cell system for FUDS.
Fig. 15. Power supplied by battery bank for FUDS.
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Fig. 16. Power supplied by super capacitor bank for FUDS.
Table 8 Vehicle parameters (adapted from [4]) m hh n g rw kR g q Cd Af Jw 1191 kg 0.0 rad 9.0 0.9 0.282 m 0.009 9.81 m sÀ2 1.2 kg mÀ3 0.335 2.00 m2 0.004 kg m2
Fig. 17. Total input power for FUDS (with vehicle parameters in Table 8).
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4. Animation of HEV An important feature of the VTB is its advanced visualization system, which allows full motion animation of the mechanical components. The visualization can operate either interactively or off-line. During an interactive session, the simulation output data is streamed to the visualization sub-system [5]. On the other hand, data generated in an off-line simulation is first stored in the form of a text file and then interfaced to the visualization system by a plug-in device [5].
Fig. 18. Animation view of the vehicle body.
Fig. 19. Animation view of the vehicle dashboard.
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This aspect of the VTB has been utilized to achieve the full motion animation of the HEV. Figs. 18 and 19 display the screen snapshots that come from the animation. Fig. 18 is the animation view of the vehicle body while Fig. 19 is the animation view of the vehicle dashboard. During the animation, the vehicle travels on the ground level at varying speeds specified by the driving cycle, while the gauges on the dashboard indicate the instant values of the corresponding variables.
5. Conclusions A virtual prototype for a HEV was developed and also numerically verified by simulation results within the VTB environment. The virtual prototyping was achieved using the VTB native models of the components. Also, based on the simulation results, a full motion animation of the HEV was performed to demonstrate the advanced visualization capabilities of the VTB. One of the unique features of the virtual prototype is that it includes all possible energy devices (fuel cell system, battery bank, and super capacitor bank) for the next generation HEVs. Further, to be consistent with the real world applications, the nonlinear dynamics, ohmic losses, and voltage/current limits of the components are taken into account.
Acknowledgements This work was supported by the Office of Naval Research under Grants N0001496-1-0926 and N00014-00-1-0131.
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