The Pennsylvania State University. The Graduate School. Department of Mechanical and Nuclear Engineering

Transcription

1 The ennsylvania State University The Graduate School Departent of Mechanical and Nuclear Engineering SCALING OF HYBRID-ELECTRIC VEHICLE OWERTRAIN COMONENTS FOR HARDWARE-IN-THE-LOO SIMULATION A Thesis in Mechanical Engineering by Michael D. etershei 28 Michael D. etershei Subitted in artial Fulfillent of the Requireents for the Degree of Master of Science May 28

2 ii The thesis of Michael D. etershei was reviewed and approved* by the following: Sean N. Brennan Assistant rofessor of Mechanical Engineering Thesis Advisor Chris D. Rahn rofessor of Mechanical Engineering Karen A. Thole rofessor of Mechanical Engineering Head of the Departent of Mechanical Engineering *Signatures are on file in the Graduate School

3 iii ABSTRACT Hardware in the loop (HIL) siulation enables experiental study of prototype hardware systes or control algoriths via real-tie interaction between physical hardware and virtual siulations. As a result, this ethod is a particularly valuable tool for hybrid vehicle powertrain analysis. In the case where novel or prototype hardware is being exained, it is often necessary to scale the signals in and out of the prototype syste in order to represent production-sized coponents. This scaling process is usually done in an ad-hoc anner. In this work, a foral ethod is presented that derives appropriate input/output signal conditioning to correctly scale electric vehicle coponents, particularly the following subsystes: electric otor, battery pack, ultracapacitor pack, engine, and fuel cell.

4 iv TABLE OF CONTENTS LIST OF FIGURES...vi LIST OF TABLES...ix ACKNOWLEDGEMENTS...x Chapter Introduction.... Motivation Hybrid Electric Vehicles Hardware-in-the-Loop Scale Models Diensional Analysis The enn State Hardware-in-the-Loop Syste Thesis Outline...7 Chapter 2 The Diensionless Variable Method Applied to a Motor Model Case : Electric Motor Model fro the SAT Library The Diensionless Variable Method Siulation Results...5 Chapter 3 Battery ack Model Scaling Factors Case 2: Dynaic Battery ack Model fro the SAT Library Siulation Results...27 Chapter 4 Ultracapacitor ack, Engine, and Fuel Cell Scaling Case 3: Ultracapacitor ack Model fro the SAT Library Case 4: Engine Model fro the SAT Library Engine Scaling Siulation Results Case 5: Fuel Cell Model fro the SAT Library...46 Chapter 5 Battery Scaling Experient Setup of the Experient Batteries Vehicle owertrain Models Scaling Factors Control Equipent Coplete Experiental Syste Experiental Results...65

5 Chapter 6 Conclusions and Future Work...7 v 6. Conditions for Use of Scaling Factors Conclusion Future Work...7 Bibliography...72 Appendix A Modification of SAT Models for HIL...75 A. Use of SAT odels for HIL...75 A.. reparation of the SAT odel to run independently of SAT...75 A... SAT Version A...2 SAT Version A..2 reparation of the Siulink odel to run on an ebedded syste xc Target required...8 A..3 Addition of inputs/outputs to a Siulink odel TeraSoft library required for Advantech...8 A..4 Control of the ABC-5 fro an ebedded coputer requires additional C running Windows, hereafter known as Link, equipped with serial port, with Borland C, LabView or Visual Basic requires AeroVironent serial port driver: SD.EXE...82 A.2 Setup of Advantech UNO-372 coputers to boot xc Target fro CopactFlash...83 A.2. Creation of and bootup fro a DOS floppy...83 A.2.2 Configuration of CopactFlash with xc Target Boot Kernel (After booting with the DOS floppy)...85 A.2.3 Operation of the ebedded coputer, hereafter known as Target requires a C with xc Target, hereafter known as Host...86

6 vi LIST OF FIGURES Figure -: Networked hybrid electric vehicle powertrain HIL syste under developent at the ennsylvania State University...6 Figure -2: General representation of a powertrain HIL test...7 Figure 2-: Coparison of saple M and induction otor torque-speed curves.... Figure 2-2: Motor odel inputs and outputs.... Figure 2-3: Diensionless torque-speed curve coparison...5 Figure 2-4: Diensionless torque-speed curves of fifteen AC induction and peranent agnet DC otors fro the SAT otor odel library....6 Figure 2-5: Torque coand input to otor odels during first s of siulation....7 Figure 2-6: Voltage input to otor odels during first s of siulation...7 Figure 2-7: Shaft speed input to otor odels during first s of siulation...8 Figure 2-8: Torque trace of otor odels during first s of siulation....8 Figure 2-9: Difference between torque traces of original and scaled otors....9 Figure 2-: Current trace of otor odels during first s of siulation....9 Figure 2-: Difference between current traces of original and scaled otors...2 Figure 3-: Tie constant of two typical cells Figure 3-2: Dynaic resistance of two typical cells...22 Figure 3-3: Open circuit voltage of two typical cells Figure 3-4: Battery pack odel signals Figure 3-5: Scaled current loads on two NiMH battery packs in SAT siulation of Honda Insight on US6 driving cycle Figure 3-6: Voltage trace coparison of SAT siulation of Honda Insight on the first 3 s of the US6 driving cycle with two NiMH battery packs Figure 3-7: Difference between voltages of prototype and scaled NiMH battery packs....29

7 Figure 3-8: Scaled current loads on two NiMH battery packs in SAT siulation of Honda Insight on US6 driving cycle....3 Figure 3-9: Voltage trace coparison of SAT siulation of Honda Insight on the first 3 s of the US6 driving cycle with prototype NiMH and scaled Li-Ion battery packs....3 Figure 3-: Difference between voltages of prototype NiMH and scaled Li-Ion battery packs, copared with difference between voltages of prototype and scaled NiMH battery packs...3 Figure 4-: Internal resistance of an ultracapacitor as a function of current Figure 4-2: Capacitance of a typical ultracapacitor as a function of current Figure 4-3: Ultracapacitor pack odel signals Figure 4-4: Engine odel inputs and output...39 Figure 4-5: Engine diensionless power...43 Figure 4-6: Engine shaft speed inputs...44 Figure 4-7: Engine throttle inputs...44 Figure 4-8: Engine torque outputs, scaled to atch the 9 kw engine Figure 4-9: Difference between torques of prototype and scaled engines...45 Figure 4-: Cold hydrogen ass flow rate Figure 4-: Hot hydrogen ass flow rate Figure 4-2: Fuel cell input and output...48 Figure 5-: Experient configuration Figure 5-2: Experient configuration Figure 5-3: FreedoCar Maxiu ower-assist (5 Wh) Efficiency and Baseline Cycle Life ower Deand rofile [26] Figure 5-4: Measured and estiated voltage of Deka battery Figure 5-5: Measured and estiated voltage of the Odyssey battery...58 Figure 5-6: Experient configuration....6 vii

8 Figure 5-7: Experient configuration....6 Figure 5-8: Experient configuration Figure 5-9: Aerovironent ABC-5 ower rocessing Syste Figure 5-: Coplete experiental syste Figure 5-: Current load applied to batteries in the AR siulation Figure 5-2: Voltage response of batteries, scaled to pack size, in the AR siulation Figure 5-3: Difference between voltages of batteries in the AR siulation Figure 5-4: Current load applied to batteries in the EV siulation...67 Figure 5-5: Voltage response of batteries, scaled to full pack size, in the EV siulation Figure 5-6: Difference between voltage responses in the EV siulation...68 viii

9 ix LIST OF TABLES Table 2-: araeters Relevant to Motor Scaling...2 Table 2-2: Motor Scaling i-groups...3 Table 2-3: Motor Scaling Equivalency...5 Table 3-: araeters Relevant to Battery ack Scaling...24 Table 3-2: Battery ack Scaling i-groups...25 Table 3-3: Battery ack Scaling Equivalency...26 Table 4-: araeters Relevant to Ultracapacitor ack Scaling...36 Table 4-2: Ultracapacitor ack Scaling i-groups...37 Table 4-3: Ultracapacitor ack Scaling Equivalency...37 Table 4-4: araeters Relevant to Engine Scaling...4 Table 4-5: Engine Scaling i-groups...4 Table 4-6: Engine Scaling Equivalency...4 Table 4-7: araeters Relevant to Fuel Cell Scaling...48 Table 4-8: Fuel Cell Scaling i-groups...49 Table 4-9: Fuel Cell Scaling Equivalency...5 Table 5-: Battery Testing Discharge/Charge rofile...55 Table 5-2: Battery characteristic estiation statistics...57 Table 5-3: Characteristic battery pi-paraeters...58 Table 5-4: Battery characteristics...59 Table 5-5: HIL scaling factors...62

10 x ACKNOWLEDGEMENTS This work was supported in part by the U.S. Departent of Energy under the Graduate Autootive Technology Education progra.

11 Chapter Introduction Hardware in the loop (HIL) siulation enables experiental study of prototype hardware systes or control algoriths via real-tie interaction between physical hardware and virtual siulations. As a result, this ethod is a particularly valuable tool for hybrid vehicle powertrain analysis. In the case where novel or prototype hardware is being exained, it is often necessary to scale the signals in and out of the prototype syste in order to represent production-sized coponents. This scaling process is usually done in an ad-hoc anner. In this work, a foral ethod is presented that derives appropriate input/output signal conditioning to correctly scale electric vehicle coponents, particularly the following subsystes: electric otor, battery pack, ultracapacitor, engine, and fuel cell. This introduction explains the otivation for the work, giving an overview of hybrid electric vehicles, hardware-in-the-loop, scale odels, and diensional analysis. A suary of the enn State hardware-in-the-loop syste follows, along with a thesis outline.

12 2. Motivation.. Hybrid Electric Vehicles The Toyota rius, the first ass-produced hybrid electric vehicle (HEV), went on sale in Japan in Deceber 997, and was a surprising success []. Since then, the nuber of HEVs on the arket increases annually. Selling points of HEVs include their reduced fuel consuption and reduced exhaust eissions. The latter point has recently grown in iportance with increased concern about global waring. The ennsylvania State University is involved with the developent of HEV technology in several ways: Student groups have constructed several HEVs for national copetitions. Research involving coponents of HEV powertrains is perfored by various faculty and research staff, soe of which are ebers of the Advanced Energy Storage Center. enn State hosts a Graduate Autootive Technology Education (GATE) center sponsored by the U.S. Departent of Energy. The center offers several courses annually, including HEV Lab...2 Hardware-in-the-Loop Hardware-in-the-loop (HIL) siulation enables the interaction of virtual coputer-based siulation odels of a syste or subsyste with actual coponents of the syste in real-tie. Because this perits the inclusion of coponents for which accurate coputer odels do not yet exist or for which intense coputing resources are required, this ethod is finding increasing use in nearly every discipline. HIL systes

13 have been eployed for decades in nuerous disciplines to evaluate novel hardware or 3 software designs including earth-oving vehicles, ocean-going vessels, suspension systes, earthquake-proof buildings, powertrain controllers, unanned underwater vehicles, autootive safety systes, achine tools, sonar systes, and aircraft [2, 3, 4, 5, 6]. If one assues that the huan is a subsyste central to vehicle control, then all driving siulators can also be classified as a type of HIL syste. HIL testing is increasingly useful in applications involving hybrid electric vehicle powertrains [5, 7, 8, 9,, ]. The use of HIL can replace, to significant extent, the construction of expensive prototypes to test drivetrain systes. In any cases, the prototype hardware is a reduced-scale surrogate for actual size hardware, built to evaluate perforance and feasibility rather than actually power a coercial vehicle. Exaples include prototype fuel cells, engines, batteries, and electric otors [7, 8, 9,,, 2]. In nearly all cases, construction of a full-sized prototype is onerous and/or unnecessarily expensive...3 Scale Models Closed-loop HIL testing of benchtop prototypes are especially useful to understand the interaction between the highly coupled subsystes typically found in an electric or hybrid-electric vehicle. In this way, one prototype cell of a fuel cell stack ay be tested in a HIL environent to estiate the perforance of an entire pack of cells in a production vehicle. Or a short string of a battery pack ay be used to infer the perforance of a large string of batteries, etc.

14 Scale odels have been used to infer the behavior of a full-size prototype since 4 Willia Froude tested ship odels in water tanks [3]. Wilbur and Orville Wright built the first wind tunnel to try various configurations of scale aircraft wings, resulting in the first successful flying achine. Scale odels were eployed in the design of lunar rovers in the 96s [7]. Scale odels of road vehicles have been in use since 934 [9]. More recently, the ennsylvania State University Rolling Roadway Siulator (URRS) operates a scale vehicle on a treadill for vehicle rollover testing [9]. A key proble with coparisons is that scaling effects arise when hardware of one size is siulated by hardware of another size [2]. Doubling the nuber of cells in series within a fuel cell stack does not double the available electrical current. And when theral effects are included, a production-sized pack of cells ay overheat under typical environental and packaging conditions whereas a single benchtop cell would operate without incident. Furtherore, it is often not the intent to scale or operate the prototype syste such that it tracks the input/output behavior of an existing syste. Nor is it desirable in general to design high-gain feedback controllers that force the prototype to track a reference perforance of existing hardware. Both ad-hoc ethods negate the very intent of ost prototype systes, that is, to observe differences in behavior relative to existing systes.

15 5..4 Diensional Analysis What is needed therefore is an understanding of how to copare dissiilarly sized coponents using scaling factors that are physically based, e.g. tied to experientally easurable variations in key paraeters rather than nuerical ethods. This understanding should be generalized and validated by coparing dissiilarly scaled systes that share coon dynaic liitations. If, under the chosen scaling factors, we observe that dissiilarly sized coponents ap to the sae general odel behavior in a diension-free setting, then we have confidence that the sae scaling ethods ight appropriately ap a bench-scale prototype to the expected production-level coponent. The goal of this work is to apply the use of diensionless variables, as defined by the i Theore [4, 5, 6], to hybrid electric vehicle powertrain coponents for the purpose of taking into account the relevant scaling effects. Siilar work has been conducted before [2, 7, 8, 2, 2], but not on the coponents entioned herein. Diensional analysis has its roots in work by Euler, Newton, Fourier, Maxwell, and Rayleigh [7]. The ethod of diensional scaling was foralized as the i Theore by Buckingha [5]. Szirtes provided an explanation of a painless ethod for obtaining diensionless paraeters using the diensional set atrix [4]. Brennan further developed the concepts of diensional analysis by its application to sensitivity analysis [7]. Kittirungsi et al enhanced the effectiveness of the ethod by coupling it with activity based odel reduction [2].

16 6..5 The enn State Hardware-in-the-Loop Syste The otivation for the present study is the developent of a networked hybrid electric vehicle powertrain hardware-in-the-loop (HIL) syste underway at the ennsylvania State University (see Figure -). In this project, HIL equipent in various laboratory settings across capus is linked via Ethernet. These include an electrical power processing achine, engine dynaoeters, chassis dynaoeters, and ultracapacitor and fuel cell test benches. The HIL syste is used for graduate course labs, student vehicle copetitions, and industry-sponsored projects. The eventual goal is to allow collaborative testing both between research laboratories at enn State as well as off-capus industry and governent laboratories. Electric Motor Lab IC Engine Lab Chassis Dyno Lab Flywheel Lab enn State Capus Ultracapacitor Lab Fuel Cell Lab Battery Lab Driving Siulator Figure -: Networked hybrid electric vehicle powertrain HIL syste under developent at the ennsylvania State University. As a basis for incorporating individual powertrain coponents into HIL siulations, powertrain odels fro the well-known owertrain Systes Analysis Toolkit (SAT) fro Argonne National Laboratory [22] are utilized within a

17 MATLAB/Siulink/xC Target TM environent [23]. One or ore coponents of the 7 powertrain are replaced by a set of output(s) and input(s) fro/to equipent which controls the individual hardware coponent(s) (Figure -2). Typically the hardware is not full-size, in which case input and output signal scaling factors ust be ipleented in the software environent to copare appropriately to full-sized vehicle coponents. Deterination of these scaling factors, shown as triangles in Figure -2, is the focus of this work. odel input powertrain odel odel output HIL coponent software rescale scale HIL control equipent hardware Figure -2: General representation of a powertrain HIL test...6 Thesis Outline The reainder of this work is organized as follows: In Chapter 2, a procedure is developed via the diensionless variable ethod to derive input/output scaling factors, and is applied to a steady state otor odel in the context of a vehicle powertrain siulation. In Chapter 3, the sae ethod is applied to a dynaic battery odel, also in the context of siulation. In Chapter 4, scaling factors are derived for additional powertrain coponents including ultracapacitors, engines, and fuel cells. In Chapter 5, a

18 presentation is ade of the setup and results of an experient with actual hardware. 8 Chapter 6 suarizes the ain results and points the way for future work.

19 Chapter 2 The Diensionless Variable Method Applied to a Motor Model 2. Case : Electric Motor Model fro the SAT Library The proposed ethod for obtaining scaling factors and deterining dynaic siilarity of systes involves the foration of an equivalent syste representation using diensionless variables [7, 24]. This ethod will be illustrated first with an electric otor, and later with a battery. To investigate scaling effects related to electric vehicle drive systes, the owertrain Systes Analysis Toolkit (SAT) [22] electric otor odel library was used which includes ainly AC induction otors and large peranent agnet (M) DC otors. In the SAT software, one otor can be substituted for another during software prototyping of new vehicle design, hence soe siilarity in perforance across the any otor odels in this software is expected. To investigate potential siilarity of the otors, the steady-state torque-speed curves of each otor were plotted. Steady-state was chosen because transient effects of each otor are inor copared to their steady-state perforance during typical driving cycles. A saple torque-speed curve coparison is shown in Figure 2-. One can observe siilarity in the curve shapes, yet little atch between torque speed values theselves.

20 Figure 2-: Coparison of saple M and induction otor torque-speed curves. The SAT otor odel takes as inputs: DC voltage V, shaft speed Ω, and a torque coand signal θ with range [-, ], defined as desired torque T ref divided by axiu torque T ax. Outputs are current I and torque T. Inputs and outputs are shown in Figure 2-2. Torque coand θ DC voltage V Shaft speed Ω Motor odel Current I Torque T Figure 2-2: Motor odel inputs and outputs. The rest of the SAT otor odel follows: A derived quantity is power. Steady-state paraeters are: axiu current I ax, axiu torque T ax, and axiu

21 power ax. Since the application of the otor is for a traction drive, the rotational inertia of the otor is negligible in coparison to the inertia of the vehicle. Thus the dynaics of the otor are neglected and only steady-state input-output relationships are considered. The siplest relationships also neglect efficiency, as shown in Eq. 2.. T =θ I = T Ω I = V ax V Ω 2. The paraeters T and are saturated by T ax and ax, as in Eq T ax ax T T ax ax The Diensionless Variable Method To apply the diensionless variable ethod, let N be the nuber of syste paraeters, and let M be the nuber of physical diensions required to describe all the N paraeters in the governing equation. The otor syste has N = 3 paraeters, I ax, T ax, ax, coposed of M = 4 diensions, length, ass, tie, and current. In the SI unit syste, the unit basis vector is u = [ kg s A] T. In addition to the paraeters, there are signals S, which will also be rescaled, for exaple, V, Ω, θ, I, T, which represent inputs and outputs. The signals and paraeters are shown with their diensions in Table 2-. In the SAT environent, the torque coand signal θ is diensionless, and is thus excluded fro diensional scaling.

22 2 Table 2-: araeters Relevant to Motor Scaling Variable Sybol Diension current I A torque T -2 2 kg s voltage V - 2 kg s -3 A rotational speed Ω s - axiu current I ax A axiu power ax -3 2 kg s axiu torque T ax -2 2 kg s The nuber of fundaental diensions is four, but the [ 2 ] diension and the [kg] diension always appear together, so the two are cobined into a new coposite diension, leaving a total of M = 3 diensions. To transfor a nondiensional representation to a diensional (classic) representation and back again requires rescaling with respect to M independently diensioned paraeters or signals, also known as repeating paraeters. These ay be arbitrarily chosen, but they ust aong theselves contain all of the diensions of the syste. For the present exaple, I ax, T ax, and ax, being the only paraeters, ust be chosen as repeating paraeters. The repeating paraeters, signals to be rescaled, diensions, and diensionless groups, also known as pi-groups, ay be represented in atrix for, as in Eq. 2.3, where A D is square and full rank. The nuber of pi-groups is Q = N + S M. In this case, Q = 4. diensions π - groups other paraeters B I D repeating paraeters A C D S 2.3 With the proble thus forulated, the only unknown atrix, C S, is deterined according to Eq Details can be found in [4].

23 3 C S = ( A B ) T 2.4 D D The nuber of repeating paraeters is therefore also three, so the last three paraeters are selected as the repeating paraeters. The copleted diensional set atrix is given in Eq π π π π 2 kg s A, ot 2, ot 3, ot 4, ot I T 2 V 3 Ω I ax ax 3 T ax The resulting pi-groups, with the addition of the torque coand signal θ, are given in Table 2-2. Table 2-2: Motor Scaling i-groups Diensionless Variable Variable Grouping π,ot - I I ax π 2,ot - T T ax π 3,ot - V I ax ax π 4,ot π 5,ot Ω ax - T ax θ The diensionless odel representation of Eq. 2. is given in Eq T T ax I I ax V I =θ = T T ax ax ax Ω T ax Ω T ax ax ax V I ax ax 2.6

24 In pi-variable for, the above becoes Eq π π 2, ot, ot = π = π 5, ot 2, ot π π 3, ot 4, ot / π / π 4, ot 3, ot Two systes a and b are dynaically siilar when their syste pi-groups have the sae values, respectively, i.e. π = π, π = π, etc [7]. Thus, an input V (t) of, a, b 2, a 2, b a prototype otor odel ay be transfored into the corresponding input V H (t) of a scaled HIL otor H by using an input scaling factor. Alternately, the output T H (t) of the scaled HIL otor H ay be retransfored into the output T (t) of the prototype otor odel with an output scaling factor. The scaling factors are fored by equating the relevant pi-groups and solving for the variable in question, as in Eq For exaple, to scale prototype voltage, V, to hardware voltage, V H : π 3, ot, H =π 3, ot, VH I V H ax, H ax, H = V I V I = ax, ax, ax, I ax, H ax, ax, H 2.8 Applying this process to each variable, the resulting input-output scaling equivalency is shown in Table 2-3.

25 5 Table 2-3: Motor Scaling Equivalency HIL Coponent I T H V H Ω H θ H I I ax, H T ax, ax, H Tax, H rototype Model Iax, ax, H V I Ω T ax, ax, ax, θ I T T ax, H ax, H ax, H 2.3 Siulation Results The use of diensionless variables to plot syste characteristics is illustrated by a second look at the two otors copared earlier (Figure 2-) in the diensionless doain. This plot is shown in Figure 2-3. Figure 2-3: Diensionless torque-speed curve coparison.

26 The use of diensionless variables to plot torque vs. speed for M and AC 6 induction otors results in visibly atching characteristic curves. For copleteness, a diensionless coparison was ade of all fifteen M and AC induction otors listed in the SAT odel library, with the results shown in Figure 2-4. Again, agreeent is obvious. Figure 2-4: Diensionless torque-speed curves of fifteen AC induction and peranent agnet DC otors fro the SAT otor odel library. Using this scaling ethod, a siulation of a Toyota rius hybrid electric vehicle on the US6 driving cycle [29] was perfored using SAT. Details of how the rius odel was set up to run independently of SAT are given in the Appendix, section A... Inputs to the 3 kw M rius otor were scaled to atch a level equivalent to a 35 kw induction otor also found in the SAT otor odel library.

27 Torque coand input to both otor odels is shown in Figure Figure 2-5: Torque coand input to otor odels during first s of siulation. Voltage input to both otor odels is shown in Figure 2-6. Figure 2-6: Voltage input to otor odels during first s of siulation.

28 Shaft speed input to both otors is shown in Figure Figure 2-7: Shaft speed input to otor odels during first s of siulation. Resulting torque output traces fro both otor odels are shown in Figure 2-8. Figure 2-8: Torque trace of otor odels during first s of siulation.

29 The difference between torque traces is plotted in Figure 2-9. The root ean 9 square error for the cycle is 7.4 N-. Figure 2-9: Difference between torque traces of original and scaled otors. Resulting current output traces fro both otor odels is shown in Figure 2-. Figure 2-: Current trace of otor odels during first s of siulation.

30 The difference between current traces is plotted in Figure 2-. The root ean 2 square error for the cycle is A. Figure 2-: Difference between current traces of original and scaled otors. The torque trace of the prototype rius otor in Figure 2-8 was closely predicted by the torque trace of the scaled HIL otor. In addition, the current trace of the prototype rius otor in Figure 2- was closely predicted by the current trace of the scaled HIL otor. It is assued that if otor efficiency were included in the steady-state equations, then an even closer atch of the traces would result. Since, however, HIL is often perfored in order to predict the efficiency of the prototype, such efficiency is generally unknown and ust necessarily be left out of the scaling.

31 Chapter 3 Battery ack Model Scaling Factors 3. Case 2: Dynaic Battery ack Model fro the SAT Library In the case of the battery pack as an electric vehicle coponent, the dynaics are relatively slow and can be neglected only by accepting significant error in the voltage prediction. The SAT battery pack odel library contains both steady-state and firstorder battery odels, but to aintain accuracy, only the ore accurate first-order odels are considered hereafter. The dynaic syste equations according to the SAT libraries are given in Eq. 3., where current I is the input, voltage V is the output, SOC is the state of charge, V c is a dynaic voltage, n cells is the nuber of cells in the pack, τ is a firstorder tie constant, R c is a dynaic resistance, R int is the internal resistance of a cell, and V OC is the steady state open circuit voltage. The paraeters τ, R c, and V OC are a function of SOC. SOC & = I Q V& c = τ V = V + c Rc( SOC) ncells Vc + ( SOC) τ( SOC) n ( V ( SOC) I R ) cells OC int I 3. The tie constant τ of two typical batteries fro the SAT library, a 6 ap-hour nickel etal hydride cell and a 4 ap-hour Li-Ion cell, is shown as a function of SOC in Figure 3-.

32 22 Figure 3-: Tie constant of two typical cells. The dynaic resistance R c of the sae two cells is shown in Figure 3-2. Figure 3-2: Dynaic resistance of two typical cells.

33 The open circuit voltage V OC of the sae two cells is shown in Figure Figure 3-3: Open circuit voltage of two typical cells. An input-output diagra of the battery pack odel is shown in Figure 3-4. Tie t Current I Battery pack odel Voltage V Figure 3-4: Battery pack odel signals. Again applying the diensionless variable ethod, the battery pack syste has N = 5 paraeters, Q, R c, τ, R int, V OC, coposed of M = 4 diensions, length, ass, tie, and current. The nuber of fundaental diensions is four, but as with the otor exaple, the [ 2 ] diension and the [kg] diension always appear together, so the two

34 24 are cobined into a new coposite diension, leaving a total of M = 3 diensions. The nuber of repeating paraeters is therefore also three. Whereas with the otor exaple, all paraeters becae repeating paraeters, in this exaple a choice is necessary. It is advantageous if the repeating paraeters each have a single diension, are constant, are easily easured, etc. The only constant, R int, shall therefore be selected. Q is a constant in SAT, but is typically specified by anufacturers as a function of the agnitude of I, and is constant only when specified for a particular agnitude of I. The other paraeters are a function of SOC. Repeating paraeters need not be constants, but for convenience a noinal voltage V no is defined, as in Eq The tie constant τ shall be selected for its single diension. With the addition of V no, there are now a total of N = 6 paraeters. V ( ) V SOC =.5 no OC 3.2 To the paraeters shall be added S = 4 signals and state, t, V, V c, I. The signals, state, and paraeters are shown with their diensions in Table 3-. The nuber of cells n cells and the state of charge SOC are already diensionless, and are thus excluded. Table 3-: araeters Relevant to Battery ack Scaling Variable Sybol Diension capacity Q s A dynaic resistance R c -2 2 kg s -3 A voltage V - 2 kg s -3 A dynaic voltage V c - 2 kg s -3 A open circuit voltage V OC - 2 kg s -3 A current I A tie t s tie constant τ s noinal resistance R int -2 2 kg s -3 A noinal voltage V no - 2 kg s -3 A

35 The nuber of pi-groups is Q = N + S M = 7. The copleted diensional set atrix is given in Eq π π π π π π π kg s A, bat 2, bat 3, bat 4, bat 5, bat 6, bat 7, bat Q R c 3 2 V 3 V c 3 V OC 3 I t τ R int 3 2 V no The resulting pi-groups, including the nuber of cells n cells and the state of charge SOC, are given in Table 3-2. Table 3-2: Battery ack Scaling i-groups Diensionless Variable Variable Grouping π,bat Q R int τ - V - no π 2,bat - R c R int π 3,bat - V V no π 4,bat - V c V no π 5,bat - I R int V no π 6,bat - V OC V no π 7,bat t τ - π 8,bat π 9,bat n cells SOC

36 The resulting input-output scaling equivalency is shown in Table Table 3-3: Battery ack Scaling Equivalency HIL Coponent rototype Model t H τ H t τ V H I H no, H cells, H I R V int, no, Vno, ncells, V V n V no, H R int, H The equations of otion are rearranged in diensionless for in Eq τ V ( SOC) τ V ( SOC) ( SOC) V& V R ( SOC) no no n V n I R SOC & = V cells cells c = V = V no V no c n no c cells int n cells τ + V + OC Q R c ( SOC) V R no V int int no I R V no I R V no int int 3.4 The pi-variables are substituted in Eq. 3.5, where the derivative operator is also diensionless, i.e. () τ( d ' SOC). dt π 9, bat π π π π 4, bat 8, bat 3, bat 8, bat π = π π = π 5, bat, bat π = π 4, bat 8, bat 4, bat 8, bat + π + π 2, bat 6, bat π π 5, bat 5, bat 3.5 Again, for dynaic siilarity of two systes, the syste pi-groups need to have identical values [7]. By definition, any ratio of diensionless variables can also be

37 27 defined as a pi-group, such as the ratios π 3,bat /π 8,bat and π 4,bat /π 8,bat. These new pi-groups are equivalent between two systes by Eq. 3.5 as long as π,bat, π 2,bat, π 5,bat, π 6,bat, and π 7,bat are equivalent. By use of an input scaling factor, π 5,bat has been set equivalent in Table 3-3, so there reain four requireents, as shown in Eq π,bat,h = π,bat, π 2,bat,H = π 2,bat, π 6,bat,H = π 6,bat, π 7,bat,H = π 7,bat, 3.6 As an option with the last requireent, to avoid using different tie scales during HIL, an alternative requireent could be τ H (SOC) = τ (SOC). 3.2 Siulation Results The diensionless variable ethod was applied to battery pack scaling in a SAT siulation with a Honda Insight vehicle odel on the US6 driving cycle. Scaling was applied to input I, output V, and paraeters R c and τ. The scaled current loads on the prototype 6 ap-hour, 2 cell nickel etal hydride (NiMH) battery pack and a substitute 2.5 ap-hour, 2 cell NiMH battery pack are shown in Figure 3-5.

38 28 Figure 3-5: Scaled current loads on two NiMH battery packs in SAT siulation of Honda Insight on US6 driving cycle. The resulting pack voltage traces of the battery odels are shown in Figure 3-6. Figure 3-6: Voltage trace coparison of SAT siulation of Honda Insight on the first 3 s of the US6 driving cycle with two NiMH battery packs.

39 As seen in Figure 3-6, the voltage traces of the two battery pack odels are 29 inial. The root ean square error for the entire 6 s cycle is.82 V. The difference between voltage traces is plotted in Figure 3-7. Figure 3-7: Difference between voltages of prototype and scaled NiMH battery packs. In an actual HIL application, however, it is only possible to scale paraeters that are not inputs or outputs by the deliberate choice or construction of the HIL coponent. To illustrate the need for this with a second siulation, scaling was applied to only to input I and output V, leaving paraeters R c and τ at their original values.

40 The current load on the prototype 6 ap-hour, 2 cell NiMH battery pack and a substitute 4 ap-hour, 96 cell Li-Ion battery pack are shown in Figure Figure 3-8: Scaled current loads on two NiMH battery packs in SAT siulation of Honda Insight on US6 driving cycle.

41 The resulting pack voltage of the battery odels is shown in Figure Figure 3-9: Voltage trace coparison of SAT siulation of Honda Insight on the first 3 s of the US6 driving cycle with prototype NiMH and scaled Li-Ion battery packs. The difference between pack voltage traces is plotted in Figure 3-. Figure 3-: Difference between voltages of prototype NiMH and scaled Li-Ion battery packs, copared with difference between voltages of prototype and scaled NiMH battery packs.

42 The root ean square error for the first 3 s of the cycle is V, copared 32 with.369 V for the first 3 s of the cycle with atched battery packs. With a bias error of 3.2 V reoved, root ean square error is reduced to 2.55 V. Siulation of the entire 6 s cycle could not be copleted with the degree of isatch present in this coparison. The significant variation in predicted voltage in Figure 3- illustrates the need for atched battery characteristics as well as diensionally atched input and output scaling.

43 33 Chapter 4 Ultracapacitor ack, Engine, and Fuel Cell Scaling In this chapter, scaling for an ultracapacitor pack, internal cobustion engine, and fuel cell is perfored. In addition, results are given for siulation of scaling for an engine. 4. Case 3: Ultracapacitor ack Model fro the SAT Library The dynaic syste equations for an ultracapacitor pack according to the SAT libraries [22], neglecting teperature dependence, are given in Eq. 4., where current I is the input, voltage V is the output, n cells is the nuber of cells in the pack, C is the capacitance, R is the internal resistance of a cell, and V OC is the steady state open circuit voltage. Capacitance and internal resistance are a function of current. Voltage V is saturated by V ax. V& OC = I C ( I) ( V I R( I) ), ncells OC V = Vax, V < V V ax, V > Vax ax V ax V V ax 4.

44 The internal resistance R of a typical cell fro the SAT library, the Maxwell 34 C25, is shown as a function of current in Figure 4-. Figure 4-: Internal resistance of an ultracapacitor as a function of current. The capacitance C of the sae ultracapacitor is shown in Figure 4-2. Figure 4-2: Capacitance of a typical ultracapacitor as a function of current.

45 35 As seen in the above two figures, the values of R and C vary only slightly with I. As such, it will be assued that they ay be regarded as constants, and the dynaic syste equations ay be siplified, as in Eq I V& OC = C ncells OC V = Vax, V < V V ax, V > Vax ( V I R) ax, V ax V V ax 4.2 An input-output diagra of the ultracapacitor pack odel is shown in Figure 4-3. Tie t Current I Ultracapacitor pack odel Voltage V Figure 4-3: Ultracapacitor pack odel signals. Applying the diensionless variable ethod, the ultracapacitor pack syste has N = 3 paraeters: C, R, V ax, coposed of M = 4 diensions: length, ass, tie, and current. To the paraeters shall be added S = 4 signals and states, t, V, V OC, I. The signals, states, and paraeters are shown with their diensions in Table 4-. The nuber of cells n cells is already diensionless, and is thus excluded.

46 36 Table 4-: araeters Relevant to Ultracapacitor ack Scaling Variable Sybol Diension tie t s voltage V - 2 kg s -3 A open circuit voltage V OC - 2 kg s -3 A current I A Capacitance C 2 - kg - s 4 A internal resistance R -2 2 kg s -3 A noinal voltage V ax - 2 kg s -3 A The nuber of fundaental diensions is four, but the [ 2 ] diension and the [kg] diension always appear together, so the two are cobined into a new coposite diension, leaving a total of M = 3 diensions. The nuber of repeating paraeters is therefore also three, so the three paraeters are selected as the repeating paraeters. The nuber of pi-groups is Q = N + S M = 4. The copleted diensional set atrix is given in Eq π π π π 2 s A kg, ult 2, ult 3, ult 4, ult t V 3 V I C R OC V ax

47 The resulting pi-groups, including the nuber of cells n cells, are given in Table Table 4-2: Ultracapacitor ack Scaling i-groups Diensionless Variable Variable Grouping π,ult t R - C - π 2,ult - V V ax π 3,ult V OC V ax π 4,ult - I R V ax π 5,ult n cells The resulting input-output scaling equivalency is shown in Table 4-3. Table 4-3: Ultracapacitor ack Scaling Equivalency HIL Coponent V H t H I H ax,h cells, H rototype Model RH C H t RC R Vax,H I V R ax, Vax, ncells, V V n H The dynaic syste equations are rearranged in diensionless for in Eq R C d VOC I R dt V = ax Vax V VOC I R = V n V V ax cells ax ax 4.4 The pi-paraeters are substituted in Eq. 4.5, where the derivative operator is also d diensionless, i.e. () ' R C. dt

48 π π π 3, ult 2, ult 5, ult = π = π 4, ult 3, ult π 4, ult For dynaic siilarity of two systes, the syste pi-groups need to have identical values [7]. By definition, any ratio of diensionless variables can also be defined as a pi-group, such as the ratio π 2,ult /π 5,ult. This new pi-group is equivalent between two systes by Eq. 4.5 as long as π 4 and π are equivalent. By use of an input scaling factor, π 4 has been set equivalent in Table 4-3, so it reains to require that π,ult,h = π,ult,. As an option, to avoid using different tie scales during HIL, an alternative requireent would be R H C H = R C. 4.2 Case 4: Engine Model fro the SAT Library The equation of otion for an engine according to the SAT libraries is given in Eq. 4.6, where throttle coand θ cd is an input, with a range of [, ]; rotational speed ω is another input, torque T is the output; and T ax is the axiu torque as a function of speed ω. T ( ) (. θ.) = T ax cd ω 4.6 An input-output diagra of the engine odel is shown in Figure 4-4.

49 39 Throttle coand θ cd Shaft speed ω Engine odel Torque T Figure 4-4: Engine odel inputs and output. An epirical forula Eq. 4.7 was adopted fro [25] for T ax, where ax is axiu power, ω ax is the speed at which axiu power occurs, and and 2 are diensionless coefficients. Typical values for and 2 are and for spark ignition engines, and.6 and.4 for copression ignition engines. T 4.7 ax ax ax 2 ax = + 2 ω ω 2 3 ωax ωax ωax Thus, a new equation of otion for an engine is Eq ax ax ax 2 = + 2 ω ω 2 3 ω ax ω ax ωax T (..) Applying the diensionless variable ethod, the engine syste has N = 2 paraeters: ax and ω ax, coposed of M = 3 diensions: length, ass, and tie. To the paraeters shall be added S = 2 signals: T and ω. The signals and paraeters are shown with their diensions in Table 4-4. The throttle coand θ cd and the coefficients and 2 are already diensionless, and are thus excluded. cd θ 4.8

50 4 Table 4-4: araeters Relevant to Engine Scaling Variable Sybol Diension torque T -2 2 kg s speed ω s - axiu power ax -3 2 kg s noinal voltage ω ax s - The nuber of fundaental diensions is three, but the [ 2 ] diension and the [kg] diension always appear together, so the two are cobined into a new coposite diension, leaving a total of M = 2 diensions. The nuber of repeating paraeters is therefore also two, so the two paraeters are selected as the repeating paraeters. The nuber of pi-groups is Q = N + S M = 2. The copleted diensional set atrix is given in Eq π π 2 s kg, eng 2, eng T 2 ω ax 3 ω ax 4.9 The resulting pi-groups, including the throttle coand θ cd and the coefficients and 2, are given in Table 4-5. Table 4-5: Engine Scaling i-groups Diensionless Variable Variable Grouping π,eng - T ω ax ax π 2,eng - ω ω ax π 3,eng π 4,eng 2 π 5,eng θ cd The resulting input-output scaling equivalency is shown in Table 4-6.

51 4 Table 4-6: Engine Scaling Equivalency T HIL Coponent ω θ cd,h ω H rototype Model θ cd, ω ω ω ax,h ax, H T ax,h ω ax, ax,h ax, The equation of otion is rearranged in diensionless for in Eq. 4.. T ω ax ax = ω ω 2 (. θ.) + 2 cd ωax ωax 4. The pi-paraeters are substituted in Eq ( π + π π π ) (. π.), eng = 3, eng 4, eng 2, eng 2, eng 5, eng π 4. For dynaic siilarity of two systes, the syste pi-groups need to have identical values [7]. The pi-group π,eng is equivalent between two systes by Eq. 4. as long as π 2,eng, π 3,eng, π 4,eng, and π 5,eng are equivalent. By use of input scaling factors, π 2,eng and π 5,eng have been set equivalent in Table 4-6, so it reains to require that π 3,eng,H = π 3,eng, and π 4,eng,H = π 4,eng,, that is,,h =, and 2,H = 2,. In other words, a gasoline engine cannot predict a diesel engine s perforance, or vice versa. Of special interest is the effect of the diensional approach on the function noted in Eq The iterations undergone by this function are developed in Eq T ax T = ax f ( ω) ω ax ω ax ω = ax ax ax ax + f 2 ( ω) ω ax ax ω ω + 2 ax ω ax ax ω ω ω ax ω ax 2 2 ω ωax 4.2

52 The function f ay be redefined as the diensionless function d, as in Eq ω d ωax + ω ω 2 ω ax ω ax A generalization ay be ade for functions of unspecified order. Instead of the requireent that the function coefficients of odel and prototype ust be equal, an equivalent requireent is that the function in its diensionless for ust be the sae for both odel and prototype, i.e., d H = d, at least over the range being tested. 4.3 Engine Scaling Siulation Results The diensionless variable ethod was applied to engine scaling in a SAT siulation. The vehicle odel was a series hybrid gasoline electric, and the engines being copared were a 9 kw.8 L 4-cylinder Toyota and a 2 kw 4. L 6-cylinder Ford. To verify that both engines had siilar power vs. rotational speed curves, these were plotted, along with the plot of epirical forula of Eq. 4.7, in Figure 4-5.

53 43 Figure 4-5: Engine diensionless power. While soe siilarity is evident between the odel and both engines, it is necessary to proceed with the siulation in order to deterine if the siilarity observed is sufficient. The vehicle was siulated on the Federal Urban Dynaoeter Schedule (FUDS) driving cycle. Scaling was applied to input rotational speed ω and output torque T of the 2 kw engine.

54 The scaled shaft speed inputs of both engines are shown in Figure Figure 4-6: Engine shaft speed inputs. The scaled throttle inputs of both engines are shown in Figure 4-7. Figure 4-7: Engine throttle inputs.

55 The torque output, scaled to atch the 9 kw engine, is plotted in Figure Figure 4-8: Engine torque outputs, scaled to atch the 9 kw engine. The error in torque prediction is plotted in Figure 4-9. Figure 4-9: Difference between torques of prototype and scaled engines.

56 46 The root ean square error for the 6-second cycle is 2.5 N*. The differences between the 2 kw engine scaled torque output and the 9 kw engine torque output evident in Figure 4-8 ay be attributed to the differences visible in Figure 4-5 between the power vs. speed curves of the two engines. 4.4 Case 5: Fuel Cell Model fro the SAT Library The equations of otion for a fuel cell according to the SAT libraries are given in Eq. 4.4, where reference power ref is the input, power is the output, T is diensionless teperature ratio with range [, ], ax,c is the axiu power output when cold, ax,h is the axiu power output when hot, hydrogen as a function of power when the fuel cell is cold, & is the ass flow rate of H, c 2 & is the ass flow rate of H, h 2 hydrogen when the fuel cell is hot, & is the axiu ass flow rate of hydrogen, H, ax 2 τ h is the hot teperature tie constant, τ c is the cold teperature tie constant, and τ is the power tie constant. T& = τ h ref ( T) ax,c + T ax,h & H h &, H, c & 2 2 T + & H, ax τ c τ h & 2 H & = ( ref ) τ & = H c f 2, 2 ax,h Note : & H, h = f 2 ax,h H 2, c 2, ax 4.4

57 47 The cold H 2 ass flow rate & H 2, c of a typical fuel cell fro the SAT library is shown in Figure 4-. Figure 4-: Cold hydrogen ass flow rate. The hot H 2 ass flow rate & of a typical fuel cell is shown in Figure 4-. H 2, c Figure 4-: Hot hydrogen ass flow rate.

58 An input-output diagra of the fuel cell odel is shown in Figure Reference power ref Fuel cell odel ower Tie t Figure 4-2: Fuel cell input and output. Applying the diensionless variable ethod, the fuel cell syste has N = 8 paraeters: ax,c, ax,h, &, & H h, & H ax, τ h, τ c, and τ. They are coposed of M = 3 H 2, c 2, 2, diensions: length, ass, and tie. To the paraeters shall be added S = 3 signals: t, ref, and. The signals and paraeters are shown with their diensions in Table 4-7. The teperature ratio T is already diensionless, and is thus excluded. Table 4-7: araeters Relevant to Fuel Cell Scaling Variable Sybol Diension tie t s hot teperature tie constant τ h s cold teperature tie constant τ c s reference power ref -3 2 kg s power -3 2 kg s cold ax power ax,c -3 2 kg s cold hydrogen ass flow rate & H 2, c kg s - hot hydrogen ass flow rate & H 2, h kg s - power tie constant τ s axiu hydrogen ass flow rate & H 2, ax kg s - axiu power ax,h -3 2 kg s

59 There are a total of M = 3 diensions. The nuber of repeating paraeters is 49 therefore also three, so the three constant paraeters ax,h, & H 2, h, and τ are arbitrarily selected as the repeating paraeters. In this exaple, ax,c and either of the other tie constants could have served as well as those actually selected. The nuber of pi-groups is Q = N + S M = 8. Non-repeating paraeters with the sae diensions are grouped together for siplicity. The copleted diensional set atrix is given in Eq π π kg s,2,3, fc π 4,5,6, fc 7,8, fc t, τ, τ h c ref,, 2 3 &, & ax, c H 2, c H 2, h H 2, ax τ & ax, h The resulting pi-groups, including the teperature T, are given in Table 4-8. Table 4-8: Fuel Cell Scaling i-groups Diensionless Variable Variable Grouping π,fc t τ - π 2,fc τ h τ - π 3,fc τ c τ - π 4,fc - ref ax,h π 5,fc - ax,h π 6,fc - ax,c ax,h π 7,fc π 8,fc π 9,fc & & H c 2, H 2, ax & H h 2, & H 2, ax T

60 5 The resulting input-output scaling equivalency is shown in Table 4-9. The equations of otion are rearranged in diensionless for in Eq Note that since the functions f and f 2 already take diensionless arguents, they undergo no change of for. They only need to be scaled by the factor ax H, 2 &. Table 4-9: Fuel Cell Scaling Equivalency HIL Coponent rototype Model t H H t τ τ ref,h ax,h H ax,h ref,,, H ax,h ax,h H,, ( ) = = + = + = + ax,h ax H ax H c H ax,h ax H ax H h H ax,h ref ax,h ax,h ax H c H h c ax H c H ax H h H h ax,h ax,c ax,h ref f f T T T T 2,,,,,,,,,,,, Note : & & & & & & & & & & & & & & τ τ τ τ τ τ τ τ 4.6

61 The pi-paraeters are substituted in Eq. 4.7, where the derivative operator is 5 d also diensionless, i.e. () ' τ. dt π 9, fc π = π 4, fc 2, fc ( π ) ( π π ) π 8, fc 5, fc 9, fc 7, fc = π 5, fc π 6, fc π + π + π 3, fc 4, fc 9, fc π 9, fc π + π 7, fc 2, fc 4.7 For dynaic siilarity of two systes, the syste pi-groups need to have identical values [7]. The pi-groups π 5,fc and π 9,fc are equivalent between two systes by Eq. 4.7 as long as the other pi-groups are equivalent. By use of an input scaling factor, π 4,fc has been set equivalent in Table 4-9, so the requireents are those listed in Eq π,fc,h = π,fc, π 2,fc,H = π 2,fc, π 3,fc,H = π 3,fc, π 6,fc,H = π 6,fc, π 7,fc,H = π 7,fc, π 8,fc,H = π 8,fc, 4.8 As an alternative, to avoid using different tie scales during HIL, the requireents for π,fc, π 2,fc, and π 3,fc translate into the requireents that τ H = τ, τ c,h = τ c,, and τ h,h = τ h,.

62 Chapter 5 Battery Scaling Experient In order to test and deonstrate the scaling procedures derived in this work, an experient was developed and undertaken coparing the responses of two sealed leadacid batteries: a 3.6 Ah Enersys Odyssey C68 battery and a 2 Ah Deka 6TAGM battery. The Deka was chosen to be the prototype, and the Odyssey was chosen as the scale odel to be tested to estiate the characteristics of the prototype. This chapter will describe the coponents of the experient, as shown in Figure 5-, in this order: battery, powertrain odel and drive cycle, the scale and rescale ultipliers, and the ABC- 5 power syste. Finally, the results of the scaling coparison will be presented. drive cycle powertrain odel vehicle speed Battery software voltage current rescale scale ABC5 ower Syste hardware Figure 5-: Experient configuration.

63 53 5. Setup of the Experient 5.. Batteries this section. The battery portion of the experient, highlighted in Figure 5-2, is the topic of drive cycle powertrain odel vehicle speed Battery software voltage current rescale scale ABC5 ower Syste hardware Figure 5-2: Experient configuration. Two sealed lead-acid absorbed glass at batteries were selected for scaling coparison: a 3.6 Ah Enersys Odyssey C68 battery and a 2 Ah Deka 6TAGM battery. Both batteries were of siilar construction and cheistry. Although the battery characteristic pi-paraeters, which will be reviewed below, were assued to be equivalent, both batteries were subjected to testing to deterine if this were so. Based on techniques described in [26], a series of cycles of the FreedoCar Maxiu ower- Assist (5 Wh) Efficiency and Baseline Cycle Life Test profile was applied to both batteries, with easureent ade of battery voltage throughout the cycle. The profile, shown in Figure 5-3, is designed to aintain state of charge, assuing a discharge/charge efficiency of 9%. The agnitude of the profile is designed for an entire battery pack, and is designed to be scaled down when an individual battery

64 is being tested. The characteristics to be deterined by the test are assued to be a 54 function of state of charge only, so the degree to which the profile is scaled is considered to be of inor iportance, since the battery reains at approxiately the sae state of charge throughout the test. What is iportant in scaling the profile is that the battery voltage does not go outside its acceptable range during testing, which for the Odyssey is [7.2, 4.7] V [27], and for the Deka is [9.6, 4.75] V [28]. Figure 5-3: FreedoCar Maxiu ower-assist (5 Wh) Efficiency and Baseline Cycle Life ower Deand rofile [26]. It was assued that an appropriate battery pack would have a size of 3 2-volt batteries, for a noinal pack voltage of 36 V. Hybrid-electric vehicle battery packs are typically liited to 4 V for reasons of safety. Since only one battery out of each pack was tested, the power deand of the profile was divided by 3. Applying the reduced profile to the Odyssey battery, however, caused it to exceed the upper voltage liit of 4.7 V. Since none of the characteristics being deterined are considered to be a function of the agnitude of current load in the current odel, the particular scaling is assued to

65 be of inor iportance. Thus, to prevent the Odyssey battery fro exceeding its 55 axiu voltage, the profile was divided by 6 instead of 3. The resulting profile for each battery is described in Table 5-. Table 5-: Battery Testing Discharge/Charge rofile Discharge/Charge Magnitude (kw) Tie (s) Full rofile Odyssey C68 Deka 6TAGM Constant Discharge ulse Discharge Constant Charge ulse Charge A new variable, dynaic current I c, is defined, as shown in Eq. 5., to allow the use of linear regression to deterine of battery characteristics, cell dynaic resistance R c and cell internal resistance R int. I c c ( R n ) V / 5. c cells The equations of otion for the battery, previously described in Eq. 3., were odified by the substitution of I c, as shown in Eq I& V c = τ = ( I I ) c ( I c Rc I Rint + VOC) ncells 5.2 For the purposes of regression analysis, an estiated voltage Vˆ was calculated according to Eq. 5.3, with ˆ R c, bat being the estiated battery dynaic resistance, Rˆ int, bat being the estiated battery internal resistance, and V OC, bat ˆ being the estiated battery open circuit voltage.

66 Rˆ Rˆ Vˆ c, bat int,bat OC, bat Vˆ = I R c c R V int OC Rˆ n c, bat cells n n cells cells I Rˆ int,bat + Vˆ OC, bat Based on easured current during the profile, and an estiated tie constant τˆ, dynaic current was calculated for each tie step according to Eq. 5.4 [26]. I c, i = + + { [ exp( t / ˆ τ) ]/( t / ˆ τ) } I i {[ exp( t / ˆ τ) ]/( t / ˆ τ) exp( t / ˆ τ) } { exp( t / ˆ τ) } I c, i I i 5.4 Thus there were four estiated paraeters: ˆ, Rˆ int, bat, ˆ OC bat, and τˆ. The R c, bat V, statistic used as a easure of cobined estiation accuracy was the coefficient of deterination, r 2, which is calculated according to Eq In this equation, V is the easured voltage, V is the ean easured voltage, and Vˆ is the estiated voltage. 2 2 [ ( V V) ( V Vˆ ) ]/ ( V V) Each estiated paraeter was varied increentally for each battery until a axiu value of r 2 was obtained. Results for both batteries are suarized in Table 5-2. The lead-acid batteries under test each were coposed of 6 cells, so the estiated paraeters on a per-cell basis are also given. 2 r = 5.5 2

67 57 Table 5-2: Battery characteristic estiation statistics araeter Enersys Odyssey C68 Deka 6TAGM ˆ (V) V OC, bat ˆ (Ω) R c, bat Rˆ int, bat (Ω) τˆ (s) r Estiated cell V OC (V) Estiated cell R c (Ω) Estiated cell R int (Ω) The easured and estiated voltage for the Deka battery are shown in Figure 5-4. Figure 5-4: Measured and estiated voltage of Deka battery.

68 The easured and estiated voltage for the Odyssey battery are shown in 58 Figure 5-5. Figure 5-5: Measured and estiated voltage of the Odyssey battery. The characteristic pi-paraeters for batteries are π,bat and π 2,bat, as derived in Chapter 3, section 3., and shown in Table 5-3. Table 5-3: Characteristic battery pi-paraeters Diensionless Variable Variable Grouping π,bat Q R int τ - V - no π 2,bat - R c R int The paraeters required for calculating π,bat and π 2,bat, as well as the calculated pi-paraeters theselves, are shown in Table 5-4. The value for cell capacity Q is specified by the anufacturer [27, 28], and the value for noinal voltage V no for both batteries, since both have lead-acid cheistry, was arbitrarily chosen to be V OC at 5% state of charge, that is, 2.83 V.

69 59 Table 5-4: Battery characteristics araeter Enersys Odyssey C68 Deka 6TAGM Estiated cell V OC (V) Estiated cell R c (Ω) Estiated cell R int (Ω) Estiated τ (s) Specified Q (s A) Specified V no (V) π,bat π 2,bat As seen in Table 5-4, the values for π,bat and π 2,bat are not equal, although they are within an order of agnitude. The question is, are they close enough? The answer to this question will be deterined by the experient that follows. Note that the above easureent was perfored at only one state of charge. A full coparison of both batteries characteristics would require repetition of the sae test at ultiple states of charge, which tests are beyond the scope of this work.

70 Vehicle owertrain Models The vehicle powertrain and drive cycle portions of the experient, highlighted in Figure 5-6, are the topic of this section. drive cycle powertrain odel vehicle speed Battery software voltage current rescale scale ABC5 ower Syste hardware Figure 5-6: Experient configuration. Two Siulink vehicle powertrain odels were created using SAT, both a GM EV electric vehicle powertrain (EV) and a Honda Insight parallel hybrid vehicle powertrain (AR) using the US6 Suppleental Federal Test rocedure [29] as the drive cycle. The Siulink odel of each vehicle was saved, along with the workspace variables. Two odifications were ade to the odels. First, the current input signal to the battery portion of each odel was connected to a UD Send block fro the xc Target library of Siulink. This UD signal supplied a current coand for an AeroVironent ABC-5 ower rocessing Syste, described below. Second, the output of an ADC block providing a easureent of battery voltage replaced the voltage output signal of the battery portion of each odel. Third, another ADC block was included to record easureent of current load on the battery. Using the Real Tie

71 Workshop, each siulation was copiled to run on an industrial C with data acquisition capabilities, using the xc Target real tie operating syste [23] Scaling Factors The scaling factors, labeled scale and rescale, highlighted in Figure 5-7, are the topic of this section. drive cycle powertrain odel vehicle speed Battery software voltage current rescale scale ABC5 ower Syste hardware Figure 5-7: Experient configuration. The label scale refers to the scaling applied to any signals that ust be transfored fro the prototype doain to the hardware doain, in this case the battery current. The label rescale, in contrast, refers to the scaling applied to any signals that ust be transfored fro the hardware doain back to the prototype odel doain, in this case the battery voltage. In the case of the present experient, the prototype () is a pack of 3 Deka 6TAGM batteries (8 cells) connected in series. The hardware (H) is alternately a single Odyssey C68 battery (6 cells) and a single Deka 6TAGM battery (6 cells). The scale and rescale ultipliers are given in Table 5-5. They were derived in Chapter 3, Section 3..

72 Table 5-5: HIL scaling factors araeters scale rescale Forula ack of 3 Deka Odyssey Deka 6TAGM () C68 (H) 6TAGM (H) V no (V) R int (Ω) n cells Rint, Vno, H V R N/A.359 V V no, no, no, H n n int, H cells, cells, H N/A Control Equipent The ABC-5 ower Syste portion of the experient, highlighted in Figure 5-8, is the topic of this section. drive cycle powertrain odel vehicle speed Battery software voltage current rescale scale ABC5 ower Syste hardware Figure 5-8: Experient configuration. The equipent used to control the current load applied to the batteries under test was AeroVironent s ABC-5 ower rocessing Syste. It can source or sink up to 445 VDC, 53 ADC, or 25 kw. The ABC-5, pictured in Figure 5-9, ay be controlled either anually by controls on the front panel, or reotely, via RS232. AeroVironent provides a progra that executes siple coand scripts, as well as a

73 63 serial port driver that can be integrated into custo controls designed for the Windows operating syste. In this experient, the forer was used for easureent of battery characteristics above, and the latter for the HIL siulation below. For HIL, a Visual Basic control was ipleented that receives UD signals transitted across the local area network, and translates the into ABC-5 coands. Figure 5-9: Aerovironent ABC-5 ower rocessing Syste.

74 Coplete Experiental Syste The coplete experiental syste is pictured in Figure 5-. On the left is the industrial C, with data acquisition board, running the vehicle siulation in real tie. In the center is the Enersys Odyssey C68 battery, with an aeter claped around one of the power cables. On the right is a coputer running the Visual Basic control, which translates current coands fro UD to RS232. In the background is the ABC-5 power processing syste. Figure 5-: Coplete experiental syste.

75 Experiental Results Two HIL siulations were perfored with both batteries, one a Honda Insight parallel hybrid vehicle powertrain (AR) and the other a GM EV electric vehicle powertrain (EV). The current load applied to both batteries in the AR siulation is shown in Figure 5-. Figure 5-: Current load applied to batteries in the AR siulation.

76 The voltage response of both batteries, scaled to full pack size, in the AR 66 siulation is shown in Figure 5-2. Figure 5-2: Voltage response of batteries, scaled to pack size, in the AR siulation. The difference between voltage traces is plotted in Figure 5-3. Figure 5-3: Difference between voltages of batteries in the AR siulation.

77 67 With a 2.2 V bias in pack V OC reoved, the root ean square error for the cycle is.63 V, which is.3% of initial V OC of V. The current load applied to both batteries in the EV siulation is shown in Figure 5-4. Figure 5-4: Current load applied to batteries in the EV siulation.

78 The voltage response of both batteries, scaled to full pack size, in the EV 68 siulation is shown in Figure 5-5. Figure 5-5: Voltage response of batteries, scaled to full pack size, in the EV siulation. The difference between voltage traces is plotted in Figure 5-6. Figure 5-6: Difference between voltage responses in the EV siulation.