Modeling and Optimal Supervisory Controller Design for a Hybrid Fuel Cell Passenger Bus

Transcription

1 Modeling and Optimal Supervisory Controller Design for a Hybrid Fuel Cell Passenger Bus THESIS Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University By Kyle Simmons Graduate Program in Mechanical Engineering The Ohio State University 2013 Master's Examination Committee: Dr. Yann Guezennec, Advisor Dr. Shawn Midlam-Mohler

2 Copyright by Kyle Simmons 2013

3 Abstract This thesis presents the modeling and optimal supervisory energy management of a fuel cell/battery-powered passenger bus. The work presented was completed in conjunction with the DesignLine Corporation and the National Fuel Cell Bus Program. With growing concerns about petroleum usage and greenhouse gas emissions in the transportation sector, finding alternative methods for vehicle propulsion is necessary. Proton Exchange Membrane (PEM) fuel cells are viable possibilities due to their high efficiencies and zero emissions. It has been shown that the benefits of PEM fuel cells can be greatly improved through hybridization, which requires an energy management system. First, the modeling of an energy-based, forward-simulator representative of the bus is presented. Each component of the powertrain is modeled separately for ease of modification. Experimentally obtained data was used to represent components, when available. Several different battery cells were modeled through experimental identification at The Center for Automotive Research at The Ohio State University. These models were used in the simulator to aid in battery examination and selection for the actual hybrid fuel cell bus. The formal definition of the energy management control problem of the hybrid fuel cell bus is then outlined. Literature has provided numerous techniques for ii

4 conventional hybrid vehicle control, many of which can be extended to a fuel cell hybrid. One such technique uses Pontryagin s Minimum Principle (PMP). PMP is a very powerful tool in optimal control theory. It can provides a set of necessary conditions to ensure global optimality of a constrained control problem An optimal controller for the hybrid fuel cell bus control problem is developed by applying PMP. The PMP controller finds the optimal control trajectory to follow a given velocity profile that minimizes hydrogen fuel consumption by the fuel cell while maintaining battery state of charge, and satisfying physical limitations of the components. Finally, numerous simulations were completed using the PMP controller. Multiple drive cycles were examined, with and without road grade profiles to ensure every possible operating condition of the bus was explored. A range of different bus weights, battery sizes and different battery chemistries were also simulated. The optimal PMP controller was able to achieve a fuel economy between 4.0 and 8.7 miles per kilogram hydrogen (4.5 and 9.8 miles per diesel gallon equivalent), depending on the drive cycle and bus weight. It was found that the optimal control trajectories of the battery and fuel cell were nearly identical, regardless of battery chemistry. For the component sizing used in the bus, the optimal results show that the battery supplies most of the transit power demand, while the fuel cell operates around the average power demand of the given cycle. Because this average power demand varies greatly with the drive cycle considered, the fuel cell operation is strongly dependent on the severity of the drive cycle. A practical, implementable controller can be designed iii

5 based on the trends seen from the optimal PMP results. To conclude the work, a possible algorithmic controller that can be implemented on the bus is briefly discussed. iv

6 To my family v

7 Acknowledgments The completion of this work would not have been possible without the help and support from numerous people. First, I would like to thank my family and friends for their continuous support, encouragement, and motivation throughout this process. I would like to thank Dr. David Mikesell for sparking my interest in the automotive field and pushing me to continue my education. My time at The Center for Automotive Research (CAR) here at The Ohio State University has been extremely enjoyable and intellectually stimulating. I am very grateful for the world-class researchers and professors I have come in contact with here at CAR. I would like to thank my advisor Dr. Yann Guezennec and Dr. Simona Onori for giving me the opportunity to complete me research under their direction. Dr. Guezennec s knowledge, time, feedback, and support has been invaluable to my learning experience and the completion of this thesis. Dr. Onori has been a constant source of information. This thesis would not have materialized without her. Her willingness to help, her work ethic, and her wealth of knowledge have given me a great deal of respect for her. Finally, I would like to thank the entire staff at CAR and The Ohio State University for making this experience possible and so gratifying for me. vi

8 Vita B.S. Mechanical Engineering, Ohio Northern University 2011 to Graduate Teaching Associate, Department of Mechanical and Aerospace Engineering, The Ohio State University 2012 to present...graduate Research Associate, The Center for Automotive Research, The Ohio State University Fields of Study Major Field: Mechanical Engineering vii

9 Table of Contents Abstract... ii Acknowledgments... vi Vita... vii Table of Contents... viii List of Tables... xi List of Figures... xiii Nomenclature... xvi Chapter 1: Introduction Background National Fuel Cell Bus Program Hybrid Vehicle Energy Management Objective of the thesis Organization of the thesis... 6 Chapter 2: Vehicle Structure and Modeling Powertrain architecture... 8 viii

10 2.2 Hybrid Fuel Cell Bus Simulator Driver Model Driving Cycles Supervisory Controller Model Powertrain Model Fuel Cell System DC/DC Converter Battery System Auxiliary Loads Electric Motors Gearbox of Constant Gear Ratio Front and Rear Brakes Front and Rear Wheels Vehicle Dynamics Chapter 3: Control Strategy Energy Management in a HFCB Thermostatic Control Proportional Control Pontryagin s Minimum Principle ix

11 3.3 Defining the optimal control problem Applying PMP to the control problem Chapter 4: Simulation Results Manhattan Simulation Example Acceleration and Speed Tests Chapter 5: Results Analysis Battery Sizing Study Weight Sensitivity Study Optimal PMP Controller Results Finding Optimal Control Analysis of Different Battery Chemistries Chapter 6: Conclusions and Future Work Bibliography x

12 List of Tables Table 1: Powertrain component sizing Table 2: Drive model parameters Table 3: Driving cycle statistics Table 4: DC/DC converter parameters Table 5: Battery model parameters for each battery chemistry Table 6: Auxiliary Load parameter Table 7: Gearbox parameter values Table 8: Tire model parameters Table 9: Vehicle Dynamics Parameter Table Table 10: Thermostatic controller parameters Table 11: Acceleration and Speed capabilities of the HFCB Table 12: LG Chem pack geometry for different nominal sizing Table 13: Battery operation summary metrics for different pack sizes for all simulations Table 14: Fuel economy observed for different battery pack sizes Table 15: Average fuel economy for differently bus weights Table 16: Acceleration performance of the bus at different overall vehicle weights Table 17: Pack arrangement for each battery chemistry xi

13 Table 18: Average fuel economy of different battery models Table 19: values for each battery chemistry Table 20: values for each battery chemistry xii

14 List of Figures Figure 1: 2012 World energy consumption by sector... 2 Figure 2: World transportation sector energy source... 2 Figure 3: Powertrain structure as proposed by DesignLine... 9 Figure 4: HFCB powertrain topology Figure 5: Schematic of a forward simulator Figure 6: Screenshot of simulator in Simulink Figure 7: Various driving cycles Figure 8: Artificial grade imposed on Manhattan Drive Cycle Figure 9: Road grade profiles of real-world drive cycles Figure 10: Experimentally obtained fuel cell operation data Figure 11: Fuel cell model Figure 12: Compressor model Figure 13: Battery n-order equivalent electrical circuit model diagram Figure 14: OCV vs. SOC for different battery cells Figure 15: Battery cell arrangement Figure 16: Electric motor efficiency map and power limitations Figure 17: Thermostatic control Figure 18: Proportional control xiii

15 Figure 19: Velocity trace performance of Simulator Figure 20: Driver outputs Figure 21: Power demand from battery and fuel cell as determined by supervisory controller Figure 22: Battery operation Figure 23: Battery C-rate histogram Figure 24: Heat generated by battery pack Figure 25: Battery SOC trajectory Figure 26: Fuel cell operation Figure 27: Fuel cell efficiencies Figure 28: Fuel cell operation histogram Figure 29: Instantaneous hydrogen mass flow rate Figure 30: Hydrogen consumed Figure 31: Electric motor operating points plotted in torque-speed plain Figure 32: EM torque ouput Figure 33: Power at the wheel supplied by the powertrain Figure 34: Environmental Forces acting on the bus Figure 35: SOC trajectory for different battery pack sizes for 3 repeated HDUDDS cycles Figure 36: SOC trajectory for different values of Figure 37: Fuel cell operation for different values Figure 38: Hydrogen consumed using different values of xiv

16 Figure 39: Battery operation during Manhattan cycle for different battery chemistries.. 72 Figure 40: Battery SOC trajectory of different chemistries Figure 41: Optimal Fuel cell operation using different battery chemistries Figure 42: vs. time for different battery chemistries Figure 43: vs. time for the Manhattan cycle Figure 44: Optimal fuel cell operation for different drive cycles xv

17 Nomenclature * Superscript to denote optimal trajectory Frontal area of the bus [ ] Root mean square acceleration [ ] Aerodynamic drag coefficient i th R-C branch capacitance [ ] Rolling resistance coefficient C-rate (scaled battery current) Vector set of admissible fuel cell states Aerodynamic drag force [ ] Road grad force [ ] Rolling resistance force [ ] Force at wheel supplied by powertrain [ ] ( ) Terminal cost of system state Hamiltonian function Current through battery cell [ ] Fuel cell current [ ] Integral cost function of optimal control problem xvi

18 Derivative gain Integral gain Proportional gain ( ) Instantaneous cost of system state Mass of bus [ ] Hydrogen mass flow rate [ ] Maximum admissible power of battery [ ] Minimum admissible power of battery [ ] Compressor power consumption [ ] Electrical power at EM [ ] Maximum admissible power of EM [ ] Minimum admissible power of EM [ ] Fuel cell stack output power [ ] Heat power generated by battery [ ] High power output level of fuel cell [ ] DC/DC convertor input power [ ] DC/DC convertor power consumption [ ] Low power output level of fuel cell [ ] Mechanical power at EM [ ] DC/DC convertor output power [ ] Fuel cell system output power [ ] xvii

19 Total power demand [ ] Power at the wheel [ ] Battery capacity [ ] Battery cell capacity [ ] Battery internal resistance [ ] i th R-C branch resistance [ ] Tire radius [ ] Vector set of admissible states Relative sensitivity Initial value of state of charge [ ] High SOC limit [ ] Low SOC limit [ ] Maximum admissible SOC [ ] Minimum admissible SOC [ ] EM output torque [ ] Conventional braking torque on front wheels [ ] Convectional braking torque on rear wheel [ ] Torque supplied to rear wheel by EM [ ] Total torque at the wheel [ ] Vector of control inputs Vector set of admissible control inputs xviii

20 Output voltage of battery [ ] Voltage across i th capacitor [ ] Voltage loss due to hysteresis [ ] Battery load voltage [ ] Maximum velocity [ ] Mean velocity [ ] Battery open circuit voltage [ ] Root mean square velocity [ ] Acceleration command, Coefficients of algorithmic controller Brake command DC/DC convertor efficiency EM efficiency Fuel cell stack efficiency Fuel cell system efficiency Gearbox efficiency Road grade angle [ ] Vector of co-states [ ] Initial value of the co-state vector [ ] Normalized value [ ] xix

21 Vector of controllable states Density of air [ ] Gearbox gear ratio ( ) Terminal cost of optimal control problem EM rotational speed [ ] Wheel rotational speed [ ] APU CABS CC CLN CTE EM FTA GPS HDUDDS HEV HFCB HVAC LFP LHV Auxiliary Power Unit Campus Area Bus Service Central Connector Campus Loop North Center for Transportation and the Environment Electric Motor Federal Transit Authority Global Positioning System Heavy Duty Urban Dynamometer Driving Schedule Hybrid Electric Vehicle Hybrid Fuel Cell Bus Heating, Ventilation, and Air Conditioning Lithium Iron Phosphate battery cell Lower Heating Value xx

22 NCA NFCBP OCV OSU PEM PID PMP SOC UDDS Lithium Nickel Cobalt Oxide battery cell National Fuel Cell Bus Program Open Circuit Voltage The Ohio State University Proton Exchange Membrane Proportional-Integral-Derivative Pontryagin s Minimum Principle State of Charge Urban Dynamometer Driving Schedule xxi

23 Chapter 1: Introduction The work presented in this thesis was completed in conjunction with The Center for Transportation and the Environment (CTE) and the DesignLine Corporation, under funding from the Federal Transit Authority (FTA) and the National Fuel Cell Bus Program (NFCBP). The purpose of the work in this thesis was to develop a mathematical simulator to represent a proposed Hybrid Fuel Cell Bus (HFCB) that could be used to assist in the analysis and design of the powertrain and supervisory energy management system. 1.1 Background The transportation sector accounted for approximately 26% of the World s overall energy consumption in 2012, with 94% of that energy being produced by burning petroleum [1]. Figures 1 and 2 show the World s energy split and the World s transportation energy source split respectively. 1

24 Figure 1: 2012 World energy consumption by sector Figure 2: World transportation sector energy source Burning fossil fuels releases numerous greenhouse gas emissions that can adversely affect the environment. It is estimated that the transportation sector contributes around 20% of the world s total greenhouse gas emissions [2]. Governments and private companies alike are committed to find alternative methods for energy generation in an 2

25 effort to reduce fossil fuel usage and greenhouse gas emissions, and to create safe, sustainable energy. In the transportation sector, these factors have led to tremendous amounts of research being completed to increase fuel economy in today s vehicles, and to find alternative methods for vehicle propulsion. The Proton Exchange Membrane (PEM) fuel cell is a potential alternative method for vehicle propulsion. As electrochemical devices, fuel cells convert chemical energy into electrical energy directly without mechanical processes. PEM fuel cells are favorable for their zero emissions, relatively high efficiency, and low noise generation [3]. They are also favorable for automotive application for their compactness, and ability to follow dynamic loads. However, their high sticker price and short life-time make commercialization difficult. Further development of the fuel cell technology and their integration into vehicles is needed in order for significant market penetration to be possible. To help increase the rate of commercialization, the FTA created the NFCPB. 1.2 National Fuel Cell Bus Program The FTA established the NFCBP in The overall goal of the program is to assist in development and demonstration of fuel cell technology for transit buses, and to improve commercial viability [4]. Through the program, the FTA hopes to achieve the following: Facilitate the development of fuel cell technology, primarily for full-size, heavy-duty transit bus applications 3

26 Improve transit bus efficiency, reduce petroleum consumption, and reduce emissions Improve fuel cell durability, reliability, and reduce overall fuel cell bus cost Establish a globally competitive U.S. industry for fuel cell bus technology Increase public awareness and acceptance of fuel cell vehicles. As technologies for powering transit buses evolves, the FTA sees fuel cells being uniquely positioned to take advantage of many of these technological advancements [5]. In addition to the advantages of fuel cells mentioned previously, such as no emissions and quite operation, fuel cells can be used in conjunction with new battery technology, new electric drives with increased efficiencies, and advances in wireless inductive charging. With the low-cost of natural gas, hydrogen reforming from natural gas for fuel cell usage is also viable. All of these potential advantages have led the FTA to commit nearly $90 million to the NFCBP, with an equal amount coming from private companies. This has funded the development of 25 fuel cell bus demonstrations that are currently in operation, with 7 more demonstrations under development. These projects are all competitively selected by the FTA and are located across the country. One of the program s fuel cell bus demonstrators is currently being developed by the DesignLine Corporation. DesignLine is the prime contractor on designing the bus prototype, and is solely responsible for its architecture. DesignLine proposed a hybrid powertrain containing two separate power sources (fuel cell and battery), which led to the 4

27 need for a supervisory energy management controller. The Ohio State University (OSU) was asked to act as a sub-contractor on the project. OSU was asked to develop an energybased model of the bus and to assist in the design of the supervisory energy management controller. This is the focus of the work in this thesis. 1.3 Hybrid Vehicle Energy Management A hybrid configuration in a vehicle introduces the need for an energy management control strategy. The strategy must satisfy certain constraints while trying to achieve some system-level performance objectives such as maximizing fuel economy, maintaining the battery state-of-charge (SOC), or improving the life of the components. Recent literature contains numerous control techniques for hybrid electric vehicles (HEV), many of which can be extended to a hybrid fuel cell vehicle [6-13]. These strategies can be categorized into three types: Rule based strategies Instantaneous optimization strategies Global optimization strategies Rule based strategies can be easily implementable for real-time application and are usually based on heuristics. Performance of these strategies can be improved through the use of fuzzy logic or adaptively altering rules during a driving event [14,15]. Instantaneous optimization strategies minimize a performance metric such as fuel consumption at every instance in-time, through the use of an equivalent fuel consumption for sources that do not use a conventional fuel (i.e. batteries). Global 5

28 optimization strategies minimize a performance metric for a specified drive cycle, which must be known a priori. Because of this, these strategies are not implementable in real time. 1.4 Objective of the thesis The first objective of the work presenting in this this is to develop an energybased simulator of the HFCB demonstrator being developed by DesignLine. For supervisory energy management controller design, it is the aim of the work in this thesis to develop and implement an optimal controller based on Pontryagin s Minimum Principle (PMP). PMP is a very powerful tool in optimal control theory, as it provides a set of necessary conditions to ensure global optimality of a constrained control problem. An in-depth look at PMP and its application to the energy management control problem for the HFCB is presented in Chapter 3 of this thesis. Results from the optimal controller will then be used to develop an implementable, rule-based control strategy. 1.5 Organization of the thesis In the next chapter, the modeling approach taken for each component of the HFCB simulator is described. It provides details on the structure of the simulator, the various function blocks of the simulator, and the mathematical equations used for modeling each component of the simulator. In the third chapter, the general definition of the energy management control problem for the HFCB is presented. Several simple 6

29 control strategies are presented. Then, the optimal control problem is formulated and PMP is applied. The fourth chapter presents extensive results from the simulator for one driving event. This is meant as an illustrative example of the simulator outputs available for analysis. Every variable presented in this chapter is produced for every simulation of the simulator. Chapter 5 provides a summary of the results of the optimal PMP controller for numerous drive cycles and several component combinations. Also, several sensitivity studies that were conducted are presented. The final chapter provides conclusions, contributions, and future work related to the work and results presented in this thesis. The main contributions of the thesis are the following: An energy-based, forward-looking simulator of a Hybrid Fuel Cell Bus A formal definition of the optimal control problem in a hybrid fuel cell vehicle The implementation of a PMP based energy management controller in a hybrid fuel cell vehicle A detailed analysis of the PMP based energy management controller for further development of an implementable rule-based control strategy for a HFCB 7

30 Chapter 2: Vehicle Structure and Modeling In this chapter, the vehicle simulator that was developed and used for vehicle energy analysis and control strategy design is presented. The simulator was developed in the Simulink /MATLAB environment. Schematics and snapshots of the simulator are provided. Each component of the simulator is explained and the modeling techniques for those components are described. The component parameters used are also presented. 2.1 Powertrain architecture The powertrain architecture was determined by DesignLine to be a parallel hybrid, battery dominated powertrain with a fuel cell functioning as an auxiliary power unit (APU). The battery and fuel cell supply electrical power directly to the bus s two rear-wheel electric traction motors as well as to the auxiliary loads of the bus (HVAC, lighting, etc.). Figure 3 shows a diagram of the proposed powertrain that was supplied by DesignLine. 8

31 Figure 3: Powertrain structure as proposed by DesignLine The powertrain consists of the following components: Fuel Cell o Integrated Compressor to pressurize air supply to Fuel Cell DC/DC Converter Battery Electric Motors (2) Auxiliary Loads Gearbox of constant gear ratio Front and Rear Brakes Front and Rear Wheels 9

32 Information about the components of the bus were provided by DesignLine and the component manufacturers, where available. This provided a starting point for the modeling of each component for implementation in the simulator. From the powertrain structure provided by DesignLine, an energy flow diagram was constructed to understand how to model the powertrain architecture in the simulator. This can be seen in Figure 4. Table 1 summarizes the parameters of the various components of the powertrain. Table 1: Powertrain component sizing Component Fuel Cell Fuel Cell Compressor Battery Electric Motors Gearbox Power Electronics Vehicle Details Ballard FC velocity HD6, 75 kw max power Eaton Unspecified manufacturer and size, to be determined using Simulator 2 ZF motors, 240 kw max power, Nm max torque, 1150 rad/s max speed, Single gear ratio Acceptable Voltage range: [480,692] V kg, 7.5 m 2 frontal area, 0.54 drag coefficient, m tire radius 10

33 Figure 4: HFCB powertrain topology With this flow diagram and the available information on the HFCB powertrain components, the simulator was designed. 2.2 Hybrid Fuel Cell Bus Simulator The HFCB simulator is a forward-looking, energy-based simulator. Each component is self-sustained and modular for the ease of restructuring of the simulator and the switching of components and control strategies. Figure 5 provides a schematic of the forward simulator. The simulator consists of the following function blocks: Driver Supervisory Controller Hybrid Powertrain Vehicle Dynamics 11

34 V cyc acc/ P FC T wheel V veh brake P BATT Figure 5: Schematic of a forward simulator As a forward simulator, it consists of a driver model which provides an acceleration or deceleration command at each time step based on the difference between the desired velocity and the current velocity of the simulated HFCB, which is fed back. A supervisory controller converts that command to a power demand for the powertrain. That power demand is converted into a tractive force at the wheel through the powertrain dynamics of the simulator. Through the vehicle dynamics, the velocity of the HFCB is calculated. The HFCB simulator runs at a sampling rate of 10 Hz with the ODE3 solver in Simulink. The following sections of this chapter will provide details about the function blocks previously listed, and about the components of those blocks. Figure 6 provides a screenshot of the simulator in Simulink. 12

35 13 Figure 6: Screenshot of simulator in Simulink

36 2.3 Driver Model The Driver is modeled as a PID controller which tries to minimize the difference between the current vehicle velocity and that of the desired velocity. The desired velocity is taken from a given drive cycle, which will be described in the next section. The outputs of the Driver block are the acceleration and brake pedal commands. At any moment in time, either the acceleration or the brake command is zero. If the PID output is greater than zero, then the acceleration command,, is given by Equation 2.1: ( {( )} ( ) ( ) ) (2.1) where,,, are the derivative, proportional, and integral gain constants respectively, is the desired velocity, and is the actual velocity of the simulated bus. is saturated to 1. Similarly, if the PID output is less than zero, then the deceleration command,, is given by Equation 2.2: ( {( )} ( ) ( ) ) (2.2) The parameters for the PID controller used within the Driver model can be seen in Table 2. Table 2: Drive model parameters Parameter Value used in Simulator

37 2.3.1 Driving Cycles The velocity profile that the vehicle is required to follow in the simulator is a sequence of desired velocities versus time, (t). These profiles can be standard or extracted from real world driving. Standard cycles are used across the automotive industry for a variety of purposes, and are publically available. Real world profiles can be captured experimentally from a test vehicle. Many standard cycles are developed for light duty vehicles and do not apply to the application of the work in this thesis. The various driving cycles that were considered are: Manhattan driving cycle Urban Dynamometer Driving Schedule (UDDS) Heavy Duty Urban Dynamometer Driving Schedule (HDUDDS) OSU Campus Area Bus Service (CABS) real world drive cycles, Campus Loop North (CLN) and Central Connector (CC) Figure 7 shows the various drive cycles. 15

38 Velocity (mph) Velocity (mph) Velocity (mph) Velocity (mph) Velocity (mph) 30 MAN 60 HDUDDS Time [s] Time [s] a) Manhattan b) HDUDDS 60 UDDS 50 CABS CC Time [s] Time [s] c) UDDS d) OSU CABS CC 40 CABS CLN Time [s] e) OSU CABS CLN Figure 7: Various driving cycles 16

39 For each of the drive cycles, statistics about the drive cycle can be calculated. These can be used for comparison between drive cycles. It is important to ensure every possible driving condition the bus will experience is considered. Table 3 summarizes several statistics for each drive cycle. Table 3: Driving cycle statistics Cycle V rms V mean V max (mph) (mph) (mph) a rms (m/s 2 ) Manhattan HDUDDS UDDS CABS CC CABS CLN The CABS routes were obtained experimentally from global positioning system (GPS) data acquired during actual operation of a CABS passenger bus. This also provided road grade data during the route as well. Road grade is an important aspect of the driving cycle. Grade has an influence on the vehicle s performance by changing the power requirements needed to follow the velocity trace. Because standard drive cycles do not have a corresponding grade profile, artificial grade profiles are used, such as the sinusoidal grade seen in Figure 8. This artificial sinusoidal grade has an amplitude of 3% and completes two periods through the duration of the drive cycle. The real road grade profiles of the experimentally obtained CABS routes can be seen in Figure 9. Each driving cycle is examined with zero road grade as well as with an artificial or real grade (if available) profile. 17

40 grade [%] grade [%] grade [%] time [s] Figure 8: Artificial grade imposed on Manhattan Drive Cycle time [s] time [s] a) CABS CLN road grade profile b) CABS CC road grade profile Figure 9: Road grade profiles of real-world drive cycles 18

41 2.4 Supervisory Controller Model Because supervisory controller design is a main focus of the work in this thesis, a description of this function block will be extensively addressed in Chapter Powertrain Model A quasi-static modeling approach has been used to model the various powertrain components. Every component of the powertrain specified by DesignLine needed to be modeled separately to adequately analyze the energy flow and consumption of the HFCB. The components were modularly modeled for easy modification and exchange of components in the simulator. The following sections provide a detailed explanation of the modeling techniques and equations used to model each component used in the simulator Fuel Cell System The fuel cell model used in the simulator is a static model which neglects dynamic behavior. This is adequate for the purpose of the simulator, energy analysis and fuel consumption estimation. The temperature, air pressure and humidification of the fuel cell were neglected as it is expected that the manufacture s controller adequately maintains these in accordance with the fuel cell operating point. Experimental data of the fuel cell operation was provided by the manufacture and is shown in Figure 10. The corresponding power consumption of the integrated compressor for the fuel cell was also provided. 19

42 Module Current (A) 75kW Module Voltage (V) Beginning of Life End of Life Gross Power (kw) HD6-75kW Figure 10: Experimentally obtained fuel cell operation data Only the beginning of life operation is considered for the simulator. Experimental data provided by the manufacturer allowed for a table interpolation of the power-current relationship of the fuel cell. Because very few data points were provided, curve-fitting was done to improve the resolution of the model. Figure 11 shows the experimental data as well as the 2 nd order polynomial curve-fit used to improve the model. 20

43 Current (A) Experimental Data Curve Fit Power (kw) Figure 11: Fuel cell model The curve-fit used is defined in Equation 2.3. (2.3) where is the required current in amps to produce a stack power output, in kilowatts. The hydrogen mass flow rate of the fuel cell is given as an increasing linear relationship to the electrical current level. Equation 2.4 was experimentally obtained by the manufacturer and implemented directly in the simulator as a hydrogen consumption calculation of the fuel cell. (2.4) where is the mass flow rate of hydrogen in grams per second, and is the operating current of the fuel cell in amps. 21

44 Compressor A compressor is a sub-component of the fuel cell system. It is needed to pressurize the air supply to the fuel cell stack for proper functioning and optimal operation. This affects the overall efficiency of the fuel cell system. A compressor model is needed to accurately represent the overall efficiency of the fuel cell system model. Experimental data of the power consumption of the compressor at a given fuel cell operating point was provided. As was done for the fuel cell itself, a 2 nd order polynomial curve fit was used to improve the resolution of the compressor model. The model is a static model, similar to the fuel cell stack. The curve fit equation is shown in Equation 2.5. Figure 12 shows the experimental data provided and the curve fit. (2.5) where is the power consumption of the compressor in kilowatts at a fuel cell operating current,, in amps. 22

45 Compressor Power Consumption (kw) 8 7 Experimental Data Curve Fit FC Current (A) Figure 12: Compressor model DC/DC Converter The DC/DC converter converts a direct current from one voltage level to another. Because the output voltage of the fuel cell system is not within the acceptable voltage range of other powertrain components on the bus, a DC/DC converter is needed. This ensures voltage supplied to other electrical systems on the bus is within the acceptable range. The DC/DC converter is modeled as having a constant efficiency with a constant power loss, as shown in Equation 2.6 (2.6) 23

46 where is the power output, is the input power, is the efficiency of the DC/DC converter, and is a constant power loss. Table 4 shows the parameter values used in the simulator. Table 4: DC/DC converter parameters Parameter Parameter Description Value used in Simulator Constant consumption 1 kw Constant efficiency Battery System An accurate dynamic model of the battery system is essential for accurate determination of the state of charge of the electrical energy available in the battery. The chemical dynamics within a battery are very complex. Many researchers have shown that the current-to-voltage behavior of batteries used in hybrid vehicle platforms display significant dynamical behavior which are linked to electrochemistry, ion diffusion etc. [16-17]. These factors are very complex and difficult to predict, however it has been shown that the net electrical dynamical behavior can be predicted through approximation by an equivalent electrical circuit of reduced order [18]. An equivalent electrical model of a battery is shown in Figure 13. The circuit consists of an internal resistance with a number of R-C pairs. As the number of R-C pairs increases, so does the accuracy of the model. The number of unknown parameters 24

47 Figure 13: Battery n-order equivalent electrical circuit model diagram also increases. is the open circuit voltage (OCV), is the internal resistance of the battery, is the voltage across the capacitor, and are the resistance and capacitance of the R-C branch, is the voltage loss due to hysteresis, is the load voltage across the cell terminals, and is the current through the cell. This hysteresis phenomenon is not always realized and its magnitude is dependent on the chemistry of the battery. The circuit output equation is given by Equation 2.7: (2.7) where is the number of R-C circuits chosen for the battery model. Previous literature has concluded that these parameters are dependent on various conditions such as SOC, current direction, and temperature of the battery. Each R-C circuit is described by an ordinary differential equation obtained using Kirchoff s current law and the definition of an ideal capacitor: (2.8) 25

48 The SOC of the battery cell is the ratio of the amount of charge left in a cell and the total charge capacity,, of the cell. This is very important when considering supervisory control strategies, as battery operation at very high and very low levels of SOC adversely affect the battery and diminish the lifespan of the battery. Through current integration, the SOC at each time step in the simulator can be calculated. ( ) ( ) (2.9) The dynamics of the SOC can then be expressed as: (2.10) Because the parameters of the battery circuit rely on the SOC, current direction, and temperature, etc., Equation 2.10 becomes a complex non-linear equation. This equivalent electrical circuit model provides a structure for any battery chemistry. The parameters of a specific battery can be experimentally determined as shown by Yurkovich et al. [19]. For this work, several different battery chemistries were considered. A second order model, with two R-C pairs was identified for the following three battery chemistries. LG Chem lithium-ion polymer battery cell GAIA Lithium nickel cobalt oxide (NCA) battery cell GAIA Lithium iron phosphate (LFP) battery cell The identification process was completed for a SOC range of [30-80]%. This will suffice because the battery SOC will be limited to this range for operation of the HFCB. Over this SOC range, it was found that all parameters of the battery are not dependent on SOC, 26

49 except for the OCV. Another simplification to the model is the assumption of proper heat removal from the pack, limiting the temperature variation in the cells, which eliminates the battery parameters dependence on temperature. The battery output equation for each chemistry is given by: ( ) ( ( )) ( ( )) ( ( )) (2.11) where the open circuit voltage is dependent on SOC and the internal resistance is dependent on the direction of the current. The capacitance voltages are calculated from Equation (2.8) which shows dependence on current direction. The values of,,,,, and in charge and discharge can be seen Table 5. Figure 14 shows the OCV for each battery cell over the entire SOC range. Table 5: Battery model parameters for each battery chemistry LG Chem NCA LFP Parameter Charge Discharge Charge Discharge Charge Discharge [Ω] 1.0e e e e e e -5 [F] 1.0e 4 1.0e e e 4 2.0e 4 2.0e 4 [Ω] 1.8e e e e e e -4 [F] 2.0e 5 2.0e e e 5 2.0e 5 2.2e 4 [Ω] 2.5e e e e e e -4 [V] 1.0e e e e e e -3 27

50 Open Circuit Voltage [V] Open Circuit Voltage [V] Open Circuit Voltage [V] Battery SOC [%] Battery SOC [%] a) LG Chem b) NCA Battery SOC [%] c) LFP Figure 14: OCV vs. SOC for different battery cells It is necessary to use multiple battery cells in order to increase the size of the battery pack for use in the HFCB. To achieve a desired pack capacity and voltage, cells are placed in series and parallel, as shown in Figure 15. The battery model at the cell level is scaled in the same fashion for use in the simulator. The voltage output of the battery cell model is multiplied by the number of cells in series, while the electrical current of the battery back is divided by the number of parallel strings of battery cells. 28

51 N parallel N series Figure 15: Battery cell arrangement Auxiliary Loads The auxiliary loads for a passenger bus can be much greater than those of a light duty passenger vehicle. The power required for heating and cooling, the numerous electronics, automatic doors, etc. can be a significant portion of the overall power demand for the bus. For this reason, taking these auxiliary loads into account for the purpose of energy analysis is important. While these auxiliary loads vary with time, a constant auxiliary power demand is used in the simulator to represent the average power demand from all auxiliary loads, and the value used is shown in Table 6. Table 6: Auxiliary Load parameter Parameter Parameter Description Value used in Simulator Average power demand by auxiliary loads 10 kw 29

52 2.5.5 Electric Motors The electric motors (EM) convert the electrical power supplied by the fuel cell and battery into a rotational mechanical power. The motors are modeled as static models which use an experimentally obtained efficiency map for calculations. The maximum power curves of the electric motors were supplied by the manufacturer. Because no experimental data on the electric motor efficiencies was available, a similar motor s efficiency map was scaled to fit the speed-power map of the electric motors used in the bus. To accelerate the bus, the electrical power,, sent to the motors is converted into mechanical power,, which involves an efficiency loss,, shown in Equation The mechanical torque output,, is then determined from this power and the current rotational speed,, of the EM using Equation At this time, the maximum torque limitations of the motors are also taken into account. ( ) (2.12) (2.13) is the EM efficiency at the given power demand and rotational speed. is found using a table look-up of the scaled efficiency map. For deceleration, the mechanical power from the motors that is converted into electrical power is governed by Equations 2.14 and Because the total desired braking force must be split between the front and rear wheels, and the electric motors are only attached to the rear axle, not all of the desired braking force can be done using the electric motors as regenerative devices. For stability purposes, 60% of the total braking 30

53 EM Desired Power [kw] force is done with the front wheels, and 40% is done with the rear. In order to maximize the amount of energy regeneration, of this 40% the electric motors are used until their power limits are reached, and then conventional friction braking is used. Figure 16 shows the efficiency map and power limitations of the electric motor model. (2.14) ( ) (2.15) Max Power Curve Efficiency EM Speed [rpm] Figure 16: Electric motor efficiency map and power limitations Gearbox of Constant Gear Ratio The electric motor gearbox consists of a constant gear ratio,, as specified by the manufacturer. Losses due to friction are considered in the model by the introduction 31

54 of a constant gearbox efficiency,. For positive torques (acceleration) the torque supplied to the rear wheels is: (2.16) The current electric motor speed is also calculated by: (2.17) where is the wheel speed at the current velocity. When the electric motors are acting as generators under braking, the efficiency is reversed and Equation 2.16 becomes: (2.18) The parameter values used for the gearbox model within the simulator can be seen in Table 7. Because little information about the actual gearbox being used in the HFCB was available, the efficiency value is estimated. Table 7: Gearbox parameter values Parameter Parameter Description Value used in Simulator Constant gear ratio Constant gearbox efficiency Front and Rear Brakes The front mechanical brakes are used in parallel with the regenerative braking of the electric motors. For stability, 60% of the total braking torque required by the driver is 32

55 done with the front brakes. The rear friction brakes are only used when the required braking torque at the rear wheels exceeds the torque limits of the electric motors. The torque provided by the mechanical brakes is combined with the electric motor braking torque to deliver a total braking torque to the wheel. (2.19) Front and Rear Wheels The wheels are implemented as a static model which is sufficient for the work in this thesis. Under this model, the current velocity of the vehicle is converted into an angular velocity of the wheel through the radius of the wheel, which is assumed to be constant. (2.20) where is the angular velocity of the front and rear wheels, is the linear velocity of the bus, and is the radius of the tires. The tire radius used for the model can be seen in Table 8. The wheel model also converts the total torque supplied by the powertrain into a force at the wheel through the radius of the wheel. (2.21) Table 8: Tire model parameters Parameter Parameter Description Value used in Simulator Radius of HFCB tires m 33

56 2.6 Vehicle Dynamics Because the simulator s main purpose is for supervisory controller design and powertrain analysis, lateral dynamics have little effect, so they are ignored. The longitudinal dynamics are implemented using simple equations that translate forces at the wheel to an equivalent acceleration, and in-turn the velocity of the bus. It has been shown that the acceleration and deceleration commands from the driver are converted to a total force supplied to the wheel through the powertrain dynamics. This force is combined with environment forces on the bus such as rolling resistance, aerodynamic drag, and force due to grade to determine the actual acceleration of the bus. (2.22) where is the mass of the bus, is the longitudinal acceleration of the bus, and,, and are the rolling resistance, aerodynamic drag, and grade forces respectively. These are calculated by: (2.23) (2.24) (2.25) where is the grade angle, is the rolling resistance coefficient, is the density of air, is the aerodynamic drag coefficient, and is the frontal area of the bus. 34

57 From Equation 2.22, the vehicle acceleration can be found. Integrating this signal with respect to time provides the velocity of the vehicle. This is then sent back to the driver for comparison with the desired drive cycle. Table 9 provides the values used in the simulator for the vehicle dynamics parameters. Table 9: Vehicle Dynamics Parameter Table Parameter Parameter Description Value used in Simulator Vehicle mass lbs Gravitational Acceleration 9.81 Rolling Resistance coefficient.006 Density of air 1.29 Aerodynamic Drag coefficient 0.54 Frontal surface area of bus 7.5 This chapter provided a description and the mathematical equations related to the various blocks within the HFCB simulator. These blocks govern the responses within the simulator. In the next chapter, the Supervisory Controller block, and specifically the PMP optimal controller is described. 35

58 Chapter 3: Control Strategy The supervisory control strategy of any hybrid vehicle determines when and how to use the multiple power sources available on-board. This can be done very simply using a constant split between the two, or in a variety of more complicated methods. One motivation for hybrid vehicle technology is the potential improvement in overall efficiency. In order to maximize that potential benefit, the power sources must be operated in an optimal manner. In the first part of this chapter, several simple energy management control methods will be presented. These will act as a starting point for controller design for the Hybrid Fuel Cell bus, while giving baseline results for comparison to other more complicated control strategies. One method for operating the power sources in an optimal manner is by applying Pontryagin s Minimum Principle. PMP is used in optimal control theory as a strategy for taking a dynamical system from one state to another. The second portion of this chapter deals with the development of the PMP based optimal control strategy for use with energy management in hybrid vehicles, and more specifically with a hybrid fuel cell vehicle. The simulation results from the PMP controller can be used in comparison to other control techniques, as it will provide the best possible control strategy in terms of fuel consumption. 36

59 3.1 Energy Management in a HFCB In general, an energy management controller in a HFCB must determine what power source to use at what time and at what level in order to meet the overall power demand by the driver. It must also take other constraints into account, which are listed below: Do not exceed physical limitations of powertrain components Maintain safe SOC operational region of Battery For a charge sustaining hybrid electric vehicle, it is very common to limit the SOC range of the battery. This ensures safe battery operation and limits battery degradation. Two simple control techniques that can be used in energy management of the HFCB are Thermostatic and Proportional, which will be described next. Both of these control methods use the fuel cell to ensure that the battery SOC stays within acceptable limits Thermostatic Control A thermostatic energy management controller is very similar to a climate control thermostat in your home. In its simplest form, the controller switches the fuel cell between two set points, depending on the SOC level of the battery. This leads to four parameters that can be tuned to change the controller s performance. Figure 17 depicts the operation of the controller. The controller operates the fuel cell at a constant, high current density, and therefor power output until the battery s SOC reaches a high limit. 37

60 Once that high SOC limit is reached, the fuel cell is switched to a lower power output. This fuel cell operation level is maintained until the battery s SOC reaches a low limit, at which point the fuel cell is switched back to the high power output level. Figure 17: Thermostatic control Table 10 summarizes the parameters of the thermostatic controller. All of these parameters are tunable to achieve a certain desired operation. In order to improve controllability, the number of SOC limits and fuel cell operating points can be increased. Table 10: Thermostatic controller parameters Parameter Parameter Description High power output level of fuel cell Low power output level of fuel cell High SOC limit Low SOC limit 38

61 3.1.2 Proportional Control Similarly to the thermostatic controller, the proportional controller relates the fuel cell operation level to the battery SOC level. In its simplest form, the proportional controller inversely relates the fuel cell operating point to the battery SOC linearly. Figure 18 shows this relationship graphically. Figure 18: Proportional control As the battery SOC decreases from a high limit to a low limit, the fuel cell operation increases from a low operating point to a high operating point. The proportional controller consists of the same four parameters as the thermostatic controller, all of which can be tuned in a similar fashion to achieve desirable controller performance. 39

62 3.2 Pontryagin s Minimum Principle Prontryagin s Minimum Principle is a very powerful tool in optimal control theory. It provides a set of necessary conditions to ensure global optimality of a constrained control problem. Under PMP, the optimal control,, if found such that the system ( ) ( ( ) ( ) ) (3.1) follows the admissible trajectory and the performance measure ( ( ) ) ( ( ) ( ) ) (3.2) is minimized. Here ( ( ) ) is the terminal cost of the system state while ( ( ) ( ) ) is the instantaneous cost. The constraints of the system dynamics can be adjoined to by introducing a time varying multiplier vector, called the co-state vector. This leads to the construction of the Hamiltonian, ( ( ) ( ) ( ) ) ( ) ( ) ( ( ) ( ) ) (3.3) PMP states that the optimal control trajectory, optimal state trajectory, and corresponding Lagrange multiplier vector minimize the Hamiltonian such that: ( ( ) ( ) ( ) ) ( ( ) ( ) ( ) ) (3.4) While the following relations and constraints must hold: ( ) ( ( ) ( ) ) (3.5) ( ) ( ( ) ( ) ) (3.6) ( ( ) ) (3.7) ( ) (3.8) 40

63 ( ) ( ) (3.9) ( ) (3.10) where Equation 3.7 is the terminal state constraint, ( ) is the set of admissible control inputs, ( ) is the set of admissible states of the system, and is the known initial state of the system. The solutions which satisfy the PMP conditions are said to be the extremal solutions. PMP ensures that if a global optimal solution exists for the control problem, it is an extremal solution. 3.3 Defining the optimal control problem In general, optimal energy management in a hybrid vehicle is determining how to accelerate the vehicle over a certain driving event to minimize a certain cost. This cost can be fuel consumed, emissions of greenhouse gases, aging of components, or any combination of these. For this thesis, only the fuel economy was considered. In the hybrid fuel cell bus, the controller operates the fuel cell and battery in such a way to minimize the hydrogen consumption by the fuel cell over a given trip. The controller must take physical constraints of the components into account while also taking charge sustainability of the battery into account. In other words, for the bus to continually operate in the safe state of charge region of the battery, the controller must be nominally charge sustaining for the battery over a given drive cycle. 41

64 Since the SOC of the battery is the dynamic constraint of the system, it can be considered the state which needs to be optimally controlled. It is required that the ending SOC be equal to the initial SOC, and the optimal trajectory that satisfies this would: Lead to the minimum fuel consumption possible over the drive cycle. Maintain physical limitation of the fuel cell, battery, and electric motors. Maintains safe SOC region operation at all times. In order to follow this optimally trajectory, the controller will determine the optimal power split between the fuel cell and battery in order to meet the total power demand on the road at every instance in time, while taking the requirements and constraints of the system into account. The energy management of the HFCB can be formulated as a constrained optimization problem where the mass of hydrogen consumed,, is minimized over a given drive cycle, subject to the following dynamic and static constraints: ( ) (3.11) (3.12) (3.13) ( ) ( ) (3.14) (3.15) (3.16) (3.17) 42

65 where and are the minimum and maximum allowable state of charge of the battery, and is the total duration of the drive cycle. Equations 3.15 to 3.17 are the power limitations of the battery, fuel cell, and electric machine respectively. 3.4 Applying PMP to the control problem It has been shown in [20] that PMP can be applied to a conventional hybrid electric vehicle energy management control problem. In a similar fashion, it can be adapted to the fuel cell bus as well. The static battery current can be calculated from the equivalent electric circuit of the battery, described in Equation For a second order equivalent electrical circuit model, the battery current is found by: ( ) ( ) ( ) ( ) ( ) (3.18) Equation 3.18 can be substituted into Equation 3.12 to define. Clearly the SOC dynamics is a non-linear function of the power output and the SOC level. Considering the performance criterion of PMP in Equation 3.11, ( ) (3.19) 43

66 the Hamiltonian is then defined as: ( ) ( ( ) ( ) ) ( ( ) ) (3.20) The fuel consumption of the fuel cell is related to the battery power due to the fact that the summation of the two must equal the total power demand at every instance in time. The necessary conditions for optimality as described in Equations 3.5 to 3.10 are: ( ) (3.21) ( ) ( ) (3.22) ( ) (3.23) ( ) (3.24) ( ) ( ) (3.25) ( ) (3.26) where the admissible states and control inputs, ( ) and ( ) are defined below. The state of the system has been defined as the battery SOC such that [ ] is the set of admissible states. The control input is the power demand from the battery such that is the admissible power demand from the battery. changes instantaneously based on the admissible powers of the electric machines and fuel cell, as well as with the total power demand from the driver. Because the admissible power demand from the fuel cell is a fixed range,, can be found using Equation (3.27) 44

67 where is the total power demand from the driver. This total power demand is calculated based on the pedal position from the driver, while taking battery, fuel cell, and electric motor physical limitations into account. The vector spaces ( ) and ( ) can be searched at every instant to find the optimal control split between and which minimizes the Hamiltonian. The dynamic equations given in Equations 3.21 and 3.22 are dependent on their initial conditions. The initial SOC of the battery is known a-priori. However, the initial condition of the co-state, is unknown. This initial value of the co-state is important in determining the SOC trajectory for a given drive cycle. The value of that satisfies Equation 3.24 and leads to the optimum SOC trajectory is the principle parameter of the PMP optimal controller. The value of can be tuned through trial and error by completing multiple simulations and checking that ( ). This is referred to as the shooting method. Because is unique to each driving event, it is necessary to find a value for each drive cycle. The process of finding will be illustrated in Chapter 5. Once is found, the PMP controller provides the optimal SOC trajectory and control input trajectory for a given drive cycle which minimizes the hydrogen fuel consumption of the fuel cell. 45

68 Chapter 4: Simulation Results In this chapter, an exhaustive example of the types of variables and graphs capable of being drawn from the results of the simulator will be presented. While this example will examine the simulation of just one drive cycle, the same analysis can be extended to all drive cycles that were studied. 4.1 Manhattan Simulation Example The Manhattan drive cycle is often used to represent the velocity profile of urban passenger bus routes for its low average speed and multiple stops. An in-depth look at the simulator performance for this drive cycle follows. The optimal PMP controller was used to produce these results. A description of how was found for the controller can be found in Sections 3.5 and 5.3. The component parameters used can be found in Table 1. The battery model used for this example is the LG Chem pouch cells. The pack consisted of 163 cells in series and 6 strings of cells in parallel. This produced a 87 Ah, 60 kwh pack size. The desired velocity profile of the Manhattan drive cycle along with the actual velocity observed from the simulator can be seen in Figure

69 Vehicle Velocity [mph] Desired Actual Time [s] Figure 19: Velocity trace performance of Simulator As seen in Figure 19, the driver in the simulator is capable of accurately following the velocity profile. The accelerator and brake pedal positions as determined by the driver model can be seen in Figure

70 Accelerator pedal position Brake pedal position Time [s] a) Accelerator pedal position b) Brake pedal position Figure 20: Driver outputs Time [s] From these pedal positions, the PMP controller determines the power split between the fuel cell and the battery. The desired power from both devices can be seen in Figure 21 48

71 Controller Power Command [kw] Battery Power Command FC Power Command Time [s] Figure 21: Power demand from battery and fuel cell as determined by supervisory controller These power demands are sent to the battery and fuel cell models. The battery model calculates the current and voltage of the battery, both of which can be seen in Figure

72 Battery Voltage [V] Battery Current [A] Time [s] a) Battery voltage b) Battery Current Figure 22: Battery operation Time [s] Analysis of the battery voltage is important to ensure that the supplied voltage is within the acceptable range of the components being powered by the battery (power electronics, EMs, pumps, etc.). Examining the battery current is also important to ensure the battery is being used in a safe manner. An important metric used when looking at the operation of a battery is the C-rate, defined by Equation 4.1. High C-rates can lead to damage of the battery and excessive heat generation. Figure 23 is a histogram of the battery C-rate for the Manhattan cycle. (4.1) where is the batter current and is the nominal capacity of the battery pack. 50

73 Occurances C-Rate Figure 23: Battery C-rate histogram A simple calculation, shown in Equation 4.2, can be done to calculate the heat generated by the battery. ( ) (4.2) where is the heat generated, is the output voltage of the battery cell, is the open circuit voltage, and is the electrical current supplied to the battery. Figure 24 shows the heat generated at every instant in time. A more meaningful metric is the average heat generation of the battery over a given amount of time. This will help ensure that the battery cooling system is capable of removing the necessary amount of heat being generated by the battery in order to sustain safe temperature levels of the battery pack. 51

74 Heat Generated by Pack [kw] Time [s] Figure 24: Heat generated by battery pack The SOC of the battery is the state which is optimally controlled by the PMP controller. Because charge sustaining behavior that stays within the SOC limits of the battery is necessary, the SOC trajectory is also important to examine. This trajectory can be seen in Figure

75 SOC [%] 60.2 Battery State of Charge [%] Time [s] Figure 25: Battery SOC trajectory Minimizing fuel consumption is the main goal of our controller design; therefor the operation of the fuel cell over the drive cycle is very important. The fuel cell stack output power as well as the system output power are shown in Figure

76 Fuel Cell Power [kw] Stack Power System Power Time [s] Figure 26: Fuel cell operation The system power is defined by Equation 4.3, and is the net output power by the fuel cell system, after taking power consumption by the fuel cell s compressor into account. (4.3) where is the fuel cell stack output power and the compressor power consumption is related to the fuel cell current, calculated using Equation 2.5. It is also possible to calculate a stack and system efficiency for the fuel cell using Equations 4.4 and 4.5. (4.4) (4.5) 54

77 FC efficiency where is the hydrogen fuel consumption by the fuel cell, calculated using Equation 2.4, and is the lower heating value of hydrogen. Figure 27 plots the observed fuel cell efficiency vs. net power for the Manhattan cycle Stack Efficiency System Efficiency FC Net Power [kw] Figure 27: Fuel cell efficiencies To see the distribution of the operating points of the fuel cell, a histogram can be seen in Figure

78 Occurrences FC Power [kw] Figure 28: Fuel cell operation histogram The instantaneous fuel consumption of the fuel cell is shown in Figure 29. Integrating this, the total fuel consumed over time can be found and is shown in Figure

79 Hydrogen Consumption [kg] Hydrogen mass fuel rate [kg/s] 4.5 x Time [s] Figure 29: Instantaneous hydrogen mass flow rate Time [s] Figure 30: Hydrogen consumed 57

80 EM Torque [Nm] The output power from the battery and the fuel cell are combined and sent to the electric motors and auxiliary loads. The power sent to the EM s is converted into a torque output of the EM by the model. The operating points of the EM s can be seen in the torquespeed plain in Figure Max Power Curve Efficiency Operating Points EM Speed [rpm] Figure 31: Electric motor operating points plotted in torque-speed plain The total torque output from both EMs in the HFCB vs. time for the Manhattan cycle can be seen in Figure

81 Total EM Torque Output [Nm] Time [s] Figure 32: EM torque ouput This torque is converted into a force at the wheel through the gearbox and tire models in the simulator. This force at the wheel is used in the vehicle dynamics model to calculate the acceleration of the bus. This force can also be used to calculate the power at the wheel by Equation 4.6. This is useful when considering the overall powertrain efficiency of the HFCB. (4.6) where is the force at the wheel, and is the velocity of the bus. The power at the wheel with respect to time over the drive cycle can be seen in Figure

82 Wheel Power supplied by powertrain [kw] Time [s] Figure 33: Power at the wheel supplied by the powertrain It is also beneficial to examine the environmental forces acting on the bus as well. These include rolling resistance, aerodynamic, and grade forces as described in Section 2.6. These forces are calculated at every instance in time within the simulator and can be seen in Figure

83 Force [N] Rolling Resistance Force Force due to Grade Aerodynamic Force Time [s] Figure 34: Environmental Forces acting on the bus. 4.2 Acceleration and Speed Tests The simulator is also capable of performing acceleration tests. The driver accelerates the vehicle as fast as possible to a desired velocity. This is important in determining if the bus can meet certain performance requirements. The acceleration capabilities of the bus using the same parameters as the previous example are summarized in Table

84 Table 11: Acceleration and Speed capabilities of the HFCB Metric Value Achieved Top Speed [mph] mph Time [s] mph Time [s] mph Time [s] mph Time [s] 11.4 In this chapter, simulation results for one drive cycle and one combination of powertrain components and control strategy was presented. These same results are produced for every simulation case. In order to examine different aspects of the HFCB, numerous simulations were completed. The next chapter provides a summary of several different studies that were conducted using the simulator, as well as an examination of the PMP controller results. 62

85 Chapter 5: Results Analysis In this chapter, the analysis of extensive simulation results is presented. A detailed analysis of the PMP based controller results for multiple drive cycles and battery chemistries is presented. While controller design is the main focus of the simulator, several different studies were also completed to analyze different aspects of the bus. The effects that variables such bus weight, battery size, and battery chemistry had on the HFCB operation and performance were examined. These studies depict how the simulator can be used as a tool for design and analysis. These studies will also be presented in this chapter. 5.1 Battery Sizing Study OSU was asked to explore the affects that different battery pack sizes would have on the operation of the bus, in order to assist DesignLine with their battery pack design decision. Oversizing the battery pack can lead to excessive cost and weight, while under sizing the pack would result in reduced performance and excessive loads on the battery. Using the simulator, numerous simulations with different pack sizes were completed at little cost. Results from the simulator can be used to ensure that the bus meets cycle requirements while maintaining safe operation of the components of the bus. 63

86 Vehicle Velocity [mph] For this study, the LG Chem battery cells were used. Three different pack sizes were examined. The pack dimensions and nominal sizing is shown in Table 12. Table 12: LG Chem pack geometry for different nominal sizing Nominal Pack size [kwh] # cells in series # strings in parallel Each pack size was simulated over multiple drive cycles, with and without grade, to ensure the extremes of operation were captured. Figure 35 shows the SOC trajectory during 3 repeated HDUDDS drive cycles for each battery pack size kwh Pack 30 kwh Pack 60 kwh Pack Time [s] Figure 35: SOC trajectory for different battery pack sizes for 3 repeated HDUDDS cycles 64

87 It is evident from Figure 35 that as the pack size decreases, the range of SOC operation increases. The electrical current demand per cell on the battery also increases as the pack size decreases. This increases the average C-rate, which can cause more rapid degradation of the battery cells. It is important to examine the average C-rate to ensure the battery does not have to operate in a harmful manner. Also, the voltage range of the battery needs to be examined to ensure that the output voltage from the battery stays within the acceptable range of the HFCB. Table 13 provides a summary of these metrics for every simulation completed. Table 13: Battery operation summary metrics for different pack sizes for all simulations Nominal Pack size [kwh] Maximum Voltage Variation [V] Maximum SOC Variation [%] Average Absolute C-rate Average Pack Heat Generation [kw] The affects battery sizing has on fuel economy is also an important factor. Table 14 shows the average fuel economy for all drive cycles for each battery pack size. 65

88 Table 14: Fuel economy observed for different battery pack sizes Nominal Pack size [kwh] Average Hydrogen Fuel Economy [miles/kg H 2 ] Average Diesel Equivalent Fuel Economy [miles/gal] Percent change from baseline % % From the results, it can be seen that as pack size decreases, the battery must be used in a more aggressive manner, however the overall fuel economy is not significantly affected. 5.2 Weight Sensitivity Study The weight of a passenger bus significantly varies while in operation, as passengers enter and exit the bus. These fluctuations in weight could have major impacts in the fuel economy, performance, and optimal operation of the bus. A sensitivity analysis was conducted in order to study the relationship between bus weight, fuel economy, and performance of the bus. The fuel economy achieved for several different bus weights is provided below. The relative sensitivity of the fuel economy to variations in bus weight is calculated using Equation 5.1. (5.1) where is the change in fuel economy, is the original fuel economy, is the change in weight, and is the original weight of the bus. 66

89 Table 15: Average fuel economy for differently bus weights Bus Weight [lbs] Average Hydrogen Fuel Economy [miles/kg H 2 ] Average Diesel Equivalent Fuel Economy [miles/gal] Sensitivity It is also important to explore how the performance of the bus (acceleration, top speed, etc.) is affected as weight increases. It is important that the bus is able to meet certain criterion for safe travel on the road. Table 16 provides a summary of different performance metrics for several different weights of the bus. Table 16: Acceleration performance of the bus at different overall vehicle weights Bus Weight [lbs] 0-10 mph time [s] 0-20 mph time [s] 0-30 mph time [s] 0-40 mph time [s] 0-10 MPH time on 10% Grade[s] 0-20 MPH time on 5% Grade[s] Maintainable Speed on 5% Grade [mph] As expected, as the weight of the bus increases, fuel economy and acceleration capabilities of the bus are adversely affected. 67

90 5.3 Optimal PMP Controller Results As previously stated, the PMP controller provides the optimal SOC trajectory and control input trajectory which minimizes the hydrogen fuel consumption of the fuel cell. In order to be charge sustaining, the beginning and ending SOC of the battery must be equal for a given drive cycle. The value of that produces that charge sustaining behavior must be found for each drive cycle. This is done through trial and error, called the shooting method. This procedure will be shown in the following section Finding A value for is first selected and the simulator is run for the desired drive cycle. The ending SOC of the battery is then examined and the value of is adjusted accordingly. This process is repeated until the ending SOC is equal to the initial SOC. The SOC trajectories for different values of simulated for the Manhattan drive cycle is shown in Figure

91 Battery SOC [%] = = = = = Time [s] Figure 36: SOC trajectory for different values of The different values of also lead to different operation of the fuel cell. Figure 37 shows the different operation of the fuel cell observed for different values. 69

92 Fuel Cell Power [kw] = = = = = Time [s] Figure 37: Fuel cell operation for different values A lower value leads to a lower average fuel cell power output, which correlates to lower overall fuel consumption. This does not correspond to the optimal solution however because the operation does not produce charge sustaining behavior of the battery. Figure 38 shows the fuel consumption over the Manhattan drive cycle for different values of. 70

93 Fuel Consumption [kg] x [kg] Figure 38: Hydrogen consumed using different values of This process of finding is repeated for every unique case (component and drive cycle combination) to be simulated in order to find the globally optimal solution. Next, the optimal control results for several different battery chemistries will be presented Optimal Control Analysis of Different Battery Chemistries Because several different battery chemistries have been modeled, it is possible to examine the optimal controller results while using these different battery models in the simulator. This is useful to determine if optimal operation is dependent on the battery chemistry. 71

94 Battery Voltage [V] Battery Current [A] The different battery chemistry models presented in Section were each implemented in the simulator. Cells were arranged in the manner shown in Table 17 to produce a nominally 60 kwh battery pack for each chemistry while always staying within the acceptable voltage range of all the power electronics of the bus. Table 17: Pack arrangement for each battery chemistry Battery # cells in series # of string in parallel LG Chem NCA LFP Simulation of each battery chemistry using the PMP controller over the Manhattan drive cycle produced the results shown in the following figures. Figure 39 shows the battery s output voltage and current demand during the cycle for all three chemistries LG Chem NCA LFP LG Chem NCA LFP Time [s] Time [s] a) Battery Current vs. time b) Battery Current vs. time Figure 39: Battery operation during Manhattan cycle for different battery chemistries 72

95 Battery SOC [%] The difference in battery pack voltage is an artifact of pack sizing, and is not depictive of different control of the batteries. Figure 40 shows the optimal battery SOC trajectory found from the PMP controller for the Manhattan cycle. Figure 41 shows the fuel cell output trajectory corresponding to each battery chemistry as well LG Chem NCA LFP Time [s] Figure 40: Battery SOC trajectory of different chemistries 73

96 Fuel Cell Power [kw] LG Chem NCA LFP Time [s] Figure 41: Optimal Fuel cell operation using different battery chemistries From these figures, it can be seen that the optimal control of the battery and fuel cell is very similar for each battery chemistry. Results of other drive cycles provide more evidence that the optimal SOC trajectory is nearly identical regardless of battery chemistry. Table 18 shows the average fuel economy achieved for several drive cycles for each of the battery chemistries, which in nearly identical for each battery chemistry. Table 18: Average fuel economy of different battery models Battery Average Fuel Economy [miles/kg H 2 ] Average Diesel Equivalent Fuel Economy [miles/gal] LG Chem NCA LFP

97 While optimal operation is somewhat independent of the battery chemistry used, the value of is not. This value if significantly different for each battery chemistry. These values are summarized in Table 19. Table 19: values for each battery chemistry Battery % difference LG Chem NCA LFP By normalizing this value using the nominal pack energy capacity of each chemistry as shown in Equation 5.2, this variation diminishes. (5.2) where is the nominal pack capacity and is the initial pack voltage. Table 20 shows the values of. This result shows that is dependent on the initial energy capacity of the pack and the given drive cycle, not on the chemistry of the battery cells. Table 20: values for each battery chemistry Battery % difference LG Chem NCA LFP

98 It has been shown in Chapter 3 that is a function of the parameters of the battery model however. An analysis of for the different battery chemistries shows this relationship. Figure 42 shows vs. time for the Manhattan drive cycle. Figure 42: vs. time for different battery chemistries It is important to note that is very small however in relation to, resulting in being essentially constant. This leads to the conclusion that can be approximated to be zero, regardless of battery chemistry. This is shown graphically for the LG Chem battery in Figure 43. varies less than 0.003% over the entire cycle. 76