An ECMS-Based Controller for the Electrical System of a Passenger

An ECMS-Based Controller

for the Electrical System of a Passenger Vehicle

THESIS

Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University

Jeremy R. Couch

B.S. (Case Western Reserve University) 2011

Graduate Program in Mechanical Engineering

The Ohio State University

2013

Master's Examination Committee:

Professor Marcello Canova, Advisor

Professor Giorgio Rizzoni, Committee Member

Dr. Lisa Fiorentini, Committee Member

Jeremy R. Couch

2013

Abstract

A primary concern for automotive manufacturers is increasing the fuel economy of their vehicles. One way to accomplish this is by reducing the losses associated with operating the ancillary loads such as the loads of the vehicle’s electrical system. In the electrical system of a vehicle, the alternator provides current to the electrical loads. The difference between the load current demand and the current provided by the alternator is either accepted or supplied by the battery. Therefore, the current demand of the electrical loads can be met by the alternator, the battery or a combination thereof. While improving the efficiency of the actual components of the electrical system (alternator, battery and electrical loads) is beneficial, additional gains can be realized with a smart control strategy for the alternator.

Conventional alternator control strategies make little use of the battery; the power demand from the electrical loads is almost solely met by the alternator. However, since the alternator is directly connected to the engine, this results in increased fuel consumption, particularly at idle speed conditions. To this extent, more advanced control strategies could be implemented to make use of the battery energy buffer to limit the use of the alternator at low engine efficiency conditions.

The focus of this thesis is the design of an advanced alternator control strategy. First, a model of a vehicle’s electrical system is developed with control design in mind. The system is modeled starting from a lumped-parameter, energy-based characterization of the battery and alternator. This is followed by a thorough calibration using experimental data and, finally, validation on a vehicle chassis dynamometer considering a standard

(production) alternator control strategy.

Next, a novel alternator control algorithm is designed by applying the Equivalent

Consumption Minimization Strategy (ECMS), a well known energy management approach often used to control the powertrain of hybrid electric vehicles. This strategy works by determining the optimal alternator current to minimize the instantaneous fuel consumption while complying with input and state of charge constraints.

The ECMS algorithm was extensively calibrated for a variety of drive cycles and load current profiles. This proposed control strategy was then compared in simulation to the production alternator controller and fuel consumption reductions of up to 2.18% have been shown. An adaptive ECMS (A-ECMS) is then defined, using feedback from the battery’s state of charge to dynamically tune the ECMS calibration parameter in real- time. Simulation results for the A-ECMS show fuel savings compared to the baseline alternator control strategy that are on the same order of magnitude as the ECMS.

Furthermore, a robustness study verifies the A-ECMS is insensitive to model inaccuracies, poor tuning of the parameters and variations in the load current profile.

iii

Acknowledgements

I have had a great experience as a graduate student at The Ohio State University and, in particular, the Center for Automotive Research (CAR). I owe much thanks to those who have helped me in my time here. Thank you to my advisor, Professor Marcello Canova, for bringing me into CAR, guiding me into a rewarding project, and supporting me throughout these two years. Thank you to Dr. Lisa Fiorentini for her infinite patience and for making time for me when she had none for herself. Thank you to Dr. Fabio Chiara for sharing his knowledge and sense of humor when things got tough. Thank you to

Professor Giorgio Rizzoni for his insight on the ECMS and Dr. Shawn Midlam-Mohler for his expertise on hardware instrumentation. Thank you to Yann Guezennec for his valuable input on battery modeling and John Neal for helping conduct the battery testing.

Thank you to Sabarish Gurusubramanian for his assistance with experimental testing and

Quansheng Zhang for answering all my questions, no matter how simple. I would also like to thank Benjamin Grimm and Neeraj Agarwal for laying the foundation for my work. Finally, many thanks to Kyle Merical for keeping me sane during the more trying times. I appreciate you all.

To my family.

Vita

2007...... Cloverleaf High School

2011...... B.S. Mechanical Engineering,

Case Western Reserve University

2011 to present ...... Graduate Fellow,

Department of Mechanical and Aerospace

Engineering, Center for Automotive

Research, The Ohio State University

Fields of Study

Major Field: Mechanical Engineering

Table of Contents

Abstract ...... ii

Acknowledgements ...... iv

Vita ...... vi

Table of Contents ...... vii

List of Tables ...... xi

List of Figures ...... xv

Nomenclature ...... xxiii

Chapter 1: Introduction ...... 1

Section 1.1 Scope of Work ...... 1

Section 1.2 Document Layout ...... 2

Chapter 2: State of the Art ...... 3

Section 2.1 Fuel Consumption in the Transportation Sector ...... 3

Section 2.2 Industry Response ...... 7

2.2.1 Powertrain ...... 7

Powertrain Design ...... 9

vii

Energy Savings/Recovery ...... 12

2.2.2 Ancillary Loads ...... 18

Lubrication System ...... 18

Cooling System ...... 20

AC System ...... 20

Alternator ...... 22

2.2.3 Electrical System Control ...... 23

Section 2.3 Equivalent Consumption Minimization Strategy ...... 26

2.3.1 The ECMS ...... 26

2.3.2 The Adaptive ECMS ...... 29

Chapter 3: Model Development, Calibration and Validation ...... 32

Section 3.1 Experimental Setup ...... 32

3.1.1 Engine ...... 33

3.1.2 Vehicle ...... 35

3.1.3 Battery Testing ...... 38

Section 3.2 Overview of the Vehicle Energy Simulator ...... 39

3.2.1 Driver ...... 40

3.2.2 Sensors ...... 40

3.2.3 Chrysler Control ...... 41

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3.2.4 OSU Control ...... 41

3.2.5 Actuators ...... 41

3.2.6 Vehicle Plant...... 42

Powertrain ...... 42

Thermal System ...... 43

AC System ...... 45

Section 3.3 Electrical System Model ...... 46

3.3.1 Alternator Model ...... 47

3.3.2 Battery Model ...... 52

3.3.3 Voltage Regulation Control Strategy ...... 68

3.3.4 Electrical Loads ...... 69

3.3.5 Electrical System Validation ...... 70

Section 3.4 VES Validation ...... 73

Section 3.5 Simplified Vehicle Fuel Consumption Model ...... 76

Chapter 4: Design of Control Strategies ...... 88

Section 4.1 Alternator Control Problem ...... 88

Section 4.2 The ECMS for Alternator Control ...... 89

Section 4.3 Calibration and Results ...... 95

Section 4.4 Sensitivity Analysis ...... 106

4.4.1 Equivalence Factors ...... 107

4.4.2 Calibration Parameters ...... 109

4.4.3 Model Inaccuracies ...... 113

Section 4.5 The Adaptive ECMS ...... 115

4.5.1 Continuous SOC Feedback ...... 116

4.5.2 Discrete SOC Feedback ...... 119

4.5.3 Results ...... 121

4.5.4 Evaluation of Robustness ...... 129

Model Inaccuracies ...... 129

Calibration Parameter ...... 134

4.5.5 Validation ...... 136

Chapter 5: Conclusions and Future Work ...... 139

Section 5.1 Conclusions ...... 139

Section 5.2 Future Work ...... 141

References ...... 143

Appendix A: Additional Electrical Model Validation ...... 148

Appendix B: Corrected Fuel Consumption...... 153

Appendix C: Additional Sensitivity Analysis Results ...... 154

Appendix D: Additional A-ECMS Results ...... 158

List of Tables

Table 1: Engine specifications...... 33

Table 2: Engine dyno testing summary [42]...... 35

Table 3: Vehicle specifications...... 36

Table 4: Battery specifications...... 39

Table 5: RMS error in the battery voltage for three SOC levels...... 68

Table 6: Coefficients of fit for fuel consumption map...... 78

Table 7: Parameters for the ECMS calibration...... 96

Table 8: Description of the performance metrics. All variables are for 1 cycle unless otherwise noted...... 100

Table 9: Results for VR on the FTP cycle...... 101

Table 10: Results for the ECMS on the FTP cycle...... 101

Table 11: Results for VR on the ARTEMIS cycle...... 101

Table 12: Results for the ECMS on the ARTEMIS cycle...... 101

Table 13: Comparison of performance metrics between VR and the ECMS. All values are percents...... 103

Table 14: Sensitivity analysis results for a suboptimal equivalence factor. The variables in the top two rows are associated with the value in the corresponding cell of each shaded or white section...... 109 xi

Table 15: Sensitivity analysis results for a maximum battery voltage of 14.6 V...... 110

Table 16: Sensitivity analysis results for a maximum battery voltage of 16 V...... 111

Table 17: Sensitivity analysis results for a controller sample time of 1 second...... 112

Table 18: Sensitivity analysis results for a controller sample time of 10 seconds...... 112

Table 19: Sensitivity analysis results for a maximum rate of change of the current split factor of 0.5/s...... 113

Table 20: Sensitivity analysis results for an inaccurate battery model...... 114

Table 21: Sensitivity analysis results for an inaccurate fuel consumption map...... 115

Table 22: Parameters for the A-ECMS with continuous feedback on the SOC...... 118

Table 23: Parameters for the A-ECMS with discrete feedback on the SOC...... 120

Table 24: Results for VR control for the FTP cycle and various load current magnitudes.

...... 122

Table 25: Results for the ECMS calibrated for the FTP cycle and load current magnitude.

...... 122

Table 26: Results for the cA-ECMS over the FTP cycle...... 122

Table 27: Results for the dA-ECMS over the FTP cycle...... 122

Table 28: Comparison of performance metrics between VR and the ECMS. All values are percents...... 123

Table 29: Comparison of performance metrics between VR and the cA-ECMS. All values are percents...... 123

Table 30: Comparison of performance metrics between VR and the dA-ECMS. All values are percents...... 124

xii

Table 31: Comparison of performance metrics between the tuned ECMS and both versions of the A-ECMS for the FTP cycle. All values are percents...... 127

Table 32: Sensitivity results for the dA-ECMS with an inaccurate battery model...... 129

Table 33: Sensitivity results for the dA-ECMS with an inaccurate fuel consumption map.

...... 133

Table 34: Suboptimal equivalence factor. FTP cycle with s 10% less than the optimal value...... 154

Table 35: Suboptimal equivalence factor. ARTEMIS cycle with s 10% greater than the optimal value...... 154

Table 36: Suboptimal equivalence factor. ARTEMIS cycle with s 10% less than the optimal value...... 155

Table 37: Inaccurate calibration parameter. ARTEMIS cycle with a max battery voltage of 14.6 V...... 155

Table 38: Inaccurate calibration parameter. ARTEMIS cycle with a max battery voltage of 16 V...... 155

Table 39: Inaccurate calibration parameter. ARTEMIS cycle with 1 s controller sample time...... 156

Table 40: Inaccurate calibration parameter. ARTEMIS cycle with 1 s controller sample time...... 156

Table 41: Inaccurate calibration parameter. ARTEMIS cycle with a maximum rate of change of the current split factor of 0.5/s...... 156

Table 42: Model inaccuracy. ARTEMIS cycle with a battery model off by 10%...... 156

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Table 43: Model inaccuracy. ARTEMIS cycle with a fuel consumption map off by 10%.

...... 157

Table 44: Results for the ECMS calibrated for the ARTEMIS cycle and load current magnitude...... 158

Table 45: Results for the A-ECMS with continual SOC feedback over the ARTEMIS cycle...... 158

Table 46: Results for the A-ECMS with discrete SOC feedback over the ARTEMIS cycle...... 158

Table 47: Comparison of performance metrics between the tuned ECMS and both versions of the A-ECMS for the ARTEMIS cycle. All values are percents...... 159

xiv

List of Figures

Figure 1: Liquid fuel supply in the U.S. (millions of barrels per day) [4]...... 4

Figure 2: U.S. energy consumption by fuel (quadrillion BTU per year) [4]...... 4

Figure 3: Average sales-weighted MPG since October 2007 (as reported by the

University of Michigan’s Transportation Research Institute) [9]...... 6

Figure 4: Fuel and brake energy divisions for EPA city and highway cycles [11]...... 8

Figure 5: Shift of the fuel economy map by downsizing and turbocharging the engine

[15]...... 10

Figure 6: Automatic stop (top) and start (bottom) procedure for BMWs with manual transmissions [23]...... 15

Figure 7: Potential energy savings with electric oil pumps [26]...... 19

Figure 8: Bench test comparing fixed and variable displacement AC compressors [29]. 21

Figure 9: Comparison of output between a conventional alternator and one with an increased slot fill factor [30]...... 22

Figure 10: Comparison between a parallel HEV powertrain and the electrical system on a conventional vehicle...... 25

Figure 11: Energy path for equivalent fuel consumption of the battery during discharge

(adapted from [32])...... 27

Figure 12: Comparison of the SOE over UDDS cycle for three different methods [34]. . 28 xv

Figure 13: Comparison of the SOC over the FTP cycle with an optimal and a sub-optimal equivalence factor [41]...... 29

Figure 14: Comparison of SOC feedback strategies for ARTEMIS Urban plus Extra

Urban cycle (adapted from [37])...... 31

Figure 15: Engine dynamometer test cell...... 34

Figure 16: Dyno DAQ system...... 34

Figure 17: Vehicle on chassis dynamometer...... 37

Figure 18: Vehicle DAQ schematic (left) and components (right)...... 38

Figure 19: Battery testing setup: environmental chamber (left); battery inside the chamber

(center); cycler (right)...... 39

Figure 20: Structure of VES model in Simulink...... 40

Figure 21: High-level block diagram of the mechanical system (adapted from [42])...... 43

Figure 22: Input/output structure of receivers (left) and flow control devices (right)...... 44

Figure 23: Thermal system architecture...... 44

Figure 24: Schematic of AC system...... 45

Figure 25: Schematic of vehicle electrical system...... 46

Figure 26: Simplified alternator model (adapted from [47])...... 47

Figure 27: Alternator model as a set of 3-dimensional maps...... 48

Figure 28: Instrumented electrical system...... 49

Figure 29: Section of alternator test at 1700 rpm...... 50

Figure 30: Alternator current map for Vbat = 14 V...... 51

Figure 31: Alternator model validation...... 51

xvi

Figure 32: 1st order equivalent circuit of the battery...... 52

Figure 33: Capacity test showing the steps listed above...... 54

Figure 34: Test for the open circuit voltage...... 55

Figure 35: Battery voltage data during steady-state fit with an exponential function...... 57

Figure 36: Open circuit voltage curves. The final curve is the average from fitting (green line)...... 58

Figure 37: Battery test for parameter identification...... 59

Figure 38: Current step and corresponding voltage response...... 60

Figure 39: Equivalent circuit during a step in current...... 61

Figure 40: Equivalent circuit during steady-state...... 62

Figure 41: Example of a least-squares curve fitting result...... 64

Figure 42: R as a function of the SOC and current level...... 65

Figure 43: R0 as a function of the SOC and current level...... 65

Figure 44: C0 as a function of the SOC and current level...... 66

Figure 45: Battery current profile used for battery model validation...... 67

Figure 46: Battery model validation for a SOC of 90%...... 67

Figure 47: Voltage regulation block diagram...... 69

Figure 48: Measured (blue) and filtered (green) load current as loads are turned on and off...... 69

Figure 49: Battery current comparison over FTP cycle with base electrical loads for electrical system validation...... 71

xvii

Figure 50: Alternator current comparison over FTP cycle with base electrical loads for electrical system validation...... 71

Figure 51: Battery voltage comparison over FTP cycle with base electrical loads for electrical system validation...... 72

Figure 52: Duty cycle comparison over FTP cycle with base electrical loads for electrical system validation...... 72

Figure 53: Comparison of experimental and VES vehicle velocity...... 74

Figure 54: Comparison of experimental and VES torque converter turbine torque...... 74

Figure 55: Comparison of experimental and VES engine speed...... 75

Figure 56: Comparison of experimental and VES fuel flow rate...... 75

Figure 57: Comparison of experimental and VES fuel consumption...... 76

Figure 58: Block diagram of the simplified fuel consumption model...... 77

Figure 59: Fuel consumption map built using multiple regression techniques...... 79

Figure 60: Contour fuel consumption map built using multiple regression techniques. .. 79

Figure 61: Lines fitted to the interpolated fuel consumption data...... 80

Figure 62: Fuel consumption map built by fitting lines to the data for each engine speed.

...... 81

Figure 63: Contour fuel consumption map built by fitting lines to the data for each engine speed...... 81

Figure 64: Fuel consumption map built by fitting second order curves to the data...... 83

Figure 65: Contour fuel consumption map built by fitting second order curves to the data.

...... 83

xviii

Figure 66: Comparison of fuel flow rate for LF Map...... 85

Figure 67: Comparison of fuel flow rate for MR Map...... 85

Figure 68: Comparison of experimental and predicted fuel consumption for LF map. ... 86

Figure 69: Comparison of experimental and predicted fuel consumption for MR map. .. 86

Figure 70: Experimental and predicted fuel consumption over the course of the cycle. .. 87

Figure 71: Electrical system schematic...... 89

Figure 72: Block diagram of the ECMS algorithm...... 90

Figure 73: Alternator model with alternator current as an input instead of the duty cycle.

...... 92

Figure 74: Block diagram of alternator fuel consumption calculation...... 92

Figure 75: Block diagram of battery equivalent fuel consumption calculation...... 93

Figure 76: Connection of the ECMS optimizer and the electrical system model...... 95

Figure 77: SOC and low pass filtered SOC over 5 FTP cycles...... 97

Figure 78: SOC as a function of the equivalence factors. Points shown are where SOC

= 0...... 98

Figure 79: Fuel consumption as a function of the equivalence factors. Points shown are the corresponding fuel consumptions for the points where SOC = 0 in Figure 78...... 98

Figure 80: Optimal equivalence factors versus the load current for the FTP cycle...... 99

Figure 81: Optimal equivalence factors versus the load current for the ARTEMIS cycle.

...... 100

Figure 82: Improvement in fuel consumption using the ECMS...... 102

Figure 83: Decrease in alternator energy consumption with the ECMS...... 102

xix

Figure 84: Increase in battery use with the ECMS...... 103

Figure 85: Comparison of battery current between VR and the ECMS over a section of the FTP cycle...... 104

Figure 86: Comparison of alternator current between VR and the ECMS over a section of the FTP cycle...... 105

Figure 87: Comparison of battery voltage between VR and the ECMS over a section of the FTP cycle...... 105

Figure 88: Comparison of battery SOC between VR and the ECMS over the FTP cycle.

...... 106

Figure 89: Continuous feedback adaptation strategy...... 116

Figure 90: System behavior for adaptive equivalence factor with continuous PI control.

...... 118

Figure 91: Discrete feedback adaptation strategy...... 119

Figure 92: System behavior for adaptive equivalence factor with discrete updates every

60 seconds...... 120

Figure 93: Change in fuel consumption between the A-ECMS versions and the calibrated

ECMS...... 125

Figure 94: Change in alternator energy consumption between the A-ECMS versions and calibrated the ECMS...... 125

Figure 95: Change in battery usage between the A-ECMS versions and the ECMS. .... 126

Figure 96: Comparison of system behavior for the calibrated ECMS and both the A-

ECMS versions over 5 FTP cycles with a 75 A load current...... 128

Figure 97: System behavior for the dA-ECMS with an inaccurate battery model...... 130

Figure 98: System behavior for the dA-ECMS with a predicted SOC that is continually above the reference...... 131

Figure 99: System behavior for the dA-ECMS with safety modifications and a that is continually above the reference...... 132

Figure 100: System behavior for the dA-ECMS with a predicted SOC that is 10% high.

...... 133

Figure 101: System behavior for the dA-ECMS with inaccurate fuel consumption map over 5 consecutive FTP cycles...... 134

Figure 102: System behavior for adaptive equivalence factor with discrete updates every

1000 seconds...... 136

Figure 103: Load current profile used for dA-ECMS validation...... 137

Figure 104: dA-ECMS controller operating with random electrical loads over 5 FTP cycles...... 137

Figure 105: Alternator and battery currents dictated by dA-ECMS controller over 5 FTP cycles...... 138

Figure 106: Battery current comparison over FTP cycle with moderate electrical loads for electrical system validation...... 148

Figure 107: Alternator current comparison over FTP cycle with moderate electrical loads for electrical system validation...... 149

Figure 108: Battery voltage comparison over FTP cycle with moderate electrical loads for electrical system validation...... 149

xxi

Figure 109: Duty cycle comparison over FTP cycle with moderate electrical loads for electrical system validation...... 150

Figure 110: Battery current comparison over ARTEMIS cycle with base electrical loads for electrical system validation...... 150

Figure 111: Alternator current comparison over ARTEMIS cycle with base electrical loads for electrical system validation...... 151

Figure 112: Battery voltage comparison over ARTEMIS cycle with base electrical loads for electrical system validation...... 151

Figure 113: Duty cycle comparison over ARTEMIS cycle with base electrical loads for electrical system validation...... 152

xxii

Nomenclature

Throttle command Brake command Current split factor

Maximum rate of change of the current split factor

Alternator efficiency State of charge penalty magnitude Time constant of potential difference across the capacitance

Alternator speed

Engine speed

Battery usage metric

Nominal capacity of the battery

Capacitance Duty cycle Deceleration fuel shutoff command

Open circuit voltage of the battery

Alternator energy consumption

State of charge penalty function

Alternator current

Desired alternator current

Maximum alternator current

Battery current

Maximum battery current

Minimum battery current

Alternator field current

Current demand of the electrical loads

Proportional gain

Integral gain

xxiii

Equivalent fuel consumption of the battery

Mass of fuel

Alternator power

Battery power

Power consumed by the electrical loads

Lower heating value of gasoline Internal resistance of the battery

Over voltage resistance of the battery Equivalence factor

Base equivalence factor

Charging equivalence factor

Discharging equivalence factor State of charge of the battery

Maximum state of charge

Minimum state of charge

Reference value for the state of charge

Alternator torque

Battery temperature

Controller sample time

Engine torque

Update time for discrete SOC feedback version of A-ECMS

Battery voltage

Reference value for the battery voltage

Potential difference across the capacitance

Maximum battery voltage

Minimum battery voltage

Nominal system voltage

Maximum rate of change of the battery voltage

xxiv

Chapter 1: Introduction

The United States’ automotive industry is under considerable pressure to produce more fuel efficient vehicles. Consumers want vehicles with greater fuel economy so they can spend less at the pump, and the government is enacting fuel economy mandates for a variety of environmental, economic and security reasons. As a result, the industry is working to develop new technology to reduce fuel consumption. While some of this technology completely changes the architecture of the vehicle, other improvements are on a smaller scale yet still yield major benefits. The work described in this thesis is one example of a control improvement that reduces fuel consumption and requires no hardware modifications to the vehicle.

Section 1.1 Scope of Work

The Ohio State University’s Center for Automotive Research (CAR) is working with

Chrysler LLC on a large research project focused on advanced technology powertrains for light-duty vehicles. The project is jointly funded by Chrysler and the U.S.

Department of Energy, and the overall goal is to improve fuel economy for a Chrysler

Town & Country minivan by 25% over the Federal Test Procedure drive cycle using only non-hybrid powertrain enhancements. CAR is responsible for the development of a supervisory Vehicle Energy Manager to improve fuel economy by 4-8% through vehicle

ancillary load reduction (VALR) and advanced thermal management systems (TMS). On the TMS side, the aim is to reduce fluid warm-up time during cold start and maintain stable temperatures thereafter. Details of the TMS modeling, analysis and control development can be found in [1] and [2]. This document focuses on the VALR aspect of the project, specifically on the electrical system control development.

Section 1.2 Document Layout

The remainder of the document is structured as follows:

Chapter 2: State of the Art discusses the steps being taken by the industry to reduce the fuel consumption of vehicles with a conventional architecture (non-hybrid). In addition, an overview of the Equivalent Consumption Minimization Strategy (ECMS) and its applications is given in this chapter.

Chapter 3: Model Development, Calibration and Validation focuses on the structure and development of the Vehicle Energy Simulator with particular emphasis on the electrical system model. Calibration and validation results are included where relevant.

Chapter 4: Design of Control Strategies contains the majority of the original work presented in this document. The electrical system control problem is formally defined and the design of the ECMS is shown in detail. Simulation results for the ECMS and the baseline control strategy are compared to highlight the potential of this work. The adaptive ECMS is demonstrated to confirm the feasibility for real-time control.

Chapter 5: Conclusions and Future Work summarizes the most important findings from Chapter 4 and details future work that should be undertaken to extend this study.

Chapter 2: State of the Art

Section 2.1 Fuel Consumption in the Transportation Sector

According to the 2011 International Energy Outlook, the world’s energy consumption has risen steadily since 1990 and is projected to increase by an average of 1.6% per year through 2035 [3]. Furthermore, the vast majority of the world’s energy demand is still met by nonrenewable fossil fuel sources [4]. This is troubling, as there are a number of consequences associated with the burning of fossil fuels.

First, the use of fossil fuels contributes to certain environmental issues. The United

States’ Environmental Protection Agency (EPA) reports that greenhouse gas emissions have increased by 10.5% since 1990 [5]. Specifically, the EPA claims 94.4% of CO2 emissions, which directly contribute to global warming by absorbing radiation, are caused by fossil fuel combustion. In addition, the burning of fossil fuels emits oxides of nitrogen (NOx) and other gases which indirectly contribute to global warming by

“influencing the formation or destruction of greenhouse gases” [5]. The United States

Global Change Research Program has found that global warming will stress water resources, challenge crop and livestock production, damage land and property (especially along coasts) and threaten human health [6].

Second, and of particular importance to the United States, there are economic justifications for using less fossil fuels. As can be seen in Figure 1, the U.S. imports a significant portion of the liquid fuel they consume due to a sizable production deficit.

Figure 1: Liquid fuel supply in the U.S. (millions of barrels per day) [4].

This is especially costly given that liquid fuels are the primary source of energy for the

United States, as shown in Figure 2.

Figure 2: U.S. energy consumption by fuel (quadrillion BTU per year) [4]. 4

The U.S.’s dependence on oil cost the economy $71 billion in lost gross domestic product in 2011 [7]. In addition to the immediate economic impacts of dependence on foreign oil, the United States will have limited energy security as long as it is importing fuel. As of 2011, the strategic petroleum reserve would only supply the U.S. for 37 days if used exclusively [7]. Therefore, given the current consumption and production trends, the

United States would not be able to meet its liquid fuel demand for an extended period of time if outside sources become unavailable.

Clearly, there is no lack of motivation for the United States, and the world as a whole, to reduce its energy consumption. This is especially true for the transportation sector since it is a primary consumer of fossil fuels. As the main end user of oil, the transportation sector accounts for roughly 72% of the United State’s liquid fuel consumption [8]. This percentage is only expected to increase: from 2008 to 2035, the transportation sector is predicted to account for over 82% of the increase in liquid fuel use worldwide [8]. For these reasons, the automotive industry is under considerable pressure, from both governments and consumers, to produce more fuel efficient vehicles.

The United States, as an example, has mandated automakers’ corporate average fuel economy (CAFE) be, at minimum, 54.5 MPG by 2025 [8]. Achieving this goal will benefit the country in several ways. To start, if these standards are met, an estimated 6 billion metric tons of CO2 pollution will be eliminated by 2025 [8]. The average U.S. consumer spends over $2000 a year on gas and oil [7]. If more fuel efficient vehicles were on the road, the average American could spend less on transportation costs and

invest more money in the U.S. economy. Not only will this benefit the economy, but it will also improve the nation’s energy security since net imports will drop, decreasing dependence on foreign sources.

In order to meet these mandated regulations on CAFE, the automotive industry must continue to develop all aspects of their products to enhance their overall efficiency. In doing so, the automakers will also position themselves for success in the long term: since

October 2007, the average sales-weighted miles per gallon (MPG) of vehicles sold in the

U.S. has risen from 20.1 to 24.1, as shown in Figure 3 [9].

Figure 3: Average sales-weighted MPG since October 2007 (as reported by the University of Michigan’s Transportation Research Institute) [9].

Both the government and consumers are demanding more fuel efficient vehicles. It is up to the industry to respond.

Section 2.2 Industry Response

The automotive industry has approached the fuel consumption problem from a number of different angles. Not only have improvements been made to the engines, transmissions and ancillary loads of vehicles with conventional powertrains, but many manufacturers have also brought various forms of powertrain electrification to production, including hybrid electric vehicles, plug-in hybrids and fully electric vehicles (these are grouped as x-EVs). While x-EVs have delivered significant fuel savings, this section will focus on advances made with conventional architectures and only minor modifications (or none at all) since this is within the scope of the work. For a summary of the potential benefits associated with x-EVs, refer to [10].

2.2.1 Powertrain

One of the major challenges for auto makers is to more efficiently convert fuel energy into motive force to power the vehicle. Figure 4 summarizes the energy losses calculated for a mid-sized sedan over the EPA city and highway cycles.

Figure 4: Fuel and brake energy divisions for EPA city and highway cycles [11].

As is apparent, only 20-30% of fuel energy is converted to useful energy at the engine crankshaft. Roughly one third of the fuel energy is lost to the coolant system and another third is lost out of the exhaust. In addition, a fraction of the fuel energy is used to power the ancillary loads. The effort being made to reduce these losses is discussed more thoroughly in Section 2.2.2. In addition, approximately a quarter of the brake energy is lost while transferring the power through the transmission to the wheels. Furthermore, a significant portion of the brake energy that could be used to power the vehicle is wasted during engine idle, coasting events and braking events. This energy could be saved through methods such as engine stop-start or salvaged with brake energy recovery techniques.

There is an endless stream of new technologies seeking to reduce vehicle fuel consumption by improving the efficiency of the powertrain. While several of the technical solutions implemented to date are based on changes to the design of the engine and transmission, considerable benefits can also be achieved by developing novel control algorithms for the powertrain system. The following two sections highlight a few of the more promising technologies that fall under these categories. These sections are organized as follows:

 Powertrain Design o Downsizing and Turbocharging o Dual-Clutch Automated Manual Transmission o Gasoline Direct Injection  Energy Savings/Recovery o Cylinder Deactivation o Engine Stop-Start o Brake Energy Recovery

Powertrain Design

A predominant trend to reduce the fuel consumption of an automotive powertrain is by downsizing the internal combustion engine and coupling it with an advanced turbocharging system to retain peak performance [12]. Equally important, the downsized engines will work in concert with a more efficient transmission, such as dual-clutch automated manuals, to deliver more of the engine power to the wheels. Even simply increasing the number of gears in an automatic transmission from 4 to 8 reduces fuel consumption by 6-8% by allowing the engine to operate in more efficient regions of the engine map [13].

Downsizing and Turbocharging

Engine downsizing not only reduces the overall vehicle mass but it also leads to reduced friction losses. As a result, the engine operates at higher loads where specific fuel consumption values are lower [11]. To describe it another way, the operating region that gives the best fuel economy is brought closer to the steady-state road load line, as shown in Figure 5. This figure also shows that turbocharging the downsized engine is necessary to restore performance. Since the downsized engine’s operating region is shrunk compared to a larger engine, there is a much smaller torque margin for acceleration.

Turbocharging increases this torque margin, allowing for the same, or even improved, acceleration performance compared to the larger engine. For the same power, turbocharging and engine downsizing improves fuel economy by 8-10% [15].

Figure 5: Shift of the fuel economy map by downsizing and turbocharging the engine [15].

Dual-Clutch Automated Manual Transmission

As opposed to conventional manual transmissions, a dual-clutch automated manual transmission (DCAMT) does not require the driver for clutch actuation or gear shifting.

Instead, these actions are handled automatically by the transmission control unit directing the necessary actuators. DCAMTs combine the benefits of manual transmissions (MTs) and automatic transmissions (ATs). Borrowing from MTs, DCAMTs are lightweight, small in size and do not require a torque converter. The elimination of the torque converter leads to a major efficiency increase over ATs, with further improvements in efficiency resulting from the programming of optimal shift points [13]. On the other hand, DCAMTs are comparable to ATs in regards to shift quality and degree of traction interruption during shifting since they utilize two clutches and are able to pre-select gears

[14]. With a 4-speed automatic transmission as the baseline, estimates of 6-8% and 5-

10% fuel economy improvements for a six-speed DCAMT are reported by [13] and [14], respectively.

Gasoline Direct Injection

Gasoline direct injection (GDI) is different from port fuel injection in that the fuel is injected directly into the combustion chamber instead of the intake port. This allows for more control over the mixing of the charge in the combustion chamber. For instance, the charge can be stratified, with a richer charge near the spark plug, to favor ignition and reduce the combustion delay, and a lean charge on the piston side. This stratification, along with more complete fuel vaporization, reduces the knock tendency. As a result, higher compression ratios are possible, leading to greater cycle thermal efficiency [16]. 11

This is apparent when one considers the thermal efficiency for an ideal constant-volume thermodynamic (Otto) cycle [17]:

(2.1)

An absolute compression ratio increase of 1.5 to 2 points from a 9.5 to 10 base is the main contributor to a 3-4% improvement in fuel economy. In addition, torque and power are increased by up to 5% [13].

GDI engines in production today generally operate in stoichiometric mode due to the presence of the three-way catalyst. However, GDI engines have the ability to operate with much higher air-to-fuel ratios at low loads if coupled with advanced aftertreatment systems. Estimates of fuel economy improvements for lean burn engines using GDI are as high as 25% [13]. If emission considerations are addressed, with a cost-effective NOx absorbing catalyst, for instance, GDI has the potential to be a major factor in the automotive industry’s quest to reduce fuel consumption.

Energy Savings/Recovery

There are a number of powertrain control strategies that save energy. Chief among these strategies is cylinder deactivation and engine stop-start. Along with energy saving strategies, there are also strategies with the ability to recover energy that would otherwise be lost. Brake energy recovery is the most promising of these techniques.

Cylinder Deactivation

Given a slightly modified engine architecture and control strategy, including flexible valve actuation, some cylinders may be deactivated, or not used to produce torque at the crankshaft, during partial load operation. There is a considerable development cost associated with cylinder deactivation, but they are easily outweighed by the benefits when implemented on the right engine. The right engine, in this case, has a minimum of six cylinders. With fewer than six cylinders, noise, vibration and harshness issues arise, negatively impacting drivability and the durability of the system [13]. Cylinders are typically deactivated by deactivating the valves of that cylinder. Since the valves remain closed, the air in the deactivated cylinders acts as a spring as the crankshaft rotates.

However, since the valves remain closed, pumping losses are reduced [18]. Thermal losses to the coolant are also reduced when a number of the cylinders are no longer firing.

Furthermore, the active cylinders operate at a higher load to meet the same power requirement. Operating at higher load reduces throttling losses and results in a higher overall engine efficiency. It has been shown that fuel consumption can be reduced by 7% for a V8 engine on the New European Drive Cycle (NEDC) using cylinder deactivation

[19]. Results of this magnitude are confirmed by [18], which reports fuel consumption decreases of up to 16% at low loads.

Engine Stop-Start

A vehicle equipped for engine stop-start (or idle-stop) has the ability to turn off the engine when idling to eliminate fuel consumption. Traditionally, this has been implemented on hybrid powertrains since the alternative energy source is large enough to 13

meet the vehicle’s ancillary power requirements without fear of being unable to restart the engine on-demand. However, engine stop-start need not be limited to hybrid powertrains. The following examples will proceed from the most to the least modified conventional vehicle architectures.

General Motors has developed a stop-start system for a 4-cylinder engine with an automatic transmission [20]. The predominant hardware changes are:

1) Removal of alternator and starter and replacement with a 7 kW motor-generator.

2) Replacing the 12 V battery with a 36 V battery pack.

3) Addition of liquid-cooled power electronics.

4) Minor modifications to the transmission to allow for full compatibility with the

new system.

The system operates with the battery pack at a high state of charge (SOC). This limits the formation of sulfate crystals, which leads to a reduced battery life [21]. However, this is at the cost of efficiency since the dynamic charge acceptance (DCA) is inversely related to the SOC [22]. Although simulation results suggest fuel economy improvements of up to 20% for this stop-start system with brake energy recovery, drivability considerations drop this number to approximately 12% for experimental testing.

BMW has introduced an auto-start-stop function (ASSF) [23]. This function operates on a conventional powertrain with the only addition being an Intelligent Battery Sensor

(IBS) to measure the voltage, current and temperature of the battery. For a vehicle with a manual transmission, the engine stop and start are initiated as illustrated in Figure 6.

When the vehicle comes to a stop and the clutch is released, the engine will turn off.

When the clutch is re-engaged, the engine turns back on.

Figure 6: Automatic stop (top) and start (bottom) procedure for BMWs with manual transmissions [23].

Software algorithms also make use of information from the IBS to override the basic decision process depicted above. In combination with a 5 second minimum engine-off time period to combat the fuel cost of restarts, the ASSF can achieve fuel savings of 3.5% for the NEDC.

Recent work by Ford has also shown the fuel saving potential of a start-stop system on conventional vehicle architectures [24]. Since a standard 12 V electrical system is being used, the battery must be recharged quickly in order to stop the engine often and realize the potential of the system. To this effect, Ford maintains a high DCA of the battery to maximize its charging power limit. To determine when the engine should be turned on or off, a model monitors the evaporator core temperature and the electrical loads. The current electrical loads are used to determine whether to stop the engine based on how quickly the battery will be discharged. Based on the evaporator core temperature, the 15

engine may be turned back on before a torque request from the driver to maintain cabin temperatures for passenger comfort. According to Ford, this stop-start system for a conventional vehicle improves fuel efficiency by 3.5% and pays for itself in 18 months.

Brake Energy Recovery

On conventional vehicles, friction brakes are typically used to decelerate and this energy is lost as heat to the environment. Hybrid electric vehicles (HEVs), on the other hand, are able to slow the vehicle, to an extent, by using an electric machine (EM) as a generator. A portion of this energy can then be stored in the battery and reused at a later time to operate the EM as a motor. Conventional vehicles can use a variation of this strategy, for the remainder of this section it will be referred to as crankshaft energy harvesting, to recuperate some energy that would otherwise be lost.

The major distinction between the brake energy recovery on HEVs and crankshaft energy harvesting is the source of the reaction torque used to slow the vehicle and where the energy is subsequently stored. With crankshaft energy harvesting, the energy is not necessarily stored in the battery, but it can instead be used to provide instant power to the ancillary loads such as the air conditioning (AC) system compressor or the radiator fan.

In order to accomplish this, the energy must be extracted at the engine-level. This style of brake energy recovery does not require any additional components.

Starting from the theoretical maximum energy savings during braking events, the limitations of crankshaft energy recovery will be discussed. The dynamic equation for the linear motion of a vehicle is given by [25]:

(2.2)

Here, is the mass of the vehicle, is the vehicle velocity, is the tractive force at the wheels and is the road load force. The required tractive power at the wheels is therefore given by

(2.3)

Since the road load force is a function of the vehicle speed, this means the required power profile can be calculated directly from the vehicle velocity trace alone [25]. The total braking energy of the cycle is then just the integration of the power trace limited to conditions of negative instantaneous power. As a result, the total braking energy at the wheels is approximately 3200 kJ for the first 1350 seconds of the Federal Test Procedure

(FTP) cycle. This is the theoretical maximum amount of energy that could be recovered.

However, not all of this energy is actually available for recovery due to the limitations of a conventional powertrain. First, since the energy is extracted at the engine-level, there are losses resulting from transferring the power from the wheel-level through the powertrain. These losses result from inefficiencies in the components such as the transmission and torque converter. Then, once at the engine-level, the energy sink

(whatever is accepting the recovered energy) has both power and energy limits. Finally,

there is an energy conversion efficiency to consider. For instance, some energy is lost when converting mechanical energy into electrical energy. Given the constraints and efficiencies of the system, the amount of energy that can reasonably be considered available for recovery is only a fraction of the total braking energy. Nevertheless, any potential for fuel savings should be explored and therefore crankshaft energy recovery should not be dismissed.

2.2.2 Ancillary Loads

As noted before, powering ancillary loads consumes an appreciable portion of the fuel energy. Since ancillary load management is a focus of The Ohio State University’s work with Chrysler, this section will go into further detail about the work industry is doing to reduce various ancillary loads. Given the topic of this thesis is the control of a vehicle’s electrical system, particular emphasis will be placed upon the electrification of ancillary loads.

Lubrication System

A typical mechanically-driven oil pump restricts the flow of oil to the engine using a pressure relief valve. This is necessary at high speeds when the oil pump would otherwise provide more oil than the engine demands. However, energy is wasted with this style of pump since excess oil is being pumped through the pressure relief valve.

Figure 7 shows the key difference between a mechanical pump and an electrical pump: the mechanical pump continues to pump more oil, thus consuming more power, as engine

speed increases while the electric pump only pumps as much oil as is demanded by the engine. Consequently, electric oil pumps consume less energy than their mechanical counterparts at higher engine speeds. A 0.5% fuel economy improvement is expected with an electric oil pump [13].

Figure 7: Potential energy savings with electric oil pumps [26].

Substituting an electric oil pump for a mechanical one does more than improve fuel economy. The electric pump can be mounted external to the engine since it is no longer directly powered by the engine crankshaft. Moreover, pre-startup lubrication, to eliminate dry starts, and post-shutdown lubrication, to reduce bearing wear and oil coking, are both possible with an electric pump system [26]. Post-shutdown oil flow can also be used in concert with an electric coolant pump to cool down the engine, thus extending its life.

Cooling System

Traditional belt-driven coolant pumps operate at a speed directly proportional to the engine speed. Therefore, they must be sized to perform at all engine speeds. As a result, coolant pumps are oversized for all operating conditions except extremely high loads. In addition, expansion thermostats (solid-to-liquid phase wax actuators) do not allow for control of the coolant temperature for optimum engine efficiency. These issues can be resolved using an electric coolant pump and electrically operated radiator bypass valve.

The advantage of making these components electric is the ability to control them independent of engine speed and coolant temperature, respectively.

Using these two new components during cold-start conditions, higher coolant and oil temperatures are achieved and the duration of the engine cold-start is shortened [27].

This reduces the fuel consumed since engine friction is reduced. Furthermore, a fraction of the coolant flow is used with the electric pump compared to the mechanical pump.

These two factors combine to improve fuel economy. For various engine operating points, the Swiss Federal Institute of Technology reports a fuel consumption reduction of

2.7 to 4.5% [27]. By comparison, a maximum of only 1% fuel consumption reduction is reported by [28].

AC System

Fixed displacement swash-plate AC compressors control the cooling load by on/off operation. Since they operate at a maximum tilt angle, and therefore a maximum

pressure difference between the suction and discharge sides, the compressor efficiency is low due to high friction and leakage [29]. To highlight this point, Figure 8 compares the torque of a fixed and variable displacement compressor operating at 3000 rpm and 25°C.

Clearly, the variable displacement compressor operates at a lower average torque.

Figure 8: Bench test comparing fixed and variable displacement AC compressors [29].

The fuel economy numbers verify the expected result: the variable displacement compressor achieves a fuel economy improvement of 6.1 to 8.6% over a fixed displacement compressor, depending on the operating conditions [29]. In addition, the variable displacement compressor is better able to hold the cabin temperature at the desired value.

Alternator

The electrical energy demand from the vehicle ancillary loads is continually rising in vehicles of all types. In order to meet this demand, especially at low speeds, the output and efficiency of alternators must be improved. Venkkateshraj et al. discuss some methods to accomplish this goal [30]. The first method to increase the alternator’s output and efficiency is to change to a rectangular winding for the stator. This switch raises the slot fill factor to 77% (up from 55% with round conductor). As is apparent in Figure 9, this change alone increases the maximum output of the alternator by approximately 25 amps. Furthermore, the peak efficiency increases from 54% to 66%.

Figure 9: Comparison of output between a conventional alternator and one with an increased slot fill factor [30].

To further increase the maximum output current, the number of turns in the stator can be reduced. However, this also decreases the output at lower speeds. To combat this, additional magnets are added between the rotor claws. Not only does this restore the low-speed output by reducing the leakage flux between the poles, but this design also results in a peak efficiency of 69%. These changes produce a more efficient alternator with higher output for today’s high electrical power demands.

2.2.3 Electrical System Control

As discussed in Section 2.2.2, many manufacturers are reducing ancillary loads by switching to electrically driven components. When this occurs, the electrical system is under greater demand and requires enhanced control strategies to meet the system requirements while being mindful of battery aging. Although many issues may be resolved by going to a higher voltage system, the importance of developing new electrical system control strategies is not diminished. Even if the ancillary loads are not electrified, advanced electrical system control has the potential to improve fuel economy. Two electrical system control strategies that have shown promise are presented below.

BMW has tested a partial-SOC operation strategy for a conventional 12 V battery [23].

Since the dynamic charge acceptance of the battery is inversely proportional to the SOC, the goal is to keep the SOC well below 100% while driving. Then, during opportune times, the battery can more readily accept charge, thus saving energy. If the SOC is above 85% the battery provides electrical energy, reducing the power required from the alternator and thus the engine. When the SOC is 79-85%, the battery voltage is held at its

current value in order to maintain a partial-SOC. BMW also implemented battery

“refresh” charging. Periodically, the battery is refreshed (charged to 100% SOC) to prevent the formation of lead sulfate crystals. This improves the charge acceptance and extends the life of the battery [20]. Using these techniques in conjunction with mild brake energy recovery, fuel efficiency was improved by 3% [23].

Kessels et al. have developed an energy management strategy for the electrical system of a conventional drivetrain that takes advantage of two characteristics of the system: 1) the battery is an energy storage device and 2) some loads have a flexible power demand [31].

Loads can be characterized as flexible if they are able to accept more or less power than the requested amount without significant performance degradation. For example, heating and cooling loads are often labeled as flexible. The use of the battery provides an additional degree of freedom when determining the alternator power demand. Similarly, having some flexible loads serves as another degree of freedom to help further reduce fuel consumption. The problem is then solved as an optimization problem; determining the best combinations of alternator and load power to minimize fuel consumption over the drive cycle given the constraints on the components. In order to accomplish this, a parameter that represents the engine fuel cost for charging or discharging the battery, an equivalence factor, must be determined. This is accomplished using a PI controller acting on the equivalence factor to maintain the state of energy to a reference state of energy. Using this energy management strategy, fuel economy improvements up to 1.5% and 2.6% were seen for simulation and experimental testing, respectively.

The strategy developed in [31] is adapted from a basic HEV control strategy. The structure of a conventional vehicle’s electrical system is similar to the topology of a parallel HEV powertrain. Figure 10 shows this comparison.

Figure 10: Comparison between a parallel HEV powertrain and the electrical system on a conventional vehicle.

For HEV powertrains, the power demanded by the driver can be supplied by the engine, the electric machine or a combination of the two. Similarly, for the electrical system of a conventional vehicle, the required load current can be supplied by the alternator, battery or a combination of the two. Therefore, it is practical to consider HEV control strategies for electrical system control. One HEV control strategy, the Equivalent Consumption

Minimization Strategy (ECMS), will be discussed in detail in the following section.

Section 2.3 Equivalent Consumption Minimization Strategy

The ECMS was first proposed by Paganelli et al. as a supervisory energy management strategy for charge-sustaining HEVs [32]. Since then, it has been modified for a variety of applications and implemented as a real-time control strategy (see [33]-[37]).

2.3.1 The ECMS

In its first incarnation, the ECMS was designed as an online energy management strategy for a parallel hybrid vehicle [32]. This strategy minimizes the instantaneous fuel consumption by finding the optimal torque split between the internal combustion engine and the electric motor. The underlying concept behind this strategy is that, for a charge- sustaining system, all energy must ultimately come from the fuel. Therefore, any energy depleted from the battery at a given time must be replaced at a future time and vice versa.

As a result, the use of the battery can be considered a virtual fuel consumption which is positive for a discharge and negative for a charge.

Figure 11 depicts how this virtual, or equivalent, fuel consumption of the battery is determined during a discharge. In this case, since battery energy is being used to provide power to the vehicle, it must be replaced by the motor operating as a generator at some future time. The amount of fuel it takes to replace this energy is the equivalent fuel consumption. Since the operating point of this recharge is not known, a mean efficiency of the energy path is taken. An equivalence factor relates the battery energy to the fuel energy, taking into account the fact that there will be an efficiency penalty since the energy extracted now must be replaced in the future. At each instant in time, the optimal 26

torque split is determined by finding the minimum combined engine fuel consumption and equivalent fuel consumption of the battery.

Figure 11: Energy path for equivalent fuel consumption of the battery during discharge (adapted from [32]).

The ECMS has been shown to deliver significant fuel economy improvements. For example, a 2000 Chevrolet Suburban was converted into a parallel HEV and achieved

21.69 MPG using the ECMS (a 150% increase from the original Suburban) [33]. While not all of this fuel economy improvement can be directly attributed to the ECMS, a hybrid electric powertrain cannot reap any benefits without an advantageous control strategy. 27

For a more direct comparison, consider the work done by Serrao [34]. In his Ph.D. dissertation he presents two case studies, both series HEVs (one a truck, the other a mid- size SUV), where energy-based powertrain models were developed to apply and verify the ECMS. The results were compared against the optimal solution. The optimal solution was determined using two separate approaches, both of which require a priori knowledge of the drive cycle: Dynamic Programming (DP) and Pontryagin’s Minimum

Principle (PMP). DP is a numerical method to solve the optimization problem [38].

PMP is an analytical approach to solve for the optimal solution given that the system can be accurately represented using simple equations [39]. Compared to these two solutions, the ECMS averaged only 3% higher fuel consumption over a variety cycles. Figure 12 shows the variation in the state of energy (SOE) over the Urban Dynamometer Driving

Schedule (UDDS) for all three methods.

Figure 12: Comparison of the SOE over UDDS cycle for three different methods [34].

The ECMS can be shown to be equivalent to PMP under certain conditions [40]. With sufficient tuning of the equivalence factor, the ECMS can achieve a near-optimal solution. However, the equivalence factor must be tuned for each drive cycle. If the equivalence factor is not properly tuned for a particular drive cycle, the powertrain can behave such that the system is not charge-sustaining, as shown in Figure 13.

Figure 13: Comparison of the SOC over the FTP cycle with an optimal and a sub-optimal equivalence factor [41].

Since a single equivalence factor does not result in the desired performance for all driving conditions, the ECMS is not suited for real-time control except on the cycle for which it has been tuned. To solve this problem, the equivalence factor is made adaptive.

2.3.2 The Adaptive ECMS

The adaptive ECMS (A-ECMS) is the ECMS with the ability to estimate a near-optimal equivalence factor in real-time to account for changing driving conditions. With this

modification, the A-ECMS can be considered a robust online control strategy. Several methods have been employed to make the equivalence factor adaptive. The most popular approaches are compared in [37] and summarized here:

1. Drive cycle prediction. This approach is founded on a simple principle: the

optimal solution cannot be guaranteed if information regarding the future drive

cycle is not available. The future drive cycle is estimated by some method (an

autoregressive model, for example) and then the equivalence factor is directly

optimized based on this prediction of the future conditions.

2. Driving pattern recognition. A time window of recent past driving conditions is

used to characterize the current driving pattern. An equivalence factor,

determined offline, is selected based on the driving pattern. To ensure a charge-

sustaining system, a PI controller maintains the SOC around a reference value.

3. Only SOC feedback. SOC feedback is used to correct the equivalence factor ( ).

This strategy can be continuous (at each time step, is updated) or discrete ( is

updated every seconds, where is a tuning parameter). The manner in which

SOC feedback is utilized drastically changes the strategy since it will impact how

the SOC fluctuates over the drive cycle.

The authors found that the methods involving only SOC feedback give results that are only slightly suboptimal compared to the ECMS which has been tuned. Figure 14 shows the evolution of the SOC and equivalence factor for the tuned ECMS and the A-ECMS with three different adaptation strategies: continuous with a P controller, continuous with a PI controller and discrete with = 120 seconds. The corrected fuel consumptions, 30

taking into account the difference in the initial and final SOC, are 1-2% greater than the tuned ECMS for all strategies.

Figure 14: Comparison of SOC feedback strategies for ARTEMIS Urban plus Extra Urban cycle (adapted from [37]).

Furthermore, this method, whether continuous or discrete, is robust in the sense that it maintains charge-sustaining behavior. The authors suggest that only minimal improvements can be expected from more complex strategies such as drive cycle prediction.

Chapter 3: Model Development, Calibration and Validation

The Ohio State University’s overarching goal for this project is to deliver a supervisory

Vehicle Energy Management (VEM) strategy to improve fuel economy. In order to develop these strategies, a Vehicle Energy Simulator (VES) is needed. The VES is a forward-looking, energy-based model that captures the low frequency energy and power dynamics of the vehicle. While the VES is used for energy analysis purposes, it is also employed for control model development and control strategy testing. In this chapter, the experimental setup used for data collection is described. The experimental data is used for the calibration of the VES models. This is followed by a brief overview of the VES and a detailed exploration of the electrical system model. For in-depth insight into the other subsystem models (powertrain, thermal, air conditioning, etc.) refer to [42] and [1].

Section 3.1 Experimental Setup

Experimental data is used to calibrate and validate the models. This data is collected using an engine, a 2011 Chrysler Town & Country minivan (equipped with the same engine) and battery testing equipment which includes an environmental chamber and a programmable cycler. Additional experimental data, such as data from test vehicles equipped with an advanced thermal management system, is collected by Chrysler.

3.1.1 Engine

The naturally aspirated spark-ignition engine under consideration is a production unit installed on the 2011 Chrysler Town & Country minivan. The specifications of this 3.6L

V6 are listed in Table 1.

Table 1: Engine specifications.

Displacement [L] 3.6 No. of Cylinders 6 Bore [mm] 96 Stroke [mm] 83 Compression Ratio 10.2 Max Torque [Nm @ rpm] 353 @ 4400 Max Power [kW @ rpm] 216 @ 6350

This engine is experimentally characterized at The Ohio State University’s Center for

Automotive Research using a 300 HP dynamometer (dyno). The test cell is equipped with a Horiba Mexa 7500 emission analyzer and a 128-channel data acquisition (DAQ) system. An image of the dynamometer test cell is shown in Figure 15 and a schematic of the DAQ system follows in Figure 16.

Figure 15: Engine dynamometer test cell.

Figure 16: Dyno DAQ system. 34

The experimental data acquired on the engine dyno is used to calibrate and validate models of the main engine components and subsystems. Table 2 lists key tests completed on the engine along with the motivation for the test.

Table 2: Engine dyno testing summary [42].

Test Motivation 1. Validate engine warm-up curves Constant speed and load warm-up 2. Verify correct engine calibration Control valve characterization Validate external cooling circuit 1. Validate the steady state data received from Chrysler “Big Grid” data points 2. Add points not covered by the Big Grid Characterize FMEP based on engine speed, engine torque FMEP characterization and oil temperatures Catalyst testing Calibration of the exothermic heat release sub-model

An experiment of particular importance is a collection of steady-state points covering the entire engine operating region (speed and torque). This test is a standard procedure accepted in industry to provide a preliminary performance characterization of an engine in its entire operating domain. At Chrysler, this testing procedure is named “Big Grid”, and from this point forward this term will be used to denote the data set generated according to this testing procedure. The Big Grid data set available for this work contains numerous engine operating variables (pressures, temperatures, flow rates, etc.) at

247 different engine speed and torque combinations.

3.1.2 Vehicle

Along with an engine, The Ohio State University (OSU) also has a production vehicle for testing. Table 3 gives the notable vehicle specifications.

Table 3: Vehicle specifications.

Make, Model and Year 2011 Chrysler Town & Country Mass 2154 kg Frontal Area 2.42 m2 Aerodynamic Drag Coefficient ( ) 0.33 Gear Ratios (1-6) 4.127 - 2.842 - 2.284 - 1.452 - 1.0 - 0.690 Final Drive Ratio 3.16 Tire Radius 0.3514 m Engine 3.6L V6 SI (see Table 1) Transmission 62TE 6-Speed Automatic Transmission

The vehicle is used to collect data sets that are impossible or impractical for the engine dyno setup to collect. For instance, the vehicle is relied upon if any experimental data is needed for the electrical system, transmission, air conditioning (AC) system or any other component not present in the engine dyno setup. As another example, complete drive cycles with an array of variables are needed for calibration and validation purposes.

While impractical for the engine dyno, these drive cycles can be easily completed with the vehicle on a chassis dyno.

The chassis dyno at OSU is fitted with two 24" rolls and is designed for vehicle testing up to 150 HP. A driver's aid station running a LabVIEW graphical user interface assists a driver in following both standard and user-defined drive cycles by displaying the upcoming velocity trace. Figure 17 shows the vehicle on the chassis dyno.

Figure 17: Vehicle on chassis dynamometer.

A schematic and image of the in-vehicle DAQ system are displayed in Figure 18. The vehicle is instrumented with a number of thermocouples to measure temperatures of interest and shunts to measure electrical system currents.

Figure 18: Vehicle DAQ schematic (left) and components (right).

The laptop used in the DAQ system runs ETAS’s INCA software, which is an interface for communication with the ETAS ES1000 measurement and rapid prototyping board

[43]. The ES1000 receives signals directly from the vehicles’ engine control unit (ECU), among other sources. Signals can be added and removed from experiments for recording or monitoring purposes.

3.1.3 Battery Testing

Battery testing is necessary for battery parameter calibration and model validation. The battery in the Town & Country has the specifications given in Table 4.

Table 4: Battery specifications.

Type Lead-Acid AGM Nominal Capacity 75 A-h Nominal Voltage 12 V Max Charging Current 120 A

CAR has a Cincinnati Sub-Zero MicroClimate environmental chamber to maintain the battery temperature during testing, which is important since the battery parameters are a function of the battery temperature. A Maccor Series 4000 programmable load and supply system (battery cycler) administers a battery current trace defined by the user.

Figure 19 shows this battery testing setup. All relevant variables (current, voltage and temperature) are recorded on the test computer.

Figure 19: Battery testing setup: environmental chamber (left); battery inside the chamber (center); cycler (right).

Section 3.2 Overview of the Vehicle Energy Simulator

The VES is a forward-looking, energy-based model of a 2011 Chrysler Town & Country minivan’s powertrain and ancillary systems. A top-level view of the VES’s Simulink structure is shown in Figure 20. The models making up the Vehicle Plant are organized into the powertrain, thermal system, AC system and electrical system.

Figure 20: Structure of VES model in Simulink.

Signals are passed from one subsystem to the next in the order shown. The role of each subsystem will be briefly discussed in the following subsections. The electrical system will be discussed in more detail in Section 3.3.

3.2.1 Driver

The Driver subsystem contains the logic that mimics a human following a vehicle speed trace. PID controllers act on the velocity error and generate brake ( ) and throttle ( ) commands. In addition, idle speed controllers output these commands when the cycle velocity is zero. The driver model is discussed in [42].

3.2.2 Sensors

The Sensors subsystem transfers signals from the Vehicle Plant to the Chrysler Control block, making any necessary conversions in between.

3.2.3 Chrysler Control

The Chrysler Control subsystem contains the control algorithms developed by Chrysler.

Models within this subsystem generate commands to control transmission shifting, torque converter lockup, deceleration fuel shut off and engine torque reduction during a shift.

These control strategies are necessary to run the Vehicle Plant models. In addition, select signals from the Sensors subsystem are passed through the Chrysler Control block to the

OSU Control subsystem. For a more detailed discussion of these control strategies and their implementation in the VES, refer to [42].

3.2.4 OSU Control

The OSU Control subsystem contains the VEM strategies developed by OSU. For instance, the electrical system control strategy detailed in this work will be located here.

The OSU Control subsystem makes use of signals from the Vehicle plant in addition to outputs from the Chrysler Control subsystem. Select outputs from the Chrysler Control subsystem are passed through the OSU Control block to the Actuators subsystem. For the VES validation, this subsystem will be empty.

3.2.5 Actuators

The Actuators subsystem transfers commands given by the OSU Control block to the various actuators located in the Vehicle Plant, making any necessary conversions in between.

3.2.6 Vehicle Plant

The Vehicle Plant subsystem contains all the models describing the operation of the powertrain and the primary ancillary components. These models are grouped into four systems: powertrain, thermal, AC and electrical. All but the electrical system is described below.

Powertrain

The majority of the powertrain and its associated models are explored in detail in [42].

The Mean Value Engine Model is discussed in [1]. Figure 21 shows a high-level view of the system. The transmission subsystem includes calculations for the engine dynamics, torque converter, automatic transmission and the tractive force model. The vehicle dynamics subsystem is responsible for:

1) Transferring inertia to the wheel-level.

2) Determining the road loads.

3) Calculating the vehicle dynamics.

Figure 21: High-level block diagram of the mechanical system (adapted from [42]).

As is shown in Figure 21, torque is passed from the engine-level to the wheels and speed is fed back from the wheel-level to the engine level.

Thermal System

A 0-D lumped capacitance method is used to model the thermal system. This approach only captures the low-frequency input/output behavior of the system and is particularly useful for predicting the heat transfer between bodies with complicated geometries since one “lump” is used to represent the entire body [44]. The models are built by combining flow control devices and receivers. For each of these receivers (control volumes), the mass and energy conservation equations are applied, utilizing other relevant equations, such as the ideal gas law, where applicable. For the flow control devices, the quasi-static relationships for isentropic, compressible flow through a restriction are used. Refer to 43

Figure 22 for a representation of the inputs and outputs of both receivers and flow control devices. Finally, calibration parameters are necessary to account for the unresolved space and time scales inherent in a 0-D model.

Figure 22: Input/output structure of receivers (left) and flow control devices (right).

The thermal system includes models for the catalytic converter, transmission (including the sump, torque converter and transmission internals) and coolant-oil loop (including the engine, engine oil cooler, radiator, transmission oil cooler and cabin heater core).

Figure 23 is a schematic of the system architecture.

Figure 23: Thermal system architecture.

Refer to [1] and [2] for an in-depth look at these models. 44

AC System

The four major components of the automotive air conditioning system are the compressor, condenser, expansion valve and evaporator. Figure 24 is a simple graphical representation of the system.

Figure 24: Schematic of AC system.

The compressor and expansion valve are modeled as static components because their dynamics are much faster than the dynamics of the condenser and evaporator. The dominant dynamics of the system originate from the heat transfer between the condenser and ambient air, the heat transfer between the evaporator and cabin air, and the pressure gradients associated with the compressor and expansion valve. The pressure drop across each heat exchanger is considered negligible. The moving boundary modeling method is used to characterize the heat exchangers because it is only marginally less accurate and considerably less computationally burdensome than the finite element method [45]. This method divides each heat exchanger volume into regions based on the phase of the refrigerant. This results in six ordinary differential equations (ODEs) for the condenser and four ODEs for the evaporator. 45

Section 3.3 Electrical System Model

The vehicle’s electrical system consists of three main components: the battery, alternator and electrical loads. Figure 25 illustrates a simple block diagram of the system.

Figure 25: Schematic of vehicle electrical system.

The ECU controls the alternator duty cycle ( ), which ultimately generates a field current ( ) for the alternator. The field current, in conjunction with the engine speed

( ) and battery voltage ( ), determines the amount of current produced by the alternator ( ). The battery current ( ) is the difference between the current demanded by the electrical loads ( ) and the alternator current. Depending on the balance between the alternator current and load current, the battery can either accept or supply current. The battery voltage is dependent on the state of the system and the battery current. The models of the alternator and battery, along with the baseline control strategy implemented in the ECU (termed Voltage Regulation), will be described in further detail in the following sections.

3.3.1 Alternator Model

A low frequency alternator model is described in [46] and a mathematical, physics-based model of an alternator is detailed in [47]. A simplified alternator circuit is illustrated in

Figure 26.

Figure 26: Simplified alternator model (adapted from [47]).

The models described in [46] and [47] are used as motivation for the development of the alternator model. However, the calibration of an explicit model, as described in the literature, would be challenging given the information available for the alternator. On the other hand, the experimental data required to calibrate a map-based model is readily available. For this reason, an implicit, map-based model is developed.

Maps for the alternator torque and alternator efficiency haven been provided by Chrysler as a function of the field current, alternator speed and battery voltage:

(3.1)

(3.2)

While the alternator speed and battery voltage are signals accessible through the ECU, the field current is not available. Therefore, a map for the field current must be built with experimental data collected at OSU. Since the average field current is directly related to the alternator duty cycle, the field current can be considered a function of the duty cycle, engine speed and battery voltage. In addition to the field current map, a map for the alternator current is also needed and will be characterized as a function of the same variables.

(3.3)

(3.4)

These functions are implemented as 3-dimensional maps arranged as shown in Figure 27.

Figure 27: Alternator model as a set of 3-dimensional maps.

In order to build the field current and alternator current maps, the electrical system is fully instrumented with shunts to measure the battery, alternator and field currents in addition to the duty cycle and battery voltage that are already recorded through the ECU.

Figure 28 shows the instrumented electrical system.

Figure 28: Instrumented electrical system.

To populate the maps, steady-state values for and need to be determined for all combinations of the duty cycle, engine speed and battery voltage. As a result, the test is conducted by setting constant vehicle speed (and therefore engine speed, given a set gear) on the chassis dyno while the alternator duty cycle is set in the ECU through ETAS’s

INCA software. The battery voltage is then varied from 11.8 to 14.2 V using a 1.5 kW programmable load connected in parallel to the battery. A section of test data for an engine speed of 1700 rpm is displayed in Figure 29. From approximately 660 to 1090 seconds, the battery voltage is gradually stepped down while the duty cycle is held at

25%. Once the minimum battery voltage of interest is reached, the ECU is allowed to control the duty cycle again in order to recharge the battery. Then, at approximately

1220 seconds, the duty cycle is imposed to 37.5% and the voltage is once again stepped down. This process repeats for nine evenly spaced duty cycles from 0-100% and a range of engine speeds from 600 to 3000 rpm. 49

100

Duty [%] Cycle 0 800 1000 1200 1400 1600 15

Battery Voltage [V] Voltage Battery 12 800 1000 1200 1400 1600 200

100

Alternator Current [A] Alternator 800 1000 1200 1400 1600 6

Field Field Current [A] 0 800 1000 1200 1400 1600 Time [s]

Figure 29: Section of alternator test at 1700 rpm.

The resulting data is interpolated to generate 3D maps of and . As an example, the

2-dimensional map for corresponding to = 14 V is shown in Figure 30.

Analogous maps are derived for the remaining values of battery voltage.

Battery Voltage = 14V

200

150

100

50 Alternator Current [A] Alternator

0 3000 2500 100 2000 80 1500 60 40 1000 20 500 0 Engine Speed [rpm] DC [%]

Figure 30: Alternator current map for Vbat = 14 V.

Combining the field current and alternator current maps with the alternator torque and efficiency maps provided by Chrysler completes the static alternator model. The model is validated against data collected over a Federal Test Procedure (FTP) cycle at OSU.

Figure 31 shows the comparison of the predicted alternator current from the model with the experimental data. The RMS error is 5.3 amps for the duration of the cycle.

160 Data 140 Model

120

100

40 Alternator Current [A] 20

-20 0 100 200 300 400 500 600 700 800 900 1000 Time [s]

Figure 31: Alternator model validation. 51

3.3.2 Battery Model

For the purpose of control development, batteries are typically modeled as a Randle equivalent circuit [47]. The first order equivalent circuit used for model development is shown in Figure 32.

Figure 32: 1st order equivalent circuit of the battery.

The battery terminal voltage is given by

(3.5) where is the open circuit voltage, is the internal resistance, is the battery current and is the potential difference across the capacitance. The differential equation describing is [48]

(3.6)

with the over-voltage resistance and the capacitance. The state of charge (SOC) of the battery is computed through current integration according to [48]

(3.7)

where is the initial SOC at time and is the nominal capacity of the battery. According to literature, in order to complete the battery model , , and are characterized as functions of the battery temperature ( ), SOC, sign of the battery current and C-rate (discharge current normalized by the battery capacity) [49], [50]. For the remainder of this document, the C-rate and sign of the battery current will be combined into one variable called current level. The current level is defined as

(3.8)

Although the current level is specific to the battery under consideration, it is easily generalized for other batteries whose nominal capacity is known. Therefore, the parameters can be described as

(3.9)

(3.10)

Since the battery parameters are temperature dependent, all testing is conducted in an environmental chamber. For the remainder of this section, the parameter identification procedure will be shown for one temperature only (25°C). This procedure must be repeated for a series of temperatures (e.g. -10°C, 0°C, 10°C and 40°C) to complete the model. The SOC and are varied using a battery cycler. For all tests, the battery is considered fully charge when the battery voltage is at its maximum value (14.8 V) and the battery current is less than 2 amps. The battery is considered fully discharged when the battery voltage is less than or equal to 10.5 V.

First, the capacity of the battery must be determined. To accomplish this, the test depicted in Figure 33 is conducted. The test proceeds as follows:

1. The battery is fully charged.

2. The battery is fully discharged at a constant current level.

3. The battery is charged at a constant current level until the upper voltage limit is

reached. Then the battery is completely recharged at a constant voltage.

Figure 33: Capacity test showing the steps listed above. 54

The battery current is integrated for steps 2 and 3 to give the discharging and charging capacities, respectively. Then, the battery capacity is the average of the charging and discharging capacities. For the specific battery being tested, the nominal capacity is

72.3 A-h.

The open circuit voltage is characterized by the battery temperature and the SOC [50].

Therefore, the next step is to identify the open circuit voltage as a function of the SOC for each battery temperature. Figure 34 shows the battery test used for this purpose.

Current Current [A] -10

-20

-30

-40 0 2 4 6 8 10 12 4 Time [s] x 10

Figure 34: Test for the open circuit voltage.

The test proceeds as follows:

1. The battery is fully discharged.

2. The battery is charged at a constant current level (unless the upper voltage limit is

reached) to increase the SOC by 5%.

3. The battery is rested for a period of time.

4. Steps 3 and 4 are repeated until the battery is fully recharged.

5. The battery is discharged at a constant current level (unless the lower voltage

limit is reached) to decrease the SOC by 5%.

6. The battery is rested for a period of time.

7. Steps 5 and 6 are repeated until the battery is fully discharged.

8. The battery is fully recharged.

The open circuit voltage is the battery voltage at steady-state when there is no battery current. This is apparent when one considers Equations (3.5) and (3.6) for the case with

= 0. Integrating Equation (3.6) in this condition gives

(3.11)

Then, Equation (3.5) is

(3.12)

Therefore, once the potential difference across the capacitor decays to zero, the battery voltage equals the open circuit voltage. Consequently, the open circuit voltage at different values of the SOC can be approximated by taking the value of the battery voltage after the rest period at that particular SOC. However, this assumes that the rest

period is sufficiently long for to decay to zero. Since the time constant for this decay

( ) is unknown at this point, it is beneficial to let the battery rest for a long time to give a better estimate of the open circuit voltage. In the interest of minimizing test time, the rest periods are limited to 30 minutes and then an equation of the form

(3.13) is fit to the battery voltage data. A least-squares curve fitting procedure, which is described in detail later in this section – see Equation (3.23), is used to evaluate , and

. The value of is then taken as the estimate of the open circuit voltage. Figure 35 shows a typical profile for the relaxing battery voltage along with its fit. Not all 1800 seconds of the data during the rest period are used to establish the fit because the initial portion of the rest phase has a significantly different time constant than the remainder of the resting phase.

12.22 Data -Ct 12.2 Fit: A+Be

12.18

12.16 Battery Voltage [V] Voltage Battery 12.14

12.12 0 500 1000 1500 2000 2500 3000 3500 4000 Time [s]

Figure 35: Battery voltage data during steady-state fit with an exponential function. 57

Using this procedure, the charging and discharging curves are found. The final curve is the average of these two curves. All three curves are shown in Figure 36 (the curves marked fit). For comparison, the curves found by taking the voltage after the rest period are also shown (curves marked rest). The two sets of curves are nearly identical, which suggests 30 minutes is long enough to consider the battery to be in steady-state.

12.5

0 12 E Charge - Fit Charge - Rest Discharge - Fit 11.5 Discharge - Rest Average - Fit Average - Rest 11 0 20 40 60 80 100 SOC [%]

Figure 36: Open circuit voltage curves. The final curve is the average from fitting (green line).

To complete the battery model, , and are characterized as functions of , SOC and . A potential consequence of implementing the alternator control strategies developed in this work is the battery will be subject to higher than normal usage and more dynamic current profiles. To account for this, the calibration of the battery model should capture the characteristics of the battery under all potential conditions. The following test (see Figure 37) allows for the identification of the remaining parameters for all relevant variables except multiple battery temperatures. For each , the test proceeds as follows: 58

1. The battery is fully charged.

2. The battery is subjected to a series of current levels (0, ±20, ±40, ±50 and ±60

amps) plus current steps. The test switches between positive and negative current

levels and current steps in order to maintain a nominally constant SOC.

3. The battery is discharged at a constant current level to a new SOC.

4. Steps 2 and 3 are repeated until a desired minimum SOC is reached.

Figure 37: Battery test for parameter identification. 59

This test is repeated for a range of battery temperatures and these tests are used to identify the first order dynamics of the model. Figure 38 will be used as a reference for the following discussion on how to identify these parameters.

Figure 38: Current step and corresponding voltage response.

First, the actual step in battery current is used to compute . During a step in the current, the capacitor’s behavior can be estimated as a short. This follows from the impedance of a capacitor:

(3.14)

During a step, and therefore . Figure 39 depicts the circuit during a step in the current.

Figure 39: Equivalent circuit during a step in current.

Therefore,

(3.15)

If and are considered constant for the step, then

(3.16)

(3.17)

is the battery voltage pre-step, is the battery voltage after the step, is the battery current pre-step and is the battery current after the step. The values for

the variables with subscript “1” are taken at the red point on Figure 38. Subscript “2” corresponds to the orange point.

During steady-state, the capacitor behaves like an open circuit. Again using Equation

(3.14): during steady-state, and therefore . Figure 40 depicts the circuit during steady-state.

Figure 40: Equivalent circuit during steady-state.

Consequently,

(3.18)

(3.19)

The last point before the step begins is used for the values of and (the red point in Figure 38). Finally, rearranging Equation (3.5) gives

(3.20)

The response of to a step in has a time constant, , given by

(3.21)

Given the time constant is the time it takes for to reach 63.2% of its steady-state value

(see Figure 38), the capacitance can be calculated as [49]

(3.22)

Using these methods, estimates of the parameters are identified for each combination of

SOC, current level and step magnitude. These values are then used as the initial estimations for a least-squares curve fitting procedure to refine their values. The open circuit voltage for each SOC is used as a constant in the curve fitting procedure; only ,

and are allowed to vary.

The curve fit is performed using MATLAB’s lsqcurvefit function, which solves nonlinear curve-fitting problems in the least-squares sense. The inputs given to the function are: the current step profile, the resulting voltage response, the initial estimations for the parameters and upper and lower bounds for the final values of the parameters. This function finds the set of parameters , starting from initial estimations , that solves

(3.23)

without allowing to go outside of the upper and lower bounds for each parameter.

Here, is the input data (current), is the observed output data (voltage) and

is the nonlinear function relating the input to the output [51]. The function

, in this case, is a simple Simulink model solving Equations (3.5) and (3.6) for the battery voltage ( ). The result is a set of parameters ( , , and ) that accurately predict the battery voltage given the battery current and the relevant battery

variables ( , SOC, ). Figure 41 shows the result of this procedure for a particular set of conditions. The output of the model with the initial estimation of the parameters is shown in red and the output using the refined parameters is shown in green. CHARGE: SOC = 0; [R R C ] = [0.019657 0.042 3526.4775]; R = 0.013697, R = 0.022635, C = 356.8128 0 0 init 0 0 13.5 Experimental Initial Curve Fit 13

12.5

12 Battery Voltage [V]

11.5

11 0 50 100 150 200 250 300 350 400 Time [s]

Figure 41: Example of a least-squares curve fitting result.

Since the current step magnitude cannot be predicted, the parameter values are averaged across the step magnitude for each combination of SOC and . Finally, the parameters are plotted versus SOC in order to identify their dominant trends. Any outliers are revalued and the curves are manually “smoothed” to match their trends. This process helps combat overfitting, which can result in a model that only works when given the data with which it is calibrated [52]. The parameters , and are plotted as a function of the SOC and for 25°C in Figure 42 through Figure 44. In these figures, some current levels cannot be seen because they were set equal to the closest current level as part of the manual process of smoothing and adjusting their values.

-3 I [A] x 10 level 10 -60 9 -50 -40 -20 8 0 20 7 40

] 50

 6 60 R R [ 5

2 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 SOC [-]

Figure 42: R as a function of the SOC and current level. I [A] level 0.11 -60 0.1 -50 -40 0.09 -20 0 0.08 20 40

] 0.07 50 

[ 60 0

R 0.06

0.05

0.04

0.03

0.02 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 SOC [-]

Figure 43: R0 as a function of the SOC and current level.

I [A] level 1500 -60 -50 -40 -20 0 1000 20 40 50

[F] 60

0 C

500

0 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 SOC [-]

Figure 44: C0 as a function of the SOC and current level.

From literature, the trend of the parameters is expected to change at high values for the

SOC. For instance, is expected to sharply increase as the SOC approaches 100%.

However, this behavior is not seen in the parameters since the maximum SOC the parameters were identified at is 95%.

For reasons discussed previously, a dynamic battery current profile is necessary for proper validation of the battery model. The battery was subjected to the current profile shown in Figure 45 at three values of the SOC (100, 90 and 80%). This current profile was generated using a preliminary version of the Equivalent Consumption Minimization

Strategy (ECMS) developed in Chapter 4. This preliminary version of the ECMS used a simplified battery model. Figure 46 is the comparison of the battery voltage between the model and the data at a SOC of 90%. 66

0 Current Current [A]

-20

-40 0 200 400 600 800 1000 1200 1400 Time [s]

Figure 45: Battery current profile used for battery model validation.

13.5

12.5 Battery Voltage [V]

Data Model 11.5 0 200 400 600 800 1000 1200 1400 Time [s]

Figure 46: Battery model validation for a SOC of 90%.

The root mean square (RMS) error is 0.15 V. Table 5 summarizes the RMS error in the battery voltage for all three values of the SOC. The RMS error for 100% SOC is higher than for the other cases because there are a few instances where the model is inaccurate at this high SOC. Given the control strategies for the alternator developed in this work, the battery will not be operating at 100% SOC, so the increased error in this condition is not a concern.

Table 5: RMS error in the battery voltage for three SOC levels.

SOC [%] RMS Error [V] 100 0.35 90 0.15 80 0.13

Considering its accuracy in predicting the battery voltage, this battery model can be considered satisfactory for the evaluation of alternator control strategies.

3.3.3 Voltage Regulation Control Strategy

Figure 47 shows a block diagram of the electrical system with the production alternator control strategy. This strategy is referred to as Voltage Regulation (VR) because the

ECU compares feedback on the battery voltage to a temperature dependent reference

voltage ( ) and generates a duty cycle correction to regulate the battery voltage to the reference. The gains of the PID controller were manually tuned for the best match with experimental data. This model was developed by OSU based on information provided by

Chrysler. It establishes the baseline for which other control strategies will be compared.

Figure 47: Voltage regulation block diagram.

3.3.4 Electrical Loads

The individual electrical loads are not modeled in the VES. Figure 48 shows the load current measured on the test vehicle as various loads are turned on and off. Here, the blue signal is the measured current and the green signal is this measured current subjected to a low pass filter.

Defrost Heated Seats 70  

Load Current [A] 20

10   Defrost+AC All 0 0 50 100 150 200 250 Time [s]

Figure 48: Measured (blue) and filtered (green) load current as loads are turned on and off. 69

Turning on or off a load translates to roughly a step up or down in the required load current. The transient, for the purposes of this work, can be disregarded. This means that in order to model the operation of a load, a constant value just needs to be added to the

“base” load current. The base load is the current needed to power the components that are required to operate the vehicle (fuel injectors, ECU, etc.). In addition, if one wants to test the electrical system model (or the whole VES) with a particular load current profile, this profile can be used as an input to the electrical system.

3.3.5 Electrical System Validation

The complete electrical system model is validated against experimental data collected at

OSU. Three separate cycles are used for an extensive validation: the FTP with only base electrical loads, the FTP with a variety of electrical loads activated and the ARTEMIS cycle with base electrical loads. The validation plots for the FTP with only base electrical loads are shown in Figure 49 through Figure 52.

150 Data Model 100

-50 Battery Current [A]

-100

-150 0 500 1000 1500 Time [s]

Figure 49: Battery current comparison over FTP cycle with base electrical loads for electrical system validation. 160 Data 140 Model

120

100

40 Alternator Current [A] 20

-20 0 500 1000 1500 Time [s]

Figure 50: Alternator current comparison over FTP cycle with base electrical loads for electrical system validation.

14.5

13.5

12.5

Battery Voltage [V] 12

11.5 Data Model 11 0 500 1000 1500 Time [s]

Figure 51: Battery voltage comparison over FTP cycle with base electrical loads for electrical system validation. 100 Data 90 Model

40 Duty Cycle [%] 30

0 0 500 1000 1500 Time [s]

Figure 52: Duty cycle comparison over FTP cycle with base electrical loads for electrical system validation.

The model results are only shown for the time after the cranking period is over because the model is not designed to characterize the cranking phase. After the cranking period is over, the model is reasonably accurate and certainly adequate for ancillary load control development. Please refer to Appendix A for the validation plots of the FTP with moderate electrical loads and the ARTEMIS with base electrical loads.

Section 3.4 VES Validation

Before the VES is validated as a whole, each sub-model, then component model, then system model is validated against experimental data. The entire VES is validated against experimental data collected by Chrysler for the first 1369 seconds of the Environmental

Protection Agency’s FTP cycle. This includes the cold start phase plus the transient phase and is equivalent to the Urban Dynamometer Driving Schedule (UDDS). For the remainder of this document, the “FTP” refers to the UDDS unless otherwise noted. The primary validation plots for the VES are presented in Figure 53 through Figure 57.

30 Experimental 25 VES

Velocity [m/s] Velocity 10

0 0 200 400 600 800 1000 1200 Time [s]

Figure 53: Comparison of experimental and VES vehicle velocity.

400 Experimental 300 VES

200

100

Turbine Torque [Nm] 0

-100 0 200 400 600 800 1000 1200 Time [s]

Figure 54: Comparison of experimental and VES torque converter turbine torque.

3000 Experimental 2500 VES

2000

1500

1000 Engine Speed [rpm] 500

0 0 200 400 600 800 1000 1200 Time [s]

Figure 55: Comparison of experimental and VES engine speed.

-3 x 10 6 Experimental 5 VES

2 Fuel Flow [g/s] Rate 1

0 0 200 400 600 800 1000 1200 Time [s]

Figure 56: Comparison of experimental and VES fuel flow rate.

1.4 Experimental 1.2 VES 1

0.8

0.6

0.4 Fuel Consumption [kg] 0.2

0 0 200 400 600 800 1000 1200 Time [s]

Figure 57: Comparison of experimental and VES fuel consumption.

Section 3.5 Simplified Vehicle Fuel Consumption Model

For the design of alternator control strategies, the standalone electrical system model will be used instead of the full VES. This will greatly reduce the time necessary for testing strategies and running simulations. However, the fuel consumption of the engine is still needed since this is a crucial metric for the performance of the strategies developed. A simplified vehicle fuel consumption model will serve this purpose. Figure 58 is a block diagram of this model.

Figure 58: Block diagram of the simplified fuel consumption model.

There are three inputs to the fuel consumption map: the engine speed, the sum of engine torque and alternator torque, and the deceleration fuel shutoff (DFSO) command. When the DFSO command is active, the fuel consumption is zero. The fuel consumption map is built from the Big Grid data. Three different methods for the construction of the map were considered. The end result of all three methods is a map of the mass flow rate of fuel ( ) as a function of engine speed ( ) and total torque ( ).

1. Multiple Regression. For this method, multiple regression techniques are used to

fit the data for to an equation of the form

(3.24)

The decision to use this form for the equation is based on the shape of the data

plus trial and error. The coefficients through are found using [53]

(3.25)

where is defined as

(3.26)

and is

(3.27)

is the first value of engine speed in the Big Grid data, is the first value of total torque and is the corresponding value of fuel flow rate. This naming convention extends to the th, and final, point of the Big Grid data. The resulting coefficients are

Table 6: Coefficients of fit for fuel consumption map.

0.2960 3.179e-4 -9.530e-3 7.199e-6 2.592e-5

Equation (3.24) is now used to evaluate the mass flow rate of fuel over a grid of and values that covers the entire operating region. Figure 59 shows the surface plot of the resulting map along with the points from the Big Grid data while

Figure 60 is a contour line representation of the map.

Map Data 20

0 400

Mass Flow of Fuel Mass Rate [g/s] 8000 200 6000 4000 2000 Total Torque [Nm] 0 0 Engine Speed [rpm]

Figure 59: Fuel consumption map built using multiple regression techniques.

16 12 8 300 14 4 250 10 200

150 6

100 Total Total Torque [Nm]

50 2

1000 2000 3000 4000 5000 6000 Engine Speed [rpm]

Figure 60: Contour fuel consumption map built using multiple regression techniques.

This method results in a smooth surface for the mass flow rate of fuel which

captures the general trends of the data.

2. Linear Fitting. The first step for this method is to interpolate the experimental

data to a grid of operating points ( and combinations). Then, a line is fit to

these map values of for each engine speed. These lines are then used to

evaluate the mass flow rate of fuel at engine operating points outside the range of

experimental data. Although this method best approximates the mass flow rate of

fuel at low engine speeds and torques, it should be noted that these lines are only

used to evaluate map values in regions where Big Grid data is not available.

Therefore, the engine is not anticipated to operate in these extrapolated regions,

but they are included for completeness. The idea for this approach came from the

Willans line method, which is typically used for scaling engine maps [54], [55].

Figure 61 shows the fitted lines and the data points. Willans Lines

0 400

Mass Flow of Fuel Mass Rate [g/s] 8000 200 6000 4000 2000 Total Torque [Nm] 0 0 Engine Speed [rpm]

Figure 61: Lines fitted to the interpolated fuel consumption data.

Figure 62 shows the surface plot of the resulting map along with the points from

the Big Grid data while Figure 63 is a contour line representation of the map. 80

Map Data 20

0 400

Mass Flow of Fuel Mass Rate [g/s] 8000 200 6000 4000 2000 Total Torque [Nm] 0 0 Engine Speed [rpm]

Figure 62: Fuel consumption map built by fitting lines to the data for each engine speed. 18 12 16 300 8 4 14 250

200 10

150 6

100 Total Total Torque [Nm]

50 2

1000 2000 3000 4000 5000 6000 Engine Speed [rpm]

Figure 63: Contour fuel consumption map built by fitting lines to the data for each engine speed.

This method results in a fuel consumption map that is similar to the one generated

using the first method, but because interpolation is done between experimental

data, the surface is not as smooth.

3. 2nd Order Curve Fitting. Similar to the previous method, the first step for this

method is to interpolate the experimental data to a grid of operating points ( and

combinations). Then, a second order curve is fit to these map values of

for each engine speed. If there is a sufficient number of data points at a particular

engine speed (defined here as half of the maximum number of points) then the

curve is used to evaluate the mass flow rate of fuel at engine operating points

outside the range of experimental data. Otherwise, the curve is not used since it

does not have enough data points for a satisfactory fit. Then, the same procedure

is completed for each value of total torque. As before, a second order curve is fit

to the map values and is then used to extrapolate to points outside of the range of

experimental data. Figure 64 shows the surface plot of the resulting map along

with the points from the Big Grid data while Figure 65 is a contour line

representation of the map.

Map Data 20

0 400

Mass Flow of Fuel Mass Rate [g/s] 8000 200 6000 4000 2000 Total Torque [Nm] 0 0 Engine Speed [rpm]

Figure 64: Fuel consumption map built by fitting second order curves to the data.

16 12 18 8 300 4 14 250 2 10 200

150 6

100 Total Total Torque [Nm]

1000 2000 3000 4000 5000 6000 Engine Speed [rpm]

Figure 65: Contour fuel consumption map built by fitting second order curves to the data.

As opposed to the first two methods, this method results in less predictable mass

flow rates of fuel for the extrapolated regions.

Two of the fuel consumption maps, the one generated using multiple regression techniques (MR map) and the one built using the linear fitting method (LF map), appear suitable because these maps agree well with the Big Grid data and the regions of extrapolation are reasonable, as evidenced by the contour plots. However, in order to select one of these maps and have confidence in the prediction of fuel consumption it makes, they must be validated against experimental data over a drive cycle. The drive cycle used for validation here is the FTP cycle immediately followed by the Highway

Fuel Economy Test cycle [56]. The experimental data is provided by Chrysler.

To validate the fuel consumption maps, the engine speed and torque from the data are fed into the maps to predict a fuel flow rate, which is then integrated to get the fuel consumption. This predicted fuel flow rate and fuel consumption is compared to the corresponding variables from the experimental data. The error in the prediction of fuel consumption for the entire cycle is only -3.735% for the LF map, but it is 16.614% for the MR map. However, this error cannot be used as the sole deciding factor for which map is more accurate. For instance, the LF map could be overestimating the fuel flow rate in some conditions and underestimating it in others, resulting in an overall fuel consumption that is in agreement with experimental data. Therefore, the fuel flow rate prediction for each map is compared with experimental data. Figure 66 and Figure 67 show the comparison of experimental and predicted fuel flow rate for a section of the cycle for the LF map and MR map, respectively. The LF map shows greater agreement with experimental data over the section pictured, and this holds for the entire cycle.

-3 x 10 2 Experimental Predicted 1.5

0.5 Fuel Flow [kg/s] Rate

0 700 720 740 760 780 800 820 840 Time [s]

Figure 66: Comparison of fuel flow rate for LF Map.

-3 x 10 2.5 Experimental Predicted 2

1.5

Fuel Flow [kg/s] Rate 0.5

0 700 720 740 760 780 800 820 840 Time [s]

Figure 67: Comparison of fuel flow rate for MR Map.

To confirm this conclusion, Figure 68 and Figure 69 compare the experimental and predicted fuel flow rates against each other for the LF map and the MR map, respectively. 10% error lines are included in these figures to help clarify the amount the

predicted fuel flow rate is off from the experimental. From these comparisons, it is obvious that LF map is far more accurate at predicting the fuel flow rate.

-3 x 10 5 Data y = x 4 +10% Error -10% Error 3

1 Predicted Fuel Flow Predicted [kg/s] Rate 0 0 0.5 1 1.5 2 2.5 3 3.5 -3 Experimental Fuel Flow Rate [kg/s] x 10

Figure 68: Comparison of experimental and predicted fuel consumption for LF map.

-3 x 10 5 Data y = x 4 +10% Error -10% Error 3

1 Predicted Fuel Flow Predicted [kg/s] Rate 0 0 0.5 1 1.5 2 2.5 3 3.5 -3 Experimental Fuel Flow Rate [kg/s] x 10

Figure 69: Comparison of experimental and predicted fuel consumption for MR map.

Given the results of this analysis, the LF fuel consumption map is selected. While the prediction of fuel flow rate is not perfect, it is close for most operating conditions and the error in the prediction of fuel consumption over the cycle is less than 4%. Figure 70 compares the experimental and predicted fuel consumption versus time using this map.

2.5 3.7353% Error  2

1.5

Fuel Consumption [kg] 0.5 Experimental Predicted 0 0 500 1000 1500 2000 2500 Time [s]

Figure 70: Experimental and predicted fuel consumption over the course of the cycle.

At the beginning of the cycle, there is some deviation from the experimental data, but after this initial departure, the prediction mirrors the experimental. Although the model underestimates the fuel consumption, it is more important for the map to give consistent, reliable results so that they can be used for comparing different control strategies. This fuel consumption map is well suited for this purpose.

Chapter 4: Design of Control Strategies

Section 4.1 Alternator Control Problem

The production alternator control strategy, Voltage Regulation (VR), is conservative in the sense that the battery is only used when strictly necessary after engine start-up. While the VR strategy (see Section 3.3.3) does meet the electrical load demands, it does not consider energy optimization. If, on the other hand, the battery is regarded as a legitimate current source for meeting the electrical load current demand, energy optimization can be considered when determining how to meet this demand. The ultimate goal is to design a control algorithm that operates the electrical system (through the alternator duty cycle) to split the current demand between the alternator and battery to minimize the energy consumption over a drive cycle while taking into account the operating conditions of the system and still:

1. Providing the desired current to the loads at any given time.

2. Satisfying a set of constraints on the battery and system performance.

Figure 71 shows a schematic of the electrical system and its connection to the engine.

Figure 71: Electrical system schematic.

is the battery power, is the alternator power and is the electrical load power demand. As was noted in Section 2.2.3, the structure of a conventional vehicle’s electrical system is similar to the topology of a HEV powertrain. Therefore, it is logical to consider HEV control strategies for the alternator control problem. In particular, the

Equivalent Consumption Minimization Strategy (ECMS) is selected for this task since it reduces a global minimization problem to a realizable, local problem. As a result, it is both relatively simple and computationally cheap [32]. Since the ECMS outputs an optimized alternator current value, a low-level alternator controller, which generates the alternator duty cycle required to achieve this optimized current value, is necessary.

Section 4.2 The ECMS for Alternator Control

Figure 72 shows a high-level block diagram of the proposed control algorithm. For a review of the ECMS and its terminology, please refer to Section 2.3.

Figure 72: Block diagram of the ECMS algorithm.

First, a current split factor is defined:

(4.1)

For the remainder of this document, all variables in bold font are vectors. This current split factor is multiplied by the maximum alternator current at the present operating conditions ( ) to give a full set of potential solutions ranging from not using the alternator to providing the maximum alternator current. At each time step, the algorithm proceeds by passing these candidate alternator currents through a set of constraints to get a vector of viable alternator currents ( ). These constraints are a combination of component limitations and restrictions based on consumer acceptability as defined by

Chrysler:

(4.2)

(4.3)

(4.4)

(4.5)

and are the minimum and maximum battery currents, and are the minimum and maximum battery voltage, is the maximum rate of change of the battery voltage, and is the maximum rate of change of the current split factor. A

summary of all the ECMS parameters and their values is given in Table 7 in the following section. The constraint described by Equation (4.5) is upheld by directly eliminating any potential solutions where would vary too much from the previous current split factor in relation to the time step of the simulation.

The set of potential battery currents is found by taking the difference between the load current demand at that instant of time and the set of candidate alternator currents:

(4.6)

Depending on the required load current and the selected alternator current, the battery may either supply or accept current. The battery current constraint is then enacted by eliminating any current split factors that result in a battery current outside of the range specified in Equation (4.2).

In order to constrain the battery voltage, Equation (4.3), and the rate of change of the battery voltage, Equation (4.4), each element of is fed to the battery model to calculate the battery voltage that would result if that current split factor is selected. Then, the current split factors that result in a violation of these constraints are eliminated.

After having determined all feasible current splits (pairs of values from the and vectors), the next step is to calculate the fuel consumption associated with operating the alternator and the equivalent fuel consumption associated with using the battery for each of these current splits. To compute the equivalent fuel consumption for the alternator, each potential alternator current is fed into a slightly modified alternator model.

Figure 73 shows this alternator model, which is partially the inverse of the model depicted in Figure 27. In fact, this modified model uses the alternator current as an input, instead of the duty cycle, and calculates the required duty cycle using a map derived by inverting the alternator current map. Then, the alternator torque is determined in the same manner as the original model.

Figure 73: Alternator model with alternator current as an input instead of the duty cycle.

As shown in Figure 74, the next step is to add the alternator torque to the engine torque and, along with the engine speed, use this total torque at the crankshaft to determine the alternator fuel consumption through the fuel consumption map constructed in Section 3.5.

During deceleration fuel shutoff (DFSO), the alternator fuel consumption is set to zero.

Figure 74: Block diagram of alternator fuel consumption calculation.

The equivalent fuel consumption of the battery is dependent on the battery power, the state of the system and an equivalence factor. See Figure 75 for a representation of this calculation.

Figure 75: Block diagram of battery equivalent fuel consumption calculation.

Each potential battery current from the vector is multiplied by the battery voltage to get a battery power. Then, the battery power is divided by the lower heating value of gasoline ( ) to put it in terms of a fuel flow rate. Since the result is a fuel flow rate of gasoline, this value is multiplied by an equivalence factor ( ), which relates the use of the battery to future gasoline consumption (or savings). In addition, a penalty function ( ) is added to the equivalence factor to ensure the battery is charge-sustaining. As defined by

Equation (4.7), if the SOC of the battery is outside of the desired range, the penalty function equals either a positive or negative value of magnitude which is added to the equivalence factor to discourage or encourage the use of the battery accordingly. If the

SOC is below the minimum desired value ( ), the large positive value from the penalty function promotes values of that are negative and therefore recharges the battery. On the other hand, if the SOC is above the maximum desired value ( ), the large negative value from the penalty function promotes values of that are positive and therefore discharges the battery. A piece-wise penalty function is used so 93

the SOC is able to fluctuate freely unless it reaches its upper or lower bounds. This provides the ECMS more freedom to find an optimal solution.

(4.7)

This entire calculation for the battery equivalent fuel consumption is summarized by

Equation (4.8).

(4.8)

For both the alternator and the battery fuel consumption calculations, the battery voltage used is the “future” battery voltage because the voltage dynamics are much quicker than the sample time of the controller. The future battery voltage is the voltage the battery will go to if that particular current split factor is selected. This value is calculated using a simplified, 0-order battery model.

Once, the fuel consumptions associated with the alternator and the battery are found, these two vectors are summed to give a vector of total equivalent fuel consumptions. The final step in the algorithm is to determine the current split factor associated with the minimum value of the total equivalent fuel consumption. This value of has a corresponding value of the alternator current associated with it, and this value is the

desired alternator current ( ). Given (see Figure 72), the duty cycle map (shown in

Figure 73) is used to determine the duty cycle required to generate this alternator current given the operating conditions of the system. For the purpose of testing this control strategy in simulation, this is all that is required. 94

The connection between the ECMS optimizer and the model of the vehicle’s electrical system is shown in Figure 76. The Trigger block only activates the ECMS Optimizer every seconds to get an updated value for the desired alternator current. The parameter is the update time of the algorithm and is defined in Table 7 in the following section. The optimizer outputs this desired alternator current, which is converted into a DC command and sent to the electrical system plant model.

Figure 76: Connection of the ECMS optimizer and the electrical system model.

Section 4.3 Calibration and Results

For the ECMS to yield satisfactory results, it must be calibrated properly. Since the efficiency of the battery is dependent on the sign of the battery current, two equivalence factors are used: one for charging current ( ) and one for discharging current ( ) [34].

Depending on the current, the correct value will be used for in Figure 75. For a HEV powertrain control application, these equivalence factors are generally calibrated based on the drive cycle. For alternator control, however, the equivalence factors must be calibrated for combinations of the drive cycle and the magnitude of the electrical load current since the electrical system’s operation is dependent on both. Before the 95

calibration can be conducted, a number of parameters and constraints for the model are defined in Table 7.

Table 7: Parameters for the ECMS calibration.

Parameter Value Description

0.95 Initial value of the state of charge 0.99 Maximum desired value of the state of charge 0.75 Minimum desired value of the state of charge 1000 Value of the state of charge penalty function 100 Size of potential solution set (size of ) 1/s Maximum rate of change of the current split factor 15 V Maximum battery voltage 11.6 V Minimum battery voltage A Maximum battery current -120 A Minimum battery current 3.4 V/s Maximum rate of change of the battery voltage 3 s Controller sample time 5 Number of cycles to repeat for the simulation

The ECMS is calibrated for both the FTP and ARTEMIS cycles. Constant load currents of 30, 45, 60, 75, 90, 105 and 120 amps are evaluated. For each combination of drive cycle and current magnitude, a design of experiments (DOE) is conducted: both and are varied throughout a range (0 to 5), running the ECMS Electrical System model for every combination. After each simulation, the total fuel consumption, calculated using the fuel consumption map (from Section 3.5), and the change in the SOC are computed.

However, the actual SOC variable computed by the model is not used to determine the change in the SOC because the actual SOC can vary greatly throughout the simulation and often oscillates around a certain value. Therefore, the last value of this variable may suggest the system is not charge-sustaining when the general trend of the SOC is charge- sustaining. To avoid this issue, the SOC is passed through a low pass filter with a time

constant of one eighth of the total simulation time. This variable captures the trend in the

SOC. The final value of this low pass filtered variable is used to determine the change in the SOC. Figure 77 shows the SOC (Actual) and the SOC passed through a low pass filter (Filtered). Clearly, the SOC is trending downwards, but if the actual SOC signal were used it would suggest the system is charge-sustaining due to the oscillations.

Therefore, the filtered signal will be more reliable for determining the change in the SOC.

1 Actual 0.98 Filtered

0.96

0.94 SoC [-]

0.92

0.9 0 1000 2000 3000 4000 5000 6000 Time [s]

Figure 77: SOC and low pass filtered SOC over 5 FTP cycles.

Once the DOE is complete for a particular combination of drive cycle and load current magnitude, the change in SOC and the fuel consumption are plotted versus the charging and discharging equivalence factors. Figure 78 and Figure 79 are examples of these respective plots.

Figure 78: SOC as a function of the equivalence factors. Points shown are where SOC = 0.

Figure 79: Fuel consumption as a function of the equivalence factors. Points shown are the corresponding fuel consumptions for the points where SOC = 0 in Figure 78.

From these maps, the optimal equivalence factors can be determined. Here, the optimal equivalence factors are defined as the set of and that result in charge-sustaining operation while minimizing fuel consumption. The first step in determining these optimal values is to find sets of and from the map in Figure 78 where the SOC approximately equals zero (charge-sustaining). These points are shown in the figure as magenta circles. Then, the map in Figure 79 is interpolated to these sets of equivalence factors. This results in a vector of fuel consumptions with corresponding equivalence factors (once again, magenta circles in the figure). The optimal and are the equivalence factors corresponding to the minimum fuel consumption from this vector.

Figure 80 and Figure 81 are the result of this calibration: charging and discharging equivalence factors for each combination of drive cycle and load current magnitude to ensure charge-sustaining operation. These values are the individual points shown in the figures. A simple polynomial is fit to these points to show a general trend in the results. FTP Cycle 1.5

s calibration

c Optimal Equiv.Optimal Factor s fit c s calibration d s fit d 0.5 20 30 40 50 60 70 80 90 100 110 120 130 Load Current [A]

Figure 80: Optimal equivalence factors versus the load current for the FTP cycle. 99

ARTEMIS Cycle 2

1.5

s calibration

c Optimal Equiv.Optimal Factor 0.5 s fit c s calibration d s fit d 0 20 30 40 50 60 70 80 90 100 110 120 130 Load Current [A]

Figure 81: Optimal equivalence factors versus the load current for the ARTEMIS cycle.

Now that the ECMS has been calibrated for a variety of situations, its performance can be compared to the VR strategy. Table 8 summarizes the performance metrics that will be used to compare the performance of the two strategies for different values of constant load current ( ) and different drive cycles. The fuel consumption values are not corrected and a justification for this decision is made in Appendix B.

Table 8: Description of the performance metrics. All variables are for 1 cycle unless otherwise noted.

Variable Units Description - Difference between the final state of charge and the initial value of 0.95 kJ Alternator energy consumption kg Mass of fuel consumed A-h Battery usage: integration of absolute value of the battery current over cycle kg Mass of fuel consumed over 5 consecutive cycles MPG Miles per gallon calculated after 5 consecutive cycles

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Table 9 through Table 12 contain the results of this analysis.

Table 9: Results for VR on the FTP cycle.

30 0.050 1142 0.971 4.71 4.556 45 0.050 1515 0.978 4.22 4.585 60 0.050 1965 0.986 4.12 4.625 75 0.050 2428 0.995 4.44 4.669 90 0.050 2893 1.004 4.63 4.712 105 0.038 3292 1.012 4.27 4.755 120 -0.031 3185 1.010 4.46 4.724

Table 10: Results for the ECMS on the FTP cycle.

30 0.009 624 0.959 13.37 4.495 45 0.002 1087 0.966 19.19 4.529 60 0.002 1449 0.973 16.31 4.562 75 0.012 1875 0.980 16.90 4.590 90 0.002 2096 0.985 17.47 4.617 105 0.005 2337 0.990 19.13 4.642 120 0.006 2655 0.996 17.56 4.681

Table 11: Results for VR on the ARTEMIS cycle.

30 0.045 793 0.571 3.49 2.562 45 0.047 1097 0.577 3.88 2.583 60 0.040 1352 0.581 3.30 2.611 75 0.038 1648 0.587 3.35 2.638 90 0.038 1975 0.593 3.59 2.669 105 0.020 2188 0.597 3.09 2.692 120 -0.041 1998 0.594 4.02 2.668

Table 12: Results for the ECMS on the ARTEMIS cycle.

30 -0.009 416 0.564 7.02 2.522 45 0.004 846 0.572 12.53 2.547 60 -0.003 1014 0.574 12.39 2.570 75 0.001 1239 0.578 11.05 2.590 90 0.008 1465 0.582 11.32 2.607 105 0.012 1625 0.585 11.96 2.621 120 0.007 1781 0.588 10.73 2.645

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From the tables, the first major difference between VR and the ECMS is apparent: the

ECMS is charge-sustaining while VR tends to recharge the battery. In addition, the

ECMS results in lower alternator energy consumption, decreased fuel consumption and increased battery usage. Figure 82 through Figure 84 clarify the degree to which these metrics change from VR control to the ECMS for the FTP cycle. FTP Cycle -1.2

-1.4

-1.6

[%] fuel

M -1.8 

-2

-2.2 20 40 60 80 100 120 Load Current [A]

Figure 82: Improvement in fuel consumption using the ECMS. FTP Cycle -15

-20

-25

-30

[%] alt

E -35  -40

-45

-50 20 40 60 80 100 120 Load Current [A]

Figure 83: Decrease in alternator energy consumption with the ECMS. 102

FTP Cycle 400

350

300

[%] bat

Ah 250 

200

150 20 40 60 80 100 120 Load Current [A]

Figure 84: Increase in battery use with the ECMS.

, and are the percent change in their respective variable going from

VR to the ECMS control. For instance, can be calculated as

(4.9)

These values are tabulated in Table 13 for both drive cycles.

Table 13: Comparison of performance metrics between VR and the ECMS. All values are percents.

FTP ARTEMIS [A] 30 -1.28 -45.41 183.78 -1.31 -47.50 100.92 45 -1.22 -28.25 355.16 -0.85 -22.83 223.13 60 -1.32 -26.25 295.74 -1.25 -25.02 275.35 75 -1.46 -22.76 280.61 -1.50 -24.83 229.93 90 -1.89 -27.55 277.66 -1.85 -25.85 215.01 105 -2.18 -29.03 348.49 -2.10 -25.71 286.64 120 -1.35 -16.62 293.78 -1.01 -10.87 167.17

Fuel consumption decreases anywhere from just below 1% to just over 2%, with greater improvements tending to be with higher electrical load current requirements. Higher electrical loads enable greater fuel economy gains because there is more freedom in the 103

selection of the alternator current. However, with extremely high electrical loads (the

120 A case) this freedom is reduced because of battery current and voltage limitations.

The same issue arises with low load currents; many current split factors are eliminated due to constraints of the battery and this hinders the performance of the ECMS. In addition, the alternator consumes considerably less energy, especially at lower electrical loads. The decrease in fuel consumption is made possible by utilizing the battery more

(up to 355% increase, in one case). The values for are strikingly high because the battery usage is exceptionally low for the VR controller.

Figure 85 through Figure 88 compare the relevant variables between VR and the ECMS for the FTP cycle with a constant 75 A load current. Figure 85 through Figure 87 only show a portion of the FTP cycle from 600 to 800 seconds for ease of comparison.

150

100

-50 Battery Current [A] Battery -100 VR ECMS -150 600 650 700 750 800 Time [s]

Figure 85: Comparison of battery current between VR and the ECMS over a section of the FTP cycle.

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150

100

-50 Alternator Current [A] Alternator -100 VR ECMS -150 600 650 700 750 800 Time [s]

Figure 86: Comparison of alternator current between VR and the ECMS over a section of the FTP cycle.

14.5

13.5

13 Battery Voltage [V] Voltage Battery 12.5 VR ECMS 12 600 650 700 750 800 Time [s]

Figure 87: Comparison of battery voltage between VR and the ECMS over a section of the FTP cycle.

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1 0.99 0.98 0.97 0.96

SOC [-] 0.95 SOC 0.94 0 VR 0.93 ECMS

0 500 1000 1500 Time [s]

Figure 88: Comparison of battery SOC between VR and the ECMS over the FTP cycle.

As was noted before, and is depicted in Figure 88, the battery is recharged for the VR control case while the ECMS is charge-sustaining. The other notable difference from the plots is the ECMS makes considerably more use of the battery than the VR controller.

However, the battery current tends to stay below a 50 A magnitude for the ECMS.

Section 4.4 Sensitivity Analysis

The sensitivity of the ECMS performance metrics (fuel consumed and the final SOC) are evaluated for three distinct reasons.

1. Equivalence Factors. Since the ECMS depends on the calibration of the

equivalence factors in order to function as intended, it is important to understand

how the optimizer behaves for the case in which the equivalence factors are not

the optimal values for the drive cycle and load current profile.

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2. Calibration Parameters. When the ECMS is calibrated, a set of parameters are

defined that impact the system (see Table 7). For instance, the battery voltage

limitations, the maximum rate of change of the current split factor and the

controller sample time all may have a strong influence over the ECMS’s

operation.

3. Model Inaccuracies. The ECMS is dependent on models for its algorithm. How

will the system perform if the battery voltage prediction, fuel consumption map or

SOC estimation are off?

In particular, two questions must be answered for each of these situations: 1) Will the system still be charge-sustaining? 2) How much will the fuel consumption change?

4.4.1 Equivalence Factors

The ECMS for alternator control must be calibrated for the particular drive cycle and load current profile of interest. However, in reality, the actual drive cycle and load current profile will be different from those with which the ECMS is calibrated. Therefore, the equivalence factors will not be optimal. Even if the drive cycle and load current profile are the ones for which the calibration was done, the calibration process may not determine the true optimal set of equivalence factors due to limitations of this calibration process. Therefore, it is highly unlikely the equivalence factors will be optimal. The sensitivity of the SOC to a suboptimal equivalence factor is

(4.10)

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where is the final SOC with the suboptimal equivalence factor, is the final SOC with the “optimal” equivalence factors (as defined by the calibration process),

is the suboptimal equivalence factor and is the optimal equivalence factor.

Similarly, the sensitivity of the mass of fuel consumed to a suboptimal equivalence factor is defined as

(4.11)

Since there are two equivalence factors, the sensitivity to both will be explored separately and subscripts will be used to distinguish between them. For instance, is the optimal charging equivalence factor and is the sensitivity of the SOC to a suboptimal charging equivalence factor. To evaluate these sensitivities, the model is run over 1 FTP cycle with the equivalence factor slightly changed from its calibrated value. is equal to 110% of and is 0.95 for all cases. The results are summarized in Table 14.

For results when is equal to 90% of and results for the ARTEMIS cycle refer to

Appendix C.

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Table 14: Sensitivity analysis results for a suboptimal equivalence factor. The variables in the top two rows are associated with the value in the corresponding cell of each shaded or white section.

[A] [kg]

0.579 0.9591 0.9601 0.00149 0.01310 30 0.9589 0.9589 1.000 0.9611 0.9743 0.02229 0.16103 1.250 0.9700 0.9807 0.04148 0.29739 45 0.9660 0.9523 0.836 0.9664 0.9560 0.00444 0.03860 0.894 0.9746 0.9656 0.01588 0.13733 60 0.9731 0.9525 1.250 0.9742 0.9626 0.01190 0.10601 1.000 0.9814 0.9686 0.01166 0.06872 75 0.9803 0.9619 1.372 0.9817 0.9693 0.01490 0.07644 1.000 0.9849 0.9540 0.00268 0.01870 90 0.9846 0.9522 1.394 0.9874 0.9680 0.02814 0.16622 0.895 0.9897 0.9554 0.00091 0.00832 105 0.9897 0.9546 1.395 0.9914 0.9638 0.01804 0.09664 1.268 0.9972 0.9637 0.01061 0.08179 120 0.9961 0.9559 1.500 0.9976 0.9646 0.01426 0.09094

As expected, the mass of fuel consumed increases since one of the equivalence factors is no longer optimal. However, the maximum sensitivity for the mass of fuel is only

0.04148, which suggests the fuel consumption has very low sensitivity to a suboptimal equivalence factor. On the other hand, the final SOC is more sensitive to a suboptimal equivalence factor. For one case, the SOC increases by almost 3% with 10% greater than the optimal value. While this is not drastic, it does mean the system is no longer charge-sustaining. For the case presented here, with the equivalence factor greater than its optimal value, the battery will recharge. However, if the equivalence factor is less than its optimal value, the battery will be discharged and the electrical system may fail.

4.4.2 Calibration Parameters

The ECMS is calibrated with a set of parameters that constrain certain components or impact the optimizer algorithm. For example, there are battery voltage limitations. The

109

choice of these limitations impacts the optimizer’s performance. If the ECMS is calibrated with one set of battery voltage limitations but then another set is used in practice, the system may behave differently. The sensitivity of the SOC to a change in the maximum battery voltage is

(4.12)

The sensitivity of the mass of fuel consumed to a change in the maximum battery voltage is similarly defined as

(4.13)

The results for equal to 14.6 V for the FTP cycle are given in Table 15. Table 16 contains the results for equal to 16 V for the FTP.

Table 15: Sensitivity analysis results for a maximum battery voltage of 14.6 V.

[A] [kg] 30 0.9589 0.9589 15 0.9588 0.9475 0.00580 0.44499 45 0.9660 0.9523 15 0.9647 0.9354 0.04956 0.66708 60 0.9731 0.9525 15 0.9719 0.9362 0.04386 0.63902 75 0.9803 0.9619 15 0.9789 0.9410 0.05078 0.81457 90 0.9846 0.9522 15 0.9838 0.9339 0.02954 0.72275 105 0.9897 0.9546 15 0.9886 0.9334 0.03824 0.83361 120 0.9961 0.9559 15 0.9954 0.9380 0.02634 0.70371

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Table 16: Sensitivity analysis results for a maximum battery voltage of 16 V.

[A] [kg] 30 0.9589 0.9589 15 0.9609 0.9864 0.03113 0.43089 45 0.9660 0.9523 15 0.9674 0.9861 0.02242 0.53218 60 0.9731 0.9525 15 0.9751 0.9874 0.03074 0.55064 75 0.9803 0.9619 15 0.9813 0.9866 0.01637 0.38396 90 0.9846 0.9522 15 0.9869 0.9856 0.03540 0.52573 105 0.9897 0.9546 15 0.9919 0.9865 0.03351 0.50033 120 0.9961 0.9559 15 0.9981 0.9848 0.03012 0.45372

The fuel consumption decreases with a lower value of the maximum battery voltage, but this is at the expense of the battery’s SOC. The battery is no longer charge-sustaining with this lower . In some cases, the SOC decreases by over 0.8% for a 1% decrease in the maximum battery voltage. The opposite is true when the maximum battery voltage is higher than the value used for calibration. The fuel consumption and the battery’s SOC both increase. Once again, the system is no longer charge-sustaining.

Another parameter of the ECMS is the sample time of the controller. The desired alternator current is updated every seconds. By increasing or decreasing this sample time, the ECMS will operate differently since it can only react to constraints as often as it is sampled. The results for a sample time of 1 second during the FTP cycle are shown in Table 17. Table 18 shows the results for a sample time of 10 seconds during the FTP cycle.

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Table 17: Sensitivity analysis results for a controller sample time of 1 second.

[A] [kg] 30 0.9589 0.9589 3 0.9578 0.9582 0.00177 0.00095 45 0.9660 0.9523 3 0.9653 0.9542 0.00097 -0.00295 60 0.9731 0.9525 3 0.9716 0.9527 0.00225 -0.00039 75 0.9803 0.9619 3 0.9791 0.9618 0.00180 0.00021 90 0.9846 0.9522 3 0.9833 0.9522 0.00202 0.00001 105 0.9897 0.9546 3 0.9886 0.9543 0.00162 0.00050 120 0.9961 0.9559 3 0.9948 0.9550 0.00203 0.00141

Table 18: Sensitivity analysis results for a controller sample time of 10 seconds.

[A] [kg] 30 0.9589 0.9589 3 0.9608 0.9522 0.00085 -0.00298 45 0.9660 0.9523 3 0.9675 0.9444 0.00068 -0.00357 60 0.9731 0.9525 3 0.9752 0.9503 0.00095 -0.00096 75 0.9803 0.9619 3 0.9823 0.9586 0.00089 -0.00147 90 0.9846 0.9522 3 0.9870 0.9494 0.00106 -0.00126 105 0.9897 0.9546 3 0.9924 0.9525 0.00120 -0.00095 120 0.9961 0.9559 3 0.9979 0.9538 0.00078 -0.00093

Obviously, the sample time of the ECMS has minimal impact on the fuel consumption and the final SOC of the battery. However, if the sample time is too long, the system will not function as intended since the system will violate constraints before the ECMS is sampled and able to correct the desired alternator current accordingly.

Finally, the maximum rate of change of the current split factor decides how quickly the current split factor can change from one sample of the ECMS to the next. This parameter can be used to limit how quickly the alternator and battery current change. However, this may reduce the effectiveness of the ECMS. Table 19 contains the results for a of

0.5/s.

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Table 19: Sensitivity analysis results for a maximum rate of change of the current split factor of 0.5/s.

[A] [kg] 30 0.9589 0.9589 1 0.9610 0.9760 -0.00424 -0.03566 45 0.9660 0.9523 1 0.9680 0.9834 -0.00426 -0.06530 60 0.9731 0.9525 1 0.9746 0.9852 -0.00309 -0.06870 75 0.9803 0.9619 1 0.9831 0.9761 -0.00569 -0.02953 90 0.9846 0.9522 1 0.9845 0.9489 0.00013 0.00697 105 0.9897 0.9546 1 0.9900 0.9486 -0.00064 0.01252 120 0.9961 0.9559 1 0.9968 0.9579 -0.00127 -0.00412

The fuel consumption tends to increase as the maximum rate of change of the current split factor is reduced, as expected. However, the fuel consumption only increases by a fraction of a percent for each case. The SOC of the battery, on the other hand, tends to stay approximately the same or increase a few percent. This analysis suggests that reducing may be a useful way to increase the SOC of the battery with only a small cost to the fuel consumption. Refer to Appendix C for sensitivity analysis results for the calibration parameters over the ARTEMIS cycle.

4.4.3 Model Inaccuracies

The ECMS algorithm relies on a variety of models including the battery model and the vehicle fuel consumption map. If these models are not accurate, the ECMS’s performance may suffer. The sensitivity of the fuel consumption and the final SOC to model inaccuracies is tested by multiplying the output of these models by a constant.

The battery model is used in the ECMS algorithm to predict the battery voltage that would result if a certain current split factor were selected. This value is used for two purposes: select only current split factors that ensure the battery voltage constraints are met and calculate the alternator and equivalent battery fuel consumptions. Table 20

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shows the results for the FTP cycle with a battery voltage calculation that is increased by

10%. The sensitivity of the final SOC is calculated using

(4.14)

The percent change in the SOC is divided by 10% since the battery voltage calculation is

10% off. The sensitivity of the fuel consumption is calculated in the same manner.

Table 20: Sensitivity analysis results for an inaccurate battery model.

[A] [kg] 30 0.9589 0.9589 0.9669 0.9984 0.08345 0.41196 45 0.9660 0.9523 0.9736 0.9984 0.07879 0.48407 60 0.9731 0.9525 0.9776 0.9884 0.04626 0.37678 75 0.9803 0.9619 0.9810 0.9656 0.00723 0.03764 90 0.9846 0.9522 0.9864 0.9614 0.01771 0.09635 105 0.9897 0.9546 0.9912 0.9623 0.01562 0.07992 120 0.9961 0.9559 1.0006 0.9816 0.04458 0.26871

With the future battery voltage calculation being inaccurate, the fuel consumption increases and the system is no longer charge-sustaining. Instead, the battery tends to charge because the higher estimation of the battery voltage allows current split factors to be used that would have otherwise been eliminated due to the constraint.

The fuel consumption map is used in the calculation of the alternator fuel consumption.

The results for the FTP cycle with a fuel consumption calculation that is increased by

10% is given in Table 21.

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Table 21: Sensitivity analysis results for an inaccurate fuel consumption map.

[A] [kg] 30 0.9589 0.9589 0.9576 0.9448 -0.01430 -0.14702 45 0.9660 0.9523 0.9631 0.9285 -0.02918 -0.25009 60 0.9731 0.9525 0.9705 0.9346 -0.02638 -0.18728 75 0.9803 0.9619 0.9771 0.9405 -0.03252 -0.22311 90 0.9846 0.9522 0.9826 0.9399 -0.02004 -0.12969 105 0.9897 0.9546 0.9878 0.9419 -0.01891 -0.13326 120 0.9961 0.9559 0.9947 0.9458 -0.01489 -0.10601

With an inaccurate fuel consumption map (increased by 10%), the fuel consumption decreases at the cost of the battery’s SOC. This occurs because the fuel consumption map is off by 10% across the board, meaning the greater fuel consumption areas are altered by a larger amount than the areas of low fuel consumption. Therefore, the algorithm tends to favor the lower values of fuel consumption, which are associated with low alternator currents and higher battery currents. The consequence is a system that is no longer charge-sustaining.

Section 4.5 The Adaptive ECMS

As was discussed in Section 2.3, the ECMS is not suitable for real-time control since it must be calibrated with a priori knowledge of the drive cycle (and load current profile, for this application). Besides real world driving situations, the sensitivity analysis shows that suboptimal equivalence factors, inaccurate calibration parameters and model inaccuracies can all cause the ECMS to fail, too. Failure, in this case, is defined as the battery not being charge-sustaining and/or increased fuel consumption compared to

Voltage Regulation controller. It is of particular importance that the system be charge-

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sustaining, or at least not charge-depleting, for component safety and reliable vehicle operation. For these reasons, the equivalence factor of the ECMS will be made adaptive.

In essence, the adaptive ECMS (A-ECMS) is the ECMS with closed-loop feedback control on the equivalence factor. Since the primary goal of making the ECMS adaptive is to ensure charge-sustaining operation, the feedback will be from the SOC of the battery. Two adaptation methods will be considered: feedback with a PI controller at every instant of time (continuous) and feedback at only discrete times (discrete). For both methods, only a single equivalence factor ( ) will be used for both charging and discharging. Work done by Musardo et al. has shown that using a single equivalence factor is only slightly suboptimal [35].

4.5.1 Continuous SOC Feedback

The scheme for continuous SOC feedback to adapt the equivalence factor is shown in

Figure 89.

Figure 89: Continuous feedback adaptation strategy.

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Two terms are summed to give the equivalence factor every time step. The first term is a starting point for the equivalence factor and is the output of a lookup table built using the results of the calibration process. The ECMS is calibrated for combinations of the drive cycle (FTP or ARTEMIS) and load current magnitude (30 to 120 A). The optimal charging and discharging equivalence factors are therefore known for each combination.

Since the A-ECMS will be using a single equivalence factor, the optimal charging and discharging equivalence factors are averaged for this application. The mean velocities of the drive cycles are used to represent the drive cycles in the table and the current vehicle velocity, , is the input for this dimension of the table.

The second term is a correction for the first term. The SOC is compared to a reference

SOC ( ) and the error is the input to a PI controller. Equation (4.15) summarizes the complete calculation done in Figure 89 [37].

(4.15)

The reference SOC is the nominal value around which the SOC is desired. The integrator can be reset every time the error in the SOC crosses zero (as detected by the Hit Cross block) so that the equivalence factor instantly changes trajectory when the reference SOC is crossed. However, using this reset tends to cause the SOC to remain on one side of the

, so the Hit Cross block is deactivated for the analysis conducted here. The proportional ( ) and integral ( ) gains must be tuned for this strategy. These PI gains are manually tuned to allow sufficient travel of the SOC while still maintaining a charge- sustaining system. Table 22 lists the parameters used for this strategy. 117

Table 22: Parameters for the A-ECMS with continuous feedback on the SOC.

Parameter Value 0.95 1 0.05

Figure 90 shows the behavior of the system over 5 consecutive FTP cycles with an adaptive equivalence factor using PI control with SOC feedback.

Velocity [m/s] Velocity 0 0 1000 2000 3000 4000 5000 6000 7000 SOC 1 ref SOC

0.95 SOC [-]

0.9 0 1000 2000 3000 4000 5000 6000 7000

1 s s

base Equiv. Equiv. Factor 0 0 1000 2000 3000 4000 5000 6000 7000 Time [s]

Figure 90: System behavior for adaptive equivalence factor with continuous PI control.

As the SOC drifts below the reference value, the equivalence factor increases, encouraging current split factors that recharge the battery. Then, when the SOC crosses the reference, the equivalence factor decreases, gradually bringing the SOC back to the reference. All results for the A-ECMS will be summarized in Section 4.5.3.

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4.5.2 Discrete SOC Feedback

As opposed to the continuous feedback method, the discrete feedback method only updates the equivalence factor every seconds. The block diagram of this strategy is given in Figure 91.

Figure 91: Discrete feedback adaptation strategy.

The Trigger block activates the equivalence factor update subsystem (dashed box) every

seconds and then this equivalence factor is used for the next seconds. Equation

(4.16) shows the equation to calculate the new equivalence factor [57].

(4.16)

This is an autoregressive moving average model that works by taking the average of the two previous equivalence factors and adding the SOC error multiplied by a proportional gain. This gain, , is a tuning parameter for this method. It is manually tuned to ensure 119

a charge-sustaining system while also allowing adequate travel of the SOC. In addition, an initial guess of the equivalence factor, , must be made. Table 23 lists the parameters used for this strategy.

Table 23: Parameters for the A-ECMS with discrete feedback on the SOC.

Parameter Value 0.95 1 1.2 60

Figure 92 shows the behavior of the system over 5 repeated FTP cycles with an adaptive equivalence factor updated every 60 seconds.

Velocity [m/s] Velocity 0 0 1000 2000 3000 4000 5000 6000 7000

1 SOC ref SOC

0.95 SOC [-]

0.9 0 1000 2000 3000 4000 5000 6000 7000

1.5

0.5

Equiv. Equiv. Factor 0 0 1000 2000 3000 4000 5000 6000 7000 Time [s]

Figure 92: System behavior for adaptive equivalence factor with discrete updates every 60 seconds.

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As the SOC drifts down, the equivalence factor increases to compensate. However, the equivalence factor does not change rapidly. There are two reasons for this: 1) the calculation of the next equivalence factor directly depends on the values of the last two equivalence factors and 2) it is only updated every seconds, not every time step. An update time of 60 seconds was chosen because it maintains charge conservation without severely limiting the range of the SOC. The results for both discrete SOC feedback and continuous SOC feedback are contained in Section 4.5.3.

4.5.3 Results

The A-ECMS will be compared to both the calibrated ECMS results and the results using

VR control. The VR and the ECMS results are replicated here in Table 24 and Table 25, respectively. Table 26 and Table 27 contain the same results for the A-ECMS with continual SOC feedback (cA-ECMS) and the A-ECMS with discrete SOC feedback (dA-

ECMS), respectively.

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Table 24: Results for VR control for the FTP cycle and various load current magnitudes.

Table 25: Results for the ECMS calibrated for the FTP cycle and load current magnitude.

Table 26: Results for the cA-ECMS over the FTP cycle.

30 -0.025 500 0.957 14.74 4.497 45 -0.005 1278 0.970 20.31 4.541 60 -0.005 1621 0.976 19.14 4.573 75 -0.008 1895 0.981 19.73 4.599 90 -0.013 2094 0.985 19.65 4.626 105 -0.016 2259 0.988 20.41 4.648 120 -0.020 2529 0.994 18.57 4.683

Table 27: Results for the dA-ECMS over the FTP cycle.

30 0.022 786 0.962 11.98 4.495 45 -0.004 1141 0.967 16.43 4.531 60 -0.001 1588 0.975 16.52 4.567 75 -0.014 1814 0.979 17.21 4.597 90 -0.017 2054 0.984 17.61 4.625 105 -0.009 2333 0.990 18.42 4.647 120 -0.016 2602 0.995 17.18 4.681

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The ECMS and both versions of the A-ECMS are nominally charge-sustaining. Values for the only get as high as 2.5% for the A-ECMS controllers due to the oscillations of the SOC. To better compare the other performance metrics between VR and both of the A-ECMS versions, the same type of tables generated in Section 4.3 using equations of the same form as Equation (4.9) will be employed here. Table 13, comparing VR and the standard ECMS, is copied here in Table 28 for ease of comparison. Table 29 and Table

30 compare both of the A-ECMS versions with VR.

Table 28: Comparison of performance metrics between VR and the ECMS. All values are percents.

Table 29: Comparison of performance metrics between VR and the cA-ECMS. All values are percents.

FTP ARTEMIS [A] 30 -1.51 -56.27 212.90 -1.31 -47.43 67.88 45 -0.81 -15.69 381.87 -1.11 -23.76 167.92 60 -1.03 -17.47 364.43 -1.33 -24.06 249.27 75 -1.42 -21.95 344.33 -1.63 -25.27 265.10 90 -1.86 -27.62 324.81 -1.99 -27.66 233.75 105 -2.30 -31.40 378.39 -2.24 -27.85 295.91 120 -1.56 -20.60 316.42 -1.15 -13.32 174.86

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Table 30: Comparison of performance metrics between VR and the dA-ECMS. All values are percents.

FTP ARTEMIS [A] 30 -1.00 -31.22 154.27 -0.45 -12.78 83.92 45 -1.12 -24.72 289.68 -0.82 -16.01 125.36 60 -1.13 -19.17 300.72 -0.73 -10.47 192.57 75 -1.59 -25.27 287.71 -1.18 -16.78 218.81 90 -1.96 -28.98 280.72 -1.81 -25.02 208.01 105 -2.18 -29.13 331.71 -2.05 -25.31 265.64 120 -1.44 -18.31 285.25 -1.05 -11.90 153.98

All three versions of the ECMS (standard and both of the A-ECMS versions) result in reduced fuel consumption compared to VR control. This is achieved through decreased alternator energy consumption, which is made possible by more extensive use of the battery. The cA-ECMS tends to save the most fuel and use the battery the most. The dA-

ECMS, on the other hand, saves less fuel but also uses the battery less. Since both of the

A-ECMS versions are an improvement over VR control, in the sense that they lead to reduced fuel consumption, it may be more beneficial to compare them directly to the calibrated ECMS.

While the fuel consumption numbers for both of the A-ECMS versions are on the same order of magnitude as the calibrated ECMS, there is more deviation in the battery usage since the A-ECMS does not obtain overall charge conservation in the same manner as the calibrated ECMS. Figure 93 through Figure 95 clarify the degree to which these metrics change from the calibrated ECMS to the two versions of the A-ECMS for the FTP cycle.

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FTP Cycle 0.6 Continuous 0.4 Discrete

0.2

[%] fuel

M 0 

-0.2

-0.4 20 40 60 80 100 120 Load Current [A]

Figure 93: Change in fuel consumption between the A-ECMS versions and the calibrated ECMS. FTP Cycle 30

[%]

alt E

 0

-10 Continuous Discrete -20 20 40 60 80 100 120 Load Current [A]

Figure 94: Change in alternator energy consumption between the A-ECMS versions and calibrated the ECMS.

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FTP Cycle 20 Continuous 15 Discrete 10

[%] 5

bat 0

Ah  -5

-10

-15 20 40 60 80 100 120 Load Current [A]

Figure 95: Change in battery usage between the A-ECMS versions and the ECMS.

As before, , and are the percent change in their respective variable going from one case to another (in this case, the calibrated ECMS to the adaptive

ECMS). For instance, can be calculated as

(4.17)

These values are tabulated in Table 31 for the FTP cycle and both equivalence factor adaptation algorithms.

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Table 31: Comparison of performance metrics between the tuned ECMS and both versions of the A-ECMS for the FTP cycle. All values are percents.

Continual SOC Feedback Discrete SOC Feedback [A] 30 -0.22 -19.90 10.26 0.28 26.00 -10.40 45 0.42 17.51 5.87 0.10 4.93 -14.39 60 0.29 11.90 17.36 0.18 9.60 1.26 75 0.04 1.04 16.74 -0.13 -3.26 1.86 90 0.03 -0.09 12.48 -0.07 -1.98 0.81 105 -0.13 -3.34 6.67 0.00 -0.15 -3.74 120 -0.21 -4.77 5.75 -0.09 -2.02 -2.17

For both of the A-ECMS versions, the fuel consumption goes from increasing to decreasing compared to the calibrated ECMS as the electrical load current magnitude increases. At worst, the fuel consumption increases by 0.42% compared to the ECMS and at best it decreases by 0.22%. It should be noted that the A-ECMS only results in less fuel consumption than the ECMS in some instances because its final value of the

SOC is lower than the final SOC for the ECMS. Although the A-ECMS algorithms ensure charge-sustaining operation in the long term, the final value of the SOC does not have to equal the initial value. As expected, the alternator energy consumption follows the same trend as the fuel consumption. Compared to the calibrated ECMS, the battery usage is generally higher for the cA-ECMS and generally lower for the dA-ECMS.

Figure 96 compares the SOC and equivalence factor evolution between the calibrated

ECMS (ECMS), the cA-ECMS (Continuous) and the dA-ECMS (Discrete) for the FTP cycle with a 75 A load current.

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Velocity [m/s] Velocity 0 0 1000 2000 3000 4000 5000 6000 7000 ECMS 1 Continuous Discrete

0.95 SOC [-]

0.9 0 1000 2000 3000 4000 5000 6000 7000

1 ECMS Charge

ECMS Discharge Equiv. Equiv. Factor 0 0 1000 2000 3000 4000 5000 6000Continuous7000 Time [s] Discrete

Figure 96: Comparison of system behavior for the calibrated ECMS and both the A-ECMS versions over 5 FTP cycles with a 75 A load current.

Over the course of five cycles, all three strategies are nominally charge-sustaining.

However, the SOC oscillates by varying amounts depending on the strategy. The ECMS has two constant equivalence factors, one for charging and one for discharging currents.

Both the continuous and discrete SOC feedback versions for the A-ECMS result in an equivalence factor that fluctuates around the approximate average of the and from the calibrated ECMS. For results for the ARTEMIS cycle, refer to Appendix D.

Although both the A-ECMS versions appear to be acceptable for use as a real-time control strategy, the A-ECMS with discrete SOC feedback will be used for the remainder of the analysis because the equivalence factor is more stable with this version than with 128

the A-ECMS with continual SOC feedback. In addition, the dA-ECMS reduces battery usage with only marginally greater fuel consumption compared to the calibrated ECMS.

4.5.4 Evaluation of Robustness

Although the dA-ECMS adapts its equivalence factor automatically, it is still susceptible to model inaccuracies and poor calibration parameters. From the sensitivity analysis for the ECMS (see Section 4.4), the fuel consumption is, in general, much less sensitive than the final SOC to these situations. Therefore, the ability to achieve charge conservation will be the primary concern when evaluating the robustness of the dA-ECMS.

Model Inaccuracies

Table 32 shows the sensitivity results for the FTP cycle with a battery voltage estimation that is increased by 10%.

Table 32: Sensitivity results for the dA-ECMS with an inaccurate battery model.

[A] [kg] 30 0.9617 0.9719 0.9681 0.9979 0.06746 0.26779 45 0.9669 0.9463 0.9749 0.9977 0.08234 0.54234 60 0.9749 0.9493 0.9759 0.9696 0.01055 0.21382 75 0.9790 0.9365 0.9792 0.9410 0.00222 0.04806 90 0.9839 0.9330 0.9847 0.9400 0.00768 0.07543 105 0.9897 0.9407 0.9899 0.9441 0.00193 0.03539 120 0.9953 0.9338 0.9962 0.9406 0.00923 0.07247

The final SOC is highly sensitive to an inaccurate battery model for lower values of the load current magnitude. For these cases, the battery becomes fully charged, with the max

SOC and max battery voltage constraints being activated. In the other extreme, with a battery voltage estimation that is decreased by 10%, the SOC is highly sensitive for high

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values of the load current magnitude. In this situation, the SOC tends to drift down as shown in Figure 97. Although the system is not charge-sustaining, it can still be considered safe because the battery voltage and SOC are still constrained. In fact, the battery voltage constraints are actually tightened due to the inaccurate prediction.

0 1000 2000 3000 4000 5000 6000 7000 Battery Voltage [V] Voltage Battery

1 SOC ref SOC

0.9 SOC [-]

0.8 0 1000 2000 3000 4000 5000 6000 7000

Equiv. Equiv. Factor 0 0 1000 2000 3000 4000 5000 6000 7000 Time [s]

Figure 97: System behavior for the dA-ECMS with an inaccurate battery model.

The results with an inaccurate estimation of the SOC are similar to the results with an inaccurate battery model. The only situation that leads to unsafe operation is if the estimation of the SOC ( ) is continually above the reference value, as shown in

Figure 98. This situation would lead to the complete discharge of the battery at the lower voltage limit. However, this situation is only possible if there is a problem with the SOC estimator.

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0 1000 2000 3000 4000 5000 6000 7000 Battery Voltage [V] Voltage Battery

0.8 SOC ref 0.6 SOC SOC [-] SOC pred 0.4 0 1000 2000 3000 4000 5000 6000 7000

1.5

0.5

Equiv. Equiv. Factor 0 0 1000 2000 3000 4000 5000 6000 7000 Time [s]

Figure 98: System behavior for the dA-ECMS with a predicted SOC that is continually above the reference.

Although this situation is highly unlikely, the controller must have safeties in place to prevent a complete discharge of the battery. If the equivalence factor is equal to zero for an extended period of time, this is a good indication that the strategy has failed. In this situation, it is best to completely recharge the battery. Therefore, if the equivalence factor equals zero for two consecutive updates, the reference SOC will be set to 100%.

The results for the same situation (SOC estimate always above the reference) with the updated model are shown in Figure 99.

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0 1000 2000 3000 4000 5000 6000 7000 Battery Voltage [V] Voltage Battery

0.8 SOC ref 0.6 SOC SOC [-] SOC pred 0.4 0 1000 2000 3000 4000 5000 6000 7000

1.5

0.5

Equiv. Equiv. Factor 0 0 1000 2000 3000 4000 5000 6000 7000 Time [s]

Figure 99: System behavior for the dA-ECMS with safety modifications and a that is continually above the reference.

As can be seen, the battery is no longer fully discharged as it was before. Instead, the equivalence factor is able to recover and recharge the battery.

If the SOC estimator just predicts an SOC that is 10% higher than the actual value, the battery will only discharge to a 10% lower value of the SOC (see Figure 100). This is a far less critical situation, although the performance of the system will be affected.

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15 14 13 12

0 1000 2000 3000 4000 5000 6000 7000 Battery Voltage [V] Voltage Battery

1 SOC ref SOC

0.9 SOC [-]

0.8 0 1000 2000 3000 4000 5000 6000 7000

1.5

0.5

Equiv. Equiv. Factor 0 0 1000 2000 3000 4000 5000 6000 7000 Time [s]

Figure 100: System behavior for the dA-ECMS with a predicted SOC that is 10% high.

Table 33 shows the sensitivity results for the FTP cycle with a fuel consumption map output that is increased by 10%.

Table 33: Sensitivity results for the dA-ECMS with an inaccurate fuel consumption map.

[A] [kg] 30 0.9617 0.9719 0.9609 0.9615 -0.00837 -0.10683 45 0.9669 0.9463 0.9661 0.9375 -0.00911 -0.09351 60 0.9749 0.9493 0.9737 0.9382 -0.01205 -0.11652 75 0.9790 0.9365 0.9777 0.9277 -0.01373 -0.09397 90 0.9839 0.9330 0.9831 0.9273 -0.00875 -0.06142 105 0.9897 0.9407 0.9886 0.9327 -0.01053 -0.08542 120 0.9953 0.9338 0.9938 0.9210 -0.01439 -0.13691

At first glance, it appears the final SOC is sensitive to an inaccurate fuel consumption map since the final SOC values are relatively low after one cycle. However, Figure 101

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shows that the system once again becomes charge-sustaining after the equivalence factor has time to adapt.

0 1000 2000 3000 4000 5000 6000 7000 Battery Voltage [V] Voltage Battery

1 SOC ref SOC

0.95 SOC [-]

0.9 0 1000 2000 3000 4000 5000 6000 7000

Equiv. Equiv. Factor 0 0 1000 2000 3000 4000 5000 6000 7000 Time [s]

Figure 101: System behavior for the dA-ECMS with inaccurate fuel consumption map over 5 consecutive FTP cycles.

Calibration Parameter

The discrete A-ECMS updates the equivalence factor every seconds. This time must be tuned to give the desired performance. Updating the equivalence factor every 60 seconds allows the system to maintain charge conservation without severely limiting the range of the SOC. If a much shorter update time is used, the SOC keeps closer to the

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reference value, but this limits the effectiveness of the ECMS. On the other hand, if a much longer update time is used, the system constraints may be violated. One advantage of the discrete feedback algorithm is the autoregressive moving average model tends to make the system charge-sustaining in the long-term regardless of the update time. This occurs because the updated equivalence factor is calculated using an average of the previous two values plus a correction term. Therefore, the system is continually fine- tuning its estimation of the equivalence factor. Figure 102 shows the behavior of the system over 10 consecutive FTP cycles with an adaptive equivalence factor updated every 1000 seconds. Although the system is not charge-sustaining initially, after 6 updates of it begins to oscillate around the reference SOC in much the same way as shown in Figure 92. Even in the extreme case, with equivalence factor only updated every 1000 seconds, the system will operate as desired, even though the fuel consumption will be higher than with a proper update time.

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Velocity [m/s] Velocity 0 0 5000 10000 15000

0.9

0.8 SOC

SOC [-] ref SOC 0.7 0 5000 10000 15000

1.5

0.5

Equiv. Equiv. Factor 0 0 5000 10000 15000 Time [s]

Figure 102: System behavior for adaptive equivalence factor with discrete updates every 1000 seconds.

4.5.5 Validation

The final model for the discrete A-ECMS will be validated against a random load current profile. The FTP cycle with moderate electrical loads which was used to validate the electrical system model (see Appendix A) will be used to validate the dA-ECMS. This load current profile was generated by turning on and off various electrical loads, so it meets the requirements for a “random” current profile. The load profile repeated five times is shown in Figure 103.

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250

200

150

100 Load Current [A] 50

0 0 1000 2000 3000 4000 5000 6000 7000 Time [s]

Figure 103: Load current profile used for dA-ECMS validation.

The results of the validation are presented in Figure 104 and Figure 105.

0 1000 2000 3000 4000 5000 6000 7000 Battery Voltage [V] Voltage Battery

0.98 SOC ref 0.96 SOC

0.94 SOC [-]

0.92 0 1000 2000 3000 4000 5000 6000 7000

1.5

0.5

Equiv. Equiv. Factor 0 0 1000 2000 3000 4000 5000 6000 7000 Time [s]

Figure 104: dA-ECMS controller operating with random electrical loads over 5 FTP cycles. 137

150

100

0 Current [A]Current

-50

Alternator Battery -100 0 200 400 600 800 1000 1200 1400 Time [s]

Figure 105: Alternator and battery currents dictated by dA-ECMS controller over 5 FTP cycles.

As expected, the equivalence factor adjusts to keep the SOC around the reference value.

In addition, the system constraints are not violated and the battery current generally stays between -50 and 50 amps. Finally, 4.3 kg of fuel are consumed, which is 1.64% less than with the Voltage Regulation controller.

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Chapter 5: Conclusions and Future Work

Section 5.1 Conclusions

The alternator control strategy used on the production Chrysler Town & Country

(Voltage Regulation or VR) makes little use of the battery after engine start-up because it only regulates the battery voltage to a reference value. Instead, if the battery current is used as another degree of freedom in the electrical system, energy optimization can be considered. The Equivalent Consumption Minimization Strategy (ECMS) is used to determine the optimal current for the alternator to provide, which may result in the battery charging, discharging or not being used.

While the ECMS leads to charge-sustaining operation when properly calibrated, the VR controller tends to keep the battery near 100% SOC. Although operating near 100% SOC is safe, it also leads to low dynamic charge acceptance which translates into low charging efficiency. Of particular importance, the ECMS results in decreased fuel consumption compared to VR. Simulation results for two drive cycles and a range of load current magnitudes see a fuel consumption decrease anywhere from 0.85% to 2.18%, with greater improvements tending to be with higher load current requirements. Higher electrical loads enable greater fuel economy gains because there is more freedom in the selection of the alternator current. These fuel economy gains are enabled by an increased

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utilization of the battery. For the same simulations, the battery was used up to 355% more. However, the peak battery current magnitude is generally limited to less than 50 amps, so it is unclear whether battery aging will be an issue in the long term. A battery aging analysis will be one focus of future work.

A major drawback of the ECMS is the need to calibrate it for the drive cycle and load current profile being considered. This requirement alone makes the strategy unsuitable for real-time control applications. Furthermore, a sensitivity analysis shows that suboptimal equivalence factors, inaccurate calibration parameters and model inaccuracies can all cause the ECMS to fail. Therefore, the ECMS must be made robust. The adaptive ECMS (A-ECMS) is the ECMS with closed-loop feedback control on the equivalence factor, which is the calibration parameter for the standard ECMS. Two separate adaption algorithms were tested: continuous SOC feedback with a PI controller and discrete SOC feedback using an autoregressive moving average model.

Similarly to the standard ECMS, both of the A-ECMS versions achieve charge conservation but with one major improvement: they do not need to be calibrated for the drive cycle or load current profile in order to accomplish this. Furthermore, the A-ECMS is able to correct for model inaccuracies and perform as expected. Still, for the A-ECMS to be deemed worthy for implementation on a vehicle, it must result in fuel savings on the same order as the ECMS. This is the case, as the A-ECMS only uses 0.42% more fuel than the ECMS in the worst case. As with the ECMS, the A-ECMS uses the battery

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considerably more than the VR control (up to a 382% increase). However, the A-ECMS with discrete SOC feedback generally uses the battery less than the ECMS.

These results suggest that the discrete SOC feedback version of the A-ECMS is suitable for replacing the VR strategy for real-time control applications and that fuel economy improvements of up to 2% can be expected.

Section 5.2 Future Work

The following tasks should be completed to build upon the work presented here.

1. Improved Battery Model. The current battery model validates well against

experimental data, but there are still areas where it can be improved. Adding

hysteresis voltage, perhaps with the model proposed by Hu et al., may assist in

determining the battery voltage given its previous state [48]. In addition,

characterizing the Peukert effect would help predict the apparent battery capacity

based on the discharge rate [58].

2. Enhanced Robustness for the A-ECMS. Learning parameters may be used to

enhance the robustness of the A-ECMS. For example, if the equivalence factor

for the discrete A-ECMS consistently increases from the initial value, the initial

value could be updated and stored in memory. For the continuous A-ECMS, the

equivalence factor lookup table, which gives , could be automatically

updated if the values tend to be corrected significantly.

3. SOC Estimator. Another way to ensure the A-ECMS is robust is by developing

an accurate SOC estimator. A linear Kalman filter is under development for SOC 141

estimation. This filter is based on the work by [59] and adapted for this

application. A reliable SOC estimator is especially crucial once the A-ECMS is

to be implemented on the vehicle.

4. Experimental Validation. Although the validation of the A-ECMS’s

effectiveness on the VES is encouraging, the next step is to validate the control

strategy on the vehicle. To do this, ETAS’s INTECRIO prototyping software is

used to run the A-ECMS model with inputs from the vehicle [43]. The model will

output a duty cycle command to send to the vehicle’s alternator. The

experimental change in fuel consumption and battery usage will then be known.

5. Battery Aging Analysis. Battery aging may be of concern since the ECMS saves

fuel by increasing the utilization of the battery. An analysis should be conducted

to determine how battery current profiles of the variety which the ECMS demands

affect battery aging. This analysis could help determine additional constraints for

the ECMS algorithm that ensure satisfactory battery life.

6. Load Shedding. The ECMS could be extended to allow for the shedding of

individual loads based on the current operating conditions. For example, the

heated seats may be turned off for short periods when decreasing the electrical

loads would benefit the system. Of course, this strategy would only work for

certain loads and the maximum duration a load is allowed to be shed would need

to be calibrated for driver acceptability.

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References

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Appendix A: Additional Electrical Model Validation

The electrical system validation plots for the FTP cycle with moderate electrical loads are given in Figure 106 through Figure 109. The electrical system validation plots for the

ARTEMIS cycle with base electrical loads are given in Figure 110 through Figure 113.

200 Data Model 150

100

Battery Current [A] -50

-100

-150 0 500 1000 1500 Time [s]

Figure 106: Battery current comparison over FTP cycle with moderate electrical loads for electrical system validation.

148

160 Data 140 Model

120

100

40 Alternator Current [A] 20

-20 0 500 1000 1500 Time [s]

Figure 107: Alternator current comparison over FTP cycle with moderate electrical loads for electrical system validation.

14.5

13.5

12.5 Battery Voltage [V] 12

11.5 Data Model 11 0 500 1000 1500 Time [s]

Figure 108: Battery voltage comparison over FTP cycle with moderate electrical loads for electrical system validation.

149

100 Data 90 Model

40 Duty Cycle [%] 30

0 0 500 1000 1500 Time [s]

Figure 109: Duty cycle comparison over FTP cycle with moderate electrical loads for electrical system validation.

200 Data Model 150

100

Battery Current [A] -50

-100

-150 0 100 200 300 400 500 600 700 800 900 1000 Time [s]

Figure 110: Battery current comparison over ARTEMIS cycle with base electrical loads for electrical system validation.

150

160 Data 140 Model

120

100

40 Alternator Current [A] 20

-20 0 100 200 300 400 500 600 700 800 900 1000 Time [s]

Figure 111: Alternator current comparison over ARTEMIS cycle with base electrical loads for electrical system validation.

14.5

13.5

12.5

Battery Voltage [V] 12

11.5 Data Model 11 0 100 200 300 400 500 600 700 800 900 1000 Time [s]

Figure 112: Battery voltage comparison over ARTEMIS cycle with base electrical loads for electrical system validation.

151

100 Data 90 Model

40 Duty Cycle [%] 30

0 0 100 200 300 400 500 600 700 800 900 1000 Time [s]

Figure 113: Duty cycle comparison over ARTEMIS cycle with base electrical loads for electrical system validation.

152

Appendix B: Corrected Fuel Consumption

The following is a justification for not correcting the fuel consumption values based on the change in the SOC. All equations are from [60]. The net energy change (NEC) is defined as

(B.1) where is the nominal system voltage. Then, the total cycle energy (TCE) is

(B.2) with TFE the total fuel energy, which is defined as

(B.3) where is the lower heating value of gasoline and is the mass of fuel consumed. Finally, the battery energy ratio (BER) is

(B.4)

To determine if the fuel consumption value needs to be corrected for the , the BER is compared to 1. If the BER is less than 1, the value does not need to be corrected. The maximum value of the BER for any simulation using VR control is 0.58. This value is slightly inflated, too, because the simplified fuel consumption map underestimates the fuel consumption. Therefore, the fuel consumption values do not need to be corrected for the change in the SOC. 153

Appendix C: Additional Sensitivity Analysis Results

Table 34: Suboptimal equivalence factor. FTP cycle with s 10% less than the optimal value.

[A] [kg]

0.579 0.9588 0.9574 0.00141 0.01528 30 0.9589 0.9589 1.000 0.9578 0.9480 0.01191 0.11351 1.250 0.9638 0.9386 0.02292 0.14388 45 0.9660 0.9523 0.836 0.9652 0.9418 0.00779 0.11072 0.894 0.9727 0.9500 0.00440 0.02631 60 0.9731 0.9525 1.250 0.9711 0.9382 0.02004 0.14974 1.000 0.9790 0.9537 0.01273 0.08553 75 0.9803 0.9619 1.372 0.9779 0.9451 0.02366 0.17468 1.000 0.9838 0.9459 0.00859 0.06637 90 0.9846 0.9522 1.394 0.9829 0.9417 0.01737 0.11054 0.895 0.9895 0.9530 0.00154 0.01665 105 0.9897 0.9546 1.395 0.9878 0.9422 0.01870 0.12981 1.268 0.9955 0.9511 0.00674 0.05035 120 0.9961 0.9559 1.500 0.9948 0.9476 0.01344 0.08738

Table 35: Suboptimal equivalence factor. ARTEMIS cycle with s 10% greater than the optimal value.

[A] [kg]

0.648 0.5647 0.9525 0.01979 0.11961 30 0.5636 0.9413 1.102 0.5672 0.9702 0.06309 0.30729 0.000 0.5719 0.9537 - - 45 0.5719 0.9537 1.899 0.5732 0.9594 0.02266 0.05929 0.606 0.5741 0.9480 0.00163 0.01369 60 0.5740 0.9467 1.500 0.5744 0.9491 0.00627 0.02516 0.913 0.5794 0.9639 0.02353 0.13162 75 0.5780 0.9514 1.500 0.5790 0.9571 0.01734 0.06006 0.898 0.5831 0.9675 0.02118 0.09617 90 0.5818 0.9583 1.500 0.5825 0.9626 0.01133 0.04530 1.000 0.5849 0.9628 0.00090 0.00381 105 0.5849 0.9624 1.255 0.5857 0.9682 0.01403 0.06042 1.045 0.5883 0.9586 0.00493 0.02013 120 0.5880 0.9567 1.500 0.5888 0.9617 0.01304 0.05233

154

Table 36: Suboptimal equivalence factor. ARTEMIS cycle with s 10% less than the optimal value.

[A] [kg]

0.648 0.5637 0.9403 -0.0013 0.01075 30 0.5636 0.9413 1.102 0.5626 0.9339 0.01722 0.07796 0.000 0.5719 0.9537 - - 45 0.5719 0.9537 1.899 0.5707 0.9488 0.02030 0.05195 0.606 0.5740 0.9461 0.00105 0.00674 60 0.5740 0.9467 1.500 0.5730 0.9407 0.01737 0.06333 0.913 0.5768 0.9410 0.01999 0.10881 75 0.5780 0.9514 1.500 0.5772 0.9467 0.01428 0.04950 0.898 0.5804 0.9435 0.02539 0.15454 90 0.5818 0.9583 1.500 0.5810 0.9527 0.01407 0.05783 1.000 0.5847 0.9618 0.00291 0.00600 105 0.5849 0.9624 1.255 0.5841 0.9569 0.01336 0.05754 1.045 0.5879 0.9561 0.00164 0.00615 120 0.5880 0.9567 1.500 0.5875 0.9530 0.00961 0.03778

Table 37: Inaccurate calibration parameter. ARTEMIS cycle with a max battery voltage of 14.6 V.

[A] [kg] 30 0.5636 0.9413 15 0.5633 0.9372 0.01993 0.16313 45 0.5719 0.9537 15 0.5704 0.9412 0.10158 0.49128 60 0.5740 0.9467 15 0.5732 0.9352 0.05550 0.45511 75 0.5780 0.9514 15 0.5766 0.9344 0.08900 0.66976 90 0.5818 0.9583 15 0.5804 0.9380 0.09508 0.79142 105 0.5849 0.9624 15 0.5844 0.9496 0.02716 0.49933 120 0.5880 0.9567 15 0.5874 0.9444 0.04197 0.48176

Table 38: Inaccurate calibration parameter. ARTEMIS cycle with a max battery voltage of 16 V.

[A] [kg] 30 0.5636 0.9413 15 0.5671 0.9865 0.09215 0.72018 45 0.5719 0.9537 15 0.5738 0.9854 0.05094 0.49799 60 0.5740 0.9467 15 0.5748 0.9704 0.01907 0.37482 75 0.5780 0.9514 15 0.5803 0.9872 0.05898 0.56521 90 0.5818 0.9583 15 0.5835 0.9861 0.04245 0.43537 105 0.5849 0.9624 15 0.5854 0.9836 0.01323 0.32991 120 0.5880 0.9567 15 0.5890 0.9760 0.02453 0.30355

155

Table 39: Inaccurate calibration parameter. ARTEMIS cycle with 1 s controller sample time.

[A] [kg] 30 0.5636 0.9413 3 0.5628 0.9426 0.00202 -0.00214 45 0.5719 0.9537 3 0.5719 0.9548 0.00013 -0.00176 60 0.5740 0.9467 3 0.5733 0.9489 0.00181 -0.00345 75 0.5780 0.9514 3 0.5769 0.9522 0.00281 -0.00133 90 0.5818 0.9583 3 0.5808 0.9581 0.00265 0.00029 105 0.5849 0.9624 3 0.5837 0.9634 0.00304 -0.00153 120 0.5880 0.9567 3 0.5873 0.9582 0.00196 -0.00248

Table 40: Inaccurate calibration parameter. ARTEMIS cycle with 1 s controller sample time.

[A] [kg] 30 0.5636 0.9413 3 0.5648 0.9455 0.00094 0.00191 45 0.5719 0.9537 3 0.5720 0.9559 0.00011 0.00099 60 0.5740 0.9467 3 0.5757 0.9528 0.00127 0.00274 75 0.5780 0.9514 3 0.5798 0.9561 0.00133 0.00214 90 0.5818 0.9583 3 0.5829 0.9582 0.00076 -0.00001 105 0.5849 0.9624 3 0.5868 0.9638 0.00142 0.00061 120 0.5880 0.9567 3 0.5895 0.9572 0.00110 0.00023

Table 41: Inaccurate calibration parameter. ARTEMIS cycle with a maximum rate of change of the current split factor of 0.5/s.

[A] [kg] 30 0.5636 0.9413 1 0.5650 0.9540 -0.00483 -0.02706 45 0.5719 0.9537 1 0.5738 0.9696 -0.00647 -0.03337 60 0.5740 0.9467 1 0.5763 0.9848 -0.00779 -0.08036 75 0.5780 0.9514 1 0.5819 0.9775 -0.01348 -0.05491 90 0.5818 0.9583 1 0.5829 0.9655 -0.00370 -0.01509 105 0.5849 0.9624 1 0.5847 0.9589 0.00046 0.00716 120 0.5880 0.9567 1 0.5885 0.9590 -0.00152 -0.00495

Table 42: Model inaccuracy. ARTEMIS cycle with a battery model off by 10%.

[A] [kg] 30 0.5636 0.9413 0.5694 0.9875 0.10283 0.49112 45 0.5719 0.9537 0.5715 0.9618 -0.00671 0.08480 60 0.5740 0.9467 0.5788 0.9843 0.08239 0.39629 75 0.5780 0.9514 0.5786 0.9556 0.01088 0.04431 90 0.5818 0.9583 0.5830 0.9656 0.02040 0.07640 105 0.5849 0.9624 0.5861 0.9692 0.02129 0.07058 120 0.5880 0.9567 0.5907 0.9717 0.04606 0.15681

156

Table 43: Model inaccuracy. ARTEMIS cycle with a fuel consumption map off by 10%.

[A] [kg] 30 0.5636 0.9413 0.5626 0.9324 -0.01815 -0.09414 45 0.5719 0.9537 0.5709 0.9489 -0.01843 -0.05044 60 0.5740 0.9467 0.5730 0.9403 -0.01829 -0.06845 75 0.5780 0.9514 0.5762 0.9381 -0.03145 -0.13920 90 0.5818 0.9583 0.5796 0.9397 -0.03787 -0.19401 105 0.5849 0.9624 0.5841 0.9569 -0.01329 -0.05722 120 0.5880 0.9567 0.5874 0.9525 -0.01031 -0.04371

157

Appendix D: Additional A-ECMS Results

Table 44 through Table 47 are the ECMS and the A-ECMS results for the ARTEMIS cycle.

Table 44: Results for the ECMS calibrated for the ARTEMIS cycle and load current magnitude.

30 -0.016 416 0.564 7.02 2.522 45 0.003 846 0.572 12.53 2.547 60 -0.007 1014 0.574 12.39 2.570 75 -0.002 1239 0.578 11.05 2.590 90 0.007 1465 0.582 11.32 2.607 105 0.018 1625 0.585 11.96 2.621 120 0.010 1781 0.588 10.73 2.645

Table 45: Results for the A-ECMS with continual SOC feedback over the ARTEMIS cycle.

30 -0.013 417 0.564 5.87 2.524 45 0.008 836 0.570 10.39 2.551 60 -0.005 1027 0.574 11.53 2.574 75 -0.004 1232 0.577 12.22 2.593 90 0.003 1429 0.581 11.99 2.611 105 0.009 1578 0.584 12.25 2.625 120 0.003 1732 0.587 11.04 2.646

Table 46: Results for the A-ECMS with discrete SOC feedback over the ARTEMIS cycle.

30 0.026 691 0.568 6.43 2.527 45 0.013 921 0.572 8.74 2.551 60 0.018 1211 0.577 9.66 2.575 75 0.014 1372 0.580 10.67 2.595 90 0.006 1481 0.582 11.06 2.611 105 0.013 1634 0.585 11.31 2.625 120 0.001 1760 0.588 10.20 2.647

158

Table 47: Comparison of performance metrics between the tuned ECMS and both versions of the A-ECMS for the ARTEMIS cycle. All values are percents.

Continual SOC Feedback Discrete SOC Feedback [A] 30 -0.04 -3.43 20.10 -0.86 -39.81 9.25 45 0.64 19.35 22.92 -0.03 -8.12 43.38 60 0.07 -1.47 8.70 -0.53 -16.24 28.30 75 0.00 -2.54 -7.50 -0.33 -9.67 3.49 90 0.04 0.13 -3.75 -0.05 -1.10 2.27 105 0.08 1.78 -1.18 -0.05 -0.54 5.74 120 0.15 2.90 -2.84 0.04 1.17 5.19

159