Pre-flight Mission Simulation Model for Estimating State-of-Energy (SoE) in Hybrid Aircraft Design and Development of Aircraft Performance and Mis- sion Simulation Model, and Analysis of Dynamic Programming Based Optimal Energy Management Strategy Master’s Thesis in Systems Control and Mechatronics W A Volanka Stepson Nilantha Dadallage DEPARTMENT OF ELECTRICAL ENGINEERING CHALMERS UNIVERSITY OF TECHNOLOGY Gothenburg, Sweden 2024 www.chalmers.se www.chalmers.se Master Degree project report 2024 Pre-flight Mission Simulation Model for Estimating State-of-Energy (SoE) in Hybrid Aircraft Design and Development of Aircraft Performance and Mission Simulation Model, and Analysis of Dynamic Programming Based Optimal Energy Management Strategy W A Volanka Stepson Nilantha Dadallage Department of Electrical Engineering Chalmers University of Technology Gothenburg, Sweden 2024 Pre-flight Mission Simulation Model for Estimating State-of-Energy(SoE) in Hybrid Aircraft Design and Development of Aircraft Performance and Mission Simulation Model, and Analysis of Dynamic Programming Based Optimal Energy Management Strat- egy W.A.Volanka Stepson Nilantha Dadallage © W A Volanka Stepson, Nilantha Dadallage, 2024. Supervisor: Etienne Lemarchand, Heart Aerospace Supervisor and Examiner: Anders Grauers, Department of Electrical Engineering, Chalmers University of Technology Masters Thesis 2024 Department of Electrical Engineering Chalmers University of Technology SE-412 96 Gothenburg Sweden Telephone +46 31 772 1000 Cover: Illustration of the pre-flight mission simulation model in MATLAB Simulink, including system models and user interface for generating simulation results. Typeset in LATEX, template by Kyriaki Antoniadou-Plytaria Gothenburg, Sweden 2024 iv Pre-flight Mission Simulation Model for Estimating State-of-Energy (SoE) in Hybrid Aircraft Design and Development of Aircraft Performance and Mission Simulation Model, and Analysis of Dynamic Programming Based Optimal Energy Management Strat- egy W.A.Volanka Stepson | Nilantha Dadallage Department of Electrical Engineering Chalmers University of Technology Abstract Accurate estimation of state-of-energy (SoE) is crucial for energy management func- tions within the aircraft Flight Management System (FMS). In the context of hybrid- electric aircraft, where multiple energy sources are available, estimating SoE becomes a complex challenge. To address this, a pre-flight mission simulation model has been developed and verified for hybrid-electric aircraft. This model serves two primary purposes: first, it aids in developing energy management related FMS functions for hybrid-electric aircraft; second, the simulation model acts as an aircraft per- formance model, which can be used for developing energy management strategies for hybrid-electric aircraft. The simulation model facilitates detailed mission plan- ning, simulation of different atmospheric conditions, while the simulation model accounts for varying aircraft weight. The methodology for developing and verify- ing the simulation model is described, and simulation results for various aircraft missions are presented. Furthermore, Dynamic Programming (DP) based optimal energy management strategy is proposed. This algorithm generates the optimal mode-of-operation profile for a given flight mission, ensuring that the specified bat- tery energy reserves remain intact while minimizing the fuel consumption. The performance of this algorithm is analyzed using the simulation model for various missions. Keywords: modeling, simulation, hybrid-electric aircraft, flight management system (FMS), pre-flight mission simulation, state-of-energy (SoE), energy management strategy, optimization, dynamic programming (DP) v Acknowledgements We would like to express our sincere gratitude to our industrial supervisor at Heart Aerospace, Etienne Lemarchand, for his invaluable guidance and encouragement throughout the thesis project. His willingness to share his time and expertise has been immensely helpful. Our heartfelt thanks go to our academic supervisor and examiner at Chalmers, Pro- fessor Anders Grauers, for his technical expertise, generous time, and enthusiastic support. His insights and dedication have been instrumental to our work. Lastly, we extend our deepest appreciation to our families for their unwavering support throughout this journey. Their encouragement has been a constant source of strength. Volanka Stepson Nilantha Dadallage Gothenburg June 2024 vii List of Acronyms Below is the list of acronyms that have been used throughout this thesis listed in alphabetical order: AGL Above Ground Level AMSL Above Mean Sea Level CAS Calibrated Air Speed CoG Centre of Gravity DISA Delta ISA DP Dynamic Programming EPS Electrical Propulsion System EPACS Electrical Propulsion Actuation and Control System ECM Equivalent Circuit Model FMS Flight Management system FoB Fuel on Board HPACS Hybrid Propulsion Automated Control System IAS Indicated Airspeed ISA International Standard Atmosphere MSL Mean Sea Level OAT Outside Air Temperature OCV Open Circuit Voltage PA Pressure Altitude PBU Propulsion Battery Unit PMSM Permanent Magnet Synchronous Motors RoC Rate of Climb RoD Rate of Descent SAF Sustainable Aviation Fuel SoC State of Charge SoE State of Energy TAS True Air Speed TES Turbine Engine System ToC Top of Climb ToD Top of Descent ix Nomenclature Below is the nomenclature of indices, sets, parameters, and variables that have been used throughout this thesis. Indices t Index for continuous time k Index for discrete time step Sets W Set of possible shaft speed values Wvalid Set of valid shaft speed values X Set of state values U Set of control state values Parameters and Variables h Altitude v Aircraft true air speed (TAS) v̇ Aircraft acceleration γ Flightpath angle vW ind Wind speed disa Temperature deviation from ISA qnh QNH hp Pressure altitude Ps Static pressure ρ Air density xi a Speed of sound mzf Aircraft zero-fuel weight mfuel,init Initial FoB SoCinit Initial PBU SoC m Aircraft weight Daero Aerodynamic drag Dfriction Friction force µ Friction coefficient CD Drag coefficient CD0 Zero-lift drag coefficient CL Lift coefficient CT Propeller thrust coefficient CP Propeller power coefficient J Propeller advance ratio Mtip Propeller tip mach number η efficiency xsoc PBU SoC state xfob Remaining FoB state NU Discretization for control input Nsoc Discretization for PBU SoC state Nfob Discretization for FoB state kp Control state penalizing factor xii Contents List of Acronyms ix Nomenclature xi List of Figures xvii List of Tables xxi 1 Introduction 1 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Heart Aerospace and ES-30 Aircraft . . . . . . . . . . . . . . . . . . . 2 1.3 Purpose, Scope and Contribution . . . . . . . . . . . . . . . . . . . . 3 1.4 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.5 Ethics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Literature Survey 7 2.1 Simulation Tools for Hybrid Aircraft . . . . . . . . . . . . . . . . . . 7 2.2 Energy Management in Hybrid Aircraft . . . . . . . . . . . . . . . . . 9 3 Theory 11 3.1 Flight Management System and Energy Management in Hybrid Aircraft 11 3.2 Aircraft Mission Profile . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.3 ES-30 Propulsion System Architecture . . . . . . . . . . . . . . . . . 16 3.4 Forward and Inverse Simulation Approaches . . . . . . . . . . . . . . 17 3.5 Hybrid-electric Propulsion Architectures . . . . . . . . . . . . . . . . 19 3.6 Ambient Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.6.1 Standard Atmosphere . . . . . . . . . . . . . . . . . . . . . . 20 3.6.2 Temperature at Altitude . . . . . . . . . . . . . . . . . . . . . 21 3.6.3 Ambient Pressure at Altitude . . . . . . . . . . . . . . . . . . 22 3.6.4 Air Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.6.5 Speed of Sound . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.6.6 Mach Number . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.6.7 Pressure Altitude . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.6.8 Density Altitude . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.6.9 True Air Speed and Calibrated Air Speed . . . . . . . . . . . 23 3.7 Aerodynamic Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.8 Aircraft Point-mass Model . . . . . . . . . . . . . . . . . . . . . . . . 26 xiii Contents 3.9 Propellers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.10 Permanent Magnet Synchronous Machine . . . . . . . . . . . . . . . . 31 3.11 Turbine Engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.12 Battery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.13 Dynamic Programming . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4 Methods 41 4.1 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.1.1 Mission Planner . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.1.1.1 Mission Segment Calculator . . . . . . . . . . . . . . 46 4.1.1.2 Mission Profile Generator . . . . . . . . . . . . . . . 48 4.1.2 Weather Model . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.1.2.1 Pressure Altitude Model . . . . . . . . . . . . . . . . 51 4.1.2.2 Outside Air Temperature Model . . . . . . . . . . . 51 4.1.2.3 Static Pressure Model . . . . . . . . . . . . . . . . . 52 4.1.2.4 Air Density Model . . . . . . . . . . . . . . . . . . . 52 4.1.2.5 Speed of Sound Model . . . . . . . . . . . . . . . . . 53 4.1.3 Mode Selector . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.1.4 Aircraft Model . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.1.4.1 Aircraft Point-mass Model . . . . . . . . . . . . . . . 56 4.1.4.2 Aircraft Lift-drag Polar Model . . . . . . . . . . . . 57 4.1.4.3 Aircraft Mass Model . . . . . . . . . . . . . . . . . . 59 4.1.4.4 Remaining Fuel Model . . . . . . . . . . . . . . . . . 60 4.1.5 Master Controller Model . . . . . . . . . . . . . . . . . . . . . 62 4.1.6 Electric Propulsion System Model . . . . . . . . . . . . . . . . 65 4.1.6.1 Electric Propulsion System Propeller Model . . . . . 65 4.1.6.2 PMSM Model . . . . . . . . . . . . . . . . . . . . . . 70 4.1.6.3 Inverter-loss Model . . . . . . . . . . . . . . . . . . . 72 4.1.7 TES Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.1.7.1 TES Propeller Model . . . . . . . . . . . . . . . . . . 74 4.1.7.2 PSFC Model . . . . . . . . . . . . . . . . . . . . . . 75 4.1.8 Battery Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.2 Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.2.1 Verification of Mission Planner . . . . . . . . . . . . . . . . . 80 4.2.2 Verification of Weather Model . . . . . . . . . . . . . . . . . . 81 4.2.3 Verification of Mode Selector . . . . . . . . . . . . . . . . . . . 84 4.2.4 Verification of Aircraft Model . . . . . . . . . . . . . . . . . . 86 4.2.5 Verification of Electrical Propulsion System Model . . . . . . . 86 4.2.6 Verification of TES . . . . . . . . . . . . . . . . . . . . . . . . 87 4.3 Dynamic Programming Based Optimal Energy Management Strategy 88 5 Result and Discussion 91 5.1 Simulation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.2.1 Hybrid Aircraft Typical Mission Simulation . . . . . . . . . . 99 5.2.1.1 Mission Profile . . . . . . . . . . . . . . . . . . . . . 100 5.2.1.2 Mode Schedule . . . . . . . . . . . . . . . . . . . . . 101 xiv Contents 5.2.1.3 Ambient Parameters . . . . . . . . . . . . . . . . . . 103 5.2.1.4 Thrust . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5.2.1.5 Power . . . . . . . . . . . . . . . . . . . . . . . . . . 105 5.2.1.6 Fuel-on-Board . . . . . . . . . . . . . . . . . . . . . . 106 5.2.1.7 Aircraft Weight . . . . . . . . . . . . . . . . . . . . . 107 5.2.1.8 Battery State-of-Charge . . . . . . . . . . . . . . . . 108 5.2.1.9 Battery Parameters . . . . . . . . . . . . . . . . . . 108 5.2.1.10 Operating Points . . . . . . . . . . . . . . . . . . . . 109 5.2.1.11 Propeller Operating Point Efficiency . . . . . . . . . 110 5.2.2 Comparison Against Baseline Mission Data . . . . . . . . . . . 111 5.2.3 Cruise Altitude Survey . . . . . . . . . . . . . . . . . . . . . . 113 5.2.4 Cruise Speed Survey . . . . . . . . . . . . . . . . . . . . . . . 119 5.2.5 Effect of Accounting for Varying Aircraft Weight . . . . . . . 122 5.2.6 Effect of Weather Parameters . . . . . . . . . . . . . . . . . . 124 5.2.6.1 Impact of Headwind . . . . . . . . . . . . . . . . . . 125 5.2.6.2 Impact of DISA . . . . . . . . . . . . . . . . . . . . . 128 5.2.6.3 Impact of QNH . . . . . . . . . . . . . . . . . . . . . 131 5.3 Optimal Energy Management Strategy . . . . . . . . . . . . . . . . . 136 5.3.1 DP-based Optimal Mode Schedule . . . . . . . . . . . . . . . 136 5.3.2 Impact of Control State Penalizing Factor (kp) . . . . . . . . . 142 6 Conclusion 145 Bibliography 147 xv Contents xvi List of Figures 1.1 Heart Aerospace ES-30 hybrid-electric regional aircraft. . . . . . . . . 3 3.1 Illustration of ES-30 cockpit avionics suite. . . . . . . . . . . . . . . . 12 3.2 Conceptual interface block diagram for FMS in hybrid-electric aircraft. 13 3.3 Aircraft mission profile . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.4 ES-30 independent hybrid propulsion architecture. . . . . . . . . . . . 16 3.5 Simulation workflow in forward simulation approach for an aircraft. . 18 3.6 Simulation workflow in inverse simulation approach for an aircraft. . 18 3.7 Aircraft Hybrid-electric Propulsion Architectures. . . . . . . . . . . . 19 3.8 Lift and drag forces and related angles for an typical aircraft wing airfoil. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.9 Illustration of aircraft drag curve. . . . . . . . . . . . . . . . . . . . . 26 3.10 Aircraft principle axes and roll, pitch yaw rotations . . . . . . . . . . 27 3.11 Aircraft free-body diagram with flightpath variables and forces. . . . 28 3.12 Angles and parameters related to the aerodynamics of a propeller blade. 29 3.13 IPMSM and SPMSM architecture [32]. . . . . . . . . . . . . . . . . . 32 3.14 Illustration of PT6A Turboprop engine [33]. . . . . . . . . . . . . . . 33 3.15 Basic ECM for Rint battery model. . . . . . . . . . . . . . . . . . . . 36 3.16 Principal of optimality explanation illustration. . . . . . . . . . . . . 38 4.1 Flow diagram for the simulation model for estimating the SoE of hybrid aircraft. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.2 Model architecture with input signals, output signals and input pa- rameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.3 Input, Application and Output Layers with arrows pointing the di- rection of data flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.4 Output signal of the Mission Planner. . . . . . . . . . . . . . . . . . . 45 4.5 Kinematic diagram of aircraft for takeoff segment. . . . . . . . . . . . 46 4.6 Kinematic diagram of aircraft for climb segment. . . . . . . . . . . . . 47 4.7 Kinematic diagram of aircraft for cruise segment. . . . . . . . . . . . 47 4.8 Stateflow implementation of Mission Profile Generator model within Mission Planner Model. . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.9 Simulink implementation of the Mission Planner. . . . . . . . . . . . 49 4.10 Input and output signals of the Weather Model. . . . . . . . . . . . . 50 4.11 Inputs and output of Pressure Altitude Model. . . . . . . . . . . . . . 51 4.12 Inputs and output of Outside Air Temperature Model. . . . . . . . . 51 4.13 Inputs and output of Static Pressure Model. . . . . . . . . . . . . . . 52 xvii List of Figures 4.14 Inputs and output of Air Density Model. . . . . . . . . . . . . . . . . 52 4.15 Inputs and output of Speed of Sound Model. . . . . . . . . . . . . . . 53 4.16 Simulink implementation of the Weather Model. . . . . . . . . . . . . 53 4.17 Input and output signal of Mode Selector. . . . . . . . . . . . . . . . 54 4.18 Simulink implementation of the Mode Selector. . . . . . . . . . . . . 54 4.19 Input and output signals of Aircraft Model. . . . . . . . . . . . . . . 55 4.20 Input and output signals of Aircraft Point-mass Model. . . . . . . . . 56 4.21 Simscape based implementation of the Aircraft Point-mass Model. . . 57 4.22 Input and output signals of Aircraft Lift-drag Polar Model. . . . . . . 57 4.23 Simulink implementation of the Aircraft Lift-drag Polar Model. . . . 59 4.24 Input and output signals of the Aircraft Mass Model. . . . . . . . . . 59 4.25 Simulink implementation of the Aircraft Mass Model to determine the changing aircraft mass due to fuel burn. . . . . . . . . . . . . . . 60 4.26 Simulink model of the remaining fuel model to update the state of remaining amount of fuel. . . . . . . . . . . . . . . . . . . . . . . . . 60 4.27 Simulink model of the remaining fuel model to update the state of remaining amount of fuel. . . . . . . . . . . . . . . . . . . . . . . . . 61 4.28 Simulink implementation of the Aircraft Model. . . . . . . . . . . . . 61 4.29 Input and output signals of Master Controller Model. . . . . . . . . . 62 4.30 Simulink model of Master Controller . . . . . . . . . . . . . . . . . . 62 4.31 Input and output signals of Electric Propulsion System model . . . . 65 4.32 Input and output signals of Electric Propulsion System propeller model 66 4.33 Propeller performance maps for β, CT and ηprop when Mtip = X. . . . 67 4.34 Visualization of valid operating points and the optimal operating point resulting the maximum efficiency in propeller performance map for ηprop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.35 Simulink implementation of EPS propeller model. . . . . . . . . . . . 70 4.36 PMSM efficiency maps . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.37 Input and output signals of PMSM Model. . . . . . . . . . . . . . . . 71 4.38 Simulink implementation of the PMSM Model . . . . . . . . . . . . . 72 4.39 Input and output signals of Inverter-Loss Model . . . . . . . . . . . . 72 4.40 Input and output signals of Inverter-Loss Model . . . . . . . . . . . . 73 4.41 Simulink implementation of the EPS Model . . . . . . . . . . . . . . 73 4.42 Input and output signals of TES Model . . . . . . . . . . . . . . . . . 74 4.43 Inputs and outputs of the TES Propeller Model . . . . . . . . . . . . 74 4.44 Simulink implementation of the TES Propeller Model . . . . . . . . . 75 4.45 Inputs and output of PSFC Model . . . . . . . . . . . . . . . . . . . 75 4.46 PSFC map in kg / kWh against pressure altitude hp and shaft power PShaft. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 4.47 SFC in kg/s against pressure altitude hp and shaft power PShaft. . . . 77 4.48 Simulink implementation of the PSFC Model. . . . . . . . . . . . . . 77 4.49 Simulink implementation of the TES Model. . . . . . . . . . . . . . . 78 4.50 Input and output of Battery Model. . . . . . . . . . . . . . . . . . . . 78 4.51 Variation of Open Circuit Voltage (OCV) of battery cell with varying SoC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.52 Simulink implementation of the PBU Model. . . . . . . . . . . . . . . 79 xviii List of Figures 4.53 Comparison of mission profile from mission planner model with base- line data for hybrid aircraft mission. . . . . . . . . . . . . . . . . . . . 81 4.54 Comparison of ambient parameter values from weather model for ISA condition with corresponding values from ISA table. . . . . . . . . . . 82 4.55 Comparison of ambient parameter values from weather model for tem- perature DISA = +10 0C condition with corresponding values from baseline data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4.56 Comparison of ambient parameter values from weather model for pressure deviation from ISA condition (QNH = 1000 hPa) with cor- responding values from baseline data. . . . . . . . . . . . . . . . . . . 84 4.57 Mode selector verification results for Scenario 1. . . . . . . . . . . . . 85 4.58 Mode selector verification results for Scenario 2. . . . . . . . . . . . . 85 4.59 Mode selector verification results for Scenario 3. . . . . . . . . . . . . 86 4.60 Comparison of lift-to-drag ratio (CL/CD) for varying aircraft speed from aircraft model and baseline data. . . . . . . . . . . . . . . . . . 86 4.61 Comparison of propeller efficiency of Electrical Propulsion System model and and baseline data. . . . . . . . . . . . . . . . . . . . . . . 87 5.1 Pre-flight mission simulation model. . . . . . . . . . . . . . . . . . . . 92 5.2 Weather Model mask which facilitates the user to specify atmospheric conditions for the simulation. . . . . . . . . . . . . . . . . . . . . . . 93 5.3 Mission Planner mask which facilitates the user to generate mission profiles for the simulation. . . . . . . . . . . . . . . . . . . . . . . . . 93 5.4 Enabling and specifying parameters for a go-around scenario. . . . . . 94 5.5 The altitude profile as the preview result of the generated mission profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 5.6 Mode Selector mask for mission profile without go-around scenario. . 95 5.7 The altitude profile and mode schedule previewed by the Mode Se- lector mask. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 5.8 Mode Selector mask for mission profile with a Go-Around scenario. . 97 5.9 The altitude profile and mode schedule previewed by Mode Selector mask for a mission profile with a go-around scenario. . . . . . . . . . 98 5.10 The mask of the Aircraft Model. . . . . . . . . . . . . . . . . . . . . . 98 5.11 Typical mission simulation results: Mission Profile . . . . . . . . . . . 100 5.12 Hybrid aircraft typical mission simulation results: Mode Schedule . . 102 5.13 Hybrid aircraft typical mission simulation results: Ambient Parameters103 5.14 Hybrid aircraft typical mission simulation results: Thrust . . . . . . . 104 5.15 Hybrid aircraft typical mission simulation results: Power . . . . . . . 106 5.16 Hybrid aircraft typical mission simulation results: Fuel-on-Board . . . 107 5.17 Hybrid aircraft typical mission simulation results: Aircraft Weight . . 107 5.18 Hybrid aircraft mission simulation results: Battery SoC . . . . . . . . 108 5.19 Hybrid aircraft typical mission simulation results: PBU Parameters . 109 5.20 Hybrid aircraft typical mission simulation results: Turbine Engine Operating Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 5.21 Hybrid aircraft typical mission simulation results: PMSM Operating Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 xix List of Figures 5.22 Hybrid aircraft typical mission simulation results: Propeller Operat- ing Point Efficiencies. . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 5.23 Comparison typical mission simulation results against baseline mis- sion data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 5.24 Cruise altitude survey: Mission profile. . . . . . . . . . . . . . . . . . 114 5.25 Cruise altitude survey: OAT and air density ambient parameters. . . 115 5.26 Cruise altitude survey: Aircraft-level required thrust and propulsive power. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 5.27 Cruise altitude survey: PBU SoC and FoB. . . . . . . . . . . . . . . . 117 5.28 Cruise altitude survey: Turbine engine fuel consumption. . . . . . . . 118 5.29 Cruise altitude survey: PBU SoC and FoB at the end of flight for different cruise altitudes. . . . . . . . . . . . . . . . . . . . . . . . . . 118 5.30 Cruise speed survey: Mission profile. . . . . . . . . . . . . . . . . . . 119 5.31 Cruise speed survey: Aircraft-level required thrust and propulsive power. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 5.32 Cruise speed survey: PBU SoC and remaining FoB. . . . . . . . . . . 121 5.33 Cruise speed survey: Turbine engine fuel consumption. . . . . . . . . 121 5.34 Cruise speed survey: PBU SoC and FoB at the end of flight for dif- ferent cruise speeds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 5.35 Impact of accounting for varying weight: Aircraft weight. . . . . . . . 123 5.36 Impact of accounting for varying weight: Aircraft-level thrust re- quired and propulsive power required. . . . . . . . . . . . . . . . . . . 123 5.37 Impact of accounting for varying weight: PBU SoC. . . . . . . . . . . 124 5.38 Impact of accounting for varying weight: Fuel onboard. . . . . . . . . 124 5.39 Impact of headwind: Mission profile. . . . . . . . . . . . . . . . . . . 125 5.40 Impact of headwind: Aircraft-level required thrust and propulsive power. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 5.41 Impact of Headwind: SoC and FoB. . . . . . . . . . . . . . . . . . . . 127 5.42 Impact of DISA: Mission Profile. . . . . . . . . . . . . . . . . . . . . 128 5.43 Impact of DISA: OAT and Air Density. . . . . . . . . . . . . . . . . . 129 5.44 Impact of DISA: Aircraft-level thrust and propulsive power. . . . . . 130 5.45 Impact of DISA: SoC and FoB. . . . . . . . . . . . . . . . . . . . . . 131 5.46 Impact of QNH: Mission Profile. . . . . . . . . . . . . . . . . . . . . . 132 5.47 Impact of QNH: Ambient parameters. . . . . . . . . . . . . . . . . . . 133 5.48 Impact of QNH: Aircraft-level required thrust and propulsive power. . 134 5.49 Impact of QNH: SoC and FoB. . . . . . . . . . . . . . . . . . . . . . 134 5.50 Simulation results with with user specified mode schedule. . . . . . . 136 5.51 Control and state trajectories results from the DP based optimization algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 5.52 The optimal state trajectory in the state-space of SoC, FoB and time. 139 5.53 SoE evolution with optimal mode schedule from DP-based optimiza- tion algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 5.54 Simulation results for different mission profiles with DP-based opti- mal mode schedules with SoCfinal,min = 30%. . . . . . . . . . . . . . . 141 5.55 DP-based optimization results for control and SoC trajectories for varying kp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 xx List of Tables 3.1 ISA atmospheric conditions. . . . . . . . . . . . . . . . . . . . . . . . 21 4.1 Input parameters of the mission planner. . . . . . . . . . . . . . . . . 45 4.2 Signals in the FPData signal-bus output from Mission Planner. . . . . 49 4.3 Input Parameters for the Weather Model . . . . . . . . . . . . . . . . 50 4.4 Ambient parameter signals from the Weather Model. . . . . . . . . . 50 4.5 Input Parameters for the Aircraft Model . . . . . . . . . . . . . . . . 55 4.6 Input Parameters for the PBU Model . . . . . . . . . . . . . . . . . . 78 5.1 Buttons for generating simulation results in the simulation model and the corresponding plots. . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.2 Parameter values used for the hybrid aircraft typical mission simulation.100 5.3 ES-30 typical mission flight times for different wind conditions. . . . . 126 5.4 End of flight SoC and FoB values for the ES-30 typical mission under different wind conditions. . . . . . . . . . . . . . . . . . . . . . . . . . 128 5.5 ES-30 typical mission flight times for different DISA values. . . . . . 129 5.6 End of flight SoC and FoB values for the ES-30 typical mission under different temperature DISA conditions. . . . . . . . . . . . . . . . . . 131 5.7 End of flight SoC and FoB values for the typical mission under dif- ferent QNH conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . 135 5.8 Initial parameter values for the simulation to analyze DP-based op- timization algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 5.9 Discretization parameters for the DP solver. . . . . . . . . . . . . . . 137 5.10 Processing times for the DP-based optimization for different missions. 142 xxi List of Tables xxii 1 Introduction 1.1 Background The air transportation sector continues to be a fundamental element of the global economy, serving both passenger and cargo transportation and it experiences rapid expansion. The latest figures in January 2024 indicate an increase of total passenger traffic by 16.6% year-on-year revenue-passenger kilometers, and marks a remarkable resilience reaching 95.7% of pre-pandemic figures[1]. This demonstrates a strong recovery and suggests a bright future for the sector, underscoring its ability to meet and potentially exceed previous air passenger traffic projections. This data sug- gests that the air transportation is rapidly expanding in direct correlation with the growing demand. However, it accounts for approximately 2.5% of global CO2 emissions, and it is predicted to increase with the high demand and the annual growth of the aviation industry[2] [3]. The contribution of emissions from short-to- medium-haul flights is significant due to their high fuel consumption per passenger kilometer[4]. These flights need attention and innovative solutions within the avia- tion sector to mitigate their substantial carbon footprint[4]. To mitigate the impact of air transportation on the environment, challenging goals have been set by the Advisory Council for Aviation Research and Innovation in Europe (ACARE). As per the ACARE’s Flightpath 2050 Europe’s Vision for a clean sky program, a 75% reduction of CO2 emissions per passenger kilometer, a 90% reduction in NO× emis- sions, and a 65% reduction in the perceived noise emission are to be achieved by 2050[5]. To meet these emission reduction goals, several futuristic electric aircraft concepts have been proposed by industry leaders, academia, governmental bodies, and start up companies[3]. They have employed different technologies such as electric verti- cal takeoff and landing (eVTOL) and fixed-wing all-electric and fixed-wing hybrid- aircraft, and are expected to enter service at different time frames. Although all- electric airplanes offer benefits, including zero CO2 emissions, low noise, and low operational costs, there are many challenges to overcome to produce all-electric air- planes that can meet the needs of commercial aviation. One of the main factors preventing developments of the all-electric commercial airplanes is the limited en- ergy density of today’s battery technology. In addition to that, the current electric motor technology also has limitations to overcome. Studies show that motors need to achieve specific power densities over 20kW/kg with efficiencies greater than 96% to realize commercially viable all-electric airplanes[6]. These are technically chal- lenging targets and therefore, all-electric airplanes cannot match the range of fossil 1 1. Introduction fuel-driven commercial airplanes with the current technology. The hybrid-electric airplanes have gained attention as they can leverage the ben- efits of both electric and fossil-fuel driven technologies. Hybrid-electric airplanes can achieve a fraction of the CO2 emission goals while addressing the range limi- tations inherent to all-electric airplanes. Hybrid-electric airplanes use two or more energy sources with different configurations to power the propulsion systems of the airplanes[7]. The multiple sources of energy in the propulsion systems in the hybrid- electric airplanes results in added complexities, especially in terms of energy manage- ment. Optimal management of hybrid-energy for a flight mission ensuring minimum emissions, maintaining required energy reserves without compromising the safety of the flight is a complex problem[8]. 1.2 Heart Aerospace and ES-30 Aircraft Heart Aerospace, a startup company based in Gothenburg, Sweden, is committed to transform the future of air travel with the mission to decarbonize and democra- tize air travel. Heart Aerospace aims not only to lower the emissions, but to make flying accessible for the many around the world by unlocking cheaper, convenient and effective regional air travel. Since, the hybrid-electric airplanes are cheaper to operate, they will enable increased connectivity by reopening routes that were pre- viously unprofitable with conventional fossil-fuel based aircraft. They aim to cut greenhouse gas emissions by 20% to 95% in short-haul flights that currently con- tributes to one-third of the aviation industry’s emissions. Heart Aerospace is developing ES-30, a 30 seat regional hybrid-electric aircraft aim- ing to enter the market around 2030. The ES-30 offers 200km all-electric range and optimized hybrid-electric range up to 400km with full passenger capacity. It has the capability to extend range up to 800km with reduced passenger capacity of 25 providing, airlines with greater operational flexibility. The turnaround time for the ES-30 is expected to be 30 minutes with fast charging capability while the runway length needed for operating ES-30 is 1100m. The ES-30 consists of two electric propulsion units mounted in-board on the wing and two small turboprop engines mounted out-board on the wing, in a novel inde- pendent hybrid propulsion architecture as shown in Figure(1.1). The primary source of energy for ES-30 is the electric energy, and fuel is used for reserve and range ex- tension purposes. The turboprop engines compatible with Sustainable Aviation Fuel (SAF) reduce the carbon footprint of ES-30 in the extended range missions. ES-30 can perform low-noise takeoffs and landings reducing the sound pollution near air- ports. Additional to these advantages, the low electricity cost compared to jet-fuel and low maintenance cost of electric motors offer lower operating costs for the air- lines. 2 1. Introduction Figure 1.1: Heart Aerospace ES-30 hybrid-electric regional aircraft. 1.3 Purpose, Scope and Contribution The purpose of this project is to develop the concept of energy management in ES- 30 hybrid-electric aircraft. This work involves the concept development of energy management functions for the ES-30 and defining the functional interfaces for them. The energy management function for ES-30 encompasses various functions includ- ing pre-flight and in-flight functions. The primary emphasis of this project was on the pre-flight energy management function of ES-30, and the scope of the work was narrowed down to the pre-flight estimation of state-of-energy (SoE) of the ES-30 aircraft for a given mission. The main contribution from this work lies in the development and verification of the comprehensive simulation model that focuses the pre-flight estimation of the SoE in ES-30 aircraft for given flight mission. While this simulation model can aid in the development of energy management related Flight Management System (FMS) functions, it also can serve as an aircraft performance model for analyzing and eval- uating the energy management strategies specific to the ES-30 aircraft. What sets this simulation model apart from existing literature is its multi-disciplinary approach which accounts for the varying aircraft weight and atmospheric conditions. The sim- ulation model is designed to be modular and flexible, allowing for future adaptations based on company requirements. Numerous simulation analyses were conducted and presented, revealing the impact of different weather parameters, aircraft weight on the aircraft state-of-energy (SoE). Further, simulation based analysis results to find optimal cruise altitude and cruise speed for different goals such as minimum time en-route, minimum fuel consumption and minimum battery energy consumption is presented. Additionally, an optimal energy management strategy based on Dynamic Program- ming (DP) is proposed for ES-30. The algorithm determines the most effective 3 1. Introduction operation mode profile for a given flight mission, ensuring that the specified reserves remain intact with minimum fuel consumption. The performance of this energy management strategy is analysed using the developed simulation model for various flight missions. 1.4 Thesis Outline The Section 2 comprises of a detailed literature survey, which summarizes different simulation models and techniques found in the literature related to the interested problem, followed by different the energy management strategies used in hybrid- electric aircraft. The Section 3 presents the theoretical background arranged in different topics. The readers can enhance their knowledge about different areas including aircraft FMS, simulation approaches, aviation weather conditions, aircraft performance and dy- namics, aircraft propulsion systems and system modeling techniques followed by theory related to Dynamic Programming (DP) based optimization. Section 4 explains the steps followed, and techniques used in modeling the different system models of the simulation model. This includes the modeling architecture for each model, considered input and output signals along with the practical aspect of modeling different system models. Additionally, it presents the verification process and the corresponding results. At last, the problem formulation for DP based energy management strategy is explained. Section 5 starts with presenting the obtained simulation model, and an explanation of the readily available plots from the simulation model. Then, the various simula- tions and the obtained simulation results are presented, also the findings from the simulation results are discussed. Finally, the DP based optimal energy management related results are presented and discussed. Finally, Section 6 summarizes the outcomes of the thesis highlighting the main find- ings and offers suggestions for future work. ** Due to confidentiality reasons and at the company’s request, sensitive informa- tion has been replaced with the placeholder "x", and the axes containing sensitive information in the diagrams have been obscured ** 1.5 Ethics Reducing the impact of air transportation on the environment stands as a primary goal for the entire ES-30 project and the company. The successful outcome of this project will contribute to Heart Aerospace’s overarching mission: to create the world’s greenest, most affordable, and most accessible form of transportation. This project exposes the team members to sensitive information and intellectual properties (IP) of Heart Aerospace. These sensitive information will be handled with utmost care throughout the project. Our approach throughout the project 4 1. Introduction will demonstrate integrity in all aspects, and the scientific research and information sources used in our project work will be diligently cited, credited, and acknowledged. 5 1. Introduction 6 2 Literature Survey A comprehensive literature survey was conducted to explore the state of the art and available simulation tools for estimating the SoE in hybrid aircraft. Additionally the literature survey was expanded to study the energy management strategies employed in hybrid aircraft. 2.1 Simulation Tools for Hybrid Aircraft With the increased interest in hybrid-electric aircraft in recent years, there is strong interest in research and development of tools and method for different purposes from analysing and quantifying fuel saving potential to design space exploration in hybrid electric aircraft. A physics-based simulation platform has been developed by Zhao et al. for design, optimization and analysis of hybrid aircraft [9]. This platform uses comprehensive gas turbine performance models based on thermodynamic models. The electrical power system consists of electrical machine, power electronics converter and battery models. The mission model in the platform defines the flight profile trajectory in terms of altitude and Mach number. Further, it consists of an aircraft structural model and a thermal management system models. The platform is developed in Python environment and the platform has been able to analyse trade-offs between sizing and performance characteristics of different subsystems and also many pa- rameters including state of charge of the battery and gas turbine related efficiencies and losses in different sections of the turbine engines. Cameretti et al. developed a code based model to simulate a flight mission for a turboprop based aircraft with two other gas turbines in hybrid configuration [10]. Numerical investigations have been conducted using a commercial code for the flight simulation initially, followed by MATLAB based optimization for calculating battery pack weight. The turbine engine modelling has been done considering the thermo- dynamic cycle of turbine engine. The lack of public information for turbine engine components performance maps had been a challenge. Specific fuel consumption map has been used to determine the fuel consumption of the turbine engines. The simu- lation is based on the mission profile derived from a commercial flight information extracted from Flightradar24 and the considered parameters for the mission pro- file were altitude and speed versus time. The power profile was calculated through mechanical flight equations implemented in MATLAB considering the altitude and 7 2. Literature Survey speed profile along with aerodynamic data of ATR42-300 aircraft. This model could compare fuel consumption and emissions for the hybrid configuration. Modelica based flexible and modular, hybrid-electric aircraft modeling architecture has been developed by Batteh et al. to be used in virtual and physical demonstrator system, National Research Council of Canada (NRC) [11]. This architecture uses multi-physics component models to describe the performance and dynamics of the different systems in hybrid-aircraft. The Aircraft Dynamics Library in Modelon has been extensively utilized for the implementation of the models. 6DOF representa- tion of the aircraft dynamics has been used with a simplified high level turboprop surrogate model as the power train. Analyses on integrated electric aircraft perfor- mance has been conducted using Modelon libraries and extended range of mission profiles including takeoffs and landing has been simulated. This model could sim- ulate and the energy consumption as well as the dynamics of the aircraft and and also the aircraft-sub systems. PLAtform for New Environment-friendly Solutions (PLA.N.E.S), a simulation soft- ware for assessing performance, environmental impact and advanced configurations have been developed and validated by Donateo et al [12]. The simulation is based on backward paradigm also know as inverse simulation approach where the flight mission is assumed to be known, and the instantaneous power required and the cor- responding fuel consumption is calculated. PLA.N.E.S consists of many power-train configurations to be chosen by the user including conventional, all-electric, different hybrid configurations etc. Further the platform consists of series of blocks for mis- sion generation, simulation, post processing and optimization. PLA.N.E.S has been applied to a medium altitude medium endurance unmanned aerial vehicle as a case study [12]. A simulation tool has been developed to analyse the mission performance of regional hybrid-electric aircraft dynamics by Palaia et al. [13]. A point-mass model has been used to model the aircraft dynamics in the longitudinal plane of the aircraft. The simulation have been conducted for a parallel hybrid-electric power-train architec- ture where thermal engine and electric motor can independently supply power to the same propeller. Power management strategy have been considered where the power required to fly the aircraft have been spllited between the thermal engine and the electric motor. Average constant efficiency values for propeller efficiency and gear efficiency have been used for computing the required power. The analy- sis results obtained by the simulation for parallel hybrid aircraft configuration has shown considerable potential in terms of reduction of fuel consumption. Further the simulation results from this tool has given insights into operational envelopes as a function of number of passengers and aircraft range. Mission, Aircraft and System Simulation (MASS), a modular and parametric tool chain has been developed for analysing the performance of hybrid-electric aircraft for a given reference mission under European Union’s Horizon 2020 research and innovation program [14]. The parametric analysis tool chain allows for performance 8 2. Literature Survey analysis of hybrid-electric aircraft and also it allows sensitivity analysis and opti- mization studies to support conceptual and multi-disciplinary aircraft design with hybrid-electric propulsion systems. Longitudinal flight path without turning move- ments are assumed and the aircraft point-mass model considering the longitudi- nal movement of the aircraft has been implemented within MATLAB environment. Mission model in the tool chain reads a pre-defined table with altitude, speed, flap and landing gear setting as a function of horizontal distance. The aircraft model computes the required thrust from the flight path variables and the corresponding aerodynamic coefficients based on flaps and landing gear setting. A simulation study has been performed for an Airbus A320neo reference aircraft and parameters such as fuel consumption and total energy consumption have been analysed. Most of the simulation approaches rely on constant efficiency values derived from an average operating point approach for modeling the propeller, motor and turbine engine performance [14] [13]. Further, the mission profiles considered in most of the simulation tools are simplified mission profiles considering altitude and speed of the aircraft [10] as the primary flight path variables. It is crucial to recognize that the ambient conditions play a significant role in flight operations. Factors such as headwind component and ambient temperature can profoundly affect both aircraft and propulsion system performance. However, the ambient parameters have often been overlooked in the existing simulation tools available in the literature. The simulation model proposed in this work possesses the capability to generate a detailed mission profile that closely align with the ES-30 hybrid-electric aircraft missions. Detailed performance maps provided by the company are used to model various sub-systems to ensure that the model captures the real-world system per- formance as close as possible. Further, a weather model has been implemented to provide accurate ambient parameters for the simulation, effectively addressing a current research gap. 2.2 Energy Management in Hybrid Aircraft Hybrid-electric aircraft in contrast to a conventional aircraft has extra degree of freedom in delivering the requested propulsion power as it has multiple sources of energy onboard. Energy management in a hybrid-aircraft is managing these multi- ple energy sources during a mission, fulfilling operational and safety requirements while the ensuring the energy sources operate within their limits [15]. Many energy management strategies have been explored in the hybrid-electric vehicle context, and these methods have been adopted for energy management in the hybrid-electric aircraft. The main energy management strategies found in literature can be divided into two, which are rule-based and optimization-based energy management strategies. The rule-based energy management strategies rely on control schemes governed by predefined rules and operational modes. These rules are determined by the ex- perts considering the performance characteristics and limitations of the different 9 2. Literature Survey propulsion systems. These rules are implemented in supervisory controllers in the form of state-machines, look-up tables or similar. The rule-based strategies take instantaneous power requests and other relevant parameters as inputs, providing corresponding outputs based on these input parameters. Notably, rule-based strate- gies focus solely on instantaneous inputs. Therefore, the rule-based strategies often do not require knowledge about the future trajectory of the aircraft to take control decision at the present moment. When optimization techniques are used for the energy management strategies, they are referred to as optimal energy management strategies. One such well-known strat- egy is the Equivalent Consumption Minimization Strategy (ECMS), which relies on an instantaneous cost function. The primary objective of ECMS is to minimize energy consumption by identifying local minima among all feasible instantaneous operating points for both electric and fuel engines. The cost function in ECMS in hybrid-electric context introduces a equivalence factor which converts electrical en- ergy consumption into equivalent fuel consumption to unify the electric energy and fuel consumption to be used in the cost function. As ECMS solves a local instanta- neous optimization problem, this method is suitable for online application such as in-flight energy optimization as it is computationally efficient. Dynamic Programming (DP) is a numerical optimization method based on Bell- man’s principle of optimality [16]. The DP algorithms are widely used in energy management problems to provide global optimal solution. The application of DP for energy management problem in hybrid electric aircraft has been investigated for parallel hybrid-electric Unmanned Air Vehicle(UAV) [17]. This algorithm optimizes power management and torque-split of the hybrid power-train while considering final state constraints on state variables. Applying DP algorithm for energy management in fuel-cell powered hybrid-electric aircraft has been studied accounting the varying aircraft weight into consideration [18]. An aircraft performance model has been used along with DP algorithm to find the optimal energy management strategy for an aircraft flying an pre-defined trajectory. A method to determine the optimal energy management for hybrid aircraft has been studied considering the battery State-of- charge (SoC) and aircraft weight as the states of the system [19]. Further optimal strategies with constrained and unconstrained final SoC targets have been explored. Comparison results of DP algorithm with other energy management strategies has shown DP performs superior in terms of minimum fuel consumption objective. While the DP algorithm requires the mission profile to be known a priori, the com- putational cost increases exponentially with the number of states of the problem, which is often referred to as "the curse of dimensionality". Although these charac- teristics of DP algorithm often hinders the usage of DP for real-time applications, DP based algorithms can be used for development and performance evaluation of the rule-based strategies as it provides globally optimal solution. 10 3 Theory 3.1 Flight Management System and Energy Man- agement in Hybrid Aircraft Flight Management System (FMS) plays a pivotal role in modern aircraft avionics. It seamlessly automates a wide variety of pre-flight and in-flight tasks related to planning, navigation and performance. By handling these responsibilities, the FMS significantly reduces the workload on the flight crew. The FMS receives inputs from various sources, perform computations related to various aspects of an entire flight and delivers accurate information to the flight crew or control commands to the aircraft systems ensuring both safety and operational efficiency of the flight [20]. Some of the typical functions of a FMS in a conventional aircraft are, 1. Flight profile planning and optimization 2. Providing aircraft performance information 3. Determining flight routes for the aircraft to achieve strategic goals 4. Guiding the aircraft along the computed flight profile and monitoring 5. Deriving the optimal speed and altitude based on accumulated performance data From a system perspective, the FMS comprises several interconnected systems and components, each playing a crucial role. Among these, the following can be consid- ered the main components. 1. Flight Management Computer (FMC): The FMC serves as the central brain for the FMS where it handles multitude of critical computations relevant to the flight such as performance computation, fuel and energy management related computations, flightpath adjustment con- sidering the weather, wind and other relevant parameters. 2. Automatic Flight Guidance System (AFGS): AFGS is an integral part of the FMS and it is responsible for executing the computed flight path. In the modern aircraft, the FMS can compute four dimensional flight path (longitude, latitude, altitude and time), and do the necessary changes to the flight path via AFGS. It maintains precise control during various flight phases from takeoff to landing. Further, at any time the FMS commands can be overruled by the pilots using Flight Control Unit(FCU) 11 3. Theory or flying the aircraft manually. 3. Navigation Systems: The FMS can perform navigation related computations for an entire flight mis- sion from departure airport to the destination via waypoints, using airports databases and navigational aids also supplemented by various sensor inputs. 4. Electronic Flight Instrument System (EFIS): The EFIS serves as the human-machine interface within the aircraft cock- pit. In a simple general aviation aircraft the EFIS can be one or few dis- plays or interfaces while the EFIS is a modern airliner can comprise of a wide variety of displays and instruments. The main components of an EFIS are Primary Flight Displays(PFD), Multi-Function Displays(MFD), Engine Indi- cation and Crew Alerting System (EICAS) and Multi-purpose Control and Display Units(MCDU). With the current advancement of avionics, most of these can feature touch-screens combining display and control functions and serve multi-purpose. As shown in Figure(3.1), the different avionics are distributed throughout the cockpit, interfaced together to work hand-in-hand to serve the FMS functions. Figure 3.1: Illustration of ES-30 cockpit avionics suite. In the context of hybrid-electric aircraft, certain functions of the FMS take on greater prominence and complexity as the hybrid-electric aircraft uses multiple en- ergy sources. The FMS must intelligently manage these diverse energy sources to optimize the performance and efficiency of the flight. A conceptual interface block diagram indicating the interfacing of different systems and components to form the FMS in a hybrid-electric aircraft is depicted in Figure(3.2). 12 3. Theory Figure 3.2: Conceptual interface block diagram for FMS in hybrid-electric aircraft. With the added complexities due to multiple energy sources, the FMS in a hybrid aircraft should serve more functionalities to reduce the workload of the pilots. The following key functions related to energy management becomes more prominent in the FMS in the context of the hybrid-electric aircraft. 1. Estimation of Available Energy Onboard Aircraft: Available energy levels and the resulting range and endurance information are crucial for safe operation of a flight. Estimating these parameters with multi- ple energy sources is a challenging task as these parameters vary with power demand, modes of operation, weather parameters etc. The FMS should con- sider all these factors and provide accurate estimations for energy levels and the resulting range and endurance information to flight crew both pre-flight and in-flight. 2. Mission Planning and Optimal Flight Strategy: The FMS should plan the flight mission, considering both conventional and electric energy sources and it should determine the optimal operation mode schedule for optimal energy utilization of the aircraft considering factors such as available energy levels, weather conditions etc. It should also ensure the aircraft systems operate within their limits throughout the flight without de- pleting its energy reserves. 3. Target-Progress Performance Calculation: The FMS should compute the flight performance related information, includ- ing the takeoff speeds, distances, climb rates, cruise speeds, power levels and other relevant performance parameters. There could be changes to the original flight plans due to changed weather conditions, in-flight diversions, air traffic 13 3. Theory control(ATC) requests and similar. Nevertheless, the FMS should perform the necessarily corrections and re-computations during the flight to accurately estimate the remaining energy onboard and the resulting range and endurance information. Furthermore, FMS may suggest optimal airspeed, altitude which optimize the overall energy consumption or to achieve specific performance goals such as minimum-time en-route, minimum fuel consumption or mini- mum battery energy consumption. The combination of these functions along with many others, constitutes the energy management function of the FMS in hybrid aircraft. Notably, estimating the State of Energy (SOE) for a flight mission both pre-flight and in-flight, holds paramount importance within the energy management function of FMS in hybrid aircraft. 3.2 Aircraft Mission Profile Figure 3.3: Aircraft mission profile Figure(3.3) depicts the main flight segments for a typical aircraft mission. Taxi-out: The taxi-out phase refers to the segment where the aircraft moves from the gate or parking area to the runway for takeoff. Take-off roll: Take-off roll is the phase where the aircraft gradually acceler- ates to the lift-off and climb-out speeds along the runway. The pilot smoothly advances the throttle to takeoff position and maintains the directional control with rudder pedals while accelerating. Normally the takeoffs are made nearly into the wind for two reasons. First, the aircraft already have some of true airspeed in headwind even before start moving hence the lift-off is quick. Sec- ond, the headwind results lower ground speed hence the aircraft uses shorter runway length before the lift-off and also in case of a rejected take-off, it is more easy for the aircraft to come to a stop in headwind. Initial climb: The initial ascent after take-off until circuit height of 1500ft AGL. Typically after lift-off, the aircraft is accelerated to VY , the speed result- ing a the best rate-of-climb (RoC). This is the speed at which the aircraft gains 14 3. Theory the most altitude in the shortest period of time. In case of obstacle clearance after take-off, VX also known as best angle-of-climb speed is maintained until the obstacle is cleared. VX is the speed which results the maximum altitude gain in the minimum longitudinal distance. Typically aircraft configuration changes such as landing gear retraction, flap retraction from takeoff flap setting and reducing the aircraft throttle from takeoff to climb setting are performed in this phase to prepare the aircraft for the climb. Climb: In the climb segment, the aircraft gradually ascents to the cruising altitude. Depending on the ATC, climb is normally performed at an shallow angle of climb with an higher airspeed, which is comfortable for the passengers onboard and also economical for the aircraft. The top-of-climb (ToC) is the point where the climb segment finishes and the cruise segment starts. At this point the aircraft attitude is changed from climb to cruise flight and accelera- tion to the cruise speed is also typical in flight missions. Cruise: The level flight at the designated cruising altitude during the main portion of the journey. The cruising is done at an altitude which is most ef- ficient for the aircraft operation. Many factors are considered to decide the cruise altitude such as wind direction, ATC requests, fuel efficiency at altitude and trip distance etc. The last point where the cruise segment finishes and the descent segment starts is called the top-of-descent (ToD). At this point the aircraft typically decelerates to the descent speed and prepares for the descent. Descent: The gradual descent from cruise altitude to circuit height typically 1500ft AGL. This segment typically requires less power as the aircraft converts its potential energy into kinetic energy during the descent. Approach: The descent to the destination airport, aligning with the runway for landing. Typically, the aircraft configuration changes such as landing gear deployment, changing flaps to landing setting and decelerating the aircraft to its approach and landing speed occurs within this segment. Due to the extra drag force created by the configuration changes may require higher power to maintain flight. Landing roll: This is the period the aircraft decelerates to a stop or exit the runway after touchdown on the runway. Typically aircraft use brakes with supplemented by high drag surfaces such as spoilers to slowdown the aircraft. Aircraft with variable propeller pitch can operate the propellers in beta range to slow down the aircraft. Taxi-in: The movement of the aircraft from the runway to the gate or parking area after landing. Missed approach: In case of a rejected landing, the aircraft performs a go- around and climbs back up. This is a intense phase of flight where the pilots 15 3. Theory use maximum thrust or power available. The reason for this is the aircraft approaching in its approach configuration with high drag configuration should change its attitude and gain altitude as well as airspeed as quick as possible. Climb to alternate cruise altitude: In case of diversion, the climb to an alternate cruising altitude for en-route to the alternate airport. Holding: Due to reasons such as ATC requests, traffic congestion, poor weather or similar the aircraft delays from proceeding on course and keeps flying in a holding pattern. The Typical Mission of the ES-30 aircraft is a reference mission defined to evaluate the aircraft and system performance of the ES-30. This mission is focused for a short-haul regional flight mission and comprises of the different flight phases de- scribed above. The typical mission is regarded as the baseline mission for energy management related performance analysis. 3.3 ES-30 Propulsion System Architecture The ES-30 propulsion system architecture comprises of a novel independent hybrid propulsion architecture and the high-level architecture is Illustrated in Figure 3.4. Figure 3.4: ES-30 independent hybrid propulsion architecture. Throttle Lever Angle (TLA): TLA refers to command for the propulsion system from the throttle quadrant, Auto Flight Control (AFC) or the FMS. This command corresponds to the aircraft-level requested thrust from the aircraft propulsion system and the TLA is an input for the master controller. 16 3. Theory Master Controller: The master controller serves as the supervisory controller of the ES-30 propulsion system. This system has various functions including supervisory control of the dif- ferent propulsion units in the aircraft. Based on the TLA request, different mode of operations and SoE of the aircraft, master controller is responsible for commanding the local controllers of the electrical propulsion system and turbine engine propulsion system to ensure the requested thrust or power is consistently available throughout the entire aircraft mission. Additionally, master controller plays an integral role in energy management, working in conjunction with the FMS. Electrical Propulsion System: The Electrical Propulsion System of the ES-30 encompasses a comprehensive suite of components necessary for electrical propulsion. These include electric motors, propellers, inverters and power electronics, and Electrical Propulsion Actuation and Control System. The Electrical Propulsion System relies on electric motors to drive the propellers, providing the thrust for the aircraft while the required electrical en- ergy is supplied from the Propulsion Battery. The Local controller serves as the local controller for the Electrical Propulsion System, responsible for the simultane- ous coordination of motors and propellers to ensure the delivery of requested thrust by the master controller. It sends motor speed commands to the motor controllers and adjusts the propeller pitch through the propeller controllers. They work as closed-loop controllers, continuously monitoring sensor readings related to motor speed, torque and propeller pitch parameters and these parameters are strategically optimized to maximize operational efficiency throughout each phase of flight. Turbine Engine Propulsion System (TES): The TES consists of the turbine engines, propeller systems and the Full Authority Digital Engine Control (FADEC). This system is managed by FADEC to ensure optimal performance and efficiency throughout the aircraft operation. FADEC is an advanced control system that manages all aspects of turbine engine entirely through electronic means. This system is typically equipped with dual redundancy for enhanced reliability; it can operate with two identical channels to maintain full functionality even if one fails, or it can operate on a single channel backed up by a simplified electronic or hydro-mechanical system for continued operation under alternative modes [21]. 3.4 Forward and Inverse Simulation Approaches The forward simulation approach, also known as dynamic simulation for an air- craft, relies on a mathematical representation of the problem. In this approach, the various aircraft systems are modeled using sets of ordinary differential equations. These equations capture the underlying physics and dynamics of the aircraft. The kinematics of the aircraft, which encompass flight-path parameters like speed, ac- celeration, and the flight-path angle are the result of the balance of aerodynamic, gravitational, and propulsive forces [12]. A block diagram illustrating the workflow 17 3. Theory of the dynamic simulation approach for an aircraft is shown in Figure(3.5). Figure 3.5: Simulation workflow in forward simulation approach for an aircraft. Essentially, this approach determines the flight profile of the aircraft based on in- puts such as pilot commands, the performance capabilities of the propulsion system, and the external forces acting on the aircraft. The forward simulation approach is widely used for analysing the control and stability aspects of the aircraft. While the forward simulation approach provides valuable insights into the dynamic behavior of the aircraft, it does come with certain limitations. High complexity and significant computational costs are drawbacks associated with this method. The inverse simulation approach also known as the backward simulation is based on the concept of quasi-static process. In the quasi-static process, the system of interest is considered to be driven very slowly such that any transient dynamics are not engaged. For an aircraft, the inverse simulation is based on the mission profile of the aircraft, which encompasses the aircraft’s kinematics defined by the flight-path variables. The total simulation time is considered to be a combination of sequence of very short time intervals. Within each time interval, the flight- path parameters of the aircraft are considered to remain constant. The thrust required for the aircraft is computed using the flight-path parameters, aerodynamic and force balance. Subsequently, the power requirements and energy consumption are determined. The simulation workflow for inverse simulation approach is shown in Figure(3.6). Figure 3.6: Simulation workflow in inverse simulation approach for an aircraft. The mission profile has to be predefined for the inverse simulation approach to work effectively. This is quite common and suitable for aircraft mission simulations as the flight missions are known in advance for most of the commercial aircraft missions. These characteristics of the inverse simulation combined with the updated aircraft weight considered in each time-step, makes it suitable for analysis of energy consumption in aircraft missions. 18 3. Theory 3.5 Hybrid-electric Propulsion Architectures The integration of electric and fuel-based propulsion systems has led to the de- velopment of various hybrid-electric propulsion architectures in aviation. These configurations leverage different electric technologies, including batteries, motors, and generators. Six key hybrid-electric propulsion architectures identified in the literature are illustrated in Figure(3.7) [22]. (a) All Electric (b) Parallel Hybrid (c) Series Hybrid (d) Series/Parallel Partial Hybrid (e) Fully Turbo-electric (f) Partially Turbo-electric Figure 3.7: Aircraft Hybrid-electric Propulsion Architectures. The all-electric propulsion architecture employs batteries as the only source of propulsion power for the aircraft as shown in Figure (3.7a), exclusively relying on them to drive electric motors and generate thrust throughout every phase of flight. Primarily suited for smaller aircraft like general aviation and commuter planes, all- electric systems offer a cleaner, quieter, and more environmentally friendly alterna- tive to conventional propulsion methods. In a parallel hybrid system, a combination of battery-powered electric motors and turbofan(TF) engines work in tandem to propel the aircraft. Both the electric motors and the turbofan engine are mounted on a shared shaft that drives the fan,as shown in Figure (3.7b). This configuration 19 3. Theory allows for seamless transition between the two power sources, with either or both providing propulsion as needed during different flight conditions. Series hybrid propulsion systems distinguish themselves by mechanically separating the turbo-shaft(TS) engine from the propulsive fans. Instead of directly driving the fans, the turbine engine powers an electrical generator, which then supplies electric- ity to the onboard motors, Figure (3.7c). These electric motors, in turn, drive the fans and/or recharge the batteries. Series hybrid configurations enable distributed propulsion concepts, utilizing multiple small motors and fans for enhanced efficiency and maneuverability. The series/parallel partial hybrid system combines elements of both series and parallel configurations. It features fans that can be directly driven by a turbofan engine, as well as additional fans exclusively powered by electric motors, Figure (3.7d). These motors can draw energy from either a battery or a turbine-driven generator. This hybrid approach maximizes propulsion efficiency by leveraging the benefits of both electric and gas turbine power sources. Fully turbo-electric systems rely entirely on turbo-shaft driven generators to power electric motors, without any battery storage as shown in Figure (3.7e). In this configuration, the combustion engine directly powers an electrical generator, which then provides electrical power to electric motors responsible for driving the fan. This architecture completely eliminates the need for traditional mechanical transmission systems found in conventional aircraft engines. On the other hand, partial turbo- electric systems combine elements of fully turbo-electric architecture with traditional turbofan engines as shown in Figure (3.7f). In this configuration, some power from the combustion engines is used to directly drive the fans, similar to the parallel hybrid architecture. The remaining power is generated by gas turbine-driven gener- ators and supplied to electric motors to assist in fan propulsion. 3.6 Ambient Parameters The performance of an aircraft is significantly influenced by atmospheric properties. These properties include ambient pressure, temperature, air density, and the speed of sound. As an aircraft ascends or descends, these primary atmospheric properties change. Additionally, they play a crucial role in calculating other parameters like pressure altitude and density altitude, which are essential for analyzing aircraft performance. Modeling these parameters becomes essential when evaluating how different ambient conditions impact energy consumption in an aircraft. 3.6.1 Standard Atmosphere The performance of aircraft and propulsion systems depends on several atmospheric properties. These properties are never constant at any particular time or place. Therefore, an idealized steady-state representation of the earth’s atmosphere, re- ferred as the International Standard Atmosphere (ISA) have been introduced by the International Civil Aviation Organization (ICAO) [23]. The ISA model divides the atmosphere into several layers based on assumed linear distribution of absolute temperature with altitude. The Mean Sea Level (MSL) 20 3. Theory is considered to be the zero altitude. The first layer extending from the MSL into 11000 m is the Troposphere. The subsequent layer, extending from 11000 m to 20000 m is the Stratosphere. The Troposphere and Stratosphere are separated by the imaginary boundary known as the Tropopause. Since the operational ceiling of the ES-30 is well below the Tropopause, the conditions of the Troposphere is only considered in this study. According to the ISA model, the following conditions presented in Table(3.1) are assumed to be held in ISA condition. Table 3.1: ISA atmospheric conditions. Parameter Symbol Value ISA temperature at MSL (T0)ISA 288.15 K ISA air density at MSL (ρ0)ISA 1.225 kg m−3 ISA pressure at MSL (P0)ISA 101325 N m−2 ISA speed of sound at MSL (a0)ISA 340.294 m s−1 Temperature lapse-rate in Troposphere λ -0.0065 K m−1 Other important parameters considered in computing the atmospheric properties are, Gravitational acceleration g = 9.80665 m s−2 Real gas constant for air R = 287.04 m2 K−1s2 As the real atmospheric conditions can deviate from the ISA conditions, the de- viation from ISA can be considered to perform more realistic computations for at- mospheric properties. The main two parameters to indicate the deviation from ISA conditions are temperature deviation (∆TISA), often called as Delta-ISA (DISA) and the pressure deviation (∆PISA). The temperature at MSL T0, under the atmospheric condition with the temperature DISA, ∆TISA is given by, T0 = (T0)ISA + ∆TISA (3.1) Similarly, the atmospheric pressure at MSL P0 with the pressure deviation from ISA ∆PISA is, P0 = (P0)ISA + ∆PISA (3.2) 3.6.2 Temperature at Altitude The Outside Air Temperature (OAT) is an important parameter for aircraft perfor- mance. The thrust force generated by the propulsion system is decreased, with the increasing OAT as the air density reduces with increasing temperature. The true air speed (TAS) of the aircraft must be increased to compensate for the reduction in air density and hence the take-off distance is increased. Another effect of increased OAT is the reduced rate of climb of the aircraft due to the reduction of the excess thrust of the aircraft. 21 3. Theory The temperature also has an effect on the indicated altitude in altimeter in the cockpit instruments. As a result of that, if the temperature is higher at a constant indicated altitude, the true altitude that the aircraft is flying is higher. Therefore, altitude temperature correction tables are used to correct the altitude deviations due to temperature [24]. The temperature at an altitude can be performed considering the temperature at MSL, and the temperature gradient in the atmosphere. Th, the temperature at an altitude of h is given by, Th = T0 + λh (3.3) where, T0 is the temperature at MSL and λ is the temperature gradient. 3.6.3 Ambient Pressure at Altitude The ambient pressure also known as static pressure at altitude depends on the variation of pressure and temperature. The static pressure Ph at altitude h is given by, Ph = P0 + [ 1 + λ T0 h ]− g λR (3.4) where, T0 and P0 are the temperature and pressure at MSL respectively., 3.6.4 Air Density Air density is an important atmospheric property which affects the aircraft perfor- mance in many ways, most notably aircraft engine systems, aerodynamic perfor- mance of air-frame and propellers. The air density is influenced by atmospheric pressure, temperature and humidity. Considering the dry-air assumption, the air density ρh at an altitude h is given by, ρh = ρ0 [ Th T0 ]− g λR −1 (3.5) here, ρ0 is the air density at MSL: ρ0 = (ρ0)ISA · (T0)ISA T0 (3.6) 3.6.5 Speed of Sound The speed of sound vary with ambient temperature. The speed of sound at an altitude below Tropopause can be computed as a function of ambient temperature Th by, ah = (a0)ISA · √ Th (T0)ISA (3.7) 22 3. Theory 3.6.6 Mach Number The Mach Number is a ratio between the aircraft TAS and the speed of sound. The Mach Number M for an aircraft flying at VTAS speed and altitude h is given by, M = VTAS ah (3.8) 3.6.7 Pressure Altitude The Pressure Altitude (PA) is the theoretical altitude of an aircraft with respect to the standard datum defined by the ISA conditions [47]. Pressure altitude is the altitude in the ISA model that has the same atmospheric pressure as at the altitude of interest. Pressure altitude is important and widely used as a basis for defining aircraft performance and also important when assigning flight levels to aircraft op- erating at or above 18000 ft. Pressure altitude affects the aircraft and engine performance. When the pressure altitude is increased the air density is reduced and the TAS of the aircraft has to be increased to compensate the reduction in air density As the increased pressure altitude reduces the available thrust and it results longer takeoff distances and reduced climb performance[24]. The pressure altitude (PA) for a given altitude h can be computed considering the inverse of pressure lapse-rate ΓP and atmospheric pressure at sea level at the inter- ested location P0 which is often called as QNH in aviation. PA = h + ΓP [(P0)ISA − P0] (3.9) The ΓP = 27 ft / h Pa in the lower part of the atmosphere while it can take higher values that that in the higher parts of the atmosphere. As a rule-of-thumb, ΓP = 30 ft / h Pa value is commonly used by the aviation community when computing PA. 3.6.8 Density Altitude The Density Altitude (DA) is the pressure altitude corrected for non-standard tem- perature and it represents the combined effect of pressure altitude and the ambient temperature. Density altitude is also used in calculating aircraft performance. Higher density altitudes results in reduced engine and propeller performance, and it also results in longer take-off distances as well as reduced climb performance [25]. The density altitude can be computed from pressure altitude, ambient temperature at pressure altitude TPA and inverse of temperature lapse-rate ΓT as DA = PA + ΓT [Th − (TP A)ISA] (3.10) Here (TP A)ISA is the ISA temperature at the pressure altitude. 3.6.9 True Air Speed and Calibrated Air Speed The True Air Speed (TAS) is the speed of an aircraft relative to the air it is flying through. The Indicated Air Speed (IAS) is the speed indicated in cockpit indicators 23 3. Theory for pilots. The Calibrated Air Speed (CAS) is the IAS corrected for sensor and instrumentation errors. The TAS differs to CAS due to the variation of air density at altitudes and atmospheric conditions. The conversion from CAS m s−1 to TAS m s−1 can be performed as, VTAS =  2 µ Ph ρh 1 + (P0)ISA Ph (1 + µ 2 (ρ0)ISA (P0)ISA V 2 CAS ) 1 µ − 1 µ − 1  1 2 (3.11) where, Ph and ρh are ambient pressure and air density at aircraft altitude respectively. µ = K−1 K with K = 1.4 (Adiabatic index of air). 3.7 Aerodynamic Forces An airfoil for a typical aircraft wing and the corresponding parameters are illustrated in Figure(3.8). Figure 3.8: Lift and drag forces and related angles for an typical aircraft wing airfoil. Chord line: Chord line is the imaginary line joining the leading and trailing edges of the airfoil. AoA: Angle of Attack (AoA) is the angle between the chord line and the relative wind. AoI: Angle of Incidence (AoI) is the angle between the chord line and the longitudinal axis. CoP: Center of Pressure (CoP) is considered to be the focal point on which the lift force is acting upon. The position of the CoP vary with the change of AoA. Pitch: Pitch angle is the angle between the horizontal axis and the longitu- dinal axis. Flightpath angle: The angle between horizontal axis and the flightpath vector or the relative wind. When the aircraft moves forward through the air, the airfoil shape of its wing results low pressure over the wing and higher pressure underneath. This pressure difference 24 3. Theory creates the lift force according to the Bernoulli’s principle. The lift force is always perpendicular to the flightpath vector by definition. The aerodynamic force acting in the opposite direction of the movement of the aircraft is called the induced drag force. The lift force (L) depends on many factors including aircraft true air speed, air density, reference wing area and the shape of the airfoil and the angle of attack. Further the compressibility and the viscosity of the air also affects the lift force. The various complex dependencies of the shape, AoA and flow conditions on the lift force are lumped together into lift coefficient (CL) and it is usually determined experimentally. The lift equation to compute lift force L is, L = 1 2 CL ρ v2 Sref (3.12) where, ρ Air density v Aircraft TAS Sref Reference wing area The term 1 2ρv2 in Equation(3.12) is called the dynamic pressure and denoted by q or Q. The dynamic pressure q can be incorporated into the Equation(3.12) and can be expressed as, L = CL q Sref (3.13) The drag force is the net force acting opposing the movement of the aircraft. This is parallel and opposite to the flightpath vector. The drag force consists of two types of drag forces. The first of which is the parasite drag and it can further be splitted to skin friction, interference and form drag. The form drag is the resistance force acted upon the structure of the aircraft when it moves through air as a result of the roughness and shape of the air-frame and structures. The skin drag occurs as a result of the boundary layer which is station- ary relative to the aircraft skin surface. Interference drag occurs as a result of the aerodynamic interference of the different structures of the aircraft for instance the wing struts and extended landing gears. Parasite drag can be simply explained as the total drag independent of the lift force. The induced drag is the drag occurred as a result of creating the lift force. The behaviour of parasite and induced drag is different with respect to air speed. While induced drag reduces when airspeed is increased, the parasite drag increases. The total drag is the sum of the induced and parasite drag values. Figure(3.9) illustrates the behaviour of induced, parasite and total drag with aircraft TAS which is often called as the aircraft drag curve. 25 3. Theory Figure 3.9: Illustration of aircraft drag curve. The drag coefficient CD can be expressed as a parabolic function of CL. Here the CD is divided into its main components as, CD = CD0 + KC2 L + ∆CDF lap + ∆CDLG (3.14) where, CD0 Zero-lift drag coefficient K Induced-drag factor CL Lift coefficient ∆CDF lap Drag coefficient component due to flap extension ∆CDLG Drag coefficient component due to landing gear extension The K value is given by, K = 1 π AR ϕ (3.15) where, ϕ is the Oswald efficiency factor and the Aspect Ratio AR is given by, AR = Wing-span2 Sref (3.16) The aerodynamic drag force D can be determined using the drag coefficient CD by, D = 1 2 CD ρ v2 Sref = CD q Sref (3.17) 3.8 Aircraft Point-mass Model The aircraft has 3 principle axes as illustrated in Figure(3.10) and they are, • Longitudinal Axis: Imaginary axis drawn through the body of the aircraft from tail to nose through the aircraft center-of-gravity (CoG) in the normal 26 3. Theory direction of flight. • Lateral Axis: Imaginary line drawn through the aircraft CoG, parallel to the line drawn from left wing-tip to the right wing-tip and perpendicular to the longitudinal axis. • Vertical Axis: Imaginary line drawn through the aircraft CoG and perpendic- ular to both longitudinal and lateral axes. Figure 3.10: Aircraft principle axes and roll, pitch yaw rotations The aircraft has six Degrees-of-Freedom (DoF) with respect to the three principle axes. They are the transnational motions along longitudinal, lateral and vertical axes and the rotational motions around those three axes which are roll, pitch and yaw respectively. The motion of the aircraft and the forces acting on the aircraft is important in studies related to energy consumption. There are mainly two approaches in describ- ing the aircraft motion. The Total Energy Model (TEM) approach [26] [27] relates the rate of work done by the forces acting on the aircraft to the changes in kinetic and potential energy. The other approach is developing aircraft model in in terms of the so called point- mass model. In this approach, all the forces acting on the aircraft are considered to be applied on the aircraft CoG and the force balance equations are used to develop the relation between the flightpath variables and the forces [28]. Different versions of these models can be developed based on the interested parameters and the desired level of fidelity. Reduced number of DoFs can be considered to develop a simplified point-mass model of the aircraft. Common approach used for aircraft performance models is modeling aircraft as a 3 DoF point-mass model considering the longitudinal movement and 27 3. Theory the flightpath angle of the aircraft. A free body diagram depicting the forces acting on the aircraft and the relevant other parameters is illustrated in Figure(3.11). Figure 3.11: Aircraft free-body diagram with flightpath variables and forces. γ Flightpath angle γ̇ Rate of change of flightpath angle v Aircraft TAS v̇ Rate of change of TAS L Lift force W Aircraft weight (W = m g) D Aircraft drag T Aircraft thrust Considering the free-body diagram of the point-mass model of the aircraft, the following equations can be derived. For the force balance along the aircraft flightpath: T −D −W sin(γ) = m v̇ (3.18) For the force balance perpendicular to the the aircraft flightpath: L−W cos(γ) = m v γ̇ (3.19) The mvγ̇ component in equation(3.19) is the centrifugal force created when changing the flightpath angle of the aircraft (pitch change around the lateral axis) and this force is perpendicular to the flightpath vector. 3.9 Propellers The purpose of the propeller is to convert the engine shaft power into linear thrust force which propels the aircraft forward. This should be done as efficiently as possible in the range of the aircraft speeds and ambient conditions. The thrust from the propeller is generated by accelerating a mass of air from a lower velocity to a higher velocity. The propeller blade can be considered as an airfoil moving through the 28 3. Theory air, and the lift force created by this airfoil contributes to the thrust force generated by the propeller. The propeller blade related important angles and parameters are illustrated in Figure(3.12). Figure 3.12: Angles and parameters related to the aerodynamics of a propeller blade. Chord line: The chord line of a propeller blade is the imaginary line joining its leading and trailing edges. Relative airflow: While the propeller rotates around the propeller hub, the aircraft is also moving forward. Therefore, the relative airflow is the combined effect of both the forward speed of the aircraft and the rotational motion of the propeller. Rotational component: This speed component is a result of the circular motion of the propeller blade and it is proportional to the propeller angular speed n and propeller diameter D. Airspeed component: This speed component is equal to the TAS of the aircraft. Pitch angle is the angle between the chord line and rotational component or the rotational plane of the propeller. Angle of attack: The AoA is the angle between the chord line and the rela- tive airflow of the propeller. The main two categories of aircraft propellers are the fixed pitch propellers and the variable-pitch propellers. As the name implies, the fixed-pitch propellers are manu- factured to a fixed pitch angle. However, the propeller efficiency highly depends on the aircraft TAS, and the fixed pitch propellers are typically designed for optimal efficiency at cruise setting. However the fixed pitch propellers cannot operate effi- ciently in the other flight segments such as takeoff, climb and descent. The variable pitch propellers can change their pitch angle and operate with optimal efficiency at a wide range of aircraft conditions. The propeller pitch is controlled with different mechanisms such as hydro-mechanical governors or electronic control. The pilots can control the propeller pitch in different settings such as Fine, Coarse, 29 3. Theory Feather or Reverse Pitch depending on the phase or the condition of the flight. Propellers play an extremely important part of a propeller based aircraft propulsion system. Capturing the characteristics of the propellers are an important task when modeling the propulsion system with propellers. There are mainly three approaches in modeling propellers in the literature. They are, 1. Constant efficiency 2. Constant pitch 3. Propeller performance maps In constant efficiency based propeller modeling approach, constant values are as- signed to propeller propulsive efficiency. Typically, different efficiency values are used during different phases of the mission such as takeoff, climb, cruise, descent and landing. In the constant pitch based propeller modeling approach, the propellers are con- sidered to be fixed-pitch propellers and the relation of propellers rotational speed to the required power Preq and altitude h is mathematically expressed according to Equation(3.20) [29]. ωprop = ωprop,nom 3 √ Preq ρh Pprop,nom ρ0 (3.20) where, Pprop,nom Nominal power ωprop,nom Nominal rotational speed ρ0 Air density at MSL ρh Air density at altitude h The propeller efficiency is calculated with the blade element theory considering the specifications of the propeller. Propeller modeling using the propeller performance maps are typically used for con- stant speed propellers. The propellers are characterized by means of propeller maps which contains propeller performance information for a wide range of operation range. The propeller maps are expressed in terms of the following dimensionless parameters. Advance Ratio (J): Advance ratio is the distance the propeller advances forward per revolution in terms of its diameter. J = v n D (3.21) where n is the propeller rotational speed in revolutions per second, v is aircraft TAS and D is the propeller diameter. 30 3. Theory Propeller Tip Mach (MT ip): Propeller tip mach is the ratio between the propeller tip speed and the speed of sound. The propeller tip speed is the resultant of aircraft TAS and the rotational component explained above. MT ip = √ v2 + ( n D 2 )2 a (3.22) Thrust Coefficient (CT ): The thrust coefficient relates how much thrust the propeller creates for the given parameters. CT = T ρ n2 D4 (3.23) where T is the thrust force. Torque Coefficient (CQ): The torque coefficient relates how much torque is ex- erted on the shaft by the propeller. CQ = Q ρ n2 D5 (3.24) where Q is the shaft torque. Power Coefficient (CP ): The power coefficient relates to how much power it takes to turn the propeller, which is often called as the absorbed power and this is equal to the shaft power. The power coefficient and the its relation to the torque coefficient is given by, CP = PShaft ρ n3 D5 = 2 π CQ (3.25) where PShaft is the shaft power or absorbed power. The propulsive power is different to the shaft power. The propulsive power generated by the rotating propeller is calculated in terms of the propeller thrust and the aircraft TAS as, PP ropulsive = T v (3.26) Propeller Efficiency (ηP rop): The propeller efficiency is the ratio of propulsive power to the absorbed power. The propeller efficiency is given by, ηP rop = PP ropulsive PShaft = T v PShaft = CT J CQ (3.27) 3.10 Permanent Magnet Synchronous Machine The electric motors play a pivotal role in hybrid-electric propulsion systems, con- verting electric energy into mechanical energy through the interaction of magnetic and electric fields. Among the various motor types available, Permanent Magnet Synchronous Motors (PMSM) are widely used in aircraft applications due to their 31 3. Theory advantages such as high efficiency, reduced maintenance, quiet operation, and high power density [30]. In the design of PMSMs for aeronautical applications, certain critical specifications must be addressed. The weight of the PMSM is directly linked to the energy consumption of the aircraft, whether in terms of thermal or electric energy. Therefore, minimizing the weight of the motor is crucial for enhancing the overall efficiency and performance of the aircraft [31]. PMSMs are typically classified into two types based on the arrangement of per- manent magnets: Surface Permanent Magnet Synchronous Motors (SPMSMs) and Interior Permanent Magnet Synchronous Motors (IPMSMs), as illustrated in Figure (3.13). SPMSMs feature permanent magnets mounted entirely on the rotor’s surface. On the other hand, IPMSMs incorporate magnets within the rotor structure. This internal placement of magnets enhances their versatility and performance, making them particularly suitable for aviation applications [32]. Figure 3.13: IPMSM and SPMSM architecture [32]. The motor generates shaft power, which is transmitted to the propeller shaft through either direct drive or gear drive. This facilitates electric propulsion, resulting in thrust output. The choice between direct coupling and gear-driven configurations depends on the specific requirements and design choices of the aircraft. The common approaches for modeling motors include first-principle-based modeling and performance map-based modeling. The first-principle approach utilizes differ- ential equations and mathematical relations related to motor dynamics, relying on internal parameters that are often proprietary information. In contrast, performance map-based modeling represents motors at a high level, using data tables and maps derived from empirical tests. Although this approach does not capture internal mo- tor parameters, it provides more realistic results in terms of overall performance and energy-related parameters. 3.11 Turbine Engines A turboprop is a gas turbine engine which drives a propeller connected to its output shaft. The working principle of turboprop closely follows the general working princi- 32 3. Theory ple of a gas turbine engine. A turbine engine mainly consists of intake, compressor, combustion chamber, turbines and exhaust. The output shaft is rotated by the hot combustion gas expand through the turbine blades. Contrast to the turbojet and turbofan engines, the turboprop engines does not create significant amount of thrust by the exhaust gases, instead almost all the power generated by the engine is used to drive the connected propeller. Compared to piston engines, the turboprop engines have greater power-to-weight ratio which allows relatively shorter take-offs and they are also fuel efficient as they can operate at higher altitudes than the piston engines. The turboprop engines can operate efficiently at subsonic speeds below 400 knots. These characteristics of tur- boprop engines has enable them to be used widespread in regional airline market for example aircraft such as ATR 42/62/72, Bombardier Q400, De Havilland Canada Dash 8-100, 200, 300 and Saab 340 use turboprop engines. A simplified layout of a Pratt and Whitney PT6 turboprop engine depicting the main component is illus- trated in Figure(3.14). Figure 3.14: Illustration of PT6A Turboprop engine [33]. Turboprop engines can be modeled using various approaches, each differing in terms of accuracy, complexity, and the specific aspects and parameters of interest. One such approach involves thermodynamic modeling. In this method, the different components of the turboprop engine such as the intake, compressors, combustion chamber, turbine, and exhaust are modeled based on their thermodynamic proper- ties and relations. The thermodynamic approach for turbine engines is rooted in the Brayton cycle, which ensures the conservation of energy and momentum across the engine system. Within this cycle, compression and expansion processes are consid- ered isentropic and adiabatic, while combustion occurs at constant pressure [34]. To characterize the operation of compressors and turbines, performance maps are em- ployed. These maps are non-linear empirical models generated from computational fluid dynamics, experimental data, or estimations. Additionally, mechanical losses such as bearing friction, gearbox losses, and thermodynamic losses are factored in to determine the engine output power. While this approach provides valuable insights 33 3. Theory into parameters like internal temperatures at different locations within the engine and overall performance, its complexity remains a disadvantage. Furthermore, ob- taining the necessary input parameters for the model can be challenging, as they often constitute proprietary information held by engine manufacturers. Another approach in modeling turbine engines is modeling the turbine engine in terms of fuel consumption maps. In this approach the engine is modelled based on the engine efficiency and the fuel consumption to deliver a specific power output. The output power of a turboprop engine corresponds to the engine shaft power and the energy needed to generate this power is delivered from the combusted fuel. Fuel consumption maps take into account the ambient parameters because, the fuel con- sumption and engine efficiency are significantly affected by the ambient conditions. Typically, these maps consider factors such as pressure altitude, Delta ISA (DISA), and shaft power as the breakpoints or input parameters. Although this approach is simple and provides the accurate information for energy consumption related pa- rameters, this method fails to capture the internal parameters of the engine. In a turbine engine that produces shaft power, fuel consumption is identified by Brake-Specific Fuel Consumption (BSFC). BSFC = ṁfuel PShaft (3.28) where ṁfuel is the fuel flow-rate and PShaft is the shaft power. When a considerable thrust is produced by the exhaust of the turboprop engine, the fuel consumption is expressed in terms of Equivalent Brake-Specific Fuel Consump- tion (ESFC). ESFC = ṁfuel ESP (3.29) where ESP is the equivalent shaft power which accounts for both the delivered shaft power and the thrust created by the exhaust gas. These specific fuel consumption maps are based on empirical data and provide very close results to the reality. The specific fuel consumption values are often expressed in kg / kWh or (lb / h) / hp [35]. 3.12 Battery Batteries store energy in the fo