Energy Optimization of a Hybrid Unmanned Aerial Vehicle (UAV) Thesis Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University By Danielle Meyer, BS, BA Graduate Program in Electrical and Computer Engineering The Ohio State University 2018 Thesis Committee: Dr. Jiankang Wang, Advisor Dr. Mahesh Illindala ABSTRACT Unmanned Aerial Vehicles (UAV) have continued to receive attention from corpo- rations and governmental agencies due to their wide range of potential applications and hybrid nature. More Electric Aircraft (MEA) promise many benefits (e.g., re- duced weight, decreased fuel consumption, and high reliability) and their development continues to be the trend. Hybrid UAVs are an ideal prototype to implement con- cepts of aircraft electrification due to their small size and the DC nature of their power systems. However, papers addressing the energy optimization UAV electric power sys- tems fail to consider the importance of high accuracy and computational speed. This thesis proposes an energy optimization method to enhance the energy durability of a UAV through a novel approach integrating an optimization formulation and a detailed UAV simulation model, with physical circuitry characteristics. This approach allows for increased computation efficiency while still capturing physical system constraints experienced during real world flight, which are complex and highly nonlinear due to aerial, thermal, and electrical dynamics. Optimization formulations created within this work are based on dynamic programming and moving-horizon model predictive control (MPC). The efficacy of this method is proven on a realistic UAV system. Within the MPC formulation, various charge strategies are implemented and fuel consumption is calculated to provide insight into the trade-offs inherent within the UAV system, wherein battery discharging is required for high demand dash periods, i but additional charge can only be supplied via increased output engine power. That is, minimal fuel consumption must be considered in light of the need for non-optimal output engine power to charge the battery such that a total mission can be completed. Algorithmic considerations regarding horizon size for MPC and algorithmic enhance- ments, considering random loads and renewable generation capacity on-board the UAV are presented. These results regarding enhanced algorithmic elements provide insight into the capability of the algorithm to function within a real-time environment and the benefit of solar arrays to provide additional generation. Using MPC as the optimization technique of choice allows for the development of an algorithm capable of handling both missions with a deterministic load and within online implementations, as deterministic cases represent a downsized problem where algorithmic considera- tions can be studied and iterated to reach satisfactory online implementation. While this thesis approaches the problem from the perspective of UAV design, i.e., opti- mization for a deterministic load profile, the algorithmic enhancements provided here represent initial steps towards online implementation. ii Dedicated to my parents iii ACKNOWLEDGMENTS This thesis would not have been possible without the support of my advisor and mentor, Dr. Jiankang Wang, and my parents. iv VITA 2009 - 2016 . BS, Electrical and Computer Engineer- ing, The Ohio State University 2009 - 2016 . BA, German, The Ohio State Univer- sity 2016 - present . MS, Graduate Research Associate, Department of Electrical and Com- puter Engineering, The Ohio State University PUBLICATIONS Research Publications D. Meyer, J. Choi, J.K. Wang, "Increasing EV public charging with distributed generation in the electric grid," 2015 IEEE Transportation Electrification Conference and Expo (ITEC), Dearborn, MI, 2015, pp. 1-6. D. Meyer, R. Alexander, J.K. Wang, "A simple method for energy optimization to enhance durability of hybrid UAV power systems," 2017 North American Power Symposium (NAPS), Morgantown, WV, 2017, pp. 1-6. D. Mao, D. Meyer, J.K. Wang, "Evaluating PEV's impact on long-term cost of grid assets," 2017 IEEE Power Energy Society Innovative Smart Grid Technologies Conference (ISGT), Arlington, VA, pp. 1-5. In Press. D. Meyer, J.K. Wang, "Integrating Ultra-Fast Charging Stations within the Power Grids of Smart Cities: A Review," IET Smart Grid. In Press. Ziran Gao, D. Meyer, J.K. Wang, "Visualizing the Impact of PEV Charging on the Power Grid," 2018 IEEE Transportation Electrification Conference & Expo (ITEC), Long Beach, CA, pp. 1-5. v FIELDS OF STUDY Major Field: Electrical and Computer Engineering vi TABLE OF CONTENTS Page Abstract . .i Dedication . iii Acknowledgments . iv Vita.........................................v List of Tables . ix List of Figures . .x Dynamic Programming - Nomenclature . xii Model Predictive Control - Nomenclature and Symbols . xiii Chapters: 1. Introduction . .1 1.1 Prior Work . .2 1.2 Motivation . .4 1.3 Organization of Thesis . .6 2. Characterization of the UAV System . .8 2.1 UAV System Representation . .8 2.2 UAV Power Demand . 10 2.3 Energy Management Considerations . 12 vii 3. Dynamic Programming for UAV Energy Management . 13 3.1 Dynamic Programming . 13 3.2 Application of Dynamic Programming to UAV Energy Management 15 3.2.1 Algorithmic Implementation . 18 3.3 UAV System Model . 20 3.4 Results . 22 3.5 Conclusion . 24 4. Model Predictive Control for UAV Energy Management . 25 4.1 Model Predictive Control (MPC) . 25 4.2 Application of MPC to UAV Energy Management . 27 4.2.1 Algorithmic Development . 30 4.3 UAV System Model . 33 4.4 Results . 34 4.4.1 Energy Management for a 50cc Engine . 34 4.4.2 Energy Management for a 28cc Engine . 42 4.5 Conclusion . 54 5. Additional Algorithmic Considerations - MPC for UAV Energy Optimization 57 5.1 The Importance of Horizon Length within the MPC for UAV Energy Optimization . 58 5.2 MPC in the Presence of Load Uncertainty . 62 5.3 Integrating Renewable Generation . 71 5.4 Conclusion . 77 6. Conclusions and Future Work . 80 Bibliography . 85 viii LIST OF TABLES Table Page 4.1 Fuel Consumption for Four Test Cases of the 50cc Engine . 35 4.2 Parameter, Horizon Length, and Saved Solution Values for Test Cases 1-4 (50cc Engine) . 38 4.3 Fuel Consumption Comparisons for MPC Output and UAV Model Sim- ulation (50cc Engine) . 39 4.4 Fuel Consumption for Two Cases of No Charging (28cc Engine) . 43 4.5 Fuel Consumption and Battery Size Comparisons for 24 and 36 Hour Missions . 48 4.6 Fuel Consumption for MPC Output and UAV Model Simulation (28cc Engine) . 51 4.7 Fuel Consumption of MPC Output and UAV Model Simulation in the Case of an Extended Mission (28cc Engine) . 54 5.1 Solution Speeds per Iteration for Various Horizon Lengths . 67 5.2 Double Junction Gallium Arsenide PV Product Characteristics [1] . 73 ix LIST OF FIGURES Figure Page 1.1 The proposed technique, wherein an optimization algorithm provides control decisions U to a realistic UAV model, which implements the decisions in a real-world scenario including non-linear dynamics. Per- formance is interpreted by operators, who provide algorithm alterations H......................................5 2.1 A simplified, block diagram representation of the UAV system under study. 10 2.2 The predetermined load profile developed based on a known mission. This profile is used during the planning scope, i.e., determining the cor- rect sizing of components to ensure minimum fuel consumption while completing the entire mission duration. 11 3.1 Illustration of the possible paths the system can take under a fixed C-rate assumption, showing the transition from SOC1 to SOC2.... 18 3.2 UAV Simulink model developed to validate results of the algorithm according to dynamics within the operating system. 21 3.3 A comparison of the DP Formulation simulation and the Simulink UAV model simulation. 22 4.1 An illustration of the moving horizon of the MPC algorithm imple- mented. Predefined values of saved solutions m = 5; 000 and horizon length h = 10; 000 are used. The algorithm starts at time zero and solves for solutions up to the black line. 5; 000 solutions are then saved, up to the green line. The horizon then shifts forward by 10; 000 and solves from the green line to the blue line. This process repeats until the entire mission is solved. 31 x 4.2 The UAV Simulink model developed to validate results and for use within real-time implementation with the MPC formulation. This model considers the dynamics of the UAV. 33 4.3 Energy Source Output results of the MPC algorithm for four cases of UAV operation: (i) no charging needed for the duration of the mission, (ii) aggressive charging behavior, (iii) a gradual charge pattern, and (iv) linear charging to meet future dash demand. Battery power is shown in blue, load power is shown in yellow, and engine power is shown in red. 36 4.4 Battery SOC results of the MPC algorithm for four cases of UAV op- eration: (i) no charging needed for the duration of the mission, (ii) aggressive charging behavior, (iii) a more gradual charge pattern, and (iv) linear charging to meet future dash demand. 37 4.5 A comparison of algorithmic and UAV model results for two cases. The first case does not charge the battery, with battery power and SOC results shown in (a) and (b), respectively. The second case implements aggressive charging, with battery power shown in (c) and SOC shown in (d). 40 4.6 A comparison of algorithmic and UAV model results for two cases of charging. The first case follows a gradual charge strategy, with battery power and SOC results shown in (a) and (b), respectively. The second case implements linear charging, with battery power shown in (c) and SOC shown in (d). 41 4.7 Energy source output power (first row) and SOC (second row) results of the MPC algorithm for cases of no charging where (i) engine power is optimal and (ii) battery discharge equals zero during cruise periods.