Energy management and system design for fuel cell hybrid unmanned aerial vehicles

Abstract

The growth in the use of unmanned aerial vehicles (UAVs) has created an increasing demand for energy‐efficient and green power systems. In this paper, we have evaluated energy management strategies (EMSs) and system optimization design methodologies for fuel cell/battery‐powered hybrid UAVs (HUAVs). EMSs aimed at the optimization of flight endurance and fuel cell durability were proposed based on fuzzy logic, dynamic programming, equivalent consumption minimization, and Pontryagin's minimum principle (PMP). System optimization design methodologies, including static design and synergistic sizing optimization design, were also devised. The synergistic sizing optimization was based on multiobjective optimization, while optimization of the EMS used a non‐dominated sorting genetic algorithm. The effectiveness of the proposed EMSs and optimization design were then validated by simulation. Results showed that the proposed EMSs have both long flight time and good fuel cell durability, with the improved PMP prolonging the fight endurance by 4.64% and reducing the mean current of the fuel cell by 16.1% compared with fuzzy logic. Substantial improvements were obtained by using sizing optimization, and parameter sensitivity was addressed. The findings of this study can aid in the future development of fuel cell‐powered UAVs.

INTRODUCTION

Advancements in microprocessor technologies have enabled unmanned aerial vehicles (UAVs) with advantages such as low cost and high mobility; these UAVs have attracted considerable attention in the past few years.¹ The UAV market is expected to achieve a compound annual growth rate equating to a market value of $45.8 billion by 2025.² Electric multirotor UAVs are favored due to their reliability, reduced noise and thermal pollution, high efficiency, none pollutant emission, self-starting capability, and high maneuverability.³

Improving flight endurance is important to enhance operational capability for UAVs. Currently, electric power is provided mainly by batteries, which cannot supply sufficient energy over long periods. Extending UAVs flight endurance, therefore, requires the use of additional power sources, while still complying with mass and space restrictions. Habib reviewed the electric vehicles drive train architecture, applicable energy storage system, and the balancing circuit categories.⁴ It was found that one potential innovation is to use a hybrid electric propulsion system that has at least two power sources. The rapid growth of fuel cell-based research and technology has paved great prospects for hybrid electric vehicles (HEVs), which has reference significance for other fields.⁵ Studies have shown that hybrid-electric propulsion systems can improve the long endurance of UAVs,⁶ and several technologies have been adapted for use in hybrid UAVs (HUAVs).⁷ Hydrogen fuel cells are considered the most promising in the aviation industry, as fuel cells have high efficiency and specific energy.⁸ Fuel-cell-powered UAVs have been built and shown to have long endurance.⁹ Wang reviewed the current developments in fuel cell hybrid propulsion systems applied to UAVs.¹⁰ The development of new designs for high-performance fuel cell hybrid power systems is a priority for mobility and aviation applications.¹¹

The growing interest in fuel cell/battery-powered HUAVs is reflected in the ever-increasing number of studies concerning the electrification or hybridization of existing power systems,¹² with a particular focus on partnering fuel cells with lithium-ion batteries to extend flying time. However, to date, even for advanced systems, HUAV designs have seldom considered the possible synergy between sizing optimization and energy management strategies (EMSs) in the context of the mission profiles. One of the main objectives of this study is to correct this by presenting comprehensive energy management and sizing optimization methodologies. Advanced motion control methods can ensure that UAV can achieve various flight movements, such as adaptive and feedback theory.¹³ These control methods can still be transplanted to HUAVs, but new problems after the introduction of a hybrid power system need to be considered. For the hybridization of UAVs, the first step is to optimize the size of the onboard energy sources. Mazur and Domanski have studied the feasibility of adapting environmental-friendly energy sources for use as UAVs propulsion systems and found that this approach offers high efficiency, reliability, controllability, and a lack of thermal and noise signatures, thus, providing quiet and clean propulsion with low vibration levels.¹⁴ The key factors to consider are energy efficiency, system mass, energy density, power density, power changes, flight endurance, the lifetimes of the power sources, and the maturity of the technology. For a small UAV with a fuel cell system, a significant improvement in flight endurance can be achieved simply through design optimization.¹⁵ During the design process, the size of the power sources can be optimized in a quantitative way to tailor the EMS according to the mission profile. Donateo proposed an optimization based on a non-dominated sorting genetic algorithm-II (NSGA-II) and an S-metric selection evolutionary multiobjective algorithm, with the optimization being performed at two different levels to explore the synergic effect of hybridization.¹⁶ In contrast, Kamjoo used NSGA-II in the design of a hybrid renewable energy system with the twin objectives of minimum system total cost and maximum reliability.¹⁷ This study investigates the synergy between EMS choice and the sizing optimization process. NGSA was used as the optimization algorithm, following a performance analysis.

The performance of HUAVs is essentially reliant on the system architecture, size parameters, and EMS. Power has to be optimally split between sources for efficient energy usage, and to enable high-performance operation, while also extending the flight time as much as possible. EMS must reasonably distribute the hybrid system while considering system efficiency and endurance time. Karunarathne proposed a hybrid electric propulsion system for fuel cell/battery UAVs, and introduced an energy management system to optimize the system performances.¹⁸ A hybridization architecture with an optimal EMS is therefore crucial. EMSs of HUAVs can be divided into two main types: rule-based algorithms and optimal control algorithms.^19,20 The use of the former, which has predefined conditions, is widespread due to its simplicity and reliability. The most representative of these algorithms is fuzzy logic, typically characterized by a very low computational cost that enables an online EMS. Zhang proposed an online fuzzy EMS for a UAV propelled by a hybrid fuel cell/battery power system.²¹ A fuzzy logic-based EMS can improve energy efficiency by enhancing the allocation in the HUAV power supply.

Optimal control algorithms have been widely discussed for fuel cell HEVs, and they are fully applicable to various HUAVs because of the same working principles. Optimal control algorithms can be based on dynamic programming, Pontryagin's minimum principle (PMP), linear programming, equivalent consumption minimization strategy (ECMS), and model predictive control (MPC).²² These algorithms are crucial for resolving the complex energy management problems of HUAVs. Dynamic programming can achieve a global optimum, but normally requires complete knowledge of the future driving conditions, as well as intensive calculations. It is therefore often performed offline and used as a benchmark instead.²³ Ansarey proposed an optimal solution to the energy management problem in fuel cell HEV for fuel economy using multidimensional dynamic programming.²⁴ PMP can optimize the power distribution online, and the cost function can consider the fuel cell performance and fuel economy. Ou developed an adaptive supervisory EMS and an adaptive PMP for optimizing the fuel cell/battery hybrid operating system.²⁵ Nguyen proposed a simplification of the PMP EMS to avoid the adaptation mechanism in real-time, which is effective for generating near-optimal results that are similar to those achieved by dynamic programming.²⁶ ECMS and MPC are two typical causal algorithms. ECMS is a good candidate for solving energy management problems, which can calculate the optimal fuel consumption online instantaneously. Tian presented a practicality-oriented adaptive EMS for a parallel HEV, which combines the adaptive neuro-fuzzy inference system and ECMS.²⁷ Li presented an online adaptive ECMS for HEV powered by a fuel cell, battery, and supercapacitor. The strategy is designed to adjust equivalent factors and fuel cell dynamic current along with the state of health of the fuel cell and battery, to prolong the lifetime of the fuel cell.²⁸ MPC can repeatedly optimize decisions online over short future time horizons without the requirement for prior knowledge. He proposed an MPC EMS to distribute power flows, with a novel objective function within the defined lifetime constraints and battery state of charge (SoC) limitations.²⁹ We have previously proposed EMSs for fuel cell HEVs and found that the above algorithms achieve a good control effect.^30,31 EMS should be shaped by the characteristics and performance requirements of the HUAV. Another objective of this study is to develop appropriate EMS for HUVAs and evaluate different EMSs for long endurance.

The aim objective of this study is to evaluate the application of fuel cell hybrid systems for UAVs and contribute to the future development of HUAVs, especially in the optimization design of system parameters. Therefore, the primary contributions of this paper are summarized as follows:

• (1)

  A mathematical model of the fuel cell HUAV is established, including the propulsion system and the hybrid system. The model provides a model basis for system optimization design and EMS development.

• (2)

  EMSs optimized for long flight endurance and fuel cell lifetime for HUAVs are proposed based on fuzzy logic, dynamic programming, ECMS, and PMP algorithms. The effectiveness of the proposed EMSs is validated and compared in the simulation.

• (3)

  The synergy between the sizing optimization and EMSs in HUAVs is explored for better system design. A multiobjective NAGA-III approach is proposed for the effective optimization design of system parameters. This system optimization design method can achieve reasonable scheme results with the specific objective.

• (4)

  Based on the system's optimal design, parameter sensitivity for HUAVs is analyzed. Sensitivity analysis can provide a better analysis of design results, which can help to optimize system design.

Then, the paper is organized as follows: In Section 2, we establish a model system of the multirotor HUAV. In Section 3, we describe five EMSs for fuel cell HUAVs. In Section 4, we propose a system optimization design methodology. In Section 5, we present the simulation results, which are followed by a discussion. Finally, in Section 6, we present the summary and conclusions.

SYSTEM MODELING System description

In this section, we present the system structure, mathematical modeling, and the theoretical foundations of HUAVs. Although these principles are based on a small multicopter, to aid understanding and for practical implementation, they can be generalized to any HUAV. Herein, the example system structure has fuel cell/batteries. Lithium batteries are commonly used as an energy source because they are adaptable, require little maintenance, and have high energy density and low self-discharge rates. Among the available hybrid system architectures, active, semi-active, and passive structures have all been considered extensively.³² We use a semi-active structure, where the batteries are connected to the DC bus by a bidirectional DC/DC converter, which also serves as the regulator.³³ The architecture for the fuel cell/battery hybrid system is shown in Figure 1. The fuel cells are connected to the DC bus by a unidirectional DC/DC converter, while the batteries are connected by a bidirectional one. The Brushless DC motors drive the propellers to provide flight power for UAV. The controller on the motherboard, various sensors, and some other electronic loads consume a certain amount of power. In this paper, these power consumptions are assumed as a constant value.

Figure 1. HUAV system structure. (A) Power system, and (B) quad-, hexa-, and octo-rotor configurations for UAVs. HUAV, hybrid unmanned aerial vehicle; UAV, unmanned aerial vehicle.

The fuel cells and batteries, working in parallel, can fulfill the power requirements. As shown in Figure 1, they deliver power to the DC bus through unidirectional and bidirectional converters. These converters receive signals from the energy management controller that handles power distribution. The bidirectional converter can charge and discharge the batteries, reduce the peak power, or fill the power valley. The two major objectives of this study are to optimize the size of the power sources and develop appropriate EMSs. An accurate system model is therefore needed. Due to the variety of flight motions, the establishment of a complete kinematic and dynamic model has little significance on parameter design. The performance of a HUAV is mainly determined by the propulsion system, which consists of propellers, motors, electronic speed controllers (ESCs), fuel cells, batteries, and the DC/DC convertor. In HUAV, there is a power relationship as described in Equation (1). That is, the output power of the fuel cell through DCDC, and the output power of the battery through DCDC, provide power for the overall unit. The consumed power of HUAV is primarily the consumption of driving motors. The controllers also consume a certain amount of power, which is quite small. The mathematical expression of the thrust and power can be obtained based on the propeller and motor models, which will be further used to derive the power change of the fuel cell and battery. In this study, all model inputs were based on the manufacturer recommendations and the literature. [Image Omitted. See PDF]where P_FCDC and P_BDC denote the output power of the fuel cell through DCDC, and the output power of the battery through DCDC, respectively. P_m denotes the driving power of the motor. P_aux denotes the power consumed by the controllers. num_m is the number of the motors.

Propeller

The propulsion system is the main onboard device responsible for power consumption and converts electrical energy into mechanical power. We present a propeller model based on circuit theories discussed in the literature.³⁴ During hovering, propeller performance depends on the thrust and torque, expressed as follows: [Image Omitted. See PDF] [Image Omitted. See PDF] [Image Omitted. See PDF] [Image Omitted. See PDF]where m, m_N, and, m_L denote the total mass, no-load mass, and load mass of HUAV, respectively. m₀, m_p, m_m, m_FC, m_B, $${m}_{{H}_{2}}$$, and m_DC, denote the mass of UAV airframe, propeller, motor, single fuel cell, battery cell, hydrogen tank per liter, and DC/DC converters, respectively. num_P, num_FC, num_B, and  $$nu{m}_{{H}_{2}}$$ are the number of propellers, fuel cells, battery cells, and hydrogen, respectively. F_P, N_P, and T_P denote the thrust, speed, and torque of the propeller, respectively. N_m denotes the motor speed. g is the gravity coefficient; ρ denotes the air density of the flight environment; D_P is the propeller diameter; C_T and C_M are the thrust coefficient and torque coefficient of the propeller. N_m is the motor speed which is the same as N_P.

Motor

The DC motors used in multirotor UAVs are brushless, identical to permanent-magnet DC motors. Their equivalent currents and voltages represent the loads on the ESC.³⁵ The latter can be expressed as follows. [Image Omitted. See PDF]where I_m and U_m denote the equivalent voltage and current of the motor, respectively. I_m0 and U_m0 are the motor nominal no-load current and voltage, which are approximately constant. R_m is the motor armature resistance, and K_V is the nominal no-load motor constant.

Electronic speed controller

The ESC operates as a motor speed controller, responding to the flight controller's throttle signal. It can be described as follows: [Image Omitted. See PDF] [Image Omitted. See PDF]where I_e, R_e, U_e, and P_e denote the ESC input current, resistance, voltage, and power, respectively. The ESC voltage is supplied by the fuel cells and batteries through DC/DC converter.

Fuel cell

The fuel cell power system provides power for UAVs. Fuel cell models mainly include the empirical model and mechanism model.³⁶ The mechanism model is quite complex, and the empirical model is widely used in the research of hybrid systems, which is mainly based on the parameters obtained from the experiments. In this paper, a representative fuel cell model is established as follows: [Image Omitted. See PDF] [Image Omitted. See PDF]where U_OC denotes the reversible open circuit voltage, and I_FC denotes the FCS current. A_T denotes the slope of the Tafel line, and r represents the area-specific resistance. A denotes the active area of the fuel cell, and B and C are constants in the mass-transfer overvoltage equation. $${m}_{{H}_{2}}$$, $${M}_{{H}_{2}}$$, n_e, F, U_FC, I_FCS, and P_FC denote the hydrogen consumption, the molar mass of hydrogen, number of electrons, and Faraday's constant, working voltage, working current, and output power of fuel cell, respectively. These coefficients of the fuel cell are from literatures.^37,38

Fuel cell durability

Fuel cells and batteries tend to degenerate following long-term use.^39,40 In the hybrid system, the fuel cell lifetime is more sensitive to load.⁴¹ It must be pointed out that the fuel cell and battery provide power together. When one power source is conservative, the other power source will be radical. To ensure the smooth output of the fuel cell, the battery needs to fluctuate with the load. Therefore, in view of the characteristics, cost, and durability of fuel cells, it is necessary to give priority to ensuring the fuel cells' lifetime. A degenerated fuel cell can restrict flight capabilities and cause maneuverability issues, in turn increasing the likelihood of collisions. Therefore, the fuel cell lifetime should be considered during optimization, and fuel cell aging should be considered in the context of long-term performance.

Many factors decrease fuel cell performance and capacity. The degradation rate of the fuel cell lifetime significantly increased over time at a high current density.⁴² The time and the current density highly affect the durability of the fuel cell system. In general, the driving cycle is used as a kind of standard protocol reflecting different times and current densities.⁴³ Therefore, the durability model of the fuel cell can be simulated to evaluate the degradation rate under different driving cycles.⁴⁴ Therefore, in this paper, the current load characteristics of the fuel cell are considered in terms of their effect on fuel cell lifetime. Many eigenvalues can be extracted from the current data, representing the mean load, amplitude, standard deviation, extreme values, etc. Considering the difficulty of extracting the eigenvalues from the current load, in this study we extracted two representative eigenvalues: (1) The mean value, which reflects the overall current level. (2) The standard deviation, which reflects the degree of dispersion and fluctuation in the current. With a larger mean, the fuel cell load is bigger. A larger standard deviation reflects more severe load fluctuation. [Image Omitted. See PDF] [Image Omitted. See PDF]where $$\bar{{I}_{B}}$$ and S_I denote the mean value and standard deviation of the fuel cell current, respectively.

Battery

Batteries are important energy storage devices in HUAVs. Wen presented an overview of the research for improving battery energy storage density and renewable energy conversion efficiency.⁴⁵ Lithium-ion batteries have higher working voltages, higher specific energies, a lighter weight, and lower self-discharge rates, which is suitable for HUAVs.^40,46 Here, the battery model is based on an improved PNGV model, as shown in Figure 2. The battery model is as follows: [Image Omitted. See PDF] [Image Omitted. See PDF]where U_B, P_B, U_OCV, I_B, and R_B denote polarization voltage, output power, ideal open-circuit voltage, load current, and internal resistance of the battery, respectively. R_P1 and R_P2 are the resistances, C_P1 and C_P2 are the capacitors. U_P10 and U_P12 denote the initial polarization voltage. SoC_B denotes the battery SoC, and Q_B denotes the battery capacity. The parameters of model components can not be measured directly and need to be identified. There are standard identification methods and specific processes for circuit parameter identification.^46,47

Figure 2. Equivalent circuit model of battery

DC/DC convertor

DC/DC converters are important devices for regulating power. The time constants of the inductors are assumed to be much longer than the switching period. Kirchhoff's law has been used to determine converter efficiency. A DC/DC converter that uses an equivalent static model can therefore be expressed as follows: [Image Omitted. See PDF] [Image Omitted. See PDF]where U_IN, U_DC are the input and output voltage of the converter. R_L denotes the inductor resistor, and L is the inductance, κ_DC is a coefficient. I_L and I_DC are current through the inductor and the output current of the converter, respectively. η_DC is the efficiency of the converter.

DEVELOPMENT OF THE EMS

The EMS is responsible for determining how the energy distribution from different sources is optimized to meet specific objectives. This paper develops EMS for use with HUAVs, considering the specific requirements of UAVs: Long flight endurance time and fuel cell durability. We propose five representative EMSs for fuel cell HUAVs, based on fuzzy logic, dynamic programming, ECMS, and PMP algorithms.

Therefore, fuzzy logic is an important EMS, which is usually used as a benchmark.

Fuzzy logic-based strategy

The fuzzy logic method has strong robustness and fault tolerance, does not need models, and is especially suitable for real-time online control in a complex environment. Fuzzy logic is a classical controller in the field of energy management for HEVs, and usually serves as a reference for online energy management problems. In this paper, a fuzzy logic-based EMS is proposed. The control objective is to adjust the fuel cell output according to the power demand and battery SoC, combined with expert experience. Depending on the real-time power demand and SoC, this strategy can distribute power effectively. Although fuzzy logic cannot achieve optimal endurance time, its strong robustness can ensure system stability in the complex environment of UAVs. The input parameters are the normalized demand power and battery SoC, and the output parameter is the output power of the fuel cell. Demand power and battery SoC used bilateral Gaussian membership functions, and fuel cell power used triangular membership functions. Demand power is converted to [0, 1] by normalization function, and the output power is converted to [0, P_FCmax] by inverse normalization function. The schematics of the strategy and surface of the regulars are designed in MATLAB® (MathWorks) fuzzy logic designer as shown in Figure 3. The control system needs to operate under certain constraints, including for the motor, battery, and fuel cell, and with respect to the electricity regulation, as shown as follows: [Image Omitted. See PDF]where I_mmin, I_{B min}, I_{B max}, and I_{FC max} denote constraints of motor current, battery current, and fuel cell current; ΔI_{B min}, ΔI_{B max}, and ΔI_{FC max} denote constraints of battery current change rate and fuel cell current change rate; SOC_Bmin and SOC_Bmax denote constraints of battery SoC.

Figure 3. Schematics of the Fuzzy logic-based strategy. (A) Schematics and (B) surface of the regulars.

Dynamic programming-based strategy

Dynamic programming is a numerical method that solves multistage problems and involves some decision-making. It ensures a globally optimal solution. Generally, a full understanding of the future is required, so the benchmark is usually calculated offline. Here we propose an EMS for HUAVs based on offline dynamic programming. Within the control framework, the battery SoC is a variable. While the endurance time cannot be calculated directly, it is usually converted into a real-time hydrogen consumption of the fuel cell. The objective function generated by dynamic programming is the minimum energy consumption, as shown as follows: [Image Omitted. See PDF]where α₁ and α₂ are coefficients, SoC_BRef is a median battery SoC value. In this paper, they are set α₁ = 0.25, and α₂ = 0.001.

According to Behrman's principle, the recursive equation that solves the above objective function is as follows: [Image Omitted. See PDF]where $${J}_{k}^{* }$$ denotes the optimal solution at kth moment, and $${J}_{N}^{* }$$ = 0.

As Equation (18) shows, the objective function for dynamic programming consists of a constraint on the hydrogen consumption, a constraint on the SoC deviation, and a constraint on the fuel cell current. The controller must satisfy certain constraints, which are shown in Equation (17). The core function of dynamic programming is to decompose a multistage process into a series of inter-related single processes and to then solve the series in order or in reverse.

ECMS-based strategy

The ECMS is an algorithm for online control usually associated with lower fuel consumption than other algorithms. As a causal control algorithm, it is not restricted by any specific condition and aims to minimize consumption on every sampling occasion. The presented strategy divides the total energy consumption into two parts: the hydrogen consumption by the fuel cell and the equivalent consumption by the battery. The energy change in the battery should therefore be identical to that of the fuel cell. The cost function is as follows: [Image Omitted. See PDF]where k_S, β, and β₀ are coefficients. These coefficients can be selected by a large amount of experimental or empirical data. In this paper, they are set k_S = 0.5 and β₀ = 0.8.

Here, the instantaneous energy consumption rate is given by the mass of consumed hydrogen plus the equivalent energy consumed by the battery. To calculate the consumption rate accurately, ECMS uses a variable equivalent coefficient (β), determined based on the working conditions of the HUAV, and then adjusted in real-time according to the battery SoC.

PMP-based strategy

The PMP-based EMS can provide effective offline and online solutions for maximizing HUAV flight times and fuel cell lifetime. To achieve a long endurance time and fuel cell lifetime, a scenario must determine the optimal power distribution between the fuel cell and battery while minimizing the energy supplied to the hybrid system per unit time. PMP is an instantaneous optimization algorithm that can obtain a locally optimal solution. We consider two types of PMP: one that only considers energy consumption, and one that also considers the specific objectives. It is widely known that high-frequency, peak current changes decrease the operation lifetime of a fuel cell.

To prolong fuel cell lifetime, we consider the fuel cell current and rate of change in the optimization process. According to the model for fuel cell aging, it is theoretically possible to prolong the fuel cell lifetime by controlling these two variables. For all power units, we must therefore consider their output power limitations and instantaneous rate of change. The Hamiltonian function of a basic PMP is defined in Equation (21), and that of the improved PMP is defined in Equation (22). [Image Omitted. See PDF] [Image Omitted. See PDF]where λ is co-state variable. γ₁ and γ₂ are tuning parameters. These coefficients can be selected by a large amount of experimental or empirical data. In this paper, they are set λ = −2.5, γ₁ = 0.05, and γ₂ = 0.005.

The Hamiltonians used to solve the above equations are as follows. [Image Omitted. See PDF] [Image Omitted. See PDF]where * denotes the optimal variable value.

A set of necessary constraints is shown in Equation (21), and some terminal constraints are shown as follows: [Image Omitted. See PDF] [Image Omitted. See PDF] [Image Omitted. See PDF]where T_end denotes the end time of the flight.

SYSTEM OPTIMIZATION DESIGN

Multicopters have many design parameters. To design a HUAV, components satisfying certain performance requirements, such as good hovering endurance, system efficiency, and maximum load, etc., must be considered. Many designs are the result of experimentation or experience, and often show inefficient performance and high cost. How the choice of components is related to the performance remains a complex problem that is hard to solve by experimentation or experience alone. For a HUAV, component size is a complex parameter and is usually calculated theoretically. In this paper, we consider the synergy between sizing optimization and the EMS, for a realistic representation of the actual operating conditions of HUAV. Here, the task of parameters design is divided into two parts: static design, and synergistic sizing optimization. The former task focuses on the basic flight parameters, such as the hovering state, and constant speed. The dynamic power load is taken to represent the propellers and motors. The latter task focuses on adjusting the system parameters according to the performance of the control strategies.

Static design

The algorithm for static parameters design is consistent with the traditional design method. The parameters of each component are calculated according to the desired performance. We adopted a backward deduction approach, with the starting point being the performance requirement. The information is passed backward via the power components, including the propellers, motors, ESC, and power sources. Backward deduction considers the conversion efficiency of the overall powertrain, as well as the interactions among the components. The electric energy demanded by the components is split in an appropriate way. This approach needs an accurate mathematical system model, as presented in Section 2. The process of the design method is: Generate all design parameter combinations, and select a group of design parameters at random; Set the design parameters of the system model; Take the representative load spectrum of UAV as the input of the system model; Start the model simulation with the specific EMS; Evaluate the design scheme according to the simulation results, including hydrogen consumption, endurance time, the current state of fuel cell; Repeat the above process to obtain all effective design parameter combinations. Therefore, a flowchart of the static design is illustrated in Figure 4.

Figure 4. Schematics of the static design

There are many design parameters of HUAV, and some important parameters are of special concern, such as propeller size, and battery size. These critical parameters are closely related to product performance. Therefore, designers should fully be well aware of the parts' performance to design a better HUAV. This paper focuses on the parameter design methodology. In the given case, it is assumed that the propellers belong to the same characteristics and that the motor and ESC can provide enough power in a large range. It is assumed that the rated power of the single fuel cell is 5 W, and the battery cell is a 3.7 V/3700 mhA module. Finally, this paper selects propeller diameter, propeller number, fuel cell stack power, number of battery cells, and capacity of hydrogen tank as variables to test the proposed methodology. That is, the design variable is $$X={\{}^{{D}_{P},nu{m}_{P},nu{m}_{FC},nu{m}_{B},nu{m}_{{H}_{2}}}$$. The range of the design variables is listed in Table 1, together with their lower and upper bounds.

Table 1 Range of the design variables

Design variables	Unit	Lower bound	Upper bound
Propeller diameter (DP)	inch	5	20
Propeller number (Even) (numP)		4	8
Fuel cell rated power (5numFC)	W	500	3000
Number of battery cell (numB)		4	12
Hydrogen tank capacity $$\left((,nu{{m}_{H}}_{2},)\right)$$	L	3	9

Note: These variables belong to the powertrain parameters, and characterize the size and operating conditions of the different components of the hybrid system. Note also the large number of constraints, which ensures that the results are physically and geometrically feasible. Constraints for hybrid system of the HUAV have been shown as Equation (17). Some model parameters and performance constraints of the HUAV are shown in Tables 2 and 3.

Using the parameters given in Tables 1–3, several design results can be obtained through static design methodology. For quad-, hexa-rotor, and octo-rotor schemes, there are many applicable design results, several examples of which are given in Table 4. The performance criteria include minimum mass, maximum lift (maximum load mass), and flight endurance time. When calculating the maximum lift, it is assumed that the performance of the motors and propellers is good enough under given constraints. As maximum load mass is the load capacity under maximum lift, these two criteria belong to the same optimization goal. [Image Omitted. See PDF]where $${E}_{{H}_{2}}$$  and E_BAT are the electricity supplied by hydrogen and battery, respectively. T_FET is the flight endurance time of an HUAV.

Table 2 Model parameters

Performance	Unit	Vaule
Motor mass (mm)	kg	0.15
DC/DC converter mass (mDC)	kg	0.3
Single fuel cell mass (mFC)	kg	0.0075
Gravity coefficient (g)	N/kg	9.8
Air density (ρ)	kg/m3	1.293
Nominal no-load motor constant (KV)	rpm/V	900
Motor armature resistance (Rm)	Ω	0.08
Motor nominal no-load voltage (Um0)	V	10
Motor nominal no-load current (Im0)	A	0.6
ESC resistance (Re)	Ω	0.008
Battery cell capacity (QB/numB)	mAh	3700
Battery cell voltage	V	3.7
Battery cell mass (mB)	kg	0.05
Airframe mass (m0)	kg	1

Table 3 Design constraints

Performance	Unit	Vaule
Load mass (mL)	kg	≥1
Take-off mass (m)	kg	≤7
No-load flight endurance time	min	≥120
Body radius	m	≤1.2
Flight altitude	m	≥150
Maximum motor current (Im max)	A	≤60
Propeller and motor speed (NP)	rpm	≤8000
Propeller tip speed (πDPNP)	Ma	≤0.7
Propeller pull (TP)	Nm	≤60
Hovering throttle	%	≤65
Battery cell voltage	V	3.7
Battery cell discharge rate (ΔIB max)	C	≤30
Battery cell charge rate (ΔIBmin)	C	≤5

Table 4 Examples of design results

Design variables	Unit	Scheme 1	Scheme 2	Scheme 3	Scheme 4
Optimization objective		Minimum mass		Maximum endurance	Maximum lift
Propeller diameter (DP)	inch	15	15	16	14
Propeller number (numP)		4	6	8	8
Fuel cell rated power (5numFC)	W	1900	1400	1200	2000
Number of batteries (numB)		4	7	4	4
Hydrogen tank capacity $$\left((,nu{{m}_{H}}_{2},)\right)$$	L	3	6	6	3
Flight endurance time	min	121.2	265.7	319.7	147.6
No-load mass (mN)	kg	5.16	5.79	5.68	5.96
Maximum lift (numPTP)	Nm	76.4	76.74	75.8	101.8
Maximum load mass (mL)	kg	1.63	1.04	1.06	3.43

As can be seen from Table 4, long flight endurance time and heavy load capacity are achievable goals. For scheme 1 (quadcopter), the no-load mass is only 5.16 kg with a 3 L hydrogen tank, although using a small hydrogen tank led to a shorter flight endurance time. However, for light and small-size UAV applications, scheme 1 is feasible. Scheme 2 (hexacopter) uses a 1400 W fuel cell, seven battery cells, and a 6 L hydrogen tank, and the flight-endurance time of scheme 2 is second only to scheme 3. Among the octocopter schemes, scheme 3 has the lowest fuel cell power (1200 W) but the longest flight-endurance time (319.7 min). This scheme is appropriate for extremely long-endurance UAVs. Scheme 4 has the largest maximum load mass (3.43 kg) and the maximum fuel cell power (2000 W), making it suitable for carrying heavy accessories. Overall, these schemes are reasonable and feasible, as they meet the basic performance requirements of the HUAV and have outstanding advantages in some specific performance criteria. The optimal scheme can be selected according to the actual situation or specific performance requirements, as shown in Figure 4. How each parameter affects performance is very important for HUAV design. This will be analyzed in detail in Section 5.

In the approach detailed above, the parameters of each HUAV component were calculated reversely according to the specific requirements before arriving at a representative operation point. This approach is suitable for a simple power system but is difficult to apply to a system with multiple power sources. The synergy of workload and EMS also cannot be considered in this approach, and the performance of the fuel cells and battery cannot be effectively evaluated.

Analysis of design variables sensitivity

During system design, it is very necessary to clarify how the design variables affect the system performances. The performance characteristics of the HUAV will change with changes in the design variables. Therefore, this paper analyses the design variables' sensitivity. Based on static design, this paper focuses on two important performances of HUAV—flight endurance time and load mass, and analyses the change in performance with the change in design variable. Based on the performance requirements and design variable bounds listed in Tables 1–3, this paper has selected several sets of specific design variables for use in this analysis, keeping other design variables unchanged. The design variables are taken from the minimum value interval to the maximum value. The static design method is used to obtain the corresponding performance with the selected parameters. The results are shown in Figures 5–9.

Figure 5. Performance of a HUAV with propeller size (8 propellers, 1200 W fuel cell, 4 battery cells, 6 L Hydrogen tank). HUAV, hybrid unmanned aerial vehicle.

Figure 6. Performance of a HUAV with the number of propellers (16-inch propeller diameter, 1600 W fuel cell, 4 battery cells, 9 L Hydrogen tank). HUAV, hybrid unmanned aerial vehicle.

Figure 7. Performance of a HUAV with fuel cell size (16-inch propeller diameter, 8 propellers, 4 battery cells, 9 L Hydrogen tank). HUAV, hybrid unmanned aerial vehicle.

Figure 8. Performance of a HUAV with battery size (16-inch propeller diameter, 8 propellers, 1600 W fuel cell, 6 L Hydrogen tank). HUAV, hybrid unmanned aerial vehicle.

Figure 9. Performance of a HUAV with hydrogen tank size (16-inch propeller diameter, 8 propellers, 1600 W fuel cell, 4 battery cells). HUAV, hybrid unmanned aerial vehicle.

It can be seen from Figure 5 that when the size of the propellers gradually increases to 15–16 inches, the flight endurance time and load mass gradually improve, and the endurance can be increased by 10.9%, and the load mass by 23.8%. When the propeller sizes continue to increase, the performance starts to decline. In theory, the larger the propeller size, the longer the hovering time, as, with a large propeller, a lower speed provides the same thrust. However, this relationship is valid only within a certain range. These results suggest that the selection of propeller sizes needs to be appropriate to the application. As can be seen from Figure 6, performance gradually improved with an increasing number of rotors, with flight endurance for the hexa- and octo-rotor layouts compared to the quad-rotor layout increasing by 18.8% and 31%, respectively, while for load mass, the increase was 35% and 65%, respectively. In general, when the take-off mass is the same, the more rotors, the longer the hovering time, and therefore, having more rotors can lead to better overall performance.

As Figure 7 shows, the flight endurance gradually decreases, and load mass gradually increases with increasing fuel cell size. While Figure 8 shows that flight endurance gradually decreases with increasing battery size, but the difference is no more than 7.5%. At the same time, the load mass changes from 3.3 to 3.4 kg, which means the variable is not insensitive. Finally, Figure 9 shows that hydrogen tank size has a significant impact on flight endurance. When the hydrogen tank size is increased from 5 to 9 L, the flight endurance increases from 210.5 to 377.4 min—an increase of 179.3%. This result suggests that hydrogen tank size is the primary variable that determines flight endurance. However, the load mass does not change with different hydrogen tank sizes. So, in summary, it is necessary to carefully consider the sensitivity of design variables and choose parameters according to the application.

Synergistic sizing optimization

In a hybrid system, the energy flows are much more complex. The EMS affects the energy distribution, which has a direct impact on the performance of each component. To optimize the system parameters of the HUAV, the effect of the EMSs must be considered. This requires a system model as shown in Section 2, and an appropriate EMS as shown in Section 3. For a hybrid system, the operating conditions will also affect the parameters design. Under variable demand power conditions, the advantages of the hybrid system will be fully apparent, and synergistic sizing optimization is needed. We propose a synergistic sizing optimization method based on multiple objective optimizations. Optimization objectives should be established according to work demand, with flight endurance as the primary objective. We include the mean value and standard deviation of the fuel cell current as optimization objectives in this study. Therefore, in this optimization problem, the optimization variable is still $$X={\{}^{{D}_{P},nu{m}_{P},nu{m}_{FC},nu{m}_{B},nu{m}_{{H}_{2}}}$$, and the optimization objectives are optimal endurance time and fuel cell lifetime, as shown in Equation (29). The constrains are the same as static design method.[Image Omitted. See PDF]

Synergistic sizing optimization is based on optimization theory and the EMS. The actual workload is used as the input, and a specific EMS is used to simulate the actual working conditions. Synergistic sizing optimization is characterized by multiobjective optimization and the introduction of simulation data under typical working conditions with the specific EMS. Therefore, synergistic sizing optimization design is more in line with the actual working conditions and control system for HUAV design. A multiobjective optimization algorithm was adopted to obtain a set of optimal front solutions. Research shows that, for low-dimensional multiobjective optimization problems, the NSGA-Ⅲ algorithm is very effective, which is efficient for finding the optimal Pareto solution set.⁴⁸ In this study, a classic NSGA-Ⅲ from literature⁴⁹ is used to solve the multiobjective sizing optimization problem. The detailed flowchart of the optimization scheme is illustrated in Figure 10. The pseudo-code of NSGA-Ⅲ is shown in Table 5. The design parameters of all groups were optimized within a single run. The accuracy of the results, discussed in Section 5, depends on the quality of the models.

Figure 10. Schematics of the synergistic sizing optimization

Table 5 Pseudo-code of NSGA-Ⅲ

Input: Population size N, probability of crossover and mutation, mutation strength, etc.

Output: Optimal solutions

1: Initialize population and iteration number

2: While Termination criteria is not achieved

3: Calculate the power flow of the population P(k), and calculate each objective function

4: Fast non-dominated sorting, and stratifying the population according to the value of the objective function

5: Reference point-based selection operation

6: Perform genetic operations, and obtain the offspring population Q(k)

7: Merge the parent population and the offspring population and obtain new population R(k)

8: Calculate the power flow of R(t), and calculate the value of each objective function

9: Fast non-dominated sorting according to the value of the objective function

10: Select preferable individuals to enter the next generation of population P(k + 1)

11: end

12: Output optimal solutions

13: Return

RESULTS AND DISCUSSION

To fully verify the superiority of the proposed EMSs, a small HUAV was tested. The HUAV's specifications for simulation are listed in Table 6. The simulations were performed in MATLAB. System parameters design is a function of the working load, but due to complex working conditions, there is no standard load for the UAVs. Therefore, in this study, a reference electric power request curve generated by a small all-electric hexacopter taken from the literature⁵⁰ is used, as shown in Figure 11. Since the power required is proportional to the mass raised to the power 1.5, it is possible to obtain the power required for larger multicopters from this.⁵¹ The proposed EMSs were verified by analyzing the working conditions through simulation. During the simulations, the load spectrum shown in Figure 11 was applied twice in succession.

Table 6 Reference HUAV specifications

Performance	Unit	Vaule
No-load mass (mN)	kg	5.14
Take-off mass (m)	kg	6.14
Load mass (mL)	kg	1
Propeller diameter (DP)	inch	15
Propeller number (numP)		6
Body radius	m	0.6
Flight altitude	m	150
Fuel cell rated power (5numFC)	W	800
Number of battery cell (numB)		4
Hydrogen tank capacity (31.4 g/L) $$\left((,nu{{m}_{H}}_{2},)\right)$$	L	3

Abbreviation: HUAV, hybrid unmanned aerial vehicle.

Figure 11. Representative power request of the reference UAV (taken from Donateo et al.50)

Analysis of EMSs

Based on the system model, the EMSs are simulated and validated in MATLAB, with a calculation period of 0.1 s. In the process of system simulation, the representative power is inputted into the system model. According to the set EMS, the output of the fuel cell and battery will be dynamically distributed. So that the HUAV can respond to the power request, and achieves energy management objectives. Five EMSs based on fuzzy logic, dynamic programming, ECM, PMP, and improved PMP are adopted to distribute power between the fuel cell and battery. The evaluation criteria include equivalent hydrogen consumption that has converted the battery SoC change into hydrogen consumption, theoretical flight endurance time, and mean and standard deviation of the current of a single fuel cell. The results of simulation results are presented in Table 7 and Figures 12–14.

Table 7 Simulation results of EMSs

EMS	Equivalent hydrogen consumption (g)	Flight endurance (min)	Mean current (A)	Standard deviation	Calculation time per cycle (ms)
Fuzzy logic	2.48	319.2	1.61	0.23	0.44
Dynamic programming (DP)	2.56	309.2	1.73	0.48	-
ECMS	2.46	321.8	1.69	0.45	0.14
PMP	2.40	331.2	1.35	0.40	0.52
Improved PMP	2.37	334	1.35	0.23	0.53

Abbreviations: EMS, energy management strategy; PMP, Pontryagin's minimum principle.

Figure 12. Fuel cell power under the different EMS employed. EMS, energy management strategy.

Figure 13. Battery power under the different EMS employed. EMS, energy management strategy.

Figure 14. Battery SoC under the different EMS employed. EMS, energy management strategy.

As it can be seen from Figure 12, the fuel cell power curves differ greatly under different EMSs. The fuel cell power under improved PMP is remarkedly smooth and stable. While under dynamic programming, it fluctuates greatly between 650 W and 224 W, the largest swing of all the strategies. This is because dynamic programming can make full use of the load information, and obtain the global optimal solutions, while there is no restriction on the fuel cell power change rate, so the fluctuations are relatively large within the limited range (80 W/S). ECMS also has obvious power fluctuations and a large rate of change. This stems from the fact that ECMS is designed to minimize equivalent consumption and has no constraints on power change rate. The power changes under fuzzy logic are very characteristic, with minimal swings between maxima and minima. This is because of the robust character of fuzzy logic. Therefore, fuzzy logic is a very practical online control method. Both power curves under the two PMPs have definite fluctuations. Except for when the load changes are greatest, the power changes very smoothly. This is because PMP considers battery SoC to minimize fluctuation. The improved PMP considers the mean and standard deviation of the fuel cell current based on the basic PMP, and so the fuel cell current fluctuates particularly smoothly under the improved PMP.

Figures 13 and 14 show the variations in battery power and SoC, which are directly related. The battery power can be considered to be the difference between the load and the fuel cell power. In Figure 13, the results with dynamic programming and ECMS differ from those of the other strategies. The battery under dynamic programming tends to provide a more stable output/input of between 308.8 and 240.6 W. Therefore, the corresponding battery SoC in Figure 14 also changes little, ranging between 0.798 and 0.811. Under ECMS, the battery does not contribute to power compensation most of the time, so the battery power is close to 0. And the battery SoC fluctuation in Figure 14 is also very small, ranging between 0.8 and 0.811. Under fuzzy logic, the battery always works to maintain the balance of SOC, and due to its robustness, the fluctuations in battery power are not large. The corresponding battery SoC ranges between 0.732 and 0.806. Under both basic and improved PMP, the battery power fluctuates more obviously than with the other algorithms, and it also fluctuates all the time. The control effect of both PMP-based strategies is similar, but the power fluctuation of the improved PMP is the smaller of the two. This is because PMP-based strategies tend to make full use of the battery. The basic and improved PMP-strategy SoC curves fluctuate and fall in the range of [0.604, 0.8] and [0.595, 0.8], respectively.

Table 7 gives the performance metrics of the simulation. The equivalent hydrogen consumption under the fuzzy logic, dynamic programming, ECMS, PMP, and improved PMP strategies are 2.48, 2.56, 2.46, 2.40, and 2.37 g, respectively. Assuming the HUAV keeps flying under the given cyclic load, then, the corresponding theoretical flight endurance time would be 319.2, 309.2, 321.8, 331.2, and 334 min, respectively. Dynamic programming has the highest hydrogen consumption, while improved PMP has the lowest. This is because, under dynamic programming, fuel cell power fluctuates greatly, reducing energy efficiency. Fuel cell power is most stable under the improved PMP, so its energy consumption under that scenario is also the lowest. Improved PMP increases flight endurance by 8% compared to dynamic programming and by 4.64% compared to fuzzy logic. Although ECMS aims at the lowest energy consumption, due to the large fluctuations in fuel cell power, it saves only 0.8% more hydrogen consumption than fuzzy logic. These results show that PMP strategies, especially improved PMP, can achieve longer flight endurance than other strategies. The mean currents of the fuel cell under the five strategies are 1.61, 1.73, 1.69, 1.35, and 1.35 A, respectively, and the corresponding standard deviations are 0.23, 0.48, 0.45, 0.40, and 0.23, respectively. These correspond to the power change of the fuel cell, as discussed above. The more drastic the change of fuel cell power is, the larger the mean current and the standard deviation are. The improved PMP-based EMS improved the fuel cell lifetime by reducing the mean and standard deviation current of the fuel cell by 22% and 52.1%, respectively, compared with dynamic programming, and reducing the mean current by 16.1% compared with fuzzy logic. These results demonstrate that the improved PMP-based EMS effectively achieves the optimization objectives. In theory, the fuel cell lifetime and durability are greatly improved.

In general, dynamic programming, as an offline evaluation strategy, can obtain the global optimum, but its control effect is not necessarily as required. The robustness of fuzzy logic is strong, and the actual control effect is acceptable, which is a fundamental online control strategy. In contrast, the control effect of ECMS is less than desirable. When multiple objectives are considered, PMP can still achieve better results, and it is a recommended online control algorithm.

Analysis of sizing optimization

As the results of the previous section show, the three optimization objectives are maximum flight endurance time and minimum mean and standard deviation of the current of the fuel cell. This is a typical multiobjective optimization problem, which, in this study, we solve using the NSGA-III algorithm. The population size was set to 200, the mutation rate to 0.02, and both the crossover and mutation percentages to 0.5. The performance of the NSGA-III algorithm in the optimization process was analyzed, especially during the acceleration phase (reflected in the optimal front; Figure 15).

Figure 15. Optimization results of NSGA-III for (A) the Quadcopter, (B) the Hexarotor, and (C) the octocopter. NSGA-III, non-dominated sorting genetic algorithm-II.

Figure 15 shows plots of the normalized curve for the optimal front, which denotes the optimal solution calculated by NSGA-III, in terms of maximizing the flight endurance time and minimizing the mean and standard deviation of the fuel cell current. Three NAGA-III obtained effective front solutions, and the sizing optimization was most responsible for the performance improvements achieved. The multiattribute decision-making method can be used to evaluate the Pareto frontier solution set and find an optimal solution. While the optimization objectives are classified according to the attribute characteristics. The flight endurance time belongs to the benefit index, the mean current to the qualitative attribute, and the current standard deviation to the cost attribute. Multiattribute decision-making generally compares the ranking of comprehensive attribute values of the solution set with the decision information being aggregated by weighting the arithmetic average operator. For the three layout schemes, the synergy between the sizing optimization and EMS makes it possible for the optimal configuration to be determined, even though the three objectives have certain contradictions. The final configuration chosen depends on the relative importance of the three objectives, and, based on their priorities, designers may need to flexibly adjust the weight.

CONCLUSIONS

In this paper, we proposed a sizing optimization methodology and five EMSs for fuel cell/battery-powered HUAVs. A mathematical model of a HUAV was established. With the objectives of improving flight endurance and fuel cell lifetime, the five EMSs are based on fuzzy logic, dynamic programming, ECMS, PMP, and improved PMP. The EMSs were validated by MATLAB simulations, which showed that the power flow between the sources was effective. The improved PMP-based EMS prolonged the fight endurance by 4.64% and 8% compared with fuzzy logic and dynamic programming EMS, respectively. It also improved the fuel cell lifetime by reducing 22% mean current and 52.1% standard deviation of the fuel cell compared with dynamic programming and reducing 16.1% mean current compared with fuzzy logic. The sizing optimization scheme for the HUAVs is divided into two parts, that is, a static design, and synergistic sizing optimization. By considering the synergy between aircraft design and the EMSs, a methodology for multiobjective optimization was proposed. Improving the flight endurance and fuel cell lifetime were the objectives of the optimization process. The calculations were performed by NSGA-Ⅲ. Numerical results showed that NSGA-Ⅲ well approximated the front solutions. Large performance improvements were possible by considering the synergy between the aircraft design and control strategy, where synergy gave optimal solution set to the overall performances. Design variables sensitivity was also addressed for better HUVA design. Importantly, this study shows that HUAV design can benefit from consideration of the EMS. The performance of HUAVs could be further improved through EMS optimization. During the missions of UAV, there are many scheduled flight and trajectory tracking flights. How to make effective use of motion control information and combine EMS with motion control, is an issue worthy of in-depth study. We will investigate the integration of EMS and motion control for HUVAs in the near future.

ACKNOWLEDGMENTS

This study was supported by the National Natural Science Foundation of China [grant number 51805200]; the Scientific Research Project of Jilin Provincial Department of Education [grant number JJKH20220978KJ]; and the Fundamental Research Funds for the Central Universities.

CONFLICT OF INTEREST

The authors declare no conflict of interest.