# Integrated Optimal Design for Hybrid Electric Powertrain of Future Aircrafts

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## Abstract

**:**

_{2}emissions and environmental impacts of the aviation sector.

## 1. Introduction

_{2}emissions [1]. COVID-19 has transiently slowed down air traffic and has strengthened the need to respect the environment as focused in the “Clean Sky” framework. The ACARE (Advisory Councilor Aviation Research and Innovation in Europe) sets environmental objectives for 2050 technologies with a 75% reduction in CO

_{2}emissions per passenger kilometer and a 90% reduction in NOx emissions. The perceived noise emission of flying aircrafts should be reduced by 65%. These figures are relative to the capabilities of a typical new aircraft in 2000. More generally, the aviation industry actually faces the “revolution towards more electric aircrafts” [2,3,4,5,6,7,8]. In this context, more than 200 projects of electrically propelled aircrafts have emerged in recent years [3,8]. Some of them are supported by well-known industrial companies (Airbus, Boeing, Rolls Royce), others from start-ups or new companies born in the aeronautical industry. In the USA, NASA is also active with the “X-57 LEAPTECH” project investigating an aircraft with distributed propulsion [9]. In France, ONERA [10,11] also studies other aerodynamic concepts such as “Dragon” or “Ampere”.

#### 1.1. Literature Review

#### 1.2. Main Contributions

- -
- The proposed MDO based on technological models which emphasize the innovation and sensitivity of technological progress in future hybrid electric aircrafts. Local optimizations (i.e., motor weight minimization) are compared with global optimizations (i.e., minimization of the whole powertrain, then fuel burn reduction at aircraft level). As previously mentioned, technological aspects are often quite simplified in the state of the art of the MDO process. The MDO process is introduced in Section 2;
- -
- Here, main physical fields (electrical, mechanical, thermal) and main environmental constraints (partial discharges, thermal limits, etc.) are integrated in technological models of the powertrain devices which assess weights and losses (efficiencies) in power electronics, electric motors and cooling devices, with high power ranges involving high voltage insulation with partial discharges consideration. These technological models are gathered inside the MDO process with the other powertrain devices (gas turbines, fuel cells, distribution bus, cables, gearbox), which are modelled;
- -
- The MDO process is all the more complex in that technological models are integrated in system optimization: thus, device models must be “just enough accurate but not too complex” to assess both weights and efficiencies with respect to the design variables set (the decision variables for optimization) at the model input, with acceptable computation time. A set of design surrogate models based on analytical derivation or response surfaces is synthesized in Section 3, but readers may find a more detailed description on technological models in several papers referenced in this section;
- -
- “Snowball effects” are strongly influent in aircraft applications and correspond to complex couplings between weight variations at device level and structural, aerodynamic and propulsion requirements at aircraft level: the higher the embedded weight, the larger the structure (wing surface) and consequently the higher the fuel burn, with more fuel weight also meaning more embedded weight. In most of the MDO process, these snowball effects are integrated by means of really simplified design models [4,8,26,27,28,29]. In that paper, in order to face the complexity issue to optimize the whole powertrain from technological models, a simplified integration process is proposed by breaking the coupling with the aircraft structure. The proposed process decouples optimization of the powertrain from the aircraft structure by linearizing thrust needs with respect to the device mass variations during the convergence of the optimization loop. This issue is presented in Section 4;
- -
- Several papers also propose MDO approaches coupled with the flight mission of the aircraft but are usually based on rough models related to specific powers/energies and efficiency figures [15]. Here the integrated optimal process based on technological models is also coupled with a flight mission operating two different EMS during typical regional flight.
- -
- The proposed MDO formulation highlights typical (a priori unexpected) systemic couplings: for example, the optimization results would lead to oversized propeller diameter in order to maximize its efficiency and to optimize the system performance in terms of fuel burn.

## 2. The HASTECS Project: A Series Hybrid Electric Powertrain for Regional Aircraft

## 3. MDO-Oriented Modeling of the Hybrid Electric Powertrain

#### 3.1. Introduction to the MDO Process

- -
- requirements (flight mission: aircraft speed, altitude, thrust);
- -
- an environment model setting pressure and temperature variations over the flight mission;
- -
- a set of technological models constituting the integrated powertrain, each model identifying mass and efficiency of each component. As illustrated in Figure 2a, the powertrain design is addressed sequentially, starting from propulsion (thrust, speed) requirements specified over the flight mission, then crossing the powertrain models from downstream elements (propeller and gearbox) to upstream elements, i.e., the power sources (gas turbine and fuel cell) for which power is shared by the EMS. In the middle of the propulsion chain, the actuator part consisted of a voltage source inverter-fed permanent magnet synchronous motors (PMSM), which is really sensitive in terms of weight and efficiency;
- -

- -
- As illustrated in the chart above, the hybrid electric powertrain design process progresses step by step, starting from downstream devices (propeller and gearbox), then assessing the actuation sub system (voltage inverter-fed electric motor) and completing the design with upstream (hybrid power sources) powertrain devices. Indeed, based on mission requirements specified by propulsion needs (i.e., aircraft thrust and speed), efficiencies of downstream elements progressively increase the power needs of upstream devices. In this manner, power sources (gas turbines and fuel cells) and storage (hydrogen tank and fuel mass) are finally designed in that process by operating an energy management strategy (EMS) that shares power flows between both sources over the flight mission;
- -
- A single objective function is derived by means of all technological model outputs. Several optimization formulations are compared in Section 4: a local one, only minimizing the electric motor (“Emotor”) mass, and two global optimization loops, minimizing the whole powertrain mass then the fuel burn. For each algorithm iteration, the clearing proposes a set of “decision variables” (X) which are set at the input of each design model;
- -
- These design models derive the set of constraints and participate to build the objective function. This latter (Y) is sometimes penalized if one of all constraints (C) is not fulfilled. As illustrated on the synoptic, a large set of design constraints related to all devices are progressively analyzed during the process. Some of them are a priori tested to assess the feasibility of the design to simulate the flight mission: for example, the stator winding feasibility of Emotors is a priori verified by taking account of partial discharge phenomena in the system environment (temperature, pressure) and regarding the voltage ratings. A second set of constraints is analyzed during the whole mission for each flight sequence. It is, for example, the case for thermal constraints in both power electronics and electric motors.
- -
- An EMS sharing the power between both sources is also operated during the virtual flight: thermal power source based on gas turbines (pink colored in the synoptic) vs. electric power source based on fuel cells (green colored in the synoptic).

#### 3.2. Review of MDO-Oriented Technological Models

- -
- Analytical models are to be used when possible, being often accurate with good convergence capabilities for optimization: in this study, power electronics as well as electromechanical and thermal cooling parts of electric motors are analytically derived. A particular modelling effort has been paid on that device which is the most sensitive component inside the powertrain regarding both weight and efficiency indicators. More details on sensitivity aspects can be found in [37].
- -
- Design models based on similarity laws [30] constitutes another efficient way to derive surrogate models: in our case study, the propeller design model exploits that approach by coupling analytical equations to derive the propeller efficiency with similarity laws to estimate its weight.
- -
- Finally, surface response-based models are often the solution when analytical derivation or similarity laws are impossible or too complex: in this study, it has been the case for several studies such as gas turbines and gearbox.
- -
- All model details cannot be provided in this paper and only some major aspects are summarized and referenced in the next sub section, starting from downstream (propeller) and going to upstream (hybrid power sources) powertrain devices.

#### 3.2.1. Modelling of Propulsion Devices

_{prop}) during the flight (see Figure 3): given the aircraft thrust (T

_{A/C}) and speed (V

_{A/C}) specified by requirements over the flight mission, the disk actuator theory allows us to analytically derive the mechanical power (P

_{shaft}) of the propeller shaft and its efficiency. The “sizing model” allows us to assess, in particular, the propeller mass (M

_{prop}). This estimation is based on a similarity law (scaling model) referenced from the design of the existing propeller related to the ATR72 aircraft from which the propeller mass versus diameter ratio is known. Input/output variables are displayed in Table 1, and more details on that surrogate model are proposed in [8,35]

#### 3.2.2. Modelling of the Electric Motor (Emotor)

- -
- First, the turn-to-turn voltage is assessed depending on the power electronics structure. The PDIV (partial discharge inception voltage) is then derived, taking account of temperature and pressure (altitude) conditions. Then, the insulation thickness is calculated together with insulation material choices [43];

- -
- Second, the liner (bottom of the slots) thickness is estimated from the maximum voltage between turns and yoke.

#### 3.2.3. Modelling of Power Electronics with Its Thermal Cooling

#### 3.2.4. Modelling of Hybrid Power Sources

## 4. Multidisciplinary Design Optimization of the HASTECS Hybrid Electric Powertrain

#### 4.1. Integrated Design of A Hybrid Electric Aircraft with a “Simple Hybridization Scenario”

- (1)
- A “local optimization” only minimizing the electric motor mass;
- (2)
- A “powertrain optimization” minimizing its whole mass;
- (3)
- A “fuel burn optimization”.

_{c}= 1 and p

_{m}= 1%). Due to the stochastic nature of the clearing algorithm, multiple runs were repeated for each optimization case. It contributes to increase the reproducibility of results. The CPU time required for solving each optimization case on a standard computer was about seven days.

#### 4.2. Integrated Design of a Hybrid Electric Aircraft with an Optimal Hybridization Scenario

## 5. Conclusions and Prospects

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Multidisciplinary design optimization of the hybrid electric powertrain: (

**a**) the set of design models coupled in the MDO process; (

**b**) the MDO process integrating environment.

**Figure 4.**Regression model for gearbox weight assessment (see [17]).

**Figure 5.**Analytical multifaceted model (

**a**) with geometry, (

**b**) design and performance of Emotor (PMSM).

**Figure 13.**Parametric regression of the turboshaft design model; SFC is the ratio between weight and the energy fed by the gas turbine.

**Figure 17.**Comparison of optimization results for three MDO formulations. (

**a**) Fuel mass; (

**b**) powertrain mass; (

**c**) Emotor specific power; (

**d**) powertrain efficiency; (

**e**) propeller diameter; (

**f**) UHVDC voltage.

**Figure 18.**Energy management system (EMS) optimization. (

**a**) Hybrid ratio with the simple EMS; (

**b**) Hybrid ratio with the optimized EMS; (

**c**) Power sharing with the simple EMS; (

**d**) Power sharing with the optimized EMS.

**Table 1.**Input/output variables for propeller model (in bold, the decision variables for optimization).

INPUT VARIABLES THE DECISION VARIABLE FROM OPTIMIZATION (IN BOLD) | ||
---|---|---|

${\rho}_{air}\left(t\right)$ | $\left[\mathrm{KG}.{\mathrm{M}}^{-3}\right]$ | AIR DENSITY |

${V}_{A/C}\left(t\right)$ | $\left[\mathrm{M}.{\mathrm{S}}^{-1}\right]$ | A/C VELOCITY |

${T}_{A/C}\left(t\right)$ | $\left[\mathrm{N}\right]$ | A/C THRUST |

${\mathit{D}}_{\mathit{p}\mathit{r}\mathit{o}\mathit{p}}$ | $\left[\mathrm{m}\right]$ | PROPELLER DIAMETER |

OUTPUT VARIABLES | ||

${P}_{shaf{t}_{}}\left(t\right)$ | $\left[\mathrm{W}\right]$ | PROPELLER SHAFT DIAMETER |

${\eta}_{prop}\left(t\right)$ | $\left[\%\right]$ | PROPELLER EFFICIENCY |

${M}_{prop}$ | $\left[\mathrm{KG}\right]$ | PROPELLER MASS |

${N}_{prop}{}_{max}$ | $\left[\mathrm{RPM}\right]$ | MAXIMUM PROPELLER ROTATIONS SPEED |

${D}_{prop}{}_{check}$ | $\left[\mathrm{M}\right]$ | PROPELLER DIAMETER CHECKING LAW |

INPUT VARIABLES: 10 Decision Variables for Optimization (In Bold) | ||
---|---|---|

${R}_{alesage}$ | $\left[m\right]$ | Bore radius of the electric motor |

${R}_{Dro{t}_{lm}}$ | $\left[\%\right]$ | Rotor diameter/rotor length ratio |

${R}_{{g}_{ral}}$ | $\left[\%\right]$ | Air gap thickness/bore radius ratio |

${R}_{h{s}_{ral}}$ | $\left[\%\right]$ | Slot height/ bore radius ratio |

${R}_{p{m}_{ral}}$ | $\left[\%\right]$ | Magnet thickness/bore radius ratio |

${\tau}_{magnet}$ | $\left[\%\right]$ | Pole pitch (=100%) |

${\tau}_{slot}$ | $\left[\%\right]$ | Slot pitch (=100% full pitch winding) |

${k}_{carbon}$ | $\left[-\right]$ | Carbon fiber constant for sleeve equation |

$p$ | $\left[-\right]$ | Number of pole pairs |

$q$ | $\left[-\right]$ | Number of phases |

$nepp$ | $\left[-\right]$ | Number of slots per pole and per phase |

${N}_{ce}$ | $\left[-\right]$ | Number of conductors per slot |

${k}_{fill}$ | $\left[-\right]$ | Fill factor in the slot |

${J}_{a}$ | $\left[\mathrm{T}\right]$ | Permanent magnet flux density |

${B}_{yoke}$ | $\left[T\right]$ | Stator yoke flux density |

${B}_{teeth}$ | $\left[\mathrm{T}\right]$ | Stator teeth flux density |

${B}_{yok{e}_{rotor}}$ | $\left[\mathrm{T}\right]$ | Rotor yoke flux density |

${V}_{uHVDC}$ | $\left[\mathrm{V}\right]$ | Ultra high voltage direct current |

OUTPUT VARIABLES | ||

${M}_{motor}$ | $\left[\mathrm{kg}\right]$ | Electric motor mass |

$PF\left(t\right)$ | $\left[-\right]$ | Power factor mission |

${m}_{a}\left(t\right)$ | $\left[-\right]$ | Modulation depth mission |

${P}_{JDC}\left(t\right)$ | $\left[\mathrm{W}\right]$ | DC Joule losses |

${P}_{Iron}\left(t\right)$ | $\left[\mathrm{W}\right]$ | Iron losses |

${P}_{R}\left(t\right)$ | $\left[\mathrm{W}\right]$ | Friction losses |

${P}_{Aero}\left(t\right)$ | $\left[\mathrm{W}\right]$ | Aerodynamic losses |

${h}_{XX},{e}_{XX},{L}_{XX},{R}_{XX},{w}_{XX}$ | $\left[\mathrm{m}\right]$ | Sizes of the e-motor |

INPUT VARIABLES: The Decision Variables for Optimization (In Bold) | ||
---|---|---|

$m{a}_{mission}\left(t\right)$ | $\left[-\right]$ | Modulation depth over mission |

$F{P}_{mission}\left(t\right)$ | $\left[-\right]$ | Power factor over mission |

${f}_{ele{c}_{emot}}\left(t\right)$ | $\left[\mathrm{Hz}\right]$ | Electric frequency |

$n{b}_{phase}$ | $\left[-\right]$ | Number of phases |

$COM$ | $\left[-\right]$ | Control of the power electronics (PE) |

$TOPO$ | $\left[-\right]$ | Topology of the PE |

${I}_{rating}$ | $\left[\mathrm{A}\right]$ | Current rating of IGBTs |

${V}_{uHVDC}$ | $\left[\mathrm{V}\right]$ | Ultra-high direct current voltage |

${P}_{ele{c}_{mission}}\left(t\right)$ | $\left[\mathrm{W}\right]$ | Electric power over mission |

OUTPUT VARIABLES | ||

${M}_{cooling}$ | $\left[\mathrm{kg}\right]$ | Cooling mass |

${M}_{inverter}$ | $\left[\mathrm{kg}\right]$ | Inverter mass |

${\eta}_{inverter}\left(t\right)$ | $\left[\%\right]$ | Inverter efficiency over mission |

${P}_{D{C}_{cable}}{}_{mission}\left(t\right)$ | $\left[\mathrm{W}\right]$ | Electric power required at the PE input |

Decision Variables | Name of Variables | Lower Bound | Upper Bound |
---|---|---|---|

$RThrust$$$] | Thrust ratio due to snowball effect | 1 | 1.26 |

${D}_{pro{p}_{siz}}\left[\mathrm{m}\right]$ | Propeller diameter | 2 | 5 |

${R}_{gbox}\left[-\right]$ | Gearbox ratio | 1 | 20 |

${V}_{uHVDC}\left[V\right]$ | Ultra-high direct current voltage | 540 | 5000 |

${R}_{alesage}\left[\mathrm{m}\right]$ | Inner radius of the stator | 0.05 | 0.25 |

${R}_{dro{t}_{Lm}}\left[\%\right]$ | Ratio between the rotor diameter and the active length | 50 | 125 |

${R}_{h{s}_{ral}}\left[\%\right]$ | Ratio between the stator slot and the inner radius | 10 | 150 |

${R}_{{g}_{ral}}\left[\%\right]$ | Ratio between the air gap thickness and the inner radius of the stator | 1 | 10 |

${R}_{p{m}_{ral}}\left[\%\right]$ | Ratio between the magnet thickness and the inner radius of the stator | 5 | 50 |

${B}_{teeth}{}_{max}\left[T\right]$ | Maximum teeth flux density | 1 | 1.53 |

${B}_{yoke}{}_{max}\left[T\right]$ | Maximum yoke flux density | 1 | 1.53 |

${N}_{ce}\left[-\right]$ | Number of conductors per slot | 1 | 4 |

${n}_{epp}\left[-\right]$ | Number of slot per pole per phase | 1 | 3 |

$p\left[-\right]$ | Number of pole pairs | 1 | 7 |

Fuel Cell—Liquid H_{2} | 2025 Target | 2035 Target |
---|---|---|

Specific Power (Fuel Cell + BoP ^{1}) | 1 kW/kg | 1.3 kW/kg |

LH_{2} Compactness | 20% | 25% |

^{1}BoP: Balance of plant including air compressor, H2 recirculation pump, cooling w/o external heat exchanger.

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## Share and Cite

**MDPI and ACS Style**

Pettes-Duler, M.; Roboam, X.; Sareni, B.
Integrated Optimal Design for Hybrid Electric Powertrain of Future Aircrafts. *Energies* **2022**, *15*, 6719.
https://doi.org/10.3390/en15186719

**AMA Style**

Pettes-Duler M, Roboam X, Sareni B.
Integrated Optimal Design for Hybrid Electric Powertrain of Future Aircrafts. *Energies*. 2022; 15(18):6719.
https://doi.org/10.3390/en15186719

**Chicago/Turabian Style**

Pettes-Duler, Matthieu, Xavier Roboam, and Bruno Sareni.
2022. "Integrated Optimal Design for Hybrid Electric Powertrain of Future Aircrafts" *Energies* 15, no. 18: 6719.
https://doi.org/10.3390/en15186719