## 1 Introduction  
In the context of global warming and its increasingly serious and alarming consequences, the need to reduce greenhouse gas (GHG) emissions coming from human activities is a major global issue. This concerns all sectors of activity, and the transport sector, fundamentally linked to fossil fuels, is not spared. The aviation sector in particular, which today represents around 3% of total GHG emissions from human activities is regularly singled out [1]. To tackle this issue, the aviation world continually seeks to innovate in order to offer ever-less-polluting aircraft through various projects such as the European Clean Sky project and by setting ambitious targets for decarbonization. These targets were announced by the International Air Transport Association (IATA) with the major objective of reducing GHG emissions by 50% by 2050 compared to 2005 [2]. To achieve this objective, a technological revolution must take place in the aviation sector and today this revolution is embodied by the more electrical aircraft and especially the electrification of aircrafts propulsion [3; 4; 5], as electric power chains do not produce GHG emissions during their operation. More and more projects [6; 7; 8] are related to electric or hybrid electric propulsion, emphasizing the main advantages (energy efficiency, distributed propulsion capabilities, etc.) and key challenges (weight reduction, reliability, etc.). In [9] a review of all hybrid electric architectures and the optimization of the most promising ones is proposed. In addition, the electrification of the propulsion allows dissociating the generation of power from the aircraft thrust, which opens the field of possibilities towards innovative configurations for aircraft propulsion:  
* In hybrid-electric aircraft, this power-thrust dissociation enables the optimization of the design of the generation of power, in particular if an auxiliary power source hybridizing the main thermal source is used, thus offering precious degrees of freedom to optimize the thermal generator;
* Moreover, distributed propulsion [10; 11], made possible through electrification, is likely to provide aerodynamic gains as well as useful degrees of freedom in terms of operational safety. In this context, the number of projects for electrically propelled aircrafts is growing significantly with over 200 projects in recent years [1; 4; 9], including the one considered in this paper. * _Literature Review_  
However, the electrification of aircraft propulsion leads to a significant increase in the aircraft weight [9]; minimizing weight and optimizing conversion efficiencies is therefore an essential concomitant challenge. [PERSON] [9] has shown that adding 1 ton embedded to the MTOW (Max. Take Off Weight) of a regional (70 px) aircraft would lead to an increase in the fuel consumption by 6% on a flight mission of 400 nautical miles. In order to tackle this issue, the electric powertrain architecture considered in this paper is composed only of permanent magnet synchronous machines without power electronics. The use of these machines was greatly democratized during the second half of the last century with the development of components for power electronics as well as tools for modelling and piloting these machines [12]. Indeed, they have many advantages including [12; 13]:  
* A high specific power;
* A good efficiency and an excellent heat dissipation;
* Low maintenance requirement in the absence of brushes. Due to these advantages, its use has been extended to all electrical networks, whether on land or on board, particularly in the context of electrification of the various means of mobility. However, the use of permanent magnet synchronous machines in every field of electrification (land power grid [14; 15], automotive industry [12; 16], railway industry [12; 17] naval industry [12; 18; 19; 20] or aeronautical industry [3]) is usually conditioned by the presence of power electronics.