## 5 Conclusions  
This paper relates to a typical electric powertrain for aircraft propulsion which is composed exclusively of permanent magnet synchronous machines (PMSM) without any power electronics. In particular, each PM synchronous generator is directly connected through an AC bus with a single or multi PM synchronous motor distribution set that drives the propelling system. Suppressing power electronics offers substantial gains in terms of embedded weight: some figures are proposed as example of weight reduction in the introductive section. However, suppressing power electronics and considering a direct (\"rigid\") AC coupling of two or several PMSMs involves stability issues that are the main focus of the paper.  
Before analyzing the system stability, several models and tools are built: a nonlinear transient state model of the AC electric propulsion architecture is firstly developed. In the framework of a time simulation, this model is compared with a circuit time simulation on the Saber solver showing the accordance between both tools.  
Based on that nonlinear state model, a small-signal linearization is analytically derived, leading to the root locus definition of the AC powertrain that characterizes stable and unstable domains. This analytical approach allows achieving a sensitivity analysis linking system parameters with stability conditions.  
This set of linear and nonlinear analysis tools is compared with a reduced power scale experimentation emulating the power architecture. Regarding the dynamic behavior and the system stability, all analysis means of study are quite in accordance, emphasizing the existence of unstable subdomains which depend on the physical and control parameters of the powertrain.  
The sensitivity analysis shows that full stable operation may be obtained with specific system sizing and control tuning.  
Figure 17: Time simulation result of the stability analysis for the previous coupled parametric modification with a bandwidth of 1 Hz for the generator speed control and with coupled modifications of electric and mechanical parameters.  
Let us note that the PMSMs studied in this paper correspond to small power machines for industry applications: these machines were the ones installed in the experimental reduced power scale test bench which has allowed us to validate the state models for stability analysis. It is clear that such machines differ from \"specific machines\" for aircraft propulsion. In our current studies, we are analyzing \"scale one\" electric machines more representative of the aircraft application. Preliminary results not presented in the paper show that major trends in terms of stability are mainly reproduced with these machines.  
Furthermore, the trends shown are not necessarily compatible with a design that can be integrated into an aircraft that must ensure a robust and full stable system operation. On the other hand, the tools developed in this paper allow us to consider corrective solutions to the instability problem which constitutes the main prospect of this study.  
During his PhD thesis, [PERSON] developed the complete study related to this paper's contributions plus other issues not mentioned here. [PERSON], [PERSON] and [PERSON] ensured the academic research direction of the thesis, contributing to the definition of models and tools for stability analysis. [PERSON] was the industrial coordinator and was deeply involved in the scientific choices and their relevance to the aircraft application constraints. All authors have read and agreed to the published version of the manuscript.  
This research based on a SAFRAN TECH--LAPLACE agreement received no external funding.  
Not applicable.  
The authors declare no conflict of interest.