## 1 Introduction  
The presented study deals with unconventional structures of Permanent Magnet Synchronous (shortened as PMS) electrical machines. In the following, these machines are called segmented machines. Studies of these kinds of machine appear in the literature for some years [1; 2; 3; 4]. In these particular structures of electrical machines, the stator [1; 2; 3] or the rotor [4] is divided into several parts which contain active parts (named sectors) which are separated by non-active areas (called gaps and which does not contain active parts). Figure 1 presents structures with a segmented stator or a segmented rotor with \(n_{s}=2\) sectors. The ratio between total gap width and circumference is equal to \(p_{gap}=0.125\) for the stator-segmented structure and \(p_{gap}=0.25\) for the rotor-segmented machine.  
The gaps can be filled with magnetic materials (for example, specific resin) or soft ferromagnetic materials (iron laminations). Indeed, using ferromagnetic materials in the gap leads to a better cooling than if non-metallic gaps are used because the internal heat sources (losses) can be evacuated by these non-active metallic parts.  
These very unconventional structures can be used to reduce the losses part related to the end-windings in very large diameter electrical machines with small axial length and/or to increase efficiency and reliability [5; 6]. These structures can be for example used in Rim-Driven machine for tidal turbine or marine propeller where the machine diameter is directly linked to the turbine or propeller external diameter.  
Test cases corresponding to a high power Rim-Driven generator for tidal turbine are considered. In a Rim-Driven system, the electric generator active parts are located in a duck surrounding the turbine blades. In this configuration, if a non-segmented design is used for a Rim-Driven turbine, the axial active length of the electrical machine is very small and the majority of copper is located in the end-windings (almost 80% for the non-segmented reference machine presented in [7]). This is why segmented stator PM machines have the expected advantage to reduce the part of the end-windings copper volume and so the global copper losses into Rim-Driven systems as shown in [5]. Furthermore, these low-speed generators have a high number of pole pairs which allow many rotor and stator segmentation possibilities. Rotor-segmented structures are proposed here to reduce the mass of magnets. Only structures with segmented stator or segmented rotor with magnetic gaps are studied in this paper. The combination of both segmented structures is not studied in this paper.  
This article is a significantly extended version of the conference paper presented in Compumag 2019 [6], where an estimation of cogging torque in the case of a segmented stator was studied based on the same non-segmented reference machine.  
To estimate the electromagnetic performances of an electrical machine, a Finite Element Method (FEM) could be used. In the case of a segmented structure, the increase of the simulation domain leads to increase the computation time. In order to evaluate the performances in a faster way, analytical models could be used. Those ones can be useful at the pre-design step or can be integrated into a systematic design process. Analytical magnetic flux density, cogging torque, electromotive forces, and global torque calculation models have been presented and used in the literature for classical non-segmented slotted machines. In the presented work, these models are modified to be adapted for stator-segmented structures and rotor-segmented structures. Original analytical methods which are presented in this paper allow precise and fast estimation of the EM performances of such structures. They allow also estimating the impact of the suppression of active parts of the stator or the rotor. A sensibility analysis is done for different gap ratios and different numbers of gaps to estimate the validity domain of the proposed methods.