## 4 Validation
### Methods and Objectives
#### 4.1.1 Non-Segmented Reference Machines  
The segmented structures are based and compared to a reference machine design with a non-segmented structure. This reference machine has been previously designed by our team in previous works and corresponds to the specifications of a 300 kW/15 rpm Rim-Driven generator for tidal turbine [7]. The stator internal diameter value is, in this case, equal to 11.151 m. In this reference design, around 80% of copper volume (and consequently Joule losses) corresponds to the end-windings parts. These large losses leads to a significant reduction of electrical machine efficiency. In order to solve this problem, unconventional machine structures with segmentation of active parts can be an interesting solution. The common characteristics of all the studied machines (segmented and non-segmented structures) are presented in Table 1.  
Figure 12: Modulation function to take into account the parts without magnet for a structure with \(p_{gap}\) around 20% and \(n_{gap}=6\) gaps. To reduce copper volume, a first machine, directly derived from [7], is proposed with a concentrated winding (with a number of slot per pole and per phase equal to \(S_{pp}\) = 1/2). Thus, the geometric parameters are determined to have a half slot per pole per phase. This machine (named RS-machine) will be used to study the rotor segmentation effects. Because the winding of this first machine is not divisible due to a two layers winding topology, a second machine (named SS-machine) is proposed to study the stator segmentation. This machine is also derived from [7] and keeps the characteristics given in Table 1. The winding is modified and a machine with a fractional number of slots per pole and per phase equal to 2/5 is chosen. The choice is motivated by the 1 st harmonic winding coefficient close to 1 [14] and a relatively small winding periodicity (10 poles). In this case, the number of pole pairs should be slightly modified. Tables 2 and 3 present the different geometric parameters determined for both reference machines. Figure 13 depicts these geometric parameters. Studies of this kind of machine with large diameter, large air gap, and a small axial length, like Rim-Driven systems, show that strong leakage 3D effects on the axial ends of the machines modify the EM behavior of the structure. Due to this phenomenon, 2D calculation (numerical and analytical) overestimates the magnetic fluxes, EMF or torque. In [15], a correction factor \(\zeta_{3D}\) corresponding to the relative error related to the 3D effects is introduced. The relative error depends on the magnetic air gap length \(g_{m}\) (which includes \begin{table}
\begin{tabular}{l l} \hline Power \(P\) (kW) & 300 \\ \hline Turbine speed \(N\) (rpm) & 15 \\ \hline Air gap length \(h_{g}\) (m) & 0.02 \\ \hline Linear electric loading \(A_{L}\) (kA\(\times\)m\({}^{-1}\)) & 60 \\ \hline Current density \(J\) (A\(\times\)mm\({}^{-2}\)) & 4 \\ \hline Magnet width (\(\tau_{m}\)) to pole pitch (\(\tau_{p}\)) ratio \(\beta_{m}\) & 0.7 \\ \hline Stator internal diameter \(D\) (m) & 11.151 \\ \hline Magnet remanence \(B_{r}\) (T) & 1.2 \\ \hline Magnet relative permeability \(\mu_{r}\) & 1.05 \\ \hline \end{tabular}
\end{table} 
Table 1: Main parameters of Rim-Driven machine (derived from [7]). Figure 13: Representation of the geometric parameters. both mechanical air gap and magnet height) to the axial length \(L_{z0}\) ratio. The expression of the corrective factor is given by (10). \[\zeta_{3D}=1-0.2\times\frac{g_{m}}{L_{z0}} \tag{10}\]  
Including this corrective factor, Equation (11) expresses the EM torque. \[T_{em}=\zeta_{3D}\times\sqrt{2}\times k_{w}\times A_{L}\times B_{1}\times cos( \psi)\times L_{z0}\times\frac{\pi D^{2}}{4} \tag{11}\]  
\(B_{1}\) corresponds to the fundamental of the air gap flux density (due to rotor at no load) and is estimated using 2D analytical method as in [9]. \(k_{w}\) is the first harmonic winding coefficient (see Tables 2 and 3), and \(A_{L}\) is the linear electric loading.