Hybrid electric aero-propulsion requires high power-density electric motors. The use of a constrained optimization method with the finite element analysis (FEA) is the best way to design these motors and to find the best solutions which maximize the power density. This makes it possible to take into account all the details of the geometry as well as the non-linear characteristics of magnetic materials, the conductive material and the current control strategy. Simulations were performed with a time stepping magnetodynamic solver while taking account the rotor movement and the stator winding was connected by an external electrical circuit. This study describes the magnetic FEA direct optimization approach for the design of Halbach array permanent magnet synchronous motors (PMSMs) and its advantages. An acceptable compromise between precision and computation time to estimate the electromagnetic torque, iron losses and eddy current losses was found. The finite element simulation was paired with analytical models to compute stress on the retaining sleeve, aerodynamic losses, and copper losses. This type of design procedure can be used to find the best machine configurations and establish design rules based on the specifications and materials selected. As an example, optimization results of PM motors minimizing total losses for a 150-kW application are presented for given speeds in the 2000 rpm to 50,000 rpm range. We compare different numbers of poles and power density between 5 kW/kg and 30 kW/kg. The choice of the number of poles is discussed in the function of the motor nominal speed and targeted power density as well as the compromise between iron losses and copper losses. In addition, the interest of having the current-control strategy as an optimization variable to generate a small amount of flux weakening is clearly shown.

Since 2018 in France, national regulation mandates that school canteens serve a weekly vegetarian meal to reduce school canteens' environmental impact in addition to previous regulations imposing nutritional composition guidelines. However, a lunch without meat is often perceived as inadequate to cover the nutritional needs of children. The present study aims to assess the nutritional quality and greenhouse gas emissions (GHGE) of vegetarian and non-vegetarian school meals served in primary schools in Dijon, France. The catering department provided the composition of 249 meals served in 2019. Nutritional content and GHGE were retrieved from national food databases. The portion size of each meal component was the standard portion size recommended by the relevant French authority (GEMRCN). Meals were classified into vegetarian meals, i.e., without meat or fish (n = 66), or non-vegetarian meals (n = 183). The nutritional adequacy of the meals for children aged from 6 to 11 years was estimated using the mean adequacy ratio (MAR/2,000 kcal) as the mean percentage of daily recommended intake for 23 nutrients and the mean excess ratio (MER/2,000 kcal) as the mean percentage of excess compared to the maximum daily recommended value for three nutrients. This analysis of actual school meals shows that both vegetarian and non-vegetarian meals had a similar good nutritional quality with MAR/2,000 kcal of 87.5% (SD 5.8) for vegetarian and of 88.5% (SD 4.5) for non-vegetarian meals, and a MER/2,000 kcal of 19.3% (SD 15.0) for vegetarian and of 19.1% (SD 18.6) for non-vegetarian meals. GHGE were more than twofold reduced in vegetarian compared to non-vegetarian meals (0.9 (SD 0.3) vs. 2.1 (SD 1.0) kgC02 eq/meal). Thus, increasing the frequency of vegetarian meals, by serving egg-based, dairy-based or vegan recipes more frequently, would reduce GHGE while maintaining adequate nutritional quality of primary school meals.

Effective methods for the design of high-performance electrical machines must use optimization techniques and precise and fast physical models. Convergence, precision and speed of execution are important issues, in addition to the ability to explore the entire domain of solutions. The finite element method (FEM) presents a high accuracy in the results but with high computational costs. Analytical models, on the other hand, solve the problem quickly but compromise the accuracy of the results. This work shows a comparison between an optimization made with an analytical electromagnetic model and a direct optimization with finite element field calculation for the optimal design of a Halbach array permanent magnet synchronous motor (PMSM). In the case of the analytical model, it is necessary to use an iterative method of correcting the model to obtain a valid solution. This method is known as Space Mapping (SM) and the analytical model can be improved with a reduced number of iterations with the FEM. The results show a rapid convergence towards an optimal solution for the SM, with more than 78% reduction in computational cost compared to a Direct FEM optimization. Both solutions have only a difference of 3% on the power density, which indicates that FEM does not improve the results obtained by SM. This represents a great advantage that allows for the consideration of a large amount of designs to analyze the domain of solutions in more detail. This study also shows that SM is a powerful method to optimize the power density or torque density of electrical machines.