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Scaling laws are used when the size of a certain machine design with known performance needs to be adjusted for a new application with known requirements, or when a machine design is geometrically scaled and one needs to determine its performance. Scaling laws derived in this study allow one to quickly and accurately recalculate parameters of a geometrically scaled permanent magnet machine. They basically consist of two separate important scaling procedures: axial scaling and radial scaling. The third and inevitable scaling procedure is rewinding, which is used to adjust the winding for a required voltage level. Exact but simple analytical equations for the various parameters (torque, power, losses, mass, resistance, inductance, efficiency etc.) of the machine are derived using three independent scaling factors, one for each scaling procedure. Special attention is given to the inclusion of end-winding influence and three-dimensional permanent magnet loss effects. Algorithms for fast determination of winding parameters for a given voltage and fast determination of scaling factors for scaling based on the torque requirement with stack length limitation are presented. All derived scaling equations are numerically validated using two state-of-the-art motor design software packages with automated extraction of parameters based on finite-element calculations.

This paper presents a comprehensive approach to design of series of permanent magnet assisted synchronous reluctance motors using combined analytical and finite element calculations. A global optimization metaheuristic algorithm (Differential Evolution) is utilized in order to achieve optimal design in terms of maximum torque per volume with numerous specific boundaries imposed on motor geometry and performance. A novel approach to calculation of the specified constant power speed range and demagnetization effect in sudden symmetrical short circuit using iterative finite element magnetostatic simulations is presented. Based on the results of optimized design, a 100 kW prototype was built and tested. 7. β/β 0-angle of the slanted magnet relative to the maximum allowed angle of the slanted magnet (β 0 = 0.5π(1 − 1/p)), 8. λp-angular span of the inner cavity relative to the pole pitch. Lower and upper boundary constraints of the variables are: 0.45 ≤Ds/Dout ≤ 0.75, 0.2 ≤hys/[(Dout − Ds)/2] ≤ 0.6, 0.3 ≤bt/τu ≤ 0.7, 0.05 ≤λm ≤ 0.5, 0.2 ≤λ md1 ≤ 0.6, 0.05 ≤λ md2 ≤ 0.4, 0.5 ≤β/β 0 ≤ 1.0, 0.75 ≤λp ≤ 0.95. Variables with constant value, i.e. design parameters that do not change during the optimization procedure (preset parameters) according to Fig. 1 are: 1. δ = 0.8 mm-air-gap length,