Three-Dimensional Loss Effects of a Solenoidal Inductor with Distributed Gaps

This thesis investigates the disparities in losses between 2D-based design simulations and a 3D realization of solenoidal inductors featuring distributed gaps. The inductor geometry entails a solenoidal copper winding enveloped by sintered ferrite rings and end caps, with the air gap required for energy storage distributed over multiple smaller discrete gaps. The simulated 3D structure possesses higher losses than its 2D cross-section due to inherent structural features. The research culminates in two contributions. First, a practical two-variable design approach is presented, leveraging matrix algebra to succinctly represent the decision quantities as functions of the two most important variables to the application. The procedure results yield several informative plots that assist in selecting a design that meets the efficiency and thermal limits. Second, a detailed explanation is provided on the 3D loss effects, along with the recommended design considerations and a method to estimate the dominant 3D loss effect using simple 2D simulations. The design recommendations address a 26-fold increase in the core loss of the outer ferrite rings. They also reduce the copper loss due to the termination effect by 55% using spacer ferrite layers. A simple 2D simulation method is proposed to accurately predict the increased 3D copper loss due to the axial shift of the winding to within 3% and runs 60 times faster than the equivalent 3D simulation. Additionally, a derived equation for the optimal turn spacing aligns with the simulation results with <6% error, offering practical insights for design optimization. These results enable the design of a low-loss solenoidal inductor and accurate loss estimations without running lengthy and complicated 3D simulations. A 13 µH, 150 Arms solenoidal inductor prototype for operation in a 10 kV-to-400 V, 50 kW converter cell serves as empirical validation, corroborating the efficacy of the proposed analysis and design methodology.