Inductance Calculation and Energy Density Optimization of the Tightly Coupled Inductors Used in Inductive Pulsed Power Supplies

Abstract

The air-core flat spirals of strip coil structure is a typical type of the tightly coupled energy storage inductors used in inductive pulsed power supplies. This paper improves the speed and the parameter scope of the inductance calculation method for these inductors. Specifically, the analytical expressions using the structural parameters to represent the performance parameters, e.g., the inductance, the resistance, and the current conducting capability of the primary inductor and the secondary inductor L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1limit</sub> , I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2limit</sub> , the total volume V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tot</sub> , and the energy density ω, are given. The validity of this method is confirmed by practical measurements of a set of constructed inductors with 2.67-mH total inductance. The absolute error is within 0.02 mH. On the basis of this method, parameter optimization on energy density is conducted for the 70-kJ energy level module. Results show that the energy density can reach 11.2 MJ/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> when the total inductance is 5.07 mH and the total volume is 6.3 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> .