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Top1. Introduction
Dry-type air core reactors are essential equipment for high-voltage transmission systems, which have a simple structure, easy maintenance, and a stable inductance, and are used for harmonic reduction, current limitation, and reactive power compensation (Wang et al., 2018; Liang, 2020). Due to the high voltage level and large capacity of the high-voltage transmission systems, a reactor is subjected to increasingly severe temperature rise and vibration deformation problems during operation, which affect the safety of personnel and even destroy the electrical system stability. Because of this, it is essential to analyze the multi-physical-field characteristics of reactors and propose an optimal design method.
At present, scholars have conducted a lot of research on the simulation and optimization of the multi-physical-field coupling of electromagnetic field-temperature field-structure field of dry-type air core reactors. In terms of multi-physical-field coupling, the magnetic field distribution characteristics of dry-type air core reactors are obtained in the literature (Yang, & Zhao, 1998; Lu et al., 2021; Du et al., 2012; Li et al., 2010) through numerical calculation methods to guide the reactor fault monitoring. In the literature (Liu et al., 2003; Zhang et al., 2014; Jiang et al., 2015), the temperature rise distribution characteristics of reactors are analyzed by establishing a two-dimensional simulation model of the coupled electromagnetic field-flow field-temperature field of the reactors, without considering the influence of structures such as star frames on the temperature field. In the literature (Li et al., 2017; Wu et al., 2019; You et al., 2017; Chen et al., 2017), an actual three-dimensional model is constructed for the reactor fluid-temperature field coupling, the temperature rise distribution laws of the reactor encapsulation coil in different path directions are analyzed, and the correctness of the simulation is verified through tests. In the literature (Guimarães et al., 2013; Bakshi et al., 2014; Yun et al., 2016), the characteristics of transient electromagnetic forces on transformer windings are analyzed by coupling the electromagnetic forces into a structural field to obtain the winding deformation distribution. As for the optimization design of inductors, the equal-current-phase method is proposed in literature (Ma et al., 2017) to derive a formula for the number of turns of an encapsulation layer coil, which can significantly reduce the inductor losses. A multi-objective optimization algorithm is introduced in literature (Zhang et al., 2010; Chen et al., 2019) for air core reactors, and Pareto solution sets are obtained for reactor metal conductor usage and losses, which can be designed according to the actual engineering requirements. In the literature (Yu, & Wang, et al., 2015), finite element is combined with reactor optimization design to achieve the optimal loss and temperature rise of reactors, but the effect of structural changes on the vibration of reactors is not considered in the method. In the literature (Yang et al., 2019), a multi-objective Pareto optimal algorithm for dry hollow reactors is proposed with the constraints of minimizing the raw material cost of reactors, as well as the operating cost of layer equal resistance voltage, envelope equal temperature rise, and envelope equal height to improve the structural utilization of reactors, but the method is only applicable to reactors with rectangular cross-section winding. The magnetic field distribution law and force characteristics of a coil are obtained in the literature (He et al., 2020; Lan et al., 2018; Bakshi, & Kulkarni, 2014; Ahn et al., 2016) through the finite element method, based on which the structural stability of the coil is evaluated and analyzed, and the results of the study have some reference significance for the structural optimization of reactor coils.