# Frequency response analysis of a current limiting reactor.

2022

## Abstract

With the demand for electricity continuously increasing, power systems are required to increase capacity to meet such demands which can entail integrating renewable energy resources to the grid. This increase in capacity would mean a likewise increase in fault levels in the network which can result in costly damage to components such as circuit breakers, transformers and cables. Air-core reactors are commonly employed to prevent such damages from occurring, however, the increase in fault levels must also be accounted for in the design of reactors as they are also subject to transients. This dissertation documents the development of models to accurately represent an Air-core reactor in order to gain a better understanding of the design considerations required. Two models are developed for two desktop reactors using different methods as a form of cross-validation. The first model is developed in MATLAB r2020a and utilises an analytical approach through an equivalent circuit method (ECM). Equations are used to compute the inductive, capacitive and resistive components which are then used to guide the development of the FEM models. The second model is developed using COMSOL Multiphysics software which is based on the Finite Element Method (FEM) approach. A 2D-axisymmetrical model is constructed and simulated using COMSOL’s Magnetic and Electric field physics in the frequency domain from which a frequency response is obtained as well as values for the inductive, resistive and capacitive components. Final validation of the FEM models is done through comparisons to measured results of the two desktop reactors. FEM simulated RLC components showed fairly good agreement to the measured values, particularly the inductance having a difference of 3.4 μH and a capacitance difference of 1 pF for Reactor 1. The FEM simulated frequency response of 1.5 MHz differed by 0.4 MHz when compared to the measured frequency response for Reactor 2 of 1.9 MHz. A sensitivity analysis is conducted for the FEM model in order to obtain an understanding of the design considerations required for the air-core reactor. Simulations are performed on the FEM model with changes to geometry, permittivity of the insulation medium and resistivity of the copper coil. The effects of these changes on the RLC parameters and resonance frequencies are documented. The FEM model is then scaled to a full-scaled reactor which showed good agreement between the expected inductance of 2.24 mH and the simulated inductance of 2.28 MH. The resultant resonant frequency was observed to occur at 380 kHz. The aim of this is to develop an understanding of parameters and equations that should be considered in the design process of reactors which will then be employed in the development of a superconducting fault current limiter (SFCL).

## Description

Masters Degree. University of KwaZulu-Natal, Durban.