Theory And Application Of Rogowski Coil For Current Measurement

Various types of Rogowski coils current transformers are widely used in high magnitude and high frequency current measurement due to their advanced merits such as non-magnetic saturation,wide measurement frequency bandwidth,and simple structure.Yet the measurement accuracy,bandwidth and sensitivity of the Rogowski coil are still affected by many factors in practical applications,such as the shape and position of the primary current-carrying conductors,the amplitude and frequency of the primary current,and the structure of the coil itself.Hence,it is essential to accurately predict and analyze the operating performance of Rogowski coils in engineering-oriented applications.To date,finite element method implemented in commercial software and numerical analysis method are becoming the mainstream to investigate the electromagnetic properties of Rogowski coils.However,it is difficult for the former method to mesh and simulate the complex Rogowski coils(over thousands of turns)due to the compatibility between computing efficiency and accuracy.On the other hand,the latter method is only appropriate to specific cases with ideal assumptions,showing a limited applicability.This research aims to develop a novel method to calculate and predict the operating parameters of Rogowski coils,and systematically study the technical difficulties occurring in the process of design,production and application of Rogowski coils.To underpins practical applications,this dissertation focuses on theory,comprising the following research:Firstly,a novel analytical method is derived to calculate the mutual inductance(sensitivity)between a Rogowski coil of arbitrary skeleton shape and a primary currentcarrying conductor of arbitrary shape and position.For the common circular skeleton,this dissertation also presents a new calculation method,which is much simpler than the traditional method.In order to verify the proposed new theoretical method,an experimental platform is built to measure the mutual inductance between the home-made Rogowski coils and the primary current-carrying conductors.In the measurement,three kinds of flexible skeleton shapes(circular,elliptical and double-loop skeleton)are designed for the Rogowski coils,while five common shape for primary current-carrying conductors.The experimental data successfully validates the theoretical method,showing a great agreement with the analytical results(with less than 1% error).The influence of the position of the primary current-carrying conductors on the mutual inductance of Rogowski coils with circular,elliptical,square and double-loop skeleton are explored.In addition,according to the numerical results and experimental data,some suggestions are put forward to improve the measurement accuracy.Secondly,an improved lumped parameter circuit model is established to explore the influencing factors of the measured bandwidth.This model is suitable for single or double turns layer Rogowski coils(with arbitrary skeleton shape)and the primary currentcarrying conductors(with arbitrary position and shape).The self-inductance of each turn,the mutual inductance between any two turns,the parasitic capacitance between two adjacent turns,the capacitance between each turn and the shielding layer,and the resistance of each turn affected by the skin depth effect are considered in this model.Moreover,the method is fast because there is no need to meshing.Experimental results of the tested Rogowski coils all verify the model.The tested Rogowski coils include double-wound,single-wound,shielded and unshielded coils.In addition,based on this model,the effects of the number of turns,external damping resistance,winding density,shielding layer,the position of primary current-carrying conductor and the uneven distribution of winding on the measuring bandwidth of the Rogowski coil are systematically studied.Then,this dissertation presents a calculation method of mutual inductance between the high-turn-density PCB Rogowski coil with arbitrary turn's straight trace and the primary straight current-carrying conductor of any position,and an improved lumped parameter circuit model for studying the bandwidth of the PCB Rogowski coil with arbitrary turn's straight trace is also built.This dissertation analyzes the calculation methods for the mutual inductance between any two turn segments,for capacitance between adjacent turn segments,and for self-inductance and resistance of each turn segment.In order to verify this method,a PCB Rogowski coil with a complex structure mentioned in many literatures is taken as an example.The experimental results verify the theoretical derivation.Finally,this dissertation presents a method to increase the measurement bandwidth without compromising on sensitivity and accuracy.The principle is to divide the original coil into several sections,and then combining each section together via the designed electronic circuit,without changing the coil's size.The experiments include the tests of the single-layer,double-layer,shielded and unshielded coils on the sinusoidal signal test platform and the dynamic performance test platform of the HV-IGBT collector switch transient current.The experimental results show the range of measurable bandwidth is positively correlate with the dividing section number of Rogowski coil,(e.g.,the bandwidth is increased to 2.25 times and 2.75 times after segmenting a double-layer Rogowski coil into a two-section coil and three-section coil).Furthermore,a corresponding error compensation method is also proposed for the bandwidth improvement method,which is well verified by experiments.