Distributed Parameter Circuit Model Research Articles

Analysis of Resonance Mechanism of AC Submarine Cable Delivery System for Offshore Wind Power

Abstract Several resonant overvoltage accidents caused by machine-grid interaction in offshore wind power generation systems have led to significant economic losses over the years. To solve this problem, based on the equivalent distributed parameter circuit model of AC submarine cable delivery system, a method combining impedance simulation-time domain simulation and spectrum analysis is proposed to reveal the mechanism of resonant overvoltage and its influencing factors. First of all, considering the phase locked loop (PLL) model and the cable distribution parameter model, an impedance model of AC submarine cable delivery system for offshore wind power is established, which takes into account the dynamic characteristics of PLL and current loop, and provides a model basis for the theoretical analysis. Then, equations for current and frequency at the point of common coupling (PCC) are derived to analyze the mechanism of resonant overvoltage generation and the influence of submarine cable length and power grid strength on resonance. Finally, PSCAD is used to verify the resonance mechanism of AC submarine cable delivery system and its influencing factors.

Novel Differential Protection for a Powerformer Considering Capacitive Current Compensation

A Powerformer is a special type of generator whose peak capacitive current is approximately 30 times larger than that of conventional generators with the same rated apparent power. Powerformer stator fault relays may be misoperated by using conventional differential protection strategies, thus degrading network reliability. Therefore, a novel differential protection scheme for a Powerformer is proposed in this paper. First, the nonlinear distribution laws of the Powerformer stator winding capacitance and induced electromotive force (EMF) are analyzed. Next, an equivalent distributed parameter circuit model of the Powerformer considering cable-windings with graded insulation is established and verified by using FEM-based analysis. Furthermore, to eliminate the influence of the capacitive current on the differential protection, the capacitive current is analyzed, and a novel differential protection scheme considering capacitive current compensation is proposed. A simulation model is established by using MATLAB and PSCAD, and extensive simulation studies verify the effectiveness of the proposed protection approach.

A new method for solving arcs of pantograph network based on Newton’s iterative method

It has been verified that the discharge pulse generated by the pantograph-catenary system has the biggest impact on the high-speed EMU as the electromagnetic interference source. But the spectrum obtained from the existing pantograph discharge model does not contain high frequencies and is far from the measurement results. In this paper, a novel scheme based on Newton’s method and finite difference time domain (FDTD) algorithm was presented to solve this problem. Firstly, Newton’s method was utilized to solve the Habedank model, and the dynamic conductance of the arc was obtained. Then, the equivalent distributed parameter circuit model of the traction power supply system was established, which was solved by the FDTD and state variable method to obtain the time-domain waveform of the arc voltage. The significant features of this scheme are that it can realize the synchronous calculations of the arc dynamic conductance and the voltage responses along the catenary. Through this scheme, a stable arc voltage time domain waveform can be obtained, and the arc voltage spectrum is highly consistent with the test results.

The Impact of Connection Failure of Bonding Wire on Signal Transmission in Radio Frequency Circuits

Bonding wires are widely used in microwave circuits and chip packaging. The exposure to harsh environments may lead to connection failure in these wires. In this article, the impact of such failures on signal transmission was studied using model analysis and experimental testing. The effects of gold bonding wire failure on both the dc and high frequency characteristics were analyzed. Signal reflection and loss caused by failed gold bonding wire at different positions and a number of failed gold bonding wire were also investigated. Based on computational electromagnetics and transmission line theory, a 3-D electromagnetic field numerical calculation model and a distributed parameter circuit model were developed. The electromagnetic field model results are in good agreements with those obtained from the distributed parameter circuit model. The results obtained by the model simulation are validated using experimental tests. The results of this investigation provide a better understanding of the influence of the position and the number of failed bonding wires on the signal integrity of the circuit and theoretical support for identifying failure features in fault diagnosis.

Modeling and Analysis of Signal Integrity of High-Speed Interconnected Channel With Degraded Contact Surface

High-speed interconnected channels, including printed circuit boards (PCBs) and high-speed connectors, are widely used in digital baseband communication systems. Connector degradation may lead to deterioration of the integrity of digital signals and is one of the major causes of low communication quality. In this work, the effect of electrical contact degradation on signal integrity was investigated using model analysis and experimental testing. A 3-D electromagnetic field model of a high-speed channel with a degraded contact surface was developed to evaluate transmission loss, signal reflection, and crosstalk. Using multiconductor transmission line theory and contact physics, a distributed parameter circuit model of a high-speed channel with a degraded contact surface was also developed. The electromagnetic field model results are in good agreement with those obtained from the distributed parameter circuit model. Both the electromagnetic field model and the circuit model results are validated using experimental tests. The results of this investigation provide a better understanding of the characteristics of signal transmission through a degraded contact surface in a high-speed channel and theoretical support for identifying failure features in fault diagnosis.

High-Frequency Behavior Analysis and Modeling of Silver Plated Printed Circuit Board with Electrochemical Migration

Silver-plated electronic devices are extensively used in microwave circuits. The electrochemical migration of silver in these circuit boards can affect high-frequency characteristics and signal integrity. In this work, the effect of silver migration on signal transmission of printed circuit boards was evaluated using both experimental testing and analytic modeling. The S parameters of circuit boards with silver migration were measured. Based on multi-conductor transmission line theory and electrical properties of dendrite-like electrochemical migrated silver, a distributed parameter circuit model for the circuit board with silver migration was developed. The model results are in good agreement with those obtained from the experimental tests. The results of this investigation provide a better understanding of the high-frequency behavior of a circuit board with silver migration and theoretical support for identifying failure features in fault diagnosis.

A Deep-Sea Pipeline Skin Effect Electric Heat Tracing System

In order to ensure deep-water flowline safety, this paper combined the axial temperature distribution model of the submarine pipeline and the distributed parameter circuit model of the skin effect electric heat tracing system; such work is conducive to proving that the heating effect of the skin effect electric heat tracing system depends on the distributed circuit parameters and power frequency of the system. Due to the complexity of the power supply device, the frequency cannot be increased indefinitely. Therefore, for the case that the input of the skin electric heat tracing system is constrained, a generalized predictive control algorithm introducing the input softening factor is proposed, and the constrained generalized predictive control strategy is applied to the electric heating temperature control system of the submarine oil pipeline. Simulation results demonstrated that the control quantity of the skin effect electric heat tracing system is effectively controlled within a constraint range, and also the values of heating power and power frequency are obtained by theoretical calculations rather than empirical estimations. Moreover, compared with the conventional control algorithm, the proposed constrained generalized predictive algorithm unfolds more significant dynamic response and better adaptive adjustment ability, which verifies the feasibility of the proposed control strategy.

One to 40 GHz ultra‐wideband RF MEMS direct‐contact switch based on GaAs MMIC technique

This study presents a 1–40 GHz ultra-wideband radio frequency (RF) micro-electro-mechanical systems (MEMS) direct-contact switch based on a GaAs microwave monolithic integrated circuit (MMIC) process. The proposed switch utilises an inline cantilever membrane and a pull-in electrode to achieve ‘off’ and ‘on’ states. It has been manufactured by micro-machining, which is completely compatible with the GaAs MMIC process. An equivalent distributed parameter circuit model of the switch is established to analyse the microwave performances. The measured S-parameters show that the isolation (S21) in the ‘off’ state is better than 22.5 dB from 1 to 40 GHz. In the ‘on’ state, the input reflection coefficient (S11) is less than −20.9 dB and the forward transmission coefficient (S21) is better than −0.25 dB over the complete band. In addition, the measured pull-in voltage is ∼17.5 V. The measured maximum power handling capacity is 36.5 dBm. A lifetime of 2.4 × 107 switching cycles is also verified by this design. The whole structure is designed with the purpose of expanding its working bandwidth and achieving higher microwave performances over current state of art.

Lumped and Distributed-Parameter Circuit Models of the Electromagnetic Clamp

This paper presents two circuit models of the electromagnetic (EM) clamp defined in Standard IEC 61000-4-6 for conducted-immunity (CI) testing. First, a lumped-parameter circuit model is extracted from measurements of scattering parameters. This model is merely behavioral since it provides a valid representation of the EM clamp at external ports up to 1 GHz, whereas physical interpretation of the involved sources/impedances is possible under 10 MHz only. To extend physical insight at higher frequencies, a distributed-parameter circuit model is proposed, which is based on the description of the internal structure of the EM clamp as a three-conductor transmission line. Unknown model parameters (such as the magnetic permeability of ferrite rings) are identified by optimized fitting of ad hoc measurements. Both models are eventually validated by experiments performed in an idealized CI test setup. Several observations on the operating principles and features of the EM clamp are inferred from the two complementary modeling approaches.

Frequency Response Characteristics of a Grounding Grid

The dissipation current distribution, potential rises and frequency-dependent impedances of the grounding grid were investigated. The computational simulations are made using the simplified EMTP-based model. Based on experimental and simulation results, the dissipation current at a frequency above ～100㎑ intensively converged near the current injection point of the grounding grid, and decreased far from the current injection point. When the test current was injected at the center of the grounding grid, the high frequency grounding impedances were lower than those measured at the corner or side of the grounding grid. The trend of simulation results for the grounding impedance and dissipation current distribution calculated using a non-uniform distributed parameter circuit model are similar to the data measured at the test site.

탄소접지극 접지임피던스의 주파수의존성과 과도응답특성의 해석

This paper presents transient response behavior and frequency-dependent ground impedance of a single carbon ground electrode. The ground impedance of the carbon ground electrode was measured as a function of frequency of injected currents and simulated by using the distributed parameter circuit model with due regard to the frequency-dependent soil parameters, and the transient response behavior of the carbon ground electrode against impulse currents were investigated. As a consequence, the frequency-dependent ground impedance of the carbon ground electrode showed the capacitive behavior, that is, the ground impedance decreases with increasing the frequency of injected currents and lowers at the fast front time of impulse current. It was found that the carbon ground electrode is effective in grounding system for lightning protection. The ground impedance simulated with due regard to the frequency-dependent soil parameters was in good agreement with the measured data. The adequacy of the simulation technique and the distributed parameter circuit model for the carbon ground electrode was verified. It is expected that the simulation methodology, which analyzes the frequency-dependent ground impedance of the carbon ground electrode proposed in this work, can be used in the design of a grounding system for protection against lightning.

Frequency-dependent grounding impedance of the counterpoise based on the dispersed currents

When surges and electromagnetic pulses from lightning or power conversion devices are considered, it is desirable to evaluate grounding system performance as grounding impedance. In the case of large-sized grounding electrodes or long counterpoises, the grounding impedance is increased with increasing the frequency of injected current. The grounding impedance is increased by the inductance of grounding electrodes. This paper presents the measured results of frequency-dependent grounding impedance and impedance phase as a function of the length of counterpoises. In order to analyze the frequency-dependent grounding impedance of the counterpoises, the frequency-dependent current dissipation rates were measured and simulated by the distributed parameter circuit model reflecting the frequency-dependent relative resistivity and permittivity of soil. As a result, the ground current dissipation rate is proportional to the soil resistivity near the counterpoises in a low frequency. On the other hand, the ground current dissipation near the injection point is increased as the frequency of injected current increases. Since the high frequency ground current cannot reach the far end of long counterpoise, the grounding impedance of long counterpoise approaches that of the short one in the high frequency. The results obtained from this work could be applied in design of grounding systems.

매설지선의 접지임피던스의 주파수의존성에 대한 모사기법

A counterpoise is commonly employed in grounding systems installing near the ground surface of low resistivity soils and radial-type counterpoises are used in the limited space. Recently some studies on the evaluation of ground impedance of paralleling ground electrodes have carried out, but the data for providing the frequency-dependent ground impedances considering potential interferences are not yet sufficient. In order to provide the information about the design of grounding systems for surge protection, the simulations of the frequency-dependent ground impedance of various shaped counterpoises are carried out by using the distributed parameter circuit model including the effect of potential interferences. This paper presents the theoretical simulations and actual experiments of the frequency-dependent ground impedance of paralleling and 3 or 4-arms star counterpoises. The accuracy of the simulation methodology is examined by the comparison with the measured results, and the results show a good agreement between the simulation and the experiment.

Electrical Circuit Flashover Model of Polluted Insulators under AC Voltage Based on the Arc Root Voltage Gradient Criterion

In order to study the flashover mechanism of polluted insulators under AC voltage, a new arc propagation criterion which is based on an arc root voltage gradient is proposed. This criterion can explain the variation of the arc root voltage gradient in the arc propagation process. Based on this criterion, a new distributed parameter electrical circuit flashover model of polluted insulators is presented. The arc channel is considered as an equivalent distributed parameter circuit model instead of using the arc voltage-gradient equation. The parameters of the arc model are obtained from the electromagnetic field distribution of the arc and the gas discharge theories. The arc root is considered as parallel paths including the polluted layer. The variation of the voltage on the arc root is related to the capability of arc propagation. This model takes the microscopic mechanism of arc root ionization into consideration, which can improve the accuracy of the flashover model. The results obtained from the presented model are in good agreement with other mathematical and experimental results.

병렬로 시공된 수직 접지전극의 합성접지임피던스의 주파수의존성 분석

This paper deals with the experimental results of the frequency-dependent resultant ground impedance of vertical ground electrodes installed with a regular n-polygon. In order to propose an effective method of installing the vertically-driven multiple ground electrodes used to obtain the low ground impedance, the resultant ground impedance of ground electrodes installed with a regular n-polygon were measured as functions of the number of ground electrodes and the frequency of test currents and the results were discussed based on the potential interferences among ground electrodes. As a consequence, the effect of potential interference on the resultant ground impedance of vertical ground electrodes is frequency-dependent and it is significant in the low frequency of a few hundreds [Hz]. The resultant ground impedance of multiple vertical ground electrodes is not decreased in linearly proportion to the number of ground electrodes due to the overlapped potential interferences. Also the distributed-parameter circuit model considering the potential interference, the frequency-dependent relative permittivity and resistivity of soil was proposed. The simulated results of the frequency-dependent resultant ground impedance of multiple vertical ground electrodes are in good agreement with the measured data.

Critical Length Estimation of Counterpoise Subjected to Lightning Stroke Currents

The conventional grounding impedance of a counterpoise is calculated as a function of the length of the counterpoise by use of the distributed parameter circuit model with an application of the EMTP(Electromagnetic Transient Program). The adequacy of the distributed parameter circuit model is examined and verified by comparison of the simulated and the measured results. The conventional grounding impedance of the counterpoise is analyzed for the first short stroke and subsequent short stroke currents. As a result, the simulated results show that the minimum conventional grounding impedance gives at a specified length of the counterpoise. The shorter the time taken to reach the peak of injected currents, the shorter the length of the counterpoise having the minimum conventional grounding impedance. We also present the critical lengths of the counterpoise for short stroke currents as a function of soil resistivity. Based on these results, it is necessary to compute the length of the counterpoise in a specified soil resistivity which satisfies both the low conventional grounding impedance requirement whilst also providing a suitable ground resistance in order to obtain an economical design and installation of the counterpoise.

다층 대지구조에서 수직 접지전극의 임계길이 산정

접지임피던스는 접지전극의 크기를 증가시켜도 낮아지지 않고, 토양의 특성과 주파수 조건에 따라 접지 임피던스가 최소값을 보이는 접지전극의 길이가 존재하며, 이 접지전극의 길이를 각 토양 특성과 주파수에 따른 임계길이라 한다. 본 논문에서는 대지구조의 조건을 고려하는 새로운 분포정수회로모델을 제안하였으며, 새로이 제안된 해석모델을 적용하여 MATLAB프로그램으로 수직접지전극의 임계길이와 접지임피던스를 해석하였다. 그 결과, 수직접지전극의 임계길이와 접지임피던스의 주파수의존성에 대한 대지구조의 영향이 크며, 접지시스템의 최적 설계를 위해서는 대지구조를 고려하는 것이 바람직한 것으로 밝혀졌다.

Analysis for the Grounding Impedance of Vertical Grounding Electrodes using the Distributed Parameter Circuit Model

A grounding electrode has the transient grounding impedance characteristics against lightning surges. So the performance of grounding electrodes should be evaluated as a grounding impedance as well as the ground resistance. The frequency-dependent grounding impedance is varied with the shape and size of grounding electrode and is divided into both inductive and capacitive behaviors. This paper presents a theoretical analysis for the grounding impedance determined by the size of grounding electrode using the distributed parameter circuit model. EMTP and Matlab programs were used in calculating the frequency-dependent grounding impedances of vertical grounding electrodes. It was found that the frequency-dependent grounding characteristics of vertical grounding electrodes are characterized by the distributed parameters which are changed in the dimension of grounding electrodes.

Simulations of Frequency-dependent Impedance of Ground Rods Considering Multi-layered Soil Structures

Lightning has a broad frequency spectrum from DC to a few MHz. Consequently, the high frequency performance of grounding systems for protection against lightning should be evaluated, with the distributed parameter circuit model in a uniform soil being used to simulate grounding impedances. This paper proposes a simulation method which applies the distributed parameter circuit model for the frequency-dependent impedance of vertically driven ground rods by considering multi-layered soil structures where ground rods are buried. The Matlab program was used to calculate the frequency-dependent ground impedances for two ground rods of different lengths. As a result, an increase of the length of ground rod is not always followed by a decrease of grounding impedance, at least at a high frequency. The results obtained using the newly proposed simulation method considering multi-layered soil structures are in good agreement with the measured results.

직선형 접지전극의 임계길이의 산정

뇌전류와 같이 고주파성분을 함유한 서지전류나 전자통신기기의 전자기장해를 유발하는 고주파 이상전류에 대하여 접지전극은 주파수에 의존적인 상당히 복합적인 임피던스의 특성을 보인다. 접지전극의 접지임피던스는 접지전극의 크기를 증가시켜도 낮아지지 않고, 대지의 특성과 주파수 조건에 따라 접지임피던스가 최소값을 보이는 접지전극의 길이가 존재하며, 이 접지전극의 길이를 대지의 특성과 주파수 조건에 대한 임계길이라 정의한다. 본 논문에서는 분포정수회로모델을 이용하여 수직접지전극과 수평접지전극의 임계길이를 산정하였으며, 실험결과와의 비교를 통해 타당성을 확인하였다.