Distributed Parameter Line Model Research Articles

Partially coupled transmission line fault location using single-ended measurements

Accurate fault location technology can not only speed up fault search but also enhance the power supply reliability. This paper introduces a single-ended fault location framework for single line to ground faults, taking into account the effects of partially coupled lines. The proposed framework relies only on local measurements. Within the proposed framework, the two methods proposed in this paper are based on the impedance line model and the fully distributed parameter line model, respectively. The impedance model based fault location method does not require iteration and has no risk of divergence, while the method based on the fully distributed parameter model has higher accuracy. The estimated results of the impedance-based method can be used as the initial values of the solution of the distributed parameter model based method. The proposed methods are validated through a number of testing cases, encompassing various fault locations, resistances, and coupling ratios.

Fault location for general AC/DC transmission lines: Multi-phase, non-homogeneous, partially mutually coupled and multi-terminal lines

The complexity of a general AC/DC transmission line is mainly caused by the components such as multi-phase line, non-homogeneous line, partially mutually coupled line and multi-terminal line. This paper proposes a systematic methodology to accurately locate faults in a general complex AC/DC transmission line. Instantaneous measurements only at line terminals are required. First, the modeling methodologies of symmetrical/asymmetrical multi-phase line, non-homogeneous (including partially mutually coupled) line and multi-terminal line are proposed. The distributed parameter line model is fully considered with partial differential equations (PDEs) in time domain. Second, the voltage distribution along the entire line is obtained via numerical solutions. Third, the faulted segment and fault location is determined based on the calculated voltage distribution. The proposed method is carefully designed to ensure applicability for a general AC/DC transmission line, independent of the numbers of phases/poles, non-homogeneous (including partially mutually coupled) sections, terminals, and joint points. Numerical experiments in two example complex transmission lines prove that the proposed method can accurately identify faulted segments and locate faults under different fault conditions. The method works with a relatively low sampling rate of 20k samples/sec and a data window of 5 ms after the fault occurs.

Research on concentrated frequency-dependent parameter model for short overhead transmission lines based on first-order rational function fitting

The impedance of power lines is influenced by geological conditions and skin effect, resulting in frequency-dependent characteristics. In this study, a centralized parameter frequency-dependent line model based on first-order rational function fitting is investigated for short overhead transmission lines. The proposed model incorporates a parallel branch consisting of resistance and inductance obtained through rational function fitting, which mimics the frequency-dependent behavior of the line. The coupling between multiple conductors is represented using controlled sources. Comparative analysis of fitting accuracy and computational efficiency across various orders of rational functions reveals that the first-order rational function fitting offers superior computational efficiency while maintaining high accuracy in the medium and low-frequency range. Simulation results demonstrate that the proposed model, when disregarding wave propagation effects, exhibits comparable accuracy to the distributed parameter line model while achieving higher computational efficiency. Moreover, in transient analysis predominantly influenced by power frequency, the proposed model outperforms the frequency-independent pi(π) line model in terms of accuracy.

Fault properties identification scheme for hybrid MTDC system based on LCC signal injection and distributed parameter line model

AbstractA fault properties identification scheme for a hybrid multi‐terminal DC (MTDC) system is proposed to improve the power supply reliability in the system recovery stage. Firstly, a current signal injection strategy based on line commutated converter (LCC) is proposed using the fault control capability. Secondly, the difference between the calculated value (CV) and the measured value (MV) of the current signal under permanent and temporary faults is analyzed for the distributed parameter line model. By introducing the dynamic time warping (DWT) algorithm to represent the difference between CV and MV, a fault properties identification scheme for permanent fault identification is constructed. Finally, the proposed scheme for permanent fault location with the distributed parameter model is obtained by introducing the trust region reflection (TRR) algorithm. The simulation results show that the proposed fault properties identification scheme has the function of permanent fault identification and location. The proposed scheme fully considers the effects of fault impedance, sampling rate, noise, and data loss. It can be applied to high voltage DC long‐distance transmission lines with LCC.

A robust transient and sustainable faults location approach for AC microgrid based on voltage and current difference measurements

The most challenging problem to protect the microgrids is the integration of different types of distributed generations, which leads to the bidirectional load flow and different fault current levels. On the other hand, the use of voltage and current measurements in nodes increases the cost of fault location methods. This paper proposes a technique to calculate the distance and branch of fault for microgrids in islanded and grid-connected modes by calculating the current and voltage difference at the terminals of each branch. This method obtains the voltages and currents of all nodes by installing measuring devices at the point of common coupling and the location of distributed generations. This technique uses a distributed parameter line model and node data to determine fault locations in the microgrid, considering distributed generation such as wind turbines, photovoltaic systems, fuel cells, and electric vehicles. This technique does not require distributed generation models. Moreover, it requires less than a quarter of the data of a cycle. The efficiency of proposed the technique is investigated by a modified IEEE 15-bus in MATLAB/SIMULINK and a 7-bus test system in the power system simulator. Besides, studies are conducted on the impacts of various fault resistance and inductance, different fault locations, different fault inception angles, measurements error, and ARC faults. The results showed that the proposed approach is extremely accurate compared to other fault location methods in microgrids.

A Closed Form Solution for Line Parameter-Less Fault Location With Unsynchronized Measurements

This paper presents a novel two-terminal fault location algorithm without using line parameters. The algorithm is formulated using unsynchronized voltage and current phasors of the fundamental frequency at both ends. The novelty of the proposed method lies in the fact that it takes into account different angles of synchronism mismatch in pre-fault and fault conditions while considering distributed parameter line model and its solution is in closed form. Simulation results and performance comparison with existing methodology are presented under different fault conditions. The simulations were performed on EMTP-RV platform. The algorithm has also been tested with practical data of Power Grid Corporation of India Limited (PGCIL). The test result shows the validity and accuracy of the developed fault location algorithm.

Fast and reliable differential protection based on traveling waves for HVDC transmission line

High voltage direct current (HVDC) technology is the ideal solution for long distance bulk power transmission. However, different from AC systems, differential protection of HVDC lines still faces a lot of challenges. We claim that from the perspective of state estimation, the essence of differential protection is to estimate state variables using measured data, of which the validity indicates whether there is a fault. Therefore, the performance of the differential protection is highly related to the model accuracy. Using a detailed distributed parameter line model, this paper developed a novel differential protection method for HVDC lines based on traveling waves with high reliability. The optimal differential point is also discussed to enhance protection rapidity. Experiments demonstrate that the proposed protection could soon detect internal faults with high fault resistance while maintaining reliability when external faults occur.

A fault‐location algorithm for parallel line based on the long short‐term memory model using the distributed parameter line model

A fault‐location algorithm for parallel line based on the long short‐term memory model using the distributed parameter line model

Transmission line fault location by solving line differential equations

The present paper describes a new algorithm for reliably locating the faults that frequently take place on electrical transmission lines. The proposed fault location technique considers a distributed-parameter line model that is given in the form of Partial Differential Equations (PDEs) whose boundary conditions are taken as synchronized time-domain data recorded from both sending and receiving terminals. The Adomian Decomposition Method is employed to spatially solve the sampled-time line model. The obtained solution provides phase voltages and currents profiles at each sample time as a function of line length. This function is expressed as a polynomial whose coefficients are simply determined by an easily-applied recursive procedure. One of the main interesting features of the developed scheme is that it can handle the case of unsymmetrical transmission lines without the need of modal decomposition that decouples the original three-phase system to an equivalent three independent single-phase systems. Simulations and calculations are all proceeded with MATLAB. The obtained results through different simulations show that the new methodology is operational, applicable, and accurate.

Circuit Model of Vertical Double-Circuit Transmission Tower and Line for Lightning Surge Analysis Considering TEM-mode Formation

The electromagnetic fields, which are produced by lightning currents flowing into a transmission tower and into overhead ground wires, spherically expand with time, and propagate as non-transverse electromagnetic (TEM) waves at least within the round trip time of the traveling wave along the tower. In this paper, a distributed-parameter line model of a vertical double-circuit transmission tower with an overhead line struck by lightning is composed considering the non-TEM characteristics. The surge impedances of the tower, ground wires, and phase conductors increase with time and reach their TEM-mode or steady state values with time constants determined from the configuration. In addition, the significant wave attenuation along the tower is included in the circuit model according to the propagation characteristic determined by the tower configuration. The virtual inductive grounding impedance or damping circuits for approximately representing the wave attenuation is no longer needed. The proposed model is applied to four types of transmission towers. Waveforms of voltages across insulator strings computed by the finite-difference time-domain method, which are regarded as the reference, are well reproduced by the proposed model. Computation efficiency is drastically improved by the proposed model comparing to the numerical electromagnetic field analysis.

PMU-based Fault Location Technique for Three-terminal Parallel Transmission Lines with Series Compensation

This study introduces a fault location technique for three-terminal series-compensated untransposed parallel transmission lines utilizing the three terminals’ synchronized data. The proposed technique is applicable for short or long lines as distributed parameter line model is employed and the potential couplings are considered. The fault location for both uncompensated line sections is obtained adopting previously introduced fault location technique. The faulty phases are required initially to be recognized for series-compensated transmission line. The adopted fault location technique for series-compensated line section is derived based on the resistive nature of the fault impedance. The obtained fault locations for each line section are compared with each other to distinguish the faulty branch and obtain the fault location. DIgSILENT Power Factory and MATLAB programs are utilized for simulation studies and required calculations. The obtained results prove the efficacy of the introduced technique.

Time-domain based fault location for series compensated transmission lines without requiring fault type

Accurate fault location algorithms enable a quicker return to operation of faulted lines. The previously published fault location algorithms for series compensated transmission lines need the fault type and/or the compensator model to be known before fault location estimation. Thus, the accuracy of them is highly related to the fault type classification method and/or modelling of the compensator. This article suggests a fault location scheme for transmission lines compensated by series devices without requiring fault type based on synchronized instantaneous values collected from both ends of the line along with taking advantage of the distributed parameter line model in the time domain. The main advantages of this method are: (1) It not only determines faulty phases, but also estimates the fault location, simultaneously; (2) It is also independent on models of the series devices, so that the scheme is valid for transmission lines compensated by any series compensator. This paper examines the accuracy of the new algorithm for different fault situations with wide variations in system operating conditions in the presence of a Thyristor-Controlled Switched Capacitor (TCSC) and a Static Synchronous Series Compensator (SSSC). The results show that the fault type-classification and location accuracy of the method is high.

A Wideband Single End Fault Location Scheme for Active Untransposed Distribution Systems

This paper presents a single end fault location scheme for distribution networks with distributed generation (DG). The high frequency transients generated when a fault occurs are used to locate the fault point. An equivalent circuit at high frequencies is derived for both inverter based and synchronous DGs. The voltages and currents measured only at the main substation are used in conjunction with the proposed DG model to create the fault location scheme. The distributed parameter line model is employed in the derivation to account for the line characteristics, e.g., inductive and capacitive mutual coupling and untransposed lines. The inverter based DG model is validated experimentally on a 400 V, three-phase system. The IEEE 34-bus feeder is simulated and used to evaluate the proposed scheme for different operating conditions, e.g., fault resistance and DG conditions. The extensive simulation studies show the accuracy of the proposed scheme with 95.3% of the test cases having an absolute error in estimation of less than 200 m.

A new single end wideband impedance based fault location scheme for distribution systems

This paper proposes an improved impedance based fault location scheme based on system analysis at non-fundamental frequencies. The fault is treated as a voltage source that injects high frequency components into the system and the analysis is carried out using these injected components. The proposed method only requires local measurements at the substation and therefore is classified as a single end method. The new contribution is that the proposed method uses the distributed parameter line model to account for inductive and capacitive effects of the line. It has been evaluated on the IEEE 34-bus feeder which is based on an actual distribution system which has the typical features such as non-homogeneous feeder sections, asymmetrical line configurations, unbalanced loads and single and three-phase laterals. The fault point, fault resistance and fault inception angle have been varied to check their influence on the accuracy of the method. The simulation results demonstrate the accuracy of the proposed method where for most cases, the error in fault location is less than 50m.

DC Fault Detection in Meshed MTdc Systems Based on Transient Average Value of Current

It is of great significance for a voltage source converter (VSC)-based multiterminal dc (MTdc) grid to isolate the dc fault lines within several milliseconds after dc fault. Existing protection schemes and fault analysis methods are mainly based on the numerical simulations, which lack the theoretical analysis. In this paper, a high-frequency (HF) equivalent model of VSC-based MTdc grid that is utilized for initial dc fault current calculation is first proposed. In the proposed model, the parallel connected capacitors of VSCs are regarded as short-circuited, and the initial fault current calculation of the fault dc line and the healthy dc line can be reduced as a simplified RL and RLC circuit. Accordingly, a novel dc fault detection method for VSC-based MTdc system is further proposed. In the proposed approach, the primary detection utilizes the transient average value of line current and the fault dc line can be identified quickly with only one-end information. In addition, the errors between the transient fault current calculation based on the distributed parameter line model and the lumped parameter line model are also evaluated. Numerous simulation studies carried out in PSCAD/EMTdc have demonstrated that the proposed HF equivalent model can be utilized for initial dc fault analysis of VSC-MTdc system and the proposed protection scheme is effective under different fault locations and high fault resistances. Compared with the traditional protection schemes based on rate of change of current, the proposed one requires relatively low sampling frequency and low computation burden, and has high fault resistance tolerance ability and high robustness with respect to the missing data.

Permanent Fault Location in Distribution System Using Phasor Measurement Units (PMU) in Phase Domain

This paper proposes a new method for locating high impedance fault in distribution systems using phasor measurement units (PMUs) installed at certain locations of the system. To implement this algorithm, at first a new method is suggested for the placement of PMUs. Taking information from the units, voltage and current of the entire distribution system are calculated. Then, the two buses in which the fault has been occurred is determined, and location and type of the fault are identified. The main characteristics of the proposed method are: the use of distributed parameter line model in phase domain, considering the presence of literals, and high precision in calculating the high impedance fault location. The results obtained from simulations in EMTP-RV and MATLAB software indicate high accuracy and independence of the proposed method from the fault type, fault location and fault resistance compared to previous methods, so that the maximum observed error was less than 0.15%

Accurate and comprehensive fault location algorithm for two‐terminal transmission lines

In this study, a novel accurate fault location algorithm is presented for two-terminal transmission lines. In contrast to conventional methods, the proposed algorithm not only utilises asynchronous samples recorded during the fault but also needs no line parameters and identification of fault type. In the presented fault-locating method, distributed parameter line model in the time domain and asynchronous data of the terminals collected during fault are applied. Fault locating as an optimisation problem has been solved by the heuristic algorithm of teaching–learning-based optimisation, and the decision variables of fault location, synchronisation time and line parameters are estimated simultaneously. The performance of the presented method was tested with different fault incidence angles, a variety of fault types, and under several system and fault conditions using the MATLAB/Simulink. These tests demonstrate the high accuracy of the presented method. Also, the proposed method did not show any dependence on the impedance of the Thevenin sources of the two sides of the line, the fault impedance and the fault incidence angle. Furthermore, it was not affected by the high resistance of the fault and the network structure.

A New Fault Location Method for Partial Coupling Double-Circuit Untransposed Transmission Line with Shared Tower and Different Voltages

This paper presents a new fault location method for partial coupling double-circuit untransposed transmission lines with shared tower and different voltages. The synchronized voltages and currents at each line terminal are needed to obtain the fault location. The proposed method is formulated based on theory of transmission lines and Taylor series expansion for distributed parameter line model. The mutual coupling between all phases and the untransposition of the line is considered to obtain accurate results. The faulted phases are recognized using Kirchhoff’s current law (KCL) and the locations of all fault types including inter-circuit faults can be determined. The power system is modeled on DIgSILENT Power Factory software, and the fault location calculations are implemented using MATLAB. The performance of the proposed method is checked under diverse values of fault types, fault resistances, and fault locations. The effect of synchrophasors errors, measurement errors, varying soil resistivity, errors in line parameters, and complex fault impedance is also verified. The simulation results prove that the proposed method achieves better performance for all test cases.

Fault location algorithm for multi‐terminal mixed lines with shared tower and different voltage levels

This study presents a new fault location algorithm for multiple-circuit shared tower transmission lines with different voltages utilising synchronised measurements. The formulation of the proposed algorithm is based on overhead transmission lines theory and Taylor series expansion of distributed-parameter line model. The untransposition of the lines and the mutual coupling between the parallel lines are considered to achieve precise fault location. Kirchhoff's current law and fault location equation are used to identify the faulty section and obtain the location of all normal shunt faults and inter-circuit faults. The power system is simulated with DIgSILENT Power Factory software and all calculations are performed by MATLAB. Numerous fault cases are conducted to demonstrate the efficacy of the proposed algorithm considering different values of fault resistances, different fault locations and all fault types. In addition, the effects of synchrophasors errors, measurement errors and the soil resistivity variations are investigated. The results of simulation prove the efficacy of the proposed algorithm for all fault cases.

Accurate Location of Evolving Faults on Transmission Lines Using Sparse Wide Area Measurements

Abstract In electric power systems, not all fault conditions remain unchanged during faults. An evolving fault has one characteristic initially and changes to a different condition subsequently. Locating evolving faults is challenging due to the change in fault type shortly after the fault initiation. This paper presents a new approach for estimating the locations of evolving faults on transmission lines. By using sparse wide area voltage measurements, this method is able to accurately locate evolving faults without requiring measurements from either end of the faulted line. There is no need to detect whether a fault is an evolving fault or not. Fault type information is not a necessity either, and the change of fault phases does not affect the estimation accuracy. In addition, the algorithm is applicable to both single-circuit and double-circuit lines, and the transmission lines can be either transposed or untransposed. Distributed parameter line model is adopted to fully consider the shunt capacitances of the transmission lines. Electromagnetic Transient Program (EMTP) is employed to simulate transmission system, and quite accurate results have been achieved.