Equivalent Source Impedance Research Articles

A physics-informed data-driven fault location method for transmission lines using single-ended measurements with field data validation

Data driven transmission line fault location methods have the potential to more accurately locate faults by extracting fault information from available data. However, most of the data driven fault location methods in the literature are not validated by field data for the following reasons. On one hand, the available field data during faults are very limited for one specific transmission line, and using field data for training is close to impossible. On the other hand, if simulation data are utilized for training, the mismatch between the simulation system and the practical system will cause fault location errors. To this end, this paper proposes a physics-informed data-driven fault location method. The data from a practical fault event are first analyzed to extract the ranges of system parameters such as equivalent source impedances, loading conditions, fault inception angles (FIA) and fault resistances. Afterwards, the simulation system is constructed with the ranges of parameters, to generate data for training. This procedure merges the gap between simulation and practical power systems, and at the same time considers the uncertainty of system parameters in practice. The proposed data-driven method does not require system parameters, only requires instantaneous voltage and current measurements at the local terminal, with a low sampling rate of several kHz and a short fault time window of half a cycle before and after the fault occurs. Numerical experiments and field data experiments clearly validate the advantages of the proposed method over existing data driven methods.

Precise Fault Location in Active Distribution Systems Using Unsynchronized Source Measurements

This article presents a phase-domain based fault location algorithm for unbalanced power distribution systems with distributed generation. Unsynchronized voltage and current measurements, taken from the sources prior and during the fault, are utilized to calculate the equivalent source impedances and the incremental current quantities required. The latter are substituted into the fault location equations, which are solved to determine the fault resistance(s), the synchronization angles, and the possible fault positions. Multiple possible fault position estimations are eliminated by applying an index-based methodology to find the exact fault position. Extensive simulations are performed for a benchmark distribution system with conventional and inverter-interfaced generation units, considering all types of common short-circuit faults, several fault resistance magnitudes, varying load levels, different distributed generation (DG) mixture, and the impact of line segment length. The results show that fault distance is accurately estimated by the proposed algorithm.

Distance Protection for Lines Connecting Converter Interfaced Renewable Power Plants: Adaptive to Grid-end Structural Changes

Typical fault current characteristics of converter interfaced renewable power plants have significant impact on the reliability of traditional line distance protection. Large degrees of system non-homogeneity introduce substantial error in the apparent impedance calculation. In this paper, an adaptive distance relaying method for lines connected to converter-interfaced renewable power plants is proposed. A range of fault current phase angles is identified using the local and remote equivalent source impedances, which are calculated using only local measurements. Corresponding to the lower and upper bound of the identified range of fault current phase angle, two apparent impedances are calculated based on priority to dependability and security of protection operation. The trip decision is made based on the weighted sum of the first and second apparent impedances. Tuning of the dependability and security weightage factors based on the calculated remote grid-end source impedance, ensures adaptability and reliability of operation, even after structural changes in the grid. The proposed method is verified using IEEE 39 bus system and validated using field data. Comparative assessment with practically proven distance and modified distance protection method for lines connected with renewables is also provided.

Resonance magnetoelectric effect analysis and output power optimization of nonlinear magnetoelectric transducer model

Magnetoelectric composites comprised of piezoelectric and magnetostrictive materials, are widely used in magnetic field sensing, energy harvesting, and transducers. This work establishes a finite element model of a laminated magnetoelectric transducer coupled with magneto-elastic-electric fields based on the constitutive equation of the nonlinear magnetostrictive material. Then, the resonant magnetoelectric effect under different biased magnetic fields is studied. Based on the equivalent circuit model and the two-port network theory, the magnetoelectric coefficient and the equivalent source impedance under the resonant state are completely solved for the first time. Introducing optimized L-section matching networks between the magnetoelectric transducer and the load resistor can increase the load power and expand the operating bandwidth. The simulation results are consistent with the data in the literature, thus confirming the accuracy and effectiveness of the model. The simulation results demonstrate that the magnetoelectric coefficient reaches 51.79 V/(cm·Oe) at 51.4 kHz and 450 Oe bias magnetic field, and the ultimate output power of –3.01 dBm at 50.4 kHz and 350 Oe bias magnetic field. To ensure the load power, the power increase of 2.30 dB and the bandwidth expansion of 2.27 times are achieved by optimizing the matching network. The nonlinear finite element model in this work takes into account of the magnetoelectric effect under the acoustic resonance state and quantifies the ultimate output power. The magnetoelectric transducer model can obtain high magnetoelectric coefficient, load power, and power density in a small volume, providing a significant advantage in terms of equilibrium. The research results are of great importance in guiding the design and performance improvement of miniaturized magnetically coupled wireless power transfer systems.

Negative-Sequence Active and Reactive Currents Compensation for Unbalanced Three-Phase Networks Subject to Various Line Impedance Attributes

In three-phase systems, voltage unbalance is incurred mainly by load unbalance under balanced lines. Based on the identical line impedance attributes between any two phases, a region of compensation (RoC) describing the relationship between the negative-sequence current vector and the line impedance attribute was presented. The RoC derivation arose primarily from the negative-sequence voltage across the equivalent source impedance. However, the source impedance attribute might be different between phases due to the embedded unbalanced load. A conversion from the source impedance to the line impedance was performed such that the mapping between the RoC and the impedance attribute becomes meaningful. The RoC is beneficial in narrowing the search and therefore simplifies the algorithm for determining the negative-sequence active and reactive current commands for a static synchronous compensator (STATCOM). To alleviate the current burden, the minimal voltage drop across the line impedance and a current weighting with safety boundary was incorporated. A quadrant of convergence (QoC) concluded from the experimental results agrees with the RoC and shows the effectiveness of the proposed approaches.

Analytical approach to modelling the interaction between power distribution systems and high impedance faults

High impedance faults (HIFs) and the associated electric arc is a topic of public safety and concern because fault currents are generally too small to be detected in a reliable way by conventional over-current relays. This study proposes an analytical model for analysing HIFs in power distribution systems. The proposed analytical model considers the complex interaction between a time-varying fault impedance, the power distribution line and an equivalent source impedance at the substation bus. Hence, this approach requires the joint solution of a partial differential equation and a single non-linear equation. The proposed methodology calculates the transient conductance, voltage and current at the substation bus, considering several contact surfaces and short circuit levels. The analytical model was validated by means of comparisons with measurements in a real distribution system, results published by other authors and computer simulations in electromagnetic transient programs. The obtained results show good agreement between the analytical model, measurements and computer simulations. A sensitivity analysis of the interaction of all the parameters associated to HIFs is also presented.

One-end impedance based fault location in double-circuit transmission lines with different configurations

• One-end impedance based fault location method for double-circuit transmission lines with eight different configurations. • Developed in phase coordinates and does not require six-order sequence component transformation. • Fault data for verification are obtained using MATLAB – Simulink. • Results shown that the method is accurate and robust. A one-end impedance based fault location method suitable for double-circuit transmission lines with different end configurations is presented in this paper. The effect of mutual coupling of the circuits is taken care of in developing the algorithm. The method is developed in phase coordinates and hence it does not require the complicated six-order sequence component transformation. It is applicable to both symmetrical and unsymmetrical lines. Depending on the terminations at both ends of the line, eight different cases are discussed. The fault data required to evaluate the effectiveness of the method are obtained by simulating faults in different types of double circuit lines using MATLAB/Simulink. The accuracy of the proposed technique is evaluated by comparing the computed fault location with the actual fault location in the simulated models. It is shown that the method is accurate and robust for small errors in estimated equivalent source impedances.

자기단 전원 임피던스 추정 기법을 사용한 병행 2회선 송전선로 고장점 표정 알고리즘

This paper presents a fault location algorithm based on the adaptively estimated value of the local sequence source impedance for faults on a parallel transmission line. This algorithm uses only the local voltage and current signals of a faulted circuit. The remote current signals and the zero-sequence current of the healthy adjacent circuit are calculated by using the current distribution factors together with the local terminal currents of the faulted circuit. The current distribution factors consist of local equivalent source impedance and the others such as fault distance, line impedance and remote equivalent source impedance. It means that the values of the current distribution factors can change according to the operation condition of a power system. Consequently, the accuracy of the fault location algorithm is affected by the two values of equivalent source impedances, one is local source impedance and the other is remote source impedance. Nevertheless, only the local equivalent impedance can be estimated in this paper. A series of test results using EMTP simulation data show the effectiveness of the proposed algorithm. The proposed algorithm is valid for a double-circuit transmission line system where the equivalent source impedance changes continuously.

Accurate fault location algorithm for transmission line in the presence of series connected FACTS devices

This paper presents a new and accurate fault location algorithm based on distributed time domain line model for a transmission line compensated with series connected FACTS device. In the proposed algorithm, in order to compute the voltage drop across the series device during the fault period, the series device model and knowledge about the operating mode of the compensating device are not utilized. For this reason, the proposed technique can be easily applied to any series FACTS compensated line. Samples of voltage and current at both ends of the line are taken synchronously and used to calculate the location and resistance of the fault. The proposed algorithm is not sensitive to fault resistance and fault inception angle and does not require any knowledge of equivalent source impedances. This method has been tested using EMTP/ATP model of a 400 kV, 300 km transmission line compensated with a series FACTS device. The results of computer simulations for different operating conditions demonstrate the very high accuracy and robustness of the algorithm.

Induced Voltages on Pipelines Installed in Corridors of AC Power Lines

An experimental reduced-scale rig was built to investigate the capacitive and inductive coupling caused by AC power transmission lines near unburied pipelines. A computer model for the experimental rig was created to investigate the different factors that may affect the coupling effect. The basic input data to the model consists of power line and pipeline geometrical configurations, conductor and pipeline physical characteristics including insulation and coating characteristics, and environmental parameters (such as soil characteristics, power source voltage, and equivalent source impedances). The model illustrates the effects of various parameters (length of parallelism, lateral distance, soil resistivity, current magnitude, and voltage magnitude) upon AC electromagnetic interference between transmission lines and nearby pipelines. The results of the computer model were verified experimentally. Good correlation between the experimental and software based simulated results is obtained, which validates the modeling approach of coupling between power transmission line and unburied pipeline.

A fault location method for parallel transmission lines

This paper presents a fault location method for one of two individually transposed parallel transmission lines. This method only utilizes voltage and current data acquired at one common end of the two lines to estimate the equivalent source impedance at the remote end. Therefore, the current through a fault resistance in the fault-path can be computed and the effects of the fault resistance and source impedance of the remote system on the accuracy of fault location can be eliminated. However, this method requires that: (1) a fault occurs only on one of the two parallel lines; and (2) the unfaulted line remains in operation until the fault is cleared.

LLAMPÜDKEÑ: A high-current, low-impedance pulser employing an auxiliary exponential transmission line

The design and constructional aspects of a novel pulse power generator for use in dense plasma research presently under construction are presented. The generator consists of two Marx capacitor banks, each of 0.25 μF, 480 kV, and 28.8 kJ. Each Marx generator drives a water transmission line, in which the live electrode is the central conductor. The transmission lines consist of a constant impedance section followed by a multielectrode gas linegap followed by an exponential taper to the load section. The novel feature is the use of an auxiliary exponential line coupled at the load. This line controls both the voltage and the effective impedance at the load section. In addition, by leaving this line circuit open, energy not coupled to the plasma in the initial high-impedance phase may be reflected back and deposited into the discharge, increasing the peak current by 50%. Circuit simulations using a real-time-varying load impedance show that the current pulse rises in an approximately linear way to a maximum of 1.2 MA at 250 ns. The current falls to zero in the following 250 ns. The current waveform may be flattened simply by disconnecting the auxiliary line, giving a rectangular pulse of 350 ns with a maximum value of 950 kA. The overall impedance of the entire system may be adjusted by varying the separation between the conductors. The equivalent source impedance at the load is 0.8 Ω. This low value is by virtue of the auxiliary line, which limits the voltage at the load section and reduces the insulator constraints. We present simulations of the generator under real load conditions. The model also is checked against analytical solutions of exponential line behavior and against other published models of pulse power generators.