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Classical multiconductor transmission line (MTL) theory, which is employed in electromagnetic transient (EMT) simulators, is built on the assumptions that the wire structure is infinitely long and has a uniform cross-section. Therefore, non-uniformities which occur in physical power systems, such as transmission line crossings, are not represented...
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... let's consider two conductors crossing each other as shown in Fig. 3. The region near the crossing is where we solve (16) for, whereas the remaining of the conductors can be solved using uniform MTL equations. The system of equations (16) along with terminal constraints can be solved using a 1D FDTD algorithm as explained in [4], [22] at each time step. The terminal constraints are imposed by the ...
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... solved using a 1D FDTD algorithm as explained in [4], [22] at each time step. The terminal constraints are imposed by the networks terminating the wires. The 1D FDTD technique employs a single space variable z. A common space variable z is applicable to the developed SFTL model as the region modeled using the proposed approach is symmetrical (see Fig. 3). It is now needed to identify the length of the segment of the line that should be modeled using the proposed model. It is shown in [19] that the effective distance of a current variation on its electromagnetic field is equal to its wavelength λ. On the other hand, transmission line models are applied for cases where the maximum cross ...
Context 3
... let's consider two conductors crossing each other as shown in Fig. 3. The region near the crossing is where we solve (16) for, whereas the remaining of the conductors can be solved using uniform MTL equations. The system of equations (16) along with terminal constraints can be solved using a 1D FDTD algorithm as explained in [4], [22] at each time step. The terminal constraints are imposed by the ...
Context 4
... solved using a 1D FDTD algorithm as explained in [4], [22] at each time step. The terminal constraints are imposed by the networks terminating the wires. The 1D FDTD technique employs a single space variable z. A common space variable z is applicable to the developed SFTL model as the region modeled using the proposed approach is symmetrical (see Fig. 3). It is now needed to identify the length of the segment of the line that should be modeled using the proposed model. It is shown in [19] that the effective distance of a current variation on its electromagnetic field is equal to its wavelength λ. On the other hand, transmission line models are applied for cases where the maximum cross ...
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Citations
... Many papers address a specific transient phenomenon to be integrated into the transient modeling of transmission lines. Gunawardana and Kordi, in [11], address the issue of the transient behavior of transmission lines crossing. The developed model utilizes the electromagnetic scattering theory to calculate space varying per unit length (PUL) parameter matrices close to the conductor crossing. ...
... The developed model utilizes the electromagnetic scattering theory to calculate space varying per unit length (PUL) parameter matrices close to the conductor crossing. The presented model in [11] considers different crossing angles for lossless and frequency-independent transmission lines. In [12], accurate transient modeling of skin effect of MTL is proposed, where the authors take into account the transient behavior of transmission line skin effects. ...
Rational function approximation is commonly used to fit the transmission line impedance over a wide frequency range. Nevertheless, it is computationally costly and challenging to implement in practical applications due to the high number of approximations required to fit the impedance curve for the high-frequency range. Therefore, a novel fitting method of multiconductor transmission line (MTL) based on the analytical impedance equation of a transmission line using the impedance frequency response measurement is presented in this paper. The proposed fitting method is a function of the transmission line length since it is based on the analytical impedance equation of a finite transmission line. Furthermore, the proposed model uses a constant set of equations and calculated parameters to fit the impedance frequency response for a wide range of frequencies. Moreover, the proposed model parameters are calculated using derived resonance equations and the impedance frequency response measurement. In addition, an algorithm is developed to further fit the proposed model to the impedance frequency response measurement of the transmission line. MTL impedance frequency response is measured using a real-time digital simulator (RTDS). To ensure the accuracy of the proposed model, a comparison between the proposed model and vector fitting (VF) is presented.
... In a recent publication by the authors [25], an EMTcompatible simulation model for lossless, crossing single-conductor (i.e. nonuniform) overhead transmission lines of finite length was proposed based on electromagnetic scattering theory. ...
... This model was later extended to a lossless multiconductor structure over perfect electric conductor (PEC) ground in [26]. In both [25], [26], a simplifying assumption was made where the conductors and ground were assumed to be lossless. ...
... where R s and R i are the distances to an observation point z from the current element and the image current element at a source point z , respectively, and β = ω √ µ 0 ε 0 is the phase constant. Equation (2) looks similar to the scattered electric field of a wire structure above PEC ground given in [25]. However, the Green's functions, given in (3), are quite different from the lossless case since they are now frequency dependent. ...
Expansion of power grids has resulted in the construction of multiple transmission lines within constrained spaces inevitably making them nonuniform in nature. Existing transmission line models available in electromagnetic transient (EMT) simulators are based on classical multiconductor transmission line (MTL) theory with the assumption that the transmission lines are infinitely long and have uniform cross-sectional dimensions. This paper develops a time-domain model, namely dispersive scattered field transmission line (DSFTL) model, for multi-conductor dispersive nonuniform overhead transmission lines above lossy, frequency-dependent ground. The proposed model which consists of closed-form equations in the time-domain has been implemented using a modified finite-difference time-domain (MFDTD) algorithm and integrated into an EMT simulator (PSCAD/EMTDC). Results have been compared with and verified by those obtained using a full-wave approach and measured data available in the literature. Simulations of nonuniform structures that include nonlinear components (such as breakers) have also been carried out under fault conditions.
... However, solving the electromagnetic scattering equations used in this model requires iterative methods [10], [11]. A method to simplify scattering equations into closed-form equations has been proposed by the authors in [12] and used to develop a scattered field transmission line (SFTL) model for lossless, single-conductor transmission line crossings. The SFTL model has been implemented using an FDTD algorithm that is compatible with EMT-type simulators. ...
... This paper extends the SFTL model developed by the authors for single conductor line crossings in [12] to multiconductor line bends. SFTL is first verified by comparing its results against those obtained from a full-wave solver in a simple transmission line bend geometry. ...
... The function g is the Green's function related to the scattered field generated by a straight, cylindrical, current carrying conductor. The derivation of the Green's function for parallel and non-parallel wires is explained in [12]. Equation (2b) suggests that the magnetic vector potential on the region before the bend, due to the currents after the bend, has a factor of cos ↵. ...
... Fundamental functionalities used in the operation of power grids, e.g., state estimation (SE) [1], [2], [3], optimal power flow (OPF)-based control [4], [5], [6], [7], , Model Predictive Control [8], [9] and optimal relay tuning [10], [11], require the knowledge of transmission line (TL) parameters at the rated system frequency. Conventionally, TL parameters are obtained either by using the physical properties of the line (such as conductor dimensions, types of wires, tower geometries, ground electrical parameters) [12], [13] or by making measurements on the line when it is off-grid [14]. The first method is applicable only when accurate conductor characteristics are known, whereas the second method, although reliable, is time consuming and difficult to implement in practice. ...
We present a new approach for estimating the parameters of three-phase untransposed electrically short transmission lines using voltage/current synchrophasor measurements obtained from phasor measurement units. The parameters to be estimated are the entries of the longitudinal impedance matrix and the shunt admittance matrix at the rated system frequency. Conventional approaches relying on the admittance matrix of the line cannot accurately estimate these parameters for short lines, due to their high sensitivity to measurement noise. Our approach differs from the conventional ones in the following ways: First, we model the line by the three-phase transmittance matrix that is observed to be less sensitive to measurement noise than the admittance matrix. Second, we compute an accurate noise covariance matrix using the realistic specifications of noise introduced by instrument transformers and phasor measurement units. This noise covariance matrix is then used in least-squares-based estimation methods. Third, we derive different least-squares-based estimation methods based on a statistical model of estimation and show that the weighted least-squares and the maximum likelihood methods, which make use of the noise covariance matrix produce the best estimates of the line parameters. Finally, we apply the proposed methods to a real dataset and show that our approach significantly outperforms existing ones.
Buried conductors crossing paths with overhead transmission lines is a common occurrence. Interference caused by overhead lines has been found capable of affecting the safe, sustainable operation of the buried conductors. Such occurrences introduce an electromagnetic problem of a nonparallel structure with conductors present in both air and ground half-spaces. Electromagnetic transient (EMT) simulations of such structures are vital in predicting the behaviour of modern power networks. This paper develops a novel EMT compatible time-domain model for nonparallel overhead wires and conductors that are buried in a frequency-dependent lossy (finitely-conducting) ground. Analytical expressions are derived for the per-unit-length (PUL) impedance and admittance matrices based on thin-wire electromagnetic scattering theory. The closed-form formulations derived in this work can be easily incorporated in an EMT simulator to calculate the coupling effect between nonparallel overhead lines and buried conductors. The validity of the proposed approach is examined for various values of the ground conductivity, the radius of the buried conductor, the crossing angle, and burial depth of the conductor by comparing with results with those obtained using a full-wave approach. A case study on the induced voltage in buried conductors due to typical lightning transients in overhead lines has also been performed.
Finite-difference time-domain (FDTD) is a popular method utilized for solving frequency-dependent transmission line structures. It is also conveniently applicable to nonuniform wires. The FDTD algorithm discretizes the transmission line problem into a finite number of space-segments and solve for the voltage and current of each segment at every time-step. Therefore, they inherently involve more computations per timestep than conventional terminal based models. In this work, parallel implementations of a modified FDTD algorithm for a frequency-dependent transmission line problem using multicore CPU and GPU architectures are proposed in order to increase its computational efficiency. Accuracy and performance of the parallel FDTD methods are discussed with examples. The results indicate that a speedup of a few folds compared to serial execution is achieved by the parallel implementation using multicore CPU architecture whereas a massive speedup is achieved by using GPU. The proposed model is also suitable for modelling transmission lines in massively parallel electromagnetic transient (EMT) simulation methods. Index Terms-Transmission line theory, electromagnetic transient analysis, time-domain analysis, finite difference methods, parallel processing.
