Untransposed Transmission Lines Research Articles

A distributed circuit model for three-phase transposed and untransposed transmission lines

A distributed model is developed for three-phase long lines. Both transposed and untransposed lines are studied and the admittance matrix and π equivalent circuit are derived as in the single-phase case. A better approximation for the π equivalent circuit is proposed that is suitable for short or medium-length lines. It is found that the completely transposed line is not a balanced network. If the line length is reduced the completely transposed line becomes a balanced network and this agrees with the general concept.

Correlation of Switching Overvoltages Over Transposed and Untransposed Transmission Lines

This paper presents a computational analysis of the difference between the values of the self parameters (resistance, inductance and potential coefficient) of some typical transmission lines. The earth return effect is included. A new coefficient of unsymmetry for the untransposed transmission line parameters is proposed. The wave mode parameters as a function of the given coefficient of unsymmetry are deduced.The balancing of the parameters of both transposed and untransposed lines is applied. The percentage error in the calculated voltage at any point of the untransposed line, if considered as transposed, is formulated.

Wave Modal Technique for Switching Transients in Untransposed Transmission Lines

This paper presents a digital analysis for the calculation of internal overvoltages in untransposed transmission lines. This analysis is based on the Laplace transform as well as on the modal technique. The frequency dependent parameters due to the earth return effect are taken into account. A general transformation matrix is determined. Its elements are evaluated numerically and then formulated theoretically. The difference between surge and characteristic impedances of a line is formulated. A formula for the voltage in wave mode coordinates of an untransposed transmission line is deduced. The sequential pole switchings of circuit breaker contacts are considered. The voltage in phase coordinates is expressed mathematically. The potential coefficients are considered as constants.

Maximum Heating and Insulation Stress on Untransposed Lines with Unbalanced Harmonic Distortion

Efficient numerical methods are presented to determine the magnitude and location of maximum overall rms current (heating), peak voltage (insulation stress) and distortion factor on untransposed three-phase transmission lines under nonsinusoidal as well as unbalanced conditions. The methods which are an extension of recently reported algorithms, guarantee convergence to the global solution. Simulation results of an unsymmetrical three-phase transmission line are included.

Electromagnetic unbalance in power systems with untransposed transmission lines

Transposition of power transmission lines represents high costs due to the required transposition towers and also results in low mechanical and electrical strengths. These disadvantages make it desirable not to transpose lines if the resulting unbalances are not adverse. This paper proposes a method to predict the electromagnetic (combination of inductive and capacitive) unbalance of untransposed lines. The method is validated by its application to typical lines under various load conditions and various geometric mean radii.

Sensitivity study of an untransposed overhead transmission line

A theory for the sensitivity analysis of the receiving-end voltage and power in an untransposed transmission line for perturbations in line parameters and line lenght is described. It is shown how the sensitivity vectors of a particular quantity can be evaluated once the sensitivity vectors of the eigenvalues and eigenvectors of the product matrix ZY are known Z and Y being the series impedance and shunt-admittance matrices of the multiconductor transmission line, respectively.

Inductive unbalance in power systems with untransposed transmission lines

In the early days of electric power systems, it was the usual practice to have frequent line transpositions to reduce capacitive and inductive unbalances on them. Transposition represents higher line costs owing to the presence of transposition towers and results in lower mechanical and electrical strength. These disadvantages make it desirable not to transpose lines if the resulting unbalances are not adverse. In this paper, the inductive unbalances of a single- and a double-circuit untransposed transmission line are analysed. Effects of loads, of line geometric mean radii and of line ground wire arrangements are included. Results for negative- and zero-sequence components which arise from such unbalances for power systems with typical lines are given and compared with those obtained using methods developed earlier.

Exact Calculation of Simultaneous Faults Involving Open Conductors and Line-to-Ground Short Circuits on Inherently Unbalanced Power Systems

The analysis of simultaneous faults, espec ially involving mutually coupled lines on inherently unbalanced power systems using the symmetrical components technique, may not be practically feasible because of the difficulties encountered in the assembly f sequence networks and their solution. To al-le- these problems, this paper presents an alternative method for digitally simulating a basically ubnlanced three-phase power system which is subjected to a shunt fault at one location and blown fuses or open conductors at another location. The method involves phase frame representation of network elements and the use of the distributed source solution technique in conjunction with the principle of superposition. e phase coordinate model of power system ele- is modified/enlarged to simulate inherent system imbalances as well as the unbalancing contributed by the change in network configuration. The unbalance conditioned by large single-phase loads, untransposed transmission lines, conductor bundles, etc. is re- flected in the polyphase admittance matrix. Consequently, line removals, additions, impedance changes, conductor and phase openings can be simulated quite easily by simply modifying the base case admittance matrix. Even the treatment of mutually coupled lines presents no computational problems, unlike the symmetrical component approach. Thus, the proposed method makes it possible to analyze simultaneous faults on basically unbalanced power systems with the same ease and simplicity as unsymmetrical faults on a balanced system with the aid of symmetrical components. The method is applicable to any combination of series and shunt faults occurring anywhere in the system.

Analysis of Single Phase Switching Field Tests on the AEP 765 KV System

Single phase switching compensation schemes for untransposed transmission lines were tested during staged fault tests on a 243 km 765 kV line. A large range Of single phase switching parameters was simulated during the tests by intentional variations of the secondary arc current and the recovery voltage on the opened phase. In 27 single phase switching tests the 60 Hz component of the secondary arc currert Was varied from 8 A rms to 80 A rms. The rate of rise of the withstand voltage for a simulated 765 kV air gap was obtained. The harmonic content of the secondary arc current was analyzed.

Wide Time-Domain Calculation of Energizing Surges in Multi-Conductor Transmission Line by a Method of Logarithmic Fourier Transformation

The energizing transients of three-phase untransposed transmission lines involving the skin-effect of conductors, the frequency dependent impedance of earth return and the complication of bus constants to form a stiff system are solved in relating to the extreme wide time-domain by the use of "Logarithmic Fourier Transformation". The results solved are accurate and the algorithm is more useful than the FFT for shortage of sampling points and saving of the computation time. This paper forms a recommendation of LFT.

Algorithms for Computation of Load Flow Under Fault Conditions

An approach for the load flow solutions during normal and fault conditions has been presented in this paper. The A,B,C,D constants of the untransposed transmission lines have been treated as matrices and not as mere constants. The analysis has been carried out entirely in the phase frame of reference. The formulas developed are suitable for digital computation.

Single-Phase Switching Parameters for Untransposed EHV Transmission Lines

Single-phase switching compensation schemes are presented and analyzed for untransposed EHV transmission lines having one, two or three shunt reactor banks. For this purpose modified and simple four-legged shunt reactor banks are utilized. A general method is developed to optimize the neutral reactor values in order to minimize the secondary arc current for different arrangements of the modified and simple four-legged reactors. As an example, a large range of 765kV lines is used and single-phase switching parameters are obtained and analyzed for different ratios between the capacities of simple and modified reactor banks. The optimum neutral reactances as well as the secondary arc current, recovery voltage and neutral reactor voltages are presented as functions of the compensation factor which is varied from 0.6 to 1.0.

Calculation of electrical transients in power systems: untransposed transmission line with frequency-dependent parameters

The paper describes the modelling of an untransposed transmission line with frequency-dependent parameters, and its implementation in an existing electromagnetic transient program based on the method of Bergeron. Only relatively short lines are used in this paper. To diminish the computation time, it is favourable to calculate the voltages and currents in a modal system; this is only possible if one tolerates certain approximations, which are dependent on the transmission-line geometry.

Compensation Scheme for Single-Pole Switching on Untransposed Transmission Lines

A Modified Four-Legged Reactor Scheme was developed for high speed, single-pole reclosing on untransposed lines. The new scheme, together with the simple four-legged reactor bank, effectively reduces the secondary arc current and the recovery voltage. Equations were derived to determine optimum neutral reactor values. Efficiency of the compensation scheme and the optimization procedure were verified by an example. The modified four-legged reactor bank includes four switches whose operations are coordinated with the line breakers. Switch parameters and suggestions for neutral reactor protection are given.

Surge propagation on Japanese 500 kV untransposed transmission line

The propagation characteristics of various surges on a 500 kV untransposed transmission line in horizontal array are described, and the test data are compared with computer results. Interesting phenomena are observed at the wavefronts of surge waves in the field test, and these are substantiated both analytically and by computer calculation.

Analysis of Power System Faults by Phase Impedance matrix Method: II-Simultaneous Unbalances and Transient Analysis

Analysis of simultaneous unbalances and transient recovery voltages of power system has been undertaken in this paper. The approach is similar to the one developed in Part I of this paper. The method requires only the assembly of the nodal admittance or impedance matrices of various elements of a power system and subsequent solution of sets of linear algebraic equations subjected to constraints. The transient analysis of a power system having untransposed transmission lines can be carried out by the application of modified Foruier transform and the steady state theory of natural modes. Finally a digital computer can be programmed to calculate the magnitudes of the fault currents and active recovery voltages.

Switching Surges on Parallel HV and EHV Untransposed Transmission Lines Studied by Analog Simulation

This paper describes techniques for analog computer simulation of coupled parallel transmission lines erected on the same right-of- way. A particular simulation is given consisting of one 500-kV and two 230-kV three-phase transmission lines interconnecting areas separated by 126 miles within the Florida Power Corporation network. Some typical results of a comprehensive line switching study are presented and discussed.

Parallel EHV Untransposed Transmission Lines Studied for Overvoltages Due to Switching Surges AND Resonance

The proposed 345-kV transmission system interconnecting three Texas utility companies was studied for overvoltages due to switching surges-and resonance. The results of the study are presented and evaluation is made of the effects of nontransposition of the lines, close coupling of parallel lineson the same tower right- of-way, and the presence of compensating reactors under particular circuital configurations. The means for carrying out the study was provided by a general purpose analog computer equipped with peripheral transport time-delay components allowing the simulation of traveling wave phenomena.

Simplified approach for estimating current unbalances in e.h.v. loop circuits

Electromagnetic and electrostatic unbalances due to the omission of transposition of transmission lines have been treated rather thoroughly, even though separately, in the literature. As e.h.v. lines become longer, and operating voltages are increased, it becomes evident that the line-charging currents are growing to the same order of magnitude as normal load currents. Consequently, it is often necessary to consider the effect of both line-charging and load currents in causing negative- and zero-sequence components of line current. When the total line is composed of sections with different cross-sectional configurations, the rigorous analysis becomes quite formidable. Therefore, a simplified equivalent circuit for an untransposed transmission-line section is proposed which relates more directly to familiar methods of circuit analysis. An important aspect of this method is that it brings out clearly the nature of the unbalance problem and thereby facilitates extrapolation, via good engineering judgement, to more complex networks.

Computation of Reflection and transfer Coefficient Matrices for Switching Transient Studies

A non-iterative method has been developed for computing reflection and transfer coefficient matrices for use in traveling wave studies on three-phase power systems. The method has been programmed, verified by reproducing field tests, and applied to a practical study. The program has the capability of including three- phase untransposed transmission lines, multi-velocity waves, single- pole switching, lightning arresters, and transformer hysteresis. All calculations of reflection and transfer coefficient matrices are done automatically to minimize data preparation.