scholarly journals Accounting for Spacers in the Mechanical Calculation of Flexible Wires for Overhead Lines and Switchgears

2019 ◽  
Vol 62 (3) ◽  
pp. 219-231 ◽  
Author(s):  
Yu. V. Bladyko
Keyword(s):  
Concentrated Loads ◽  
Total Load ◽  
Mechanical Calculation ◽  
Overhead Lines ◽  
Distributed Load ◽  
Ice Loads ◽  
Concentrated Forces ◽  
The Difference

The mechanical calculation of flexible wires of overhead lines and switchgears, in which in-phase or phase-to-phase spacers are installed, is under consideration. Spacers are considered as concentrated loads acting on the split phase. The formulas for determining the sag are given for a different number of spacers as a function of their number and the coefficient of concentrated forces. This takes into account the difference in suspension heights, tension insulators strings, wind and ice loads. These formulas, being presented in a form that is convenient for consumers, can be used for computer execution of the mechanical calculation of flexible wires in different climatic regimes, both in the presence and in the absence of phase splitting. The errors of replacing the spacers with a distributed load are demonstrated. Formulas are proposed that give the smallest error when replacing spacers with a distributed load. The greater the value of the concentrated forces from the tap-off lines and loops, the greater the error in calculating the sag of the switchgears wires. Therefore, it is not possible to replace them with a distributed load obtained by simply dividing the total load by the length of the span in the presence of the tap-off lines and loops.

scholarly journals MECHANICAL CALCULATION OF FLEXIBLE WIRES WHEN THE CONCENTRATED FORCES ARE REPLACED BY A DISTRIBUTED LOAD

2018 ◽  
Vol 61 (2) ◽  
pp. 97-107 ◽  
Author(s):  
Yu. V. Bladyko
Keyword(s):  
Parametric Method ◽  
Climatic Conditions ◽  
Concentrated Loads ◽  
Mechanical Calculation ◽  
Overhead Lines ◽  
Distributed Load ◽  
Uniformly Distributed Load ◽  
Concentrated Forces ◽  
The Wire ◽  
The One

The objective of mechanical calculation of flexible wires of substations and overhead lines is to determine the sag and tension in different climatic conditions. A wire with a uniformly distributed load is considered as a homogeneous flexible thread having the form of a parabola. Concentrated loads from spacers, barrier balls, stubs, taps to electrical apparatus and other elements are replaced with the one distributed over the span. On behalf of a span without tension springs of insulators the action of concentrated loads on the wire is considered, an error is determined when replacing the concentrated forces with the one uniformly distributed along the span by the load. The sag for the equivalent wire is determined with the aid of the ratio of the increase of the sag, due to the presence of concentrated forces. An equation of state has been drawn up which makes it possible to determine the tension after changing the number of concentrated loads, e.g., after installing spacers, hanging the barrier balls, fixing the taps. The dependence of the maximum sag on the number of concentrated forces is given. The definition of the coefficient of concentrated forces as the ratio of the sum of the concentrated loads to the weight of the wire in the span is presented. A relationship between the load factors, the increase of the sag and the coefficient of concentrated forces is established. The formula has been deduced for determining the error in the replacement of concentrated forces by a uniformly distributed load along the span as a function of the number of concentrated forces and the coefficient of concentrated forces. A decrease in the error with an increase in the number of concentrated forces has been demonstrated. A more accurate calculation of mechanical tensions and sag is possible with the use of a vector-parametric method for calculating the flexible busbar of substations and air-line wires, where the design model of wires in the form of a flexible elastic thread is placed, taking into account the spatial disposition of all structural elements.

scholarly journals Mechanical Calculation of Flexible Wires of Overhead Lines with Barrage Balls

2018 ◽  
Vol 61 (4) ◽  
pp. 299-309 ◽  
Author(s):  
I. I. Sergey ◽  
Y. V. Bladyko
Keyword(s):  
Parametric Method ◽  
Spatial Arrangement ◽  
Total Load ◽  
Mechanical Calculation ◽  
Overhead Lines ◽  
Acceptable Accuracy ◽  
Elastic Thread ◽  
Concentrated Forces ◽  
The Wire ◽  
A Chain

Aerial barrage balls serve for marking high-voltage wires in order to visually warn pilots of civil and military aviation about the presence of overhead lines. The present article deals with the mechanical calculation of flexible overhead wires of overhead lines, in which aerial warning barrage balls are installed. The wire is considered as a homogeneous flexible thread having the outline of a parabola and a chain line. The load from the aerial barrage balls must not be substituted with a distributed one by simple division of the total load into the span length, since it can cause incorrect results. The formulas for determining the sag are given for a different number of aerial barrage balls as a function of their number and the coefficient of concentrated forces. The acceptable accuracy of mechanical calculation is demonstrated when using the model of wire in the form of a parabola adopted in the design practice, provided that the components of concentrated forces are correctly determined. The equation of state is recorded, taking into account the weight and wind loads on the wire, as well as load coefficients in two planes, depending on the number of barrage balls. The performed calculations demonstrate an acceptable accuracy of the determination of the stress at various loadings of the span. For more accurate calculation of mechanical stresses and sag arrows, a vector-parametric method for calculating the flexible wires of overhead lines is suggested, where the calculated model of wires in the form of a flexible elastic thread is put taking into account of the spatial arrangement of all structural elements. The results of mechanical calculation according to the program that had been developed and to the existing methods for a different number of aerial barrier balls moved along the span are presented.

scholarly journals Mechanical Calculation of Flexible Wires in the Presence of Horizontal Concentrated Loads

2020 ◽  
Vol 63 (6) ◽  
pp. 500-514
Author(s):  
Yu. V. Bladyko
Keyword(s):  
Wind Load ◽  
Horizontal Component ◽  
Concentrated Loads ◽  
Mechanical Calculation ◽  
Overhead Lines ◽  
Load Factors ◽  
Linear Load ◽  
Flexible Wire ◽  
Concentrated Forces ◽  
The Wire

The linear wind load on the wires and cables acting perpendicular to the wire depends on the angle between the direction of the wind and the axis of the overhead line. In the methodology of mechanical calculation of wires and cables, it is recommended to take the wind directed at an angle of 90° to the axis of span and it is not specified which side the wind blows from. For spans of air, this is not so much significant as for switchgear spans, where the deviations of the wires depend on the direction of action of the taps to the electrical apparatus. The article discusses various options for the location of taps and their effect on the wire, as well as changing the direction of the wind. An algorithm for calculating the horizontal deviation of a flexible wire and its increase coefficients in the presence of horizontal concentrated loads due to the action of windon spacers, barriers, taps to electrical apparatuses and other structural elements of substations and overhead lines is given. In the absence of wind, horizontal concentrated loads and deviations occur when an arrangement of the taps is non-keel. The formulas for calculating the horizontal component of the load coefficient to solve the equation of state in the presence of horizontal concentrated forces acting in any direction have been derived. The results of the mechanical calculation are obtained for the cases of one and two horizontal concentrated forces, differently oriented with respect to the distributed wind load. In design practice it is recommended to take the wind flow in the direction of the action of horizontal concentrated forces, since in this case the greatest horizontal deviations and load factors are obtained. The reduction in the coefficients of the horizontal load occurs when the current lead is unloaded because of the opposite directions of the wind and horizontal concentrated forces. In the absence of wind, it is proposed to use the formulas for calculating horizontal deviations and load after finding the product of the coefficient of increase in horizontal deviations and the horizontal component of the coefficient of load per linear load.

scholarly journals MECHANICAL CALCULATION OF FLEXIBLE WIRES WHEN A CONCENTRATED LOAD IS BEING REPLACED WITH A DISTRIBUTED ONE TAKING INTO ACCOUNT THE STRUCTURAL ELEMENTS Y.V. BLADYKO1)

2018 ◽  
Vol 61 (3) ◽  
pp. 220-234 ◽  
Author(s):  
Y. V. Bladyko
Keyword(s):  
Parametric Method ◽  
Climatic Conditions ◽  
Structural Elements ◽  
Concentrated Loads ◽  
Concentrated Load ◽  
Mechanical Calculation ◽  
Overhead Lines ◽  
Concentrated Forces ◽  
The Wire ◽  
Electrical Apparatus

In the mechanical calculation of the flexible wires of substations and overhead lines, sags and tension are determined in various climatic conditions. Concentrated loads from spacers, barrier balls, stubs, taps to electrical apparatus and other elements are replaced with a load distributed over the span. On the example of a span with tension insulator springs, the action of concentrated loads on the wire is considered, the error is determined when the concentrated forces are replaced with a load one that is uniformly distributed along the span. It is shown that concentrated loads cannot be replaced with distributed ones by simple division of total loads by the span length, since this might result in completely incorrect findings. A relationship is established between the coefficient of the increase of the sag, the coefficient of concentrated forces, the coefficient that takes into account the presence of tension insulator springs, and the angle of inclination of the span. With wind load and the presence of taps to electrical apparatus, the deviations of the wire in two planes may be calculated independently of each other if the forces concentrated in these planes are known. A decrease in the error is shown with an increase in the number of small concentrated forces. The influence of the angle of inclination of the span and the presence of tension insulator springs on calculating the deviations of the wires of substations and overhead lines is assessed. A more accurate calculation of mechanical tensions and sags is possible with the use of a vector-parametric method for calculating the flexible bus of switchgears and wires of overhead lines, where the design model of wires in the form of a flexible elastic thread is used, taking into account the spatial disposition of all structural elements.

The Mathematical Analysis of Bow Girders of Any Shape

1956 ◽  
Vol 23 (4) ◽  
pp. 522-526
Author(s):  
M. M. Abbassi
Keyword(s):  
Mathematical Analysis ◽  
Concentrated Loads ◽  
Middle Point ◽  
Circular Arc ◽  
Distributed Load ◽  
Approximate Formulas

Abstract By using parametric equations in which the parameter is the angle included between the tangent at any point on the bow girder and the tangent at the middle point, the analysis of bow girders of shapes other than the circular arc can be treated mathematically. Exact and approximate formulas are given for symmetrical bow girders of any shape carrying a distributed load or two equal concentrated loads placed symmetrically with respect to the middle point of the girder.

Bifurcation of Circular Rings Under Normal Concentrated Loads

1973 ◽  
Vol 40 (1) ◽  
pp. 233-238 ◽  
Author(s):  
P. Seide ◽  
E. D. Albano
Keyword(s):  
Bifurcation Point ◽  
Circular Ring ◽  
Average Pressure ◽  
Uniform Pressure ◽  
Concentrated Loads ◽  
Finite Distortion ◽  
Circular Rings ◽  
Concentrated Forces

The deformation in bending of a circular ring loaded in its plane by concentrated forces is studied. The ring is assumed to be an elastica. The loads are of equal magnitudes and are equally spaced about the ring. Values of loading at which bifurcation of the symmetrical finite distortion shape occurs are determined for forces which remain normal to the ring. It is found that no bifurcation point exists for a ring under three loads. Buckling of a ring under two loads can occur only when the prebuckling configuration is an extremely distorted one. If the number of loads is five or greater, the critical average pressure does not differ greatly from the result for the ring under uniform pressure.

scholarly journals Lightning Surge Analysis for Overhead Lines Considering Corona Effect

2021 ◽  
Vol 11 (19) ◽  
pp. 8942
Author(s):  
Xiaoqing Zhang ◽  
Kejie Huang
Keyword(s):  
Equivalent Circuit ◽  
Traditional Approach ◽  
Test Results ◽  
Overhead Line ◽  
Overhead Lines ◽  
Extended Approach ◽  
Double Exponential ◽  
Damped Oscillation ◽  
The Difference ◽  
Linear Branch

Corona discharge characteristics are measured in a corona cage. The difference is found between the q–u curves under double exponential and damped oscillation surges. The behavior of the minor loops is revealed for the q–u curves under positive and negative damped oscillation surges. An extended improvement is made on the traditional approach for modeling of the q–u curves under damped oscillation surges. The extended approach has the capability of describing the complicated trajectory feature of the minor loops. On the basis of the extended approach, an efficient method is proposed for performing lightning surge analysis of overhead lines considering the corona effect. In the proposed method, an overhead line with corona is divided into a certain number of line segments. Each segment is converted into a circuit unit consisting of a non-linear branch and a linear circuit. With these circuit units connected in sequence, a complete equivalent circuit is constructed for the overhead line with corona. The transient responses can be obtained from the solution to the equivalent circuit. Then, the calculated results are compared with the field test results on a test overhead line.

scholarly journals Algorithm to select the voltage class for the gas field electricity supply system

Vestnik IGEU ◽  
2021 ◽  
pp. 32-39
Author(s):  
I.M. Bogachkov ◽  
R.N. Khamitov
Keyword(s):  
Growth Rate ◽  
Average Length ◽  
Supply System ◽  
Distribution Grid ◽  
Total Load ◽  
Overhead Lines ◽  
Gas Clusters ◽  
Discounted Costs ◽  
Gas Fields ◽  
Electric Loads

The current algorithms and mathematical models to select the voltage class based on the theory of experimental planning are developed for industrial enterprises (overhead lines with a length of up to 10 km, a power of up to 20 MV, a radial arrangement with a transformation at the end of the line). They do not consider the features of gas fields (overhead lines with a length of up to 20 km and a capacity of 1 MV with a projected growth of up to 10 MV, a transmission network with one pass-through trunk line with distributed transformation along the line). Currently, to develop a mathematical model, the following factors are considered: the average length of the power line and the total load of an enterprise. The proposed models do not allow us to quantify the dynamics of the gas fields power supply system considering the multiple growth of the electrical load in each period of the life cycle. The purpose of this study is to develop a model to solve this problem. An extreme experiment has been carried out during the research. The following input data are set: the average length of the power line; the number of gas clusters; the growth rate of the electric load. The response function is the voltage class that is optimal for the minimum discounted cost. The authors suggest the regression model. In this model the “total load” factor is split into two components, they are gas clusters and growth rate of electric loads. The algorithm to select the optimal voltage class of a distribution grid is proposed. The dynamic experiment is carried out and the growth rate of electric loads in the regressive model is being changed while other factors are being unchanged. As a result, the optimal minimum of the discounted costs of the voltage class for each period of the field life cycle is obtained. The algorithm is implemented in “PRON” software. With the help of “PRON” software, the distribution grids of several operating gas fields in Western Siberia have been investigated. The optimal voltage class of a distribution grid of gas fields is 20 kV. The reliability of the results is verified by reference models of calculating discounted costs.

Hardness Testing of Vulcanized Rubber. XI. Influence of Gauge-Spring Pressure and Friction in the Indentation Hardness Test

1948 ◽  
Vol 21 (4) ◽  
pp. 941-945
Author(s):  
J. R. Scott
Keyword(s):  
Hardness Test ◽  
Differential Method ◽  
Percentage Error ◽  
Indentation Hardness ◽  
Total Load ◽  
Ball Size ◽  
Test Taking ◽  
Vulcanized Rubber ◽  
Hardness Tests ◽  
The Difference

Abstract A discussion is given of the effects of the spring which, in many dial micrometer gauges, applies a small upward or downward force to the gauge stem, and of the effects of friction in the gauge. When hardness tests are made by the differential method, the reading being taken as the difference between the indentations produced by a small zero load and a much larger total load, the errors introduced by unbalanced gauge spring pressure and by friction may be much more serious than when a direct hardness reading, i.e., without an initial zero load, is taken. Other things being equal, the resulting percentage error in the hardness reading is greater the smaller indenting load. This is a further reason, additional to that already advanced3, for limiting the reduction of ball size and load which has been advocated to reduce the influence of the thickness of the rubber. If the gauge contains a spring, or if friction is present, it is not possible to adjust conditions so as to eliminate the resulting errors in the differential readings on all rubbers. The errors can, however, be minimized in the following ways. (1) By increasing the ratio (z) of zero load to total load. An excessive zero load, however, is undesirable for other reasons; a value of 0.05 for z is a suitable compromise. (2) By adjusting the unbalanced spring pressure to zero when the gauge stem is in a certain position which depends on the value of z and the hardness of the rubber under test. Taking z as 0.05 and the average B.S. hardness number of normal rubbers as 75 (i.e., an indentation of about 0.75 mm.), this position is that in which the tip of the indenting ball is 0.5 mm. above the surface of the rubber.

Sign in / Sign up

Export Citation Format

Share Document