2016 IEEE PES Asia-Pacific Power and Energy Conference - Xi'an - China

Sag-Tension Calculation Program for Power Substations

J. Quintana, V. Garza, C. Zamudio Transmission and Distribution Dept.

Electrical Research Institute Mexico City, Mexico

jqc@iie.org.mx, vicalegar@gmail.com, angel.cesar.zamudio@gmail.com

Abstract-This paper presents the results of a new program

developed for sag-tension calculation in power substations. The

different stages of the process are presented and explained in

detail. The main advantages of the program are explained and

compared with traditional solutions in today's market for sag­

tension calculations.

Index Terms--Power engineering computing, power system

analysis computing, power transmission, substations.

I. INTRODUCTION

Transmission systems allow for transporting electricity from the generating plants to the consumption centers. In this process, substations and transmission lines perform a fundamental role. The design of a substation is divided into two major categories: a) electromechanical design and b) civil design. One part of the electromechanical design concerns the called sag-tension calculation, which permits determining the sag values (elongations) that will have the energized conductors and the corresponding mechanical stress forces by which the structures will be subject to, for different operating conditions of the system, including: variations in temperature of the conductor, the own load variations, as well as the possible presence of ice and wind in the conductor cable. The sag calculated values allow you to define the minimum dielectric distances associated with the electromechanical design of a substation, while the forces of mechanical stress on the structures are the input data for the design of its foundations. The magnitude of mechanical stress is directly dependent on the characteristics of the elements involved in the system made up of conductors, insulators and fittings.

In many cases, sag-tension calculations only consider the effect of the conductors, neglecting the effect of insulator strings and fittings. Although this solution is valid for long spans, such as in the case of overhead transmission lines, where the conductor cable is the main component that determines the tension resulting values, for the case of substations, where spans are usually short, the story is different, because the insulator strings and fittings have an significant influence in determining the total sag and its effect -clearly- should be taken into account. In addition, in sag-

Part of this work was supported by Electrical Research Institute researcn ana aevelopment project.

978-1-5090-5417 -6/16/ $ 3l.00 ©20 16 IEEE

tension calculations, is important to consider the amount of insulator strings and the way of installation, which can be set in "I" or "V" configuration. By its nature, the insulator string is an element that contributes to additional sag caused by the conductor itself.

It is also important to consider the bundle conductors, because, in many cases, more than one conductor per phase is used, being common the use of two bundle conductors per phase for extra high voltage systems, and sometimes three conductors per phase in substation that receive power from generating plants. Therefore, it is essential to consider all the elements involved in the process of sag-tension calculation, so that the results correspond to the real conditions.

Nowadays, sag-tension calculations are made by using computer programs; however, most of these do not consider the effects of insulator strings and fittings. The few programs that take into account these factors have several problems, among them, the following can be mentioned:

• It requires investing a lot of time to train the staff responsible for operating the program for performing calculations.

• Without the ability to calculate cases of two or more conductors per phase, leads to a high probability of inconsistencies arising in the short span calculations.

• They are unintuitive and unfriendly programs, which require a lot of time and knowledge for proper handling, so it is essential to have highly specialized technical staff for the execution of calculations.

• Since the results are very difficult to interpret, more time has to be wasted to study and select them for the calculation report.

• They do not generate lying curves, so after selecting the design values, it is necessary to draw these curves manually, thus investing longer time in the entire process.

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This paper explains the characteristics of a program developed to facilitate sag-tension calculations, and its main advantages over the actual solutions in the market.

II. CONDUCTOR AND INSULA TOR STRINGS SYSTEM

The conductors and strings can be represented by elastic catenaries with two fixed points A and B which have Cartesian coordinates (0, 0) and (1, h), respectively. Therefore, the span of the cable is 1 and the relative vertical displacement of the end is h as shown in Fig. 1.

A(O,O) .-------------.. X

BU,h)

z

Fig. l. Coordinates for the elastic catenary.

Knowing the length and horizontal tension of the cable, and following some mathematical derivations, the coordinates of the supporting point B are obtained from the following equations [1]:

1 - HLo + HLo { .

h-1 (V) . h-1 (V-W)}

- - - sm - - sm --EA W H H

where:

(1)

h

H

coordinate "x" of the supporting point of the cable

coordinate "z" of the supporting point of the cable

horizontal tension of the cable

La

E

A

length of the cable

Modulus of elasticity of the cable

transversal section of the cable

W total weight of the cable

V vertical force in the supporting point

For a level span formed by a cable and insulator strings, the lowest point, which corresponds to the total sag, is found in the middle of the span. This system can be analyzed like two consecutive catenaries with points P1 (11, h1) and pz (lz, hz) as end points, respectively. The total sag is calculated by the addition of the vertical coordinates of these points, and the sum of the horizontal coordinates corresponds to the middle of the span as shown in Fig. 2. These considerations are expressed by the following equations:

11(H,L) + 1z(H,L) = 5/2 (3)

h1(H,L) + hz(H,L) = Dmax (4)

where:

11 coordinate "x" of the point P1

h1 coordinate "z" of the point P1

1z coordinate "x" of the point pz

hz coordinate "z" of the point pz

These equations depend on the length and horizontal tension of the cable. The values for11' h1' 1z and hz can be found by solving the system of simultaneous equations given by (3) and (4) for a specific condition.

Fig. 2. Conductors and insulator string system.

III. DESCRIPTION OF THE PROCESS

The solution for the simultaneous equations given by (3) and (4) is implemented by a computer program that takes into account different operation conditions, like variation in the conductor temperature and additional loads over the cable and insulator strings, imposed by the presence of ice and wind. The program works with known information of the site where the substation will be built, as well as from the conductors and insulator strings installed in the substation.

The sag and tension calculations for the different conditions are divided into four stages:

A. Calculus of length L and horizontal tension H at maximum temperature

The highest sag is analyzed in this first stahe. The length of maximum permissible sag should be an input variable and has to be set in order to meet the dielectric distances associated with the electromechanical design of the substation. This calculus is done by following the approach described in the previous section through solving the simultaneous equations explained there. These values will be taken as initial values for the next calculation stage.

B. Calculus of tension H'T for every temperature defined in the study interval

The values of length L and horizontal tension H calculated in the previous stage are taken as a reference to estimate the horizontal tension of the cable H'T at different temperatures using the change-of-state equation [2], [3]. The values of H'T for each temperature are found by solving the equation:

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(5)

When H'T is found, the sag is calculated by adding the vertical coordinates of the analyzed points as follows:

(6)

where:

H' T horizontal tension of the cable for any temperature in the study interval

DT sag for any temperature in the study interval

C. Calculus of sag DIce/wind and horizontal tension H'Ice/wind under de effect of ice and reduced wind

The effects of ice and reduced wind are modelled as extra loads in the cable and insulator strings [3], [4]. These effects are considered in the equations used to find the Cartesian coordinates of the points that have been analyzed. The value of H'Ice/wind should be calculated first, and then the

corresponding sag DIce/wind is obtained, as described in the

previous stage, using the next equations:

(7)

(8)

where:

H'Ice/Wind horizontal tension of the cable under de effect of ice and reduced wind

DIce/Wind sag under de effect of ice and reduced wind

D. Calculus of sag DMaxwind and horizontal tension H'Maxwind under de effect of maximum wind, without ice

In this last stage the maximum wind pressure has to be calculated first [5]. This extra load is taken into account to find the horizontal tension and the corresponding sag for this condition. The effect of ice is not considered for this calculation. The maximum tension and minimum sag are obtained in this situation. To do this, the next equations are used:

(9)

(10)

where:

H'Maxwind horizontal tension of the cable under de effect maximum wind, without ice

DMaxwind sag under de effect of maximum wind, without ice

The summary of the stages explained before is shown in Fig. 3.

Initial Data:

lnfol1uation from the substation design

Conductors and insulator strings charactelistics

Operation conditions

.-1. CO/CIt/liS of/englll Land IIon:Ol'lla/,enslOnH alma.Ymllllll

tempera/lire T _by solnng 'he simullane olls equatIOns system:

',U/.L) + ',(H.L) = 5/2

h, (H. L) + fI,(H. L) = Dmax

B. Ca/clI/lls oflenslOn H'Tfor eml), /emepamre defined mIlle sflldy

m,en'a/

',(H'r) + ',Uf'r) = 5/2

Sag IS ca/clI/aled 11'1111 ,lie neXI eqllallOn:

Dr = h,(H'r) + ",(H'r)

. C. Ca/clI/IIS ofs ag and IIon:Ol1la/,enslon lll1der de �ffecl of,ce and

redllcedmnd IIsmg ,lie eqllal/on:

11 (H'/c�"Vind) + 12 (rf"c./Wind ) = 5/2

Sag IS ca/clI/aled 11'1111:

Dler/Wind = 11'1 (frlce/Wlnd) + "'2(Jf'/c�fWiruJ)

D. CO/CIt/liS ofsag and IIorCOl1la/,enslOl1l1nder de effecl 0fma.tl/nllm

wmd, "lrrlh olll lce:

'1 (JI'UaxWmd ) + 12(H'MaxlVlnd) = S/2

Sag IS ca/clI/aled11'II11:

DNaxlVmd = h'l(H'MaxlVlnd) + Jr'Z(H'MaxlVind )

Fig. 3. Main stages of the process for sag-tension calculation.

IV. ILUSTRARTIVE EXAMPLE

J

To demonstrate how the proposed program works, a typical case of a level span will be used as a sag-tension calculation example. Fig. 4 shows a 400 kV switchyard of a transmission substation with breaker-and-a-half configuration. The span by which the sag-tension calculation is performed is identified as "span 1".

span 1

V

f 54. 8m

1 . . .

'\ \

Fig. 4. 400 kV switchyard of a transmission substation.

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First, the information of the site where the substation will be built is needed. These data are shown in TABLE I.

TABLE L SITE PARAMETER VALUES

Parameter Value

Altitude [meters over sea level] 34

Annual average temperature [0C] 24

Maximum wind speed [kmIh] 220

Ice thickness [mm] 6

Span length [m] 54.8

Span height [m] 23.50

Next, in order to do the computation, the conductors and insulator strings characteristics are needed. This information is summarized in TABLE II.

TABLE II. CONDUCTOR AND INSULATOR STRINGS PARAMETER VALUES

Parameter Value

Conductor weight per unit length [N/m] 18.22

Modulus of elasticity of the cable [GPa] 53.79

Transversal section of the cable [mm'] 601.56

Diameter of the cable [cm] 3.198

Length of the stTings [m] 4.19

Total weight of the strings [kg] 362.46

Finally, the conditions for calculus have to be settled, as well as the length of maximum permissible sag and the value of temperature where it happens. For substations, the maximum permissible sag is about 4% of span length, which happens at maximum temperature. In this case the study interval of temperatures is from -10 to 80°C, rising in gaps of 10 °C. TABLE III. shows the conditions for sag-tension calculation.

TABLE III. CONDITIONS FOR SAG-TENSION CALCULA nON

Parameter Value

Maximum temperature [0C] 80

Maximum sag [m] 2.192

Interval [0C] -10 to 80

The program automatically obtains the results shown in TABLE IV. , which shows the value of tension and sag for all calculated cases, the result that considers the effects of ice and wind, and the one that takes into account the effect of maximum wind, without ice.

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TABLE IV. SAG-TENSION CALCULA nON RESULTS

RESULTS

Conditions Tension [kg) Sag [m)

-10°C 1072 1.9489

O°C 1056 1.9772

10°C 1041 2.0050

20 °C 1026 2.0326

24°C 1021 2.0436

30 °C 1012 2.0599

40°C 999 2.0869

50 °C 986 2.1135

60°C 973 2.1400

70 °C 961 2.1661

80°C 949 2.1920

-10°C Ice I Wind 1259 2.0590

-10°C Max. Wind 3691 0.8200

The proposed program also draws the lying curves with the calculated values in automatic. Fig. 5 shows the generated curves.

� Tension (kg) -...- Sag(m) ,--,--------------------, 2.22

990

980

970

960

950

2.2 2.18

2.16

2.14 V> 2.1265

2.1 ]: 2.08

2.06

2.04

2.02

1.98

1.96

940 '---+--�-�-�-�-�-__.,..-�---' 1.94 ·10 10 20 30 '"

Tempe,,"ure (0C) 50

Fig. 5. Lying curves drawn by the program.

60 70

It is worthy to notice that the program mechanically performs the calculus for ice and wind loads at the minimum temperature because these conditions are likely to happen at this temperature.

It also computes the sag and tension at the annual average temperature owing to the fact that this might be the temperature site when the cable is installed.

V. CONCLUSIONS

A program for sag and tension calculation was developed which presents many advantages that might make the process of substations design faster, more reliable and accurate over the conventional methods. The main features of the program are summed up below:

• A friendly and intuitive interface enables any people to operate it, with no necessity of special training or specialization.

• Ability to compute systems conformed by more than one conductor per phase, which ensures that the results correspond to the physical actual conditions, making them more reliable.

• Easy results interpretation through automatic generation of a calculation report with tables and lying curves.

• Less execution time, that implies the entire process of sag and tension calculation can be done in just a few minutes.

These features make the program more attractive than the current technology focused to sag and tension calculation for power substations and might be successfully implemented in the substations design process worldwide.

REFERENCES

[I] H. M. Irvine, Cable Structures. The MIT Press, 1981, pp. 16 - 18.

[2] Sag-tension calculation methods for overhead lines. CIGRE B2-12 Brochure (Ref. No. 324), Jun. 2007, pp. 31-43.

[3] L. L. Grigsby, Electric Power Engineering Handbook, 2nd edition. FL: CRC Press Taylor & Francis Group, 2007.

[4] IEEE Guide for Bus Design in Air Insulated Substations, IEEE Std. 605-2008, May. 20 I O.

[5] Manual de Disefio de Obras Civiles, Diseilo por Viento. Mexico: Comision Federal de Electricidad-Instituto de Investigaciones Electricas, 2008.

[6] NORMA Oficial Mexicana Instalaciones ELectricas (utilizacion), NOM-00I-SEDE-2012, Nov. 2012.

[7] Cdlculo de Flechas y Tensiones en Lineas de Transmision, I er Edicion. Mexico: Comision Federal de Electricidad-Instituto de Investigaciones de la Industria Electrica, 1969.

[8] Design Guide for Rural Substations. USA: United States Department of Agriculture (RUS Bulletin I 724E-300), Jun. 200 I.

[9] Especificaciones de Disefio de Subestaciones, CPTT-GT-001-95, Revision 9, Ago. 2012.

[10] Electric conductors catalog, Viakon Condumex Manufacturing. [Online ].A vai lable:htlp:llwww.condumex.com.mxlES/energiaiPaginasl catalogo _ cables �ara _ transmision _y _ subtransmision.aspx?id _producto =14

[II] Insulator strings and fittings catalog, CECOHESA Manufacturing [Online]. Available: htlp:llwww.cecohesa.com.mxlbt4.html

[12] S. C. Chapra, Metodos Numericos para Ingenieros, 5a edicion. Mexico: Mc Graw Hill, 2007, pp. 164 - 166.

[13] IEEE Standard for Calculation of Bare Overhead Conductor Temperature and Ampacity Under Steady-State Conditions, IEEE Std. 738-1986, Aug. 1986.

[14] IEEE Guide for Recommended Electrical Clearances and Insulation Levels in Air-Insulated Electrical Power Substations, IEEE Std. 1427-2006, May. 2007.

[15] iEEE National Electrical Safety Code, IEEE Std. C2-2007, Oct. 2006.

[16] Normales Climatologicas, Servicio Meteorologico Nacional, [Online].

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