GB/T 36551-2018Calculation methods for properties of concentric lay overhead electrical stranded conductors (English PDF)

3.1 Symbols and units

The following symbols apply to this document.

A wire cross-sectional area in square millimeters (mm2)

AL aluminum wire cross-sectional area

AG steel wire cross-sectional area

B Width of the inner wall of the reel, in meters (m)

D wire diameter in meters (m)

D1, d2 reel side plate diameter and core diameter in meters (m)

E wire overall elastic modulus in megapascals (MPa)

EL aluminum wire elastic modulus

EG steel wire elastic modulus

f frequency in Hertz (Hz)

F wire rated tensile force in Newtons (N)

The pull of the FL aluminum wire in Newton (N)

The tensile force of the FLH aluminum alloy wire part in Newton (N)

Tension of the FG steel wire part

I wire current in amperes (A)

Relative stiffness of K1 steel wire to aluminum wire

Kc creep coefficient

Ke relative blackbody emission coefficient

Kg stratum coefficient

Kp wire forming factor

KS wire and shield gap factor

L wire maximum loading length in meters (m)

Nu Nusselt number

Pconv convection heat dissipation in watts per meter (W/m)

Pj power loss in watts per meter (W/m)

Prad radiates heat in watts per meter (W/m)

Psol sunshine heat absorption in watts per meter (W/m)

r wire radius in meters (m)

Re Reynolds number

Wire resistance at RT temperature T in ohms per meter (ohm/m)

s Steven Bozeman constant (5.67x10-8W.m-2.K-4)

Si solar radiation intensity in watts per square meter (W/m2)

t time in hours (h)

T temperature in Kelvin (K)

T1 ambient temperature in Kelvin (K)

T2 wire final equilibrium temperature in Kelvin (K)

v Wind speed in meters per second (m/s)

Winding volume on the Vdr reel, in cubic meters (m3)

Xc capacitive reactance (Mohm.km) in megaohms, with a calculation interval of 0.3m

Xi Inductive reactance (ohm/km) in ohms per kilometer, calculated radius 0.3m

alpha resistance temperature coefficient in Kelvin (K-1)

alphaL aluminum wire cross-section and overall cross-section ratio of the wire

alphaG steel wire cross-section and overall cross-section ratio of the wire

beta wire linear expansion coefficient in units of Kelvin (K-1)

betaL aluminum wire linear expansion coefficient

betaG steel wire linear expansion coefficient

deltax variable x increment

epsilon strain (unit elongation)

epsilonL aluminum wire elastic strain

epsilonC creep and permanent strain

epsilonG steel wire elastic strain

epsilonT thermal strain

Phi Creep calculation temperature (T) coefficient

gamma solar heat absorption coefficient

lambda The thermal conductivity of the air film in contact with the wire, in units of (W.m-1.K-1)

Time (t) coefficient of µ creep calculation

sigma pressure in MPa (MPa)

sigmaL The minimum standard value of tensile strength of aluminum or aluminum alloy wire before twisting, in megapascals (MPa)

sum1% The stress at 1% elongation of the steel wire (aluminum-clad steel wire) in the core, in megapascals (MPa)

Minimum standard value of tensile strength of sigmaG pre-twisted steel (or aluminum clad steel wire) in megapascals (MPa)

应力 Creep calculation of stress (sigma) coefficient

3.2 Abbreviations

The following abbreviations apply to this document.

CCC current carrying capacity (A) (currentcarryingcapacity)

Geometric mean radius (m) of the GMR wire (geometricmeanradiusoftheconductor)

4.1 General

The wire current carrying capacity (CCC) is the maximum steady-state current when the wire temperature rises under certain environmental conditions.

The current carrying capacity is related to the type of wire, resistance, maximum allowable temperature rise, environmental conditions, and the like.

4.2 Heat balance equation

According to the principle of heat balance in thermodynamics, when the heat, heat absorption and heat dissipation of the wire finally reach equilibrium, it can be expressed by the formula (1).

Pj Psol=Prad Pconv (1)

In the formula.

Pj --- the heat generated by the Joule effect;

Psol --- sunshine heat absorption on the surface of the wire;

Prad --- radiant heat dissipation of the wire;

Pconv---convection heat dissipation of the wire.

Note. Magnetic heat gain, corona heat increase or evaporative heat dissipation is not considered in equation (1).

4.3 Calculation method

For the calculation of each part of the formula (1), under the steady state conditions, the current commonly used calculation methods respectively obtain the bias between the current-carrying values.

The difference is about 10%.

4.4 Joule effect

The power loss Pj(W/m) can be calculated by the Joule effect according to equation (2).

Pj=RTI2 (2)

In the formula.

RT --- wire resistance at temperature T in ohms per meter (ohm/m);

I --- Wire current in amps (A).

4.5 Rizhao heat absorption

Sunshine heat absorption, Psol (W/m), can be calculated according to formula (3).

Psol=gammaDSi (3)

In the formula.

gamma --- solar radiation endothermic coefficient;

D --- wire diameter in meters (m);

Si---sunshine intensity in watts per square meter (W/m2).

4.6 Radiation cooling

Radiation heat dissipation, Prad (W/m), can be calculated according to formula (4).

Prad=SpiDKe(T42-T41) (4)

In the formula.

S --- Steven Bozeman constant (5.67 x 10-8W . m-2 . K-4);

D --- wire diameter in meters (m);

Ke---relative coefficient of blackbody;

T2---the final equilibrium temperature of the wire in Kelvin (K);

T1--- Ambient temperature in Kelvin (K).

4.7 convection cooling

Only forced convection heat dissipation is considered here, Pconv(W/m), which can be calculated according to equation (5).

Pconv=lambdaNu(T2-T1)pi (5)

In the formula.

lambda --- the thermal conductivity of the air film in contact with the wire (assuming it is constant and equal to 0.02585 W.m -1 . K -1);

Nu --- Nusselt number, which can be derived from equation (6).

Nu=0.65Re0.2 0.23Re0.61 (6)

In the formula.

Re --- Reynolds number, can be derived from equation (7).

Re=1.644x109vD T1 0.5T2-T1( )[ ]{ } -1.78 (7)

In the formula.

v --- wind speed, in meters per second (m/s);

D --- wire diameter in meters (m);

T1---ambient temperature in Kelvin (K);

T2---The final equilibrium temperature of the wire in Kelvin (K).

4.8 Current carrying capacity (CCC) calculation method

It can be seen from equation (1) that the steady current can calculate the current carrying capacity from equation (8).

Imax= Prad Pconv-Psol( )/RT[ ] 1/2 (8)

In the formula.

RT—The wire resistance at temperature T in ohms per meter (ohm/m).

Rhosol, Prad, and Pconv can be calculated by the formula (3), the formula (4), and the formula (5).

4.9 Determine the maximum allowable temperature of the aluminum wire

Determining the maximum allowable temperature of the aluminum wire requires consideration of the economic optimization of the line loss, or the maximum allowable tensile strength loss of the aluminum wire. Incumbent

In any case, the maximum allowable temperature should be confirmed and the appropriate margin should be retained.

4.10 Calculated value of current carrying capacity

Through the formula (8), the current carrying capacity of any wire under certain conditions can be calculated.

Appendix C gives the calculated current carrying capacity for some wire sizes under typical conditions recommended in GB/T 1179-2017. These bars

Changes in the components (especially wind speed and ambient temperature) will result in a change in the current carrying capacity, which needs to be recalculated according to equation (8).

---The speed of the transverse wind (90° on the line), v=1m/s;

---Sunlight intensity, Si=900W/m2;

--- heat absorption coefficient, gamma = 0.5;

--- Blackbody radiation coefficient, Ke = 0.6;

---The final equilibrium temperature of the wire, T2 = 353K and 373K (corresponding to 80 ° C and 100 ° C);

--- Ambient temperature, T1 = 293K (corresponding to 20 ° C);

--- The frequency is 50Hz (the corresponding values at 60Hz are very close, the difference is within 2%).

Appendix D gives the calculated current carrying capacity of some wire sizes under typical environmental conditions selected by domestic power engineering. These conditions

Changes (especially wind speed and ambient temperature) will result in a change in the current carrying capacity, which needs to be recalculated according to equation (8).

---The speed of the transverse wind (90° on the line), v=0.5m/s;

---Sunlight intensity, Si=1000W/m2;

--- heat absorption coefficient, gamma = 0.9;

--- Blackbody radiation coefficient, Ke = 0.9;

---The final equilibrium temperature of the wire, T2 = 343K, 353K and 363K [corresponding to 70 ° C, 80 ° C and 90 ° C (or 150 ° C)];

--- Ambient temperature, T1 = 308K (corresponding to 35 ° C);

--- The frequency is 50Hz.

5.1 General

The resistance of a wire is a function of wire material, length, and cross-sectional area and is affected by wire stranding. In order to calculate more accurately,

The resistance of the wire also depends on the change in current and frequency. Wires with a resistance greater than 0.02 ohm/km are given in GB/T 1179-2017.

The nominal value of the DC resistance at 20 °C. DC resistance at other temperatures can be calculated by DC resistance and temperature coefficient of resistance at 20 °C

inferred. Due to the skin effect, the current density is unevenly distributed on the wires, which increases the surface resistance of the wires. AC at a given temperature T

The resistance can be calculated from the DC resistance and the temperature T on the basis of considering the skin effect.

Two other important influencing factors caused by AC resistance are capacitive reactance and inductive reactance, which can be divided into two parts. the first part is at 0.30m.

The magnetic flux in the radius is caused; the second part is generated from the radius of 0.30 m to the equivalent circuit of the wire. Appendix E gives the first part

Inductive and capacitive values.

5.2 AC resistance

The AC resistance is calculated from the DC resistance at the same temperature. The DC resistance of the wire rises with increasing temperature and is linear

Department, can be calculated by equation (9).

RT2=RT1 1 alphaT2-T1( )[ ] (9)

In the formula.

RT2---DC resistance at temperature T2;

RT1---DC resistance at temperature T1;

alpha --- Temperature coefficient of resistance at temperature T1.

GB/T 1179-2017 and IEC 61089.1991 give the DC resistance of the wire corresponding to RT1 at 20 °C. The materials involved are

The temperature coefficient of resistance at 20 ° C is as follows.

---L type hard aluminum wire. alpha = 0.00403K-1;

---L1 type hard aluminum wire. alpha = 0.00407K-1;

---L2 type hard aluminum wire. alpha = 0.00410K-1;

---L3 type hard aluminum wire. alpha = 0.00413K-1;

---LHA1, LHA2 type aluminum alloy wire. alpha = 0.00360K-1;

---LHA3 type aluminum alloy wire. alpha = 0.00390K-1;

---LHA4 type aluminum alloy wire. alpha = 0.00380K-1;

---NRLH1 type heat resistant aluminum alloy wire. alpha = 0.00400K-1;

---NRLH2 type heat resistant aluminum alloy wire. alpha = 0.00360K-1;

--- LB various types of aluminum-clad steel wire resistance temperature coefficient is given in Appendix A of GB/T 17937-2009.

According to the temperature coefficient of resistance at 20 ° C, the corresponding DC resistance of the wire at each final equilibrium temperature can be calculated.

Due to the "skin effect", the AC resistance of the conductor is higher than the DC resistance. The reason for this phenomenon is that the inside of the conductor will pass more

The flux linkage causes the inductance inside the conductor to be higher than the inductance at the outer surface. Due to the voltage drop across any length of the conductor over the entire cross section

They must be equal, thus concentrating the current on the outer surface of the conductor, increasing the effective resistance.

The method used to calculate the AC-DC resistance ratio is quite correct. Appendix E gives the AC resistance value calculated based on the typical method.

For composite wires (Lx/Gxy wires) containing steel cores, the magnetomotive force is unbalanced due to the opposite stranding direction of adjacent layers, in the steel core

The magnetic flux changes with current, causing the AC-DC resistance ratio to change with current, especially when the number of aluminum lines is odd.

Although the magnetic effect on a single layer of Lx/Gxy wire may be significant, the magnetic effect on the 3-layer wire is not very noticeable, but does not affect

Calculation of AC resistance values for these types of wires.

5.3 Inductive reactance

The inductive reactance of the wire is calculated from the flux generated by the current flowing through the wire. To simplify the calculation, according to the commonly used 0.3m radius

Division, the resistance can be divided into two parts.

a) produced by a magnetic flux in the radius of 0.3 m (accurate value is 0.3048 m);

b) Generated by a magnetic flux from a radius of 0.3 m to the equivalent loop of the conductor.

Where part a) is the geometric coefficient (a function of the wire size) and part b) depends only on the phase-to-phase distance between the conductor and the transmission line.

Part a) is calculated as follows, and part b) can be found in the ready-made technical literature.

To calculate the inductive reactance of a wire within a radius of 0.3 m, the geometric mean radius (GMR) of the wire must be calculated first, as in equation (10).

GMR=0.5DKg (10)

In the formula.

GMR --- the average geometric radius of the wire in meters (m);

D --- wire outer diameter in meters (m);

Kg --- Strand coefficient (ratio of radius).

The stranding factor "Kg" depends only on the type and geometry of the conductor (number of conductor layers and number of single wires). Table 1 shows the different twisted shapes

The value of "Kg" is calculated.

Table 1 Twist layer coefficient "Kg" value for inductive reactance calculation

Aluminum steel

Number of layers in the root layer

Strand coefficient

Kg

Aluminum steel

Number of layers in the root layer

Strand coefficient

Kg

6 1 1 - a 45 3 7 1 0.7939

18 2 1 - 0.7765 54 3 7 1 0.8099

7 1 - - 0.7256 72 4 7 1 0.7889

22 2 7 1 0.7949 84 4 7 1 0.8005

26 2 7 1 0.8116 91 5 - - 0.7743

19 2 - - 0.7577 54 3 19 2 0.8099

37 3 - - 0.7678 72 4 19 2 0.7889

61 4 - - 0.7722 84 4 19 2 0.8005

a If there is a steel core, this value varies with the wire size. For individual wires, Kg can be calculated from the inductive reactance. When the wire structure is twisted by 6/1, its Kg is flat.

The average is 0.5090.

The inductive reactance in the radius of 0.3 m can be calculated by equation (11).

Xi=4x10-4pifln

0.3

GMR=0.1736f

/60( )lg

0.3

GMR

(11)

In the formula.

Xi --- Inductance with a radius of 0.3m, in ohms per kilometer (ohm/km);

f --- frequency in Hertz (Hz);

GMR—The geometric mean radius of the wire in meters (m).

For steel-cored aluminum stranded wires (LX/GXY), the magnetic flux on the steel core depends on the current and inductance. For the inductive reactance, there are three layers and

The wires of the upper aluminum strand or the even stranded layer produce negligible inductive reactance. Influence on the inductive reactance of a single stranded LX/GXY wire

It cannot be ignored, and Xi can be determined after the whole wire sample test.

For new conductors, such as test results for non-wired samples, Xi of a single stranded conductor can be passed with ordinary steel core aluminum stranded wire (LX/

GXY) is estimated by comparing empirical values at 25 °C. These values are not less than 3% accurate.

5.4 capacitive reactance

The capacitive reactance can also be divided into two parts.

a) capacitive reactance within a radius of 0.3 m;

b) From 0.3m to the capacitive reactance between the equivalent circuits of the conductor.

Among them, part a) is calculated as follows, and part b) can be found in the ready-made technical literature. Regarding capacitive reactance, it has nothing to do with current and steel core

Union, so the calculation is very simple, only depends on the frequency and wire diameter, can be calculated by equation (12).

Xc=(9/pif)ln2x0.3/D( )=0.109960/f( )lg2x0.3/D( ) (12)

In the formula.

Xc---the capacitive reactance in the range of 0.3m radius, in units of megaohms (Mohm.km);

f --- frequency in Hertz (Hz);

D --- wire diameter in meters (m).

5.5 Feature Table

Appendix E shows the calculated AC resistance at 50 Hz, 20 °C, 50 °C, 80 °C and 100 °C.

GB/T 1179-2017 gives the specific parameters such as the diameter and cross-sectional area of the wire.

6.1 General

Without considering the plastic elongation of the wire, the elongation of the wire is caused by the following factors.

---elastic elongation;

---thermal elongation;

--- creep;

--- elongation caused by single line slack during twisting;

--- Radial tightening and local compression of the strands of the wire strands.

Note. The elongations referred to in this standard are generalized and refer to both positive and negative elongation. When the wire is subjected to tension, the stress distribution on the single line is the same as above.

The various types of elongation in the column are closely related. This chapter discusses the various types of elongation and proposes a suitable generalized model.

6.2 Thermal elongation

Temperature changes affect the length of the wire. The unit elongation (epsilonT) of a thermal strain or a single aluminum wire can be expressed by the formula (13).

epsilonT=betadeltaT (13)

In the formula.

The coefficient of linear expansion of beta --- wire, in units of Kelvin (K-1), betaL is the coefficient of linear expansion of the aluminum part, and betaG is the linear expansion of the steel part.

Expansion coefficient

deltaT---Increment of temperature T.

Linear expansion coefficients of aluminum and aluminum alloy conductors (models L, LHA2, LHA1, L/LHA2, L/LHA1, NRLH1, NRLH2, etc.)

The betaL value is 23x10-6K-1. The linear expansion coefficient betaG of the steel wire is 11.5x10-6K-1. Appendix to GB/T 17937-2009

A gives the coefficient of linear expansion of various aluminum clad steel wires.

Since the stress and elongation in a single wire are closely related, the thermal elongation of the combined wire (LX/GXY) is more complicated. Guide used in overhead power lines

The wire is subjected to a sustained tension, and in most cases, the aluminum wire and the steel wire share the total tension according to their relative stiffness. When aluminum wire and steel

When both wires are subjected to tensile stress, the thermal strain and tensile strain generated have the following relationship. Among them, the formula (14) is applicable to the steel wire part,

The formula (15) is applied to the aluminum wire portion, and the formula (16) is applied to the entire wire.

deltaFG/AGEG=betaGdeltaT (14)

deltaFL/ALEL=betaLdeltaT (15)

deltaF/AE=betadeltaT (16)

In the formula.

deltaFG---the stress increment of the steel wire part, in megapascals (MPa);

AG --- the cross-sectional area of the steel wire, in square millimeters (mm2);

The linear expansion coefficient of betaG--steel (or aluminum-clad steel), in units of Kelvin (K-1);

deltaT --- the increment of temperature T in Kelvin (K);

deltaFL---the stress increment of the aluminum wire portion, in megapascals (MPa);

AL --- the cross-sectional area of the aluminum wire in square millimeters (mm2);

The coefficient of linear expansion of the betaL--aluminum portion in units of Kelvin (K-1);

deltaF --- the stress increment of the wire in mega...