CN102129009B - Method for measuring positive sequence parameters of ultra-high voltage transmission line based on double end measuring information - Google Patents

Abstract

The invention relates to the technical field of measuring parameters of a transmission line of a power system, in particular to a method for measuring positive sequence parameters of an ultra-high voltage transmission line based on double end measuring information. The method comprises: measuring positive sequence impedance and positive sequence capacitance of the transmission line; when measuring the positive sequence impedance of the transmission line, cutting off the to-be-measured transmission line, performing three-phase short connection to the tail end of the transmission line, adding a three-phase voltage on the front end of the transmission line; when measuring the positive sequence capacitance of the transmission line, cutting off the to-be-measured transmission line, performing three-phase opening to the tail end of the transmission line, adding the three-phase voltage on the front end of the transmission line; using a global satellite positioning system technology to simultaneously measure the three-phase voltage on two ends of the transmission line and the three-phase current on two ends of the transmission line, and synchronously sampling the three-phase voltage and three-phase current. The method in the invention solves the influence of the distributed capacitance on the transmission line to the positive sequence parameters measurement so as to greatly increase the precision of the positive sequence parameters measuring result of the transmission line.

Description

UHV transmission line measurement method for positive sequence parameter based on double-end measurement information

Technical field

The present invention relates to the power system transmission line parameter field of measuring technique, relate in particular to a kind of UHV transmission line measurement method for positive sequence parameter based on double-end measurement information.

Background technology

Transmission line of electricity is the carrier that electric power is carried, and is one of chief component of electric system, and electric system is played an important role.The power frequency parameter of transmission line of electricity mainly comprises mutual inductance between positive sequence impedance, positive sequence electric capacity, zero sequence impedance, zero sequence electric capacity and the many times mutual inductance circuits etc.; these parameters are used for electric system carries out trend calculating, calculation of short-circuit current, relay protection setting calculating and selects power system operation mode, and its accuracy is directly connected to the accuracy of these result of calculations.The parameter of obtaining exactly transmission line of electricity has important meaning for electric system, especially along with the development of China's electric system, the continuous expansion of electrical network, improving constantly of Automation of Electric Systems degree, more and more higher to the accuracy requirement of transmission line parameter.

The calculating of line parameter circuit value is comparatively complicated, is subjected to simultaneously the impact of a lot of uncertain factors, comprises the factors such as geometric configuration, electric current, environment temperature, wind speed, soil resistivity, lightning conducter erection mode and line route of circuit.The circuit of long distance powedr transmission is sagging, the random nature of the kelvin effect of alive circuit and heating, geological condition etc. bring difficulty all can for the accurate Calculation line parameter circuit value.Usually known transmission line parameter is to measure at the circuit initial stage of building up, these parameters after putting into operation since the impact of weather, temperature, environment and the factor such as geographical can more or less change.Therefore, can't only rely on the theoretical exact value of obtaining these parameters of calculating, line parameter circuit value needs periodic measurement.

Current power transmission line parameter circuit value measuring method has had deep research, and has developed corresponding measuring system device, puts into operation.Yet along with the development of electric system, the increase of transmission line length, the rising of electric pressure is so that the distributed capacitance of the transmission line of electricity of ignoring in original measuring system must be considered.

Simultaneously, UHV transmission line adopts the error of the centralized equivalence of transmission line parameter significantly to increase because electric pressure is high especially, transmission distance is long especially, at this moment must consider the impact of transmission line of electricity distributed capacitance.

Summary of the invention

Technical matters for above-mentioned existence, the purpose of this invention is to provide a kind of UHV transmission line measurement method for positive sequence parameter based on double-end measurement information, to overcome existing method large drawback of measuring error when measuring the positive order parameter of UHV (ultra-high voltage) and UHV transmission line, the transmission line of electricity positive sequence parameter measurement new method that proposes has realized the Measurement accuracy to the positive order parameter of transmission line of electricity.

For achieving the above object, the present invention adopts following technical scheme:

1. pressurization after transmission line of electricity to be measured being had a power failure obtains the positive sequence voltage and the forward-order current that calculate for measuring;

2. utilize global satellite positioning, measure simultaneously three-phase voltage and the three-phase current of transmission line of electricity head and end, this transmission line of electricity three-phase voltage and three-phase current are carried out synchronized sampling;

3. adopt the Fourier filtering algorithm to obtain three-phase fundamental voltage and the three-phase fundamental current of transmission line of electricity head and end;

4. to carrying out positive-sequence component, negative sequence component, the zero-sequence component that the order decomposition obtains the head and end fundamental voltage three-phase fundamental voltage of head and end;

5. to carrying out positive-sequence component, negative sequence component, the zero-sequence component that the order decomposition obtains the head and end fundamental current three-phase fundamental current of head and end;

6. adopt following formula to calculate the positive sequence impedance that obtains this transmission line of electricity:

Wherein, r ₁Be the positive sequence resistance of transmission line of electricity, unit is ohm, x ₁Be the forward-sequence reactance of transmission line of electricity, unit is ohm;

Be the positive sequence fundamental voltage of transmission line of electricity head end, unit is volt; With

Be the positive sequence fundamental current of transmission line of electricity head and end, unit is ampere; K ₁Be the correction factor relevant with transmission line length L, K ₁=1+L/50 * k ₁, k ₁Be corrected parameter;

7. adopt following formula to calculate the positive sequence admittance that obtains this transmission line of electricity:

g ₁Lead for the positive sequence electricity of transmission line of electricity, unit is Siemens, b ₁Be the positive sequence susceptance of transmission line of electricity, unit is Siemens;

With

Be the positive sequence fundamental voltage of transmission line of electricity head and end, unit is volt;

The positive sequence fundamental current of transmission line of electricity head end, unit are ampere; K ₂Be the correction factor relevant with transmission line length L, K ₂=1+L/50 * k ₂, k ₂Be corrected parameter.

Described step 1. in, when measuring the positive sequence impedance of transmission line of electricity, transmission line of electricity to be measured is had a power failure, with the terminal three-phase short circuit of transmission line of electricity, add three-phase voltage at the transmission line of electricity head end;

Described step 1. in, when the positive sequence admittance of measuring transmission line of electricity, transmission line of electricity to be measured is had a power failure, with the terminal three-phase open circuit of transmission line of electricity, add three-phase voltage at the transmission line of electricity head end.

Described step utilizes the time service gain-of-function error of GPS less than the time reference of 1 microsecond in 2., lower synchronously at gps time, after the transmission line of electricity head end added three-phase voltage, measuring system gathered the three-phase voltage of transmission line of electricity first and last end and the three-phase current of transmission line of electricity first and last end simultaneously.

Described step 6. in, if adopt the alien frequencies power supply to measure, then the reactance x1 that measures is revised, the reactance when obtaining power frequency, adopt following formula to revise:

Wherein, middle f _{Alien frequencies}Be the frequency of alien frequencies power supply, x _{1 power frequency}Forward-sequence reactance during for power frequency.

Described step 7. in, transmission line of electricity positive sequence electricity is led g ₁Very little, ignore, then positive sequence electric capacity c ₁Computing formula be:

Wherein, middle f is the frequency of power frequency supply, and the imaginary part component of phasor is got in Im () expression.

If adopt the alien frequencies power supply to measure, then to by

The electric capacity c that formula measures ₁Revise, obtain the positive sequence capacitance parameter under the power frequency, adopt following correction formula:

Wherein, f _{Alien frequencies}Be the frequency of alien frequencies power supply, c _{1 power frequency}Positive sequence electric capacity during for power frequency.

Described step 6. in, corrected parameter k ₁As follows with the value relation of transmission line length L, wherein the unit of L is kilometer:

As 0＜L≤100, k ₁=0.000; As 100＜L≤200,0.000＜k ₁≤ 0.001; As 200＜L≤400,0.001＜k ₁≤ 0.002; As 400＜L≤600,0.002＜k ₁≤ 0.003; As 600＜L≤800,0.003＜k ₁≤ 0.004; As 800＜L≤900,0.004＜k ₁≤ 0.005; As 900＜L≤1000,0.005＜k ₁≤ 0.006; As 1000＜L≤1100,0.006＜k ₁≤ 0.007; As 1100＜L≤1200,0.007＜k ₁≤ 0.0075; As 1200＜L≤1300,0.0075＜k ₁≤ 0.0085; As 1300＜L≤1400,0.0085＜k ₁≤ 0.0095; As 1400＜L≤1500,0.0095＜k ₁≤ 0.0105; As 1500＜L≤1600,0.0105＜k ₁≤ 0.0115.

Described step 7. in, corrected parameter k ₂With as follows with the value relation of transmission line length L, wherein the unit of L is kilometer:

As 0＜L≤50, k ₂=0.0000; As 50＜L≤100,0.0000＜k ₂≤ 0.0003; As 100＜L≤150,0.0003＜k ₂≤ 0.0005; As 150＜L≤200,0.0005＜k ₂≤ 0.0008; As 200＜L≤250,0.0008＜k ₂≤ 0.0011; As 250＜L≤300,0.0011＜k ₂≤ 0.0014; As 300＜L≤350,0.0014＜k ₂≤ 0.0017; As 350＜L≤400,0.0017＜k ₂≤ 0.0020; As 400＜L≤450,0.0020＜k ₂≤ 0.0023; As 450＜L≤500,0.0023＜k ₂≤ 0.0026; As 500＜L≤550,0.0026＜k ₂≤ 0.0029; As 550＜L≤600,0.0029＜k ₂≤ 0.0032; As 600＜L≤650,0.0032＜k ₂≤ 0.0035; As 650＜L≤700,0.0035＜k ₂≤ 0.0038; As 700＜L≤750,0.0038＜k ₂≤ 0.0041; As 750＜L≤800,0.0041＜k ₂≤ 0.0044; As 800＜L≤850,0.0044＜k ₂≤ 0.0048; As 850＜L≤900,0.0048＜k ₂≤ 0.0051; As 900＜L≤950,0.0051＜k ₂≤ 0.0055; As 950＜L≤1000,0.0055＜k ₂≤ 0.0059; As 1000＜L≤1050,0.0059＜k ₂≤ 0.0063; As 1050＜L≤1100,0.0063＜k ₂≤ 0.0067; As 1100＜L≤1150,0.0067＜k ₂≤ 0.0071; As 1150＜L≤1200,0.0071＜k ₂≤ 0.0075; As 1200＜L≤1250,0.0075＜k ₂≤ 0.0079; As 1250＜L≤1300,0.0079＜k ₂≤ 0.0083; As 1300＜L≤1350,0.0083＜k ₂≤ 0.0087; As 1350＜L≤1400,0.0087＜k ₂≤ 0.0092; As 1400＜L≤1450,0.0092＜k ₂≤ 0.0097; As 1450＜L≤1500,0.0097＜k ₂≤ 0.0102; As 1500＜L≤1550,0.0102＜k ₂≤ 0.0107; As 1550＜L≤1600,0.0107＜k ₂≤ 0.0112.

The present invention has the following advantages and good effect:

1) the present invention need to gather three-phase voltage and the three-phase current of transmission line of electricity head and end simultaneously, has taken into account the impact of the distributed capacitance on the transmission line of electricity, thereby is particularly suitable for the measurement of the positive order parameter of extra-high voltage long distance transmission line;

2) the present invention utilizes the GPS technology to solve the simultaneity problem of strange land signal measurement, not only is fit to the measurement of one the positive order parameter of transmission line of electricity, especially is fit to measure the positive order parameter of UHV transmission line;

3) the present invention not only is fit to adopt power frequency supply to measure, and also is fit to adopt the alien frequencies power supply to measure;

4) the present invention is by measuring positive sequence voltage and the forward-order current at transmission line of electricity two ends, again the mean value of circuit two ends positive sequence voltage phasor mean value and forward-order current phasor is revised, solve the distributed capacitance on the transmission line of electricity and aligned the impact that order parameter is measured, thereby greatly improved the precision of transmission line of electricity positive sequence parameter measurements.

Description of drawings

Fig. 1 is that the transmission line of electricity positive sequence impedance is measured connection diagram among the present invention.

Fig. 2 is transmission line of electricity positive sequence capacitance measurement connection diagram among the present invention.

Embodiment

The invention will be further described by reference to the accompanying drawings with specific embodiment for the below:

UHV transmission line measurement method for positive sequence parameter based on double-end measurement information provided by the invention, adopt following steps:

Step 1: tested transmission line of electricity is had a power failure.

Step 2: when measuring the positive sequence impedance of transmission line of electricity, the terminal three-phase short circuit with transmission line of electricity applies three-phase main-frequency voltage at the transmission line of electricity head end, measures wiring as shown in Figure 1.PT is voltage transformer (VT) among the figure, and CT is current transformer.Under the Global Positioning System (GPS) time synchronized, be arranged in the measuring system A of transmission line of electricity head and end and three-phase voltage that measuring system B measures the transmission line of electricity head end simultaneously and the three-phase current of transmission line of electricity head and end.

When measuring the positive sequence electric capacity of transmission line of electricity, the terminal three-phase open circuit with transmission line of electricity applies three-phase voltage at the transmission line of electricity head end, measures wiring as shown in Figure 2.PT is voltage transformer (VT) among the figure, and CT is current transformer.Under the Global Positioning System (GPS) time synchronized, be arranged in the measuring system A of transmission line of electricity head and end and three-phase voltage that measuring system B measures the transmission line of electricity head and end simultaneously and the three-phase current of transmission line of electricity head end.

Step 3: three-phase voltage and the three-phase current of the transmission line of electricity that measuring system A and B are gathered, adopt first the Fourier filtering algorithm to obtain the three-phase fundamental voltage of transmission line of electricity head and end

With the three-phase fundamental current

Recycling formula (1) and (2) carries out positive-sequence component, negative sequence component and the zero-sequence component that the order decomposition obtains the head and end fundamental voltage to head and end fundamental voltage and head and end fundamental current

Utilize formula (3) and (4) to obtain positive-sequence component, negative sequence component and the zero-sequence component of transmission line of electricity head and end fundamental current

(1)

(1) in formula, (2) formula, (3) formula and (4) formula, α=e ^{J120 °}

Step 4: with the positive sequence voltage of transmission line of electricity head end And the forward-order current of transmission line of electricity head and end

With

Substitution

(2) formula can be obtained the positive sequence impedance parameter z of transmission line of electricity ₁

K ₁Be the correction factor relevant with transmission line length L, K ₁=1+L/50 * k ₁, k ₁Value shown in following table table 1.

Table 1 k ₁Value

Transmission line length L (kilometer)	k 1
		0＜L≤100	k 1＝0.000
100＜L≤200	0.000＜k 1≤0.001
		200＜L≤400	0.001＜k 1≤0.002
400＜L≤600	0.002＜k 1≤0.003
		600＜L≤800	0.003＜k 1≤0.004
800＜L≤900	0.004＜k 1≤0.005
		900＜L≤1000	0.005＜k 1≤0.006
1000＜L≤1100	0.006＜k 1≤0.007
		1100＜L≤1200	0.007＜k 1≤0.0075
1200＜L≤1300	0.0075＜k 1≤0.0085
		1300＜L≤1400	0.0085＜k 1≤0.0095
1400＜L≤1500	0.0095＜k 1≤0.0105
		1500＜L≤1600	0.0105＜k 1≤0.0115

If adopt the alien frequencies power supply to measure, then need the reactance x that measures by (5) formula ₁Revise, obtain the forward-sequence reactance under the power frequency.Correction formula is:

Positive sequence voltage with the transmission line of electricity head and end With And the forward-order current of transmission line of electricity head end

Substitution (7) formula can be obtained the positive sequence admittance parameter g of transmission line of electricity ₁+ jb ₁

K ₂Be the correction factor relevant with transmission line length L, K ₂=1+L/50 * k ₂, k ₂Value shown in following table table 2:

Table 2 k ₂Value

Transmission line length L (kilometer)	k 2
		0＜L≤50	k 2＝0.0000
50＜L≤100	0.0000＜k 2≤0.0003
		100＜L≤150	0.0003＜k 2≤0.0005
150＜L≤200	0.0005＜k 2≤0.0008
		200＜L≤250	0.0008＜k 2≤0.0011
250＜L≤300	0.0011＜k 2≤0.0014
		300＜L≤350	0.0014＜k 2≤0.0017
350＜L≤400	0.0017＜k 2≤0.0020
		400＜L≤450	0.0020＜k 2≤0.0023
450＜L≤500	0.0023＜k 2≤0.0026
		500＜L≤550	0.0026＜k 2≤0.0029
550＜L≤600	0.0029＜k 2≤0.0032
		600＜L≤650	0.0032＜k 2≤0.0035
650＜L≤700	0.0035＜k 2≤0.0038
		700＜L≤750	0.0038＜k 2≤0.0041
750＜L≤800	0.0041＜k 2≤0.0044
		800＜L≤850	0.0044＜k 2≤0.0048
850＜L≤900	0.0048＜k 2≤0.0051

900＜L≤950	0.0051＜k 2≤0.0055
		950＜L≤1000	0.0055＜k 2≤0.0059
1000＜L≤1050	0.0059＜k 2≤0.0063
		1050＜L≤1100	0.0063＜k 2≤0.0067
1100＜L≤1150	0.0067＜k 2≤0.0071
		1150＜L≤1200	0.0071＜k 2≤0.0075
1200＜L≤1250	0.0075＜k 2≤0.0079
		1250＜L≤1300	0.0079＜k 2≤0.0083
1300＜L≤1350	0.0083＜k 2≤0.0087
		1350＜L≤1400	0.0087＜k 2≤0.0092
1400＜L≤1450	0.0092＜k 2≤0.0097
		1450＜L≤1500	0.0097＜k 2≤0.0102
1500＜L≤1550	0.0102＜k 2≤0.0107
		1550＜L≤1600	0.0107＜k 2≤0.0112

Usually, transmission line of electricity positive sequence electricity is led g ₁Very little, can ignore, then positive sequence electric capacity c ₁Computing formula be:

(8) f is work frequency in the formula, and the imaginary part component of phasor is got in Im () expression.

If adopt the alien frequencies power supply to measure, then the frequency f in (8) formula is the alien frequencies frequency, need to be to the electric capacity c that is measured by (8) formula ₁Revise, obtain the positive sequence electric capacity under the power frequency.Correction formula is:

(9) f in the formula _{Alien frequencies}Be the frequency of alien frequencies power supply, c _{1 power frequency}Positive sequence electric capacity during for power frequency.

Above embodiment is only for explanation the present invention, but not limitation of the present invention, person skilled in the relevant technique; in the situation that does not break away from the spirit and scope of the present invention; can also make various conversion or modification, so all technical schemes that are equal to, all fall into protection scope of the present invention.

Claims (8)

1. the UHV transmission line measurement method for positive sequence parameter based on double-end measurement information is characterized in that, may further comprise the steps:

1. pressurization after transmission line of electricity to be measured being had a power failure obtains the positive sequence voltage and the forward-order current that calculate for measuring;

2. utilize global satellite positioning, measure simultaneously three-phase voltage and the three-phase current of transmission line of electricity head and end, this transmission line of electricity three-phase voltage and three-phase current are carried out synchronized sampling;

3. adopt the Fourier filtering algorithm to obtain three-phase fundamental voltage and the three-phase fundamental current of transmission line of electricity head and end;

4. to carrying out positive-sequence component, negative sequence component, the zero-sequence component that the order decomposition obtains the head and end fundamental voltage three-phase fundamental voltage of head and end;

5. to carrying out positive-sequence component, negative sequence component, the zero-sequence component that the order decomposition obtains the head and end fundamental current three-phase fundamental current of head and end;

6. adopt following formula to calculate the positive sequence impedance that obtains this transmission line of electricity:

$z_1=r_1+{\mathrm{jx}}_1=\frac{2\×{\stackrel{\·}{U}}_{p1}}{({\stackrel{\·}{I}}_{p1}+{\stackrel{\·}{I}}_{q1})\×K_1}$

Wherein, r ₁Be the positive sequence resistance of transmission line of electricity, unit is ohm, x ₁Be the forward-sequence reactance of transmission line of electricity, unit is ohm;

Be the positive sequence fundamental voltage of transmission line of electricity head end, unit is volt;

With

Be the positive sequence fundamental current of transmission line of electricity head and end, unit is ampere; K ₁Be the correction factor relevant with transmission line length L, K ₁=1+L/50 * k ₁, k ₁Be corrected parameter;

7. adopt following formula to calculate the positive sequence admittance that obtains this transmission line of electricity:

$g_1+{\mathrm{jb}}_1=\frac{2\×{\stackrel{\·}{I}}_{p1}}{({\stackrel{\·}{U}}_{p1}+{\stackrel{\·}{U}}_{q1})\×K_2}$

g ₁Lead for the positive sequence electricity of transmission line of electricity, unit is Siemens, b ₁Be the positive sequence susceptance of transmission line of electricity, unit is Siemens; With

Be the positive sequence fundamental voltage of transmission line of electricity head and end, unit is volt;

The positive sequence fundamental current of transmission line of electricity head end, unit are ampere; K ₂Be the correction factor relevant with transmission line length L, K ₂=1+L/50 * k ₂, k ₂Be corrected parameter.

2. the UHV transmission line measurement method for positive sequence parameter based on double-end measurement information according to claim 1 is characterized in that:

Described step 1. in, when measuring the positive sequence impedance of transmission line of electricity, transmission line of electricity to be measured is had a power failure, with the terminal three-phase short circuit of transmission line of electricity, add three-phase voltage at the transmission line of electricity head end;

Described step 1. in, when the positive sequence admittance of measuring transmission line of electricity, transmission line of electricity to be measured is had a power failure, with the terminal three-phase open circuit of transmission line of electricity, add three-phase voltage at the transmission line of electricity head end.

3. the UHV transmission line measurement method for positive sequence parameter based on double-end measurement information according to claim 1 is characterized in that:

Described step utilizes the time service gain-of-function error of GPS less than the time reference of 1 microsecond in 2., lower synchronously at gps time, after the transmission line of electricity head end added three-phase voltage, measuring system gathered the three-phase voltage of transmission line of electricity first and last end and the three-phase current of transmission line of electricity first and last end simultaneously.

4. each described UHV transmission line measurement method for positive sequence parameter based on double-end measurement information according to claim 1-3 is characterized in that:

Described step 6. in, if adopt the alien frequencies power supply to measure, the reactance x to measuring then ₁Revise, the reactance when obtaining power frequency, adopt following formula to revise:

Wherein, f _{Alien frequencies}Be the frequency of alien frequencies power supply, x _{1 power frequency}Forward-sequence reactance during for power frequency.

5. each described UHV transmission line measurement method for positive sequence parameter based on double-end measurement information according to claim 1-3 is characterized in that:

Described step 7. in, transmission line of electricity positive sequence electricity is led g ₁Very little, ignore, then positive sequence electric capacity c ₁Computing formula be:

$c_1=\frac{\mathrm{Im}\left(\frac{2\×{\stackrel{\·}{I}}_{p1}}{({\stackrel{\·}{U}}_{p1}+{\stackrel{\·}{U}}_{q1})\×K_2}\right)}{2\mathrm{\πf}}$

Wherein, f is the frequency of power frequency supply, and the imaginary part component of phasor is got in Im () expression.

6. the UHV transmission line measurement method for positive sequence parameter based on double-end measurement information according to claim 5 is characterized in that:

If adopt the alien frequencies power supply to measure, then to by

The electric capacity c that formula measures ₁Revise, obtain the positive sequence capacitance parameter under the power frequency, adopt following correction formula:

Wherein, f _{Alien frequencies}Be the frequency of alien frequencies power supply, c _{1 power frequency}Positive sequence electric capacity during for power frequency.

7. the UHV transmission line measurement method for positive sequence parameter based on double-end measurement information according to claim 1 is characterized in that:

Described step 6. in, corrected parameter k ₁As follows with the value relation of transmission line length L, wherein the unit of L is kilometer:

As 0＜L≤100, k ₁=0.000; As 100＜L≤200,0.000＜k ₁≤ 0.001; As 200＜L≤400,0.001＜k ₁≤ 0.002; As 400＜L≤600,0.002＜k ₁≤ 0.003; As 600＜L≤800,0.003＜k ₁≤ 0.004; As 800＜L≤900,0.004＜k ₁≤ 0.005; As 900＜L≤1000,0.005＜k ₁≤ 0.006; As 1000＜L≤1100,0.006＜k ₁≤ 0.007; As 1100＜L≤1200,0.007＜k ₁≤ 0.0075; As 1200＜L≤1300,0.0075＜k ₁≤ 0.0085; As 1300＜L≤1400,0.0085＜k ₁≤ 0.0095; As 1400＜L≤1500,0.0095＜k ₁≤ 0.0105; As 1500＜L≤1600,0.0105＜k ₁≤ 0.0115.

8. it is characterized in that according to claim 1 or 7 described UHV transmission line measurement method for positive sequence parameter based on double-end measurement information:

Described step 7. in, corrected parameter k ₂As follows with the value relation of transmission line length L, wherein the unit of L is kilometer:

As 0＜L≤50, k ₂=0.0000; As 50＜L≤100,0.0000＜k ₂≤ 0.0003; As 100＜L≤150,0.0003＜k ₂≤ 0.0005; As 150＜L≤200,0.0005＜k ₂≤ 0.0008; As 200＜L≤250,0.0008＜k ₂≤ 0.0011; As 250＜L≤300,0.0011＜k ₂≤ 0.0014; As 300＜L≤350,0.0014＜k ₂≤ 0.0017; As 350＜L≤400,0.0017＜k ₂≤ 0.0020; As 400＜L≤450,0.0020＜k ₂≤ 0.0023; As 450＜L≤500,0.0023＜k ₂≤ 0.0026; As 500＜L≤550,0.0026＜k ₂≤ 0.0029; As 550＜L≤600,0.0029＜k ₂≤ 0.0032; As 600＜L≤650,0.0032＜k ₂≤ 0.0035; As 650＜L≤700,0.0035＜k ₂≤ 0.0038; As 700＜L≤750,0.0038＜k ₂≤ 0.0041; As 750＜L≤800,0.0041＜k ₂≤ 0.0044; As 800＜L≤850,0.0044＜k ₂≤ 0.0048; As 850＜L≤900,0.0048＜k ₂≤ 0.0051; As 900＜L≤950,0.0051＜k ₂≤ 0.0055; As 950＜L≤1000,0.0055＜k ₂≤ 0.0059; As 1000＜L≤1050,0.0059＜k ₂≤ 0.0063; As 1050＜L≤1100,0.0063＜k ₂≤ 0.0067; As 1100＜L≤1150,0.0067＜k ₂≤ 0.0071; As 1150＜L≤1200,0.0071＜k ₂≤ 0.0075; As 1200＜L≤1250,0.0075＜k ₂≤ 0.0079; As 1250＜L≤1300,0.0079＜k ₂≤ 0.0083; As 1300＜L≤1350,0.0083＜k ₂≤ 0.0087; As 1350＜L≤1400,0.0087＜k ₂≤ 0.0092; As 1400＜L≤1450,0.0092＜k ₂≤ 0.0097; As 1450＜L≤1500,0.0097＜k ₂≤ 0.0102; As 1500＜L≤1550,0.0102＜k ₂≤ 0.0107; As 1550＜L≤1600,0.0107＜k ₂≤ 0.0112.

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