Parameter measurement method for four-circuit alternating-current transmission lines arranged on same tower in parallel and capable of inhibiting induced voltage

Abstract

The invention discloses a same-tower parallel four-circuit alternating-current power transmission line parameter measurement method for inhibiting induced voltage. The method comprises the following steps: dividing a same-tower four-circuit power transmission line into five groups of wiring modes; measuring the short-circuit impedance in each wiring mode and the series impedance in a mode that the tail end of the line is grounded through impedance; calculating the characteristic impedance and the propagation coefficient in the corresponding wiring mode by using the impedance grounding series impedance measurement result and the line short-circuit impedance measurement result of the line in each wiring mode, and further calculating the distribution impedance and the distribution admittance in the corresponding mode; and finally, calculating the resistance, inductance and ground capacitance of each phase lead of the same-tower four-circuit line, the inter-phase coupling capacitance and inter-phase coupling inductance of the single-circuit line, and the coupling capacitance and coupling inductance between each phase lead of the four-circuit line through the distributed impedance and distributed admittance in each wiring mode and simultaneous equations. According to the method, the no-load power frequency induced voltage of the line can be effectively suppressed, and the line parameters can be accurately measured.

Description

Technical Field

[0001] The invention relates to the technical field of high-voltage AC transmission lines, and in particular to a method for measuring parameters of four-circuit AC transmission lines erected on the same tower for suppressing induced voltage. Background Art

[0002] In order to save resources, modern power systems use a method of installing AC transmission lines on the same tower, and ultra-high voltage AC transmission also uses a method of installing four lines on the same tower. Figure 1 In the geometric structure of a typical four-circuit AC transmission line on the same tower, I, II, III, and IV represent four single-circuit three-phase transmission lines. The spatial distribution of the four single-circuit AC transmission lines on the same tower in the cross section is rectangular and symmetrical, where I is the upper single-circuit line on the left, II is the upper single-circuit line on the right, III is the lower single-circuit line on the left, and IV is the lower single-circuit line on the right. The distance between I and II is equal to the distance between III and IV, and the distance between I and III is equal to the distance between II and IV (as shown in Figure 1). Figure 1 as shown).

[0003] The four single-loop AC transmission lines can be regarded as independent of each other, that is, each loop can operate normally independently. However, when one of the loops fails, such as being struck by lightning or short-circuited to the ground, it will induce zero-sequence transient voltage and current on other normal loops through the coupling capacitors and coupling inductors between the single-phase lines, thereby affecting the control and protection behavior in the substations on both sides, thereby affecting the operation of the entire system. For this reason, it is necessary to model the entire line in detail and calculate and analyze the extent of this impact. Accurate calculation requires accurate line parameters, which naturally requires the collection of distributed parameters such as the self-impedance and self-admittance of each single-phase conductor, as well as parameters such as the coupling inductance and coupling capacitance with distributed properties between the single-phase conductors.

[0004] For a four-circuit AC transmission line erected on the same tower, each phase conductor of a single-circuit line has a distributed self-impedance. , Self-admittance In addition, the phases of a single-circuit line also have a distributed coupling inductance m p and coupling capacitor c p (like Figure 2 In addition, there is a coupling inductance m between the single-phase conductors of each loop line and the single-phase conductors of other loop lines. h 、m v 、m d and coupling capacitor c h 、c v 、c d (like Figure 3As shown in Figure 1.1, the accurate measurement of the various distributed parameters of four-circuit AC transmission lines on the same tower is of great research significance for accurate simulation calculation, fault analysis, and control strategy research of four-circuit AC transmission lines on the same tower. The IEEE std.1870--2019 “IEEE Guide for the Parameter Measurement of AC-Transmission Lines” also provides a parameter measurement method for four-circuit transmission lines on the same tower, which requires the following Figure 4 , Figure 5 and Figure 6 The no-load open-circuit impedance of the line under different line combinations is measured by the method of measuring the no-load open-circuit impedance of the line under different line combinations. However, the design of the four-circuit line on the same tower is itself to save the line corridor and construction costs. The four-circuit line on the same tower is also installed in the same corridor with other ultra-high (ultra-high) voltage lines. When measuring the parameters of the newly built four-circuit line on the same tower, other lines in operation in the same corridor cannot be powered off, so an induced voltage of up to tens of thousands of volts will be induced on the measured line, which has been confirmed in actual on-site measurements. The power frequency induced voltage poses a great threat to the safety of the measurement personnel and measurement equipment, and even makes it impossible to measure the open-circuit impedance of the line.

[0005] Therefore, it is necessary to find a method that can effectively suppress the no-load power frequency induced voltage of four AC transmission lines on the same tower and accurately measure their line parameters. Summary of the invention

[0006] In order to solve the above technical problems, the present invention proposes a parameter measurement method for four-circuit AC transmission lines on the same tower that suppresses power-frequency induced voltage. While suppressing the power-frequency induced voltage, the equivalent distributed impedance and equivalent distributed admittance of the four-circuit AC lines can be accurately measured and calculated to obtain various distributed parameters of each single-phase conductor per unit length.

[0007] The technical solution of the present invention is as follows:

[0008] A parameter measurement method for four-circuit AC transmission lines on the same pole is used to combine the head end of the four-circuit lines on the same tower into five groups of circuit connection modes, and apply a non-industrial frequency ω power supply. Under the corresponding circuit combination mode, the conductors of each phase at the end of the line are short-circuited and grounded, and the short-circuit impedance is measured at the head end; and the line end is connected in different ways and then grounded through impedance Z, and the corresponding series impedance is measured at the head end. Then, according to the short-circuit impedance and series impedance under each combination mode, the characteristic impedance under each combination mode is calculated. and the propagation coefficient (i=1, 2, 3, 4, 5), and finally the various parameters of the four-circuit AC transmission lines on the same tower are calculated step by step.

[0009] In one embodiment, the method comprises:

[0010] Select one of the four AC transmission lines as the first combination mode, apply a three-phase positive sequence power supply between the three-phase conductors at the head end of the line, and measure and calculate the characteristic impedance under the first combination mode according to the following steps and methods: and the propagation coefficient :

[0011] Step A: In the first combination mode, the three-phase conductor at the end of the single-circuit line is short-circuited to ground, and the three-phase voltage output by the head-end power supply is synchronously collected. and three-phase current , calculate the three-phase positive sequence short-circuit impedance under the first combination mode :

[0012] (A1)

[0013] Step B: In the first combination mode, the three-phase conductors at the end of the single-circuit line are grounded through impedance Z, and the three-phase voltage output by the head-end power supply is synchronously collected. and three-phase current , calculate the three-phase positive sequence series impedance under the first combination mode :

[0014] (A2)

[0015] Step C: The three-phase positive sequence short-circuit impedance in the first combination mode obtained according to step A and step B and series impedance , calculate the characteristic impedance of the first combination and the propagation coefficient :

[0016] (A3)

[0017] (A4)

[0018] Where D is the line length.

[0019] In one embodiment, the method further comprises:

[0020] Connect all the phase conductors at the head end of the four-circuit AC transmission line in parallel as the second combination mode, and apply a single-phase power supply between the head end parallel short-circuit wire and the ground. Measure and calculate the characteristic impedance of the second combination mode according to the following steps and methods and the propagation coefficient :

[0021] Step D: In the second combination mode, all phase conductors at the end of the four-circuit line are grounded, and the single-phase voltage output by the head-end power supply is synchronously collected. and current , calculate the zero-sequence short-circuit impedance under the second combination mode :

[0022] (A5)

[0023] Step E: In the second combination mode, short-circuit all the phase conductors at the end of the four-circuit line and then ground them through impedance Z, and synchronously collect the single-phase voltage output by the head-end power supply and current , calculate the zero-sequence series impedance under the second combination mode :

[0024] (A6)

[0025] Step E1: Another way to replace step E is: in the second combination mode, short-circuit the phase conductors of two of the four circuits at the end and then ground them through impedance Z, and short-circuit the phase conductors of the other two circuits at the end and then ground them through impedance Z, and synchronously collect the single-phase voltage output by the head-end power supply and current , calculate the zero-sequence series impedance under the second combination mode :

[0026] (A7)

[0027] Step E2: Another way to replace step E is: in the second combination mode, the three-phase wires of each circuit at the end of the four circuits are short-circuited and then grounded through impedance Z, and the single-phase voltage output by the head-end power supply is synchronously collected. and current , calculate the zero-sequence series impedance under the second combination mode :

[0028] (A8)

[0029] Step E3: Another method to replace step E or step E1 or step E2 is: in the second combination mode, each phase conductor at the end of the four-circuit line is grounded through impedance Z, and the single-phase voltage output by the head-end power supply is synchronously collected. and current , calculate the zero-sequence series impedance under the second combination mode :

[0030] (A9)

[0031] Step F: Zero-sequence short-circuit impedance under the second combination mode obtained according to step D and step E and zero-sequence series impedance , calculate the characteristic impedance of the second combination and the propagation coefficient :

[0032] (A10)

[0033] (A11)

[0034] Where D is the line length;

[0035] Step F1: Zero-sequence short-circuit impedance under the second combination mode obtained according to step D and step E1 and zero-sequence series impedance , calculate the characteristic impedance of the second combination and the propagation coefficient :

[0036] (A12)

[0037] (A13)

[0038] Where D is the line length;

[0039] Step F2: Zero-sequence short-circuit impedance under the second combination mode obtained according to step D and step E2 and zero-sequence series impedance , calculate the characteristic impedance of the second combination and the propagation coefficient :

[0040] (A14)

[0041] (A15)

[0042] Where D is the line length;

[0043] Step F3: Zero-sequence short-circuit impedance under the second combination mode measured according to step D and step E3 and zero-sequence series impedance , calculate the characteristic impedance of the second combination and the propagation coefficient :

[0044] (A16)

[0045] (A17)

[0046] Where D is the line length.

[0047] In one embodiment, the method further comprises:

[0048] The phase conductors of the two circuits above the tower and the two circuits below the tower are connected in parallel as the third combination mode, and a two-phase positive sequence power supply is applied between the upper parallel short-circuit wire and the lower parallel short-circuit wire; the characteristic impedance under the third combination mode is measured and calculated according to the following steps and methods and the propagation coefficient :

[0049] Step G: In the third combination mode, the conductors of each phase at the end of the four-circuit line are grounded, and the two-phase voltage output of the head-end power supply is synchronously collected. , and two-phase current , , calculate the two-phase positive sequence short-circuit impedance under the third combination mode :

[0050] (A18)

[0051] Step H: In the third combination mode, the phase conductors of the upper two circuits at the end of the four-circuit line are short-circuited and then grounded through the impedance Z, and the phase conductors of the lower two circuits are short-circuited and then grounded through the impedance Z, and the two-phase voltage output of the head-end power supply is synchronously collected. , and two-phase current , , calculate the two-phase positive sequence series impedance under the third combination mode :

[0052] (A19)

[0053] Step H1: Another method to replace step H is: in the third combination mode, the three-phase wires of each circuit at the end of the four circuits are short-circuited and then grounded through impedance Z, and the two-phase voltage output of the head-end power supply is synchronously collected. , and two-phase current , , calculate the two-phase positive sequence series impedance under the third combination mode :

[0054] (A20)

[0055] Step H2: Another method to replace step H or step H1 is: in the third combination mode, the phase conductors at the end of the four-circuit line are grounded through impedance Z respectively, and the two-phase voltage output of the head-end power supply is synchronously collected. , and two-phase current , , calculate the two-phase positive sequence series impedance under the third combination mode :

[0056] (A21)

[0057] Step I: The two-phase positive sequence short-circuit impedance under the third combination mode measured according to step G and step H and two-phase positive sequence series impedance , calculate the characteristic impedance of the third combination and the propagation coefficient :

[0058] (A22)

[0059] (A23)

[0060] Where D is the line length;

[0061] Step I1: The two-phase positive sequence short-circuit impedance under the third combination mode measured according to step G and step H1 and two-phase positive sequence series impedance , calculate the characteristic impedance of the third combination and the propagation coefficient :

[0062] (A24)

[0063] (A25)

[0064] Where D is the line length;

[0065] Step I2: The two-phase positive sequence short-circuit impedance under the third combination mode measured according to step G and step H2 and two-phase positive sequence series impedance , calculate the characteristic impedance of the third combination and the propagation coefficient :

[0066] (A26)

[0067] (A27)

[0068] Where D is the line length.

[0069] In one embodiment, the method further comprises:

[0070] The phase conductors of the two circuits on the left side of the tower and the phase conductors of the two circuits on the right side of the tower are connected in parallel at the head end of the four-circuit AC transmission line, respectively, as the fourth combination mode, and a two-phase positive sequence power supply is applied between the left parallel short-circuit wire and the right parallel short-circuit wire; the characteristic impedance under the fourth combination mode is measured and calculated according to the following steps and methods and the propagation coefficient :

[0071] Step J: In the fourth combination mode, the phase conductors at the end of the four-circuit line are grounded, and the two-phase voltage output of the head-end power supply is synchronously collected. , and two-phase current , , calculate the two-phase positive sequence short-circuit impedance under the fourth combination mode :

[0072] (A28)

[0073] Step K: In the fourth combination mode, the two phase conductors of the four-circuit line on the left side of the tower at the end of the four-circuit line are short-circuited and then grounded through impedance Z. At the same time, the two phase conductors of the two-circuit line on the right side of the tower are short-circuited and then grounded through impedance Z. The two-phase voltage output of the head-end power supply is synchronously collected. , and two-phase current , , calculate the two-phase positive sequence series impedance under the fourth combination mode :

[0074] (A29)

[0075] Step K1: Another method to replace step K is: in the fourth combination mode, the three-phase wires of each circuit at the end of the four circuits are short-circuited and then grounded through impedance Z, and the two-phase voltage output of the head-end power supply is synchronously collected. , and two-phase current , , calculate the two-phase positive sequence series impedance under the fourth combination mode :

[0076] (A30)

[0077] Step K2: Another method to replace step K or step K1 is: in the fourth combination mode, the phase conductors at the end of the four-circuit line are grounded through impedance Z respectively, and the two-phase voltage output of the head-end power supply is synchronously collected. , and two-phase current , , calculate the two-phase positive sequence series impedance under the fourth combination mode :

[0078] (A31)

[0079] Step L: The two-phase positive sequence short-circuit impedance under the fourth combination mode measured according to step J and step K and two-phase positive sequence series impedance , calculate the characteristic impedance of the fourth combination and the propagation coefficient :

[0080] (A32)

[0081] (A33)

[0082] Where D is the line length;

[0083] Step L1: The two-phase positive sequence short-circuit impedance under the fourth combination mode measured according to step J and step K1 and two-phase positive sequence series impedance , calculate the characteristic impedance of the fourth combination and the propagation coefficient :

[0084] (A34)

[0085] (A35)

[0086] Where D is the line length;

[0087] Step L2: The two-phase positive sequence short-circuit impedance under the fourth combination mode measured according to step J and step K2 and two-phase positive sequence series impedance , calculate the characteristic impedance of the fourth combination and the propagation coefficient :

[0088] (A36)

[0089] (A37)

[0090] Where D is the line length.

[0091] In one embodiment, the method further comprises:

[0092] The three-phase conductors of the upper line on the left side of the head end of the four-circuit AC transmission line are short-circuited in parallel with the three-phase conductors of the lower line on the right side, and the three-phase conductors of the upper line on the right side of the tower are short-circuited in parallel with the three-phase conductors of the lower line on the left side, as the fifth combination mode, and a two-phase positive sequence power supply is applied between the two sets of parallel short-circuited wires at the head end; the characteristic impedance under the fifth combination mode is measured and calculated according to the following steps and methods and the propagation coefficient :

[0093] Step M: In the fifth combination mode, ground the conductors of each phase at the end of the four-circuit line and synchronously collect the two-phase voltage output of the head-end power supply. , and two-phase current , , calculate the two-phase positive sequence short-circuit impedance under the fifth combination mode :

[0094] (A38)

[0095] Step N: In the fifth combination mode, the three-phase conductor of the upper line on the left side of the four-circuit line end tower is short-circuited with the three-phase conductor of the lower line on the right side and then grounded through impedance Z. At the same time, the three-phase conductor of the upper line on the right side of the tower is short-circuited with the three-phase conductor of the lower line on the left side and then grounded through impedance Z, and the two-phase voltage output of the head-end power supply is synchronously collected. , and two-phase current , , calculate the two-phase positive sequence series impedance under the fifth combination mode :

[0096] (A39)

[0097] Step N1: Another way to replace step N is that in the fifth combination mode, the three-phase wires of each circuit at the end of the four circuits are short-circuited and then grounded through impedance Z, and the two-phase voltage output of the head-end power supply is synchronously collected. , and two-phase current , , calculate the two-phase positive sequence series impedance under the fifth combination mode :

[0098] (A40)

[0099] Step N2: Another way to replace step N or step N1 is that, in the fifth combination mode, the phase conductors at the end of the four-circuit line are grounded through impedance Z respectively, and the two-phase voltage output of the head-end power supply is synchronously collected. , and two-phase current , , calculate the two-phase positive sequence series impedance under the fifth combination mode :

[0100] (A41)

[0101] Step O: The two-phase positive sequence short-circuit impedance under the fifth combination mode measured according to step M and step N and two-phase positive sequence series impedance , calculate the characteristic impedance of the fifth combination and the propagation coefficient :

[0102] (A42)

[0103] (A43)

[0104] Where D is the line length;

[0105] Step O1: The two-phase positive sequence short-circuit impedance under the fifth combination mode measured according to step M and step N1 and two-phase positive sequence series impedance , calculate the characteristic impedance of the fifth combination and the propagation coefficient :

[0106] (A44)

[0107] (A45)

[0108] Where D is the line length;

[0109] Step O2: The two-phase positive sequence short-circuit impedance under the fifth combination mode measured according to step M and step N2 and two-phase positive sequence series impedance , calculate the characteristic impedance of the fifth combination and the propagation coefficient :

[0110] (A46)

[0111] (A47)

[0112] Where D is the line length.

[0113] In one embodiment, the method further comprises:

[0114] The characteristic impedance of the five different combinations will be obtained and the propagation coefficient (i=1, 2, 3, 4, 5) are substituted into the formula in pairs:

[0115] (i=1, 2, 3, 4, 5) (A48)

[0116] (i=1, 2, 3, 4, 5) (A49)

[0117] Get the equivalent distributed impedance under five different combination conditions and equivalent distributed admittance (i=1, 2, 3, 4, 5).

[0118] In one embodiment, the method further comprises:

[0119] The equivalent distributed impedance under five different combinations and equivalent distributed admittance (i=1, 2, 3, 4, 5) Combine and solve the following equations to obtain the parameters of the four-circuit AC transmission line on the same tower:

[0120] (1) Resistance per unit length of a single-phase conductor:

[0121] (A50)

[0122] (2) Conductivity per unit length of a single-phase conductor to ground:

[0123] (A51)

[0124] (3) Resistance per unit length of the earth loop:

[0125] (A52)

[0126] (4) Self-inductance of a single-phase conductor per unit length and mutual inductance between each phase conductor:

[0127] (A53)

[0128] (5) The capacitance of a single-phase conductor per unit length to ground and the coupling capacitance between each phase conductor:

[0129] (A54)

[0130] In equations (A50)-(A54), Re(·) represents a real number, Im(·) represents an imaginary number, and ω is the angular frequency of the power supply;

[0131] Where, l is the self-inductance of the single-phase conductor; c0 is the capacitance of the single-phase conductor to ground; m h and c h are the coupling inductance and coupling capacitance between the single-phase conductor of one circuit above or below the tower and the single-phase conductor of another circuit on the same horizontal plane; m v and c v are the coupling inductance and coupling capacitance between the single-phase conductor of one circuit on the upper side of the tower and the single-phase conductor of another circuit below; m d and c d They are respectively the coupling inductance and coupling capacitance between the single-phase conductor of the left circuit above the tower and the single-phase conductor of the right circuit below.

[0132] The advantages of the present invention are: by connecting the resistor Z in series to ground at the end of the line, the no-load induced voltage of the line can be effectively suppressed within a safe range, thereby ensuring the safety of the measuring personnel and equipment. Moreover, according to the short-circuit impedance of the four-circuit line ends when short-circuited in five different combinations, and the series impedance after the line ends are grounded by the impedance Z, the characteristic impedance and propagation coefficient in five different combinations can be calculated respectively, and then the equivalent distributed impedance and equivalent distributed admittance can be calculated, thereby obtaining various distributed parameters of each single-phase conductor under unit length. The constructed model is simple and reasonable, the measurement and calculation method is simple and practical, and the results are accurate and reliable. BRIEF DESCRIPTION OF THE DRAWINGS

[0133] Figure 1 A typical geometric structure diagram of a cross section along a four-circuit AC transmission line with the same tower;

[0134] Figure 2 It is a schematic diagram of coupling inductance and coupling capacitance between each phase conductor of a single-circuit line;

[0135] Figure 3 It is a schematic diagram of coupling parameters between single-phase conductors of four-circuit lines on the same tower;

[0136] Figure 4 The open circuit impedance measurement method and circuit of a single-circuit line in IEEE std 1870-2019;

[0137] Figure 5 The measurement method and circuit for zero-sequence open-circuit impedance of four-circuit lines on the same tower in IEEE std 1870-2019;

[0138] Figure 6 It is a two-phase open-circuit impedance measurement method and circuit formed by combining two of four circuits on the same tower in IEEE std 1870-2019;

[0139] Figure 7A three-phase positive sequence short-circuit impedance measurement circuit for a single-circuit line in the first combination mode;

[0140] Figure 8 A three-phase positive sequence series impedance measurement circuit when each phase conductor at the end of a single-circuit line is grounded via impedance Z in the first combination mode;

[0141] Fig. 9 A zero-sequence short-circuit impedance measurement circuit in the second combination mode;

[0142] Fig.10 This is a schematic diagram of a zero-sequence series impedance measurement circuit in the second combination mode, when the end phase conductors are short-circuited and then grounded via impedance Z;

[0143] Fig.11 It is a two-phase positive sequence short-circuit impedance measurement circuit in the third combination mode;

[0144] Fig.12 In the third combination mode, when the two circuits connected in parallel at the head end are short-circuited at the end and then grounded via impedance Z respectively, the two-phase positive sequence series impedance measurement circuit;

[0145] Fig.13 Schematic diagram of a two-phase positive sequence short-circuit impedance measurement circuit in the fourth combination mode;

[0146] Fig.14 In the fourth combination mode, when the two circuits connected in parallel at the head end are short-circuited at the end and then grounded via impedance Z respectively, the two-phase positive sequence series impedance measurement circuit;

[0147] Fig.15 Schematic diagram of a two-phase positive-sequence short-circuit impedance measurement circuit in the fifth combination mode.

[0148] Fig.16 In the fifth combination mode, when the two circuits connected in parallel at the head end are short-circuited at the end and then grounded via impedance Z respectively, the two-phase positive sequence series impedance measurement circuit;

[0149] Fig.17 This is a schematic diagram of a zero-sequence series impedance measurement circuit in the second combination mode, when two of the end conductors are connected in parallel and then grounded via impedance Z, and the other two end conductors are connected in parallel and then grounded via impedance;

[0150] Fig.18 This is a schematic diagram of a zero-sequence series impedance measurement circuit in the second combination mode, when each end loop is short-circuited and then grounded via impedance Z;

[0151] Fig.19 This is a schematic diagram of a zero-sequence series impedance measurement circuit when each phase conductor at the end is grounded via impedance Z in the second combination mode;

[0152] Fig. 20In the third combination mode, when the three-phase conductors of each end circuit are short-circuited and then grounded via impedance Z, the two-phase positive sequence series impedance measurement circuit;

[0153] Fig.21 In the fourth combination mode, when the three-phase conductors of each end circuit are short-circuited and then grounded via impedance Z, the two-phase positive sequence series impedance measurement circuit;

[0154] Fig. 22 In the fifth combination mode, when the three-phase conductors of each end circuit are short-circuited and then grounded via impedance Z, the two-phase positive sequence series impedance measurement circuit;

[0155] Fig.23 In the third combination mode, when the end phase conductors are grounded via impedance Z, the two-phase positive sequence series impedance measurement circuit;

[0156] Fig.24 In the fourth combination mode, when the end phase conductors are grounded via impedance Z, the two-phase positive sequence series impedance measurement circuit;

[0157] Fig.25 In the fifth combination mode, when the end conductors of each phase are grounded via impedance Z respectively, a two-phase positive sequence impedance measurement circuit is connected in series. DETAILED DESCRIPTION

[0158] In order to make the above-mentioned objects, features and advantages of the present invention more clearly understood, the following is a brief description of the present invention in conjunction with the attached drawings. Figure 1 —Attachment Fig.25 The present invention is further described in detail with specific implementation modes.

[0159] like Figure 1 As shown, I, II, III, and IV represent four single-circuit lines of four AC transmission lines on the same tower. I is the upper single-circuit line on the left, II is the upper single-circuit line on the right, III is the lower single-circuit line on the left, and IV is the lower single-circuit line on the right.

[0160] Each single-circuit line is arranged symmetrically in spatial geometric structure, and the parameters between the three phases are basically balanced through the phase switching technology along the line. In addition to the self-impedance of each phase conductor, each single-circuit line and admittance In addition to the same, there is also the same coupling inductance between the phase conductors and coupling capacitors ( Figure 2 ).

[0161] At the same time, there are coupling inductances and coupling capacitances between the phases of the transmission lines belonging to different loops. For example, there is a coupling inductance m between the phase a of the first loop and the phases a, b, and c of the second loop. h and coupling capacitor ch There is also a coupling inductance m between the a, b, and c phase conductors of the third circuit. v and coupling capacitor c v There is also a coupling inductance m between the a, b, and c phase conductors of the IV circuit. d and coupling capacitor c d In addition, there are coupling relationships between the phases of other circuits. Figure 3 This relationship is drawn, but for the sake of simplicity and clarity, only the coupling relationship between certain single-phase conductors in each circuit is given.

[0162] Since the cross-section of the four-circuit line is arranged in a rectangular symmetrical manner in terms of spatial geometric structure, Figure 1 The coupled distributed inductance and coupled distributed capacitance between the phase conductors of different circuits satisfy the following relationships:

[0163] For two lines arranged horizontally on the same level, there are:

[0164] (twenty four)

[0165] (25)

[0166] For two lines arranged vertically on one side of a tower, there are:

[0167] (26)

[0168] (27)

[0169] The two lines on the diagonal are:

[0170] (28)

[0171] (29)

[0172] According to circuit theory, the differential equation for a single-conductor earth return line with distributed parameter characteristics is:

[0173] (30)

[0174] (31)

[0175] Where z is the impedance per unit length of the line, and y is the admittance per unit length of the line. The solution of this differential equation forms the two-port network equation of the line:

[0176] (32)

[0177] in:

[0178] (33)

[0179] (34)

[0180] If the end of the line is short-circuited to ground, =0, then the short-circuit impedance measured at the head end of the line under this condition is:

[0181] (35)

[0182] If the end of the line is grounded via impedance Z, the series impedance measured at the beginning of the line under this condition is:

[0183] (36)

[0184] Solving equations (35) and (36) together, we can obtain the line characteristic impedance calculated by measurement: and the propagation coefficient Another set of formulas:

[0185] (37)

[0186] (38)

[0187] With characteristic impedance and the propagation coefficient , the distribution parameters of the line can be calculated:

[0188] (39)

[0189] and

[0190] (40)

[0191] Then the distributed impedance of the single-conductor earth return circuit can be calculated and distributed ground admittance ;

[0192] However, for four-circuit AC transmission lines on the same tower, each phase conductor of a single-circuit line has distributed self-impedance and self-admittance, such as Figure 2 As shown, the phase-to-phase conductors of a single-circuit line also have a distributed coupling inductance m p and coupling capacitor c p In addition, Figure 3 As shown, there is a coupling inductance m between the single-phase conductors of each loop line and the single-phase conductors of other loop lines. h 、m v 、m dand coupling capacitor c h 、c v 、c d To do this, we first need to analyze the circuit characteristics and its voltage and current propagation equations.

[0193] according to Figure 3 At a certain section of the four-circuit line on the same tower, the currents of the 12-phase conductors passing through the four-circuit line are Then through the earth resistance r g Return current for:

[0194] (41)

[0195] Figure 3 The self-impedance of the a-phase conductor of the first circuit is: , the admittance to ground is There is a coupling inductance between it and the a-phase conductor of the II circuit. and coupling capacitors There is a coupling inductance between the a-phase conductor of the third circuit and coupling capacitors There is a coupling inductance between the a-phase conductor of the IV circuit and coupling capacitors At the same time, there are also coupling inductances between the a-phase conductor of the first circuit and the b-phase and c-phase conductors of the second circuit. and coupling capacitors There are also coupling inductances between the b-phase and c-phase conductors of the third circuit. and capacitor There are also coupling inductances between the b-phase and c-phase conductors of the IV circuit. and coupling capacitors . And so on.

[0196] Reference Figure 3 The voltage and current differential equations of each phase conductor of the four-circuit line on the same tower can be written out phase by phase. Among them:

[0197] Chapter I:

[0198] (42)

[0199] (43)

[0200] (44)

[0201] (45)

[0202] (46)

[0203] (47)

[0204] II.

[0205] (48)

[0206] (49)

[0207] (50)

[0208] (51)

[0209] (52)

[0210] (53)

[0211] III.

[0212] (54)

[0213] (55)

[0214] (56)

[0215] (57)

[0216] (58)

[0217] (59)

[0218] IVth session:

[0219] (60)

[0220] (61)

[0221] (62)

[0222] (63)

[0223] (64)

[0224] (65)

[0225] The phase propagation equation of the above four-circuit line on the same tower can be written as a matrix formula expressed in the form of a single-circuit line. Therefore, the voltage increment equation of the above four-circuit line can be rewritten as:

[0226] (66)

[0227] (67)

[0228] (68)

[0229] (69)

[0230] The current increment equation of the four-circuit line can be rewritten as:

[0231] (70)

[0232] (71)

[0233] (72)

[0234] (73)

[0235] The voltage vectors in the above equation are:

[0236] , , , (74)

[0237] The current phasors are:

[0238] , , , (75)

[0239] The three-phase self-impedance matrix of a single-circuit line is:

[0240] (76)

[0241] The mutual impedance matrix between horizontally arranged double-circuit lines:

[0242] (77)

[0243] The mutual impedance matrix between vertically arranged double-circuit lines:

[0244] (78)

[0245] The mutual impedance matrix between the double-circuit lines on the diagonal:

[0246] (79)

[0247] The self-admittance matrix of a single-circuit line:

[0248] (80)

[0249] The mutual admittance matrix between horizontally arranged double-circuit lines:

[0250] (81)

[0251] The mutual admittance matrix between vertically arranged double-circuit lines:

[0252] (82)

[0253] The mutual admittance matrix between the double-circuit lines on the diagonal line is:

[0254] (83)

[0255] The voltage increment equations (66)-(69) for each conductor expressed in terms of three-phase voltage and current can be transformed into voltage increment equations expressed in terms of three-phase sequence components:

[0256] (84)

[0257] (85)

[0258] (86)

[0259] (87)

[0260] The current increment equations (70)-(73) of each circuit expressed by three-phase voltage and current are transformed into the current increment equation expressed by three-phase sequence components:

[0261] (88)

[0262] (89)

[0263] (90)

[0264] (91)

[0265] Among them, the sequence component voltage vector of each circuit is:

[0266] , , , , , , , (92) The sequence component current vectors of each circuit are:

[0267] , ,

[0268] , (93)

[0269] Sequence component impedance matrix of a single-circuit line:

[0270] (94)

[0271] Sequence component impedance matrix between horizontally arranged double-circuit lines:

[0272] (95)

[0273] Sequence component impedance matrix between vertically arranged double-circuit lines:

[0274] (96)

[0275] The sequence component impedance matrix between the double-circuit lines on the diagonal line:

[0276] (97)

[0277] The self-admittance matrix of a single-circuit line:

[0278] (98)

[0279] The sequence component coupling admittance matrix between horizontally arranged double-circuit lines is:

[0280] (99)

[0281] The sequence component coupling admittance matrix between vertically arranged double-circuit lines is:

[0282] (100)

[0283] The sequence component coupling admittance matrix between diagonally arranged double-circuit lines is:

[0284] (101)

[0285] After the three-phase sequence components of each circuit are transformed and decoupled, it can be found that the positive and negative sequence propagation equations of each single circuit are the same, and only zero-sequence coupling exists between the circuits.

[0286] Among them, the positive sequence propagation equation of each single-circuit line is:

[0287] Chapter I:

[0288] (102)

[0289] (103)

[0290] Chapter II:

[0291] (104)

[0292] (105)

[0293] Chapter III:

[0294] (106)

[0295] (107)

[0296] Chapter IV:

[0297] (108)

[0298] (109)

[0299] The positive sequence propagation equation of each single-circuit line has the same mathematical form as equations (30) and (31). And the corresponding positive sequence distributed impedance and distributed admittance of each circuit are:

[0300] (110)

[0301] (111)

[0302] The zero-sequence voltage propagation equation of each single-circuit line is:

[0303] (112)

[0304] (113)

[0305] (114)

[0306] (115)

[0307] The zero-sequence current propagation equation of each single-circuit line is:

[0308] (116)

[0309] (117)

[0310] (118)

[0311] (119)

[0312] It can be seen that the zero-sequence coupling between the single-circuit lines makes parameter measurement very difficult. If a method can be found to make the voltage and current increment equations expressed by equations (112)-(119) consistent with the single-conductor telegraph equations (30) and (31) in terms of expression, it will be possible to measure and calculate Figure 3 Various parameters in .

[0313] To this end, the present invention further simplifies the models (112)-(119) by reducing the order, and then measures the short-circuit impedance of the line under the simplified circuit mode and the series impedance under the condition of impedance at the end of the line, thereby obtaining Figure 2 and Figure 3 The various circuit parameters shown. The specific method is to measure the symmetrical three-phase positive sequence short-circuit impedance of a single-circuit line and the series impedance when the end is grounded through impedance Z. In addition, the four-circuit lines on the same tower are combined in pairs to form a zero-sequence circuit and three two-phase positive sequence circuits. The short-circuit impedance of the five groups of circuits and the series impedance when the end is grounded through impedance Z are measured to solve the various parameters. The IEEE std. 1870-2019 “IEEE Guide for the Parameter Measurement of AC Transmission Lines” provides a parameter measurement method for four-circuit transmission lines on the same tower, which requires that Figure 4 , Figure 5 as well as Figure 6 The no-load open-circuit impedance of the line under different line combinations is measured by this method. However, the design of the four-circuit line on the same tower is to save the line corridor and construction costs. The four-circuit line on the same tower is also installed in the same corridor with other ultra-high voltage (UHV) lines. When measuring the parameters of the newly built four-circuit line on the same tower, the running lines in the same corridor cannot be powered off, so an induced voltage of up to tens of thousands of volts will be induced on the measured line, which has been confirmed in actual on-site measurements. The power frequency induced voltage poses a great threat to the safety of the measurement personnel and measurement equipment, and even makes it impossible to measure the open-circuit impedance of the line.

[0314] With the above theoretical model, a specific measurement method can be designed. The measurement method is divided into short-circuit impedance measurement under 5 circuit combinations and impedance measurement with the line end grounded through impedance Z.

[0315] Combination mode 1 (single-circuit line positive sequence parameter measurement):

[0316] There is no coupling between the positive sequence propagation equations of each single-circuit line described by equations (102)-(109) and the positive sequence propagation equations of other circuits. The positive sequence voltage and current equations of each single-circuit line have the same expression as the telegraph equations (30) and (31) of the single-conductor earth return circuit, and the positive sequence distributed impedance of the single-circuit line described by equations (102)-(109) is and positive sequence distributed admittance They are:

[0317] (120)

[0318] (121)

[0319] Therefore, the single-circuit positive sequence parameters of a single-circuit line can be measured.

[0320] The specific measurement method is: refer to Figure 7 , short-circuit the three-phase conductors at the end of one of the three-phase lines to ground, apply three-phase positive sequence power to the head end, and synchronously collect the three-phase voltage output by the head end power supply and three-phase current , calculate the three-phase positive sequence short-circuit impedance of a single-circuit line according to the following formula: :

[0321] (122)

[0322] Another press Figure 8 , connect the phase conductors at the end of the corresponding single-loop three-phase line to ground through impedance Z, apply three-phase positive sequence voltage to the head end, and synchronously collect the three-phase voltage output by the head end power supply and three-phase current , calculate the three-phase positive sequence series impedance of a single-circuit line according to the following formula: :

[0323] (123)

[0324] Combination method 2 (zero-sequence circuit parameter measurement method for four-circuit AC lines on the same tower):

[0325] By algebraically adding equations (112) to (115) and equations (116) to (119) and merging similar terms, we have

[0326] (124)

[0327] (125)

[0328] because is the single-phase zero-sequence component of each circuit, and the total current of a certain section:

[0329] (126)

[0330] And under this method, the zero-sequence voltage of a certain cross-section line is:

[0331] (127)

[0332] After normalization, equations (124) and (125) are expressed as:

[0333] (128)

[0334] (129)

[0335] Equations (128) and (129) are typical expressions of telegraph equations. The corresponding distributed impedance is and distributed admittance They are:

[0336] (130)

[0337] (131)

[0338] For this purpose, please refer to Fig. 9 , short-circuit the phase conductors at the end of the four lines to the ground, and connect the phase conductors at the head end of the four lines in parallel, and apply a single-phase voltage between the parallel short-circuit wire at the head end and the ground; synchronously collect the single-phase voltage output by the head end power supply under this condition and current , calculate the short-circuit impedance under this method :

[0339] (132)

[0340] See also Fig.10 , short-circuit the phase conductors at the end of the four lines and then ground them through impedance Z. At the same time, connect the phase conductors at the head end of the four lines in parallel, and apply a single-phase voltage between the head end and the ground; synchronously collect the single-phase voltage output by the head end power supply and current , calculate the series impedance under this method :

[0341] (133)

[0342] Combination method 3 (I and II at the head end of the four-circuit AC line on the same tower are connected in parallel, and III and IV are connected in parallel to form a two-phase positive sequence circuit parameter measurement method):

[0343] Perform the following algebraic operations on formulas (112)-(115): (112)+(113) - (114) - (115); and perform the following algebraic operations on formulas (116)-(119): (116)+(117) - (118) - (119). After merging like terms, we have:

[0344] (134)

[0346] (135)

[0347] Can be ordered , , , ,at the same time:

[0348] (136)

[0349] (137)

[0350] Substituting formulas (136) and (137) into formulas (134) and (135), the normalized form is:

[0351] (138)

[0352] (139)

[0353] The corresponding distributed impedance and distributed admittance in this mode are:

[0354] (140)

[0355] (141)

[0356] For this purpose, we can refer to equations (134)-(141) and follow Fig.11 The phase conductors at the end of the line are short-circuited and grounded, and the phase conductors Ⅰ and Ⅱ at the head end of the four lines are connected in parallel, and the phase conductors Ⅲ and Ⅳ are connected in parallel. A two-phase positive sequence voltage is applied between the end of the head end line Ⅰ(Ⅱ) and Ⅲ(Ⅳ); the two-phase voltage output of the power supply is synchronously collected. , and current , , calculate the two-phase positive sequence short-circuit impedance under this combination :

[0357] (142)

[0358] See also Fig.12, short-circuit the phase conductors of the I and II circuits at the end of the line and then ground them through impedance Z, short-circuit the phase conductors of the III and IV circuits and then ground them through impedance Z, connect the phase conductors of I and II at the head end of the four lines in parallel, and connect the phase conductors of III and IV in parallel. Apply two-phase positive sequence voltage between the end of the head end line I (II) and III (IV); synchronously collect the two-phase voltage output by the power supply , and current , , calculate the two-phase positive sequence series impedance under this combination :

[0359] (143)

[0360] Combination method 4 (parameter measurement method of two-phase positive sequence circuit composed of four AC lines I and III in parallel, and II and IV in parallel on the same tower):

[0361] Perform the following algebraic operation on formula (112)-(115): (112)+(114) - (113) - (115); perform the following algebraic operation on (116)-(119): (116)+(118) - (117) - (119). After merging like terms, we have:

[0362] (144)

[0363] (145)

[0364] Similarly, the propagation equations of (144) and (145) after normalization are:

[0365] (146)

[0366] (147)

[0367] The corresponding distributed impedance and distributed admittance in this mode are:

[0368] (148)

[0369] (149)

[0370] For this purpose, we can refer to equations (144)-(147), according to Fig.13 The end of the four-circuit line is short-circuited to ground, and the first end Ⅰ and Ⅲ of the four lines are connected in parallel, and the second and fourth phases are connected in parallel. A two-phase positive sequence voltage is applied between the first end Ⅰ(Ⅲ) and Ⅱ(Ⅳ); the two-phase voltage output of the power supply is synchronously collected. , and current , , calculate the two-phase positive sequence short-circuit impedance under this combination:

[0371] (150)

[0372] according to Fig.14 In this way, the phase conductors of the I and III lines at the end of the line are short-circuited and then grounded through the impedance Z. The phase conductors of the II and IV lines are short-circuited and then grounded through the impedance Z. The phase conductors of the I and III lines at the head end of the four lines are connected in parallel, and the phase conductors of the II and IV lines are connected in parallel. The two-phase positive sequence voltage between the head end I (III) and II (IV) is synchronously collected, and the two-phase voltage output of the head end power supply is collected. , and current , , calculate the two-phase positive sequence series impedance under this combination :

[0373] (151)

[0374] Combination 5 (parameter measurement of a two-phase positive sequence circuit consisting of four AC lines I and IV connected in parallel, and II and III connected in parallel on the same tower):

[0375] Perform the following algebraic operation on formula (112)-(115): (112)+(115)-(113)-(114); perform the following algebraic operation on formula (116)-(119): (116)+(119)-(117)-(118). After merging similar terms, we have:

[0376] (152)

[0377] (153)

[0378] Similarly, the propagation equations of (152) and (153) after normalization are:

[0379] (154)

[0380] (155)

[0381] The corresponding distributed impedance and distributed admittance in this mode are:

[0382] (156)

[0383] (157)

[0384] For this purpose, we can refer to equations (152)-(155), according to Fig.15 The phase conductors at the end of the four-circuit line are short-circuited and grounded, the phase conductors Ⅰ and Ⅳ at the head end of the four lines are connected in parallel, the phase conductors Ⅱ and Ⅲ are connected in parallel, and a two-phase positive sequence voltage is applied between the head end Ⅰ(Ⅳ) and Ⅱ(Ⅲ), and the two-phase voltage output of the head end power supply is synchronously collected. , And current , , calculate the two-phase positive sequence short-circuit impedance under this combination :

[0385] (158)

[0386] according to Fig.16 In this way, the phase conductors of the I and IV loops at the end of the line are short-circuited and then grounded through the impedance Z. The phase conductors of the II and III loops are short-circuited and then grounded through the impedance Z. The phase conductors of the I and IV loops at the head end of the four lines are connected in parallel, and the phase conductors of the II and III loops are connected in parallel. A two-phase positive sequence voltage is applied between the head end I (IV) and II (III), and the two-phase voltage output of the head end power supply is synchronously collected. , and current , , calculate the two-phase positive sequence series impedance under this combination :

[0387] (159)

[0388] Parameter calculation:

[0389] The short-circuit impedance under the above-mentioned various combinations is measured. , , , , , and the series impedance after the line end is grounded through impedance Z , , , , After that, first calculate the characteristic impedance in various ways (i=1,2,3,4,5) according to the following formula :

[0390] (160)

[0391] (161)

[0392] (i=3,4,5) (162)

[0393] According to the short-circuit impedance of various combinations and characteristic impedance (i=1,2,3,4,5), calculate the propagation coefficient under the corresponding combination :

[0394] (i=1,2,3,4,5) (163)

[0395] Where D is the length of the four-circuit parallel line on the same pole, which can be obtained based on design information or survey data.

[0396] Next, the distributed impedance and distributed admittance under various combinations are calculated:

[0397] (i=1, 2, 3, 4, 5) (164)

[0398] (i=1, 2, 3, 4, 5) (165)

[0399] Subscript i=1, 2, 3, 4, 5, respectively represent different measurement combinations. Then the distributed inductance and capacitance of the line can be calculated by the following method. Among them:

[0400] , (166)

[0401] (167)

[0402] (168)

[0403] (169)

[0404] (170)

[0405] In equations (166) to (170), Re(·) represents a real number, Im(·) represents an imaginary number, and ω is the angular frequency of the power supply.

[0406] The present invention applies a positive sequence voltage to the head end of one of the four-circuit lines, and measures the open circuit impedance and short circuit impedance under the combination mode; four parallel combination modes are used at the head end of the four-circuit lines to measure the impedance of the four-circuit three-phase AC lines when the ends are grounded through small impedance and the short circuit impedance when the ends are short-circuited under different parallel combination modes at a preset frequency; according to the length of the line, and according to the open circuit impedance when the ends of the four-circuit lines are open circuited and the short circuit impedance when the ends are short-circuited under the above five different combination modes, the characteristic impedance and propagation coefficient under five different combination conditions are calculated respectively, and then the equivalent distributed impedance and equivalent distributed admittance are calculated; according to the equivalent distributed impedance and equivalent distributed admittance under different combination modes, various distributed parameters of the single-circuit single-phase conductor under unit length are obtained. The measurement and calculation method of the present invention is simple and practical, and the results are accurate and reliable.

[0407] By replacing the impedance measurement under the open circuit mode at the end of the line with the method of grounding the end of the line through a small impedance, the power frequency induced voltage on the measured line can be greatly reduced, providing safety protection for measurement personnel and equipment.

[0408] Methods to further reduce the induced voltage on the measured line:

[0409] In the zero-sequence impedance measurement of combination mode 2, if Fig.10 First, short-circuit the conductors of each phase of the four-circuit line and then ground them through impedance Z. The voltage at the end of the line is ( is the zero-sequence current flowing through Z in the single-phase line), the residual induced voltage of the line is still very high. To reduce the residual induced voltage on the line, Fig.17 As shown in the figure, at the end of the line, the phase conductors of two circuits are short-circuited and then grounded through impedance Z, and the phase conductors of the other two circuits are short-circuited and then grounded through impedance Z; in this way, the residual induced voltage on the line can be reduced to To further reduce the residual induced voltage on the line, Fig.18 As shown in the figure, after the three-phase conductors of each circuit are short-circuited at the end of the line, each circuit is grounded through impedance Z; in this way, the residual induced voltage on the line can be reduced to Further, according to Fig.19 As shown in the figure, each phase conductor at the end of the line is grounded through impedance Z; in this way, the residual induced voltage on the line can be reduced to .

[0410] In press Fig.17 After obtaining the zero-sequence series impedance, the characteristic impedance calculation formula (161) needs to be replaced by the following formula:

[0411] (172)

[0412] In press Fig.18 After obtaining the zero-sequence series impedance, the characteristic impedance calculation formula (161) needs to be replaced by the following formula:

[0413] (173)

[0414] In press Fig.19 After obtaining the zero-sequence series impedance, the characteristic impedance calculation formula (161) needs to be replaced by the following formula:

[0415] (174)

[0416] In the two-phase positive sequence impedance measurement of combination modes 3, 4, and 5, if Fig.12 , Fig.14 , Fig.16 The wiring method is to short-circuit the two parallel circuits at the end and then ground them through impedance Z. The residual induced voltage at the end of the line under this wiring method is To reduce the residual induced voltage on the line, Fig. 20 , Fig.21 , Fig. 22 As shown in the figure, after the three-phase conductors of each circuit are short-circuited at the end of the line, each circuit is grounded through impedance Z. In this way, the residual induced voltage on the line can be reduced to .

[0417] In accordance with Fig. 20 , Fig.21 , Fig. 22 Wiring method: measure the two-phase positive sequence impedance of combination 3, 4, and 5 respectively , , After that, the characteristic impedance calculation formula (162) needs to be replaced by the following formula:

[0418] (i=3,4,5) (175)

[0419] In order to further reduce the residual induced voltage on the line, Fig.23 , Fig.24 , Fig.25 The end of each phase conductor is grounded through impedance Z, and the two-phase positive sequence impedance of combination method 3, 4, and 5 is performed. , , Thus, the characteristic impedance calculation formula (162) needs to be replaced by the following formula:

[0420] (i=3,4,5) (176)

[0421] When each phase impedance at the end of the line is grounded via a small impedance, the residual induced voltage at the end of the line is only , which can basically guarantee the safety of measurement personnel and equipment.

[0422] The above-mentioned embodiment only expresses one implementation mode of the present invention, and its description is relatively specific and detailed, but it cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that for ordinary technicians in this field, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be based on the attached claims.

Claims

1. A method for measuring parameters of four AC transmission lines on the same tower to suppress induced voltage, characterized in that: The cross-section of four AC transmission lines on the same pole is distributed symmetrically in a rectangular shape with the pole tower as the center. The parameter measurement method and steps include: Step A: selecting one of the four AC transmission lines as a first combination mode, and applying a three-phase positive sequence power supply between the three-phase conductors at the head end of the line; The three-phase conductors at the end of the single-circuit line are short-circuited to ground, and the three-phase voltage output by the power supply at the head end is synchronously collected. and three-phase current , calculate the three-phase positive sequence short-circuit impedance under the first combination mode according to formula (A1): : （A1） In addition, the three-phase conductors at the end of the single-circuit line are grounded through impedance Z, and the three-phase voltage output by the head-end power supply is synchronously collected. and three-phase current , calculate the three-phase positive sequence series impedance under the first combination mode according to formula (A2): : （A2） According to the three-phase positive sequence short-circuit impedance under the first combination mode and series impedance , calculate the characteristic impedance of the first combination according to formulas (A3) and (A4) respectively and the propagation coefficient : （A3） （A4） Where D is the line length; Step B: connecting all the phase conductors at the head end of the four-circuit AC transmission line in parallel as a second combination mode, and applying a single-phase power supply between the head end parallel short-circuit wire and the ground; Ground all phase conductors at the end of the four-circuit line and synchronously collect the single-phase voltage output by the head-end power supply and current , calculate the zero-sequence short-circuit impedance under the second combination mode according to formula (A5) : （A5） In addition, all phase conductors at the end of the four-circuit line are short-circuited and then grounded through impedance Z, and the single-phase voltage output by the head-end power supply is synchronously collected. and current , calculate the zero-sequence series impedance under the second combination mode according to formula (A6) : （A6） According to the zero-sequence short-circuit impedance under the second combination mode and zero-sequence series impedance , calculate the characteristic impedance of the second combination according to formulas (A7) and (A8) respectively and the propagation coefficient : （A7） （A8） Where D is the line length; Step C: connecting the conductors of each phase of the two circuits at the top of the tower with the four-circuit AC transmission lines in parallel, and connecting the conductors of each phase of the two circuits at the bottom of the tower in parallel, as a third combination mode, and applying a two-phase positive sequence power supply between the upper parallel short-circuit wire and the lower parallel short-circuit wire; Ground each phase conductor at the end of the four-circuit line and synchronously collect the two-phase voltage output of the head-end power supply , and two-phase current , , calculate the two-phase positive sequence short-circuit impedance under the third combination mode according to formula (A9): : （A9） In addition, the two phase conductors of the upper two circuits at the end of the four-circuit line are short-circuited and then grounded through impedance Z. At the same time, the two phase conductors of the lower two circuits are short-circuited and then grounded through impedance Z. The two-phase voltage output of the head-end power supply is synchronously collected. , and two-phase current , , calculate the two-phase positive sequence series impedance under the third combination mode according to formula (A10): : （A10） According to the two-phase positive sequence short-circuit impedance under the third combination mode and two-phase positive sequence series impedance , calculate the characteristic impedance of the third combination according to formulas (A11) and (A12) respectively and the propagation coefficient : （A11） （A12） Where D is the line length; Step D: connecting the conductors of each phase of two circuits on the left side of the tower at the head end of the four-circuit AC transmission line in parallel, and connecting the conductors of each phase of two circuits on the right side of the tower in parallel, as a fourth combination mode, and applying a two-phase positive sequence power supply between the left parallel short-circuit wire and the right parallel short-circuit wire; Ground each phase conductor at the end of the four-circuit line and synchronously collect the two-phase voltage output of the head-end power supply , and two-phase current , , calculate the two-phase positive sequence short-circuit impedance under the fourth combination mode according to formula (A13): : （A13） In addition, the two phase conductors of the four-circuit line on the left side of the pole tower at the end of the four-circuit line are short-circuited and then grounded through impedance Z. At the same time, the two phase conductors of the two-circuit line on the right side of the pole tower are short-circuited and then grounded through impedance Z. The two-phase voltage output of the head-end power supply is synchronously collected. , and two-phase current , , calculate the two-phase positive sequence series impedance under the fourth combination mode according to formula (A14): : （A14） According to the measured two-phase positive sequence short-circuit impedance under the fourth combination mode and two-phase positive sequence series impedance , calculate the characteristic impedance of the fourth combination according to formulas (A15) and (A16) respectively and the propagation coefficient : （A15） （A16） Where D is the line length; Step E: short-circuit the three-phase conductors of the upper line on the left side of the pole tower at the head end of the four-circuit AC transmission line in parallel with the three-phase conductors of the lower line on the right side, and short-circuit the three-phase conductors of the upper line on the right side of the pole tower with the three-phase conductors of the lower line on the left side in parallel as the fifth combination mode, and apply a two-phase positive sequence power supply between the two groups of short-circuit wires; Ground each phase conductor at the end of the four-circuit line and synchronously collect the two-phase voltage output of the head-end power supply , and two-phase current , , calculate the two-phase positive sequence short-circuit impedance under the fifth combination mode according to formula (A17): : （A17） In addition, the three-phase conductor of the upper line on the left side of the four-circuit line end tower is short-circuited with the three-phase conductor of the lower line on the right side and then grounded through impedance Z. At the same time, the three-phase conductor of the upper line on the right side of the tower is short-circuited with the three-phase conductor of the lower line on the left side and then grounded through impedance Z. The two-phase voltage output of the head-end power supply is synchronously collected. , and two-phase current , , calculate the two-phase positive sequence series impedance under the fifth combination mode according to formula (A18): : （A18） According to the measured two-phase positive sequence short-circuit impedance under the fifth combination mode and two-phase positive sequence series impedance , calculate the characteristic impedance of the fifth combination according to formulas (A19) and (A20) respectively and the propagation coefficient : （A19） （A20） Step F: The characteristic impedances of the five different combinations obtained in steps A to E are and the propagation coefficient Substituting (i=1, 2, 3, 4, 5) into formulas (A21) and (A22) in pairs, we can obtain the equivalent distributed impedance under five different combinations: and equivalent distributed admittance (i=1, 2, 3, 4, 5); ,(i=1,2,3,4,5)(A21) (i=1,2,3,4,5)(A22) Step G: The equivalent distributed impedances of the five different combinations obtained in step F are and equivalent distributed admittance (i=1, 2, 3, 4, 5), and solve equations (A23)-(A27) to obtain the parameters of the four-circuit AC transmission line on the same tower: (1) Resistance per unit length of a single-phase conductor : （A23） (2) Conductivity per unit length of a single-phase conductor to ground : （A24） (3) Resistance per unit length of the earth loop : （A25） (4) Self-inductance of a single-phase conductor per unit length and mutual inductance between each phase conductor: （A26） (5) The capacitance of a single-phase conductor per unit length to ground and the coupling capacitance between each phase conductor: （A27） In formulas (A23)-(A27), Re(·) represents a real number, Im(·) represents an imaginary number, and ω is the angular frequency of the power supply; Where l is the self-inductance of the single-phase conductor; c0 is the capacitance of the single-phase conductor to ground; m h and c h are the coupling inductance and coupling capacitance between the single-phase conductor of one circuit above or below the tower and the single-phase conductor of another circuit on the same horizontal plane; m v and c v are the coupling inductance and coupling capacitance between the single-phase conductor of one circuit above the tower and the single-phase conductor of another circuit below; m d and c d They are respectively the coupling inductance and coupling capacitance between the single-phase conductor of the left-side circuit above the tower and the single-phase conductor of the right-side circuit below (or between the single-phase conductor of the right-side circuit above and the single-phase conductor of the left-side circuit below).

2. The method according to claim 1, characterized in that Obtain the characteristic impedance of the second combination in step B and the propagation coefficient One method of measuring and calculating includes: Connect all the phase conductors at the head end of the four-circuit AC transmission line in parallel as the second combination mode, and apply a single-phase power supply between the head end parallel short-circuit wire and the ground; Ground all phase conductors at the end of the four-circuit line and synchronously collect the single-phase voltage output by the head-end power supply and current , calculate the zero-sequence short-circuit impedance under the second combination mode according to formula (A28) : （A28） In addition, the phase conductors of two of the four circuits at the end are short-circuited and then grounded through impedance Z. At the same time, the phase conductors of the other two circuits at the end are short-circuited and then grounded through impedance Z. The single-phase voltage output by the head-end power supply is collected synchronously. and current , calculate the zero-sequence series impedance under the second combination mode according to formula (A29) : （A29） According to the zero-sequence short-circuit impedance obtained under the second combination mode and zero-sequence series impedance , calculate the characteristic impedance of the second combination according to formulas (A30) and (A31) respectively and the propagation coefficient : （A30） （A31） Where D is the line length.

3. The method according to claim 1, characterized in that Obtain the characteristic impedance of the second combination in step B and the propagation coefficient One method of measuring and calculating includes: Connect all the phase conductors at the head end of the four-circuit AC transmission line in parallel as the second combination mode, and apply a single-phase power supply between the head end parallel short-circuit wire and the ground; Ground all phase conductors at the end of the four-circuit line and synchronously collect the single-phase voltage output by the head-end power supply and current , calculate the zero-sequence short-circuit impedance under the second combination mode according to formula (A32) : （A32） In addition, the three-phase conductors of each circuit at the end of the four circuits are short-circuited and then grounded through impedance Z, and the single-phase voltage output by the head-end power supply is synchronously collected. and current , calculate the zero-sequence series impedance under the second combination mode according to formula (A33) : （A33） According to the zero-sequence short-circuit impedance obtained under the second combination mode and zero-sequence series impedance , calculate the characteristic impedance of the second combination according to formulas (A34) and (A35) respectively and the propagation coefficient : （A34） （A35） Where D is the line length.

4. The method according to claim 1, characterized in that: Obtain the characteristic impedance of the second combination in step B and the propagation coefficient One method of measuring and calculating includes: Connect all the phase conductors at the head end of the four-circuit AC transmission line in parallel as the second combination mode, and apply a single-phase power supply between the head end parallel short-circuit wire and the ground; Ground all phase conductors at the end of the four-circuit line and synchronously collect the single-phase voltage output by the head-end power supply and current , calculate the zero-sequence short-circuit impedance under the second combination mode according to formula (A36) : （A36） In addition, the phase conductors at the end of the four-circuit line are grounded through impedance Z, and the single-phase voltage output by the head-end power supply is synchronously collected. and current , calculate the zero-sequence series impedance under the second combination mode according to formula (A37) : （A37） According to the measured zero-sequence short-circuit impedance under the second combination mode and zero-sequence series impedance , calculate the characteristic impedance of the second combination according to formulas (A38) and (A39) respectively and the propagation coefficient : （A38） （A39） Where D is the line length.

5. The method according to claim 1, characterized in that: Obtain the characteristic impedance of the third combination of four AC transmission lines on the same tower in step C and the propagation coefficient One method of measuring and calculating includes: The phase conductors of the two circuits at the top of the tower are connected in parallel, and the phase conductors of the two circuits at the bottom of the tower are connected in parallel as a third combination mode, and a two-phase positive sequence power supply is applied between the upper parallel short-circuit wire and the lower parallel short-circuit wire; Ground each phase conductor at the end of the four-circuit line and synchronously collect the two-phase voltage output of the head-end power supply , and two-phase current , , calculate the two-phase positive sequence short-circuit impedance under the third combination mode according to formula (A40): : （A40） In addition, the three-phase conductors of each circuit at the end of the four circuits are short-circuited and then grounded through impedance Z, and the two-phase voltage output of the head-end power supply is synchronously collected. , and two-phase current , , calculate the two-phase positive sequence series impedance under the third combination mode according to formula (A41): : （A41） According to the measured two-phase positive sequence short-circuit impedance under the third combination mode and two-phase positive sequence series impedance , calculate the characteristic impedance of the third combination according to formulas (A42) and (A43) respectively and the propagation coefficient : （A42） (A43) Where D is the line length.

6. The method according to claim 1, characterized in that Obtain the characteristic impedance of the third combination of four AC transmission lines on the same tower in step C and the propagation coefficient One method of measuring and calculating includes: Connecting the conductors of each phase of the two circuits at the top of the tower in parallel at the head end of the four-circuit AC transmission line, and connecting the conductors of each phase of the two circuits at the bottom of the tower in parallel, as a third combination mode, and applying a two-phase positive sequence power supply between the upper parallel short-circuit wire and the lower parallel short-circuit wire; Ground each phase conductor at the end of the four-circuit line and synchronously collect the two-phase voltage output of the head-end power supply , and two-phase current , , calculate the two-phase positive sequence short-circuit impedance under the third combination mode according to formula (A44): : （A44） In addition, the phase conductors at the end of the four-circuit line are grounded through impedance Z, and the two-phase voltage output of the head-end power supply is synchronously collected. , and two-phase current , , calculate the two-phase positive sequence series impedance under the third combination mode according to formula (A45): : （A45） According to the measured two-phase positive sequence short-circuit impedance under the third combination mode and two-phase positive sequence series impedance , calculate the characteristic impedance of the third combination according to formulas (A46) and (A47) respectively and the propagation coefficient : （A46） (A47) Where D is the line length.

7. The method according to claim 1, characterized in that Obtain the characteristic impedance of the fourth combination in step D and the propagation coefficient One method of measuring and calculating includes: Connecting the conductors of each phase of the two circuits on the left side of the tower in parallel at the head end of the four-circuit AC transmission line and connecting the conductors of each phase of the two circuits on the right side of the tower in parallel as a fourth combination mode, and applying a two-phase positive sequence power supply between the left parallel short-circuit wire and the right parallel short-circuit wire; Ground each phase conductor at the end of the four-circuit line and synchronously collect the two-phase voltage output of the head-end power supply , and two-phase current , , calculate the two-phase positive sequence short-circuit impedance under the fourth combination mode according to formula (A48): : （A48） In addition, the three-phase conductors of each circuit at the end of the four circuits are short-circuited and then grounded through impedance Z, and the two-phase voltage output of the head-end power supply is synchronously collected. , and two-phase current , , calculate the two-phase positive sequence series impedance under the fourth combination mode according to formula (A49): : （A49） According to the measured two-phase positive sequence short-circuit impedance under the fourth combination mode and two-phase positive sequence series impedance , calculate the characteristic impedance of the fourth combination according to formulas (A50) and (A51) respectively and the propagation coefficient : （A50） (A51) Where D is the line length.

8. The method according to claim 1, characterized in that Obtain the characteristic impedance of the fourth combination in step D and the propagation coefficient One method of measuring and calculating includes: Connecting the conductors of each phase of the two circuits on the left side of the tower in parallel at the head end of the four-circuit AC transmission line and connecting the conductors of each phase of the two circuits on the right side of the tower in parallel as a fourth combination mode, and applying a two-phase positive sequence power supply between the left parallel short-circuit wire and the right parallel short-circuit wire; Ground each phase conductor at the end of the four-circuit line and synchronously collect the two-phase voltage output of the head-end power supply , and two-phase current , , calculate the two-phase positive sequence short-circuit impedance under the fourth combination mode according to formula (A52): : （A52） In addition, the end conductors of each phase of the four-circuit line are grounded through impedance Z, and the two-phase voltage output of the head-end power supply is synchronously collected. , and two-phase current , , calculate the two-phase positive sequence series impedance under the fourth combination mode according to formula (A53): : （A53） According to the measured two-phase positive sequence short-circuit impedance under the fourth combination mode and two-phase positive sequence series impedance , calculate the characteristic impedance of the fourth combination according to formulas (A54) and (A55) respectively and the propagation coefficient : （A54） (A55) Where D is the line length.

9. The method according to claim 1, characterized in that: Obtain the characteristic impedance of the fifth combination in step E and the propagation coefficient One method of measuring and calculating includes: The three-phase conductors of the upper line on the left side of the head end of the four-circuit AC transmission line are short-circuited in parallel with the three-phase conductors of the lower line on the right side, and the three-phase conductors of the upper line on the right side of the tower are short-circuited in parallel with the three-phase conductors of the lower line on the left side as the fifth combination mode, and a two-phase positive sequence power supply is applied between the two sets of short-circuit wires; Ground each phase conductor at the end of the four-circuit line and synchronously collect the two-phase voltage output of the head-end power supply , and two-phase current , , calculate the two-phase positive sequence short-circuit impedance under the fifth combination mode according to formula (A56): : （A56） In addition, the three-phase conductors of each circuit at the end of the four circuits are short-circuited and then grounded through impedance Z, and the two-phase voltage output of the head-end power supply is synchronously collected. , and two-phase current , , calculate the two-phase positive sequence series impedance under the fifth combination mode according to formula (A57): : （A57） According to the measured two-phase positive sequence short-circuit impedance under the fifth combination mode and two-phase positive sequence series impedance , calculate the characteristic impedance of the fifth combination according to formulas (A58) and (A59) respectively and the propagation coefficient : （A58） (A59) Where D is the line length.

10. The method according to claim 1, characterized in that Obtain the characteristic impedance of the fifth combination in step E and the propagation coefficient One method of measuring and calculating includes: The three-phase conductors of the upper line on the left side of the head end of the four-circuit AC transmission line are short-circuited in parallel with the three-phase conductors of the lower line on the right side, and the three-phase conductors of the upper line on the right side of the tower are short-circuited in parallel with the three-phase conductors of the lower line on the left side as the fifth combination mode, and a two-phase positive sequence power supply is applied between the two sets of short-circuit wires; Ground each phase conductor at the end of the four-circuit line and synchronously collect the two-phase voltage output of the head-end power supply , and two-phase current , , calculate the two-phase positive sequence short-circuit impedance under the fifth combination mode according to formula (A60): : （A60） In addition, the phase conductors at the end of the four-circuit line are grounded through impedance Z, and the two-phase voltage output of the head-end power supply is synchronously collected. , and two-phase current , , calculate the two-phase positive sequence series impedance under the fifth combination mode according to formula (A61): : （A61） According to the measured two-phase positive sequence short-circuit impedance under the fifth combination mode and two-phase positive sequence series impedance , calculate the characteristic impedance of the fifth combination according to formulas (A62) and (A63) respectively and the propagation coefficient : （A62） (A63) Where D is the line length.

11. The method according to any one of claims 1 to 10, characterized in that: The method further comprises: Get the complete characteristic impedance of the first combination and the propagation coefficient , the characteristic impedance of the second combination mode and the propagation coefficient , characteristic impedance of the third combination mode and the propagation coefficient , the characteristic impedance of the fourth combination mode and the propagation coefficient , characteristic impedance of the fifth combination and the propagation coefficient Afterwards, various parameters of the four-circuit AC transmission lines on the same tower can be calculated according to step F and step G in claim 1.

12. The method according to any one of claims 1 to 10, characterized in that: The method further comprises: Get the impedance value of the series impedance Z at the measurement frequency ω.

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