Method for measuring and calculating parameters of double-circuit alternating-current transmission line on same tower under high induced voltage

Abstract

The invention discloses a method for measuring and calculating parameters of a same-tower double-circuit alternating-current transmission line under high induced voltage. The method comprises the following steps: dividing the same-tower double-circuit transmission line into three groups of wiring modes; measuring the short-circuit impedance in each wiring mode and the line 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 measurement result of the line through impedance grounding and the line short-circuit impedance measurement result 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 double-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 double-circuit line through the distributed impedance and distributed admittance in each wiring mode and simultaneous equations. Through the method, the induced voltage on the measured circuit can be effectively reduced, and meanwhile accurate measurement can be achieved.

Description

Technical Field

[0001] The invention relates to a branch subject of power system parameter measurement in the field of electrical engineering, and in particular to a method for measuring and calculating parameters of a double-circuit AC transmission line on the same tower under a high induced voltage environment. Background Art

[0002] According to the IEEE std. 1870-2019 "Guide for the parameter measurement of AC transmission lines", when measuring the electrical parameters of a fully transposed and symmetrical double-circuit AC transmission line on the same tower, it is necessary to follow Figure 1 , Figure 2 and Figure 3 The following methods are used to measure: (1) the three-phase positive sequence open-circuit impedance of a single-circuit AC line; (2) the two-phase positive sequence open-circuit impedance of a double-circuit AC line; and (3) the zero-sequence open-circuit impedance of a double-circuit AC line. Then, the following measurement results are combined: (1) the three-phase positive sequence short-circuit impedance of a single-circuit AC line; (2) the two-phase positive sequence short-circuit impedance of a double-circuit AC line; and (3) the zero-sequence short-circuit impedance of a double-circuit AC line, and the calculation method given in IEEE std. 1870-2019 is used to calculate Figure 4 The various self-parameters and coupling parameters of the double-circuit AC line on the same tower are shown.

[0003] However, in actual measurements according to IEEE std. 1870-2019, it was found that: Figure 1 , Figure 2 and Figure 3 When measuring various open-circuit impedances, the power-frequency induced voltage on the measured line is sometimes as high as tens of thousands of volts, which seriously threatens the safety of the measurement personnel and measurement equipment. As a result, the no-load open-circuit impedance cannot be measured, and therefore the line parameters cannot be calculated.

[0004] Ultra-high voltage AC transmission lines are often erected in parallel with double circuits on the same tower, and ultra-high voltage AC lines are preferably erected in parallel with double circuits on the same tower. In order to save land resources, ultra-high (ultra-high) voltage transmission lines are often erected in parallel with other AC and DC transmission lines through the same corridor (channel). In this way, during the parameter measurement of the newly built double-circuit AC lines on the same tower, other AC and DC lines in operation often induce voltages of up to tens of thousands of volts on the measured lines. This induced voltage level has already posed a safety risk to the measurement personnel and measurement equipment. Taking a general measurement power supply as an example, its insulation withstand voltage is usually 1kV-10kV. A power supply with a higher withstand voltage level needs to increase the volume and weight of the power supply several times, and the transportation cost alone increases several times. Summary of the invention

[0005] The content of the present invention is to address the safety issue of high no-load induced voltage on the measured line mentioned above, and proposes a method for measuring and calculating parameters of a double-circuit AC transmission line on the same tower in a high induced voltage environment, which can effectively reduce the induced voltage on the measured line and accurately measure and calculate the parameters of the double-circuit AC transmission line on the same tower in a high induced voltage environment.

[0006] The present invention provides a method for measuring and calculating parameters of a double-circuit AC transmission line on the same tower under high induced voltage, comprising:

[0007] (1) The double-circuit transmission line on the same tower is set to the first circuit combination measurement mode, the second circuit combination measurement mode, and the third circuit combination measurement mode. For each circuit combination measurement mode, the line short-circuit impedance is measured under the condition that the line end is short-circuited and grounded, and the line series impedance is measured under the condition that the line end is grounded through impedance Z under each circuit combination measurement mode;

[0008] (2) Based on the measurement results of the short-circuit impedance of the line under three different circuit combinations and the measurement results of the series impedance of the line when it is grounded through impedance Z, the characteristic impedance and propagation coefficient under each circuit combination are calculated respectively;

[0009] (3) Based on the characteristic impedance and propagation coefficient under three different circuit combinations, the distribution parameters of the double-circuit transmission line on the same tower are calculated.

[0010] In one embodiment, the first circuit combination measurement method of the double-circuit transmission line on the same tower is characterized by selecting one of the circuits and applying a three-phase positive sequence power supply between the three-phase conductors at the head end, and measuring the three-phase positive sequence short-circuit impedance when the three-phase conductors at the end of the line are short-circuited to ground. The three-phase positive sequence series impedance when the three-phase conductors at the end of the line are grounded through impedance Z , and calculate the three-phase positive sequence characteristic impedance of a single-circuit line and propagation coefficient , the specific steps and methods are:

[0011] Step A: Short-circuit and ground the three-phase conductor at the end of one of the double-circuit lines, and apply a three-phase positive-sequence power supply between the three-phase conductors at the head end; 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 formula (1): :

[0012] (1)

[0013] Step B: The three-phase conductors at the end of the same circuit in step A are grounded through impedance Z, and a three-phase positive sequence power supply is applied between the three-phase conductors at the head end; 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 of a single-circuit line according to formula (2): :

[0014] (2)

[0015] Step C: Based on the three-phase positive sequence short-circuit impedance of the single-circuit line obtained in steps A and B And three-phase positive sequence series impedance , calculate the three-phase positive sequence characteristic impedance of a single-circuit line according to formulas (3) and (4): and propagation coefficient :

[0016] (3)

[0017] (4)

[0018] Where D is the length of the line.

[0019] In one embodiment, the second circuit combination measurement method of the double-circuit transmission line on the same tower is characterized by short-circuiting the three-phase conductors of each of the head ends of the double-circuit lines, treating them as a two-phase circuit and applying a two-phase positive sequence power supply at the head end; respectively measuring the two-phase positive sequence short-circuit impedance when the end of the double-circuit line is short-circuited to ground And the two-phase positive sequence series impedance of the line end grounded by impedance Z , and calculate the two-phase positive sequence characteristic impedance under the second circuit combination measurement mode and propagation coefficient In the second circuit combination measurement method, there are two circuit methods for measuring the two-phase positive sequence series impedance with the line end grounded by impedance Z. The corresponding two-phase positive sequence characteristic impedance and propagation coefficient There are two different sets of calculation formulas. The specific steps and methods are:

[0020] Step D: Short-circuit all phase conductors at the end of the double-circuit line to ground, short-circuit the three-phase conductors at the head end of the I-circuit line (also known as the first-circuit line), short-circuit the three-phase conductors at the head end of the II-circuit line (also known as the second-circuit line), and apply a two-phase positive sequence power supply between the head-end double-circuit lines; 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 of the double-circuit line according to formula (5): :

[0021] (5)

[0022] Step E: Short-circuit the three-phase wires at the end of the double-circuit three-phase line and then ground them through impedance Z, short-circuit the three-phase wires at the head end of the I-circuit line and the three-phase wires at the head end of the II-circuit line, and apply a two-phase positive sequence power supply between the double-circuit lines at the head end; synchronously collect the two-phase voltage output of the head end power supply , and two-phase current , , calculate the two-phase positive sequence series impedance of the double-circuit line according to formula (6): :

[0023] (6)

[0024] Step F: Based on the two-phase positive sequence short-circuit impedance of the double-circuit line obtained in step D and step E and two-phase positive sequence series impedance , calculate the two-phase positive sequence characteristic impedance of the double-circuit line according to formulas (7) and (8): and propagation coefficient :

[0025] (7)

[0026] (8)

[0027] Where D is the length of the line.

[0028] Step E1: Replace the above step E to measure the two-phase positive sequence series impedance of the double-circuit line Another method is: ground each phase conductor at the end of the double-circuit line through impedance Z, short-circuit the three-phase conductor at the head end of the first circuit line, short-circuit the three-phase conductor at the head end of the second circuit line, and apply a two-phase positive sequence power supply between the head end double circuit lines; synchronously collect the two-phase voltage output of the head end power supply , and two-phase current , , calculate the two-phase positive sequence series impedance of the double-circuit line according to formula (9): :

[0029] (9)

[0030] Step F1: Based on the two-phase positive sequence short-circuit impedance of the double-circuit line obtained in step D and step E1 and two-phase positive sequence series impedance , calculate the two-phase positive sequence characteristic impedance of the double-circuit line according to formulas (10) and (11): and propagation coefficient :

[0031] (10)

[0032] (11)

[0033] Where D is the length of the line.

[0034] In one embodiment, the third circuit combination measurement method of the double-circuit transmission line on the same tower is characterized by connecting the phase conductors at the head end of the double-circuit line in parallel and applying a single-phase power supply to the ground, and measuring the zero-sequence short-circuit impedance of each phase conductor at the end of the double-circuit line when it is short-circuited to ground. And the zero-sequence series impedance when the line end is grounded through impedance Z , and calculate the zero-sequence characteristic impedance under the third circuit combination measurement mode and propagation coefficient In the third circuit combination measurement method, there are three circuit methods for measuring the zero-sequence series impedance of the line end grounded through impedance Z, and there are three different calculation formulas for the corresponding zero-sequence characteristic impedance and propagation coefficient. The specific steps and methods are:

[0035] Step G: Short-circuit all the phase conductors at the end of the double-circuit line to ground, short-circuit all the phase conductors at the head end of the double-circuit line, and apply a single-phase power supply between the head end of the double-circuit line and the ground; synchronously collect the single-phase voltage output by the head end power supply and current , calculate the zero-sequence short-circuit impedance of the double-circuit line according to formula (12): :

[0036] (12)

[0037] Step H: Short-circuit all the phase conductors at the end of the double-circuit line and then ground them through impedance Z, short-circuit all the phase conductors at the head end of the double-circuit line, and apply a single-phase power supply between the head end of the double-circuit line and the ground; synchronously collect the single-phase voltage output by the head end power supply and current , calculate the zero-sequence series impedance of the double-circuit line according to formula (13): :

[0038] (13)

[0039] Step I: Based on the zero-sequence short-circuit impedance of the double-circuit line obtained in Step G and Step H and zero-sequence series impedance , calculate the zero-sequence characteristic impedance of the double-circuit line according to formulas (14) and (15): and propagation coefficient :

[0040] (14)

[0041] (15)

[0042] Where D is the length of the line.

[0043] Step H1: In place of the above step H, another method for measuring and calculating the zero-sequence series impedance of the double-circuit line is to short-circuit the three-phase wire at the end of the first circuit and then ground it through the impedance Z, short-circuit the three-phase wire at the end of the second circuit and then ground it through the impedance Z, short-circuit all the phase wires at the head end of the double-circuit line, and apply a single-phase power supply between the head end of the double-circuit line and the ground, and synchronously collect the single-phase voltage output by the head end power supply and current , calculate the zero-sequence series impedance of the double-circuit line according to formula (16): :

[0044] (16)

[0045] Step I1, based on the zero-sequence short-circuit impedance of the double-circuit line obtained in step G and step H1 and zero-sequence series impedance , calculate the zero-sequence characteristic impedance of the double-circuit line according to formulas (17) and (18): and propagation coefficient :

[0046] (17)

[0047] (18)

[0048] Where D is the length of the line.

[0049] Step H2: In place of the above step H or step H1, another method for measuring and calculating the zero-sequence series impedance of the double-circuit line is to ground each phase conductor at the end of the double-circuit line through impedance Z, short-circuit all phase conductors at the head end of the double-circuit line, and apply a single-phase power supply between the head end of the double-circuit line and the earth, and synchronously read the single-phase voltage output by the head end power supply. and current , calculate the zero-sequence series impedance of the double-circuit line according to formula (19): :

[0050] (19)

[0051] Step I2, based on the zero-sequence short-circuit impedance of the double-circuit line obtained in step G and step H2 and zero-sequence series impedance , calculate the zero-sequence characteristic impedance of the double-circuit line according to formulas (20) and (21): and propagation coefficient :

[0052] (20)

[0053] (twenty one)

[0054] In one embodiment, the three-phase positive sequence characteristic impedance of the single-circuit line obtained in step C and propagation coefficient ; The two-phase positive sequence characteristic impedance of the double-circuit line obtained in step F or step F1 and propagation coefficient ; The zero-sequence characteristic impedance of the double-circuit line obtained in step I or step I1 or step I2 and propagation coefficient , calculate the various parameters of the double-circuit three-phase line on the same tower according to formulas (22)-(31):

[0055] (1) Three-phase positive sequence impedance per unit length of a single-circuit line and admittance :

[0056] (twenty two)

[0057] (twenty three)

[0058] (2) Two-phase positive sequence impedance per unit length of double-circuit line and admittance :

[0059] (twenty four)

[0060] (25)

[0061] (3) Zero-sequence impedance per unit length of double-circuit line and admittance :

[0062] (26)

[0063] (27)

[0064] (4) Resistance per unit length of single-phase conductor:

[0065] (28)

[0066] (5) Calculate the earth return resistance per unit length:

[0067] (29)

[0068] (6) According to the formula:

[0069] (30)

[0070] Calculate the self-inductance l of a single-phase conductor per unit length and the phase-to-phase mutual inductance of a single-circuit line and the phase-to-phase mutual inductance between double-circuit lines ;

[0071] (7) According to the formula:

[0072] (31)

[0073] Calculate the capacitance of a single-phase conductor per unit length to ground , phase-to-phase coupling capacitance of a single-circuit line And the phase coupling capacitance between double circuit lines .

[0074] In the above formula, Re(•) means taking the real part of the complex number, Im(·) means taking the imaginary part of the complex number, and ω is the angular frequency of the power supply (not the industrial frequency).

[0075] In the above-mentioned method for measuring and calculating parameters of double-circuit AC transmission lines on the same tower under high induced voltage, the beneficial effects are as follows:

[0076] The present invention calculates the self-parameters of each phase conductor per unit length of the double-circuit transmission line on the same tower and the coupling parameters between the phase conductors based on the short-circuit impedance measurement results under different circuit combinations of the double-circuit transmission line on the same tower and the series impedance measurement results when the line end is grounded through impedance Z; the coupling parameters between the double-circuit transmission lines on the same tower at the measurement frequency can be accurately obtained. The various parameters under the test provide an accurate and reliable data source for various calculations of the power system, making the simulation calculation results more accurate. The method of measuring the impedance of the line head end by grounding the end through impedance Z greatly reduces the induced voltage on the measured line, ensuring the safety of the measuring equipment and measuring personnel. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 This is a schematic diagram for measuring the three-phase positive sequence open-circuit impedance of a single-circuit line in IEEE std. 1870-2019;

[0078] Figure 2 This is a schematic diagram for measuring the two-phase positive sequence open-circuit impedance of a double-circuit line in IEEE std. 1870-2019;

[0079] Figure 3 This is a schematic diagram for measuring the zero-sequence open-circuit impedance of a double-circuit line in IEEE std. 1870-2019;

[0080] Figure 4It is a schematic diagram of the phase-to-phase coupling parameters within a single-circuit line and the coupling parameters between double-circuit lines of a double-circuit line;

[0081] Figure 5 It is a single-conductor earth loop circuit diagram with distributed parameters;

[0082] Figure 6 It is a schematic diagram of a three-phase positive sequence short-circuit impedance measurement circuit for a single-circuit line;

[0083] Figure 7 It is a circuit diagram for obtaining the three-phase positive sequence series impedance when the three-phase conductors at the end of a single-circuit line are grounded via impedance Z respectively;

[0084] Figure 8 It is a schematic diagram of a two-phase positive sequence short-circuit impedance measurement circuit for a double-circuit line;

[0085] Fig. 9 It is a circuit diagram for obtaining the two-phase positive sequence series impedance of a double-circuit line when the three-phase conductors at the ends of the double-circuit line are short-circuited and then grounded via impedance Z respectively;

[0086] Fig.10 It is a schematic diagram of the zero-sequence short-circuit impedance measurement circuit of a double-circuit line;

[0087] Fig.11 It is a circuit diagram for obtaining the zero-sequence series impedance of a double-circuit line when the end phase conductors are short-circuited and then grounded via impedance Z;

[0088] Fig.12 It is a circuit for obtaining the positive sequence series impedance of two phases of a double-circuit line when each phase conductor at the end of the double-circuit line is grounded via impedance Z.

[0089] Fig.13 It is a circuit for measuring the zero-sequence series impedance of a double-circuit line when the three phases at the ends of the double-circuit line are short-circuited and then grounded via impedance Z.

[0090] Fig.14 It is a circuit for measuring the zero-sequence series impedance of a double-circuit line when each phase conductor at the end of the double-circuit line is grounded via impedance Z. DETAILED DESCRIPTION

[0091] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the technical principle of the present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0092] In general, the parameter measurement and calculation method of the double-circuit transmission line on the same tower under a high induced voltage environment provided by the present invention is the result of further improvement on the existing measurement and calculation method. It is characterized in that the characteristic impedance and propagation coefficient under each mode are calculated through the measurement results of the short-circuit impedance of the double-circuit line and the series impedance when the line end is grounded through impedance Z in the following three circuit combinations, and then the distributed impedance and distributed admittance under each mode are calculated; and then the self parameters of each phase conductor and the coupling parameters between each phase conductor are calculated in the form of a set of simultaneous equations through the distributed impedance and distributed admittance under the three groups of circuit combinations. The three combinations are: (1) measurement of the three-phase positive-sequence short-circuit impedance of the single-circuit line and the three-phase positive-sequence series impedance grounded through impedance Z at the line end; (2) measurement of the two-phase positive-sequence short-circuit impedance between the double-circuit lines and the two-phase positive-sequence series impedance grounded through impedance Z at the line end; (3) measurement of the zero-sequence short-circuit impedance of the double-circuit line and the zero-sequence series impedance after the line end is grounded through impedance Z. At the same time, after the line end is grounded through impedance Z, the induced voltage of the measured line can be effectively suppressed to ensure the safety of the measurement personnel and measurement equipment.

[0093] In order to understand this method clearly, we first review the parameter measurement method and calculation process of the single-conductor line.

[0094] 1. Measurement and calculation process of distributed parameters of a single conductor:

[0095] Single-conductor earth loop circuit with distributed parameters Figure 5 Assume the impedance of a single conductor is (where r is the distributed resistance of the wire, r g is the distributed resistance of the earth loop, l is the distributed inductance of the conductor, is the angular frequency used for measurement, j represents the imaginary part of the complex number), the admittance to ground is (where g is the distributed conductance of the wire to ground, is the distributed capacitance of the conductor to the ground), then the voltage and current differential equations of the line are:

[0096] (1-1)

[0097] (1-2)

[0098] The corresponding homogeneous equation is:

[0099] (1-3)

[0100] (1-4)

[0101] According to the current and voltage constraints at both ends of the line, the two-port network equation of the line described by the homogeneous equation is finally obtained as follows:

[0102] (1-5)

[0103] Among them, z c is the characteristic impedance of the line, is the propagation coefficient of the line, and D is the length of the line.

[0104] (1-6)

[0105] (1-7)

[0106] The two-port network described by equation (1-5) is short-circuited to ground at the end of the line ( ), the short-circuit impedance Z at the head end of the line S for:

[0107] (1-8)

[0108] If the line end is grounded via impedance Z, the line end voltage and current satisfy the following relationship:

[0109] (1-9)

[0110] At this time, the voltage and current signals measured after applying power to the first end are:

[0111] (1-10)

[0112] (1-11)

[0113] The series impedance measured at the beginning of the line is:

[0114] (1-13)

[0115] Substituting the short-circuit impedance expression (1-8) into equation (1-13), we have:

[0116] (1-14)

[0117] Therefore the characteristic impedance of the line is:

[0118] (1-15)

[0119] Propagation coefficient of the line :

[0120] (1-16)

[0121] Then, the distribution parameters of the line can be calculated:

[0122] (1-17)

[0123] (1-18)

[0124] (II) Differential equations for double-circuit three-phase lines on the same tower:

[0125] Since the double-circuit three-phase AC lines on the same tower have been fully transposed, the self-parameters of each phase conductor and the mutual parameters between each phase conductor are the same. Figure 4 , let r be the resistance of the single-phase conductor, l be the self-inductance of the single-phase conductor, is the capacitance of a single-phase conductor to ground, It is the coupling capacitance between the phase conductors of a single-circuit line. It is the coupling inductance between the phase conductors of a single-circuit line. Figure 4 , assuming that the coupling capacitance of the single-phase conductor of one circuit to each single-phase conductor of the other circuit is ; Assume that the coupling inductances between the single-phase conductors of one circuit and the single-phase conductors of the other circuit are .

[0126] Based on the above assumptions, the differential equations of the phase conductors of the double-circuit transmission line can be written. The voltage differential equation of the phase conductors of the double-circuit line is as follows:

[0127] (2-1)

[0128] (2-2)

[0129] (2-3)

[0130] (2-4)

[0131] (2-5)

[0132] (2-6)

[0133] The current differential equation of each phase conductor of a double-circuit line is as follows:

[0134] (2-7)

[0135]

[0136] (2-8)

[0137]

[0138] (2-9)

[0139] (2-10)

[0140]

[0141] (2-11)

[0142]

[0143] (2-12)

[0144] The above current and voltage differential equations can be simplified into the following matrix form:

[0145] or (2-13)

[0146] or (2-14)

[0147] in , are the voltage and current vectors of the I-th circuit respectively, and are the voltage and current vectors of the II-circuit circuit respectively, is the self-impedance matrix of a single-circuit three-phase line, is the mutual impedance matrix between double-circuit three-phase lines, is the self-admittance matrix of a single-loop three-phase line, is the mutual admittance matrix between the double-circuit three-phase lines, which are recorded as:

[0148] , , , (2-15)

[0149] , (2-16)

[0150] , (2-17)

[0151] In a three-phase power system, the abc three-phase voltage or current phasor can be decomposed into positive sequence, negative sequence and zero sequence (120) symmetrical sequence components. , are the three-phase current and voltage vectors, , are the 120-sequence component current and voltage vectors, T is the transformation matrix, which are recorded as:

[0152] , , , , , (2-18)

[0153] Then we have:

[0154] , , , (2-19)

[0155] Substituting the above transformation relationship into equations (2-13) and (2-14), we have:

[0156]

[0157] (2-20)

[0158] (2-21)

[0159]

[0160] (2-22)

[0161]

[0162] (2-23)

[0163] Among them, the 120-sequence components of the voltage and current of the I-circuit line and the II-circuit line are:

[0164] , , , (2-24)

[0165] It is the 120-sequence component self-impedance matrix of a single-circuit three-phase line:

[0166] (2-25)

[0167] is the 120-sequence component mutual impedance matrix between double-circuit lines:

[0168] (2-26)

[0169] is the 120-sequence component self-admittance matrix of the three-phase conductor:

[0170] (2-27)

[0171] is the 120-sequence mutual admittance matrix between the double-circuit line conductors:

[0172] (2-28)

[0173] By observing the 120th order impedance matrix (2-25) (2-26) and the 120th order admittance matrix (2-27) (2-28), it can be found that the expressions of the positive sequence component and the negative sequence component are the same. Therefore, it is only necessary to study the differential propagation equations under the positive sequence component and the zero sequence component.

[0174] Positive sequence voltage equation for double-circuit line:

[0175] (2-29)

[0176] (2-30)

[0177] Zero-sequence voltage equation for double-circuit lines:

[0178] (2-31)

[0179] (2-32)

[0180] Positive sequence current equation for double-circuit line:

[0181] (2-33)

[0182] (2-34)

[0183] Zero-sequence current equation for double-circuit lines:

[0184] (2-35)

[0185] (2-36)

[0186] (III) Measurement of positive sequence series impedance and short-circuit impedance of single-loop three-phase line (first circuit combination method):

[0187] First, we examine the positive sequence component differential equation of a single-circuit line. Since the positive sequence equation and its impedance and admittance of the first and second circuits are the same, we only rewrite the positive sequence differential equation of the first circuit as follows:

[0188] (3-1)

[0189] (3-2)

[0190] Formulas (3-1) and (3-2) are similar to the differential equations (1-1) and (1-2) of the single-conductor line, so the single-circuit three-phase positive sequence parameters can be measured and calculated by referring to the measurement and solution method of the single-conductor parameters. The specific measurement method is:

[0191] One of the double-circuit AC lines on the same tower is selected as the measurement object, and a three-phase positive-sequence power supply is applied between the three-phase conductors at the head end of the selected single-circuit three-phase AC transmission line to measure relevant parameters. This method is called the first circuit combination method.

[0192] Reference Figure 6 , short-circuit the three-phase conductor at the end of one of the circuits to ground, apply a three-phase positive sequence power supply between the three-phase conductors at 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: :

[0193] (3-3)

[0194] Reference Figure 7 , the three-phase conductors at the end of the same circuit are grounded through impedance Z, and a three-phase positive sequence power supply is applied between the three-phase conductors at the head end, 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 of a single-circuit line according to the following formula: :

[0195] (3-4)

[0196] Calculation of three-phase positive sequence characteristic impedance of single-circuit line and the propagation coefficient :

[0197] (3-5)

[0198] (3-6)

[0199] Calculate the three-phase positive sequence impedance per unit length of a single-circuit line and admittance :

[0200] (3-7)

[0201] (3-8)

[0202] (IV) Calculation method of two-phase system and its sequence components:

[0203] For ease of analysis, the first and second circuits can be regarded as two-phase systems respectively: that is, the three-phase wires at the first end of the first circuit are connected in parallel and regarded as one phase circuit; the three-phase wires at the first end of the second circuit are connected in parallel and regarded as one phase circuit.

[0204] Here we first introduce the two-phase system and its symmetrical sequence component decomposition method. The electrical parameters of the two-phase system can also be decomposed into two-phase positive sequence and zero sequence components. , are the voltage and current vectors on the I and II circuits respectively. and are the sequence component voltage and current vectors of the two-phase system respectively, and P is the transformation matrix, which are recorded as:

[0205] , , , , , (4-1)

[0206] Then we have:

[0207] , , , (4-2)

[0208] Considering the differential equations (2-31), (2-32), (2-35), (2-36), the zero-sequence differential equation of the double-circuit line can be rewritten as follows:

[0209] or (4-3)

[0210] or (4-4)

[0211] in:

[0212] , (4-5)

[0213] The above matrix equations (4-3)-(4-5) are regarded as the equation description of the two-phase system. They can be transformed into the following matrix equations of the zero-sequence and positive-sequence components of the two-phase system through the transformation method of the two-phase system:

[0214] (4-6)

[0215] (4-7)

[0216] in:

[0217] (4-8)

[0218] (4-9)

[0219] (V) Measurement of two-phase positive sequence series impedance and short-circuit impedance of double-circuit lines (second circuit combination):

[0220] According to formulas (4-6)-(4-7), the two-phase positive sequence equation of the double-circuit line is rewritten as follows:

[0221] (5-1)

[0222] (5-2)

[0223] Formulas (5-1) and (5-2) are the same as formulas (1-1) and (1-2) in mathematical form, and are referred to here as the telegraph equations of the two-phase positive sequence system. In circuit form, the three-phase conductors at the head end of the I-loop line are connected in parallel, the three-phase conductors at the head end of the II-loop line are connected in parallel, and a two-phase positive sequence voltage is applied between the head end of the I-loop and the II-loop lines. The impedance per unit length in the two-phase positive sequence system is and admittance They are:

[0224] (5-3)

[0225] (5-4)

[0226] Therefore, the two-phase positive-sequence short-circuit impedance of the two-phase system and the two-phase positive-sequence series impedance after the line end is grounded through impedance Z can be measured by referring to the single-conductor earth loop method.

[0227] To this end, the three-phase conductors at the head end of the I circuit are connected in parallel, the three-phase conductors at the head end of the II circuit are connected in parallel, the double circuit is regarded as a two-phase circuit, and a two-phase positive sequence power supply is applied between the double circuits to measure the relevant parameters. This circuit combination method is called the second circuit combination method.

[0228] Reference Figure 8 , short-circuit all phase conductors at the end of the double-circuit line to ground, short-circuit the three-phase conductors at the head end of the first circuit, short-circuit the three-phase conductors at the head end of the second circuit, and apply two-phase positive sequence power between the double-circuit lines at the head end; 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 between double-circuit lines according to the following formula: :

[0229] (5-5)

[0230] Reference Fig. 9 , short-circuit the three-phase wires at the ends of the double-circuit lines and then ground them through impedance Z respectively, short-circuit the three-phase wires at the head end of the I-circuit line and the three-phase wires at the head end of the II-circuit line, and apply a two-phase positive sequence power supply between the double-circuit lines at the head end; synchronously collect the two-phase voltage output of the head end power supply , and two-phase current , , calculate the two-phase positive sequence series impedance between double-circuit lines according to the following formula: :

[0231] (5-6)

[0232] Calculation of Two-Phase Positive Sequence Characteristic Impedance of Double-Circuit Transmission Line and propagation coefficient :

[0233] (5-7)

[0234] (5-8)

[0235] Calculation of two-phase positive sequence impedance per unit length of double-circuit transmission line and admittance :

[0236] (5-9)

[0237] (5-10)

[0238] (VI) Measurement of two-phase zero-sequence series impedance and two-phase zero-sequence short-circuit impedance of double-circuit lines (third combination circuit method):

[0239] According to equations (4-6)-(4-7), the zero-sequence equation of the double-circuit line is rewritten as follows:

[0240] (6-1)

[0241] (6-2)

[0242] The mathematical form of formula (6-1) and (6-2) is similar to that of formula (1-1) and (1-2). It is called the two-phase zero-sequence telegraph equation for double-circuit lines. Its zero-sequence impedance per unit length is and zero-sequence admittance They are:

[0243] (6-3)

[0244] (6-4)

[0245] That is, when the zero-sequence voltages along the two circuits are the same, , and the current is equal Therefore, the zero-sequence series impedance and zero-sequence short-circuit impedance of the double-circuit line under this condition can be measured.

[0246] To this end, the phase conductors at the head end of the double-circuit line are connected in parallel, and a single-phase power supply is applied between the head end of the double-circuit line and the earth to measure relevant parameters. This circuit combination method is called the third circuit combination method.

[0247] Reference Fig.10 , short-circuit all phase conductors at the end of the double-circuit line to ground, short-circuit all phase conductors at the head end of the double-circuit line, and apply single-phase power between the head end of the double-circuit line and the ground; synchronously collect the single-phase voltage output by the head end power supply and current , calculate the zero-sequence short-circuit impedance of the double-circuit line according to the following formula: :

[0248] ; (6-5)

[0249] Reference Fig.11 , short-circuit all the phase conductors at the end of the double-circuit line and then ground them through impedance Z, short-circuit all the phase conductors at the head end of the double-circuit line, and apply a single-phase power supply between the head end of the double-circuit line and the ground, and synchronously collect the single-phase voltage output by the head end power supply and current , calculate the zero-sequence series impedance of the double-circuit line according to the following formula: :

[0250] (6-6)

[0251] Calculate the zero-sequence characteristic impedance and propagation coefficient of double-circuit lines:

[0252] (6-7)

[0253] (6-8)

[0254] Calculation of zero-sequence impedance per unit length of double-circuit transmission lines and zero-sequence admittance :

[0255] (6-9)

[0256] (6-10)

[0257] (VII) Calculation of various distribution parameters of double-circuit lines:

[0258] When measuring and obtaining the three-phase positive sequence characteristic impedance of a single-circuit line in a double-circuit line and the propagation coefficient , the two-phase positive sequence characteristic impedance of the double-circuit line and the propagation coefficient , and the zero-sequence characteristic impedance of the double-circuit line and the propagation coefficient After that, the following calculation process and method can be used to obtain Figure 4 The distribution parameters of .

[0259] Calculate the resistance per unit length of a single-phase conductor :

[0260] (7-1)

[0261] Calculate the earth return resistance per unit length :

[0262] (7-2)

[0263] According to the formula:

[0264] (7-3)

[0265] Calculate the self-inductance l of a single-phase conductor per unit length and the mutual inductance of the phase conductors of a single-circuit line and the mutual inductance of the phase conductors between double-circuit lines ;

[0266] According to the formula:

[0267] (7-4)

[0268] Calculate the capacitance of a single-phase conductor per unit length to ground , the phase-to-phase conductor coupling capacitance of a single-circuit line And the phase-to-phase conductor coupling capacitance between double-circuit lines .

[0269] In formulas (7-1) to (7-4), Re(•) represents the real part, Im(·) represents the imaginary part, and ω is the angular frequency of the power supply.

[0270] (VIII) Measures to further reduce the power frequency induced residual voltage of the line:

[0271] (1) Reference Fig. 9 Measuring two-phase positive sequence series impedance by When the power frequency residual induced voltage at the end of the line is ( is the zero sequence current of the single-phase conductor). For this purpose, refer to Fig.12 The two-phase positive sequence series impedance is measured by this method, which can reduce the residual power frequency induced voltage at the end of the line to .exist Fig.12 In the wiring mode, the two-phase voltage of the power supply output is synchronously collected , and two-phase current , , calculate the zero-sequence series impedance:

[0272] (8-1)

[0273] However, in this way, the two-phase positive sequence characteristic impedance The sum of the propagation coefficients The calculation formula should be:

[0274] (8-2)

[0275] (8-3)

[0276] (2) According to Fig.11 Measuring the zero-sequence series impedance of double-circuit lines by When the residual induced voltage at the end of the line is ( The residual voltage is the zero-sequence current of the single-phase conductor), which may still exceed the safe allowable range. One way to reduce the residual voltage during measurement is to follow Fig.13 In this way, the three phases of each single-circuit line at the end of the double-circuit line are short-circuited and then grounded through impedance Z. At this time, the residual induced voltage at the end of the line can be reduced to When measuring, connect the phase conductors of the double-circuit line at the head end in parallel, apply a single-phase power supply between the head end and the earth, and synchronously collect the single-phase voltage output by the head end power supply. and current , calculate the zero-sequence series impedance :

[0277] (8-4)

[0278] Its corresponding zero-sequence characteristic impedance and the propagation coefficient The calculation formula should be changed to the following formula:

[0279] (8-5)

[0280] (8-6)

[0281] (3) If referring to Fig.14 The circuit shown measures the zero-sequence series impedance of a double-circuit line. When the residual induction voltage can be further reduced to The specific method is to ground each phase conductor at the end of the double-circuit line on the same tower through impedance Z, connect each phase conductor of the double-circuit line at the head end in parallel and apply a single-phase power supply to the ground, and synchronously collect the single-phase voltage output by the head end power supply and current , calculate the zero-sequence series impedance :

[0282] (8-7)

[0283] The corresponding zero-sequence characteristic impedance and the propagation coefficient The calculation formula should be changed to the following formula:

[0284] (8-8)

[0285] (8-9)

[0286] The above measurement method is strictly derived from the basic circuit theory. The series impedance Z is measured at the beginning of the line by connecting it in series at the end of the line, and the corresponding characteristic impedance and transfer coefficient of the line are calculated by pairing it with the corresponding short-circuit impedance. Finally, the various parameters of the line are calculated by the characteristic impedance and transfer coefficient. After the end of the line is grounded through the series impedance Z, the no-load induced voltage of the line can be reduced to a safe range, thereby ensuring the safety of the measurement personnel and measurement equipment.

Claims

1. A method for measuring and calculating parameters of a double-circuit AC transmission line on the same tower under high induced voltage, characterized in that: The method comprises: Step A: Select one of the circuits and apply three-phase positive sequence power between the three-phase conductors at the head end of the single circuit; 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 power supply at the head end is synchronously collected. and three-phase current , calculate the three-phase positive sequence short-circuit impedance of a single-circuit line according to formula (1): : （1） 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 of a single-circuit line according to formula (2): : （2） Step B: Based on the three-phase positive sequence short-circuit impedance of the single-circuit line obtained in step A And three-phase positive sequence series impedance , calculate the three-phase positive sequence characteristic impedance of a single-circuit line according to formulas (3) and (4): and propagation coefficient : (3) （4） Where D is the length of the line; Step C: connect the three-phase conductors at the head end of the first circuit in parallel, connect the three-phase conductors at the head end of the second circuit in parallel, regard the double circuit as a two-phase circuit, and apply a two-phase positive sequence power supply between the double circuits at the head end; Short-circuit each phase conductor at the end of the double-circuit line to ground, and synchronously collect the two-phase voltage output of the power supply at the head end , and two-phase current , , calculate the two-phase positive sequence short-circuit impedance of the double-circuit line according to formula (5): : （5） In addition, the three-phase wires at the end of the first circuit are short-circuited and then grounded through impedance Z. The three-phase wires at the end of the second circuit are short-circuited and then grounded through impedance Z. The two-phase voltage output of the head-end power supply is collected synchronously. , and two-phase current , , calculate the two-phase positive sequence series impedance of the double-circuit line according to formula (6): : （6） Step D: Based on the two-phase positive sequence short-circuit impedance of the double-circuit line obtained in step C and two-phase positive sequence series impedance , calculate the two-phase positive sequence characteristic impedance of the double-circuit line according to formulas (7) and (8): and propagation coefficient : (7) （8） Where D is the length of the line; Step E, connecting the phase conductors at the head end of the double-circuit line in parallel and applying a single-phase power supply to the ground; Short-circuit all phase conductors at the end of the double-circuit line to ground, and synchronously collect the single-phase voltage output by the head-end power supply and current , calculate the zero-sequence short-circuit impedance of the double-circuit line according to formula (9): : （9） In addition, all phase conductors at the end of the double-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 of the double-circuit line according to formula (10): : （10） Step F: Based on the zero-sequence short-circuit impedance of the double-circuit line obtained in step E and zero-sequence series impedance , calculate the zero-sequence characteristic impedance of the double-circuit line according to formulas (11) and (12): and propagation coefficient : (11) （12） Where D is the length of the line; Step G: Calculate the three-phase positive sequence characteristic impedance of the single-circuit line according to the above steps B, D, and F and propagation coefficient , double-circuit line two-phase positive sequence characteristic impedance and propagation coefficient , zero-sequence characteristic impedance of double-circuit line and propagation coefficient , according to formulas (13)-(22), the self-parameters of each single-phase conductor of the double-circuit three-phase line on the same tower and the coupling parameters between each phase conductor are calculated step by step: (1) Calculate the three-phase positive sequence impedance per unit length of a single-circuit line and admittance : （13） (14) (2) Calculate the two-phase positive sequence impedance per unit length of a double-circuit line and admittance : （15） （16） (3) Calculation of zero-sequence impedance per unit length of double-circuit lines and admittance : (17) (18) (4) Calculate the resistance per unit length of a single-phase conductor : (19) (5) Calculate the earth return resistance per unit length : (20) (6) According to the formula: （21） Calculate the self-inductance l of a single-phase conductor per unit length and the mutual inductance between the phase conductors of a single-circuit line And the mutual inductance between the phase conductors of the double-circuit line ; (7) According to the formula: （22） Calculate the capacitance of a single-phase conductor per unit length to ground , coupling capacitance between each phase conductor of a single circuit line And the coupling capacitance between the phase conductors of the double-circuit line ; Wherein, Re(·) in formulas (19)-(22) represents the real part of the complex number, Im(·) represents the imaginary part of the complex number, and ω is the angular frequency of the power supply.

2. The method according to claim 1, characterized in that: The method comprises: The following method can be used to replace the measurement and calculation of the two-phase positive sequence characteristic impedance in step C and step D: and propagation coefficient Method: Step C1: connect the three-phase conductors at the head end of the first circuit in parallel, connect the three-phase conductors at the head end of the second circuit in parallel, regard the double circuit as a two-phase circuit, and apply a two-phase positive sequence power supply between the double circuits at the head end; Short-circuit each phase conductor at the end of the double-circuit line to ground, and synchronously collect the two-phase voltage output of the power supply at the head end , and two-phase current , , calculate the two-phase positive sequence short-circuit impedance of the double-circuit line according to formula (23): : （23） In addition, the two-phase conductors at the end of the double-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 of the double-circuit line according to formula (24): : （24） Step D1: The two-phase positive sequence short-circuit impedance of the double-circuit line obtained in step C1 and two-phase positive sequence series impedance , calculate the two-phase positive sequence characteristic impedance of the double-circuit line according to formulas (25) and (26): and propagation coefficient : （25） （26） Where D is the length of the line.

3. The method according to claim 1, characterized in that The method comprises: The following method can be used to replace the measurement and calculation of the zero-sequence characteristic impedance of the double-circuit line in step E and step F: and propagation coefficient Method: Step E1: connect the phase conductors at the head end of the double-circuit line in parallel and apply a single-phase power supply to the ground; Short-circuit all phase conductors at the end of the double-circuit line to ground, and synchronously collect the single-phase voltage output by the head-end power supply and current , calculate the zero-sequence short-circuit impedance of the double-circuit line according to formula (27): : （27） In addition, the three-phase wire at the end of the first circuit is short-circuited and then grounded through impedance Z. The three-phase wire at the end of the second circuit is short-circuited and then grounded through impedance Z. The single-phase voltage output of the head-end power supply is collected synchronously. and current , calculate the zero-sequence series impedance of the double-circuit line according to formula (28): : （28） Step F1: Based on the zero-sequence short-circuit impedance of the double-circuit line obtained in step E1 and zero-sequence series impedance , calculate the zero-sequence characteristic impedance of the double-circuit line according to formulas (29) and (30): and propagation coefficient : （29） （30） Where D is the length of the line.

4. The method according to claim 1, characterized in that The method comprises: The following method can be used to replace the measurement and calculation of the zero-sequence characteristic impedance of the double-circuit line in step E and step F: and propagation coefficient Method: Step E2: connect the phase conductors at the head end of the double-circuit line in parallel and apply a single-phase power supply to the ground; Short-circuit all phase conductors at the end of the double-circuit line to ground, and synchronously collect the single-phase voltage output by the head-end power supply and current , calculate the zero-sequence short-circuit impedance of the double-circuit line according to formula (31): : （31） In addition, the phase conductors at the end of the double-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 of the double-circuit line according to formula (32): : （32） Step F2: based on the zero-sequence short-circuit impedance of the double-circuit line obtained in step E2 and zero-sequence series impedance , calculate the zero-sequence characteristic impedance of the double-circuit line according to formulas (33) and (34): and propagation coefficient : （33） （34） Where D is the length of the line.

5. The method according to any one of claims 1 to 4, characterized in that: The method further comprises: Obtain the complete three-phase positive sequence characteristic impedance of a single-circuit line and propagation coefficient , double-circuit line two-phase positive sequence characteristic impedance and propagation coefficient , zero-sequence characteristic impedance of double-circuit line and propagation coefficient After that, the self-parameters of each phase conductor and the coupling parameters between each phase conductor of the double-circuit three-phase line on the same tower can be calculated step by step according to formulas (13)-(22).

6. The method according to any one of claims 1 to 4, 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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