CN104953563A - Double-circuit non-homonymous phase overline grounding fault relay protection method based on perceptual pressure drop progressive decreasing characteristics - Google Patents

Double-circuit non-homonymous phase overline grounding fault relay protection method based on perceptual pressure drop progressive decreasing characteristics Download PDF

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CN104953563A
CN104953563A CN201510336610.3A CN201510336610A CN104953563A CN 104953563 A CN104953563 A CN 104953563A CN 201510336610 A CN201510336610 A CN 201510336610A CN 104953563 A CN104953563 A CN 104953563A
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mrow
msub
mover
mfrac
centerdot
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曾惠敏
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State Grid Corp of China SGCC
State Grid Fujian Electric Power Co Ltd
Maintenance Branch of State Grid Fujian Electric Power Co Ltd
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State Grid Corp of China SGCC
State Grid Fujian Electric Power Co Ltd
Maintenance Branch of State Grid Fujian Electric Power Co Ltd
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Abstract

The invention discloses a double-circuit non-homonymous phase overline grounding fault relay protection method based on perceptual pressure drop progressive decreasing characteristics. According to the method, zero sequence compensating current of a first circuit of double same-pole parallel circuits is calculated; the voltage drop virtual part from a non-homonymous phase overline grounding fault point to the protection installing part of the first circuit of the double same-pole parallel circuits is calculated; the voltage drop virtual part and the like from the protection adjusting range part to the protection installing part of the first circuit of the double same-pole parallel circuits are calculated; then, the voltage drop virtual part from the non-homonymous phase overline grounding fault point to the protection installing part of the first circuit of the double same-pole parallel circuits and the voltage drop virtual part from the protection adjusting range part to the protection installing part of the first circuit of the double same-pole parallel circuits are used for forming the double-circuit non-homonymous phase overline grounding fault single-end electric quantity relay protection criterion; the influence of the interline zero sequence mutual inductance, transition resistance and load current on the protection action performance is eliminated, and strong anti-transition-resistance capability and strong load-current-influence capability are realized.

Description

Double-circuit non-same-name-phase overline ground fault relay protection method based on inductive voltage drop degressive characteristic
Technical Field
The invention relates to the technical field of relay protection of power systems, in particular to a relay protection method for non-same-name-phase overline ground faults of double-circuit lines based on inductive voltage drop degressive characteristics.
Background
The double-circuit line on the same tower has the advantages of small occupied area, low manufacturing cost and stable and reliable operation of connecting a power grid, and becomes a common power transmission line connecting mode of a power system. Zero sequence mutual inductance exists between double-circuit lines on the same tower, the zero sequence mutual inductance influences a zero sequence compensation coefficient, additional impedance is further generated, the additional impedance caused by the zero sequence mutual inductance can cause the fault impedance measured by a protection device to be larger than the actual fault impedance, and when ground fault occurs at a position close to a protection setting range in a protection area of the double-circuit lines on the same tower, misoperation occurs in protection, and safety and stability operation of a power grid are not facilitated.
Even if the double-circuit line on the same tower is directly grounded through a tower, the transition resistance is near 10 omega in the area with lower soil resistivity; the transition resistance may reach 30 omega, or even higher, where the resistivity is higher. The transition resistance is not zero so that the fault impedance calculated by the protection device comprises an additional impedance generated by the transition resistance in addition to a fault impedance component reflecting the real fault distance. The additional impedance generated by the transition resistance is resistive-inductive or resistive-capacitive, which easily causes the earth impedance distance protection to reject or exceed a steady state. Protection malfunction or failure brings great loss to the safe operation of the power system, and even possibly threatens the stability of the power system.
The boundary of an action characteristic circle of the existing double-circuit line grounding distance protection on the same tower passes through the origin of coordinates, the origin of coordinates is positioned on the boundary of the action characteristic circle, dead zones exist in the protection process of protecting the forward outlet grounding fault, and the dead zones of the forward outlet are protected to be larger along with the increase of transition resistance and load current. Because the origin of coordinates is located on the boundary of the action characteristic circle, the protection of the ground fault of the reverse direction outlet has the possibility of false operation, and the larger the transition resistance is, the more the protection is easy to false operation when the ground fault of the reverse direction outlet is protected.
Because strong zero sequence mutual inductance exists between the double-circuit lines on the same tower, the existing grounding distance protection cannot acquire the zero sequence current of the other circuit line, the influence of the zero sequence mutual inductance between the lines cannot be eliminated in an algorithm model, and the influence of the zero sequence mutual inductance between the lines is received.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a relay protection method for the non-same-name-phase overline ground fault of a double-circuit line based on inductive voltage drop degressive characteristic, which utilizes the voltage drop imaginary part from a non-same-name-phase overline ground fault point to the protection installation position of the I-circuit line of the double-circuit line on the same tower and the voltage drop imaginary part from the protection setting range to the protection installation position of the I-circuit line of the double-circuit line on the same tower to form a single-end zero-sequence electrical quantity relay protection criterion, eliminates the influence of the mutual inductance between lines, the transition resistance and the load current on the protection action performance and has strong capacity of resisting the influence of the transition resistance and the load current.
In order to achieve the purpose, the invention adopts the following technical scheme:
the relay protection method for the non-same-name-phase overline ground fault of the double-circuit line based on the inductive voltage drop degressive characteristic is characterized by comprising the following steps in sequence:
(1) the protection device measures the fault phase voltage at the protection installation position of the I-loop circuit of the double-loop circuit on the same towerFault phase currentAnd zero sequence currentWherein phi is an I loop circuit A phase, an I loop circuit B phase and an I loop circuit C phase;
(2) the protection device calculates the zero sequence current phase angle alpha of the II-loop circuit of the double-loop circuit on the same tower as r1+r2-π-β;
Wherein, <math> <mrow> <msub> <mi>r</mi> <mn>1</mn> </msub> <mo>=</mo> <msup> <mi>sin</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>a</mi> <mn>3</mn> </msub> <msub> <mi>b</mi> <mn>1</mn> </msub> </mrow> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>3</mn> </msub> <msub> <mi>b</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <msub> <mi>b</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mfrac> <mo>)</mo> </mrow> <mo>;</mo> <msub> <mi>r</mi> <mn>2</mn> </msub> <mo>=</mo> <msup> <mi>sin</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <msub> <mi>b</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> <msub> <mi>b</mi> <mn>1</mn> </msub> </mrow> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>3</mn> </msub> <msub> <mi>b</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <msub> <mi>b</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mfrac> <mo>)</mo> </mrow> <mo>;</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>=</mo> <mi>Re</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>&phi;</mi> </mrow> </msub> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <mo>;</mo> <msub> <mi>b</mi> <mn>1</mn> </msub> <mo>=</mo> <mi>Im</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>&phi;</mi> </mrow> </msub> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math> <math> <mrow> <msub> <mi>a</mi> <mn>2</mn> </msub> <mo>=</mo> <mi>Re</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>&phi;</mi> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mrow> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mfrac> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>;</mo> <msub> <mi>b</mi> <mn>2</mn> </msub> <mo>=</mo> <mi>I</mi> <mi>m</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>&phi;</mi> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mrow> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mfrac> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>;</mo> <msub> <mi>a</mi> <mn>3</mn> </msub> <mo>=</mo> <msub> <mi>b</mi> <mn>3</mn> </msub> <mo>=</mo> <mo>|</mo> <mfrac> <msub> <mi>Z</mi> <mi>m</mi> </msub> <mrow> <mn>3</mn> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>|</mo> <mo>;</mo> <mi>&beta;</mi> <mo>=</mo> <mi>A</mi> <mi>r</mi> <mi>g</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mi>Z</mi> <mi>m</mi> </msub> <mrow> <mn>3</mn> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math> Zmzero sequence mutual inductance between the circuit I of the double-circuit line on the same tower and the circuit II of the double-circuit line on the same tower is achieved; zI0Zero sequence impedance of I-loop circuit of double-loop circuit on the same tower; zI1The positive sequence impedance of the I-loop line of the double-loop line on the same tower is obtained; phi is an I loop line A phase, an I loop line B phase and an I loop line C phase;is composed ofThe real part of (a);is composed ofAn imaginary part of (d);is composed ofThe real part of (a);is composed ofAn imaginary part of (d);is composed ofThe amplitude of (d);is composed ofThe phase angle of (d);is composed ofThe arcsine function value of (1);is composed ofThe arcsine function value of (a).
(3) The protection device calculates the zero sequence current of the II-loop line of the double-loop line on the same towerWherein j is a complex operator;
(4) the protection device calculates the zero sequence compensation current of the I-loop line of the double-loop line on the same tower
<math> <mrow> <mi>&Delta;</mi> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mo>=</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>&phi;</mi> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mrow> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mfrac> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mfrac> <msub> <mi>Z</mi> <mi>m</mi> </msub> <mrow> <mn>3</mn> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>I</mi> <mn>0</mn> </mrow> </msub> </mrow> </math>
(5) The protection device calculates the voltage drop from the non-same-name phase overline ground fault point to the protection installation position of the I-loop circuit of the same-tower double-loop circuitImaginary part of <math> <mrow> <mi>Im</mi> <mrow> <mo>(</mo> <mi>&Delta;</mi> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>Re</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>&phi;</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>Im</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mi>Im</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>&phi;</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>Re</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> <mi>l</mi> </mfrac> <mi>&Delta;</mi> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mo>)</mo> </mrow> <mi>Im</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mi>I</mi> <mi>m</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> <mi>l</mi> </mfrac> <mi>&Delta;</mi> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mo>)</mo> </mrow> <mi>Re</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>Im</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> <mi>l</mi> </mfrac> <mi>&Delta;</mi> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math> Wherein l is the length of the I loop of the double-loop line on the same tower; zI1The positive sequence impedance of the I-loop line of the double-loop line on the same tower is obtained; phi is an I loop line A phase, an I loop line B phase and an I loop line C phase;is composed ofThe real part of (a);is composed ofAn imaginary part of (d);is composed ofThe real part of (a);is composed ofAn imaginary part of (d);is composed ofThe real part of (a);is composed ofAn imaginary part of (d);
(6) protection device judgmentIf yes, judging that the non-same-name phase overline ground fault point is located within the I-loop circuit protection setting range of the double-loop circuit on the same tower, and sending an action trip signal; wherein lsetFor double-circuit on the same towerAnd (3) taking 0.85 time of the length of the double-circuit line I on the same tower in the protection setting range of the line I.
The invention has the characteristics and technical achievements that:
the method only uses the single-end single-loop line electric quantity, does not need to introduce another loop line electric quantity, has no influence on the action performance by the operation mode of the power system, and has strong adaptability when the operation mode of the power system is greatly changed. The method of the invention takes the influence of the zero sequence mutual inductance between the lines into account, and eliminates the influence of the zero sequence mutual inductance between the lines on the performance of the protection action. The method adopts centralized parameter modeling, and utilizes the voltage drop imaginary part from the non-same-name-phase overline ground fault point to the protection installation position of the I-loop circuit of the double-circuit line on the same tower and the voltage drop imaginary part from the protection setting range to the protection installation position of the I-loop circuit of the double-circuit line on the same tower to form the relay protection criterion for the single-end electric quantity of the non-same-name-phase overline ground fault of the double-circuit line, thereby eliminating the influence of the transition resistance and the load current on the protection action performance, having strong capacity of resisting the influence of the transition resistance and the load current, and being suitable for the relay protection of the whole fault process of the non-same-name-phase overline ground fault of the double.
Drawings
Fig. 1 is a schematic diagram of a double-circuit power transmission system on the same tower and with the application of the invention.
Detailed Description
Fig. 1 is a schematic diagram of a double-circuit power transmission system on the same tower and with the application of the invention. In fig. 1, PT is a voltage transformer, CT is a current transformer, and m and n are numbers of two ends of a double-circuit line on the same tower. The protection device measures the fault phase voltage at the protection installation position of the I-loop circuit of the double-loop circuit on the same towerFault phase currentAnd zero sequence currentWherein, phi is I loop circuit A phase, I loop circuit B phase, I loop circuit C phase.
The protection device calculates the zero sequence current phase angle alpha of the II-loop circuit of the double-loop circuit on the same tower as r1+r2-π-β;
Wherein Z ismZero sequence mutual inductance between the circuit I of the double-circuit line on the same tower and the circuit II of the double-circuit line on the same tower is achieved; zI0Zero sequence impedance of I-loop circuit of double-loop circuit on the same tower; zI1The positive sequence impedance of the I-loop line of the double-loop line on the same tower is obtained; phi is an I loop line A phase, an I loop line B phase and an I loop line C phase; <math> <mrow> <msub> <mi>a</mi> <mn>3</mn> </msub> <mo>=</mo> <msub> <mi>b</mi> <mn>3</mn> </msub> <mo>=</mo> <mo>|</mo> <mfrac> <msub> <mi>Z</mi> <mi>m</mi> </msub> <mrow> <mn>3</mn> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>|</mo> <mo>,</mo> </mrow> </math> is composed ofThe amplitude of (d); <math> <mrow> <mi>&beta;</mi> <mo>=</mo> <mi>Arg</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mi>Z</mi> <mi>m</mi> </msub> <mrow> <mn>3</mn> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math> is composed ofThe phase angle of (d);
<math> <mrow> <msub> <mi>a</mi> <mn>2</mn> </msub> <mo>=</mo> <mi>Re</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>&phi;</mi> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> </mrow> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mfrac> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math> is composed ofThe real part of (a); <math> <mrow> <msub> <mi>b</mi> <mn>2</mn> </msub> <mo>=</mo> <mi>I</mi> <mi>m</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>&phi;</mi> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mrow> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mfrac> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math> is composed ofAn imaginary part of (d); <math> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>=</mo> <mi>Re</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>&phi;</mi> </mrow> </msub> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math> is composed ofThe real part of (a); <math> <mrow> <msub> <mi>b</mi> <mn>1</mn> </msub> <mo>=</mo> <mi>I</mi> <mi>m</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>&phi;</mi> </mrow> </msub> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math> is composed ofAn imaginary part of (d); r is1、r2Is an intermediate variable, has no physical meaning, and r 1 = sin - 1 ( a 3 b 1 ( a 3 b 1 ) 2 + ( a 1 b 3 ) 2 ) , r 2 = sin - 1 ( a 1 b 2 - a 2 b 1 ( a 3 b 1 ) 2 + ( a 1 b 3 ) 2 ) ; sin - 1 ( a 3 b 1 ( a 3 b 1 ) 2 + ( a 1 b 3 ) 2 ) is composed ofThe arcsine function value of (1);is composed ofThe arcsine function value of (a).
The protection device calculates the zero sequence current of the II-loop line of the double-loop line on the same towerWherein j is a complex operator.
The protection device calculates the zero sequence compensation current of the I-loop line of the double-loop line on the same tower
<math> <mrow> <mi>&Delta;</mi> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mo>=</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>&phi;</mi> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mrow> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mfrac> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mfrac> <msub> <mi>Z</mi> <mi>m</mi> </msub> <mrow> <mn>3</mn> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>I</mi> <mn>0</mn> </mrow> </msub> </mrow> </math>
The protection device calculates the voltage drop from the non-same-name phase overline ground fault point to the protection installation position of the I-loop circuit of the same-tower double-loop circuitImaginary part of (c):
<math> <mrow> <mi>Im</mi> <mrow> <mo>(</mo> <mi>&Delta;</mi> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>Re</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>&phi;</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>Im</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mi>I</mi> <mi>m</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>&phi;</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>Re</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> <mi>l</mi> </mfrac> <mi>&Delta;</mi> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mo>)</mo> </mrow> <mi>Im</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mi>Im</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> <mi>l</mi> </mfrac> <mi>&Delta;</mi> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mo>)</mo> </mrow> <mi>Re</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>Im</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> <mi>l</mi> </mfrac> <mi>&Delta;</mi> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mo>)</mo> </mrow> </mrow> </math>
wherein l is the length of the I loop of the double-loop line on the same tower; zI1The positive sequence impedance of the I-loop line of the double-loop line on the same tower is obtained; phi is an I loop line A phase, an I loop line B phase and an I loop line C phase;is composed ofThe real part of (a);is composed ofAn imaginary part of (d);is composed ofThe real part of (a);is composed ofAn imaginary part of (d);is composed ofThe real part of (a);is composed ofThe imaginary part of (c).
If the non-same-name-phase overline ground fault point is located in the same-tower double-circuit line I loop protection setting range, the imaginary part of the voltage drop from the non-same-name-phase overline ground fault point to the same-tower double-circuit line I loop protection installation position is smaller than the imaginary part of the voltage drop from the protection setting range to the same-tower double-circuit line I loop protection installation position; if the non-same-name-phase overline ground fault point is located outside the same-tower double-circuit line I loop protection setting range, the voltage drop imaginary part of the non-same-name-phase overline ground fault point to the same-tower double-circuit line I loop protection installation position is larger than the voltage drop imaginary part of the non-same-name-phase overline ground fault point to the same-tower double-circuit line I loop protection installation position in the protection setting range; according to the characteristic, the single-ended electrical quantity relay protection criterion of the double-circuit line non-same-name-phase overline ground fault is provided as follows:
judgment ofIf yes, judging that the non-same-name phase overline ground fault point is located within the I-loop circuit protection setting range of the double-loop circuit on the same tower, and sending an action trip signal by the protection device; wherein lsetAnd taking 0.85 time of the I-loop circuit length of the double-loop circuit on the same tower for the protection setting range of the I-loop circuit of the double-loop circuit on the same tower.
The method only uses the single-end single-loop line electric quantity, does not need to introduce another loop line electric quantity, has no influence on the action performance by the operation mode of the power system, and has strong adaptability when the operation mode of the power system is greatly changed. The method of the invention takes the influence of the zero sequence mutual inductance between the lines into account, and eliminates the influence of the zero sequence mutual inductance between the lines on the performance of the protection action. The method adopts centralized parameter modeling, and utilizes the voltage drop imaginary part from the non-same-name-phase overline ground fault point to the protection installation position of the I-loop circuit of the double-circuit line on the same tower and the voltage drop imaginary part from the protection setting range to the protection installation position of the I-loop circuit of the double-circuit line on the same tower to form the single-end electric quantity relay protection criterion, thereby eliminating the influence of the transition resistance and the load current on the protection action performance, having strong capacity of resisting the influence of the transition resistance and the load current, and being suitable for relay protection of the whole fault process of the non-same-name-phase overline ground fault of the double-circuit line.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.

Claims (1)

1. The relay protection method for the non-same-name-phase overline ground fault of the double-circuit line based on the inductive voltage drop degressive characteristic is characterized by comprising the following steps in sequence:
(1) the protection device measures the fault phase voltage at the protection installation position of the I-loop circuit of the double-loop circuit on the same towerFault phase currentAnd zero sequence currentWherein phi is an I loop circuit A phase, an I loop circuit B phase and an I loop circuit C phase;
(2) the protection device calculates the zero sequence current phase angle alpha of the II-loop circuit of the double-loop circuit on the same tower as r1+r2-π-β;
Wherein, <math> <mrow> <msub> <mi>r</mi> <mn>1</mn> </msub> <mo>=</mo> <msup> <mi>sin</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>a</mi> <mn>3</mn> </msub> <msub> <mi>b</mi> <mn>1</mn> </msub> </mrow> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>3</mn> </msub> <msub> <mi>b</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <msub> <mi>b</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mfrac> <mo>)</mo> </mrow> <mo>;</mo> <msub> <mi>r</mi> <mn>2</mn> </msub> <mo>=</mo> <msup> <mi>sin</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <msub> <mi>b</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> <msub> <mi>b</mi> <mn>1</mn> </msub> </mrow> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>3</mn> </msub> <msub> <mi>b</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <msub> <mi>b</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mfrac> <mo>)</mo> </mrow> <mo>;</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>=</mo> <mi>Re</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>&phi;</mi> </mrow> </msub> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <mo>;</mo> <msub> <mi>b</mi> <mn>1</mn> </msub> <mo>=</mo> <mi>Im</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>&phi;</mi> </mrow> </msub> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math> <math> <mrow> <msub> <mi>a</mi> <mn>2</mn> </msub> <mo>=</mo> <mi>Re</mi> <mrow> <mo>(</mo> <mrow> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>&phi;</mi> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mrow> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mfrac> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>;</mo> <msub> <mi>b</mi> <mn>2</mn> </msub> <mo>=</mo> <mi>Im</mi> <mrow> <mo>(</mo> <mrow> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>&phi;</mi> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mrow> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mfrac> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>;</mo> <msub> <mi>a</mi> <mn>3</mn> </msub> <mo>=</mo> <msub> <mi>b</mi> <mn>3</mn> </msub> <mo>=</mo> <mo>|</mo> <mfrac> <msub> <mi>Z</mi> <mi>m</mi> </msub> <mrow> <mn>3</mn> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>|</mo> <mo>;</mo> <mi>&beta;</mi> <mo>=</mo> <mi>A</mi> <mi>r</mi> <mi>g</mi> <mrow> <mo>(</mo> <mrow> <mfrac> <msub> <mi>Z</mi> <mi>m</mi> </msub> <mrow> <mn>3</mn> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math> Zmzero sequence mutual inductance between the circuit I of the double-circuit line on the same tower and the circuit II of the double-circuit line on the same tower is achieved; zI0Zero sequence impedance of I-loop circuit of double-loop circuit on the same tower; zI1The positive sequence impedance of the I-loop line of the double-loop line on the same tower is obtained; phi is an I loop line A phase, an I loop line B phase and an I loop line C phase;is composed ofThe real part of (a);is composed ofAn imaginary part of (d);is composed ofThe real part of (a);is composed ofAn imaginary part of (d);is composed ofThe amplitude of (d);is composed ofThe phase angle of (d);is composed ofThe arcsine function value of (1);is composed ofThe arcsine function value of (a).
(3) The protection device calculates the zero sequence current of the II-loop line of the double-loop line on the same towerWherein j is a complex operator;
(4) the protection device calculates the zero sequence compensation current of the I-loop line of the double-loop line on the same tower
<math> <mrow> <mi>&Delta;</mi> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mo>=</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mn>1</mn> <mi>&phi;</mi> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mrow> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mfrac> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mfrac> <msub> <mi>Z</mi> <mi>m</mi> </msub> <mrow> <mn>3</mn> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>I</mi> <mn>0</mn> </mrow> </msub> </mrow> </math>
(5) The protection device calculates the voltage drop from the non-same-name phase overline ground fault point to the protection installation position of the I-loop circuit of the same-tower double-loop circuitImaginary part of <math> <mrow> <mi>Im</mi> <mrow> <mo>(</mo> <mi>&Delta;</mi> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>Re</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>&phi;</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>Im</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mi>Im</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>&phi;</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>Re</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mi>Re</mi> <mo>(</mo> <mrow> <mfrac> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> <mi>l</mi> </mfrac> <mi>&Delta;</mi> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> </mrow> <mo>)</mo> <mi>Im</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mi>Im</mi> <mo>(</mo> <mrow> <mfrac> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> <mi>l</mi> </mfrac> <mi>&Delta;</mi> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> </mrow> <mo>)</mo> <mi>Re</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>Im</mi> <mo>(</mo> <mrow> <mfrac> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> <mi>l</mi> </mfrac> <mi>&Delta;</mi> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> </mrow> <mo>)</mo> </mrow> </math> Wherein l is the length of the I loop of the double-loop line on the same tower; zI1The positive sequence impedance of the I-loop line of the double-loop line on the same tower is obtained; phi is an I loop line A phase, an I loop line B phase and an I loop line C phase;is composed ofThe real part of (a);is composed ofAn imaginary part of (d);is composed ofThe real part of (a);is composed ofAn imaginary part of (d);is composed ofThe real part of (a);is composed ofAn imaginary part of (d);
(6) protection device judgmentIf yes, judging that the non-same-name phase overline ground fault point is located within the I-loop circuit protection setting range of the double-loop circuit on the same tower, and sending an action trip signal; wherein lsetFor double-circuit line I loop on the same towerAnd (4) taking 0.85 time of the I-loop circuit length of the double-loop circuit on the same tower in the circuit protection setting range.
CN201510336610.3A 2015-06-17 2015-06-17 Double-circuit non-homonymous phase overline grounding fault relay protection method based on perceptual pressure drop progressive decreasing characteristics Pending CN104953563A (en)

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CN104764969A (en) * 2015-03-04 2015-07-08 国家电网公司 Method for positioning different-phase cross-line high-resistance ground fault of double-circuit lines based on actual measurement of ground resistance

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