CN104090213A - Double-circuit-line non-same-name phase overline ground fault positioning method - Google Patents

Abstract

The invention discloses a method for locating a non-identical phase-cross-line grounding fault of a double-circuit line. Firstly, the fault phase voltage, the mutation amount of the fault phase voltage, the fault phase current, Fault phase current mutation, zero-sequence current and two normal phase voltages, calculate the zero-sequence current phase angle of the parallel double-circuit line II circuit on the same pole, calculate the zero-sequence current of the II circuit line of the parallel double-circuit line on the same pole, and calculate Double-circuit lines on the same pole parallel to the fault phase voltage of the I-circuit line when the line is in normal operation, and then use the characteristic of the voltage mutation amplitude monotonously increasing from the double-circuit line protection installation to the non-identical phase cross-line grounding fault point to realize the double-circuit line Accurate positioning of non-identical phase-crossing ground faults, in principle, eliminates the influence of zero-sequence mutual inductance, transition resistance and load current on positioning accuracy, and has no ranging dead zone. High positioning accuracy.

Description

Locating method for cross-line grounding faults of non-identical phases in double-circuit lines

technical field

The invention relates to the technical field of electric power system relay protection, in particular to a method for locating a double-circuit line non-identical phase-cross-line grounding fault based on the zero-sequence current measurement of an adjacent line.

Background technique

Divided from the electrical quantity used for distance measurement, fault location methods can be divided into two categories: double-ended ranging and single-ended ranging. The double-terminal fault location method is a method to determine the fault location of the transmission line by using the electrical quantity at both ends of the transmission line. It needs to obtain the electrical quantity of the opposite end through the channel, so it is highly dependent on the channel, and it is also vulnerable to the double-terminal sampling value in actual use. Synchronization effects. The single-ended ranging method is a method that only uses the voltage and current data at one end of the transmission line to determine the fault location of the transmission line. Because it only needs data at one end, does not require communication and data synchronization equipment, and has low operating costs and stable algorithms, it is suitable for medium and low voltage applications. It has been widely used in the line. At present, the single-ended ranging methods are mainly divided into two categories, one is the traveling wave method, and the other is the impedance method. The traveling wave method utilizes the transmission properties of fault transient traveling waves for distance measurement. It has high precision and is not affected by the operation mode and excessive resistance. application. The impedance method uses the voltage and current after the fault to calculate the impedance of the fault loop, and performs distance measurement according to the characteristic that the length of the line is proportional to the impedance. When fault location is performed at the end of the fault, the distance measurement accuracy is seriously affected by the transition resistance of the fault point and the zero-sequence mutual inductance between the lines. There is zero-sequence mutual inductance between double-circuit lines on the same pole, and the zero-sequence mutual inductance will affect the zero-sequence compensation coefficient, which will lead to large errors in the ranging results of the impedance method. If a single-phase high-resistance grounding fault occurs on a parallel double-circuit line on the same pole, due to the comprehensive influence of the zero-sequence mutual inductance and high transition resistance between the lines, the ranging result of the impedance method often exceeds the full length of the line or there is no ranging result, which cannot provide accurate fault information Location information makes it difficult to inspect line faults, which is not conducive to rapid troubleshooting and rapid restoration of line power supply.

Contents of the invention

The purpose of the present invention is to overcome the deficiencies of the prior art, to provide a protection for the non-same-named phase cross-line grounding fault without ranging dead zone, and the ranging accuracy is not affected by the zero-sequence mutual inductance between lines, transition resistance and load. Due to the influence of the current, the method of locating the non-identical phase-cross-line ground fault of the double-circuit line is realized by using the characteristic that the voltage mutation amplitude monotonically increases from the double-circuit line protection installation to the non-identical phase-cross-line ground fault point.

The adopted technical scheme that the present invention solves its technical problem is:

The method for locating the grounding fault of non-identical phases across lines of double-circuit lines includes the following steps in sequence:

(1) The protection device measures the fault phase voltage at the protection installation of the I-circuit line of the double-circuit line on the same pole Fault phase voltage mutation fault phase current Fault phase current mutation and zero sequence current Measure the two normal phase voltages at the installation place of the I-circuit line protection of the parallel double-circuit line on the same pole Among them, φρδ is the ACB phase of the I-circuit line or the BAC phase of the I-circuit line or the CBA phase of the I-circuit line;

(2) The protection device calculates the zero-sequence current phase angle α of the double-circuit line II line on the same pole:

α＝r ₁ +r ₂ -π-β

in, $r_1={\sin }^{-1}\left(\frac{a_3{b}_1}{\sqrt{{\left(a_3{b}_1\right)}^2+{\left(a_1{b}_3\right)}^2}}\right);$ $r_2={\sin }^{-1}\left(\frac{a_1{b}_2-a_2{b}_1}{\sqrt{{\left(a_3{b}_1\right)}^2+{\left(a_1{b}_3\right)}^2}}\right);$ $a_1=\mathrm{Re}\left(\frac{{\stackrel{\&Center\; Dot;}{u}}_{\mathrm{I\φ}}}{Z_{I1}}\right);$ $b_1=\mathrm{Im}\left(\frac{{\stackrel{\&Center\; Dot;}{u}}_{\mathrm{I\φ}}}{Z_{I1}}\right);$ $a_2=\mathrm{Re}({\stackrel{\&Center\; Dot;}{I}}_{\mathrm{I\φ}}+\frac{Z_{I0}-Z_{I1}}{Z_{I1}}{\stackrel{\·}{I}}_{I0});$ $b_2=\mathrm{Im}({\stackrel{\&Center\; Dot;}{I}}_{\mathrm{I\φ}}+\frac{Z_{I0}-Z_{I1}}{Z_{I1}}{\stackrel{\&Center\; Dot;}{I}}_{I0});$ $a_3=b_3=\left|\frac{Z_m}{{3Z}_{I1}}{\stackrel{\·}{I}}_{I0}\right|;$ $\mathrm{\β}=\mathrm{Arg}\left(\frac{Z_m}{{3Z}_{I1}}{\stackrel{\·}{I}}_{I0}\right);$ Z _m is the zero-sequence mutual inductance between the I-circuit line of the parallel double-circuit line on the same pole and the II-circuit line of the parallel double-circuit line on the same pole; Z _I0 is the zero-sequence impedance of the I-circuit line of the parallel double-circuit line on the same pole; Z _I1 is the positive sequence impedance of the I-circuit line of the double-circuit line on the same pole; φρδ is the ACB phase of the I-circuit line or the BAC phase of the I-circuit line or the CBA phase of the I-circuit line;

(3) The protection device calculates the zero-sequence current of the II-circuit line of the parallel double-circuit line on the same pole ${\stackrel{\&Center\; Dot;}{I}}_{\mathrm{II}0}={\stackrel{\&Center\; Dot;}{I}}_{I0}(\cos \mathrm{\α}+j\sin \mathrm{\α});$ Among them, j is a complex number operator;

(4) The protection device calculates the φ-phase voltage of the double-circuit line on the same pole when the I-circuit line is in normal operation Among them, φρδ is the ACB phase of the I-circuit line or the BAC phase of the I-circuit line or the CBA phase of the I-circuit line; j is a complex operator;

(5) The protection device selects the initial value of the fault distance as l _x , increases with a fixed step size Δl, and calculates the voltage positioning function of each point on the I-circuit line of the parallel double-circuit line on the same pole in turn $g\left(l_x\right)=\left|\right|{\mathrm{\Δ}\stackrel{\&Center\; Dot;}{u}}_{\mathrm{I\φ}}-Z_{I1}\frac{l_x}{l}(\mathrm{\Δ}{\stackrel{\·}{I}}_{\mathrm{I\φ}}+\frac{Z_{I0}-Z_{I1}}{Z_{I1}}{\stackrel{\&Center\; Dot;}{I}}_{I0}+\frac{Z_m}{{3Z}_{I1}}{\stackrel{\&Center\; Dot;}{I}}_{\mathrm{II}0})|-|-j\frac{{\stackrel{\&Center\; Dot;}{u}}_{\mathrm{I\ρ}}-{\stackrel{\·}{u}}_{\mathrm{I\δ}}}{\sqrt{3}}\left|\right|,$ Up to the total length of the I-circuit line of the double-circuit line paralleled on the same pole; where, l is the length of the I-circuit line of the double-circuit line paralleled on the same pole; Z _I0 is the zero-sequence impedance of the I-circuit line of the double-circuit line paralleled on the same pole; Z _I1 is the positive sequence impedance of the I-circuit line of the parallel double-circuit line on the same pole; Z _m is the zero-sequence mutual inductance between the I-circuit line of the parallel double-circuit line on the same pole and the II circuit of the parallel double-circuit line on the same pole; j is a complex number operator;

(6) The protection device selects the voltage positioning function on the double-circuit line on the same pole and the I-circuit line

$g\left(l_x\right)=\left|\right|{\mathrm{\Δ}\stackrel{\&Center\; Dot;}{u}}_{\mathrm{I\φ}}-Z_{I1}\frac{l_x}{l}(\mathrm{\Δ}{\stackrel{\·}{I}}_{\mathrm{I\φ}}+\frac{Z_{I0}-Z_{I1}}{Z_{I1}}{\stackrel{\&Center\; Dot;}{I}}_{I0}+\frac{Z_m}{{3Z}_{I1}}{\stackrel{\·}{I}}_{\mathrm{II}0})|-|-j\frac{{\stackrel{\·}{u}}_{\mathrm{I\ρ}}-{\stackrel{\&Center\; Dot;}{u}}_{\mathrm{I\δ}}}{\sqrt{3}}\left|\right|$ When the minimum value is reached, the corresponding point is the grounding fault point of the non-identical phase cross-line of the double-circuit line paralleled on the same pole.

Compared with the background technology, this technical solution has the following advantages:

The method of the present invention only uses the electrical quantity of the single-ended single-circuit line, and does not need to introduce the electrical quantity of another circuit. The positioning accuracy is not affected by the operation mode of the power system, and it still has a high accuracy when the operation mode of the power system changes greatly. positioning accuracy. The method of the invention takes into account the influence of the zero-sequence mutual inductance between the lines, and eliminates the influence of the zero-sequence mutual inductance between the lines on the positioning accuracy. The method of the present invention utilizes the characteristic that the amplitude of the voltage mutation amount monotonously increases from the double-circuit line protection installation point to the non-identical phase cross-line ground fault point to realize the non-identical phase cross-line ground fault location of the double-circuit line, and eliminates the transition resistance and the cross-line ground fault in principle. The impact of load current on positioning accuracy, there is no ranging dead zone when a non-identical phase cross-line ground fault occurs at the forward exit of the protection.

Description of drawings

The present invention will be further described below in conjunction with drawings and embodiments.

Fig. 1 is a schematic diagram of a double-circuit line power transmission system on the same pole parallel to the rack applying the present invention.

Detailed ways

Fig. 1 is a schematic diagram of a double-circuit line power transmission system on the same pole parallel to the rack applying the present invention. In the figure, PT is a voltage transformer, and CT is a current transformer. The protection device measures the fault phase voltage at the protection installation place of the I-circuit line of double-circuit lines paralleled on the same pole Fault phase voltage mutation fault phase current Fault phase current mutation and zero sequence current Measure the two normal phase voltages at the installation place of the I-circuit line protection of the parallel double-circuit line on the same pole Among them, φρδ is the ACB phase of the I-circuit line or the BAC phase of the I-circuit line or the CBA phase of the I-circuit line.

The protection device calculates the zero-sequence current phase angle α of the double-circuit line II line on the same pole:

α＝r ₁ +r ₂ -π-β

in, $r_1={\sin }^{-1}\left(\frac{a_3{b}_1}{\sqrt{{\left(a_3{b}_1\right)}^2+{\left(a_1{b}_3\right)}^2}}\right);$ $r_2={\sin }^{-1}\left(\frac{a_1{b}_2-a_2{b}_1}{\sqrt{{\left(a_3{b}_1\right)}^2+{\left(a_1{b}_3\right)}^2}}\right);$ $a_1=\mathrm{Re}\left(\frac{{\stackrel{\&Center\; Dot;}{u}}_{\mathrm{I\φ}}}{Z_{I1}}\right);$ $b_1=\mathrm{Im}\left(\frac{{\stackrel{\·}{u}}_{\mathrm{I\φ}}}{Z_{I1}}\right);$ $a_2=\mathrm{Re}({\stackrel{\&Center\; Dot;}{I}}_{\mathrm{I\φ}}+\frac{Z_{I0}-Z_{I1}}{Z_{I1}}{\stackrel{\&Center\; Dot;}{I}}_{I0});$ $b_2=\mathrm{Im}({\stackrel{\&Center\; Dot;}{I}}_{\mathrm{I\φ}}+\frac{Z_{I0}-Z_{I1}}{Z_{I1}}{\stackrel{\&Center\; Dot;}{I}}_{I0});$ $a_3=b_3=\left|\frac{Z_m}{{3Z}_{I1}}{\stackrel{\&Center\; Dot;}{I}}_{I0}\right|;$ $\mathrm{\β}=\mathrm{Arg}\left(\frac{Z_m}{{3Z}_{I1}}{\stackrel{\·}{I}}_{I0}\right);$ Z _m is the zero-sequence mutual inductance between the I-circuit line of the parallel double-circuit line on the same pole and the II-circuit line of the parallel double-circuit line on the same pole; Z _I0 is the zero-sequence impedance of the I-circuit line of the parallel double-circuit line on the same pole; Z _I1 is the positive sequence impedance of the I-circuit line of the double-circuit line paralleled on the same pole.

The protection device calculates the zero-sequence current of the double-circuit line II on the same pole Among them, j is a complex number operator.

The protection device calculates the fault phase voltage of the double-circuit line on the same pole when the I-circuit line is in normal operation, that is, the φ-phase voltage Among them, φρδ is the ACB phase of the I-circuit line or the BAC phase of the I-circuit line or the CBA phase of the I-circuit line.

After a non-identical phase cross-line ground fault occurs on the parallel double-circuit line on the same pole, the voltage of the non-identical phase cross-line ground fault point is equal to the fault phase voltage of the I-circuit line of the parallel double-circuit line on the same pole, which is equal to the φ phase voltage Moreover, the magnitude of the voltage mutation from the double-circuit line protection installation to the non-identical phase-cross-line ground fault point increases monotonously. Using this voltage amplitude distribution characteristic, the double-circuit line non-identical phase-cross-line ground fault location search steps are as follows:

(1) The protection device selects the initial value of the fault distance as l _x , increases with a fixed step size Δl, and calculates the voltage positioning function of each point on the I-circuit line of the parallel double-circuit line on the same pole in turn $g\left(l_x\right)=\left|\right|{\mathrm{\Δ}\stackrel{\&Center\; Dot;}{u}}_{\mathrm{I\φ}}-Z_{I1}\frac{l_x}{l}(\mathrm{\Δ}{\stackrel{\·}{I}}_{\mathrm{I\φ}}+\frac{Z_{I0}-Z_{I1}}{Z_{I1}}{\stackrel{\&Center\; Dot;}{I}}_{I0}+\frac{Z_m}{{3Z}_{I1}}{\stackrel{\&Center\; Dot;}{I}}_{\mathrm{II}0})|-|-j\frac{{\stackrel{\&Center\; Dot;}{u}}_{\mathrm{I\ρ}}-{\stackrel{\&Center\; Dot;}{u}}_{\mathrm{I\δ}}}{\sqrt{3}}\left|\right|,$ Up to the total length of the I-circuit line of the double-circuit line paralleled on the same pole; where, l is the length of the I-circuit line of the double-circuit line paralleled on the same pole; Z _I0 is the zero-sequence impedance of the I-circuit line of the double-circuit line paralleled on the same pole; Z _I1 is the positive-sequence impedance of the I-circuit line of the parallel double-circuit line on the same pole; Z _m is the zero-sequence mutual inductance between the I-circuit line of the parallel double-circuit line on the same pole and the II-circuit line of the parallel double-circuit line on the same pole; where j is a complex operator.

(2) The protection device selects the voltage positioning function on the double-circuit line on the same pole and the I-circuit line

$g\left(l_x\right)=\left|\right|{\mathrm{\Δ}\stackrel{\·}{u}}_{\mathrm{I\φ}}-Z_{I1}\frac{l_x}{l}(\mathrm{\Δ}{\stackrel{\·}{I}}_{\mathrm{I\φ}}+\frac{Z_{I0}-Z_{I1}}{Z_{I1}}{\stackrel{\·}{I}}_{I0}+\frac{Z_m}{{3Z}_{I1}}{\stackrel{\&Center\; Dot;}{I}}_{\mathrm{II}0})|-|-j\frac{{\stackrel{\&Center\; Dot;}{u}}_{\mathrm{I\ρ}}-{\stackrel{\&Center\; Dot;}{u}}_{\mathrm{I\δ}}}{\sqrt{3}}\left|\right|$ When the minimum value is reached, the corresponding point is the grounding fault point of the non-identical phase cross-line of the double-circuit line paralleled on the same pole.

The method of the present invention only uses the electrical quantity of the single-ended single-circuit line, and does not need to introduce the electrical quantity of another circuit. The positioning accuracy is not affected by the operation mode of the power system, and it still has a high accuracy when the operation mode of the power system changes greatly. positioning accuracy. The method of the invention takes into account the influence of the zero-sequence mutual inductance between the lines, and eliminates the influence of the zero-sequence mutual inductance between the lines on the positioning accuracy. The method of the present invention utilizes the characteristic that the amplitude of the voltage mutation amount monotonously increases from the double-circuit line protection installation point to the non-identical phase cross-line ground fault point to realize the non-identical phase cross-line ground fault location of the double-circuit line, and eliminates the transition resistance and the cross-line ground fault in principle. The impact of load current on positioning accuracy, there is no ranging dead zone when a non-identical phase cross-line ground fault occurs at the forward exit of the protection.

The above is only a preferred embodiment of the present invention, so the scope of the present invention cannot be limited accordingly, that is, the equivalent changes and modifications made according to the patent scope of the present invention and the content of the specification should still be covered by the present invention within range.

Claims (1)

1. The method for positioning the double-circuit line non-same-name-phase overline ground fault is characterized by comprising the following steps of: comprises 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 towerSudden change of fault phase voltageFault phase currentPhase current break amount of faultAnd zero sequence currentMeasuring two normal phase voltages at the protection installation position of I-loop circuit of double-loop circuit on the same towerWherein phi rho delta is an I loop ACB phase, an I loop BAC phase or an I loop CBA phase;

(2) the protection device calculates the zero-sequence current phase angle alpha of the II-loop line of the double-loop line on the same tower:

α＝r₁+r₂-π-β

wherein, $r_1={\sin }^{-1}\left(\frac{a_3{b}_1}{\sqrt{{\left(a_3{b}_1\right)}^2+{\left(a_1{b}_3\right)}^2}}\right);$ $r_2={\sin }^{-1}\left(\frac{a_1{b}_2-a_2{b}_1}{\sqrt{{\left(a_3{b}_1\right)}^2+{\left(a_1{b}_3\right)}^2}}\right);$ <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> <mi>I&phi;</mi> </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>b</mi> <mn>1</mn> </msub> <mo>=</mo> <mi>Im</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mi>I&phi;</mi> </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> <mi>I&phi;</mi> </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> <math> <mrow> <msub> <mi>b</mi> <mn>2</mn> </msub> <mo>=</mo> <mi>Im</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mi>I&phi;</mi> </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> <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> <msub> <mrow> <mn>3</mn> <mi>Z</mi> </mrow> <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> <mo>;</mo> </mrow> </math> <math> <mrow> <mi>&beta;</mi> <mo>=</mo> <mi>Arg</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mi>Z</mi> <mi>m</mi> </msub> <msub> <mrow> <mn>3</mn> <mi>Z</mi> </mrow> <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> Z_mzero 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; z_I0Zero sequence impedance of I-loop circuit of double-loop circuit on the same tower; z_I1The positive sequence impedance of the I-loop line of the double-loop line on the same tower is obtained; phi rho delta is an I loop line ACB phase, an I loop line BAC phase and an I loop line CBA phase;

(3) the protection device calculates the zero sequence current of the II-loop line of the double-loop line on the same tower <math> <mrow> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>II</mi> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>cos</mi> <mi>&alpha;</mi> <mo>+</mo> <mi>j</mi> <mi>sin</mi> <mi>&alpha;</mi> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math> Wherein j is a complex operator;

(4) the protection device calculates phi phase voltage of I-loop circuit of double-loop circuit on the same tower during normal operationWherein phi rho delta is an I loop ACB phase, an I loop BAC phase or an I loop CBA phase; j is a complex operator;

(5) the protection device selects the initial value of the fault distance as l_xSequentially calculating the voltage positioning function of each point on the I-loop circuit of the double-loop circuit on the same tower by increasing the fixed step length delta l <math> <mrow> <mi>g</mi> <mrow> <mo>(</mo> <msub> <mi>l</mi> <mi>x</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mo>|</mo> <mo>|</mo> <msub> <mrow> <mi>&Delta;</mi> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> </mrow> <mi>I&phi;</mi> </msub> <mo>-</mo> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> <mfrac> <msub> <mi>l</mi> <mi>x</mi> </msub> <mi>l</mi> </mfrac> <mrow> <mo>(</mo> <mi>&Delta;</mi> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mi>I&phi;</mi> </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> <msub> <mrow> <mn>3</mn> <mi>Z</mi> </mrow> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mfrac> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>II</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>|</mo> <mo>-</mo> <mo>|</mo> <mo>-</mo> <mi>j</mi> <mfrac> <mrow> <msub> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mi>I&rho;</mi> </msub> <mo>-</mo> <msub> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mi>I&delta;</mi> </msub> </mrow> <msqrt> <mn>3</mn> </msqrt> </mfrac> <mo>|</mo> <mo>|</mo> <mo>,</mo> </mrow> </math> Until the total length of the I-loop circuit of the double-loop circuit on the same tower is reached; wherein l is the length of the I loop of the double-loop line on the same tower; z_I0Zero sequence impedance of I-loop circuit of double-loop circuit on the same tower; z_I1The positive sequence impedance of the I-loop line of the double-loop line on the same tower is obtained; z_mZero 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; j is a complex operator;

(6) the protection device selects the voltage positioning function on the I-loop circuit of the double-loop circuit on the same tower <math> <mrow> <mi>g</mi> <mrow> <mo>(</mo> <msub> <mi>l</mi> <mi>x</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mo>|</mo> <mo>|</mo> <msub> <mrow> <mi>&Delta;</mi> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> </mrow> <mi>I&phi;</mi> </msub> <mo>-</mo> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> <mfrac> <msub> <mi>l</mi> <mi>x</mi> </msub> <mi>l</mi> </mfrac> <mrow> <mo>(</mo> <mi>&Delta;</mi> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mi>I&phi;</mi> </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> <msub> <mrow> <mn>3</mn> <mi>Z</mi> </mrow> <mrow> <mi>I</mi> <mn>1</mn> </mrow> </msub> </mfrac> <msub> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>II</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>|</mo> <mo>-</mo> <mo>|</mo> <mo>-</mo> <mi>j</mi> <mfrac> <mrow> <msub> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mi>I&rho;</mi> </msub> <mo>-</mo> <msub> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mi>I&delta;</mi> </msub> </mrow> <msqrt> <mn>3</mn> </msqrt> </mfrac> <mo>|</mo> <mo>|</mo> </mrow> </math> And when the minimum value is reached, the corresponding point is a non-same-name-phase overline ground fault point of the double-circuit lines on the same tower.