CN103163413B - Single-phase ground fault type diagnosis method for ultra-high voltage alternating current transmission line - Google Patents

Abstract

The invention discloses a single-phase ground fault type diagnosis method for an ultra-high voltage alternating current transmission line. The method includes the steps: firstly, modeling by a lumped parameter model and calculating a fault distance according to the linear relation between voltage drop and the fault distance from an ultra-high voltage alternating current transmission line protection mounting position to a single-phase ground fault point; secondly, accurately describing physical characteristics of voltage and current transmission of the ultra-high voltage alternating current transmission line by a long line equation and calculating compensation current of the transmission line according to the calculated fault distance; and thirdly, accurately diagnosing single-phase ground fault types of the ultra-high voltage alternating current transmission line according to single-phase ground fault type diagnosis criteria of the ultra-high voltage alternating current transmission line. The method is applicable to single-phase low, medium and high resistance ground fault type diagnosis in the whole fault process of the ultra-high voltage alternating current transmission line, and diagnosis performances are not affected by factors such as transition resistance, load current and system operation modes.

Description

A kind of ultrahigh voltage alternating current transmission lines singlephase earth fault type diagnostic method

Technical field

The present invention relates to Relay Protection Technology in Power System field, specifically relate to a kind of ultrahigh voltage alternating current transmission lines singlephase earth fault type diagnostic method.

Background technology

The transmission of electricity corridor of ultrahigh voltage alternating current transmission lines is wide, running environment is complicated; cause the factor of ultrahigh voltage alternating current transmission lines singlephase earth fault of a great variety; after ultrahigh voltage alternating current transmission lines breaks down, itself and electrical network are isolated in tripping operation by protective relaying device action.The trouble-shooting point of then being crossed over mountain after mountain by circuit track walker, to fix a breakdown, cause line fault Exclusion Tasks heavy, and failture evacuation required time is long, is unfavorable for fast recovery of power supply, impacts social economy.

In the various fault type of ultrahigh voltage alternating current transmission lines, singlephase earth fault accounts for more than 90%, cause ultrahigh voltage alternating current transmission lines singlephase earth fault because have, floating thing causes ultrahigh voltage alternating current transmission lines low resistance singlephase earth fault, insulator arc-over causes resistance eutral grounding fault in ultrahigh voltage alternating current transmission lines, Huoshaoshan causes ultrahigh voltage alternating current transmission lines high resistance grounding fault etc.But current each protective relaying device does not all provide a kind of method that effectively can differentiate the low middle high resistance grounding fault type of ultrahigh voltage alternating current transmission lines, cause that the line fault Exclusion Tasks of electric administrative department is heavy, troubleshooting time is long.

Summary of the invention

The object of the invention is to the deficiency overcoming prior art existence, a kind of ultrahigh voltage alternating current transmission lines singlephase earth fault type diagnostic method is provided.The method can realize effective discrimination function of the low middle high resistance grounding fault type of ultrahigh voltage alternating current transmission lines.

For completing above-mentioned purpose, the present invention adopts following technical scheme:

(1) faulted phase voltage of protector measuring ultrahigh voltage alternating current transmission lines protection installation place faulted phase current fault phase negative-sequence current and zero-sequence current wherein, φ is A phase, B phase or C phase.

(2) protective device calculates leading angle θ ₁, calculate leading angle θ ₂, unit of account length ultrahigh voltage alternating current transmission lines positive sequence impedance z ₁phase angle theta ₃; Wherein, z ₁for unit length ultrahigh voltage alternating current transmission lines positive sequence impedance, z ₀for unit length ultrahigh voltage alternating current transmission lines zero sequence impedance.

(3) protective device calculates ultrahigh voltage alternating current transmission lines offset current ${\stackrel{\·}{I}}_{\mathrm{set}}=$ ${\stackrel{\·}{I}}_{\mathrm{\φ}}+(\frac{Z_0\mathrm{ch}\left({\mathrm{\γ}}_0\frac{\sin {\mathrm{\θ}}_1}{\sin ({\mathrm{\θ}}_2+{\mathrm{\θ}}_3)}\frac{{\stackrel{\·}{U}}_{\mathrm{\φ}}}{z_1({\stackrel{\·}{I}}_{\mathrm{\φ}}+\frac{z_0-z_1}{z_1}{\stackrel{\·}{I}}_0)}\right)+Z_{c0}\mathrm{sh}\left({\mathrm{\γ}}_0\frac{\sin {\mathrm{\θ}}_1}{\sin ({\mathrm{\θ}}_2+{\mathrm{\θ}}_3)}\frac{{\stackrel{\·}{U}}_{\mathrm{\φ}}}{z_1({\stackrel{\·}{I}}_{\mathrm{\φ}}+\frac{z_0-z_1}{z_1}{\stackrel{\·}{I}}_0)}\right)}{Z_{c1}\mathrm{sh}\left({\mathrm{\γ}}_1\frac{\sin {\mathrm{\θ}}_1}{\sin ({\mathrm{\θ}}_2+{\mathrm{\θ}}_3)}\frac{{\stackrel{\·}{U}}_{\mathrm{\φ}}}{z_1({\stackrel{\·}{I}}_{\mathrm{\φ}}+\frac{z_0-z_1}{z_1}{\stackrel{\·}{I}}_0)}\right)}-\frac{Z_0}{Z_{c1}}\mathrm{cth}\left({\mathrm{\γ}}_1\frac{\sin {\mathrm{\θ}}_1}{\sin ({\mathrm{\θ}}_2+{\mathrm{\θ}}_3)}\frac{{\stackrel{\·}{U}}_{\mathrm{\φ}}}{z_1({\stackrel{\·}{I}}_{\mathrm{\φ}}+\frac{z_0-z_1}{z_1}{\stackrel{\·}{I}}_0)}\right)-1)$

Wherein, φ is A phase, B phase or C phase, Z ₀for the system zero sequence equivalent impedance of ultrahigh voltage alternating current transmission lines protection installation place, γ ₁, γ ₀be respectively ultrahigh voltage alternating current transmission lines positive sequence, zero sequence propagation coefficient, Z _c1, Z _c0be respectively ultrahigh voltage alternating current transmission lines positive sequence, zero sequence wave impedance, ch (.) is hyperbolic cosine function, and sh (.) is hyperbolic sine function, and cth (.) is hyperbolic arctan function.

(4) protective device calculates phase angle α, calculate leading angle θ ₁, calculate leading angle γ; Wherein, th (.) is hyperbolic tangent function.

(5) protective device compares $\left|{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}}\frac{\sin (\mathrm{\&alpha;}+\mathrm{\&gamma;}-{\mathrm{\&theta;}}_1)}{{\stackrel{\&CenterDot;}{I}}_{\mathrm{\&phi;}2}\sin (\mathrm{\&alpha;}+\mathrm{\&gamma;})}\mathrm{ch}\left({\mathrm{\&gamma;}}_1\frac{\sin {\mathrm{\&theta;}}_1}{\sin ({\mathrm{\&theta;}}_2+{\mathrm{\&theta;}}_3)}\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}}}{z_1({\stackrel{\&CenterDot;}{I}}_{\mathrm{\&phi;}}+\frac{z_0-z_1}{z_1}{\stackrel{\&CenterDot;}{I}}_0)}\right)\right|<k_1\left|{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}\left|0\right|}\right|$ Whether set up, if set up, then judge that ultrahigh voltage alternating current transmission lines singlephase earth fault is low resistance earthing fault; Wherein, for φ phase transmission line of electricity voltage magnitude when ultrahigh voltage alternating current transmission lines normally runs, k ₁for middle resistance eutral grounding fault tuning coefficient.

(6) protective device compares $k_1\left|{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}\left|0\right|}\right|<\left|{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}}\frac{\sin (\mathrm{\&alpha;}+\mathrm{\&gamma;}-{\mathrm{\&theta;}}_1)}{{\stackrel{\&CenterDot;}{I}}_{\mathrm{\&phi;}2}\sin (\mathrm{\&alpha;}+\mathrm{\&gamma;})}\mathrm{ch}\left({\mathrm{\&gamma;}}_1\frac{\sin {\mathrm{\&theta;}}_1}{\sin ({\mathrm{\&theta;}}_2+{\mathrm{\&theta;}}_3)}\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}}}{z_1({\stackrel{\&CenterDot;}{I}}_{\mathrm{\&phi;}}+\frac{z_0-z_1}{z_1}{\stackrel{\&CenterDot;}{I}}_0)}\right)\right|<k_2\left|{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}\left|0\right|}\right|$ Whether set up, if set up, then judge that ultrahigh voltage alternating current transmission lines singlephase earth fault is middle resistance eutral grounding fault; Wherein, k ₂for high resistance grounding fault tuning coefficient.

(7) protective device compares $\left|{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}}\frac{\sin (\mathrm{\&alpha;}+\mathrm{\&gamma;}-{\mathrm{\&theta;}}_1)}{{\stackrel{\&CenterDot;}{I}}_{\mathrm{\&phi;}2}\sin (\mathrm{\&alpha;}+\mathrm{\&gamma;})}\mathrm{ch}\left({\mathrm{\&gamma;}}_1\frac{\sin {\mathrm{\&theta;}}_1}{\sin ({\mathrm{\&theta;}}_2+{\mathrm{\&theta;}}_3)}\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}}}{z_1({\stackrel{\&CenterDot;}{I}}_{\mathrm{\&phi;}}+\frac{z_0-z_1}{z_1}{\stackrel{\&CenterDot;}{I}}_0)}\right)\right|{>k}_2\left|{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}\left|0\right|}\right|$ Whether set up, if set up, then judge that ultrahigh voltage alternating current transmission lines singlephase earth fault is high resistance grounding fault.

The present invention compared with prior art, has following positive achievement:

The inventive method is applicable to the single-phase low middle high resistance grounding fault type diagnosis of the whole failure process of ultrahigh voltage alternating current transmission lines, and diagnosis performance is not by the impact of the factors such as transition resistance, load current, system operation mode.

Accompanying drawing explanation

Fig. 1 is the transmission system schematic diagram of the ultrahigh voltage alternating current transmission lines of application the inventive method.

Embodiment

Below in conjunction with embodiment, technical scheme of the present invention is expressed in further detail.

In Fig. 1, CVT is voltage transformer (VT), CT is current transformer.The current waveform of protective device to the potential and current transformers CT of the voltage transformer (VT) CVT of ultrahigh voltage alternating current transmission lines protection installation place carries out sampling and obtains voltage, current instantaneous value, and utilizes Fourier algorithm to calculate the faulted phase voltage of ultrahigh voltage alternating current transmission lines protection installation place to its voltage collected, current instantaneous value faulted phase current fault phase negative-sequence current and zero-sequence current wherein, φ is A phase, B phase or C phase.

Protective device calculates leading angle θ ₁, calculate leading angle θ ₂, unit of account length ultrahigh voltage alternating current transmission lines positive sequence impedance z ₁phase angle theta ₃; Wherein, z ₁for unit length ultrahigh voltage alternating current transmission lines positive sequence impedance, z ₀for unit length ultrahigh voltage alternating current transmission lines zero sequence impedance.

Protective device calculates ultrahigh voltage alternating current transmission lines offset current ${\stackrel{\&CenterDot;}{I}}_{\mathrm{set}}=$ ${\stackrel{\&CenterDot;}{I}}_{\mathrm{\&phi;}}+(\frac{Z_0\mathrm{ch}\left({\mathrm{\&gamma;}}_0\frac{\sin {\mathrm{\&theta;}}_1}{\sin ({\mathrm{\&theta;}}_2+{\mathrm{\&theta;}}_3)}\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}}}{z_1({\stackrel{\&CenterDot;}{I}}_{\mathrm{\&phi;}}+\frac{z_0-z_1}{z_1}{\stackrel{\&CenterDot;}{I}}_0)}\right)+Z_{c0}\mathrm{sh}\left({\mathrm{\&gamma;}}_0\frac{\sin {\mathrm{\&theta;}}_1}{\sin ({\mathrm{\&theta;}}_2+{\mathrm{\&theta;}}_3)}\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}}}{z_1({\stackrel{\&CenterDot;}{I}}_{\mathrm{\&phi;}}+\frac{z_0-z_1}{z_1}{\stackrel{\&CenterDot;}{I}}_0)}\right)}{Z_{c1}\mathrm{sh}\left({\mathrm{\&gamma;}}_1\frac{\sin {\mathrm{\&theta;}}_1}{\sin ({\mathrm{\&theta;}}_2+{\mathrm{\&theta;}}_3)}\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}}}{z_1({\stackrel{\&CenterDot;}{I}}_{\mathrm{\&phi;}}+\frac{z_0-z_1}{z_1}{\stackrel{\&CenterDot;}{I}}_0)}\right)}-\frac{Z_0}{Z_{c1}}\mathrm{cth}\left({\mathrm{\&gamma;}}_1\frac{\sin {\mathrm{\&theta;}}_1}{\sin ({\mathrm{\&theta;}}_2+{\mathrm{\&theta;}}_3)}\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}}}{z_1({\stackrel{\&CenterDot;}{I}}_{\mathrm{\&phi;}}+\frac{z_0-z_1}{z_1}{\stackrel{\&CenterDot;}{I}}_0)}\right)-1)$

Protective device calculates phase angle α, calculate leading angle θ ₁, calculate leading angle γ; Wherein, φ is A phase, B phase or C phase, and Zx is the system zero sequence equivalent impedance of ultrahigh voltage alternating current transmission lines protection installation place, γ ₁, γ ₀be respectively ultrahigh voltage alternating current transmission lines positive sequence, zero sequence propagation coefficient, Z _c1, Z _c0be respectively ultrahigh voltage alternating current transmission lines positive sequence, zero sequence wave impedance, ch (.) is hyperbolic cosine function, sh (.) is hyperbolic sine function, and cth (.) is hyperbolic arctan function, and th (.) is hyperbolic tangent function.

Protective device compares $\left|{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}}\frac{\sin (\mathrm{\&alpha;}+\mathrm{\&gamma;}-{\mathrm{\&theta;}}_1)}{{\stackrel{\&CenterDot;}{I}}_{\mathrm{\&phi;}2}\sin (\mathrm{\&alpha;}+\mathrm{\&gamma;})}\mathrm{ch}\left({\mathrm{\&gamma;}}_1\frac{\sin {\mathrm{\&theta;}}_1}{\sin ({\mathrm{\&theta;}}_2+{\mathrm{\&theta;}}_3)}\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}}}{z_1({\stackrel{\&CenterDot;}{I}}_{\mathrm{\&phi;}}+\frac{z_0-z_1}{z_1}{\stackrel{\&CenterDot;}{I}}_0)}\right)\right|<k_1\left|{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}\left|0\right|}\right|$ Whether set up, if set up, then judge that ultrahigh voltage alternating current transmission lines singlephase earth fault is low resistance earthing fault; Wherein, for φ phase transmission line of electricity voltage magnitude when ultrahigh voltage alternating current transmission lines normally runs; k ₁for middle resistance eutral grounding fault tuning coefficient.

Protective device compares $k_1\left|{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}\left|0\right|}\right|<\left|{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}}\frac{\sin (\mathrm{\&alpha;}+\mathrm{\&gamma;}-{\mathrm{\&theta;}}_1)}{{\stackrel{\&CenterDot;}{I}}_{\mathrm{\&phi;}2}\sin (\mathrm{\&alpha;}+\mathrm{\&gamma;})}\mathrm{ch}\left({\mathrm{\&gamma;}}_1\frac{\sin {\mathrm{\&theta;}}_1}{\sin ({\mathrm{\&theta;}}_2+{\mathrm{\&theta;}}_3)}\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}}}{z_1({\stackrel{\&CenterDot;}{I}}_{\mathrm{\&phi;}}+\frac{z_0-z_1}{z_1}{\stackrel{\&CenterDot;}{I}}_0)}\right)\right|<k_2\left|{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}\left|0\right|}\right|$ Whether set up, if set up, then judge that ultrahigh voltage alternating current transmission lines singlephase earth fault is middle resistance eutral grounding fault; Wherein, k ₂for high resistance grounding fault tuning coefficient.

Protective device compares $\left|{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}}\frac{\sin (\mathrm{\&alpha;}+\mathrm{\&gamma;}-{\mathrm{\&theta;}}_1)}{{\stackrel{\&CenterDot;}{I}}_{\mathrm{\&phi;}2}\sin (\mathrm{\&alpha;}+\mathrm{\&gamma;})}\mathrm{ch}\left({\mathrm{\&gamma;}}_1\frac{\sin {\mathrm{\&theta;}}_1}{\sin ({\mathrm{\&theta;}}_2+{\mathrm{\&theta;}}_3)}\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}}}{z_1({\stackrel{\&CenterDot;}{I}}_{\mathrm{\&phi;}}+\frac{z_0-z_1}{z_1}{\stackrel{\&CenterDot;}{I}}_0)}\right)\right|{>k}_2\left|{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}\left|0\right|}\right|$ Whether set up, if set up, then judge that ultrahigh voltage alternating current transmission lines singlephase earth fault is high resistance grounding fault.

The inventive method is applicable to the single-phase low middle high resistance grounding fault type diagnosis of the whole failure process of ultrahigh voltage alternating current transmission lines, and diagnosis performance is not by the impact of the factors such as transition resistance, load current, system operation mode.

The foregoing is only preferred embodiment of the present invention; but protection scope of the present invention is not limited thereto; anyly be familiar with those skilled in the art in the technical scope that the present invention discloses, the change that can expect easily or replacement, all should be encompassed within protection scope of the present invention.

Claims (1)

1. a ultrahigh voltage alternating current transmission lines singlephase earth fault type diagnostic method, comprises the following steps:

(1) faulted phase voltage of protector measuring ultrahigh voltage alternating current transmission lines protection installation place faulted phase current fault phase negative-sequence current and zero-sequence current wherein, φ is A phase, B phase or C phase,

(2) protective device calculates leading angle θ ₁, calculate leading angle θ ₂, unit of account length ultrahigh voltage alternating current transmission lines positive sequence impedance z ₁phase angle theta ₃; Wherein, z ₁for unit length ultrahigh voltage alternating current transmission lines positive sequence impedance, z ₀for unit length ultrahigh voltage alternating current transmission lines zero sequence impedance,

(3) protective device calculates ultrahigh voltage alternating current transmission lines offset current ${\stackrel{\&CenterDot;}{I}}_{\mathrm{set}}=$

${\stackrel{\&CenterDot;}{I}}_{\mathrm{\&phi;}}+(\frac{Z_0\mathrm{ch}\left({\mathrm{\&gamma;}}_0\frac{\sin {\mathrm{\&theta;}}_1}{\sin ({\mathrm{\&theta;}}_2+{\mathrm{\&theta;}}_3)}\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}}}{z_1({\stackrel{\&CenterDot;}{I}}_{\mathrm{\&phi;}}+\frac{z_1-z_1}{z1}{\stackrel{\&CenterDot;}{I}}_0)}\right)+Z_{c0}\mathrm{sh}\left({\mathrm{\&gamma;}}_0\frac{\sin {\mathrm{\&theta;}}_1}{\sin ({\mathrm{\&theta;}}_2+{\mathrm{\&theta;}}_3)}\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}}}{z_1({\stackrel{\&CenterDot;}{I}}_{\mathrm{\&phi;}}+\frac{z_0-z_1}{z_1}{\stackrel{\&CenterDot;}{I}}_0)}\right)}{Z_{c1}\mathrm{sh}\left({\mathrm{\&gamma;}}_1\frac{\sin {\mathrm{\&theta;}}_1}{\sin ({\mathrm{\&theta;}}_2+{\mathrm{\&theta;}}_3)}\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}}}{z_1({\stackrel{\&CenterDot;}{I}}_{\mathrm{\&phi;}}+\frac{z_0-z_1}{z_1}{\stackrel{\&CenterDot;}{I}}_0)}\right)}-\frac{Z_0}{Z_{c1}}\mathrm{cth}\left({\mathrm{\&gamma;}}_1\frac{\sin {\mathrm{\&theta;}}_1}{\sin ({\mathrm{\&theta;}}_2+{\mathrm{\&theta;}}_3)}\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}}}{z_1({\stackrel{\&CenterDot;}{I}}_{\mathrm{\&phi;}}+\frac{z_0-z_1}{z_1}{\stackrel{\&CenterDot;}{I}}_0)}\right)-1)$

Wherein, φ is A phase, B phase or C phase, Z ₀for the system zero sequence equivalent impedance of ultrahigh voltage alternating current transmission lines protection installation place, γ ₁, γ ₀be respectively ultrahigh voltage alternating current transmission lines positive sequence, zero sequence propagation coefficient, Z _c1, Z _c0be respectively ultrahigh voltage alternating current transmission lines positive sequence, zero sequence wave impedance, ch (.) is hyperbolic cosine function, and sh (.) is hyperbolic sine function, and cth (.) is hyperbolic arctan function,

(4) protective device calculates phase angle α, calculate leading angle θ ₁, calculate leading angle γ; Wherein, th (.) is hyperbolic tangent function,

(5) protective device compares $\left|{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}}\frac{\sin (\mathrm{\&alpha;}+\mathrm{\&gamma;}-{\mathrm{\&theta;}}_1)}{{\stackrel{\&CenterDot;}{I}}_{\mathrm{\&phi;}2}\sin (\mathrm{\&alpha;}+\mathrm{\&gamma;})}\mathrm{ch}\left({\mathrm{\&gamma;}}_1\frac{\sin {\mathrm{\&theta;}}_1}{\sin ({\mathrm{\&theta;}}_2+{\mathrm{\&theta;}}_3)}\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}}}{z_1({\stackrel{\&CenterDot;}{I}}_{\mathrm{\&phi;}}+\frac{z_0-z_1}{z_1}{\stackrel{\&CenterDot;}{I}}_0)}\right)\right|<k_1\left|{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}\left|0\right|}\right|$ Whether set up, if set up, then judge that ultrahigh voltage alternating current transmission lines singlephase earth fault is low resistance earthing fault; Wherein, for φ phase transmission line of electricity voltage magnitude when ultrahigh voltage alternating current transmission lines normally runs, k ₁for middle resistance eutral grounding fault tuning coefficient,

(6) protective device compares $k_1\left|{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}\left|0\right|}\right|<\left|{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}}\frac{\sin (\mathrm{\&alpha;}+\mathrm{\&gamma;}-{\mathrm{\&theta;}}_1)}{{\stackrel{\&CenterDot;}{I}}_{\mathrm{\&phi;}2}\sin (\mathrm{\&alpha;}+\mathrm{\&gamma;})}\mathrm{ch}\left({\mathrm{\&gamma;}}_1\frac{\sin {\mathrm{\&theta;}}_1}{\sin ({\mathrm{\&theta;}}_2+{\mathrm{\&theta;}}_3)}\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}}}{z_1({\stackrel{\&CenterDot;}{I}}_{\mathrm{\&phi;}}+\frac{z_0-z_1}{z_1}{\stackrel{\&CenterDot;}{I}}_0)}\right)\right|<k_2\left|{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}\left|0\right|}\right|$ Whether set up, if set up, then judge that ultrahigh voltage alternating current transmission lines singlephase earth fault is middle resistance eutral grounding fault; Wherein, k ₂for high resistance grounding fault tuning coefficient,

(7) protective device compares $\left|{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}}\frac{\sin (\mathrm{\&alpha;}+\mathrm{\&gamma;}-{\mathrm{\&theta;}}_1)}{{\stackrel{\&CenterDot;}{I}}_{\mathrm{\&phi;}2}\sin (\mathrm{\&alpha;}+\mathrm{\&gamma;})}\mathrm{ch}\left({\mathrm{\&gamma;}}_1\frac{\sin {\mathrm{\&theta;}}_1}{\sin ({\mathrm{\&theta;}}_2+{\mathrm{\&theta;}}_3)}\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}}}{z_1({\stackrel{\&CenterDot;}{I}}_{\mathrm{\&phi;}}+\frac{z_0-z_1}{z_1}{\stackrel{\&CenterDot;}{I}}_0)}\right)\right|>k_2\left|{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&phi;}\left|0\right|}\right|$ Whether set up, if set up, then judge that ultrahigh voltage alternating current transmission lines singlephase earth fault is high resistance grounding fault.