CN104360232A - Line phase fault discrimination method based on phase characteristics of fault position factor - Google Patents

Abstract

The invention discloses a method for discriminating faults between phases of lines based on fault location factors and phase characteristics. The method of the present invention uses the long-line equation to accurately describe the physical characteristics of the transmission line voltage and current transmission, and first calculates the fault impedance between the installation place of the transmission line protection to the phase-to-phase short-circuit fault point and the line impedance between the installation place of the transmission line protection and the setting range of the transmission line protection The phase-to-phase fault position factor b of the transmission line is obtained by the ratio, and then by judging whether the phase-to-phase fault position factor b of the transmission line is less than 0 or greater than 0, it can be accurately judged that a phase-to-phase short circuit fault occurs in the reverse direction of the transmission line protection or a phase-to-phase short circuit occurs in the forward direction of the transmission line protection In principle, it eliminates the influence of phase-to-phase short-circuit fault point voltage, transition resistance and load current on the judgment result of transmission line phase-to-phase short-circuit fault direction, effectively prevents misoperation of transmission line phase-to-phase distance protection, and is especially suitable for UHV AC transmission line phase-to-phase fault relay electric protection.

Description

Phase-to-phase fault discrimination method based on fault location factor phase characteristics

technical field

The invention relates to the technical field of electric power system relay protection, in particular to a method for distinguishing faults between phases of lines based on fault location factors and phase characteristics.

Background technique

Since distance protection is less affected by power system operation mode and structural changes, it can selectively remove various faults in transmission lines instantly, and has been widely used in power system transmission line protection. The distance protection on the high-voltage transmission line is used as the main protection of the transmission line, and the distance protection on the EHV/UHV AC transmission line is used as the backup protection of the transmission line. At present, the distance protection widely used in power system transmission lines mainly includes power frequency variation distance protection and impedance distance protection.

The power frequency variation distance protection constitutes the distance protection by reflecting the sudden change of the working voltage amplitude. This method has the advantages of being less affected by the operation mode of the power system and having a strong ability to resist transition resistance. However, since the mutation of the working voltage amplitude used in this method only exists in the initial stage of the fault, it cannot be used as a backup protection for EHV/UHV AC transmission lines.

Impedance distance protection reflects the fault distance length according to the fault impedance to distinguish whether the fault point is inside the protection zone or outside the protection zone. Impedance distance protection is less affected by power system operation mode and structural changes, and the electrical quantity used to calculate fault impedance is the total fault component, which is applicable to the entire fault process. Therefore, the impedance distance protection can be used not only for the main protection of high-voltage transmission lines, but also for the backup protection of EHV/UHV AC transmission lines.

However, the premise of the traditional impedance distance protection is that the voltage at the fault point is assumed to be zero, and the fault impedance is calculated by the ratio of the fault phase voltage to the fault phase current, and the distance of the fault point is reflected according to the fault impedance to determine whether to send a trip signal. In fact, in the power system, except for artificially constructed metallic short-circuit faults, the voltage at the fault point is almost impossible to be zero. Therefore, the voltage at the fault point will seriously affect the performance of the impedance distance protection.

In the actual power system, the voltage and current transmission of UHV AC transmission lines have obvious wave process, and the distributed capacitive current along the line is large, so the influence on the performance of impedance distance protection cannot be ignored. Considering the influence of the ground capacitance along the line, the relationship between the fault impedance and the fault distance is a hyperbolic tangent function. The characteristics of the hyperbolic tangent function determine that the resistance of the impedance relay is poor, and the additional impedance brought by the transition resistance will seriously affect the impedance of the impedance relay. action performance. The ultra-voltage AC transmission line transmits large-capacity electric energy and is a heavy-duty transmission line. The heavy-load current will reduce the action sensitivity of the impedance distance protection, and the impact of the heavy-load current on the action performance of the impedance distance protection cannot be ignored.

Contents of the invention

The purpose of the present invention is to overcome the deficiencies in the prior art and provide a method for distinguishing faults between phases of lines based on fault location factors and phase characteristics. The method of the present invention firstly calculates the ratio of the fault impedance from the installation place of the transmission line protection to the phase-to-phase short-circuit fault point and the line impedance from the installation place of the transmission line protection to the setting range of the transmission line protection, obtains the position factor b of the phase-to-phase fault of the transmission line, and then judges the transmission line Whether the position factor b of the phase-to-phase fault of the line is less than 0 or greater than 0 is established to accurately determine whether a phase-to-phase short-circuit fault occurs in the reverse direction of the transmission line protection or a phase-to-phase short-circuit fault occurs in the forward direction of the transmission line protection. If a phase-to-phase short-circuit fault occurs in the forward direction of the transmission line protection, the protection device Send an action trip signal to trip the circuit breakers at both ends of the transmission line, which in principle eliminates the influence of the phase-to-phase short-circuit fault point voltage, transition resistance and load current on the judgment results of the phase-to-phase short-circuit fault direction of the transmission line, and effectively prevents misoperation of the transmission line phase-to-phase distance protection , especially suitable for phase-to-phase fault relay protection of UHV AC transmission lines.

For accomplishing above-mentioned object, the present invention adopts following technical scheme:

The phase-to-phase fault discrimination method based on the fault location factor phase characteristic line is characterized in that it includes the following sequential steps:

(1) The protection device measures the fault phase-to-phase voltage at the protection installation of the transmission line Fault phase current and negative sequence current between fault phases Among them, φφ=AB, BC, CA phase;

(2) The protective device calculates the hyperbolic cosine function value ch(γ ₁ l _set ) of γ ₁ l _set , and calculates the hyperbolic tangent function value th(γ ₁ l _set ) of γ ₁ l _set ; where, l _set is the transmission line The protection setting range is taken as 0.85 times the length of the transmission line; γ ₁ is the positive sequence propagation coefficient of the transmission line;

(3) The protection device calculates the phase-to-phase fault position factor b of the transmission line:

$\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; Re</span>}<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}}_{\mathrm{<span\; class="notranslate">\; \&phi;\&phi;</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; Im</span>}<span\; class="notranslate">\; (</span>\frac{{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}}_{\mathrm{<span\; class="notranslate">\; \&phi;\&phi;</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; ch</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; set</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; Im</span>}<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}}_{\mathrm{<span\; class="notranslate">\; \&phi;\&phi;</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; Re</span>}<span\; class="notranslate">\; (</span>\frac{{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}}_{\mathrm{<span\; class="notranslate">\; \&phi;\&phi;</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; ch</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; set</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; Re</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; the\; th</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; set</span>}}<span\; class="notranslate">\; )</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}}_{\mathrm{<span\; class="notranslate">\; \&phi;\&phi;</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; Im</span>}<span\; class="notranslate">\; (</span>\frac{{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}}_{\mathrm{<span\; class="notranslate">\; \&phi;\&phi;</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; ch</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; set</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; Im</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; the\; th</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; set</span>}}<span\; class="notranslate">\; )</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}}_{\mathrm{<span\; class="notranslate">\; \&phi;\&phi;</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; Re</span>}<span\; class="notranslate">\; (</span>\frac{{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}}_{\mathrm{<span\; class="notranslate">\; \&phi;\&phi;</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; ch</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; set</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span>}$

Among them, φφ=AB, BC, CA phase; l _set is the transmission line protection setting range, which is 0.85 times the transmission line length; γ ₁ is the positive sequence propagation coefficient of the transmission line; Z _c1 is the positive sequence wave impedance of the transmission line; for the real part of for the imaginary part of for the real part of for the imaginary part of for the real part of for the imaginary part of

(4) The protection device judges whether the fault position factor b of the transmission line is less than 0, and if it is established, it judges that a phase-to-phase short-circuit fault occurs in the opposite direction of the transmission line protection;

(5) The protection device judges whether the fault position factor b of the transmission line is greater than 0. If it is true, it judges that a phase-to-phase short circuit fault occurs in the forward direction of the transmission line protection, and the protection device sends an action trip signal to trip the circuit breakers at both ends of the transmission line.

Compared with the prior art, the present invention has the following positive results:

The method of the invention adopts the long-line equation to accurately describe the physical characteristics of the transmission line, and has natural ability to resist the influence of distributed capacitance. The method of the present invention first calculates the ratio of the fault impedance from the installation place of the transmission line protection to the phase-to-phase short-circuit fault point and the line impedance from the installation place of the transmission line protection to the setting range of the transmission line protection to obtain the position factor b of the phase-to-phase fault of the transmission line, and then by judging the transmission line Whether the position factor b of the phase-to-phase fault of the line is less than 0 or greater than 0 is established, so as to accurately determine whether a phase-to-phase short-circuit fault occurs in the reverse direction of the transmission line protection or a phase-to-phase short-circuit fault occurs in the forward direction of the transmission line protection. If a phase-to-phase short-circuit fault occurs in the forward direction of the transmission line protection, the protection device Send an action trip signal to trip the circuit breakers at both ends of the transmission line, which in principle eliminates the influence of the phase-to-phase short-circuit fault point voltage, transition resistance and load current on the judgment result of the transmission line phase-to-phase short-circuit fault direction, and effectively prevents misoperation of the transmission line phase-to-phase distance protection , especially suitable for phase-to-phase fault relay protection of UHV AC transmission lines.

Description of drawings

Fig. 1 is a schematic diagram of a line transmission system applying the present invention.

Detailed ways

The technical solution of the present invention will be further described in detail according to the accompanying drawings.

Fig. 1 is a schematic diagram of a line transmission system applying the present invention. In Fig. 1, CVT is a voltage transformer, and CT is a current transformer. The protection device samples the voltage of the voltage transformer CVT and the current waveform of the current transformer CT at the place where the transmission line protection is installed to obtain instantaneous values of voltage and current.

The protection device uses the Fourier algorithm to calculate the fault phase-to-phase voltage at the protection installation of the transmission line on the sampled voltage and current instantaneous values Fault phase current and negative sequence current between fault phases Among them, φφ=AB, BC, CA phase.

The protective device calculates the hyperbolic cosine function value ch(γ ₁ l _set ) of γ ₁ l _set .

The protective device calculates the hyperbolic tangent function value th(γ ₁ l _set ) of γ ₁ l _set .

Among them, l _set is the setting range of transmission line protection, which is 0.85 times the length of transmission line; γ ₁ is the positive sequence propagation coefficient of transmission line.

The protection device calculates the phase-to-phase fault position factor b of the transmission line:

$\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; Re</span>}<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}}_{\mathrm{<span\; class="notranslate">\; \&phi;\&phi;</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; Im</span>}<span\; class="notranslate">\; (</span>\frac{{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}}_{\mathrm{<span\; class="notranslate">\; \&phi;\&phi;</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; ch</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; set</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; Im</span>}<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}}_{\mathrm{<span\; class="notranslate">\; \&phi;\&phi;</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; Re</span>}<span\; class="notranslate">\; (</span>\frac{{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}}_{\mathrm{<span\; class="notranslate">\; \&phi;\&phi;</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; ch</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; set</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; Re</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; the\; th</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; set</span>}}<span\; class="notranslate">\; )</span>{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}}_{\mathrm{<span\; class="notranslate">\; \&phi;\&phi;</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; Im</span>}<span\; class="notranslate">\; (</span>\frac{{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}}_{\mathrm{<span\; class="notranslate">\; \&phi;\&phi;</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; ch</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; set</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; Im</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; the\; th</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; set</span>}}<span\; class="notranslate">\; )</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}}_{\mathrm{<span\; class="notranslate">\; \&phi;\&phi;</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; Re</span>}<span\; class="notranslate">\; (</span>\frac{{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}}_{\mathrm{<span\; class="notranslate">\; \&phi;\&phi;</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; ch</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; set</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span>}$

Among them, φφ=AB, BC, CA phase; l _set is the transmission line protection setting range, which is 0.85 times the transmission line length; γ ₁ is the positive sequence propagation coefficient of the transmission line; Z _c1 is the positive sequence wave impedance of the transmission line; for the real part of for the imaginary part of for the real part of for the imaginary part of for the real part of for the imaginary part of .

The protection device judges whether the fault location factor b of the transmission line is less than 0, and if so, judges that a phase-to-phase short-circuit fault occurs in the opposite direction of the transmission line protection.

The protection device judges whether the fault location factor b of the transmission line is greater than 0. If it is true, it judges that a phase-to-phase short-circuit fault occurs in the forward direction of the transmission line protection, and the protection device sends an action trip signal to trip the circuit breakers at both ends of the transmission line.

The method of the invention adopts the long-line equation to accurately describe the physical characteristics of the transmission line, and has natural ability to resist the influence of distributed capacitance. The method of the present invention firstly calculates the ratio of the fault impedance from the installation place of the transmission line protection to the phase-to-phase short-circuit fault point and the line impedance from the installation place of the transmission line protection to the setting range of the transmission line protection, obtains the position factor b of the phase-to-phase fault of the transmission line, and then judges the transmission line Whether the position factor b of the phase-to-phase fault of the line is less than 0 or greater than 0 is established to accurately determine whether a phase-to-phase short-circuit fault occurs in the reverse direction of the transmission line protection or a phase-to-phase short-circuit fault occurs in the forward direction of the transmission line protection. If a phase-to-phase short-circuit fault occurs in the forward direction of the transmission line protection, the protection device Send an action trip signal to trip the circuit breakers at both ends of the transmission line, which in principle eliminates the influence of the phase-to-phase short-circuit fault point voltage, transition resistance and load current on the judgment results of the phase-to-phase short-circuit fault direction of the transmission line, and effectively prevents misoperation of the transmission line phase-to-phase distance protection , especially suitable for phase-to-phase fault relay protection of UHV AC transmission lines.

The above descriptions are only preferred specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto, any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention , should be covered within the protection scope of the present invention.

Claims (1)

1. based on the fault position factor phase characteristic circuit phase-to-phase fault discrimination method, it is characterized in that, comprises following sequential steps: (1) The protection device measures the fault phase-to-phase voltage at the protection installation of the transmission line Fault phase current and negative sequence current between fault phases Among them, φφ=AB, BC, CA phase; (2) The protective device calculates the hyperbolic cosine function value ch(γ ₁ l _set ) of γ ₁ l _set , and calculates the hyperbolic tangent function value th(γ ₁ l _set ) of γ ₁ l _set ; where, l _set is the transmission line The protection setting range is taken as 0.85 times the length of the transmission line; γ ₁ is the positive sequence propagation coefficient of the transmission line. (3) The protection device calculates the phase-to-phase fault position factor b of the transmission line: $\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; Re</span>}<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}}_{\mathrm{<span\; class="notranslate">\; \&phi;\&phi;</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; Im</span>}<span\; class="notranslate">\; (</span>\frac{{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}}_{\mathrm{<span\; class="notranslate">\; \&phi;\&phi;</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; ch</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; set</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; Im</span>}<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}}_{\mathrm{<span\; class="notranslate">\; \&phi;\&phi;</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; Re</span>}<span\; class="notranslate">\; (</span>\frac{{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}}_{\mathrm{<span\; class="notranslate">\; \&phi;\&phi;</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; ch</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; set</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; Re</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; the\; th</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; set</span>}}<span\; class="notranslate">\; )</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}}_{\mathrm{<span\; class="notranslate">\; \&phi;\&phi;</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; Im</span>}<span\; class="notranslate">\; (</span>\frac{{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}}_{\mathrm{<span\; class="notranslate">\; \&phi;\&phi;</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; ch</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; set</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; Im</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; the\; th</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; set</span>}}<span\; class="notranslate">\; )</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}}_{\mathrm{<span\; class="notranslate">\; \&phi;\&phi;</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; Re</span>}<span\; class="notranslate">\; (</span>\frac{{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}}_{\mathrm{<span\; class="notranslate">\; \&phi;\&phi;</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; ch</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; set</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span>}$ Among them, φφ=AB, BC, CA phase; l _set is the transmission line protection setting range, which is 0.85 times the transmission line length; _γ1 is the positive sequence propagation coefficient of the transmission line; Z _c1 is the positive sequence wave impedance of the transmission line; for the real part of for the imaginary part of for the real part of for the imaginary part of for the real part of for the imaginary part of (4) The protection device judges whether the fault position factor b of the transmission line is less than 0, and if it is established, it judges that a phase-to-phase short-circuit fault occurs in the opposite direction of the transmission line protection; (5) The protection device judges whether the fault position factor b of the transmission line is greater than 0. If it is true, it judges that a phase-to-phase short-circuit fault occurs in the forward direction of the transmission line protection, and the protection device sends an action trip signal to trip the circuit breakers at both ends of the transmission line.