CN106908692A - A kind of transmission line one-phase earth fault self adaptation reclosing determination methods - Google Patents

Abstract

A kind of transmission line one-phase earth fault self adaptation reclosing determination methods, two three-phase voltages and three-phase current at moment are gathered as input quantity in the side of transmission line of electricity；Using two voltages at moment, the corresponding positive and negative, residual voltage of Current calculation, the electric current phasor that measure；Based on Transmission Line Distributed Parameter model, respectively for two kinds of possible fault types of permanent singlephase earth fault and transient single-phase earth fault, set up equation and describe the voltage of transmission line of electricity both sides, current relationship, obtain two groups of Nonlinear System of Equations；With measuring point to the electrical source voltage of side system, equivalent system impedance, fault distance and transition resistance as unknown quantity, solve the Nonlinear System of Equations set up, draw respectively for two groups of fault localization results of Nonlinear System of Equations, and seek its ratio, ratio then judges to there occurs single-phase permanent earth fault, lock-reclosing lock function less than threshold value；Otherwise it is judged as there occurs single-phase instantaneity earth fault, implements reclosing.

Description

A kind of transmission line one-phase earth fault self adaptation reclosing determination methods

Technical field

The present invention relates to protecting electrical power system and control field, more particularly to a kind of transmission line one-phase earth fault is adaptive Answer reclosing determination methods.

Technical background

Automatic reclosing technology obtains commonly used on 110kV above transmission lines of electricity, is connect for instantaneity Earth fault can automatic recovery of power supply, but if permanent earth fault, implement reclosing power system will be produced Secondary pulse, affects the stability of system.Therefore, self adaptation reclosing technology has obtained extensive concern.

Existing self adaptation reclosing technology is mainly using failure phase line after the circuit breaker trip of failure phase both sides due to non- The fault signature that secondary arc current and Coupling Between Phases of failure phase line etc. are induced recognize whether stabilization ground connection branch Road, so as to distinguish instantaneity earth fault or permanent earth fault.But because Coupling Between Phases or secondary arc current are produced Fault signature it is more faint, it is permanent earth to identify whether just with the information after the circuit breaker trip of trouble point both sides Failure success rate is not high, is not also widely used in power system at present.

National inventing patent《Transmission line one-phase earth fault method of single end distance measurement》, application number：201310415348.2. Fault localization problem is switched into the identification problem to wire topologies, using transmission line of electricity occur singlephase earth fault after and It is interrupted before both sides breaker does not trip, and after the failure phase circuit breaker trip of circuit both sides and during the first two of reclosing The monitored equations of line of single-end electrical quantity description under face, information content is double, therefore, it is possible to accurately obtain fault distance, but simultaneously Can not solve the problems, such as that self adaptation reclosing differentiates, the information based on discontinuity surface at two is found in research process, it is false respectively If failure under two topological structures of instantaneity earth fault and permanent earth fault to attend as a nonvoting delegate equation group and calculating fault distance, The error energy direct reaction of fault localization is out of order the difference of type, and its main cause is the fault branch of stabilization with the presence or absence of will Stability of the failure phase line in 2 times voltages of moment is directly influenced, and the stability will result directly in the size of range error, Therefore it is self adaptation reclosing algorithm that can further expand Fault Location Algorithm.

The content of the invention

The purpose of the present invention is the weak point for overcoming prior art, a kind of instantaneous single-phase earthing event of transmission line of electricity of proposition Barrier self adaptation reclosing determination methods, it is self adaptation reclosing algorithm, the algorithm that can further expand Fault Location Algorithm Based on single-end electrical quantity, do not influenceed by communication；Modeled using distributed constant, do not influenceed by capacitance current, not by transition Resistance, load current, the influence of offside system impedance, with practical value very high.

In order to achieve the above object, the technical scheme is that：

A kind of instantaneous singlephase earth fault self adaptation reclosing determination methods of transmission line of electricity, comprise the following steps：

(1) defeated hypothesis electric line is M sides, the open circuit after transmission line of electricity either side, measurement faulty line singlephase earth fault The moment is the three-phase voltage phasor U at moment 1 before the single-phase tripping operation of device_mfa、U_mfb、U_mfcWith three-phase current phasor I_mfa、I_mfb、I_mfc, with And the moment is the three-phase voltage phasor U at moment 2 before reclosing after measurement failure phase circuit breaker trip_mha、U_mhb、U_mhcAnd electric current Phasor I_mha、I_mhb、I_mhc, above-mentioned measurement is used as input quantity；By following formula be calculated above-mentioned two moment corresponding positive sequence, negative phase-sequence, Residual voltage phasor U_mf1、U_mf2、U_mf0With electric current phasor I_mf1、I_mf2、I_mf0, and U_mh1、U_mh2、U_mh0With positive sequence, negative phase-sequence, zero sequence Electric current phasor I_mh1、I_mh2、I_mh0：

Wherein a=e^j2π/3；

(2) electricity that equation describes transmission line of electricity both sides is set up using step (1) voltage for being calculated, current sequence components Pressure, current relationship, obtain two groups of Nonlinear System of Equations：

Transmission line of electricity both sides voltage-current relationship equation group (1) described under permanent singlephase earth fault are：

Transmission line of electricity both sides voltage-current relationship equation group (2) under description transient single-phase earth fault are：

Wherein U_nhy1、U_nhy2、U_nhy0、I_nhy1、I_nhy2、I_nhy0Represent that 2 times hypothesis failures of moment are the event of permanent single-phase earthing Under barrier, the positive sequence voltage of the circuit offside (N sides) being calculated based on equation group (1), negative sequence voltage, residual voltage, positive sequence electricity Stream, negative-sequence current, zero-sequence current phasor；U_nhs1、U_nhs2、U_nhs0、I_nhs1、I_nhs2、I_nhs0Represent that 2 times hypothesis failures of moment are instantaneous Under property singlephase earth fault, positive sequence voltage, negative sequence voltage, the zero sequence of the circuit offside (N sides) being calculated based on equation group (2) Voltage, forward-order current, negative-sequence current, zero-sequence current phasor；L is transmission line length, γ₁It is positive sequence propagation coefficient：γ₀It is zero sequence propagation coefficient：Z_c1It is positive sequence ripple Impedance：R₁、L₁、G₁、C₁Respectively the positive sequence resistance of unit length circuit, inductance, Conductance and capacitance；

Z_c0It is zero sequence wave impedance：R₀、L₀、G₀、C₀Respectively unit length line The zero sequence resistance on road, inductance, conductance and capacitance；

A is voltage Transfer coefficient matrices, and B is impedance matrix, and C is admittance matrix, and D is electric current Transfer coefficient matrices, specifically It is defined as follows：

(3), two groups of sequence voltages of N sides three, electric current phasor U will be calculated in step (2)_nhy1、U_nhy2、U_nhy0、I_nhy1、 I_nhy2、I_nhy0And U_nhs1、U_nhs2、U_nhs0、I_nhs1、I_nhs2、I_nhs0Following formula is substituted into, calculating is respectively obtained based on failure permanently to connect N sides three-phase voltage, electric current phasor U that earth fault is assumed_nhya、U_nhyb、U_nhyc、I_nhya、I_nhyb、I_nhyc, and be instantaneous based on failure Property earth fault assume N sides three-phase voltage, electric current phasor U_nhsa、U_nhsb、U_nhsc、I_nhsa、I_nhsb、I_nhsc：

(4) unknown quantity is set：System N sides potentials E_N, positive sequence impedance Z_N1,Z_N0, fault resstance R, trouble point and system M sides it Between distance account for the percentage x of line length；Assuming that failure is permanent singlephase earth fault, equation below group (3) is write out：

Wherein：Z_sIt is system side self-impedanceZ_mIt is system side mutual impedance

The relevant parameter that will be measured in step (1)-(4) or be calculated, substitutes into (3), and by non-linear Complex in (3) Group separates real part imaginary part, changes into the Nonlinear System of Equations of real number, the zero sequence impedance Z of given system N sides_N0, use improved height This-Newton method Levenbery-Marquardt methods are solved, you can must assume that failure is the trouble point under permanent fault With the percentage x that the distance between system M sides account for line length_y；

(5) assume that failure is transient single-phase earth fault, write out equation below group (4)：

The relevant parameter that will be measured in step (1)-(4) or be calculated, substitutes into (4), and by non-linear Complex in (4) Group separates real part imaginary part, changes into the Nonlinear System of Equations of real number, the zero sequence impedance Z of given system N sides_N0, use improved height This-Newton method method solved, you can must assume that failure is the distance between the trouble point under transient fault and system M sides Account for the percentage x of line length_s；

6) ratio=is defined | x_y-x_s| × 100, instantaneity is (silent through small resistor at advance simulation calculation circuit proximal outlet Recognize 10 ohm of value) singlephase earth fault occur when ratio values as threshold value；If the ratio values being actually calculated are small Then judge to there occurs single-phase permanent earth fault, lock-reclosing lock function in threshold value；Otherwise it is judged as there occurs single-phase instantaneous Property earth fault, implement reclosing.

The features of the present invention and effect：

Before present invention utilization is monitored after transmission line of electricity generation singlephase earth fault and both sides breaker does not trip, And inscribed after the failure phase circuit breaker trip of circuit both sides and during the first two of reclosing, it is assumed that failure is permanently to connect Earth fault and instantaneity earth fault, row write equation group and ask for fault distance deviation, and equation group is to transmission line of electricity physical fault shape The description accuracy of state will be reacted directly into the deviation of fault distance solution, therefore instantaneity or permanent fault type identification Accurately, and the method be based on single-end electrical quantity, do not influenceed by communication；The inventive method is modeled using distributed constant, is not distributed The influence of capacitance current, is not influenceed, with practical value very high by transition resistance, load, offside system impedance.

Brief description of the drawings

Fig. 1 is a kind of traditional transmission system model of 220kV.

Specific embodiment

The present invention is described in detail with specific embodiment below in conjunction with the accompanying drawings.

Embodiment one

A kind of traditional transmission system model of 220kV is as shown in figure 1, line length is 100km, line parameter circuit value value such as table 1 It is shown；System M sides potential is 220 ∠, 0 ° of kV；System M sides zero sequence impedance is 26.3 ∠, 90 ° of Ω；Positive sequence impedance is：29.3∠90° Ω；System N sides potential is 220 ∠, 30 ° of kV；System N sides zero sequence impedance is 28.14 ∠, 86.74 ° of Ω；Positive sequence impedance is：32.0∠ 78.4°Ω.System M sides are arranged on using the fault location device of the inventive method, voltage, electric current are respectively from line side voltage Transformer, current transformer.Simulated fault type is A phase permanent earth faults, and failure occurs at system M side 50km, The Ω of transition resistance 100.

The 220kV transmission line of electricity major parameters of table 1

Comprised the following steps that using the embodiment of the inventive method：

(1) in M side systems side, A, B, C the three-phase voltage phase after measurement faulty line singlephase earth fault before single-phase tripping operation Amount U_mfa、U_mfb、U_mfcWith electric current phasor I_mfa、I_mfb、I_mfc, and A, B, C the three-phase voltage phase after single-phase tripping operation before reclosing Amount U_mha、U_mhb、U_mhcWith electric current phasor I_mha、I_mhb、I_mhcAs input quantity：

After singlephase earth fault, before the single-phase tripping operation of breaker：

A phase voltages U_mfa=-165.85-j 3.7579kV, B phase voltages U_mfb=60.379+j 157.27kV

C phase voltages U_mfc=105.98j 132.46kV

A phase currents I_mfa=0.1139+j 0.48731kA, B phase currents I_mfb=-0.079284-j 1.0397kA

C phase currents I_mfc=-0.83508+j 0.57169kA

After the single-phase tripping operation of breaker, before reclosing：

A phase voltages U_mha=1.6321-j 6.8967kV, B phase voltages U_mhb=62.908+j 153.34kV

C phase voltages U_mhc=108.51-j 136.39kV

A phase currents I_mha=0kA, B phase currents I_mhb=0.06361-j 0.9579kA

C phase currents I_mhc=-0.69219+j 0.65348kA

By the positive sequence voltage phasor U before single-phase tripping operation after following formula calculating faulty line singlephase earth fault_mf1, negative sequence voltage Phasor U_mf2, residual voltage phasor U_mf0, forward-order current phasor I_mf1, negative-sequence current phasor I_mf2, zero-sequence current phasor I_mf0, and be Positive and negative, residual voltage phasor U of the system M sides before single-phase automation reclosing after the single-phase tripping operation in circuit both sides_mh1、U_mh2、U_mh0 And positive and negative, zero-sequence current phasor I_mh1、I_mh2、I_mh0：

(2) it is calculated：

Positive sequence wave impedance Z_c1：

Zero sequence wave impedance Z_c0：

Positive sequence propagation coefficient γ₁：

Zero sequence propagation coefficient γ₀：

By step 1) two voltages at moment being calculated, current sequence components substitute into equation group (1), (2), obtain：

(3) by step 2) in be calculated two groups of sequence voltages of N sides three, electric current phasor U_nhy1、U_nhy2、U_nhy0、I_nhy1、I_nhy2、 I_nhy0And U_nhs1、U_nhs2、U_nhs0、I_nhs1、I_nhs2、I_nhs0Following formula is substituted into, it is permanent earth event to respectively obtain calculating based on failure Hinder N sides three-phase voltage, the electric current phasor U for assuming_nhya、U_nhyb、U_nhyc、I_nhya、I_nhyb、I_nhyc, and based on failure for instantaneity connects N sides three-phase voltage, electric current phasor U that earth fault is assumed_nhsa、U_nhsb、U_nhsc、I_nhsa、I_nhsb、I_nhsc：

(4) unknown quantity is set：System N sides potentials E_N, positive sequence impedance Z_N1,Z_N0, fault resstance R, trouble point and system M sides it Between distance account for the percentage x of line length；The relevant parameter that will be measured in step (1)-(4) or be calculated, substitutes into formula (3) real part imaginary part, and by nonlinear complex equations in (3) is separated, the Nonlinear System of Equations of real number, given system N sides is changed into Zero sequence impedance Z_N0=28.14 ∠ 86.7, are permanent fault using improve Gauss-Newton method method to be calculated hypothesis failure Under the distance between trouble point and system M sides account for the percentage x of line length_y=0.49994.

(5) unknown quantity is equally set：System N sides potentials E_N, positive sequence impedance Z_N1,Z_N0, fault resstance R, trouble point and system M The distance between side accounts for the percentage x of line length；The relevant parameter that will be measured in step (1)-(4) or be calculated, substitutes into Formula (4), and nonlinear complex equations in (4) are separated into real part imaginary part, change into the Nonlinear System of Equations of real number, given system N The zero sequence impedance Z of side_N0=28.14 ∠ 86.7, are instantaneity event using improve Gauss-Newton method method to be calculated hypothesis failure The distance between trouble point and system M sides under barrier account for the percentage x of line length_s=0.50019.

(6) ratio=is calculated | x_y-x_s| × 100=0.025, instantaneity at advance simulation calculation circuit proximal outlet is passed through Ratio values when small resistor (10 ohm of value of acquiescence) singlephase earth fault occurs are now actual to count for 0.9818 used as threshold value Ratio values are calculated for 0.025 is less than threshold value, therefore failure judgement is permanent fault, it is misaligned.

Embodiment two

A kind of traditional transmission system model of 220kV is as shown in figure 1, line length is 100km, line parameter circuit value value such as table 1 It is shown；System M sides potential is 220 ∠, 0 ° of kV；System M sides zero sequence impedance is 26.3 ∠, 90 ° of Ω；Positive sequence impedance is：29.3∠90° Ω；System N sides potential is 220 ∠, 30 ° of kV；System N sides zero sequence impedance is 28.14 ∠, 86.74 ° of Ω；Positive sequence impedance is：32.0∠ 78.4°Ω.System M sides are arranged on using the fault location device of the inventive method, voltage, electric current are respectively from line side voltage Transformer, current transformer.Simulated fault type is A phase instantaneity earth faults, and failure occurs at system M side 50km, The Ω of transition resistance 100.

The 220kV transmission line of electricity major parameters of table 1

Comprised the following steps that using the embodiment of the inventive method：

1) in M side systems side, A, B, C the three-phase voltage phasor after measurement faulty line singlephase earth fault before single-phase tripping operation U_mfa、U_mfb、U_mfcWith electric current phasor I_mfa、I_mfb、I_mfc, and A, B, C the three-phase voltage phasor after single-phase tripping operation before reclosing U_mha、U_mhb、U_mhcWith electric current phasor I_mha、I_mhb、I_mhcAs input quantity：

After singlephase earth fault, before the single-phase tripping operation of breaker：

A phase voltages U_mfa=-165.85-j 3.7579kV, B phase voltages U_mfb=60.379+j 157.27kV

C phase voltages U_mfc=105.98j 132.46kV

A phase currents I_mfa=0.1139+j 0.48731kA, B phase currents I_mfb=-0.079284-j 1.0397kA

C phase currents I_mfc=-0.83508+j 0.57169kA

After the single-phase tripping operation of breaker, before reclosing：

A phase voltages U_mha=24.112-j 2.1296kV, B phase voltages U_mhb=62.889+j 153.34kV

C phase voltages U_mhc=108.49-j 136.4kV

A phase currents I_mha=0kA, B phase currents I_mhb=0.063751-j 0.95851kA

C phase currents I_mhc=-0.69204+j 0.65287kA

By the positive sequence voltage phasor U before single-phase tripping operation after following formula calculating faulty line singlephase earth fault_mf1, negative sequence voltage Phasor U_mf2, residual voltage phasor U_mf0, forward-order current phasor I_mf1, negative-sequence current phasor I_mf2, zero-sequence current phasor I_mf0, and be Positive and negative, residual voltage phasor U of the system M sides before single-phase automation reclosing after the single-phase tripping operation in circuit both sides_mh1、U_mh2、U_mh0 And positive and negative, zero-sequence current phasor I_mh1、I_mh2、I_mh0：

2) it is calculated：

Positive sequence wave impedance Z_c1：

Zero sequence wave impedance Z_c0：

Positive sequence propagation coefficient γ₁：

Zero sequence propagation coefficient γ₀：

By step 1) two voltages at moment being calculated, current sequence components substitute into equation group (1), (2), obtain：

3) by step 2) in be calculated two groups of sequence voltages of N sides three, electric current phasor U_nhy1、U_nhy2、U_nhy0、I_nhy1、I_nhy2、 I_nhy0And U_nhs1、U_nhs2、U_nhs0、I_nhs1、I_nhs2、I_nhs0Following formula is substituted into, it is permanent earth event to respectively obtain calculating based on failure Hinder N sides three-phase voltage, the electric current phasor U for assuming_nhya、U_nhyb、U_nhyc、I_nhya、I_nhyb、I_nhyc, and based on failure for instantaneity connects N sides three-phase voltage, electric current phasor U that earth fault is assumed_nhsa、U_nhsb、U_nhsc、I_nhsa、I_nhsb、I_nhsc：

4) unknown quantity is set：System N sides potentials E_N, positive sequence impedance Z_N1,Z_N0, fault resstance R, trouble point and system M sides it Between distance account for the percentage x of line length；The relevant parameter that will be measured in step (1)-(4) or be calculated, substitutes into formula (3) real part imaginary part, and by nonlinear complex equations in (3) is separated, the Nonlinear System of Equations of real number, given system N sides is changed into Zero sequence impedance Z_N0=28.14 ∠ 86.7, are permanent fault using improve Gauss-Newton method method to be calculated hypothesis failure Under the distance between trouble point and system M sides account for the percentage x of line length_y=1.0891.

5) unknown quantity is equally set：System N sides potentials E_N, positive sequence impedance Z_N1,Z_N0, fault resstance R, trouble point and system M The distance between side accounts for the percentage x of line length；The relevant parameter that will be measured in step (1)-(4) or be calculated, substitutes into Formula (4), and nonlinear complex equations in (4) are separated into real part imaginary part, change into the Nonlinear System of Equations of real number, given system N The zero sequence impedance Z of side_N0=28.14 ∠ 86.7, are instantaneity event using improve Gauss-Newton method method to be calculated hypothesis failure The distance between trouble point and system M sides under barrier account for the percentage x of line length_s=0.50006.

6) ratio=is calculated | x_y-x_s| × 100=58.904, instantaneity at advance simulation calculation circuit proximal outlet is passed through Ratio values when small resistor (10 ohm of value of acquiescence) singlephase earth fault occurs are now actual to count for 0.9818 used as threshold value Ratio values are calculated for 58.904 are much larger than threshold value, therefore failure judgement is transient fault, carries out reclosing.

Claims (1)

1. instantaneous singlephase earth fault self adaptation reclosing determination methods of a kind of transmission line of electricity, it is characterised in that including following step Suddenly：

(1) defeated hypothesis electric line is M sides, the breaker list after transmission line of electricity either side, measurement faulty line singlephase earth fault The moment is the three-phase voltage phasor U at moment 1 before mutually tripping_mfa、U_mfb、U_mfcWith three-phase current phasor I_mfa、I_mfb、I_mfc, and survey The moment is the three-phase voltage phasor U at moment 2 before reclosing after amount failure phase circuit breaker trip_mha、U_mhb、U_mhcAnd electric current phasor I_mha、I_mhb、I_mhc, above-mentioned measurement is used as input quantity；Above-mentioned two moment corresponding positive sequence, negative phase-sequence, zero sequence are calculated by following formula Voltage phasor U_mf1、U_mf2、U_mf0With electric current phasor I_mf1、I_mf2、I_mf0, and U_mh1、U_mh2、U_mh0With positive sequence, negative phase-sequence, zero-sequence current Phasor I_mh1、I_mh2、I_mh0：

$\left[\begin{array}{c}{U}_{mf1}\\ U_{mf2}\\ U_{mf0}\end{array}\right]=\frac{1}{3}\left[\begin{array}{ccc}1& a& a^2\\ 1& a^2& a\\ 1& 1& 1\end{array}\right]\left[\begin{array}{c}{U}_{mfa}\\ U_{mfb}\\ U_{mfc}\end{array}\right],\left[\begin{array}{c}{I}_{mf1}\\ I_{mf2}\\ I_{mf0}\end{array}\right]=\frac{1}{3}\left[\begin{array}{ccc}1& a& a^2\\ 1& a^2& a\\ 1& 1& 1\end{array}\right]\left[\begin{array}{c}{I}_{mfa}\\ I_{mfb}\\ I_{mfc}\end{array}\right]$

$\left[\begin{array}{c}{U}_{mh1}\\ U_{mh2}\\ U_{mh0}\end{array}\right]=\frac{1}{3}\left[\begin{array}{ccc}1& a& a^2\\ 1& a^2& a\\ 1& 1& 1\end{array}\right]\left[\begin{array}{c}{U}_{mha}\\ U_{mhb}\\ U_{mhc}\end{array}\right],\left[\begin{array}{c}{I}_{mh1}\\ I_{mh2}\\ I_{mh0}\end{array}\right]=\frac{1}{3}\left[\begin{array}{ccc}1& a& a^2\\ 1& a^2& a\\ 1& 1& 1\end{array}\right]\left[\begin{array}{c}{I}_{mha}\\ I_{mhb}\\ I_{mhc}\end{array}\right]$

Wherein a=e^j2π/3；

(2) set up equation and describe the voltage of transmission line of electricity both sides, electricity using step (1) voltage for being calculated, current sequence components Flow relation, obtains two groups of Nonlinear System of Equations：

Transmission line of electricity both sides voltage-current relationship equation group (1) described under permanent singlephase earth fault are：

$\left[\begin{array}{c}{U}_{nhy1}\\ U_{nhy2}\\ U_{nhy0}\end{array}\right]=A\left[\begin{array}{c}{U}_{mh1}\\ U_{mh2}\\ U_{mh0}\end{array}\right]-B\left[\begin{array}{c}{I}_{mh1}\\ I_{mh2}\\ I_{mh0}\end{array}\right],\left[\begin{array}{c}{I}_{nhy1}\\ I_{nhy2}\\ I_{nhy0}\end{array}\right]=C\left[\begin{array}{c}{U}_{mh1}\\ U_{mh2}\\ U_{mh0}\end{array}\right]-D\left[\begin{array}{c}{I}_{mh1}\\ I_{mh2}\\ I_{mh0}\end{array}\right]---\left(1\right)$

Transmission line of electricity both sides voltage-current relationship equation group (2) under description transient single-phase earth fault are：

$\left[\begin{array}{c}{U}_{nhs1}\\ U_{nhs2}\\ U_{nhs0}\end{array}\right]=\left[\begin{array}{ccc}{\mathrm{cosh\γ}}_{1}L& & \\ & {\mathrm{cosh\γ}}_{1}L& \\ & & {\mathrm{cosh\γ}}_{0}L\end{array}\right]\left[\begin{array}{c}{U}_{mh1}\\ U_{mh2}\\ U_{mh0}\end{array}\right]-\left[\begin{array}{ccc}{Z}_{c1}{\mathrm{sinh\γ}}_{1}L& & \\ & Z_{c1}{\mathrm{sinh\γ}}_{1}L& \\ & & Z_{c0}{\mathrm{sinh\γ}}_{0}L\end{array}\right]\left[\begin{array}{c}{I}_{mh1}\\ I_{mh2}\\ I_{mh0}\end{array}\right]$

$\left[\begin{array}{c}{I}_{nhs1}\\ I_{nhs2}\\ I_{nhs0}\end{array}\right]=\left[\begin{array}{ccc}\frac{{\mathrm{sinh\γ}}_{1}L}{Z_{c1}}& & \\ & \frac{{\mathrm{sinh\γ}}_{1}L}{Z_{c1}}& \\ & & \frac{{\mathrm{sinh\γ}}_{0}L}{Z_{c0}}\end{array}\right]\left[\begin{array}{c}{U}_{mh1}\\ U_{mh2}\\ U_{mh0}\end{array}\right]-\left[\begin{array}{ccc}{\mathrm{cosh\γ}}_{1}L& & \\ & {\mathrm{cosh\γ}}_{1}L& \\ & & {\mathrm{cosh\γ}}_{0}L\end{array}\right]\left[\begin{array}{c}{I}_{mh1}\\ I_{mh2}\\ I_{mh0}\end{array}\right]---\left(2\right)$

Wherein U_nhy1、U_nhy2、U_nhy0、I_nhy1、I_nhy2、I_nhy0Represent that moment 2 time assumes failures under permanent singlephase earth fault, It is the positive sequence voltage of the circuit offside (N sides) being calculated based on equation group (1), negative sequence voltage, residual voltage, forward-order current, negative Sequence electric current, zero-sequence current phasor；U_nhs1、U_nhs2、U_nhs0、I_nhs1、I_nhs2、I_nhs0Represent that 2 times hypothesis failures of moment are instantaneity list Under phase earth fault, the positive sequence voltage of the circuit offside (N sides) being calculated based on equation group (2), negative sequence voltage, zero sequence electricity Pressure, forward-order current, negative-sequence current, zero-sequence current phasor；L is transmission line length, γ₁It is positive sequence propagation coefficient：γ₀It is zero sequence propagation coefficient：

Z_c1It is positive sequence wave impedance：R₁、L₁、G₁、C₁Respectively unit length circuit Positive sequence resistance, inductance, conductance and capacitance；

Z_c0It is zero sequence wave impedance：R₀、L₀、G₀、C₀Respectively unit length circuit Zero sequence resistance, inductance, conductance and capacitance；

A is voltage Transfer coefficient matrices, and B is impedance matrix, and C is admittance matrix, and D is electric current Transfer coefficient matrices, is specifically defined It is as follows：

$A=\left[\begin{array}{ccc}{Z}_{c1}{\mathrm{sinh\γ}}_{1}L\left(1-x\right)\frac{{\mathrm{cosh\γ}}_{1}Lx}{3R_g}+{\mathrm{cosh\γ}}_{1}L& Z_{c1}{\mathrm{sinh\γ}}_{1}L\left(1-x\right)\frac{{\mathrm{cosh\γ}}_{1}Lx}{3R_g}& Z_{c1}{\mathrm{sinh\γ}}_{1}L\left(1-x\right)\frac{{\mathrm{cosh\γ}}_{0}Lx}{3R_g}\\ Z_{c1}{\mathrm{sinh\γ}}_{1}L\left(1-x\right)\frac{{\mathrm{cosh\γ}}_{1}Lx}{3R_g}& Z_{c1}{\mathrm{sinh\γ}}_{1}L\left(1-x\right)\frac{{\mathrm{cosh\γ}}_{1}Lx}{3R_g}+{\mathrm{cosh\γ}}_{1}L& Z_{c1}{\mathrm{sinh\γ}}_{1}L\left(1-x\right)\frac{{\mathrm{cosh\γ}}_{0}Lx}{3R_g}\\ Z_{c0}{\mathrm{sinh\γ}}_{0}L\left(1-x\right)\frac{{\mathrm{cosh\γ}}_{1}Lx}{3R_g}& Z_{c0}{\mathrm{sinh\γ}}_{0}L\left(1-x\right)\frac{{\mathrm{cosh\γ}}_{1}Lx}{3R_g}& Z_{c0}{\mathrm{sinh\γ}}_{0}L\left(1-x\right)\frac{{\mathrm{cosh\γ}}_{0}Lx}{3R_g}+{\mathrm{cosh\γ}}_{0}L\end{array}\right]$

$B=\left[\begin{array}{ccc}{Z}_{c1}{\mathrm{sinh\γ}}_{1}L\left(1-x\right)\frac{Z_{c1}{\mathrm{sinh\γ}}_{1}Lx}{3R_g}+Z_{c1}{\mathrm{sinh\γ}}_{1}L& Z_{c1}{\mathrm{sinh\γ}}_{1}L\left(1-x\right)\frac{Z_{c1}{\mathrm{sinh\γ}}_{1}Lx}{3R_g}& Z_{c1}{\mathrm{sinh\γ}}_{1}L\left(1-x\right)\frac{Z_{c0}{\mathrm{sinh\γ}}_{0}Lx}{3R_g}\\ Z_{c1}{\mathrm{sinh\γ}}_{1}L\left(1-x\right)\frac{Z_{c1}{\mathrm{sinh\γ}}_{1}Lx}{3R_g}& Z_{c1}{\mathrm{sinh\γ}}_{1}L\left(1-x\right)\frac{Z_{c1}{\mathrm{sinh\γ}}_{1}Lx}{3R_g}+Z_{c1}{\mathrm{sinh\γ}}_{1}L& Z_{c1}{\mathrm{sinh\γ}}_{1}L\left(1-x\right)\frac{Z_{c0}{\mathrm{sinh\γ}}_{0}Lx}{3R_g}\\ Z_{c0}{\mathrm{sinh\γ}}_{0}L\left(1-x\right)\frac{Z_{c1}{\mathrm{sinh\γ}}_{1}Lx}{3R_g}& Z_{c0}{\mathrm{sinh\γ}}_{0}L\left(1-x\right)\frac{Z_{c1}{\mathrm{sinh\γ}}_{1}Lx}{3R_g}& Z_{c0}{\mathrm{sinh\γ}}_{0}L\left(1-x\right)\frac{Z_{c0}{\mathrm{sinh\γ}}_{0}Lx}{3R_g}+Z_{c0}{\mathrm{sinh\γ}}_0\end{array}\right]$

$C=\left[\begin{array}{ccc}{\mathrm{cosh\γ}}_{1}L\left(1-x\right)\frac{{\mathrm{cosh\γ}}_{1}Lx}{3R_g}+\frac{{\mathrm{sinh\γ}}_{1}L}{Z_{c1}}& {\mathrm{cosh\γ}}_{1}L\left(1-x\right)\frac{{\mathrm{cosh\γ}}_{1}Lx}{3R_g}& {\mathrm{cosh\γ}}_{1}L\left(1-x\right)\frac{{\mathrm{cosh\γ}}_{0}Lx}{3R_g}\\ {\mathrm{cosh\γ}}_{1}L\left(1-x\right)\frac{{\mathrm{cosh\γ}}_{1}Lx}{3R_g}& {\mathrm{cosh\γ}}_{1}L\left(1-x\right)\frac{{\mathrm{cosh\γ}}_{1}Lx}{3R_g}+\frac{{\mathrm{sinh\γ}}_{1}L}{Z_{c1}}& {\mathrm{cosh\γ}}_{1}L\left(1-x\right)\frac{{\mathrm{cosh\γ}}_{0}Lx}{3R_g}\\ {\mathrm{cosh\γ}}_{0}L\left(1-x\right)\frac{{\mathrm{cosh\γ}}_{1}Lx}{3R_g}& {\mathrm{cosh\γ}}_{0}L\left(1-x\right)\frac{{\mathrm{cosh\γ}}_{1}Lx}{3R_g}& {\mathrm{cosh\γ}}_{0}L\left(1-x\right)\frac{{\mathrm{cosh\γ}}_{0}Lx}{3R_g}+\frac{{\mathrm{sinh\γ}}_{0}L}{Z_{c0}}\end{array}\right]$

$D=\left[\begin{array}{ccc}{\mathrm{cosh\γ}}_{1}L\left(1-x\right)\frac{Z_{c1}{\mathrm{sinh\γ}}_{1}Lx}{3R_g}+{\mathrm{cosh\γ}}_{1}L& {\mathrm{cosh\γ}}_{1}L\left(1-x\right)\frac{Z_{c1}{\mathrm{sinh\γ}}_{1}Lx}{3R_g}& {\mathrm{cosh\γ}}_{1}L\left(1-x\right)\frac{Z_{c0}{\mathrm{sinh\γ}}_{0}Lx}{3R_g}\\ {\mathrm{cosh\γ}}_{1}L\left(1-x\right)\frac{Z_{c1}{\mathrm{sinh\γ}}_{1}Lx}{3R_g}& {\mathrm{cosh\γ}}_{1}L\left(1-x\right)\frac{Z_{c1}{\mathrm{sinh\γ}}_{1}Lx}{3R_g}+{\mathrm{cosh\γ}}_{1}L& {\mathrm{cosh\γ}}_{1}L\left(1-x\right)\frac{Z_{c0}{\mathrm{sinh\γ}}_{0}Lx}{3R_g}\\ {\mathrm{cosh\γ}}_{0}L\left(1-x\right)\frac{Z_{c1}{\mathrm{sinh\γ}}_{1}Lx}{3R_g}& {\mathrm{cosh\γ}}_{0}L\left(1-x\right)\frac{Z_{c1}{\mathrm{sinh\γ}}_{1}Lx}{3R_g}& {\mathrm{cosh\γ}}_{0}L\left(1-x\right)\frac{Z_{c0}{\mathrm{sinh\γ}}_{0}Lx}{3R_g}+{\mathrm{cosh\γ}}_{0}L\end{array}\right]$

(3), two groups of sequence voltages of N sides three, electric current phasor U will be calculated in step (2)_nhy1、U_nhy2、U_nhy0、I_nhy1、I_nhy2、 I_nhy0And U_nhs1、U_nhs2、U_nhs0、I_nhs1、I_nhs2、I_nhs0Following formula is substituted into, it is permanent earth event to respectively obtain calculating based on failure Hinder N sides three-phase voltage, the electric current phasor U for assuming_nhya、U_nhyb、U_nhyc、I_nhya、I_nhyb、I_nhyc, and based on failure for instantaneity connects N sides three-phase voltage, electric current phasor U that earth fault is assumed_nhsa、U_nhsb、U_nhsc、I_nhsa、I_nhsb、I_nhsc：

$\left[\begin{array}{c}{U}_{nhya}\\ U_{nhyb}\\ U_{nhyc}\end{array}\right]=\left[\begin{array}{ccc}1& 1& 1\\ a^2& a& 1\\ a& a^2& 1\end{array}\right]\left[\begin{array}{c}{U}_{nhy1}\\ U_{nhy2}\\ U_{nhy0}\end{array}\right],\left[\begin{array}{c}{I}_{nhya}\\ I_{nhyb}\\ I_{nhyc}\end{array}\right]=\left[\begin{array}{ccc}1& 1& 1\\ a^2& a& 1\\ a& a^2& 1\end{array}\right]\left[\begin{array}{c}{I}_{nhy1}\\ I_{nhy2}\\ I_{nhy0}\end{array}\right]$

$\left[\begin{array}{c}{U}_{nhsa}\\ U_{nhsb}\\ U_{nhsc}\end{array}\right]=\left[\begin{array}{ccc}1& 1& 1\\ a^2& a& 1\\ a& a^2& 1\end{array}\right]\left[\begin{array}{c}{U}_{nhs1}\\ U_{nhs2}\\ U_{nhs0}\end{array}\right],\left[\begin{array}{c}{I}_{nhsa}\\ I_{nhsb}\\ I_{nhsc}\end{array}\right]=\left[\begin{array}{ccc}1& 1& 1\\ a^2& a& 1\\ a& a^2& 1\end{array}\right]\left[\begin{array}{c}{I}_{nhs1}\\ I_{nhs2}\\ I_{nhs0}\end{array}\right]$

(4) unknown quantity is set：System N sides potentials E_N, positive sequence impedance Z_N1,Z_N0, fault resstance R, between trouble point and system M sides Distance accounts for the percentage x of line length；Assuming that failure is permanent singlephase earth fault, equation below group (3) is write out：

$\left\{\begin{array}{c}\left[\begin{array}{c}{E}_N\\ 0\\ 0\end{array}\right]=A\left[\begin{array}{c}{U}_{mf1}\\ U_{mf2}\\ U_{mf0}\end{array}\right]-B\left[\begin{array}{c}{I}_{mf1}\\ I_{mf2}\\ I_{mf0}\end{array}\right]+\left[\begin{array}{ccc}{Z}_{N1}& & \\ & Z_{N1}& \\ & & Z_{N0}\end{array}\right]\left(C\left[\begin{array}{c}{U}_{mf1}\\ U_{mf2}\\ U_{mf0}\end{array}\right]-D\left[\begin{array}{c}{I}_{mf1}\\ I_{mf2}\\ I_{mf0}\end{array}\right]\right)\\ a^2{E}_N=Z_s{I}_{nhyb}+Z_m{I}_{nhyc}+U_{nhyb}\\ {\mathrm{aE}}_N=Z_m{I}_{nhyb}+Z_s{I}_{nhyc}+U_{nhyc}\end{array}\right.---\left(3\right)$

Wherein：Z_sIt is system side self-impedanceZ_mIt is system side mutual impedance

The relevant parameter that will be measured in step (1)-(4) or be calculated, is substituted into (3), and nonlinear complex equations in (3) are divided From real part imaginary part, the Nonlinear System of Equations of real number, the zero sequence impedance Z of given system N sides are changed into_N0, use improved Gauss-ox Method Levenbery-Marquardt methods are solved, you can must assume failure for the trouble point under permanent fault be The distance between system M sides account for the percentage x of line length_y；

(5) assume that failure is transient single-phase earth fault, write out equation below group (4)：

$\left\{\begin{array}{c}\left[\begin{array}{c}{E}_N\\ 0\\ 0\end{array}\right]=A\left[\begin{array}{c}{U}_{mf1}\\ U_{mf2}\\ U_{mf0}\end{array}\right]-B\left[\begin{array}{c}{I}_{mf1}\\ I_{mf2}\\ I_{mf0}\end{array}\right]+\left[\begin{array}{ccc}{Z}_{N1}& & \\ & Z_{N1}& \\ & & Z_{N0}\end{array}\right]\left(C\left[\begin{array}{c}{U}_{mf1}\\ U_{mf2}\\ U_{mf0}\end{array}\right]-D\left[\begin{array}{c}{I}_{mf1}\\ I_{mf2}\\ I_{mf0}\end{array}\right]\right)\\ a^2{E}_N=Z_s{I}_{nhsb}+Z_m{I}_{nhsc}+U_{nhsb}\\ {\mathrm{aE}}_N=Z_m{I}_{nhsb}+Z_s{I}_{nhsc}+U_{nhsc}\end{array}\right.---\left(4\right)$

The relevant parameter that will be measured in step (1)-(4) or be calculated, is substituted into (4), and nonlinear complex equations in (4) are divided From real part imaginary part, the Nonlinear System of Equations of real number, the zero sequence impedance Z of given system N sides are changed into_N0, use improved Gauss-ox Method method of pausing is solved, you can the line is busy for the distance between trouble point and system M sides under transient fault must to assume failure The percentage x of road length_s；

6) ratio=is defined | x_y-x_s| × 100, through small resistor, (acquiescence takes instantaneity at advance simulation calculation circuit proximal outlet 10 ohm of value) singlephase earth fault occur when ratio values as threshold value；If the ratio values being actually calculated are less than threshold Value then judges to there occurs single-phase permanent earth fault, lock-reclosing lock function；Otherwise it is judged as there occurs that single-phase instantaneity connects Earth fault, implements reclosing.