CN103296655B - The lossfree line current traveling-wave differential protection method of the saturated impact of anti-current instrument transformer - Google Patents

Abstract

The invention discloses the lossfree line current traveling-wave differential protection method of the saturated impact of a kind of anti-current instrument transformer.First the method gathers voltage, the current traveling wave component of each sampling instant of transmission line two ends; utilize the voltage traveling wave component in front 1/4 moment in cycle of current sample time to calculate the current traveling wave component of transmission line one end of current sample time, utilize the current traveling wave component of the transmission line one end calculated to form current traveling wave differential protection criterion with this end line current traveling wave component obtained of sampling.The inventive method, without the need to being asked for the current traveling wave component of each sampling instant by interpolation arithmetic, decreases algorithm operation quantity, improves protection act speed.The inventive method can complete transmission line malfunction traveling-wave protection function in the short-data windows in 1/4 cycle, and protection act speed is fast.<!--1-->

Description

The lossfree line current traveling-wave differential protection method of the saturated impact of anti-current instrument transformer

Technical field

The present invention relates to Relay Protection Technology in Power System field, specifically relate to the lossfree line current traveling-wave differential protection method of the saturated impact of a kind of anti-current instrument transformer.

Background technology

Owing to not affecting by system operation mode and electric network composition and having natural phase-selecting function, current differential protection is the main protection of various electric pressure transmission line always.In 220kV and following electric pressure transmission line, because transmission line capacitance current along the line is very little, distributed capacitance is very little on the impact of current differential protection performance.The voltage of ultra-high/extra-high voltage transmission line of alternation current, current delivery have obvious wave process; capacitance current along the line is very large; the amplitude of the vector of two ends fundamental frequency steady-state current component is utilized to be faced with current differential protection starting current as the conventional current differential protection of actuating quantity large; and in order to prevent false protection; improving startup set point can cause again protection sensitivity not enough, governs the application of conventional current differential protection on ultra-high/extra-high voltage transmission line of alternation current.

When failure point of power transmission line is near current transformer installation place; because fault current is very large; current transformer is easily saturated; current differential protection misoperation when CT saturation can cause line protection external area error, current differential protection refused action when CT saturation can cause line protection troubles inside the sample space.

Traveling-wave differential protection considers the impact of distributed capacitance in protection algorism Mathematical Modeling, and the impact not by transmission line distributed capacitance in traveling-wave differential protection principle, has very high performance.Application number 200910034669.1 patent of invention " is applicable to the traveling-wave differential protection method of series capacitor compensated line " and solves the impact of distributed capacitance on differential protection performance; but for the situation that the time delay of row wave traveling is the non-integral multiple sampling interval; need the electric parameters obtained by interpolation arithmetic on each time point; very high to the requirement of protective device sample frequency; therefore very high to protective device hardware requirement; and each sampling time to carry out interpolation arithmetic; the required operand of protection algorism itself is large, cannot meet the requirement of protection quick-action." traveling-wave differential protection of UHV Transmission Line with Shunt Reactor " of Su Bin, Dong Xinzhou and Sun Yuan Zhang Fabiao and " traveling-wave differential protection based on wavelet transformation " of Su Bin, Dong Xinzhou and Sun Yuan Zhang Fabiao and application number 200410079501.X patent of invention " detection method of voltage zero cross near fault in travelling wave protection " are the electric parameters that the situation in non-integral multiple sampling interval also needs to be obtained by interpolation arithmetic on each time point for the time delay of row wave traveling, there is the problem that operand is large equally; Need to carry out wavelet transformation, desired data window is large, and protection detects that fault generation required time is long.

At present; the transmission line travelling wave differential protecting method that many scholars have proposed is that the situation in non-integral multiple sampling interval all needs to carry out interpolation arithmetic and asks electric parameters on its each time point to the time delay of row wave traveling; the operand of protection algorism own is large, requires high to protective device sampling hardware.Part transmission line travelling wave differential protecting method even needs to carry out wavelet transformation, and desired data window is large, extends protection and the time that fault occurs detected, cannot meet the requirement of relaying protection to quick-action.

Summary of the invention

The object of the invention is to the deficiency overcoming prior art existence, a kind of lossfree line current traveling-wave differential protection method without the need to carrying out interpolation arithmetic, the saturated impact of anti-current instrument transformer is provided.

The present invention adopts following technical scheme:

The lossfree line current traveling-wave differential protection method of the saturated impact of anti-current instrument transformer, is characterized in that, comprise the steps:

(1) protective device utilizes sampling instant transmission line m transforming plant protecting installation place 0, α, β mode voltage traveling-wave component and sampling instant transmission line n transforming plant protecting installation place 0, α, β mode voltage traveling-wave component calculate t sampling instant transmission line m transforming plant protecting installation place 0, α, β mould current traveling wave component:

$i_{m0}^{\&prime;}\left(t\right)=\frac{u_{m0}(t-\frac{T}{4})}{Z_{c0}}\frac{cos(100\mathrm{\&pi;}*\frac{l}{{\mathrm{\&nu;}}_0})}{sin(100\mathrm{\&pi;}*\frac{l}{{\mathrm{\&nu;}}_0})}-\frac{u_{n0}(t-\frac{T}{4})}{Z_{c0}\sin (100\mathrm{\&pi;}*\frac{l}{{\mathrm{\&nu;}}_0})}$

$i_{m\mathrm{\&alpha;}}^{\&prime;}\left(t\right)=\frac{u_{m\mathrm{\&alpha;}}(t-\frac{T}{4})}{Z_{c\mathrm{\&alpha;}}}\frac{cos(100\mathrm{\&pi;}*\frac{l}{{\mathrm{\&nu;}}_{\mathrm{\&alpha;}}})}{sin(100\mathrm{\&pi;}*\frac{l}{{\mathrm{\&nu;}}_{\mathrm{\&alpha;}}})}-\frac{u_{n\mathrm{\&alpha;}}(t-\frac{T}{4})}{Z_{c\mathrm{\&alpha;}}\sin (100\mathrm{\&pi;}*\frac{l}{{\mathrm{\&nu;}}_{\mathrm{\&alpha;}}})}$

$i_{m\mathrm{\&beta;}}^{\&prime;}\left(t\right)=\frac{u_{m\mathrm{\&beta;}}(t-\frac{T}{4})}{Z_{c\mathrm{\&beta;}}}\frac{cos(100\mathrm{\&pi;}*\frac{l}{{\mathrm{\&nu;}}_{\mathrm{\&beta;}}})}{sin(100\mathrm{\&pi;}*\frac{l}{{\mathrm{\&nu;}}_{\mathrm{\&beta;}}})}-\frac{u_{n\mathrm{\&beta;}}(t-\frac{T}{4})}{Z_{c\mathrm{\&beta;}}\sin (100\mathrm{\&pi;}*\frac{l}{{\mathrm{\&nu;}}_{\mathrm{\&beta;}}})}$

Wherein, t is the sampling time; L is the transmission line length connecting m transformer station and n transformer station; T is the cycle time of fundamental component; Z _c0, Z _{c α}, Z _{c β}be respectively the characteristic impedance of transmission line 0, α, β line wave component; v ₀, v _α, v _βbe respectively the propagation velocity of transmission line 0, α, β line wave component; be respectively sampling instant transmission line 0 of m transforming plant protecting installation place, the voltage traveling wave component of α, β mould; be respectively sampling instant transmission line 0 of n transforming plant protecting installation place, the voltage traveling wave component of α, β mould;

(2) protective device is by i ' _m0(t), i ' _{m α}(t), i ' _{m β}t () is carried out phase mould inverse transformation and is obtained the three-phase current traveling-wave component i ' of t sampling instant transmission line in m transforming plant protecting installation place _mA(t), i ' _mB(t), i ' _mC(t); To i ' _mA(t), i ' _mB(t), i ' _mCt () adopts Fourier algorithm to calculate the three-phase Fundamental-frequency Current component of t sampling instant transmission line in m transforming plant protecting installation place to the current traveling wave component i of the three-phase actual measurement of t sampling instant transmission line in m transforming plant protecting installation place _mA(t), i _mB(t), i _mCt () adopts Fourier algorithm to calculate the Fundamental-frequency Current component of the three-phase actual measurement of t sampling instant transmission line in m transforming plant protecting installation place

(3) protective device judges ${\mathrm{cos\&theta;}}_A\sqrt{{\&lsqb;\mathrm{Re}({\stackrel{\&CenterDot;}{I}}_{mA}^{\&prime;}+{\stackrel{\&CenterDot;}{I}}_{mA})\&rsqb;}^2+{\&lsqb;\mathrm{Im}({\stackrel{\&CenterDot;}{I}}_{mA}^{\&prime;}+{\stackrel{\&CenterDot;}{I}}_{mA})\&rsqb;}^2}>k\sqrt{{\&lsqb;\mathrm{Re}({\stackrel{\&CenterDot;}{I}}_{mA}^{\&prime;}-{\stackrel{\&CenterDot;}{I}}_{mA})\&rsqb;}^2+{\&lsqb;\mathrm{Im}({\stackrel{\&CenterDot;}{I}}_{mA}^{\&prime;}-{\stackrel{\&CenterDot;}{I}}_{mA})\&rsqb;}^2}$ Whether set up, if set up, then protective device sends trip signal, the circuit breaker at tripping A phase transmission line two ends to the circuit breaker at A phase transmission line two ends; Wherein, θ _afor leading angle; K is tuning coefficient; imaginary part; real part; for real part; for imaginary part;

(4) protective device judges ${\mathrm{cos\&theta;}}_B\sqrt{{\&lsqb;\mathrm{Re}({\stackrel{\&CenterDot;}{I}}_{mB}^{\&prime;}+{\stackrel{\&CenterDot;}{I}}_{mB})\&rsqb;}^2+{\&lsqb;\mathrm{Im}({\stackrel{\&CenterDot;}{I}}_{mB}^{\&prime;}+{\stackrel{\&CenterDot;}{I}}_{mB})\&rsqb;}^2}>k\sqrt{{\&lsqb;\mathrm{Re}({\stackrel{\&CenterDot;}{I}}_{mB}^{\&prime;}-{\stackrel{\&CenterDot;}{I}}_{mB})\&rsqb;}^2+{\&lsqb;\mathrm{Im}({\stackrel{\&CenterDot;}{I}}_{mB}^{\&prime;}-{\stackrel{\&CenterDot;}{I}}_{mB})\&rsqb;}^2}$ Whether set up, if set up, then protective device sends trip signal, the circuit breaker at tripping B phase transmission line two ends to the circuit breaker at B phase transmission line two ends; Wherein, θ _bfor leading angle; K is tuning coefficient; for imaginary part; for real part; for real part; for imaginary part;

(5) protective device judges ${\mathrm{cos\&theta;}}_C\sqrt{{\&lsqb;\mathrm{Re}({\stackrel{\&CenterDot;}{I}}_{mC}^{\&prime;}+{\stackrel{\&CenterDot;}{I}}_{mC})\&rsqb;}^2+{\&lsqb;\mathrm{Im}({\stackrel{\&CenterDot;}{I}}_{mC}^{\&prime;}+{\stackrel{\&CenterDot;}{I}}_{mC})\&rsqb;}^2}>k\sqrt{{\&lsqb;\mathrm{Re}({\stackrel{\&CenterDot;}{I}}_{mC}^{\&prime;}-{\stackrel{\&CenterDot;}{I}}_{mC})\&rsqb;}^2+{\&lsqb;\mathrm{Im}({\stackrel{\&CenterDot;}{I}}_{mC}^{\&prime;}-{\stackrel{\&CenterDot;}{I}}_{mC})\&rsqb;}^2}$ Whether set up, if set up, then protective device sends trip signal, the circuit breaker at tripping C phase transmission line two ends to the circuit breaker at C phase transmission line two ends; Wherein, θ _cfor leading angle; K is tuning coefficient; for imaginary part; for real part; for real part; for imaginary part.

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

The inventive method, without the need to being asked for the current traveling wave component of each sampling instant by interpolation arithmetic, decreases algorithm operation quantity, improves protection act speed.The inventive method can complete transmission line malfunction traveling-wave protection function in the short-data windows in 1/4 cycle, and protection act speed is fast.The inventive method eliminates the impact of CT saturation on travelling wave current differential protection performance; no matter whether current transformer is saturated; line protection external area error the inventive method is reliably failure to actuate, the inventive method correct action message during line protection troubles inside the sample space.

Accompanying drawing explanation

Fig. 1 is application multi-line power transmission system schematic of the present invention.

Embodiment

According to Figure of description, technical scheme of the present invention is expressed in further detail below.

Fig. 1 is application multi-line power transmission system schematic of the present invention.In the present embodiment, first protective device gathers the three-phase voltage traveling-wave component u of transmission line in each t sampling instant of m transforming plant protecting installation place _mA(t), u _mB(t), u _mC(t), three-phase current traveling-wave component i _mA(t), i _mB(t), i _mC(t); Gather the three-phase voltage traveling-wave component u of transmission line in each t sampling instant of n transforming plant protecting installation place _nA(t), u _nB(t), u _nC(t), three-phase current traveling-wave component i _nA(t), i _nB(t), i _nC(t); Wherein, t is any sampling time.

Protective device adopt phase-model transformation by transmission line the three-phase voltage traveling-wave component of each t sampling instant of m transforming plant protecting installation place convert to transmission line m transforming plant protecting installation place 0, α, β mode voltage traveling-wave component u _m0(t), u _{m α}(t), u _{m β}(t):

$\left[\begin{array}{c}{u}_{m0}\left(t\right)\\ u_{m\mathrm{\&alpha;}}\left(t\right)\\ u_{m\mathrm{\&beta;}}\left(t\right)\end{array}\right]={\left[\begin{array}{ccc}1& 2& 1\\ 1& -1& 0\\ 1& -1& -1\end{array}\right]}^{-1}\left[\begin{array}{c}{u}_{mA}\left(t\right)\\ u_{mB}\left(t\right)\\ u_{mC}\left(t\right)\end{array}\right]$

Protective device adopt phase-model transformation by transmission line the three-phase voltage traveling-wave component of each t sampling instant of n transforming plant protecting installation place convert to transmission line n transforming plant protecting installation place 0, α, β mode voltage traveling-wave component u _n0(t), u _{n α}(t), u _{n β}(t):

$\left[\begin{array}{c}{u}_{n0}\left(t\right)\\ u_{n\mathrm{\&alpha;}}\left(t\right)\\ u_{n\mathrm{\&beta;}}\left(t\right)\end{array}\right]={\left[\begin{array}{ccc}1& 2& 1\\ 1& -1& 0\\ 1& -1& -1\end{array}\right]}^{-1}\left[\begin{array}{c}{u}_{nA}\left(t\right)\\ u_{nB}\left(t\right)\\ u_{nC}\left(t\right)\end{array}\right]$

Protective device utilizes sampling instant transmission line m transforming plant protecting installation place 0, α, β mode voltage traveling-wave component and sampling instant transmission line n transforming plant protecting installation place 0, α, β mode voltage traveling-wave component calculate t sampling instant transmission line m transforming plant protecting installation place 0, α, β mould current traveling wave component:

$i_{m0}^{\&prime;}\left(t\right)=\frac{u_{m0}(t-\frac{T}{4})}{Z_{c0}}\frac{cos(100\mathrm{\&pi;}*\frac{l}{{\mathrm{\&nu;}}_0})}{sin(100\mathrm{\&pi;}*\frac{l}{{\mathrm{\&nu;}}_0})}-\frac{u_{n0}(t-\frac{T}{4})}{Z_{c0}\sin (100\mathrm{\&pi;}*\frac{l}{{\mathrm{\&nu;}}_0})}$

$i_{m\mathrm{\&alpha;}}^{\&prime;}\left(t\right)=\frac{u_{m\mathrm{\&alpha;}}(t-\frac{T}{4})}{Z_{c\mathrm{\&alpha;}}}\frac{cos(100\mathrm{\&pi;}*\frac{l}{{\mathrm{\&nu;}}_{\mathrm{\&alpha;}}})}{sin(100\mathrm{\&pi;}*\frac{l}{{\mathrm{\&nu;}}_{\mathrm{\&alpha;}}})}-\frac{u_{n\mathrm{\&alpha;}}(t-\frac{T}{4})}{Z_{c\mathrm{\&alpha;}}\sin (100\mathrm{\&pi;}*\frac{l}{{\mathrm{\&nu;}}_{\mathrm{\&alpha;}}})}$

$i_{m\mathrm{\&beta;}}^{\&prime;}\left(t\right)=\frac{u_{m\mathrm{\&beta;}}(t-\frac{T}{4})}{Z_{c\mathrm{\&beta;}}}\frac{cos(100\mathrm{\&pi;}*\frac{l}{{\mathrm{\&nu;}}_{\mathrm{\&beta;}}})}{sin(100\mathrm{\&pi;}*\frac{l}{{\mathrm{\&nu;}}_{\mathrm{\&beta;}}})}-\frac{u_{n\mathrm{\&beta;}}(t-\frac{T}{4})}{Z_{c\mathrm{\&beta;}}\sin (100\mathrm{\&pi;}*\frac{l}{{\mathrm{\&nu;}}_{\mathrm{\&beta;}}})}$

Wherein, t is the sampling time; L is the transmission line length connecting m transformer station and n transformer station; T is the cycle time of fundamental component; Z _c0, Z _{c α}, Z _{c β}be respectively the characteristic impedance of transmission line 0, α, β line wave component; v ₀, v _α, v _βbe respectively the propagation velocity of transmission line 0, α, β line wave component; be respectively sampling instant transmission line 0 of m transforming plant protecting installation place, the voltage traveling wave component of α, β mould; be respectively sampling instant transmission line 0 of n transforming plant protecting installation place, the voltage traveling wave component of α, β mould.

Protective device will carry out phase mould inverse transformation and obtain the three-phase current traveling-wave component of t sampling instant transmission line in m transforming plant protecting installation place

$\left[\begin{array}{c}{i}_{mA}^{\&prime;}\left(t\right)\\ i_{mB}^{\&prime;}\left(t\right)\\ i_{mC}^{\&prime;}\left(t\right)\end{array}\right]=\left[\begin{array}{ccc}1& 2& 1\\ 1& -1& 0\\ 1& -1& -1\end{array}\right]\left[\begin{array}{c}{i}_{m0}^{\&prime;}\left(t\right)\\ i_{m\mathrm{\&alpha;}}^{\&prime;}\left(t\right)\\ i_{m\mathrm{\&beta;}}^{\&prime;}\left(t\right)\end{array}\right]$

Protective device is to i ' _mA(t), i ' _mB(t), i ' _mCt () adopts Fourier algorithm to calculate the three-phase Fundamental-frequency Current component of t sampling instant transmission line in m transforming plant protecting installation place to the current traveling wave component i of the three-phase actual measurement of t sampling instant transmission line in m transforming plant protecting installation place _mA(t), i _mB(t), i _mCt () adopts Fourier algorithm to calculate the Fundamental-frequency Current component of the three-phase actual measurement of t sampling instant transmission line in m transforming plant protecting installation place

Protective device judges ${\mathrm{cos\&theta;}}_A\sqrt{{\&lsqb;\mathrm{Re}({\stackrel{\&CenterDot;}{I}}_{mA}^{\&prime;}+{\stackrel{\&CenterDot;}{I}}_{mA})\&rsqb;}^2+{\&lsqb;\mathrm{Im}({\stackrel{\&CenterDot;}{I}}_{mA}^{\&prime;}+{\stackrel{\&CenterDot;}{I}}_{mA})\&rsqb;}^2}>k\sqrt{{\&lsqb;\mathrm{Re}({\stackrel{\&CenterDot;}{I}}_{mA}^{\&prime;}-{\stackrel{\&CenterDot;}{I}}_{mA})\&rsqb;}^2+{\&lsqb;\mathrm{Im}({\stackrel{\&CenterDot;}{I}}_{mA}^{\&prime;}-{\stackrel{\&CenterDot;}{I}}_{mA})\&rsqb;}^2}$ Whether set up, if set up, then protective device sends trip signal, the circuit breaker at tripping A phase transmission line two ends to the circuit breaker at A phase transmission line two ends; Wherein, θ _afor leading angle; K is tuning coefficient; for imaginary part; for real part; for real part; for imaginary part.

Protective device judges ${\mathrm{cos\&theta;}}_B\sqrt{{\&lsqb;\mathrm{Re}({\stackrel{\&CenterDot;}{I}}_{mB}^{\&prime;}+{\stackrel{\&CenterDot;}{I}}_{mB})\&rsqb;}^2+{\&lsqb;\mathrm{Im}({\stackrel{\&CenterDot;}{I}}_{mB}^{\&prime;}+{\stackrel{\&CenterDot;}{I}}_{mB})\&rsqb;}^2}>k\sqrt{{\&lsqb;\mathrm{Re}({\stackrel{\&CenterDot;}{I}}_{mB}^{\&prime;}-{\stackrel{\&CenterDot;}{I}}_{mB})\&rsqb;}^2+{\&lsqb;\mathrm{Im}({\stackrel{\&CenterDot;}{I}}_{mB}^{\&prime;}-{\stackrel{\&CenterDot;}{I}}_{mB})\&rsqb;}^2}$ Whether set up, if set up, then protective device sends trip signal, the circuit breaker at tripping B phase transmission line two ends to the circuit breaker at B phase transmission line two ends; Wherein, θ _bfor leading angle; K is tuning coefficient; for imaginary part; for real part; for real part; for imaginary part.

Protective device judges ${\mathrm{cos\&theta;}}_C\sqrt{{\&lsqb;\mathrm{Re}({\stackrel{\&CenterDot;}{I}}_{mC}^{\&prime;}+{\stackrel{\&CenterDot;}{I}}_{mC})\&rsqb;}^2+{\&lsqb;\mathrm{Im}({\stackrel{\&CenterDot;}{I}}_{mC}^{\&prime;}+{\stackrel{\&CenterDot;}{I}}_{mC})\&rsqb;}^2}>k\sqrt{{\&lsqb;\mathrm{Re}({\stackrel{\&CenterDot;}{I}}_{mC}^{\&prime;}-{\stackrel{\&CenterDot;}{I}}_{mC})\&rsqb;}^2+{\&lsqb;\mathrm{Im}({\stackrel{\&CenterDot;}{I}}_{mC}^{\&prime;}-{\stackrel{\&CenterDot;}{I}}_{mC})\&rsqb;}^2}$ Whether set up, if set up, then protective device sends trip signal, the circuit breaker at tripping C phase transmission line two ends to the circuit breaker at C phase transmission line two ends; Wherein, θ _cfor leading angle; K is tuning coefficient; for imaginary part; for real part; for real part; for imaginary part.

The inventive method, without the need to being asked for the current traveling wave component of each sampling instant by interpolation arithmetic, decreases algorithm operation quantity, improves protection act speed.The inventive method can complete transmission line malfunction traveling-wave protection function in the short-data windows in 1/4 cycle, and protection act speed is fast.The inventive method eliminates the impact of CT saturation on travelling wave current differential protection performance; no matter whether current transformer is saturated; line protection external area error the inventive method is reliably failure to actuate, the inventive method correct action message during line protection troubles inside the sample space.

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. the lossfree line current traveling-wave differential protection method of the saturated impact of anti-current instrument transformer, is characterized in that, comprise the following steps:

(1) protective device utilizes sampling instant transmission line m transforming plant protecting installation place 0, α, β mode voltage traveling-wave component and sampling instant transmission line n transforming plant protecting installation place 0, α, β mode voltage traveling-wave component calculate t sampling instant transmission line m transforming plant protecting installation place 0, α, β mould current traveling wave component:

$i_{m0}^{\&prime;}\left(t\right)=\frac{u_{m0}\left(t-\frac{T}{4}\right)}{Z_{c0}}\frac{\cos \left(100\mathrm{\&pi;}*\frac{l}{{\mathrm{\&nu;}}_0}\right)}{sin(100\mathrm{\&pi;}*\frac{l}{{\mathrm{\&nu;}}_0})}-\frac{u_{n0}(t-\frac{T}{4})}{Z_{c0}\sin (100\mathrm{\&pi;}*\frac{l}{{\mathrm{\&nu;}}_0})}$

$i_{m\mathrm{\&alpha;}}^{\&prime;}\left(t\right)=\frac{u_{m\mathrm{\&alpha;}}(t-\frac{T}{4})}{Z_{c\mathrm{\&alpha;}}}\frac{cos(100\mathrm{\&pi;}*\frac{l}{{\mathrm{\&nu;}}_{\mathrm{\&alpha;}}})}{sin(100\mathrm{\&pi;}*\frac{l}{{\mathrm{\&nu;}}_{\mathrm{\&alpha;}}})}-\frac{u_{n\mathrm{\&alpha;}}(t-\frac{T}{4})}{Z_{c\mathrm{\&alpha;}}\sin (100\mathrm{\&pi;}*\frac{l}{{\mathrm{\&nu;}}_{\mathrm{\&alpha;}}})}$

$i_{m\mathrm{\&beta;}}^{\&prime;}\left(t\right)=\frac{u_{m\mathrm{\&beta;}}\left(t-\frac{T}{4}\right)}{Z_{c\mathrm{\&beta;}}}\frac{\cos \left(100\mathrm{\&pi;}*\frac{l}{{\mathrm{\&nu;}}_{\mathrm{\&beta;}}}\right)}{sin(100\mathrm{\&pi;}*\frac{l}{{\mathrm{\&nu;}}_{\mathrm{\&beta;}}})}-\frac{u_{n\mathrm{\&beta;}}(t-\frac{T}{4})}{Z_{c\mathrm{\&beta;}}\sin (100\mathrm{\&pi;}*\frac{l}{{\mathrm{\&nu;}}_{\mathrm{\&beta;}}})}$

Wherein, t is the sampling time; L is the transmission line length connecting m transformer station and n transformer station; T is the cycle time of fundamental component; Z _c0, Z _{c α}, Z _{c β}be respectively the characteristic impedance of transmission line 0, α, β line wave component; v ₀, v _α, v _βbe respectively the propagation velocity of transmission line 0, α, β line wave component; be respectively sampling instant transmission line 0 of m transforming plant protecting installation place, the voltage traveling wave component of α, β mould; be respectively sampling instant transmission line 0 of n transforming plant protecting installation place, the voltage traveling wave component of α, β mould;

(2) protective device is by i ' _m0(t), i ' _{m α}(t), i ' _{m β}t () is carried out phase mould inverse transformation and is obtained the three-phase current traveling-wave component i ' of t sampling instant transmission line in m transforming plant protecting installation place _mA(t), i ' _mB(t), i ' _mC(t); To i ' _mA(t), i ' _mB(t), i ' _mCt () adopts Fourier algorithm to calculate the three-phase Fundamental-frequency Current component I ' of t sampling instant transmission line in m transforming plant protecting installation place _mA, I ' _mB, I ' _mC; To the current traveling wave component i of the three-phase actual measurement of t sampling instant transmission line in m transforming plant protecting installation place _mA(t), i _mB(t), i _mCt () adopts Fourier algorithm to calculate the Fundamental-frequency Current component of the three-phase actual measurement of t sampling instant transmission line in m transforming plant protecting installation place

(3) protective device judges ${\mathrm{cos\&theta;}}_A\sqrt{{\&lsqb;\mathrm{Re}\left({\stackrel{\&CenterDot;}{I}}_{mA}^{\&prime;}+{\stackrel{\&CenterDot;}{I}}_{mA}\right)\&rsqb;}^2+{\&lsqb;\mathrm{Im}\left({\stackrel{\&CenterDot;}{I}}_{mA}^{\&prime;}+{\stackrel{\&CenterDot;}{I}}_{mA}\right)\&rsqb;}^2}>k\sqrt{{\&lsqb;\mathrm{Re}\left({\stackrel{\&CenterDot;}{I}}_{mA}^{\&prime;}-{\stackrel{\&CenterDot;}{I}}_{mA}\right)\&rsqb;}^2+{\&lsqb;\mathrm{Im}\left({\stackrel{\&CenterDot;}{I}}_{mA}^{\&prime;}-{\stackrel{\&CenterDot;}{I}}_{mA}\right)\&rsqb;}^2}$ Whether set up, if set up, then protective device sends trip signal, the circuit breaker at tripping A phase transmission line two ends to the circuit breaker at A phase transmission line two ends; Wherein, θ _afor leading angle; K is tuning coefficient; for imaginary part; for real part; for real part; for imaginary part;

(4) protective device judges ${\mathrm{cos\&theta;}}_B\sqrt{{\&lsqb;\mathrm{Re}\left({\stackrel{\&CenterDot;}{I}}_{mB}^{\&prime;}+{\stackrel{\&CenterDot;}{I}}_{mB}\right)\&rsqb;}^2+{\&lsqb;\mathrm{Im}\left({\stackrel{\&CenterDot;}{I}}_{mB}^{\&prime;}+{\stackrel{\&CenterDot;}{I}}_{mB}\right)\&rsqb;}^2}>k\sqrt{{\&lsqb;\mathrm{Re}\left({\stackrel{\&CenterDot;}{I}}_{mB}^{\&prime;}-{\stackrel{\&CenterDot;}{I}}_{mB}\right)\&rsqb;}^2+{\&lsqb;\mathrm{Im}\left({\stackrel{\&CenterDot;}{I}}_{mB}^{\&prime;}-{\stackrel{\&CenterDot;}{I}}_{mB}\right)\&rsqb;}^2}$ Whether set up, if set up, then protective device sends trip signal, the circuit breaker at tripping B phase transmission line two ends to the circuit breaker at B phase transmission line two ends; Wherein, θ _bfor leading angle; K is tuning coefficient; for imaginary part; for real part; for real part; for imaginary part;

(5) protective device judges ${\mathrm{cos\&theta;}}_C\sqrt{{\&lsqb;\mathrm{Re}\left({\stackrel{\&CenterDot;}{I}}_{mC}^{\&prime;}+{\stackrel{\&CenterDot;}{I}}_{mC}\right)\&rsqb;}^2+{\&lsqb;\mathrm{Im}\left({\stackrel{\&CenterDot;}{I}}_{mC}^{\&prime;}+{\stackrel{\&CenterDot;}{I}}_{mC}\right)\&rsqb;}^2}>k\sqrt{{\&lsqb;\mathrm{Re}\left({\stackrel{\&CenterDot;}{I}}_{mC}^{\&prime;}-{\stackrel{\&CenterDot;}{I}}_{mC}\right)\&rsqb;}^2+{\&lsqb;\mathrm{Im}\left({\stackrel{\&CenterDot;}{I}}_{mC}^{\&prime;}-{\stackrel{\&CenterDot;}{I}}_{mC}\right)\&rsqb;}^2}$ Whether set up, if set up, then protective device sends trip signal, the circuit breaker at tripping C phase transmission line two ends to the circuit breaker at C phase transmission line two ends; Wherein, θ _cfor leading angle; K is tuning coefficient; for imaginary part; for real part; for real part; for imaginary part.