CN104078948A - Transmission line positive sequence current split-phase differential protection method based on short data window - Google Patents

Abstract

The invention discloses a transmission line positive sequence current split-phase differential protection method based on a short data window. The method comprises the following steps that firstly, three-phase current instantaneous values at the two ends of a transmission line at each sampling moment are converted into current instantaneous values at the two ends of the transmission line under alpha beta 0 coordinate axes at each sampling moment, positive sequence current instantaneous values at the two ends of the transmission line under the alpha beta 0 coordinate axes at each sampling moment are worked out, coordinate axis conversion is conducted on the positive sequence current instantaneous values at the two ends of the transmission line under the alpha beta 0 coordinate axes at each sampling moment so as to obtain three-phase positive sequence current instantaneous values at the two ends of the transmission line at each sampling moment, and then the three-phase positive sequence current instantaneous values at the two ends of the transmission line at each sampling moment are used for constituting positive sequence current split-phase differential protection data. According to the method, the algorithm principle is simple, program implementation is easy, the calculation amount is small, calculation speed is high, and protection action speed of a relay can be increased greatly. A phase selection function is achieved, transition resistance and a load current have no influence on action performance, and the method is suitable for achieving a transmission line main protection function in a whole fault process after a fault occurs.

Description

Transmission line forward-order current phase segregated differential protection method based on short data window

Technical field

The present invention relates to Relay Protection Technology in Power System field, specifically relate to a kind of based on short data window transmission line forward-order current phase segregated differential protection method.

Background technology

Owing to not affected by power 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 lines always.Current differential protection can be divided into fault component differential protection and steady-state quantity current differential protection.Because Sudden Changing Rate only exists in short-term in two cycles after line fault, therefore, fault component differential protection is only applicable to the transmission line main protection function in two cycles after fault.Because the electric current phasor that fault component differential is protected and steady-state quantity current differential protection algorithm is used needs complete cycle wave datum window to calculate; causing fault component differential protection and steady-state quantity current differential protection algorithm inherent delay is a cycle; algorithm rapidity is strong not, cannot be applicable to ultrahigh voltage alternating current transmission lines main protection.

The electric current phasor that steady-state quantity current differential protection algorithm is used comprises load current; when the single-phase high resistance earthing fault of heavy load transmission line; fault current component is very little; even be less than load current; cause differential current amount to be less than stalling current amount; while causing heavy load transmission line that permanent single-phase high resistance earthing fault occurs there is tripping work in steady-state quantity current differential protection; by Zero sequence current differential protection as its backup protection tripping three phase line; electrical network is caused to powerful impact, easily cause operation of power networks unstability.

Summary of the invention

The object of the invention is to overcome the deficiency that prior art exists, provide one to have phase-selecting function, performance is not affected by transition resistance and load current, utilizes 1/4 cycle short data window to realize transmission line forward-order current phase segregated differential protection method.

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

Based on short data window transmission line forward-order current phase segregated differential protection method, it comprises following sequential steps:

(1) protective device Real-time Collection transmission line is at A, B, the C three-phase current instantaneous value i of the each t sampling instant in m transforming plant protecting installation place _mA(t), i _mB(t), i _mC(t), Real-time Collection transmission line is at A, B, the C three-phase current instantaneous value i of the each t sampling instant in n transforming plant protecting installation place _nA(t), i _nB(t), i _nC(t);

(2) protective device is by A, the B of the each t sampling instant in m transforming plant protecting installation place, C three-phase current instantaneous value i _mA(t), i _mB(t), i _mC(t) be transformed into the current instantaneous value i of t sampling instant under α β 0 reference axis _{m α}(t), i _{m β}(t), i _m0(t):

$\left[\begin{array}{c}{i}_{\mathrm{m\α}}\left(t\right)\\ i_{\mathrm{m\β}}\left(t\right)\\ i_{m0}\left(t\right)\end{array}\right]=\frac{2}{3}\left[\begin{array}{ccc}1& -\frac{1}{2}& -\frac{1}{2}\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\\ \frac{1}{2}& \frac{1}{2}& \frac{1}{2}\end{array}\right]\left[\begin{array}{c}{i}_{\mathrm{mA}}\left(t\right)\\ i_{\mathrm{mB}}\left(t\right)\\ i_{\mathrm{mC}}\left(t\right)\end{array}\right]$

(3) protective device is by A, the B of the each t sampling instant in n transforming plant protecting installation place, C three-phase current instantaneous value i _nA(t), i _nB(t), i _nC(t) be transformed into the current instantaneous value i of t sampling instant under α β 0 reference axis _{n α}(t), i _{n β}(t), i _n0(t):

$\left[\begin{array}{c}{i}_{\mathrm{n\α}}\left(t\right)\\ i_{\mathrm{n\β}}\left(t\right)\\ i_{n0}\left(t\right)\end{array}\right]=\frac{2}{3}\left[\begin{array}{ccc}1& -\frac{1}{2}& -\frac{1}{2}\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\\ \frac{1}{2}& \frac{1}{2}& \frac{1}{2}\end{array}\right]\left[\begin{array}{c}{i}_{\mathrm{nA}}\left(t\right)\\ i_{\mathrm{nB}}\left(t\right)\\ i_{\mathrm{nC}}\left(t\right)\end{array}\right]$

(4) protective device calculates the forward-order current of m transforming plant protecting installation place t sampling instant under α β 0 reference axis $i_{\mathrm{m\α}}^{+}\left(t\right),i_{\mathrm{m\β}}^{+}\left(t\right),i_{m0}^{+}\left(t\right):$

$i_{\mathrm{m\α}}^{+}\left(t\right)={0.5i}_{\mathrm{m\α}}\left(t\right)-{0.5i}_{\mathrm{m\β}}(t-\frac{T}{4})$

$i_{\mathrm{m\β}}^{+}\left(t\right)={0.5i}_{\mathrm{m\α}}(t-\frac{T}{4})+{0.5i}_{\mathrm{m\β}}\left(t\right)$

$i_{m0}^{+}\left(t\right)=i_{m0}\left(t\right)$

Wherein, for β direction of principal axis under α β 0 reference axis the current instantaneous value of the m transforming plant protecting installation place of sampling instant; i _{m β}(t) be the current instantaneous value of the m transforming plant protecting installation place of β direction of principal axis t sampling instant under α β 0 reference axis; for α direction of principal axis under α β 0 reference axis the current instantaneous value of the m transforming plant protecting installation place of sampling instant; i _{m α}(t) be the current instantaneous value of the m transforming plant protecting installation place of α direction of principal axis t sampling instant under α β 0 reference axis; T is time primitive period; i _m0(t) be the current instantaneous value of the m transforming plant protecting installation place of 0 direction of principal axis t sampling instant under α β 0 reference axis;

(5) protective device calculates the forward-order current of n transforming plant protecting installation place t sampling instant under α β 0 reference axis $i_{\mathrm{n\α}}^{+}\left(t\right),i_{\mathrm{n\β}}^{+}\left(t\right),i_{n0}^{+}\left(t\right):$

$i_{\mathrm{n\α}}^{+}\left(t\right)={0.5i}_{\mathrm{n\α}}\left(t\right)-{0.5i}_{\mathrm{n\β}}(t-\frac{T}{4})$

$i_{\mathrm{n\β}}^{+}\left(t\right)={0.5i}_{\mathrm{n\α}}(t-\frac{T}{4})+{0.5i}_{\mathrm{n\β}}\left(t\right)$

$i_{n0}^{+}\left(t\right)=i_{n0}\left(t\right)$

Wherein, for β direction of principal axis under α β 0 reference axis the current instantaneous value of the n transforming plant protecting installation place of sampling instant; i _{n β}(t) be the current instantaneous value of the n transforming plant protecting installation place of β direction of principal axis t sampling instant under α β 0 reference axis; for α direction of principal axis under α β 0 reference axis the current instantaneous value of the n transforming plant protecting installation place of sampling instant; i _{n α}(t) be the current instantaneous value of the n transforming plant protecting installation place of α direction of principal axis t sampling instant under α β 0 reference axis; T is time primitive period; i _n0(t) be the current instantaneous value of the n transforming plant protecting installation place of 0 direction of principal axis t sampling instant under α β 0 reference axis;

(6) protective device calculates A, B, the C phase forward-order current instantaneous value of m transforming plant protecting installation place t sampling instant

$\left[\begin{array}{c}{i}_{\mathrm{mA}}^{+}\left(t\right)\\ i_{\mathrm{mB}}^{+}\left(t\right)\\ i_{\mathrm{mC}}^{+}\left(t\right)\end{array}\right]=1.5{\left[\begin{array}{ccc}1& -\frac{1}{2}& -\frac{1}{2}\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\\ \frac{1}{2}& \frac{1}{2}& \frac{1}{2}\end{array}\right]}^{-1}\left[\begin{array}{c}{i}_{\mathrm{m\α}}^{+}\left(t\right)\\ i_{\mathrm{m\β}}^{+}\left(t\right)\\ i_{m0}^{+}\left(t\right)\end{array}\right]$

(7) protective device calculates A, B, the C phase forward-order current instantaneous value of n transforming plant protecting installation place t sampling instant

$\left[\begin{array}{c}{i}_{\mathrm{nA}}^{+}\left(t\right)\\ i_{\mathrm{nB}}^{+}\left(t\right)\\ i_{\mathrm{nC}}^{+}\left(t\right)\end{array}\right]=1.5{\left[\begin{array}{ccc}1& -\frac{1}{2}& -\frac{1}{2}\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\\ \frac{1}{2}& \frac{1}{2}& \frac{1}{2}\end{array}\right]}^{-1}\left[\begin{array}{c}{i}_{\mathrm{n\α}}^{+}\left(t\right)\\ i_{\mathrm{n\β}}^{+}\left(t\right)\\ i_{n0}^{+}\left(t\right)\end{array}\right]$

(8) protective device judgement whether set up, if set up, protective device sends trip signal to the circuit breaker at A phase transmission line two ends; Protective device judgement whether set up, if set up, protective device sends trip signal to the circuit breaker at B phase transmission line two ends; Protective device judgement whether set up, if set up, protective device sends trip signal to the circuit breaker at C phase transmission line two ends; Wherein, k ₁for tuning coefficient; I _setfor setting current threshold value.

The technical program is compared with background technology, and its tool has the following advantages:

First the inventive method is transformed into the three-phase current instantaneous value of the each sampling instant in transmission line two ends the current instantaneous value of the each sampling instant in transmission line two ends under α β 0 reference axis, calculate the forward-order current instantaneous value of the each sampling instant in transmission line two ends under α β 0 reference axis, the forward-order current instantaneous value of the each sampling instant in transmission line two ends under α β 0 reference axis is carried out reference axis inverse transformation and is obtained the three-phase forward-order current instantaneous value of the each sampling instant in transmission line two ends, then utilize the three-phase forward-order current instantaneous value of the each sampling instant in transmission line two ends to form forward-order current phase segregated differential protection criterion.The inventive method does not relate to complicated complex operation, only relates to simple real number algebraic operation, and algorithm principle is simple, and program realizes easily, and operand is few, and computational speed is fast, can greatly improve relaying protection responsiveness.The inventive method has phase-selecting function, and performance is not affected by transition resistance and load current, has been applicable to the transmission line main protection function of whole failure process after fault.The inventive method utilizes 1/4 cycle short data window to realize transmission line main protection function, can correct action message tripping fault phase when the single-phase high resistance earthing fault of transmission line.

Brief description of the drawings

Below in conjunction with drawings and Examples, the invention will be further described.

Fig. 1 is application transmission system schematic diagram of the present invention.

Embodiment

Fig. 1 is application transmission system schematic diagram of the present invention.In Fig. 1, CT is current transformer.In the present embodiment, protective device Real-time Collection transmission line is at A, B, the C three-phase current instantaneous value i of the each t sampling instant in m transforming plant protecting installation place _mA(t), i _mB(t), i _mC(t), Real-time Collection transmission line is at A, B, the C three-phase current instantaneous value i of the each t sampling instant in n transforming plant protecting installation place _nA(t), i _nB(t), i _nC(t).

Protective device is by A, the B of the each t sampling instant in m transforming plant protecting installation place, C three-phase current instantaneous value i _mA(t), i _mB(t), i _mC(t) be transformed into the current instantaneous value i of t sampling instant under α β 0 reference axis _{m α}(t), i _{m β}(t), i _m0(t):

$\left[\begin{array}{c}{i}_{\mathrm{m\α}}\left(t\right)\\ i_{\mathrm{m\β}}\left(t\right)\\ i_{m0}\left(t\right)\end{array}\right]=\frac{2}{3}\left[\begin{array}{ccc}1& -\frac{1}{2}& -\frac{1}{2}\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\\ \frac{1}{2}& \frac{1}{2}& \frac{1}{2}\end{array}\right]\left[\begin{array}{c}{i}_{\mathrm{mA}}\left(t\right)\\ i_{\mathrm{mB}}\left(t\right)\\ i_{\mathrm{mC}}\left(t\right)\end{array}\right]$

Protective device is by A, the B of the each t sampling instant in n transforming plant protecting installation place, C three-phase current instantaneous value i _nA(t), i _nB(t), i _nC(t) be transformed into the current instantaneous value i of t sampling instant under α β 0 reference axis _{n α}(t), i _{n β}(t), i _n0(t):

$\left[\begin{array}{c}{i}_{\mathrm{n\α}}\left(t\right)\\ i_{\mathrm{n\β}}\left(t\right)\\ i_{n0}\left(t\right)\end{array}\right]=\frac{2}{3}\left[\begin{array}{ccc}1& -\frac{1}{2}& -\frac{1}{2}\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\\ \frac{1}{2}& \frac{1}{2}& \frac{1}{2}\end{array}\right]\left[\begin{array}{c}{i}_{\mathrm{nA}}\left(t\right)\\ i_{\mathrm{nB}}\left(t\right)\\ i_{\mathrm{nC}}\left(t\right)\end{array}\right]$

Protective device calculates the forward-order current of m transforming plant protecting installation place t sampling instant under α β 0 reference axis $i_{\mathrm{m\α}}^{+}\left(t\right),i_{\mathrm{m\β}}^{+}\left(t\right),i_{m0}^{+}\left(t\right):$

$i_{\mathrm{m\α}}^{+}\left(t\right)={0.5i}_{\mathrm{m\α}}\left(t\right)-{0.5i}_{\mathrm{m\β}}(t-\frac{T}{4})$

$i_{\mathrm{m\β}}^{+}\left(t\right)={0.5i}_{\mathrm{m\α}}(t-\frac{T}{4})+{0.5i}_{\mathrm{m\β}}\left(t\right)$

$i_{m0}^{+}\left(t\right)=i_{m0}\left(t\right)$

Wherein, for β direction of principal axis under α β 0 reference axis the current instantaneous value of the m transforming plant protecting installation place of sampling instant; i _{m β}(t) be the current instantaneous value of the m transforming plant protecting installation place of β direction of principal axis t sampling instant under α β 0 reference axis; for α direction of principal axis under α β 0 reference axis the current instantaneous value of the m transforming plant protecting installation place of sampling instant; i _{m α}(t) be the current instantaneous value of the m transforming plant protecting installation place of α direction of principal axis t sampling instant under α β 0 reference axis; T is time primitive period; i _m0(t) be the current instantaneous value of the m transforming plant protecting installation place of 0 direction of principal axis t sampling instant under α β 0 reference axis; T is the sampling time.

Protective device calculates the forward-order current of n transforming plant protecting installation place t sampling instant under α β 0 reference axis $i_{\mathrm{n\α}}^{+}\left(t\right),i_{\mathrm{n\β}}^{+}\left(t\right),i_{n0}^{+}\left(t\right):$

$i_{\mathrm{n\α}}^{+}\left(t\right)={0.5i}_{\mathrm{n\α}}\left(t\right)-{0.5i}_{\mathrm{n\β}}(t-\frac{T}{4})$

$i_{\mathrm{n\β}}^{+}\left(t\right)={0.5i}_{\mathrm{n\α}}(t-\frac{T}{4})+{0.5i}_{\mathrm{n\β}}\left(t\right)$

$i_{n0}^{+}\left(t\right)=i_{n0}\left(t\right)$

Wherein, for β direction of principal axis under α β 0 reference axis the current instantaneous value of the n transforming plant protecting installation place of sampling instant; i _{n β}(t) be the current instantaneous value of the n transforming plant protecting installation place of β direction of principal axis t sampling instant under α β 0 reference axis; for α direction of principal axis under α β 0 reference axis the current instantaneous value of the n transforming plant protecting installation place of sampling instant; i _{n α}(t) be the current instantaneous value of the n transforming plant protecting installation place of α direction of principal axis t sampling instant under α β 0 reference axis; T is time primitive period; i _n0(t) be the current instantaneous value of the n transforming plant protecting installation place of 0 direction of principal axis t sampling instant under α β 0 reference axis.

Protective device calculates A, B, the C phase forward-order current instantaneous value of m transforming plant protecting installation place t sampling instant $i_{\mathrm{mA}}^{+}\left(t\right),i_{\mathrm{mB}}^{+}\left(t\right),i_{\mathrm{mC}}^{+}\left(t\right):$

$\left[\begin{array}{c}{i}_{\mathrm{mA}}^{+}\left(t\right)\\ i_{\mathrm{mB}}^{+}\left(t\right)\\ i_{\mathrm{mC}}^{+}\left(t\right)\end{array}\right]=1.5{\left[\begin{array}{ccc}1& -\frac{1}{2}& -\frac{1}{2}\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\\ \frac{1}{2}& \frac{1}{2}& \frac{1}{2}\end{array}\right]}^{-1}\left[\begin{array}{c}{i}_{\mathrm{m\α}}^{+}\left(t\right)\\ i_{\mathrm{m\β}}^{+}\left(t\right)\\ i_{m0}^{+}\left(t\right)\end{array}\right]$

Protective device calculates A, B, the C phase forward-order current instantaneous value of n transforming plant protecting installation place t sampling instant $i_{\mathrm{nA}}^{+}\left(t\right),i_{\mathrm{nB}}^{+}\left(t\right),i_{\mathrm{nC}}^{+}\left(t\right):$

$\left[\begin{array}{c}{i}_{\mathrm{nA}}^{+}\left(t\right)\\ i_{\mathrm{nB}}^{+}\left(t\right)\\ i_{\mathrm{nC}}^{+}\left(t\right)\end{array}\right]=1.5{\left[\begin{array}{ccc}1& -\frac{1}{2}& -\frac{1}{2}\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\\ \frac{1}{2}& \frac{1}{2}& \frac{1}{2}\end{array}\right]}^{-1}\left[\begin{array}{c}{i}_{\mathrm{n\α}}^{+}\left(t\right)\\ i_{\mathrm{n\β}}^{+}\left(t\right)\\ i_{n0}^{+}\left(t\right)\end{array}\right]$

Protective device judgement whether set up, if set up, protective device sends trip signal to the circuit breaker at A phase transmission line two ends; Wherein, k ₁for tuning coefficient; I _setfor setting current threshold value.

Protective device judgement whether set up, if set up, protective device sends trip signal to the circuit breaker at B phase transmission line two ends; Wherein, k ₁for tuning coefficient; I _setfor setting current threshold value.

Protective device judgement whether set up, if set up, protective device sends trip signal to the circuit breaker at C phase transmission line two ends; Wherein, k ₁for tuning coefficient; I _setfor setting current threshold value.

First the inventive method is transformed into the three-phase current instantaneous value of the each sampling instant in transmission line two ends the current instantaneous value of the each sampling instant in transmission line two ends under α β 0 reference axis, calculate the forward-order current instantaneous value of the each sampling instant in transmission line two ends under α β 0 reference axis, the forward-order current instantaneous value of the each sampling instant in transmission line two ends under α β 0 reference axis is carried out reference axis inverse transformation and is obtained the three-phase forward-order current instantaneous value of the each sampling instant in transmission line two ends, then utilize the three-phase forward-order current instantaneous value of the each sampling instant in transmission line two ends to form forward-order current phase segregated differential protection criterion.The inventive method does not relate to complicated complex operation, only relates to simple real number algebraic operation, and algorithm principle is simple, and program realizes easily, and operand is few, and computational speed is fast, can greatly improve relaying protection responsiveness.The inventive method has phase-selecting function, and performance is not affected by transition resistance and load current, has been applicable to the transmission line main protection function of whole failure process after fault.The inventive method utilizes 1/4 cycle short data window to realize transmission line main protection function, can correct action message tripping fault phase when the single-phase high resistance earthing fault of transmission line.

The above, only for preferred embodiment of the present invention, therefore can not limit according to this scope of the invention process, the equivalence of doing according to the scope of the claims of the present invention and description changes and modifies, and all should still belong in the scope that the present invention contains.

Claims (1)

1. the transmission line forward-order current phase segregated differential protection method based on short data window, is characterized in that: comprise following sequential steps:

(1) protective device Real-time Collection transmission line is at A, B, the C three-phase current instantaneous value i of the each t sampling instant in m transforming plant protecting installation place _mA(t), i _mB(t), i _mC(t), Real-time Collection transmission line is at A, B, the C three-phase current instantaneous value i of the each t sampling instant in n transforming plant protecting installation place _nA(t), i _nB(t), i _nC(t);

(2) protective device is by A, the B of the each t sampling instant in m transforming plant protecting installation place, C three-phase current instantaneous value i _mA(t), i _mB(t), i _mC(t) be transformed into the current instantaneous value i of t sampling instant under α β 0 reference axis _{m α}(t), i _{m β}(t), i _m0(t):

$\left[\begin{array}{c}{i}_{\mathrm{m\α}}\left(t\right)\\ i_{\mathrm{m\β}}\left(t\right)\\ i_{m0}\left(t\right)\end{array}\right]=\frac{2}{3}\left[\begin{array}{ccc}1& -\frac{1}{2}& -\frac{1}{2}\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\\ \frac{1}{2}& \frac{1}{2}& \frac{1}{2}\end{array}\right]\left[\begin{array}{c}{i}_{\mathrm{mA}}\left(t\right)\\ i_{\mathrm{mB}}\left(t\right)\\ i_{\mathrm{mC}}\left(t\right)\end{array}\right]$

(3) protective device is by A, the B of the each t sampling instant in n transforming plant protecting installation place, C three-phase current instantaneous value i _nA(t), i _nB(t), i _nC(t) be transformed into the current instantaneous value i of t sampling instant under α β 0 reference axis _{n α}(t), i _{n β}(t), i _n0(t):

$\left[\begin{array}{c}{i}_{\mathrm{n\α}}\left(t\right)\\ i_{\mathrm{n\β}}\left(t\right)\\ i_{n0}\left(t\right)\end{array}\right]=\frac{2}{3}\left[\begin{array}{ccc}1& -\frac{1}{2}& -\frac{1}{2}\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\\ \frac{1}{2}& \frac{1}{2}& \frac{1}{2}\end{array}\right]\left[\begin{array}{c}{i}_{\mathrm{nA}}\left(t\right)\\ i_{\mathrm{nB}}\left(t\right)\\ i_{\mathrm{nC}}\left(t\right)\end{array}\right]$

(4) protective device calculates the forward-order current of m transforming plant protecting installation place t sampling instant under α β 0 reference axis $i_{\mathrm{m\α}}^{+}\left(t\right),i_{\mathrm{m\β}}^{+}\left(t\right),i_{m0}^{+}\left(t\right):$

$i_{\mathrm{m\α}}^{+}\left(t\right)={0.5i}_{\mathrm{m\α}}\left(t\right)-{0.5i}_{\mathrm{m\β}}(t-\frac{T}{4})$

$i_{\mathrm{m\β}}^{+}\left(t\right)={0.5i}_{\mathrm{m\α}}(t-\frac{T}{4})+{0.5i}_{\mathrm{m\β}}\left(t\right)$

$i_{m0}^{+}\left(t\right)=i_{m0}\left(t\right)$

Wherein, for β direction of principal axis under α β 0 reference axis the current instantaneous value of the m transforming plant protecting installation place of sampling instant; i _{m β}(t) be the current instantaneous value of the m transforming plant protecting installation place of β direction of principal axis t sampling instant under α β 0 reference axis; for α direction of principal axis under α β 0 reference axis the current instantaneous value of the m transforming plant protecting installation place of sampling instant; i _{m α}(t) be the current instantaneous value of the m transforming plant protecting installation place of α direction of principal axis t sampling instant under α β 0 reference axis; T is time primitive period; i _m0(t) be the current instantaneous value of the m transforming plant protecting installation place of 0 direction of principal axis t sampling instant under α β 0 reference axis;

(5) protective device calculates the forward-order current of n transforming plant protecting installation place t sampling instant under α β 0 reference axis $i_{\mathrm{n\α}}^{+}\left(t\right),i_{\mathrm{n\β}}^{+}\left(t\right),i_{n0}^{+}\left(t\right):$

$i_{\mathrm{n\α}}^{+}\left(t\right)={0.5i}_{\mathrm{n\α}}\left(t\right)-{0.5i}_{\mathrm{n\β}}(t-\frac{T}{4})$

$i_{\mathrm{n\β}}^{+}\left(t\right)={0.5i}_{\mathrm{n\α}}(t-\frac{T}{4})+{0.5i}_{\mathrm{n\β}}\left(t\right)$

$i_{n0}^{+}\left(t\right)=i_{n0}\left(t\right)$

Wherein, for β direction of principal axis under α β 0 reference axis the current instantaneous value of the n transforming plant protecting installation place of sampling instant; i _{n β}(t) be the current instantaneous value of the n transforming plant protecting installation place of β direction of principal axis t sampling instant under α β 0 reference axis; for α direction of principal axis under α β 0 reference axis the current instantaneous value of the n transforming plant protecting installation place of sampling instant; i _{n α}(t) be the current instantaneous value of the n transforming plant protecting installation place of α direction of principal axis t sampling instant under α β 0 reference axis; T is time primitive period; i _n0(t) be the current instantaneous value of the n transforming plant protecting installation place of 0 direction of principal axis t sampling instant under α β 0 reference axis;

(6) protective device calculates A, B, the C phase forward-order current instantaneous value of m transforming plant protecting installation place t sampling instant

$\left[\begin{array}{c}{i}_{\mathrm{mA}}^{+}\left(t\right)\\ i_{\mathrm{mB}}^{+}\left(t\right)\\ i_{\mathrm{mC}}^{+}\left(t\right)\end{array}\right]=1.5{\left[\begin{array}{ccc}1& -\frac{1}{2}& -\frac{1}{2}\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\\ \frac{1}{2}& \frac{1}{2}& \frac{1}{2}\end{array}\right]}^{-1}\left[\begin{array}{c}{i}_{\mathrm{m\α}}^{+}\left(t\right)\\ i_{\mathrm{m\β}}^{+}\left(t\right)\\ i_{m0}^{+}\left(t\right)\end{array}\right]$

(7) protective device calculates A, B, the C phase forward-order current instantaneous value of n transforming plant protecting installation place t sampling instant

$\left[\begin{array}{c}{i}_{\mathrm{nA}}^{+}\left(t\right)\\ i_{\mathrm{nB}}^{+}\left(t\right)\\ i_{\mathrm{nC}}^{+}\left(t\right)\end{array}\right]=1.5{\left[\begin{array}{ccc}1& -\frac{1}{2}& -\frac{1}{2}\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\\ \frac{1}{2}& \frac{1}{2}& \frac{1}{2}\end{array}\right]}^{-1}\left[\begin{array}{c}{i}_{\mathrm{n\α}}^{+}\left(t\right)\\ i_{\mathrm{n\β}}^{+}\left(t\right)\\ i_{n0}^{+}\left(t\right)\end{array}\right]$

(8) protective device judgement whether set up, if set up, protective device sends trip signal to the circuit breaker at A phase transmission line two ends; Protective device judgement whether set up, if set up, protective device sends trip signal to the circuit breaker at B phase transmission line two ends; Protective device judgement whether set up, if set up, protective device sends trip signal to the circuit breaker at C phase transmission line two ends; Wherein, k ₁for tuning coefficient; I _setfor setting current threshold value.