CN104965156A - Fault pole selecting method using polarline fault voltage for PCA cluster analysis - Google Patents

Abstract

The invention relates to a fault pole selecting method using polarline fault voltage for PCA cluster analysis, which belongs to the technical field of direct current transmission line protection. According to the invention, electromagnetic transient simulation is used; under the condition that step length is 0.1ms, an assumption that positive and negative pole lines have metal grounding faults is carried out; n fault positions are set along the whole line MN from near to far, so as to acquire voltage curves of the observation ends of positive and negative pole lines; the voltage of a direct current line in normal operation is used as reference, the acquired voltage curves of the observation ends of positive and negative pole lines are respectively normalized; the normalized voltage curves are mapped to a PCA space to acquire the cluster of the voltage curves in the PCA space; according to the Euclidean distance between the PCA projection of test data and the PCA cluster center of the voltage curves, whether a pole is failed is determined; and theoretical analysis and a lot of simulation show that the fault pole selecting method provided by the invention is effective.

Description

A kind of fault utilizing polar curve false voltage to carry out PCA cluster analysis selects pole method

Technical field

The present invention relates to a kind of fault utilizing polar curve false voltage to carry out PCA cluster analysis and select pole method, belong to protection of direct current supply line technical field.

Background technology

In recent years, along with the development of high-power electric and electronic technology, D.C. high voltage transmission is also achieved.On Dec 28th, 2009 China's extra high voltage direct current transmission line cloud wide ± 800kV DC power transmission line realizes one pole and goes into operation, within 2010, realize bipolar total head and run, have again many extra high voltage direct current transmission lines to realize bipolar operation afterwards.Bipolar method of operation dirigibility is good, reliability is high, but during bipolar operation, when breaking down in a pole, non-faulting pole can exist and to be coupled the false voltage and current component of coming by fault polar curve, therefore needs to carry out fault and selects pole.

Only rely on voltage jump amount Δ u to determine fault pole in existing SIEMENS traveling-wave protection, should ensure fault pole precision maneuver and non-faulting is extremely reliably failure to actuate, its threshold value is difficult to adjust.ABB protection is constructed by the polarity of structure topotype ripple to select pole method, and have absolute selectivity, but the fault of ABB selects pole method, its threshold value is also not easy to adjust.We propose the method utilizing PCA cluster analysis, without the need to threshold value of adjusting, make fault select pole more simple.

Summary of the invention

The technical problem to be solved in the present invention proposes a kind of fault utilizing polar curve false voltage to carry out PCA cluster analysis to select pole method, in order to solve the problem.

Technical scheme of the present invention is: a kind of fault utilizing polar curve false voltage to carry out PCA cluster analysis selects the method for pole to be: suppose positive and negative electrode circuit generation metallic earthing fault respectively, along circuit MN total length by near to far establishing 300 abort situation altogether.Step-length is 0.1ms, time window be chosen for 3ms, by electromagnetic transient simulation obtain respectively positive and negative electrode circuit observe end voltage curve bunch.Voltage when normally running with DC line is benchmark, is normalized by the voltage curve bunch of the positive and negative electrode circuit of acquisition observation end respectively, obtains the cluster of voltage curve bunch in PCA space.Size according to test data Euclidean distance bunch between PCA cluster centre in PCA projection and voltage curve judges whether this pole breaks down.Concrete steps are as follows:

(1) extremely far establish 300 abort situation altogether along circuit MN total length by near, suppose positive and negative electrode circuit generation metallic earthing fault respectively.Step-length is 0.1ms, time window be chosen for 3ms, obtain by electromagnetic transient simulation the voltage curve bunch that positive pole circuit observes end, be designated as S ₁, the voltage curve bunch observed by electromagnetic transient simulation acquisition negative pole circuit, is designated as S ₂;

(2) voltage when normally running with DC line is benchmark, and 900 the false voltage curve family that amount to emulation obtained are normalized.

(3) construct positive electrode fault and select pole method PCA ₊pole method PCA is selected with structure negative pole fault _-.The voltage curve bunch of the positive pole circuit observation end after normalization is mapped to PCA space, obtains PCA ₊space.At PCA ₊spatially positive pole line fault flocks together, and forms a cluster centre C ₁₊=(q ₁₁₊, q ₂₁₊), the non-fault of positive pole circuit flocks together, and forms a cluster centre C ₂₊=(q ₁₂₊, q ₂₂₊).Meanwhile, at PCA _-spatially negative pole line fault flocks together, and forms a cluster centre C _1-=(q _11-, q _21-), the non-fault of positive pole circuit flocks together, and forms a cluster centre C _2-=(q _12-, q _22-).

(4), after protection starts, when choosing, window is chosen for the line voltage curve in 3ms, carries out PCA cluster analysis, is mapped to PCA after being normalized ₊and PCA _-, obtain projection value o _t+(q ₁₊, q ₂₊) and o _t-(q _1-, q _2-).Calculate test data in distance bunch between PCA cluster centre of PCA projection and voltage curve and Euclidean distance.

For positive pole circuit

$d_{s+}=\sqrt{{(q_{1+}-q_{1s+})}^2+{(q_{1+}-q_{2s+})}^2}---\left(1\right)$

In formula, s=1,2.Relatively d ₁₊and d ₂₊, determine faulty line.If d _min=d ₁₊, positive pole line fault, if d _min=d ₂₊, the non-fault of positive pole circuit.

In like manner, for negative pole circuit

$d_{s-}=\sqrt{{(q_{1-}-q_{1s-})}^2+{(q_{1-}-q_{2s-})}^2}---\left(2\right)$

In formula, s=1,2.Relatively d _1-and d _2-, determine faulty line.If d _min=d ₁, negative pole line fault, if d _min=d ₂₊, the non-fault of negative pole circuit.

Principle of the present invention is:

One, principal component analysis (PCA)

Principal component analysis (PCA) (Principal Component Analysis, i.e. PCA) is introduced by Pearson came, is developed by Hotelling afterwards.PCA is a kind of statistical analysis technique original multiple variable being divided into a few overall target.From mathematical angle, this is a kind of dimension-reduction treatment technology.PCA, through being usually used in the dimension reducing data set, keeps the feature maximum to variance contribution of data centralization simultaneously.Data Placement is gone out multiple major component by PCA, and low order composition often can retain the most important aspect of data.By retaining low order major component, ignoring the method for high-order major component, the basis of reservation data set information as much as possible realizes data set dimensionality reduction.For a system, if can portray Study system from p variable and describe, thus form observing matrix X, its form is

$X=\left[\begin{array}{cccc}{x}_{11}& x_{12}& ...& x_{1n}\\ x_{21}& x_{22}& ...& x_{2n}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ x_{p1}& x_{p2}& ...& x_{pn}\end{array}\right]---\left(1\right)$

PCA passes through n variable x _i(i=1,2,3 ..., n), carry out linear transformation, form new variable Z, wherein

Z＝(z _ij)＝V ^TX (2)

Wherein,

Then its a kth major component is z _k=v _k ^tx, z ₁that in major component, variance is maximum, z ₂be and z ₁least be correlated with and variance the maximum; z _kbe and z ₁, z ₂..., z _k-1uncorrelated and variance the maximum.

To the some i of under three dimensions, the coordinate of its original variable is x ₁, x ₂, x ₃, shown in (2-62) and formula (2-63).

PC ₁＝a ₁x _i1+a ₂x _i2+a ₃x _i3(3)

PC ₂＝b ₁x _i1+b ₂x _i2+b ₃x _i3(4)

Namely

$\left[\begin{array}{cc}{\mathrm{PC}}_1& {\mathrm{PC}}_2\end{array}\right]=(x_{i1},x_{i2},x_{i3})\left[\begin{array}{cc}{a}_1& b_1\\ a_2& b_2\\ a_3& b_3\end{array}\right]---\left(5\right)$

After the conversion such as, rotation flexible through coordinate translation, yardstick to original coordinate system, obtain one group of new, mutually orthogonal coordinate axis v ₁, v ₂.Visible, the process of PCA i.e. the process of rotation of coordinate, each major component expression formula is exactly the transformational relation of new coordinate system and former coordinate system, and in new coordinate system, the direction of each coordinate axis is exactly the maximum direction of raw data variance.

Two, Euclidean distance

Euclidean distance (Euclidean distance), also euclidean metric, euclidean metric is claimed, be a distance definition usually adopted, refer to the actual distance between two points in m-dimensional space, or the natural length of vector (namely this point is to the distance of initial point).Euclidean distance in two and three dimensions space is exactly the actual range between 2.

2 a (x on two dimensional surface ₁, y ₁) and b (x ₂, y ₂) between Euclidean distance:

$d_{12}=\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2}---\left(6\right)$

Three dimensions 2 a (x ₁, y ₁, z ₁) and b (x ₂, y ₂, z ₂) between Euclidean distance:

$d_{12}=\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2+{(z_1-z_2)}^2}---\left(7\right)$

Two n-dimensional vector a (x ₁₁, x ₁₂..., x _1n) and b (x ₂₁, x ₂₂..., x _2n) between Euclidean distance:

$d_{12}=\sqrt{\underset{k=1}{\overset{n}{\Σ}}{(x_{1k}-x_{2k})}^2}---\left(8\right)$

The invention has the beneficial effects as follows:

1, the fault utilizing polar curve false voltage to carry out PCA cluster analysis selects the method for pole, does not use the single setting valve of one dimension, makes protection more reliable;

2, as herein describedly select pole method, only use one-terminal data, principle is simple, does not rely on passage, invests little, form relatively simple.

Accompanying drawing explanation

Fig. 1 be embodiment of the present invention cloud wide ± 800kV DC transmission system structural drawing;

Fig. 2 is positive pole circuit observation terminal voltage curve family and PCA cluster result thereof under positive pole line fault and negative pole line fault;

Fig. 3 is negative pole circuit observation end curve family and PCA cluster result thereof under negative pole line fault and positive pole line fault.

Embodiment

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

Set up as shown in Figure 1 using cloud wide ± 800kV extra-high voltage DC transmission system is as realistic model.The AC reactive compensation capacity of rectification side and inverter side is respectively 3000 and 3040Mvar, and every pole convertor unit is composed in series by 2 12 pulse transverters, and DC power transmission line total length is 1500km.The smoothing reactor of 400mH is equipped with in circuit both sides, and DC filter is 12/24/36 three-tuned filter, and rectification side ground electrode circuit total length is 109km, and inverter side ground electrode circuit total length is 80km.The fault utilizing polar curve false voltage to carry out PCA cluster analysis selects a method for pole method, and concrete steps are as follows:

(1) extremely far 300 abort situation are established altogether along circuit MN total length by near, suppose positive and negative electrode circuit generation metallic earthing fault respectively, step-length is set to 0.1ms, time window be chosen for 0.3ms, the voltage curve bunch that positive pole circuit observes end is obtained by electromagnetic transient simulation, as Fig. 2 (a), the voltage curve bunch of negative pole circuit observation end, as Fig. 3 (a);

(2) voltage amounted to when 1200 false voltage curve family normally run with DC line emulation obtained is normalized for benchmark;

(3) construct positive electrode fault and select pole method PCA ₊pole method PCA is selected with structure negative pole fault _-.The voltage curve bunch of the positive pole circuit observation end after normalization is mapped to PCA space, obtains PCA ₊space.At PCA ₊spatially positive pole line fault flocks together, and forms a cluster centre C ₁₊=(q ₁₁₊, q ₂₁₊), the non-fault of positive pole circuit flocks together, and forms a cluster centre C ₂₊=(q ₁₂₊, q ₂₂₊).Meanwhile, at PCA _-spatially negative pole line fault flocks together, and forms a cluster centre C _1-=(q _11-, q _21-), the non-fault of positive pole circuit flocks together, and forms a cluster centre C _2-=(q _12-, q _22-).

Embodiment 1: positive pole circuit distance M holds 120km place that earth fault occurs, and transition resistance is 50 Ω.

According to step (4), when choosing, window is chosen for the line voltage curve in 3ms, carries out PCA cluster analysis, is mapped to PCA after being normalized ₊and PCA _-, obtain projection value o _t+(q ₁₊, q ₂₊) and o _t-(q _1-, q _2-).D is obtained according to formula (1) ₁₊=1.9185 and d ₂₊=3.6141, and d _min+=d ₁₊, be judged as positive pole line fault.Meanwhile, formula (2) is utilized to obtain d _1-=6.2155, d _2-=0.6960, and d _min-=d _2-, be judged as the non-fault of negative pole circuit.

Embodiment 2: negative pole circuit distance M holds 750km place that earth fault occurs, and transition resistance is 50 Ω.

According to step (4), when choosing, window is chosen for the line voltage curve in 3ms, carries out PCA cluster analysis, is mapped to PCA after being normalized ₊and PCA _-, obtain projection value o _t+(q ₁₊, q ₂₊) and o _t-(q _1-, q _2-).D is obtained according to formula (1) ₁₊=5.5713 and d ₂₊=0.0505, and d _min+=d ₂₊, be judged as the non-fault of positive pole circuit.Meanwhile, formula (2) is utilized to obtain d _1-=2.5077, d _2-=3.0372, and d _min-=d _1-, be judged as negative pole line fault.

Embodiment 3: two-wire line distance M holds 654km place that earth fault occurs, and transition resistance is 50 Ω.

According to step (4), when choosing, window is chosen for the line voltage curve in 3ms, carries out PCA cluster analysis, is mapped to PCA after being normalized ₊and PCA _-, obtain projection value o _t+(q ₁₊, q ₂₊) and o _t-(q _1-, q _2-).D is obtained according to formula (1) ₁₊=0.1954 and d ₂₊=5.4059, and d _min+=d ₁₊, be judged as positive pole line fault.Meanwhile, formula (2) is utilized to obtain d _1-=0.1510, d _2-=5.5258, and d _min-=d _1-, be judged as negative pole line fault.

By reference to the accompanying drawings the specific embodiment of the present invention is explained in detail above, but the present invention is not limited to above-mentioned embodiment, in the ken that those of ordinary skill in the art possess, various change can also be made under the prerequisite not departing from present inventive concept.

Claims (2)

1. the fault utilizing polar curve false voltage to carry out PCA cluster analysis selects pole method, it is characterized in that: suppose positive and negative electrode circuit generation metallic earthing fault respectively, extremely far 300 abort situation are established altogether by near along circuit MN total length, step-length is 0.1ms, time window be chosen for 3ms, by electromagnetic transient simulation obtain respectively positive and negative electrode circuit observe end voltage curve bunch; Voltage when normally running with DC line is benchmark, is normalized by the voltage curve bunch of the positive and negative electrode circuit of acquisition observation end respectively, obtains the cluster of voltage curve bunch in PCA space; Size according to test data Euclidean distance bunch between PCA cluster centre in PCA projection and voltage curve judges whether this pole breaks down.

2. the fault utilizing polar curve false voltage to carry out PCA cluster analysis according to claim 1 selects pole method, it is characterized in that concrete steps are:

(1) extremely far 300 abort situation are established altogether along circuit MN total length by near, suppose positive and negative electrode circuit generation metallic earthing fault respectively, step-length is 0.1ms, time window be chosen for 3ms, obtain by electromagnetic transient simulation the voltage curve bunch that positive pole circuit observes end, be designated as S ₁, the voltage curve bunch observed by electromagnetic transient simulation acquisition negative pole circuit, is designated as S ₂;

(2) voltage when normally running with DC line is benchmark, and 1200 the false voltage curve family that amount to emulation obtained are normalized;

(3) construct positive electrode fault and select pole method PCA ₊pole method PCA is selected with structure negative pole fault _-: the voltage curve bunch of the positive pole circuit observation end after normalization is mapped to PCA space, obtains PCA ₊space, at PCA ₊spatially positive pole line fault flocks together, and forms a cluster centre C ₁₊=(q ₁₁₊, q ₂₁₊), the non-fault of positive pole circuit flocks together, and forms a cluster centre C ₂₊=(q ₁₂₊, q ₂₂₊), meanwhile, at PCA _-spatially negative pole line fault flocks together, and forms a cluster centre C _1-=(q _11-, q _21-), the non-fault of positive pole circuit flocks together, and forms a cluster centre C _2-=(q _12-, q _22-);

(4), after protection starts, when choosing, window is chosen for the line voltage curve in 3ms, carries out PCA cluster analysis, and is mapped to PCA ₊and PCA _-, obtain projection value o _t+(q ₁₊, q ₂₊) and o _t-(q _1-, q _2-), calculate test data in distance bunch between PCA cluster centre of PCA projection and voltage curve and Euclidean distance:

For positive pole circuit

$d_{s+}=\sqrt{{(q_{1+}-q_{1s+})}^2+{(q_{1+}-q_{2s+})}^2}---\left(1\right)$

In formula, s=1,2, compare d ₁₊and d ₂₊, determine faulty line;

If d _min=d ₁₊, positive pole line fault

If d _min=d ₂₊, the non-fault of positive pole circuit;

In like manner, for negative pole circuit

$d_{s-}=\sqrt{{(q_{1-}-q_{1s-})}^2+{(q_{1-}-q_{2s-})}^2}---\left(2\right)$

In formula, s=1,2, compare d _1-and d _2-, determine faulty line;

If d _min=d ₁, negative pole line fault,

If d _min=d ₂₊, the non-fault of negative pole circuit.