CN108375714A - A kind of direct current distribution one-end fault ranging method - Google Patents

Abstract

The present invention relates to a kind of direct current distribution one-end fault ranging methods, including：Data sampling multigroup enough is carried out in a ranging；It is sampled as a data window with 5 times；5 times sampled data forms a coefficient matrix, ultimately forms a series of coefficient matrix of each data window of correspondences；All coefficient matrixes are sought | | A'^‑1||₁, filter out | | A'^‑1||₁A minimum coefficient matrix；X=A' is solved using the coefficient matrix filtered out^‑1B obtains high-precision fault distance.

Description

A kind of direct current distribution one-end fault ranging method

Technical field

The invention belongs to relay protection of power system and automatic field, and in particular to a kind of direct current one-end fault ranging side Method.

Background technology

In recent years, since the exhaustion of fossil energy and exploitation difficulty increase and it causes severe environmental problem, newly The energy obtains large-scale promotion, and simultaneously, the direct currents such as electric vehicle, frequency conversion equipment, LED illumination lamp, information equipment are negative The ratio that lotus accounts for total load increasingly increases, and direct-flow distribution system is with efficient, power supply capacity is big, anti-interference is good, reliability The high, advantages such as control is relatively easy, electric energy loss is low, are widely paid close attention to.

The fault localization of conventionally employed single-ended measurement amount communicates mould with localization method without a large amount of installations in a power distribution system Block and equipment, therefore with the advantages such as economic, convenient, practical, be suitble to be widely used in In the distribution system of low voltage.However more It holds in power supply system, anti-transition resistance energy force difference is as disadvantage most prominent in one-terminal data ranging or positioning principle, for a long time Its being further widely popularized and studying in relay protection of power system is limited always.Therefore, one-terminal data range measurement principle only by For the occasion that some fault resistances are small or reliability requirement is low.

Invention content

The purpose of the present invention is be directed to the offer of low pressure short-term direct current micro-grid system to ensure that there are transition resistances always There is the direct current distribution one-end fault ranging method of higher range accuracy.The present invention can be with quantitative estimation difference measurement time by right The degree for holding unknown quantity interference, effectively improves and compensates for the defect of traditional algorithm.Technical solution is as follows：

A kind of direct current distribution one-end fault ranging method, includes the following steps：

The first step carries out data sampling multigroup enough in a ranging.

Second step, to be sampled as a data window for 5 times, in data window kth time sampling fault distance and measured value have with Lower relationship：

Wherein R₀、L₀For circuit resistance per unit length, inductance parameters, L_mFor the ginseng of the inductance for measuring current changing rate Number, R_fFor transition resistance size, l_xFor fault distance；i₁ ^(k)、u₁ ^(k)、u₀ ^(k)、u_x ^(k)With i₂ ^(k)The respectively lower local terminal of kth time sampling Line current, measures inductive drop value, fault point voltage value and opposite end line current at measurement point voltage across poles.

Third walks, if l_xFor x₁, R_fFor x₂, R_f i₂ ⁽¹⁾、R_f i₂ ⁽²⁾、R_f i₂ ⁽³⁾For x₃、x₄、x₅, according to " n times sample opposite end Electric current i₂N-3 scale quotient it is equal " hypothesis supplement following two equations：

f[i₂ ⁽ⁿ⁺²⁾,i₂ ⁽ⁿ⁺¹⁾,i₂ ⁽ⁿ⁾] specific expand into：

Wherein Δ t is sampling time interval.

There is the establishment of following equation group according to (4), (5)：

It can solve：

According to formula (3), (8), 5 sampled datas in each data window form a coefficient matrix：

Ultimately form a series of coefficient matrix of each data window of correspondences.

4th step seeks all coefficient matrixes | | A'^-1||₁, filter out | | A'^-1||₁A minimum coefficient matrix；

5th step solves x=A' using the coefficient matrix filtered out^-1B obtains high-precision fault distance.

Wherein

Compared with prior art, the beneficial effects of the present invention are：

Compared to the widely used range measurement principle based on communication, the present invention is not based on communication, without installing communication module, Without communication synchronization problem, simpler easy realization, cost is lower, good economy performance.Compared to traditional one-terminal data range measurement principle, more It holds in power supply system, the present invention has higher anti-transition resistance ability and range accuracy, effectively compensates for tradition based on single The defect of the range measurement principle of looking somebody up and down.

Description of the drawings

Fig. 1 is that simple both-end electrifying system, the installation of range unit mutual inductor and variable illustrate.

Fig. 2 is norm and Error Absolute Value versus time curve after failure.

Specific implementation mode

The present invention provides a kind of high-precision using one-terminal data, highly resistance transition resistance ability Fault Location Algorithm, theory card Bright, there are in the case of transition resistance and opposite end electric current, the available effective equation number of single end distance measurement principle compares unknown quantity forever It is 2 few, therefore forever can not precision ranging.The principle quantifies to adopt by R-L model system of linear equations coefficient inverse matrix norms The sample moment by unknown quantity interference effect, is reduced as much as possible by increasing data window length with being estimated using coefficient inverse matrix norm Error improves precision.

Below in conjunction with the accompanying drawings 1 and a simple both end power supplying system the present invention is described in further detail.

Both-end electrifying system and the installation of range unit mutual inductor are as shown in Figure 1.According to R-L method classical formulas, theoretically event Hindering distance and measured value has following relationship：

u₁=R_xi₁+L_xi′₁+u_x (1)

u₁=(R₀l_x)i₁+(L₀l_x+L_m)u₀/L_m+(i₁+i₂)R_f (2)

u₁-u₀=(R₀i₁+L₀/L_mu₀)l_x+R_fi₁+R_fi₂ (3)

It is once l there are unknown quantity after sampling according to above formula_x、R_fAnd i₂.The wherein electric current i from opposite end₂It is by single Sampling it is introduced.Therefore, if having carried out k sampling, unknown number number k+2, the number of equation is forever than unknown Several numbers are few, carry out the sampling of one-terminal data anyway, equation group is without solution.

Because lacking two equations, it is believed that the opposite end electric current of last double sampling can not solve.To make equation There is solution, require supplementation with assumed condition, the principle of present principles supplement assumed condition is：Assuming that the opposite end electric current n-3 scales of n times sampling Quotient is equal.

When a length of for data window 3, after twice 0 scale quotient of opposite end electric current it is equal：

When a length of for data window 4, after twice 1 scale quotient of opposite end electric current it is equal：

When n a length of for data window, after twice opposite end electric current n-3 scale quotient it is equal：

N times are sampled with the data window to be formed, if writing linear equation according to (3) row after using every time, and assumes l_xFor x₁, R_fFor x₂, R_f i₂ ⁽¹⁾、R_f i₂ ⁽²⁾..., R_f i₂ ^(n-2)For x₃、x₄..., x_n, in conjunction with the condition (8) of supplement and (9), can obtain Differed with actual equations group coefficient matrix δ A matrix A '：

Wherein b_iWith c_i(i=1,2 ..., n-2) it is the constant obtained by formula (8) and (9).So, the coefficient square is utilized Battle array solves x=A'^-1The error for the distance measurement result that b is obtained has following relationship：

1. the proof of pair formula (11)：

Assuming that two the had more opposite end electric currents that can not be solved can be expressed as：

So arranging the system of linear equations write according to (3) is：

Wherein k₁=i₂ ^(n-1)/(i₂ ⁽¹⁾+i₂ ⁽²⁾…+i₂ ^(n-2))、k₂=i₂ ⁽ⁿ⁾/(i₂ ⁽¹⁾+i₂ ⁽²⁾…+i₂ ^(n-2)).It is so practical The matrix A of upper A and hypothesis ' between there are a δ A：

Inlet coefficient matrix A '^-11 norm, due to A=(A'- δ A), x=(x'- δ x) has after substituting into full scale equation Ax=b：

(A '-δ A) (x '-δ x)=b (16)

It is after abbreviation

δ x=-A '^-1δA(x′-δx) (17)

According to consistent norms theorem, have：

δx||₁≤||A′^-1||₁||δA||₁||x′-δx||₁ (18)

||δx||₁/||x||₁≤||A′^-1||₁(|b_i|+|c_i|+|k₁|+|k₂|) (20)

2. pair using (8), (9) that the proof of error can be reduced for supplementary condition：

Assuming that opposite end electric current i₂The x in data window section₀The Taylor expansion at place is：

For the i under 0 order derivative₂(t₂)-i₂(t₁) be：

i₂(t₂)-i₂(t₁)=a₁(t₂-t₁)+a₂[t₂ ²-t₁ ²-2t₀(t₂-t₁)]+... (22)

For the i' under 1 order derivative₂(t₂)-i'₂(t₁) be：

i₂′(t₂)-i₂′(t₁)=2a₂(t₂-t₁)+3a₃[t₂ ²-t₁ ²-2t₀(t₂-t₁)]+... (23)

For the i " under 2 order derivatives₂(t₂)-i”₂(t₁) be：

i₂″(t₂)-i₂″(t₁)=6a₃(t₂-t₁)+12a₄[t₂ ²-t₁ ²-2t₀(t₂-t₁)]+... (24)

When being that is supplementary condition according to (8), (9), the data window of use it is longer just it can be assumed that two had more not The amount of knowing has equal higher order derivative with known quantity.Therefore the lower term in their difference will be eliminated, the difference between them With regard to smaller.They are closer to assuming that the δ A introduced after its is equal are smaller, and the error obtained according to formula (20) is with regard to smaller.

To occur, containing for 5 Ω transition resistances, to sample 250 points after a failure, sample at attached system shown in Figure 1 1.0km Frequency is 20kHz.According to the norm and error such as attached drawing 2 solved after (9) construction coefficient matrix under 200 sampling instants.

According to the results show that in certain time intervals | | A^r1||₁There is minimum, corresponding | | A^r1||₁Respectively 1.5330,2.1390,2.0440,0.2586,0.1920, according to the error of the calculated measured value of (4) step and theoretical value point It Wei 7.65%, 1.35%, 0.93%, 0.86%, 0.61%.It is minimum according to choosing | | A^r1||₁For the principle of result, obtain Measurement result is 1.0061, error 0.61%.

Therefore, actual implementation shows that the algorithm has high range accuracy and anti-transition resistance ability.

Claims (1)

1. a kind of direct current distribution one-end fault ranging method, includes the following steps：

The first step carries out data sampling multigroup enough in a ranging；

Second step is sampled as a data window with 5 times, and kth time sampling fault distance has with measured value with ShiShimonoseki in data window System：

Wherein R₀、L₀For circuit resistance per unit length, inductance parameters, L_mFor the parameter of the inductance for measuring current changing rate, R_f For transition resistance size, l_xFor fault distance；i₁ ^(k)、u₁ ^(k)、u₀ ^(k)、u_x ^(k)With i₂ ^(k)Respectively this lower end line of kth time sampling Electric current, measures inductive drop value, fault point voltage value and opposite end line current at measurement point voltage across poles；

Third walks, if l_xFor x₁, R_fFor x₂, R_f i₂ ⁽¹⁾、R_f i₂ ⁽²⁾、R_f i₂ ⁽³⁾For x₃、x₄、x₅, according to " n times sample opposite end electric current i₂N-3 scale quotient it is equal " hypothesis supplement following two equations：

f[i₂ ⁽ⁿ⁺²⁾,i₂ ⁽ⁿ⁺¹⁾,i₂ ⁽ⁿ⁾] specific expand into：

Wherein Δ t is sampling time interval；

There is the establishment of following equation group according to (4), (5)：

It can solve：

According to formula (3), (8), 5 sampled datas in each data window form a coefficient matrix：

Ultimately form a series of coefficient matrix of each data window of correspondences；

4th step seeks all coefficient matrixes | | A'^-1||₁, filter out | | A'^-1||₁A minimum coefficient matrix；

5th step solves x=A' using the coefficient matrix filtered out^-1B obtains high-precision fault distance,

Wherein