CN105606955A - Numerical differentiation and empirical mode decomposition-based fault line distinguishing method - Google Patents

Abstract

The invention relates to a numerical differentiation and empirical mode decomposition-based fault line distinguishing method and belongs to the electric power system relay protection technical field. When a grounding fault occurs on power transmission lines, and zero-sequence current is generated, zero-sequence current data of the power transmission lines in a 4-millisecond time window after the grounding fault are extracted, and numerical differentiation is performed on the zero-sequence current data, so that direct-current components in the acquired data can be removed; numerical integration is performed on obtained results after the numerical differentiation; empirical mode decomposition is performed on integration results; a judgment value R<IMFhn> is calculated by using an IMF component with the highest frequency, wherein the IMF component with the highest frequency is obtained through calculation; and the judgment value R<IMFhn> is compared with a threshold value Th, so that a fault line and a normal line in a busbar can be distinguished. As indicated by theoretical analysis and simulation results, the method of the invention is correct and effective.

Description

A kind of faulty line method of discrimination based on numerical differentiation and empirical mode decomposition

Technical field

The present invention relates to a kind of faulty line method of discrimination based on numerical differentiation and empirical mode decomposition, belong to power system relayResist technology field.

Background technology

Around the discrimination of faulty line in power system, successively emerge many methods, comprise route selection, the profit of utilizing energyWith the route selection of transient current with utilize route selection of idle monitoring etc. Energy route selection method is to consider in electrical network that electric capacity and inductance only storeEnergy and consumed energy not, zero-sequence current and voltage product integrated value are within a certain period of time exactly resistive component in zero-sequence currentThe energy consuming, and this energy has the resistive feature of zero sequence, can be used as the criterion of route selection. Transient current route selection has utilizedThe feature that zero-sequence current transient state component is large, the feature of zero-sequence current transient state component is not subject to the impact of neutral grounding mode substantially, eachCircuit zero-sequence current is taking the transient state component of high frequency attenuation as main, and transient state component can reach several times, tens times of power frequency state component and even go upHundred times, therefore its easily identification and analysis. Idle detection route selection is because in neutral by arc extinction coil grounding system, fault wireThe reactive power that road detects is mainly the reactive power absorbing by perfecting circuit equivalent capacity, therefore adopts the method for Current Decomposition,Utilize transient reactive power can form failure line selection criterion. But there is following shortcoming in above-mentioned route selection method: small current neutral grounding systemSinglephase earth fault zero-sequence current is very little, may only have several amperes, and the load current that system line is carried is generally hundreds of ampere,Load current is transformed into after secondary side by current transformer, carries out signals collecting by current signal collecting device, due to electric current letterNumber collecting device certainly exists certain DC component and noise, causes the waveform collecting can produce to a certain degree distortion, impactThe route selection effect of above-mentioned selection method.

Summary of the invention

The object of this invention is to provide a kind of faulty line method of discrimination based on numerical differentiation and empirical mode decomposition, in order to solveThe problems referred to above.

Technical scheme of the present invention is: a kind of faulty line method of discrimination based on numerical differentiation and empirical mode decomposition, power transmission lineWhen earth fault occurs on road, device starts immediately, and measuring unit records the zero-sequence current of faulty line. While extracting after circuit 4msZero-sequence current data in window are carried out numerical differentiation to reject the DC component in image data, and differential acquired results is carried out to numerical valueIntegration, carries out empirical mode decomposition to integral result, extracts the high-frequency I MF component after empirical mode decomposition, calculates IMF and dividesThe judgment value R of amount_IMFhn, by R_IMFhnTh compares with threshold value: if R_IMFhn< Th, is judged as non-fault line, ifR_IMFhn>=Th, is judged as faulty line.

Concrete steps are as follows:

(1), in the time of transformer generation internal fault or excitation surge current, device starts immediately, detects and record by measuring unitEach circuit zero-sequence current;

(2) the zero-sequence current data i while extracting the rear 4ms of line fault generation in window₀₁、i₀₂、i₀₃、…i_0n, (n is busTravel permit number) 1,2,3 ... n is the n bar circuit of same bus;

(3) utilize following formula to carry out numerical differentiation to the zero-sequence current extracting, Numerical Differentiation Formulae is as follows

$\left.\begin{array}{c}{f}^{\&prime;}\left(x_0\right)=\frac{f\left(x_1\right)-f\left(x_0\right)}{h}-\frac{h}{2}{f}^{\&prime;\&prime;}\left(\mathrm{\&xi;}\right)\\ f^{\&prime;}\left(x_1\right)=\frac{f\left(x_1\right)-f\left(x_0\right)}{h}+\frac{h}{2}{f}^{\&prime;\&prime;}\left(\mathrm{\&xi;}\right)\end{array}\right\},\mathrm{\&xi;}\&Element;\&lsqb;x_0,x_1\&rsqb;$

In formula: f (x) is the zero-sequence current data of an extraction, the step-length that h is differential, f'(x) be single order derived function, f " (x) be second order derived function,ξ is x₀With x₁Between arbitrary value.

(4) to required f'(x) carry out numerical integration, remove DC component in zero-sequence current, Numerical Integral Formulas is as follows

${\&Integral;}_a^b{f}^{\&prime;}\left(x\right)dx\&ap;\underset{i=1}{\overset{n}{\&Sigma;}}{\&Integral;}_{x_i}^{x_{i+1}}g\left(x\right)dx$

In formula: a, b is integral domain, g (x) is approximate function, x_iFor discrete sampling point.

(5) extract the high fdrequency component IMF after integration, calculate by following formula:

$\left.\begin{array}{c}{h}_{11}\left(t\right)=x\left(t\right)-m_{11}\left(t\right)\\ h_{12}\left(t\right)=s_{11}\left(t\right)-m_{12}\left(t\right)\\ .\\ .\\ .\\ h_{1n}\left(t\right)=s_{1(n-1)}-m_{1n}\left(t\right)\end{array}\right\}$

$\left.\begin{array}{c}{s}_{11}\left(t\right)=h_{11}\left(t\right)/a_{11}\left(t\right)\\ s_{12}\left(t\right)=h_{12}\left(t\right)/a_{12}\left(t\right)\\ .\\ .\\ .\\ s_{1n}\left(t\right)=h_{1n}\left(t\right)/a_{1n}\left(t\right)\end{array}\right\}$

To m_iCarry out smoothing processing with moving average method and obtain m_ii(t)

The all envelope estimation functions that produce in iterative process can be obtained to envelope signal (instantaneous amplitude function) mutually at convenience

$a_1\left(t\right)=a_{11}\left(t\right)a_{12}\left(t\right)...a_{1n}\left(t\right)=\underset{q=1}{\overset{n}{\&Pi;}}{a}_{1q}\left(t\right)$

By envelope signal a₁And pure FM signal s (t)_1n(t) can obtain at convenience mutually the radio-frequency component in the IMF component of primary signalIMFh(x_i)

(6) extract IMFh (x_i), calculate judgment value R by following formula_IMFhn：

$R_{IMFhn}=\underset{i=1}{\overset{m}{\&Sigma;}}IMFh\left(x_i\right)$

In above formula, IMFh (x_i) be high fdrequency component after EMD decomposes, m is total sampled point number;

(7) by a large amount of emulation, threshold value Th=3 is set, carry out faulty line and the differentiation that perfects circuit according to criterion below:

If R_IMFhn< Th, this circuit is for perfecting circuit, if R_IMFhn>=Th, this circuit is faulty line.

Principle of the present invention is:

One, the empirical mode decomposition of zero-sequence current

Zero-sequence current data i while extracting 4ms after line fault in window₀₁、i₀₂、i₀₃、…i_0n, (n is total line number) 1,2,3 ... n is the n bar circuit of same bus;

Utilize respectively following formula to carry out empirical mode decomposition to the zero-sequence current extracting, and extract high spectrum IMF component:

$\left.\begin{array}{c}{h}_{11}\left(t\right)=x\left(t\right)-m_{11}\left(t\right)\\ h_{12}\left(t\right)=s_{11}\left(t\right)-m_{12}\left(t\right)\\ .\\ .\\ .\\ h_{1n}\left(t\right)=s_{1(n-1)}-m_{1n}\left(t\right)\end{array}\right\}---\left(1\right)$

(1) in formula

$\left.\begin{array}{c}{s}_{11}\left(t\right)=h_{11}\left(t\right)/a_{11}\left(t\right)\\ s_{12}\left(t\right)=h_{12}\left(t\right)/a_{12}\left(t\right)\\ .\\ .\\ .\\ s_{1n}\left(t\right)=h_{1n}\left(t\right)/a_{1n}\left(t\right)\end{array}\right\}---\left(2\right)$

To m_iCarry out smoothing processing with moving average method and obtain m_ii(t)(3)

The all envelope estimation functions that produce in iterative process can be obtained to envelope signal (instantaneous amplitude function) mutually at convenience

$a_1\left(t\right)=a_{11}\left(t\right)a_{12}\left(t\right)...a_{1n}\left(t\right)=\underset{q=1}{\overset{n}{\&Pi;}}{a}_{1q}\left(t\right)---\left(4\right)$

By envelope signal a₁And pure FM signal s (t)_1n(t) can obtain at convenience mutually the radio-frequency component in the IMF component of primary signalIMFh

IMFh(t)＝a₁(t)s_1n(t)(5)

Two, extract IMFh (x_i), calculate judgment value R by following formula_IMFhn：

In following formula, IMFh (x_i) be high fdrequency component after EMD decomposes, Δ t is the sampling period taking 4ms as interval;

$R_{IMFhn}=\underset{i=1}{\overset{n}{\&Sigma;}}IMFh\left(x_i\right)---\left(6\right)$

In formula: n is total sampled point number

Three, become faulty line and perfect the differentiation of circuit:

By a large amount of emulation, threshold value Th=3 is set, if R_IMFhn< Th, this circuit is for perfecting circuit, if R_IMFhn>=Th,This circuit is faulty line.

The invention has the beneficial effects as follows:

1, the DC component that can reject zero-sequence current the inside, is affected by channel noise little;

2, adopt 4ms short time-window to carry out decision analysis, it is shorter that institute takes window.

Brief description of the drawings

Fig. 1 is embodiment of the present invention single busbar three outlet single-phase-to-ground fault models;

The zero-sequence current oscillogram of 1,2,3 circuit when Fig. 2,3,4 connects fault for circuit 1;

When Fig. 5 is circuit 2 fault, the radio-frequency component IMFh oscillogram in circuit 2 in the IMF component of zero-sequence current.

Detailed description of the invention

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

When transformer generation internal fault or produce when excitation surge current, device starts immediately, and measuring unit records faulty lineZero-sequence current. Zero-sequence current data while extracting 4ms after circuit in window are carried out numerical differentiation, integration and empirical mode decomposition, carryGet the high-frequency I MF component after empirical mode decomposition, calculate the judgment value R of IMF component_IMFhn, by R_IMFhnWith threshold value ThCompare: if R_IMFhn< Th, is judged as non-fault line, if R_IMFhn>=Th, is judged as faulty line.

Concrete steps are as follows:

(2), in the time of transformer generation internal fault or excitation surge current, device starts immediately, detects and record by measuring unitEach circuit zero-sequence current;

(2) the zero-sequence current data i while extracting the rear 4ms of line fault generation in window₀₁、i₀₂、i₀₃、…i_0n, (n is busTravel permit number) 1,2,3 ... n is the n bar circuit of same bus;

(3) utilize following formula to carry out numerical differentiation to the zero-sequence current extracting, Numerical Differentiation Formulae is as follows

$\left.\begin{array}{c}{f}^{\&prime;}\left(x_0\right)=\frac{f\left(x_1\right)-f\left(x_0\right)}{h}-\frac{h}{2}{f}^{\&prime;\&prime;}\left(\mathrm{\&xi;}\right)\\ f^{\&prime;}\left(x_1\right)=\frac{f\left(x_1\right)-f\left(x_0\right)}{h}+\frac{h}{2}{f}^{\&prime;\&prime;}\left(\mathrm{\&xi;}\right)\end{array}\right\},\mathrm{\&xi;}\&Element;\&lsqb;x_0,x_1\&rsqb;$

In formula: f (x) is the zero-sequence current data of an extraction, the step-length that h is differential, f'(x) be single order derived function, f " (x) be second order derived function,ξ is x₀With x₁Between arbitrary value.

(4) to required f'(x) carry out numerical integration, remove DC component in zero-sequence current, Numerical Integral Formulas is as follows

${\&Integral;}_a^b{f}^{\&prime;}\left(x\right)dx\&ap;\underset{i=1}{\overset{n}{\&Sigma;}}{\&Integral;}_{x_i}^{x_{i+1}}g\left(x\right)dx$

In formula: a, b is integral domain, g (x) is approximate function, x_iFor discrete sampling point.

(5) extract the high fdrequency component IMF after integration, calculate by following formula:

$\left.\begin{array}{c}{h}_{11}\left(t\right)=x\left(t\right)-m_{11}\left(t\right)\\ h_{12}\left(t\right)=s_{11}\left(t\right)-m_{12}\left(t\right)\\ .\\ .\\ .\\ h_{1n}\left(t\right)=s_{1(n-1)}-m_{1n}\left(t\right)\end{array}\right\}$

$\left.\begin{array}{c}{s}_{11}\left(t\right)=h_{11}\left(t\right)/a_{11}\left(t\right)\\ s_{12}\left(t\right)=h_{12}\left(t\right)/a_{12}\left(t\right)\\ .\\ .\\ .\\ s_{1n}\left(t\right)=h_{1n}\left(t\right)/a_{1n}\left(t\right)\end{array}\right\}$

To m_iCarry out smoothing processing with moving average method and obtain m_ii(t)

The all envelope estimation functions that produce in iterative process can be obtained to envelope signal (instantaneous amplitude function) mutually at convenience

$a_1\left(t\right)=a_{11}\left(t\right)a_{12}\left(t\right)...a_{1n}\left(t\right)=\underset{q=1}{\overset{n}{\&Pi;}}{a}_{1q}\left(t\right)$

By envelope signal a₁And pure FM signal s (t)_1n(t) can obtain at convenience mutually the radio-frequency component in the IMF component of primary signalIMFh(x_i)

(6) extract IMFh (x_i), calculate judgment value R by following formula_IMFhn：

$R_{IMFhn}=\underset{i=1}{\overset{m}{\&Sigma;}}IMFh\left(x_i\right)$

In above formula, IMFh (x_i) be high fdrequency component after EMD decomposes, m is total sampled point number;

(7) by a large amount of emulation, threshold value Th=3 is set, carry out faulty line and the differentiation that perfects circuit according to criterion below:

If R_IMFhn< Th, this circuit is for perfecting circuit, if R_IMFhn>=Th, this circuit is faulty line.

Embodiment 1: set up single busbar three outlet single-phase-to-ground fault models as shown in Figure 1, wherein transformer is threeThe single-phase three-winding transformer of platform platform, adopts Yd11 connection, and its high pressure winding access 115kV system is transformer primary side, lowPressing winding access 35KV system is transformer secondary, and line parameter circuit value is as follows: circuit 1 length is 19KM, and circuit 2 length are17KM, circuit 3 length are 18KM, and transformer nominal transformation ratio is 115kV/35kV, and transition resistance is 0.2 Ω. Circuit resistanceAnti-matrix and admittance matrix are as shown in table 1,2.

Table 1

Table 2

Now suppose that in circuit 1, earth fault occurs at 7KM place, sample frequency is 1MHz, under this model, and this circuit zero sequence electricityStream waveform as shown in Figure 2, perfects circuit zero-sequence current as shown in Figure 3,4.

i_0n＝i_an+i_bn+i_cn

I in formula_0nFor the zero-sequence current of each circuit, i_an、i_bn、i_cnFor the three-phase current of each circuit. It is asked to judgment value R_IMFh1＝3.7915，R_IMFh2＝1.7732，R_IMFh3=1.3345, according to Th=k₁×i_0n，k₁Get 0.2, try to achieve Th_N＝3。

Because R_IMFh1> Th, judge that circuit 1 is for faulty line, with hypothesis always, correct judgment.

Embodiment 2: set up single busbar three outlet single-phase-to-ground fault models as shown in Figure 1, its parameter is at embodiment 1In describe in detail, be not repeated here. Now suppose that in circuit 2, earth fault occurs at 10KM place, sample frequency is 1MHz,Under this model, the radio-frequency component IMFh (x in IMF component_i) oscillogram is as accompanying drawing 5.

In like manner can try to achieve corresponding R by the data of sampled point_IMFh1＝1.7945，R_IMFh2＝3.7321，R_IMFh1＝1.3945，Th＝3。Because R_ind2＞Th_N, according to criterion, judge that circuit 2 is as faulty line. Consistent with hypothesis, correct judgment.

Claims (2)

1. the faulty line method of discrimination based on numerical differentiation and empirical mode decomposition, is characterized in that: transmission line of electricity occursWhen earth fault, device starts immediately, and measuring unit records the zero-sequence current of each circuit; While extracting after line fault 4ms in windowZero-sequence current data carry out numerical differentiation to reject the DC component in image data, differential acquired results is carried out to numerical integration,Integral result is carried out to empirical mode decomposition, extract the high-frequency I MF component after empirical mode decomposition, calculate sentencing of IMF componentDisconnected value R_IMFhn, by R_IMFhnTh compares with threshold value: if R_IMFhn< Th, is judged as non-fault line, if R_IMFhn≥Th，Be judged as faulty line.

2. according to the faulty line method of discrimination based on numerical differentiation and empirical mode decomposition claimed in claim 1, its featureBe that concrete steps are as follows:

(1), in the time of transmission line of electricity generation earth fault, device starts immediately, detects and record zero of each circuit by measuring unitOrder electric current;

(2) the zero-sequence current data i while extracting the rear 4ms of line fault generation in window₀₁、i₀₂、i₀₃、…i_0N, (N is busTravel permit number);

(3) utilize following formula to carry out numerical differentiation to the zero-sequence current extracting, Numerical Differentiation Formulae is as follows:

$\left.\begin{array}{c}{f}^{\&prime;}\left(x_0\right)=\frac{f\left(x_1\right)-f\left(x_0\right)}{h}-\frac{h}{2}{f}^{\&prime;\&prime;}\left(\mathrm{\&xi;}\right)\\ f^{\&prime;}\left(x_1\right)=\frac{f\left(x_1\right)-f\left(x_0\right)}{h}+\frac{h}{2}{f}^{\&prime;\&prime;}\left(\mathrm{\&xi;}\right)\end{array}\right\},\mathrm{\&xi;}\&Element;\&lsqb;x_0,x_1\&rsqb;$

In formula: f (x) is the zero-sequence current data of an extraction, the step-length that h is differential, f'(x) be single order derived function, f " (x) for second order is ledFunction, ξ is x₀With x₁Between arbitrary value;

(4) to required f'(x) carry out numerical integration, remove DC component in zero-sequence current, Numerical Integral Formulas is as follows:

${\&Integral;}_a^b{f}^{\&prime;}\left(x\right)dx\&ap;\underset{i=1}{\overset{n}{\&Sigma;}}{\&Integral;}_{x_i}^{x_{i+1}}g\left(x\right)dx$

In formula: a, b is integral domain, g (x) is approximate function, x_iFor discrete sampling point;

(5) extract the high fdrequency component IMF after integration, calculate by following formula:

$\left.\begin{array}{c}{h}_{11}\left(t\right)=x\left(t\right)-m_{11}\left(t\right)\\ h_{12}\left(t\right)=s_{11}\left(t\right)-m_{12}\left(t\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ h_{1n}\left(t\right)=s_{1(n-1)}\left(t\right)-m_{1n}\left(t\right)\end{array}\right\}$

$\left.\begin{array}{c}{s}_{11}\left(t\right)=h_{11}\left(t\right)/a_{11}\left(t\right)\\ s_{12}\left(t\right)=h_{11}\left(t\right)/a_{12}\left(t\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ s_{1n}\left(t\right)=h_{1n}\left(t\right)/a_{1n}\left(t\right)\end{array}\right\}$

To m_iCarry out smoothing processing with moving average method and obtain m_ii(t); The all envelopes that produce in iterative processEstimation function can obtain envelope signal mutually at convenience;

$a_1\left(t\right)=a_{11}\left(t\right)a_{12}\left(t\right)...a_{1n}\left(t\right)=\underset{q=1}{\overset{n}{\&Pi;}}{a}_{1q}\left(t\right)$

By envelope signal a₁And pure FM signal s (t)_1n(t) can obtain at convenience mutually the radio-frequency component in the IMF component of primary signalIMFh(x_i)；

(6) extract IMFh (x_i), calculate judgment value R by following formula_IMFhn：

$R_{IMFhn}=\underset{i=1}{\overset{m}{\&Sigma;}}IMFh\left(x_i\right)$

In formula, IMFh (x_i) be high fdrequency component after EMD decomposes, m is total sampled point number;

(7) by a large amount of emulation, threshold value Th=3 is set, carry out faulty line and the differentiation that perfects circuit according to criterion below:

If R_IMFhn< Th, this circuit is for perfecting circuit,

If R_IMFhn>=Th, this circuit is faulty line.