CN102005740A - Extra-high voltage direct current line boundary element method adopting polar wave wavelet energy ratio - Google Patents

Abstract

The invention provides an extra-high voltage direct current line boundary element method adopting polar wave wavelet energy ratio, belonging to the technical field of relay protection of electric power systems. The method comprises the following steps: when the direct current line has fault, computing the anode line polar wave voltage and the cathode line polar wave voltage according to the direct current voltage and direct current of the two poles measured in the relay location; selecting the discrete polar wave voltage signal with sampling sequence length of 200 after fault to undergo wavelet transform to obtain a series of high/low frequency polar wave voltage wavelet transform parameters and computing the modules of the high/low frequency polar wave voltage wavelet transform parameters; computing the ratio of high/low frequency energy of polar wave voltage after extracting the high/low frequency components of polar wave voltage according to the obtained modules; and distinguishing the area fault from the out-area fault according to the ratio of high/low frequency energy. Lots of simulation results show the method has good effect.

Description

Utilize the extra-high voltage direct-current circuit boundary element method of utmost point ripple wavelet energy ratio

Technical field

The present invention relates to the relay protection of power system technical field, specifically utilize the extra high voltage direct current transmission line boundary element method of utmost point wave voltage wavelet transformation energy ratio.

Background technology

After DC line breaks down; can utilize dc pole control system to limit and eliminate fault current fast; but simultaneously because the effect of current regulator makes fault current compare little many in alternating current circuit; size only according to fault current voltage can't make accurate judgment, thereby can consider to detect DC line fault and take correct safeguard measure by transient state component.The amplitude and the control of the uncontrolled system of direction of the transient current voltage traveling wave that line fault moment is produced is considered in traveling-wave protection just, can accurately reflect fault signature design.Traveling-wave protection has superfast performance, and the influence of factor such as its protective value is subjected to that current transformer is saturated, system oscillation and long line distributed capacitance is less, does not rely on communication system simultaneously.After the traveling-wave protection action, system will start the line fault of rectification side and recover sequential control, according to predefined number of times with remove dissociate the time total head or the reduced-voltage starting fault direct current utmost point.However, the DC line traveling-wave protection of using at present still can be subjected to the influence of factors such as smoothing reactor, DC filter, transition resistance and fault distance.

DC transmission system comprises the smoothing reactor and the DC filter at DC power transmission line and DC line two ends; they have constituted " natural " border of DC power transmission line high frequency transient amount; and the edge frequency specificity analysis shows that there is notable attribute difference in the high fdrequency component of circuit border internal and external fault signal; in view of the above, the present invention proposes a kind of novel based on transient voltage ± 800kV UHVDC circuit transient protection principle.

Summary of the invention

The purpose of this invention is to provide a kind of extra high voltage direct current transmission line boundary element method of utilizing utmost point wave voltage wavelet transformation energy ratio.

Utilize the extra high voltage direct current transmission line failure boundary element algorithm of utmost point wave voltage wavelet transformation energy ratio to carry out according to the following steps among the present invention:

(1) after DC line breaks down,, obtains electrode line utmost point wave voltage P according to the two poles of the earth direct voltage, the direct current that the protection installation place records ₁(k), negative line utmost point wave voltage P ₂(k) be:

p ₁(k)＝Z _P×i ₁(k)-u ₁(k) (1)

p ₂(k)＝Z _P×i ₂(k)-u ₂(k) (2)

In the formula, Z _pBe DC power transmission line utmost point wave impedance, u ₁(k) be anodal direct voltage, i ₁(k) be anodal direct current, u ₂(k) be the negative pole direct voltage, i ₂(k) be the negative pole direct current, k=1,2,3....N, N are sample sequence length;

(2) fault utmost point utmost point wave voltage is carried out wavelet transformation, its sample frequency is 100kHz, and sample sequence length is 200, obtains each yardstick utmost point wave voltage high frequency wavelet coefficient through wavelet transformation;

(3) each utmost point wave voltage high frequency wavelet coefficient that obtains is asked mould, calculate high frequency coefficient wavelet energy E according to following formula ₁With low frequency coefficient wavelet energy E ₂:

$\left.\begin{array}{c}{E}_1=\underset{j=1}{\overset{5}{\mathrm{\Σ}}}\underset{k}{\mathrm{\Σ}}{\left|W_j\left(k\right)\right|}^2\\ E_2=\underset{k}{\mathrm{\Σ}}{\left|W_j\left(k\right)\right|}^2,j=6\end{array}\right\}---\left(3\right)$

E is a signal energy; W (k) is a wavelet conversion coefficient, and j is the wavelet transformation number of plies.

(4) obtain the ratio k of two-layer high frequency coefficient wavelet energy ₁

$k_1=\frac{E_1}{E_2}---\left(4\right)$

(5) the examination criterion of internal fault external fault is worked as k ₁≤ 1 o'clock is external area error, works as k ₁＞1 o'clock is troubles inside the sample space.

Below be design principle of the present invention:

1, the single-ended ultrahigh speed protection philosophy of DC power transmission line

Existing DC line protection is mainly provided by ABB and SIEMENS two companies, is the criterion that constitutes single-ended fast amount protection according to voltage traveling wave sudden change amount, voltage traveling wave rate of change and electric current variable gradient.But practical operating experiences shows: when DC line during through high resistive fault, the voltage change ratio of traveling-wave protection reduces, and causes the traveling-wave protection tripping.DC transmission system comprises the smoothing reactor and the DC filter at DC power transmission line and DC line two ends; they have constituted " natural " border of DC power transmission line high frequency transient amount; and the edge frequency specificity analysis shows that there is notable attribute difference in the high fdrequency component of circuit border internal and external fault signal, can constitute single-ended transient based protection element in view of the above.The single-ended ultrahigh speed protection philosophy of the DC power transmission line figure that utilizes the high fdrequency component feature as shown in Figure 1.

2. boundary element

The extra-high voltage DC transmission system structure chart as shown in Figure 2, its power transmission capacity is 5000MW, the reactive compensation capacity of rectification side and inversion side is respectively 3000Mvar and 3040Mvar; Every utmost point convertor unit is composed in series by 2 12 pulse converters, and DC power transmission line is a six-multiple conductor, and total length is taken as 1500km, adopts J.R.Marti frequency dependence model; The smoothing reactor of 400mH is equipped with in the circuit both sides; The M point is the protection installation place.

The present invention creatively proposes to constitute with smoothing reactor and DC filter the physical boundary of DC transmission system, as shown in Figure 3, and U wherein ₁For distinguishing outer transient voltage, U ₂Be U ₁Fade to the voltage of DC line protection installation place through flank pass; B ₁, B ₂, B ₃, B ₄Be DC filter lightning arrester, D ₁Be smoothing reactor lightning arrester, D ₂Be DC bus arrester, the present invention is with lightning arrester B ₁, B ₂, B ₃, B ₄, D ₁, D ₂Be referred to as the border lightning arrester.B wherein ₁, B ₂Rated voltage is 150kV, B ₃, B ₄Rated voltage is 75kV, D ₁, D ₂Rated voltage is 824kV.

Among Fig. 3, L=400mH, L ₁=39.09mH, L ₂=26.06mH, L ₃=19.545mH, L ₄=34.75mH, C ₁=0.9 μ F, C ₂=0.9 μ F, C ₃=1.8 μ F, C ₄=0.675 μ F.

The transfer function H (j ω) that now defines boundary element is:

$H\left(\mathrm{j\ω}\right)=\frac{Z_1\left(\mathrm{j\ω}\right)}{Z_1\left(\mathrm{j\ω}\right)+Z_2\left(\mathrm{j\ω}\right)}---\left(5\right)$

In the formula, Z ₁(j ω) is the DC filter impedance, Z ₂(j ω) is the smoothing reactor impedance.Amplitude-frequency characteristic such as Fig. 4 of boundary element transfer function H (j ω).As can be seen from Figure 4: when f＜1000Hz, H (j ω) ≈ 0; When 1000Hz＜f＜2000Hz, H (j ω) spectrum curve has vibration, f=600Hz particularly, and f=1200Hz, during f=1800Hz, H (j ω)＜＜0; When f＞2000Hz, H (j ω)＜0, so the present invention to select f 〉=2000Hz be high fdrequency component, f＜2000Hz is a low frequency component.

3. the basic theories of wavelet transformation

Traditional signal analysis is to be based upon on the basis of Fourier transform, belongs to global variable, or fully in time domain, or fully at frequency domain, can't explain the time-frequency local character of signal, and this character basic and the most crucial character of non-stationary signal exactly.Wavelet transformation has obtained developing rapidly as the analysis tool that can adjust the time frequency window size with the variation of frequency automatically.

Continuous wavelet transform:

If

One quadractically integrable function is if its Fourier transform ψ (w) satisfies the admissibility condition, that is:

${\&Integral;}_{-\&infin;}^{+\&infin;}\frac{{\left|\mathrm{\&psi;}\left(w\right)\right|}^2}{w}\mathrm{dw}<+\&infin;---\left(6\right)$

Then claim

It is basic small echo, perhaps a wavelet mother function.

With wavelet mother function

Stretch and translation, can obtain the continuous wavelet basic function

In the formula, a is a contraction-expansion factor, or is called scale factor; B is a shift factor.

For function f (t) ∈ L arbitrarily ²Continuous wavelet transform (R) (continuous wavelet transform CWT) is:

In the formula,

Expression

Conjugation.

Wavelet transform:

By the notion of continuous wavelet transform as can be known, scale factor a in the continuous wavelet transform and shift factor b are continuous variablees.In actual applications, usually will

Middle continuous variable a and b get and do the integer discrete form, will

Be expressed as:

(discrete wavelet transform DWT) can be expressed as the wavelet transform of corresponding function f (t)

Because this discrete wavelet

Be by wavelet function

Through 2 ^jIntegral multiple is put, is contracted and through family of functions that the integer k translation is generated

J, k ∈ Z.Therefore, the little wave train after this disperses is commonly referred to as discrete dyadic wavelet sequence.

In wavelet decomposition, the sample rate of supposing discrete signal is f _S(HZ), discrete signal is carried out multi-scale wavelet transformation, the wavelet conversion coefficient correspondence under first yardstick is at frequency band [f so _S/ 4, f _S/ 2] signal in, j yardstick correspondence be [f _S/ 2 ^J+1, f _S/ 2 ^j] in signal, i.e. the corresponding high-frequency band signals of low frequency magnitude signal, the corresponding low band signal of high magnitude signal.

4. the definition of utmost point ripple

After DC line broke down, starting component started immediately.According to the two poles of the earth direct voltage, the direct current that the protection installation place records, obtain the utmost point ripple P of electrode line ₁(k), the utmost point ripple P of negative line ₂(k) be:

p ₁(k)＝Z _P×i ₁(k)-u ₁(k) (11)

p ₂(k)＝Z _P×i ₂(k)-u ₂(k) (12)

In the formula, Z _pBe DC power transmission line utmost point wave impedance, u ₁(k) be anodal direct voltage, i ₁(k) be anodal direct current, u ₂(k) be the negative pole direct voltage, i ₂(k) be the negative pole direct current, k=1,2,3....N, N are time window length.

5. in the district based on wavelet transformation, the examination of external area error

System shown in Figure 1 is at 100km place, distance protection installation place, and the plus earth fault takes place 0.4s, and polar wave shape is shown in Fig. 5 (a); The fault transition resistance is 0.1 Ω, and time window length is chosen 2ms after the fault, and sample frequency is 100kHz.

Among the present invention, utmost point wave voltage is carried out wavelet transformation, obtain each yardstick small echo high frequency coefficient, the conversion number of plies is set to 6 layers, and its respective frequencies is respectively:

Ground floor (j=1): 2500kHz-5000kHz

The second layer (j=2): 1250kHz-2500kHz

The 3rd layer of (j=3): 6250kHz-1250kHz

The 4th layer of (j=4): 3125kHz-6250kHz

Layer 5 (j=5): 1562.5kHz-3125kHz

Layer 6 (j=6): 781.25kHz-1562.5kHz

According to the amplitude-frequency characteristic of boundary element, select the boundary frequency of 2000Hz as high fdrequency component and low frequency component.So selecting ground floor to layer 5 is high fdrequency component, layer 6 is a low frequency component, each element in the formula (10) is asked mould after, obtain high-frequency energy and low frequency energy again.

$E_1=\underset{j=1}{\overset{5}{\mathrm{\&Sigma;}}}\underset{k}{\mathrm{\&Sigma;}}{\left|W_j\left(k\right)\right|}^2---\left(13\right)$

$E_2=\underset{k}{\mathrm{\&Sigma;}}{\left|W_j\left(k\right)\right|}^2,j=6---\left(14\right)$

In the formula, E1 is a high-frequency energy, and E2 is a low frequency energy.

As can be seen from Figure 6: during external area error, owing to the attenuation of boundary element to radio-frequency component, the high frequency content of the electrode line utmost point ripple that the protection installation place measures is much smaller than low-frequency content.During troubles inside the sample space, high fdrequency component is not passed through boundary element, so high frequency content is greater than low-frequency content.

The maximum ratio k of definition high-frequency energy and low frequency energy ₁:

$k_1=\frac{E_1}{E_2}---\left(15\right)$

Therefore, propose to distinguish interior, external area error criterion:

k ₁≤ 1 is external area error

k ₁＞1 is troubles inside the sample space

The present invention compared with prior art has following advantage:

1, this method sample frequency is 100kHz, and time window is 2ms, has avoided the transient response process of DC control system, and conclusion is more accurate.

2, this method is not subjected to the influence of noise jamming and fault distance, and the performance of tolerance transition resistance is very strong, and stronger practicality is arranged.

3, this method adopts utmost point wave voltage to analyze, and both can be used as the characteristic quantity of internal fault external fault criterion, can be used as the characteristic quantity that fault is selected utmost point criterion again.

Description of drawings

Fig. 1 is the single-ended ultrahigh speed protection philosophy of a direct current system transmission line block diagram, u among the figure ₁, i ₁Direct voltage and direct current for the acquisition of protection installation place.

Fig. 2 be cloud wide ± 800kV DC transmission system structure chart M point is for protecting the installation place.

Fig. 3 is the boundary element that smoothing reactor and DC filter constitute, U ₁For distinguishing outer transient voltage, U ₂Be U ₁Fade to the voltage of DC line protection installation place through flank pass; B ₁, B ₂, B ₃, B ₄Be the DC filter lightning arrester; D ₁Be smoothing reactor lightning arrester, D ₂Be DC bus arrester; L ₁, L ₂, L ₃, L ₄Be inductance element; C ₁, C ₂, C ₃, C ₄Be capacity cell.

Fig. 4 is the spectral characteristic figure of boundary element, and f is a frequency, and Hz is the unit of frequency, and H (j ω) is the amplitude of frequency spectrum.

Fig. 5 is polar wave shape figure, among the figure t/s be time/second, u/kV is voltage/kilovolt.Positive and negative voltage when (a) being troubles inside the sample space; Positive and negative electrode ripple when (b) being external area error.

When Fig. 6 is the electrode line fault, the distribution map of anodal wave height frequency component and low frequency component ratio, k among the figure ₁Be the ratio of high fdrequency component and low frequency component, t/s be time/second.

Embodiment

Simulation model as shown in Figure 1, the plus earth fault takes place respectively in 1km place, distance protection installation place, the fault transition resistance is 0.1 Ω, time window length is got 2ms, sample frequency is 100kHz.

(1) after DC line broke down, starting component started immediately, according to formula:

p ₁(k)＝Z _P×i ₁(k)-u ₁(k) (11)

p ₂(k)＝Z _P×i ₂(k)-u ₂(k) (12)

Obtain electrode line utmost point ripple and negative line utmost point ripple, polar wave shape as shown in Figure 5; In the formula, Z _pBe DC power transmission line utmost point wave impedance, u ₁(k) be anodal direct voltage, i ₁(k) be anodal direct current, u ₂(k) be the negative pole direct voltage, i ₂(k) be the negative pole direct current, k=1,2,3....N, N are sample sequence length;

(2) according to formula

Electrode line utmost point ripple is carried out wavelet transformation, obtain each yardstick high frequency wavelet coefficient;

(3) each floor height frequency wavelet coefficient is asked mould,, select the boundary frequency of 2000Hz as high fdrequency component and low frequency component according to the amplitude-frequency characteristic of boundary element.J=1,2,3,4,5 is high fdrequency component, j=6 is a low frequency component, according to formula

$E_1=\underset{j=1}{\overset{5}{\mathrm{\&Sigma;}}}\underset{k}{\mathrm{\&Sigma;}}{\left|W_j\left(k\right)\right|}^2---\left(13\right)$

$E_2=\underset{k}{\mathrm{\&Sigma;}}{\left|W_j\left(k\right)\right|}^2,j=6---\left(14\right)$

Obtain high-frequency energy and low frequency energy.E is a signal energy; W (k) is a wavelet conversion coefficient, and j is the wavelet transformation number of plies;

(4) obtain the ratio k of high-frequency energy and low frequency energy ₁=10.6111, according to k ₁＞1 (formula (15)) are judged as troubles inside the sample space.

Among the present invention different fault distances, different earth resistances are carried out simulating, verifying, obtained the ratio k of anodal wave voltage high-frequency energy and low frequency energy ₁, the result is as shown in table 1.

The ratio k of anodal wave voltage high-frequency energy of table 1 and low frequency energy ₁

Claims (1)

1. extra-high voltage direct-current circuit boundary element method of utilizing utmost point ripple wavelet energy ratio is characterized in that carrying out according to the following steps:

(1) after DC line breaks down,, obtains electrode line utmost point wave voltage P according to the two poles of the earth direct voltage, the direct current that the protection installation place records ₁(k), negative line utmost point wave voltage P ₂(k) be:

p ₁(k)＝Z _P×i ₁(k)-u ₁(k) (1)

p ₂(k)＝Z _P×i ₂(k)-u ₂(k) (2)

In the formula, Z _pBe DC power transmission line utmost point wave impedance, u ₁(k) be anodal direct voltage, i ₁(k) be anodal direct current, u ₂(k) be the negative pole direct voltage, i ₂(k) be the negative pole direct current, k=1,2,3....N, N are sample sequence length;

(2) fault utmost point utmost point wave voltage is carried out wavelet transformation, its sample frequency is 100kHz, and sample sequence length is 200, obtains each yardstick utmost point wave voltage high frequency wavelet coefficient through wavelet transformation;

(3) each utmost point wave voltage high frequency wavelet coefficient that obtains is asked mould, calculate high frequency coefficient wavelet energy E according to following formula ₁With low frequency coefficient wavelet energy E ₂:

$\left.\begin{array}{c}{E}_1=\underset{j=1}{\overset{5}{\mathrm{\&Sigma;}}}\underset{k}{\mathrm{\&Sigma;}}{\left|W_j\left(k\right)\right|}^2\\ E_2=\underset{k}{\mathrm{\&Sigma;}}{\left|W_j\left(k\right)\right|}^2,j=6\end{array}\right\}---\left(3\right)$

E is a signal energy; W (k) is a wavelet conversion coefficient, and j is the wavelet transformation number of plies;

(4) obtain the ratio k of high frequency coefficient wavelet energy and low frequency wavelet energy ₁:

$k_1=\frac{E_1}{E_2}---\left(4\right)$

(5) the examination criterion of internal fault external fault:

Work as k ₁≤ 1 o'clock is external area error;

Work as k ₁＞1 o'clock is troubles inside the sample space.

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