CN103427845A - Method for compressing and reconstructing harmonic data of power system on basis of two-dimensional block DCT (discrete cosine transformation) - Google Patents

Abstract

The invention discloses a method for compressing and reconstructing harmonic data of a power system on the basis of two-dimensional block DCT (discrete cosine transformation). The method includes steps of 1, transforming sampled one-dimensional time-series harmonic signals into a two-dimensional matrix; 2, performing block processing on the two-dimensional matrix to obtain various block matrixes; 3, performing LXL DCT on the block matrixes to obtain DTC result matrixes; 4, rearranging elements of the block matrixes and combining elements at the same positions with one another to form rearranged matrixes; 5, computing the average energy of the various rearranged matrixes, judging energy of the rearranged matrixes according to an energy threshold value to create quantization matrixes, setting the elements larger than the energy threshold value as 1 and setting the elements smaller than the energy threshold value as 0; 6, creating a structure array H from the quantization matrixes and the block rearranged matrixes. The structure array H is a harmonic real-time data compression result. The method has the advantages that an excellent compression effect can be realized, the compression ratio is higher than 20.2381, and standard mean-square errors are smaller than 3.291X10<-5>.

Description

Harmonious Waves in Power Systems data compression and reconstruction method based on two-dimentional block DCT transform

Technical field

The present invention relates to the Harmonious Waves in Power Systems data compression method, specifically a kind of Harmonious Waves in Power Systems data compression and reconstruction method based on two-dimentional block DCT transform.

Background technology

Along with the application in electric power system of a large amount of power electronic device, the harmonic pollution of generation is also more and more serious, and its impact on electrical network has: the energy loss that increases electrical network; Make the grid equipment misoperation, cause the accident; Increase the excess loss of grid equipment, reduce life; When harmonic frequency approaches fundamental frequency, cause flickering; The resonance, the noise and vibration that cause equipment, lost efficacy grid equipment and even damage.Therefore, the harmonic wave of electric power system has caused extensive concern both domestic and external.Round-the-clock Detecting Power Harmonics be wave recording device not only harmonic parameters (harmonic amplitude, phase angle) detected, and record the enforcement waveform of harmonic wave, in recent years, the application of Harmonic Measurer is more and more extensive.Power Harmonic Monitoring Instrument has recorded the harmonic data of magnanimity, and the communication data amount of each Power Harmonic Monitoring Instrument and monitoring center is large, and the Detecting Power Harmonics data need to guarantee high real-time and high synchronism, just can carry out effective electric harmonic analysis.And huge harmonic data amount causes the transmission time long, must carry out data compression to the Detecting Power Harmonics data thus, extraction property information, reduce data volume.

Harmonic data has periodically, the compression performance that can utilize it periodically to obtain.At present the harmonic data compression method mainly contains threshold pressure compression method, wavelet coefficient threshold pressure compression method based on FFT, improves small echo (Slantlet) threshold pressure compression method etc., revolves conversion (DCT) compression method more than discrete.

FFT threshold pressure compression method efficiency is high, but its shortcoming FFT does not have time-frequency characteristic, will lose the harmonic wave temporal information; The wavelet threshold compression has iconicity, degree of correlation advantages of higher because of it, has obtained compression effectiveness preferably.But the calculating of wavelet transformation need to consume a large amount of internal memories, calculation of complex, realize that the real-time cost is high; The base vector of dct transform matrix is similar to the characteristic vector of Toeplitz matrix, be considered to the accurate optimal mapping of performance close to the K.L conversion, there is very high time-frequency concentration of energy characteristic, but the energy of its most of signals all concentrates on the low frequency part after conversion, the compression of inapplicable harmonic wave.

Summary of the invention

The present invention, by the simplicity of property harmonic period and dct transform algorithm, makes dct transform better be applicable to the Harmonious Waves in Power Systems compression, has proposed a kind of Harmonious Waves in Power Systems data compression and reconstruction method based on two-dimentional block DCT transform.

Discrete cosine transform (Discrete Cosine Transform) is a kind of real number field conversion, and its transformation kernel is the real number cosine function.

The two-dimensional dct transform of a matrix is defined as follows:

$X=\left(\begin{array}{ccc}{x}_{\mathrm{1,1}}& K& x_{1,N}\\ M& O& M\\ x_{M,1}& L& x_{M,N}\end{array}\right)---\left(1\right)$

$B_{\mathrm{pq}}=a_p{q}_q\underset{m=0}{\overset{M-1}{\mathrm{\&Sigma;}}}\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{x}_{m,n}\cos \frac{\mathrm{\&pi;}(2m+1)p}{2M}\cos \frac{\mathrm{\&pi;}(2n+1)q}{2N}---\left(2\right)$

Wherein,

$a_p=\left\{\begin{array}{c}\frac{1}{\sqrt{M}},p=0\\ \frac{2}{\sqrt{M}},1\&le;p\&le;M-1\end{array}\right.---\left(3\right)$

$a_q=\left\{\begin{array}{c}\frac{1}{\sqrt{N}},q=0\\ \frac{2}{\sqrt{N}},1\&le;q\&le;N-1\end{array}\right.---\left(4\right)$

When p, q constantly increase, the frequency of corresponding cosine function also constantly increases.

If the sampling time sequence of Detecting Power Harmonics data is x (i), 0≤i≤m * n wherein, wherein m, n are the multiples of L, L meets

L=2 ^y

（5）

In formula, y is positive integer, and 2<y<8.

$J_{\frac{M}{L}\&times;\frac{N}{L}}^{i,j}=\left(\begin{array}{ccc}{\mathrm{<figure-callout\; id="1"\; label="j"\; filenames="HDA00003621309700022.png,HDA00003621309700032.png"\; state="\{\{state\}\}">j</figure-callout>}}_{\mathrm{1,1}}& \mathrm{<figure-callout\; id="1"\; label="K\; j"\; filenames="HDA00003621309700022.png,HDA00003621309700032.png"\; state="\{\{state\}\}">K</figure-callout>}& j_{}{}_{1,\frac{N}{L}}\\ M& O& M\\ j_{\frac{M}{L},1}& L& j_{\frac{M}{L},\frac{N}{L}}\end{array}\right)---\left(6\right)$

Wherein,

j ^i,k=x(i+(k-1)×L)?（7）

Matrix J is carried out to piecemeal, and separately dividing block size is L * L, obtains matrix as follows

$J={\left(\begin{array}{ccc}{A}_{L\&times;L}^{p,q}& K& A_{L\&times;\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="HDA00003621309700022.png,HDA00003621309700032.png"\; state="\{\{state\}\}">L</figure-callout>}}^{1,\frac{N}{L}}\\ M& O& M\\ A_{L\&times;L}^{\frac{M}{L},1}& L& A_{L\&times;L}^{\frac{M}{L},\frac{N}{L}}\end{array}\right)}_{\frac{M}{L}\&times;\frac{N}{L}}---\left(8\right)$

$A_{L\&times;L}^{p,q}={\left(\begin{array}{ccc}{a}_{\mathrm{1,1}}^{p,q}& K& a_{1,L}^{p,q}\\ M& O& M\\ a_{L,1}^{p,q}& L& a_{L,L}^{p,q}\end{array}\right)}_{L\&times;L}---\left(9\right)$

To matrix in block form Do two-dimensional dct transform, obtain each blocking factor matrix

$B_{L\&times;L}^{p,q}={\left(\begin{array}{cc}{\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="HDA00003621309700022.png,HDA00003621309700032.png"\; state="\{\{state\}\}">B</figure-callout>}}_{\mathrm{1,1}}^{p,\mathrm{<figure-callout\; id="1"\; label="q\; K\; B"\; filenames="HDA00003621309700022.png,HDA00003621309700032.png"\; state="\{\{state\}\}">q</figure-callout>}}& K& B_{}^{}{}_{1,L}^{p,q}\\ M& O& M\\ B_{L,1}^{p,q}& L& B_{L,L}^{p,q}\end{array}\right)}_{L\&times;L}---\left(10\right)$

Each blocking factor matrix Energy distribution difference is very large, and the energy of conversion coefficient concentrates on the upper left corner mostly, and has the advantages that to reduce gradually to the lower right corner.The dct transform coefficient that position in each blocking factor matrix is identical is arranged together, is about to all

The identical element in middle position forms a matrix, and matrix is rearranged, and obtains Matrix C, and Matrix C is by L * L Matrix form

Wherein,

Each piecemeal is reset in matrix, data all be in an order of magnitude and variance very little.Therefore, adopt the energy threshold method to choose and contribute large piecemeal to reset matrix to initial data, the element that the filtering average energy is less, realize the data compression of harmonic wave.Calculated the average energy value of each matrix column vector by following formula

In formula,

Mean value for this matrix column vector.

Ask capable phasor mean square deviation

In formula, k ^i,jMean average energy, obtain the L * L average energy matrix of:

$G_{L\&times;L}=\left(\begin{array}{ccc}{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA00003621309700022.png,HDA00003621309700032.png"\; state="\{\{state\}\}">k</figure-callout>}}^{\mathrm{1,1}}& \mathrm{<figure-callout\; id="1"\; label="K\; k"\; filenames="HDA00003621309700022.png,HDA00003621309700032.png"\; state="\{\{state\}\}">K</figure-callout>}& k^{}{}^{1,L}\\ M& O& M\\ k^{L,1}& L& k^{L,L}\end{array}\right)---\left(15\right)$

Define an energy threshold ε, work as k ^i,jWhile being greater than this energy threshold, corresponding matrix in block form element is put to reservation, the quantization matrix correspondence position is set to 1; Work as k ^i,jWhile being less than this energy threshold, the position that quantization matrix is corresponding is 0, and quantization matrix is

$U_{L\&times;L}=\left(\begin{array}{ccc}{\stackrel{)}{\mathrm{\&epsiv;}}}^{\mathrm{1,1}}& & {\stackrel{)}{\mathrm{\&epsiv;}}}^{1,L}\\ M& O& M\\ {\stackrel{)}{\mathrm{\&epsiv;}}}^{L,1}& L& {\stackrel{)}{\mathrm{\&epsiv;}}}^{L,L}\end{array}\right)---\left(16\right)$

In formula, It is 0,1 two-valued variable.ε is larger, and compression ratio can increase, but can produce larger error.The user can, by different requirements such as data precision, compression ratios, select the energy threshold parameter flexibly.When ε gets 0.932, it is less that the higher and standard of compression ratio is divided equally error, can realize compression effectiveness preferably, and the present invention chooses this and is worth parameter by default.According to quantization matrix, build the structure array.

Wherein, Row row matrix position, Coloum is the rectangular array position, Value is that matrix element is put.For the non-zero element of quantization matrix, record its each matrix in block form ranks position, each element value of its matrix in block form remains unchanged, and it is retained to structure array H, for quantization matrix 0 element, by each rejection of data of its matrix in block form.

The structure data that obtain, be final harmonic compression data.Shown in harmonic data compression process Fig. 1.

During data decompression, line position, column position and the original value corresponding by the structure data build matrix in block form, and blank position is filled with 0.To reset matrix according to the reverse arrangement of reordering rule, obtain each blocking factor matrix that data are recovered, then, respectively the blocking factor matrix of L * L be carried out to inverse dct transform.Through the two-dimensional dct inverse transformation, can obtain M * N Two-Dimensional Reconstruction matrix, then expand into successively One-dimension Time Series according to 2-D data, can obtain the harmonic signal after decompress(ion) reconstruct.Harmonic data reconstruct flow process as shown in Figure 2.

The outstanding substantial effect of the present invention is:

Can realize compression effectiveness preferably, compression ratio>20.2381, standardization mean square error<3.291 * 10 ^-5.

The accompanying drawing explanation

Fig. 1 is harmonic signal compression process figure.

Fig. 2 is harmonic signal reconstruct flow chart.

Fig. 3 be original harmonic signal,

Fig. 4 is two-dimensional data matrix,

Fig. 5 is the reconstruct harmonic signal

Fig. 6 is the error curve signal.

Fig. 7 is the harmonic analyzer structure chart.

Fig. 8 is that Harmonious Waves in Power Systems is host computer reconstruct harmonic wave forms figure.

Embodiment

By the following examples technical scheme of the present invention is described further.

Harmonious Waves in Power Systems data compression and reconstruction method based on two-dimentional block DCT transform of the present invention, comprise the steps:

(1) One-dimension Time Series harmonic signal sampling obtained is converted into two-dimensional matrix;

(2) two dimension is carried out to the piecemeal processing, obtain each matrix in block form;

(3) matrix in block form is carried out to L * L dct transform, obtain the dct transform matrix of consequence;

(4) the matrix in block form element is rearranged, the element of same position is formed and resets matrix;

(5) calculate the average energy of respectively resetting matrix, and carry out the energy threshold judgement, build thus quantization matrix, the element that is greater than energy threshold is put to 1, the element that is less than energy threshold sets to 0;

(6) reset matrix by quantization matrix and piecemeal and build structure array H, H is harmonic wave real-time waveform data compression result.

Data reconstruction carries out data reconstruction by the two-dimensional dct inverse transformation, by structure array reduction dct transform matrix in block form, the blank element of matrix in block form mends 0, piecemeal is reset to reconstruct and be reduced to the DCT matrix of consequence, it is carried out to the two-dimensional dct inverse transformation, obtain two-dimensional data matrix, by two-dimensional data matrix, recover to obtain one dimension harmonic wave time series.

Fig. 3 is that original harmonic signal, Fig. 4 are that two-dimensional data matrix, Fig. 5 are reconstruct harmonic signal and Fig. 5 error curve signal contrast figure, and as seen from Figure 5, the whole and part information of signal remains unchanged substantially, has reached good reconstruct effect.The compression before and the reduction after waveform error as shown in Figure 6, as seen from the figure, each point effective error<0.02p.u, reduction effect is good.

For the validity of checking compression algorithm of the present invention, the definition compression ratio

$C_R=\frac{\mathrm{Size}\left(A\right)}{\mathrm{Size}\left(B\right)}\&times;100\%---\left(17\right)$

In formula, the shared byte-sized of data after Size (A) compression, Size (B) is the shared byte-sized of primary signal data.Compression ratio is larger, and compression effectiveness is more obvious.

In order to estimate the quality of reconstruct harmonic signal, definition standardization mean square error is

$N_{\mathrm{MSE}}=\frac{\underset{p=1}{\overset{m\&times;n}{\mathrm{\&Sigma;}}}{\left|\right|f_0\left(p\right)-{\hat{f}}_0\left(p\right)\left|\right|}^2}{\underset{p=1}{\overset{m\&times;n}{\mathrm{\&Sigma;}}}{\left|\right|f_0\left(p\right)\left|\right|}^2}---\left(18\right)$

In formula, f ₀(p) be original harmonic signal,

For the reconstruct harmonic signal.The standardization mean square error is less, and humorous reconstructed wave effect is better, more approaches original waveform.

Adopt respectively the original harmonic signal of different relative harmonic contents, every kind of containing ratio is got 100 signals and is done test, and ε gets 0.9213, L and gets 16, and then pressure shrinkage and standardization mean square deviation are that mean value is done statistics, and result is as shown in table 1.

The interpretation of result of table 1 harmonic data compression verification

Relative harmonic content/(%)	C R/(%)	N MSE
			1	18.3432	1.835×10 -7
5	20.2381	3.291×10 -5
			10	23.7361	1.821×10 -8
20	26.3190	1.819×10 -10
			50	30.8316	1.127×10 -6

From table 1, for the harmonic signal of different relative harmonic contents, the compression method based on DCT all has good compression effectiveness, compression ratio>20.2381, standardization mean square error<3.291 * 10 ^-5.

Harmonious Waves in Power Systems data analyzer structure based on the inventive method as shown in Figure 7.Harmonic signal enters ADS8367 through low-pass filtering and carries out the multi-channel synchronous analog-to-digital conversion, after conversion, digital signal is sent into DSP(TMS320VC5509A) processed, TMS320VC5509A is analyzed harmonic data, obtain the harmonic datas such as harmonic parameters and harmonic wave forms, data are compressed, its compression method adopts institute of the present invention extracting method, and DSP adds the writing data into memory compressed and stored.Data can reach host computer by the TCP/IP communication modes.Host computer can be by reconstructing method reduction harmonic data of the present invention.Fig. 8 is the harmonic wave forms figure that host computer reconstruct obtains, and reconstructed image is clear, can reflect the harmonic distortion characteristic.

Claims (1)

1. the Harmonious Waves in Power Systems data compression and reconstruction method based on two-dimentional block DCT transform, is characterized in that, comprises the steps:

(1) One-dimension Time Series harmonic signal sampling obtained is converted into two-dimensional matrix;

(2) two dimension is carried out to the piecemeal processing, obtain each matrix in block form;

(3) matrix in block form is carried out to L * L dct transform, obtain the dct transform matrix of consequence;

(4) the matrix in block form element is rearranged, the element of same position is formed and resets matrix;

(5) calculate the average energy of respectively resetting matrix, and carry out the energy threshold judgement, build thus quantization matrix, the element that is greater than energy threshold is put to 1, the element that is less than energy threshold sets to 0;

(6) reset matrix by quantization matrix and piecemeal and build structure array H, H is harmonic wave real-time waveform data compression result,

Data reconstruction is to carry out data reconstruction by the two-dimensional dct inverse transformation, by structure array reduction dct transform matrix in block form, the blank element of matrix in block form mends 0, piecemeal is reset to reconstruct and be reduced to the DCT matrix of consequence, it is carried out to the two-dimensional dct inverse transformation, obtain two-dimensional data matrix, by two-dimensional data matrix, recover to obtain one dimension harmonic wave time series.

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