CN107192878A - A kind of trend of harmonic detection method of power and device based on compressed sensing - Google Patents
A kind of trend of harmonic detection method of power and device based on compressed sensing Download PDFInfo
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Abstract
The present invention provides a kind of trend of harmonic detection method of power and device based on compressed sensing.Methods described includes：S1, wavelet transformation and Gauss measurement matrix disposal are carried out to the power quality data received, are obtained measurement vector y and are perceived matrix Θ；S2, based on the measurement vector y and perception matrix Θ, primary signal is reconstructed using degree of rarefication self-adapting compressing sampling matching pursuit algorithm, and wherein atom selection carries out Regularization, and iterative process carries out variable step processing, acquisition sparse bayesian learning signalS3, based on described sparse bayesian learning signalReconstruct original power quality data.The present invention is more efficient relative to prior art, and further shorten iterations based on variable step processing, the degree of rarefication signal that can be most approached, and solves the problem of time-consuming longer and degree of rarefication estimation of signal reconstruction is inaccurate.
Description
Technical field
The present invention relates to electric energy quality harmonic detection field, more particularly, to a kind of power train based on compressed sensing
System harmonic detecting method and device.
Background technology
With the continuous expansion of power system scale, requirement more and more higher of the people to the quality of power supply is produced therewith
Power quality problem is also increasingly protruded.Due to the introducing of a large amount of nonlinear-loads and electrical equipment, it can be produced in power network tight
Harmonic wave or the m-Acetyl chlorophosphonazo pollution of weight, cause the power network quality of power supply to decline.Particularly intelligent grid construction is goed deep into, electricity consumption intelligence
Change and height self-healing property requirement make harmonic detecting and administer turn into one it is great the problem of..
The harmonic detecting problem of intelligent grid, should be had the characteristics that premised on realizing precise real-time detection：
Firstth, in the intelligent grid that a large amount of power electronic equipments come into operation, many distributed power sources pass through inverter
Access network, this allows for harmonic wave and the traditional power network of m-Acetyl chlorophosphonazo damage ratio is more serious.To meet the requirement of intelligent grid, harmonic wave inspection
Survey should fully meet requirement of real-time, while realizing the accurate detection of harmonic wave.
Secondth, the detection of harmonic data is more difficult from intelligent grid.First, the intelligent grid such as electricity consumption intellectuality it is new
It is required that result in required harmonic detecting instrument increasing number.Secondly, the increase of detection species, real-time enhancing, detection data volume are huge
Greatly, the formed mass data of detection suffers from higher requirement to data storage and transmission means in real time.
Existing frequently-used power quality detection system is all based on Nyquist sampling thheorems, on the one hand, it is required that sample rate
Hurry up, especially for higher hamonic wave and various temporary disturbances, it is desirable to the sampling interval up to millisecond even Microsecond grade, hardware requirement compared with
It is high；On the other hand, substantial amounts of data, great challenge is brought to Digital Signal Analysis and Processing, while in order to store and transmit, also needing
A large amount of compressed encodings are wanted to calculate, data user rate and efficiency are low.
Compressive sensing theory is the openness or compressibility based on signal and a kind of brand-new signal transacting reason for proposing
By.Its main thought is：Using the openness feature of signal, by trying one's best, few observation is believed to recover the most of signal
Breath.At present, compressed sensing is widely applied in fields such as Measurement of Harmonics in Power System, medical imaging, geological explorations.For
Compressed sensing, can be applied to the detection of the quality of power supply by the sparse characteristic of electric power signal.Memory data output can be solved well
The problem of big and computation complexity is high.
Compressive sensing theory mainly includes rarefaction representation, three parts of encoding measurement and restructing algorithm, wherein, restructing algorithm
It is the emphasis that we study.Conventional restructing algorithm has greedy iterative algorithm, convex optimized algorithm and combinational algorithm etc. at present.Its
In, greedy iterative algorithm is limited using the coefficient and supported collection of signal come the optimal solution of Step wise approximation primary signal, and use
Support least-squares estimation carrys out reconstruction signal, and solution is minimum l0Norm problem.This kind of algorithm includes：Orthogonal matching pursuit
(Orthogonal Matching Pursuit, OMP), regularization match tracing (Regularized Orthogonal
Matching Pursuit, ROMP), segmentation orthogonal matching pursuit (Stage wise Orthogonal Matching
Pursuit, StOMP), compression sampling match tracing (Compressed Sampling Matching Pursuit, CoSaMP),
Degree of rarefication Adaptive matching follows the trail of (Sparsity Adaptive Matching Pursuit, SAMP), and regularization degree of rarefication is certainly
Adapt to match tracing (Regularized Adaptive Matching Pursuit, RAMP etc..Algorithm above will the need for having
Degree of rarefication is as prior information, and such as OMP algorithms, what is had does not need degree of rarefication as premise, such as SAMP algorithms.Existing reconstruct is calculated
Method is in reconstructed velocity with that can not be got both on reconstruction quality.
The content of the invention
The present invention provide it is a kind of overcome above mentioned problem or solve the above problems at least in part based on compressed sensing
Trend of harmonic detection method of power and device.
According to an aspect of the present invention there is provided a kind of trend of harmonic detection method of power based on compressed sensing, including：
S1, wavelet transformation and Gauss measurement matrix disposal are carried out to the power quality data received, obtain measurement vector y
And perceive matrix Θ；
S2, based on the measurement vector y and perception matrix Θ, utilizes degree of rarefication self-adapting compressing sampling matching pursuit algorithm
Primary signal is reconstructed, wherein atom selection carries out Regularization, and iterative process carries out variable step processing, obtains sparse
Approximation signal
S3, based on the sparse bayesian learning signalReconstruct original power quality data.
According to another aspect of the present invention, a kind of Measurement of Harmonics in Power System device based on compressed sensing is also provided,
Including：
Initial processing module, for being carried out to the power quality data received at wavelet transformation and Gauss measurement matrix
Reason, obtains measurement vector y and perceives matrix Θ；
Signal reconstruction module, for based on the measurement vector y and perception matrix Θ, being adopted using degree of rarefication self-adapting compressing
Primary signal is reconstructed sample matching pursuit algorithm, and wherein atom selection carries out Regularization, and iterative process carries out change step
Long processing, obtains sparse bayesian learning signalAnd
Image-restoration module, for based on the sparse bayesian learning signalReconstruct original power quality data.
The present invention proposes a kind of trend of harmonic detection method of power and device based on compressed sensing, proposes a kind of improved
Degree of rarefication self-adapting compressing sampling matching pursuit algorithm, atom selection carries out Regularization, and iterative process is carried out at variable step
Reason, is reconstructed processing to the Harmonious Waves in Power Systems signal of reception, power quality data is reduced, so as to realize Harmonious Waves in Power Systems
Detection；It is more efficient relative to prior art, and iterations further shorten based on variable step processing, it can obtain
The degree of rarefication signal most approached, solves the problem of time-consuming longer and degree of rarefication estimation of signal reconstruction is inaccurate.
Brief description of the drawings
Fig. 1 is a kind of trend of harmonic detection method of power flow chart based on compressed sensing of the embodiment of the present invention；
Fig. 2 is the improved degree of rarefication self-adapting compressing sampling matching pursuit algorithm flow chart of the embodiment of the present invention；
Fig. 3 is emulation schematic diagrames of degree of rarefication of the embodiment of the present invention K to reconstruct performance impact；
Fig. 4 is emulation schematic diagram of the pendulous frequency of the embodiment of the present invention to reconstruct performance impact；
Fig. 5 is that reconstruct of the embodiment of the present invention to one-dimensional signal emulates schematic diagram.
Embodiment
With reference to the accompanying drawings and examples, the embodiment to the present invention is described in further detail.Implement below
Example is used to illustrate the present invention, but is not limited to the scope of the present invention.
As shown in figure 1, a kind of trend of harmonic detection method of power based on compressed sensing, including：
S1, wavelet transformation and Gauss measurement matrix disposal are carried out to the power quality data received, obtain measurement vector y
And perceive matrix Θ；
S2, based on the measurement vector y and perception matrix Θ, utilizes degree of rarefication self-adapting compressing sampling matching pursuit algorithm
Primary signal is reconstructed, wherein atom selection carries out Regularization, and iterative process carries out variable step processing, obtains sparse
Approximation signal
S3, based on the sparse bayesian learning signalReconstruct original power quality data.
The present embodiment proposes a kind of improved degree of rarefication self-adapting compressing sampling matching pursuit algorithm (Modified
Sparsity Adaptive Compressed Sampling Matching Pursuit, MSACSMP), in the base of former algorithm
Improved on plinth, i.e. atom selection carries out Regularization, and iterative process carries out variable step processing.At regularization
Reason, can reject redundancy atom, so as to improve efficiency；Due to variable step processing, can degree of rarefication estimation book select one compared with
Big step-length, is shortening step-length when meeting certain iteration stopping condition, further shorten iterations, so as to improve iteration effect
Rate.
Relative to prior art, the improved degree of rarefication self-adapting compressing sampling matching pursuit algorithm that the present embodiment is proposed
Reconstruction processing to electric harmonic signal is more efficient, the degree of rarefication signal that can be most approached, and solves signal reconstruction and takes
The problem of estimation of longer and degree of rarefication is inaccurate.
In one embodiment, matrix Θ is perceived described in S1 to obtain by following formula：
Wherein,For Gauss measurement matrix, ψ is wavelet conversion coefficient.
In this implementation, power quality data x is read in first, sparse transformation is then carried out, and conventional sparse transformation base is small
Wave conversion, obtains the sparse signal s=ψ x of transform domain, is then compressed measurement, uses gaussian random matrixFor measurement square
Battle array, obtains measured valueWherein Θ is referred to as perceiving matrix, is also sensing matrix.
In one embodiment, the S2 further comprises：
S2.1, sets initial step length S, and it is the measurement vector y to make initial surplus, meets r=y, phase is calculated by following formula
Relation number u, and choose more than maximum correlation coefficient umaxThe atom index upgrade supported collection of half,
U={ uj|uj=|<r,Θj＞ |, j=1,2 ..., N },
Wherein, ujFor surplus and atom ΘjInner product, ΘjFor the jth row of the perception matrix Θ, also referred to as atom；
S2.2, as residual error rkWhen meeting the first iteration stopping condition and being unsatisfactory for secondary iteration stop condition, change step-lengthAnd supported collection is updated, carry out next iteration, wherein symbolExpression rounds up.
Present embodiment describes Regularization and variable step condition, the Regularization, which refers to only choose, is more than maximum
Coefficient correlation umaxThe atom index upgrade supported collection of half, so as to reject redundancy atom, thus improves efficiency.In algorithm iteration
During, variable step occurs：When meeting the first iteration stopping condition but being unsatisfactory for secondary iteration stop condition, so sparse
A larger step size is first selected during degree estimation, shortens step-length again when meeting certain iteration stopping condition, so as to most be approached
Degree of rarefication；If meeting secondary iteration stop condition simultaneously, iterative process terminates.
In one embodiment, also include before the S2.1：Initialize the degree of rarefication self-adapting compressing sampling matching
The parameter of tracing algorithm, including：
Iterations t=1, starting stage number k=1, indexed setSupported collection size L=S,
In one embodiment, also include after the S2.1：Merge indexed set Λ=Λ ∪ F, and updated by following formula
Residual error rk：
Wherein, y is the column vector of the two dimensional image signal,For sparse coefficient vector, ands
For current step.
In one embodiment, the first iteration stopping condition is described in S2.2：Residual energy | | rk||2≤ε1；
The secondary iteration stop condition is：Residual energy | | rk||2≤ε2；
Wherein, ε1With ε2It is positive number, and ε2＜ ε1。
In one embodiment, the S2.2 also includes：
As residual error rkWhen being unsatisfactory for the first iteration stopping condition, if meeting | | rk||2≥||rk-1||2, then supported collection is updated
Size L=L+S, iterations t=t+1 and number of stages k=k+1, carry out next iteration；
If being unsatisfactory for | | rk||2≥||rk-1||2, then indexed set Λ, surplus r=r are updatedkWith iterations t=t+1, enter
Row next iteration.
In one embodiment, the S2.2 also includes：
As residual error rkWhen meeting the first iteration stopping condition and meeting secondary iteration stop condition, stop iteration, obtain dilute
Dredge approximation signal
As shown in Fig. 2 in above-described embodiment, the main step of improved degree of rarefication self-adapting compressing sampling matching pursuit algorithm
Suddenly include：
Input：The column vector y of two dimensional image, perceives matrix Θ, initial step length S；
Output：Column vector y K- sparse bayesian learnings
Step 1：Each parameter is initialized, initial surplus r is made0=y, iterations t=1, starting stage number k=1, indexed setSupported collection size L=S,
Step 2：Coefficient correlation u is calculated according to following formula, and selected in the corresponding index deposit J of 2L maximum；
U={ uj|uj=|<r,Θj>|, j=1,2 ..., N }；
Step 3：Select more than maximum correlation coefficient umaxIn the atom index deposit F of half；
Step 4：Merge indexed set Λ=Λ UF, and sparse coefficient vector is calculated using following formulaAnd select L maximum
In corresponding index deposit Λ；
Step 5：Update residual error
Step 6：Judge whether to meet iteration stopping condition 1, if meeting, go to step 7；If it is not satisfied, going to step 8；
Step 7：Judge whether to meet iteration stopping condition 2, if meeting, stop iteration, obtainIf it is not satisfied, turning step
Rapid 11；
Step 8：Judge whether to meet | | rk||2≥||rk-1||2If meeting, going to step 9；If it is not satisfied, going to step 10；
Step 9：Next stage is entered, supported collection size L=L+S, iterations t=t+1, number of stages k=k+ is updated
1；
Step 10：Update indexed set Λ, surplus r=rk, iterations t=t+1 goes to step 2；
Step 11：Change step-lengthSupported collection size L=L+S, k=k+1.
Fig. 3 gives influence analogous diagram of the degree of rarefication to reconstruction property.The excursion of degree of rarefication is taken as 10~70, this hair
Bright proposed improved degree of rarefication self-adapting compressing sampling matching pursuit algorithm (Modified Sparsity Adaptive
Compressed Sampling Matching Pursuit, MSACSMP) and OMP, StOMP, SP, CoSaMPSACSMP algorithm
Compare.As can be seen that as degree of rarefication K ＜ 15, these algorithms can Perfect Reconstruction signal；As K ＞ 15, OMP
The reconstruct probability of algorithm starts reduction；As K ＞ 35, the reconstruct probability of StOMP algorithms and SP algorithms is gradually reduced, and StOMP
The reduction speed of algorithm；As K ＞ 40, CoSaMP algorithms have been unable to Perfect Reconstruction with SACSMP algorithms, still
MSACSMP algorithms still can be with high probability reconstruction signal, it is seen that the algorithm has preferable reconstruction property.
Fig. 4 gives influence analogous diagram of the pendulous frequency to reconstruction property, and degree of rarefication is set as 15.As can be seen that when survey
When amount number of times reaches 60, MSACSMP algorithms just can be with Perfect Reconstruction signal, and SACSMP algorithms at least need 65 times, CoSaMP
Algorithm at least needs 75 times, and OMP algorithms at least need 100 times.It can be seen that the reconstruct efficiency of the algorithm is better than other analogous algorithms.
Fig. 5 gives signal length for N=256, degree of rarefication K=29, and calculation matrix is gaussian random matrix, stage step-length
The reconstruct analogous diagram of one-dimensional signal Harmonious Waves in Power Systems signal when taking 2.It can be seen that the algorithm can be realized and primary signal
Reconstruct, calculating obtains reconstructed error for 2.1680e-14.
The present invention also provides a kind of Measurement of Harmonics in Power System device based on compressed sensing, including：
Initial processing module, for being carried out to the power quality data received at wavelet transformation and Gauss measurement matrix
Reason, obtains measurement vector y and perceives matrix Θ；
Signal reconstruction module, for based on the measurement vector y and perception matrix Θ, being adopted using degree of rarefication self-adapting compressing
Primary signal is reconstructed sample matching pursuit algorithm, and wherein atom selection carries out Regularization, and iterative process carries out change step
Long processing, obtains sparse bayesian learning signalAnd
Data recovery module, for based on the sparse bayesian learning signalReconstruct original power quality data.
The present invention proposes a kind of trend of harmonic detection method of power and device based on compressed sensing, proposes a kind of improved
Degree of rarefication self-adapting compressing sampling matching pursuit algorithm, atom selection carries out Regularization, and iterative process is carried out at variable step
Reason, is reconstructed processing to the Harmonious Waves in Power Systems signal of reception, power quality data is reduced, so as to realize Harmonious Waves in Power Systems
Detection；It is more efficient relative to prior art, and iterations further shorten based on variable step processing, it can obtain
The degree of rarefication signal most approached, solves the problem of time-consuming longer and degree of rarefication estimation of signal reconstruction is inaccurate.
Finally, method of the invention is only preferably embodiment, is not intended to limit the scope of the present invention.It is all
Within the spirit and principles in the present invention, any modification, equivalent substitution and improvements made etc. should be included in the protection of the present invention
Within the scope of.
Claims (9)
1. a kind of trend of harmonic detection method of power based on compressed sensing, it is characterised in that including：
S1, carries out wavelet transformation and Gauss measurement matrix disposal to the power quality data received, obtains measurement vector y and sense
Know matrix Θ；
S2, based on the measurement vector y and perception matrix Θ, matching pursuit algorithm is sampled to original using degree of rarefication self-adapting compressing
Beginning signal is reconstructed, and wherein atom selection carries out Regularization, and iterative process carries out variable step processing, obtains sparse bayesian learning
Signal
S3, based on the sparse bayesian learning signalReconstruct original power quality data.
2. the method as described in claim 1, it is characterised in that matrix Θ is perceived described in S1 and is obtained by following formula：
Wherein,For Gauss measurement matrix, ψ is wavelet conversion coefficient.
3. the method as described in claim 1, it is characterised in that the S2 further comprises：
S2.1, sets initial step length S, and it is the measurement vector y to make initial surplus, meets r=y, phase relation is calculated by following formula
Number u, and choose more than maximum correlation coefficient umaxThe atom index upgrade supported collection of half,
U={ uj|uj=|<r,Θj>|, j=1,2 ..., N },
Wherein, ujFor surplus and atom ΘjInner product, ΘjFor the jth row of the perception matrix Θ, also referred to as atom；
S2.2, as residual error rkWhen meeting the first iteration stopping condition and being unsatisfactory for secondary iteration stop condition, change step-lengthAnd supported collection is updated, carry out next iteration, wherein symbolExpression rounds up.
4. method as claimed in claim 3, it is characterised in that also include before the S2.1：Initialize the degree of rarefication certainly
The parameter of compression sampling matching pursuit algorithm is adapted to, including：
Iterations t=1, starting stage number k=1, indexed setSupported collection size L=S,
5. method as claimed in claim 3, it is characterised in that also include after the S2.1：Merge indexed set Λ=Λ ∪
F, and residual error r is updated by following formulak：
<mrow>
<msub>
<mi>r</mi>
<mi>k</mi>
</msub>
<mo>=</mo>
<mi>y</mi>
<mo>-</mo>
<msub>
<mi>&Theta;</mi>
<mi>&Lambda;</mi>
</msub>
<mover>
<mi>s</mi>
<mo>^</mo>
</mover>
</mrow>
Wherein, y is the column vector of the two dimensional image signal,For sparse coefficient vector, andS is current
Step-length.
6. method as claimed in claim 5, it is characterised in that the first iteration stopping condition is described in S2.2：Residual energy | | rk
||2≤ε1；
The secondary iteration stop condition is：Residual energy | | rk||2≤ε2；
Wherein, ε1With ε2It is positive number, and ε2＜ ε1。
7. method as claimed in claim 5, it is characterised in that the S2.2 also includes：
As residual error rkWhen being unsatisfactory for the first iteration stopping condition, if meeting | | rk||2≥||rk-1||2, then supported collection size L is updated
=L+S, iterations t=t+1 and number of stages k=k+1, carry out next iteration；
If being unsatisfactory for | | rk||2≥||rk-1||2, then indexed set Λ, surplus r=r are updatedkWith iterations t=t+1, carry out next
Secondary iteration.
8. method as claimed in claim 5, it is characterised in that the S2.2 also includes：
As residual error rkWhen meeting the first iteration stopping condition and meeting secondary iteration stop condition, stop iteration, obtain sparse bayesian learning
Signal
9. a kind of Measurement of Harmonics in Power System device based on compressed sensing, it is characterised in that including：
Initial processing module, for carrying out wavelet transformation and Gauss measurement matrix disposal to the power quality data received, is obtained
Vectorial y must be measured and matrix Θ is perceived；
Signal reconstruction module, for based on the measurement vector y and perception matrix Θ, utilizing the sampling of degree of rarefication self-adapting compressing
Primary signal is reconstructed with tracing algorithm, wherein atom selection carries out Regularization, and iterative process is carried out at variable step
Reason, obtains sparse bayesian learning signalAnd
Data recovery module, for based on the sparse bayesian learning signalReconstruct original power quality data.
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| CN108931703B (en) * | 2018-06-19 | 2020-06-30 | 西华大学 | Reconstruction method for selecting single-bit sampling of power quality disturbance signal through residual error |
| CN108931703A (en) * | 2018-06-19 | 2018-12-04 | 西华大学 | A kind of residual error chooses the reconstructing method of Power Quality Disturbance single-bit sampling |
| CN110717949A (en) * | 2018-07-11 | 2020-01-21 | 天津工业大学 | Interference hyperspectral image sparse reconstruction based on TROMP |
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| CN112422133B (en) * | 2020-10-30 | 2022-10-21 | 暨南大学 | Binary sparse signal recovery method for subtraction matching pursuit and application thereof |
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