CN107576866B - It is a kind of to approach the sparse method for distinguishing multiple harmonic sources reconstructed with interior point method based on smooth - Google Patents
It is a kind of to approach the sparse method for distinguishing multiple harmonic sources reconstructed with interior point method based on smooth Download PDFInfo
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Abstract
The present invention discloses a kind of to be approached sparse reconstruct and is estimator by known quantity, harmonic injection electric current of node harmonic voltage, converts harmonic source identification problem under the premise of guaranteeing that suspect region is considerable with the method for distinguishing multiple harmonic sources of interior point method based on smoothl 1 Norm minimum model, and then it approaches the Multi-harmonic Sources that sparse restructing algorithm carries out under the conditions of the measurement of part using smooth and recognizes, and herein on basis, it is further proposed that correcting Multi-harmonic Sources identification result using the supplement optimization method of harmonic wave measure configuration, there is higher estimated accuracy and stronger anti-interference ability.
Description
Technical field
The present invention relates to Measurement of Harmonics in Power System technical field, it is specially a kind of based on it is smooth approach sparse reconstruct with it is interior
The method for distinguishing multiple harmonic sources of point method.
Background technique
A large amount of harmonic injection electric system, not only endanger its safe operation, while also bringing economic loss.With in power grid
Nonlinear-load increases the operating condition that multiple harmonic sources coexist in capacity and quantitative sharp increase, while also enhancing power grid ginseng
The dynamic characteristics such as several fluctuation, mutation bring extreme difficulties to harmonic source identification.
The harmonic source distribution of electric system has the characteristics that randomness and uncertainty, humorous in conventional harmonic analysis field
Wave divergence is theoretical and harmonic trend theory has its respective application limitation, is not suitable for the development of current harmonic problem the whole network
Situation.The prior art is mostly to be surveyed or owed quantitative based on full dose to survey, and full dose surveys the cost problem for being limited to PMU measure configuration, no
Also measuring equipment need not may be installed on every bus and Zhi Lu.It owes quantitative and surveys identification inaccuracy, precision need to be improved.
Accordingly, it is considered to arrive actual conditions, the harmonic state estimation equation measured often owes fixed, finds a kind of side
Method can still have an accurately estimation in the case where measuring insufficient situation to the harmonic wave distribution situation in network, for humorous
Wave source identification has practical significance very much.
Summary of the invention
Deficiency and influence of the newly-increased harmonic source to identification precision are measured in harmonic wave the purpose of the present invention is to provide a kind of
In the case of, that realizes the accurate recognition of Multi-harmonic Sources approaches the sparse Multi-harmonic Sources identification side reconstructed with interior point method based on smooth
Method.Technical method is as follows:
It is a kind of to approach the sparse method for distinguishing multiple harmonic sources reconstructed with interior point method based on smooth, comprising the following steps:
Step A: to harmonic source suspicion node region in power grid, using node harmonic voltage as measurement, with the injection of node
Harmonic current is estimator, and Multi-harmonic Sources identification model is
U=AI
Wherein, U is to measure harmonic voltage, is the rank vector of m × 1；A is harmonic wave measurement matrix, is m × n rank matrix；I is section
The harmonic current of point injection, i.e. quantity of state are the rank vector of n × 1；
Multi-harmonic Sources identification problem is indicated are as follows:
min||I||0S.t.AI=U
Step B: l is converted by harmonic source identification problem1Norm minimum model, and then sparse reconstruct is approached using smooth
Algorithm is solved:
It is set as ChFor h major harmonic source number, R (A) is the minimal linear correlation columns that harmonic wave measures matrix A, μ (A)
For G=ATMaximum off-diagonal element in A；If harmonic wave, which measures matrix A, meets uniqueness principle R (A) > 2ChWith equivalence principle (1
+1/μ(A)1)>2Ch, then Multi-harmonic Sources identification problem is expressed as l1Norm minimum model:
min||I||1S.t.AI=U
To above formula, using l1The harmonic current that the approach of smoothing function algorithm for design of norm solves above formula estimates l1Norm is most
Smallization model:
If I ∈ Rn, t > 0, defined functionWithThen have
Wherein, t is real variable, and n is the element number in quantity of state I；RnIndicate real number field, IiFor i-th yuan in I
Element；
Then formula min | | I | |1；S.t.AI=U is of equal value are as follows:
The angle calculated from numerical value, is rewritten into discrete expression:
Wherein, { tkBe monotonic increase integer sequence；
Step C: it is solved using interior point methodProblem obtains node harmonic electric current:
Interior point method approaches solution formula are as follows:
In formula, η > 0, siIt is then approached for slack variable when η approach 0Minimum value.
The process of the harmonic electric current of further solution node are as follows:
Step1: the node harmonic voltage U of measurement is inputted, harmonic wave measures matrix A, threshold epsilon, step-length l；
Step2: initialization k=0, tk=t0, I*(t0)=0；
Step3: it is solved using interior point methodOptimal solution I*(tk)；
Step4: if | | I*(tk)-I*(tk-1)||2> ε enables k=k+1, tk=t0+ kl returns to Step3；Conversely, output I*
(tk), the as harmonic electric current of node.
It further, further include the supplement optimization method of harmonic wave measure configuration after the step C, step is specifically such as
Under:
Step a: to harmonic source suspicion node region in power grid, harmonic wave measurement node, structure are determined using Analysis on Observability
Point set M is distributed rationally at harmonic wave measurement0, guarantee the ornamental of harmonic source suspicion node region；
Step b: node harmonic electric current that sparse restructing algorithm is estimated will be approached by the big float of amplitude by smooth
Amplitude is greater than given threshold I by sequenceεNode, be successively denoted as N by amplitude is descending1, N2..., Nr；
Step c: judge N1Whether belong to harmonic wave measurement and distributes point set M rationally0If being not belonging to, supplement optimization is enabled to match
Set point set M=M0∪N1, point set M is distributed rationally according to supplement, estimates harmonic injection electric current again；If N1Belong to M0, then according to
Secondary judgement N2~NrIf having some measuring point to be added to supplement to distribute rationally in point set M, harmonic injection electricity is estimated again
Stream；
Step d: repeating Step a~Step c, until all harmonic current amplitudes are greater than given threshold IεSection
Point is distributed rationally within point set M in supplement, and output supplement optimization measure configuration scheme and harmonic wave current estimation are as a result, accurate
It recognizes harmonic source and injects node.
The beneficial effects of the present invention are: the present invention proposes a kind of to approach sparse reconstruct and the multiple-harmonic of interior point method based on smooth
Source discrimination method is to estimate by known quantity, harmonic injection electric current of node harmonic voltage under the premise of guaranteeing that suspect region is considerable
Metering is realized the Multi-harmonic Sources under the conditions of part measures using Smoothing Approximation Algorithm and recognized, and herein on basis, further
Supplement optimization method using harmonic wave measure configuration is proposed to correct Multi-harmonic Sources identification result, have higher estimated accuracy with
Stronger anti-interference ability.
Detailed description of the invention
Fig. 1 is 34 node system figure of IEEE.
Fig. 2 is the implementation flow chart of the method for the present invention.
Specific embodiment
The present invention is described in further details in the following with reference to the drawings and specific embodiments.The present embodiment proposes that one kind is based on
The smooth method for distinguishing multiple harmonic sources for approaching sparse reconstruct and interior point method, the specific steps are as follows:
Step A: to harmonic source suspicion node region in power grid, using node harmonic voltage as measurement, with the injection of node
Harmonic current is estimator, carries out the identification of harmonic source.
Multi-harmonic Sources recognize model are as follows:
U=AI
Wherein, U is to measure harmonic voltage, is the rank vector of m × 1；A is harmonic wave measurement matrix, is m × n rank matrix；I is section
The harmonic current of point injection, i.e. quantity of state are the rank vector of n × 1.
In view of measuring cost, measurement is typically less than the estimator (m < n) of state estimation, i.e. measurement equation owes fixed.Together
When, due to harmonic source negligible amounts in power grid, distribution is in space rarefaction state, therefore the present invention is humorous using sparse reconstruct realization
Wave source identification, Multi-harmonic Sources identification problem is indicated are as follows:
min||I||0S.t.AI=U
Step B: l is converted by harmonic source identification problem1Norm minimum model, and then sparse reconstruct is approached using smooth
Algorithm is solved.
Since major harmonic source injection node is often less in electric system, the uniqueness and equivalence of harmonic wave measurement matrix
Condition is easier to meet.In consideration of it, further converting l for harmonic source identification problem1Norm minimum model, and then utilize
It is smooth to approach sparse reconstructing method and solved, realize that the harmonic source under the premise of partial amount is surveyed accurately recognizes.
It is set as ChFor h major harmonic source number, R (A) is the minimal linear correlation columns that harmonic wave measures matrix A, μ (A)
For G=ATMaximum off-diagonal element in A.If harmonic wave, which measures matrix A, meets uniqueness principle R (A) > 2ChWith equivalence principle (1
+1/μ(A)1)>2Ch, then Multi-harmonic Sources identification problem is represented by l1Norm minimum model:
min||I||1S.t.AI=U
To above formula, using l1The approach of smoothing function of norm carrys out the harmonic current estimation l that algorithm for design solves above formula1Norm
Minimize model.
If I ∈ Rn, t > 0, defined functionWithThen have
Wherein, t is real variable, and n is the element number in quantity of state I；RnIndicate real number field, IiFor i-th yuan in I
Element.
Then formula min | | I | |1；S.t.AI=U can be equivalent to
The angle calculated from numerical value, is rewritten into discrete expression
Wherein: { tkBe monotonic increase integer sequence.
Step C: it to provide accurate solving result, is solved using interior point methodProblem,
The solution formula of approaching of interior point method is
In formula, η > 0, siFor slack variable.When η approach 0, then approachMinimum value.
Fig. 1 shows calculating step, specific as follows:
Step1: the node harmonic voltage U of measurement is inputted, harmonic wave measures matrix A, threshold epsilon, step-length l；
Step2: initialization k=0, tk=t0, I*(t0)=0；
Step3: optimal solution I is solved using interior point method*(tk)；
Step4: if | | I*(tk)-I*(tk-1)||2> ε enables k=k+1, tk=t0+ kl returns to Step3；Conversely, output I*
(tk), the as harmonic electric current of node.
Harmonic wave measures configuration scheme under the premise of guaranteeing that harmonic source suspect region is considerable, reduces to the maximum extent
Harmonic wave measures cost.However, since the harmonic voltage and harmonic electric current of harmonic source injection near nodal node are with similar
Characteristic, exist interference harmonic current, measure noise or calculate error under the influence of, the ornamental of system is easily destroyed,
To be difficult to accurately recognize harmonic source.In consideration of it, using it is smooth approach sparse reconstruct and carry out harmonic source identification on the basis of, into
One step proposes the supplement optimization method using harmonic wave measure configuration to correct Multi-harmonic Sources identification result.
The step of supplement optimization method of harmonic wave measure configuration, is specific as follows:
Step a: to harmonic source suspicion node region in power grid, harmonic wave measurement node, structure are determined using Analysis on Observability
Point set M is distributed rationally at harmonic wave measurement0, guarantee the ornamental of harmonic source suspicion node region；
Step b: node harmonic electric current that sparse restructing algorithm is estimated will be approached by the big float of amplitude by smooth
Amplitude is greater than given threshold I by sequenceεNode, be successively denoted as N by amplitude is descending1, N2..., Nr；
Step c: judge N1Whether belong to harmonic wave measurement and distributes point set M rationally0If being not belonging to, supplement optimization is enabled to match
Set point set M=M0∪N1, point set M is distributed rationally according to supplement, estimates harmonic injection electric current again；If N1Belong to M0, then according to
Secondary judgement N2~NrIf having some measuring point to be added to supplement to distribute rationally in point set M, harmonic injection electricity is estimated again
Stream；
Step d: repeating Step a~Step c, (distributes newly-generated supplement rationally point set M substitution upper one
Point set M is distributed in the harmonic wave measurement of circulation rationally0, then the step of carrying out Step b and Step c) until all harmonics electricity
It flows amplitude and is greater than given threshold IεNode distributed rationally within point set M in supplement, output supplement optimization measure configuration side
Case and harmonic wave current estimation are as a result, accurate recognition harmonic source injects node.
Test verifying the method for the present invention is carried out in IEEE34 node system (as shown in Figure 1).Its A phase load is accessed, is chosen
Suspicion node be 33, respectively 1~No. 33 node.5 subharmonic current sources, harmonic are accessed in node 7,15 and 24
Size of current is respectively 2.5000+j2.0000 (A), 3.0000+j2.5000 (A) and 3.5000+j3.0000 (A).
On the basis of harmonic wave measurement is distributed rationally, smooth sparse Reconstruction Method and the least square method of approaching is respectively adopted and realizes
Multi-harmonic Sources identification, acquired results are as shown in table 1.
The Multi-harmonic Sources identification result of 1 IEEE34 node system of table (harmonic wave measurement is distributed rationally)
As can be seen from Table 1, smooth to approach estimated result that sparse Reconstruction Method obtains compared with subject to compared to least square method
Really, but for the harmonic source of node 15, two methods cannot accurately be estimated, be easy to cause erroneous judgement.Therefore, present invention proposition is adopted
Multi-harmonic Sources identification result is corrected with supplement optimization method for measurement, acquired results are as shown in table 2.
The Multi-harmonic Sources identification result of 2 IEEE34 node system of table (supplement optimization measures)
As shown in Table 2, after being measured using supplement optimization, least square method is only capable of making the harmonic source of node 15 relatively accurate
Estimation, it is and larger to the estimated bias of node 7 and 24, while erroneous judgement is be easy to cause to node 3,4,25,28 and 29.And it uses
It is accurate compared with (smooth to approach sparse reconstruct with the interior point method) result for carrying out Multi-harmonic Sources identification of the method for the present invention, and do not easily cause
Erroneous judgement.
Claims (3)
1. a kind of based on the smooth method for distinguishing multiple harmonic sources for approaching sparse reconstruct and interior point method, which is characterized in that including following
Step:
Step A: to harmonic source suspicion node region in power grid, using node harmonic voltage as measurement, with the harmonic of node
Electric current is estimator, and Multi-harmonic Sources identification model is
U=AI
Wherein, U is to measure harmonic voltage, is the rank vector of m × 1；A is harmonic wave measurement matrix, is m × n rank matrix；I is node note
The harmonic current entered, i.e. quantity of state are the rank vector of n × 1；
Multi-harmonic Sources identification problem is indicated are as follows:
min||I||0S.t.AI=U
Step B: l is converted by harmonic source identification problem1Norm minimum model, and then sparse restructing algorithm is approached using smooth
It is solved:
It is set as ChFor h major harmonic source number, R (A) is the minimal linear correlation columns that harmonic wave measures matrix A, and μ (A) is G=
ATMaximum off-diagonal element in A；If harmonic wave, which measures matrix A, meets uniqueness principle R (A) > 2ChWith equivalence principle (1+1/ μ
(A))>2Ch, then Multi-harmonic Sources identification problem is expressed as l1Norm minimum model:
min||I||1S.t.AI=U
To above formula, using l1The harmonic current that the approach of smoothing function algorithm for design of norm solves above formula estimates l1Norm minimum
Model:
If I ∈ Rn, t > 0, defined functionWithThen have
Wherein, t is real variable, and n is the element number in quantity of state I；RnIndicate real number field, IiFor i-th of element in I；
Then formula min | | I | |1；S.t.AI=U is of equal value are as follows:
The angle calculated from numerical value, is rewritten into discrete expression:
Wherein, { tkBe monotonic increase integer sequence；
Step C: it is solved using interior point methodObtain node harmonic electric current:
Interior point method approaches solution formula are as follows:
In formula, η > 0, siIt is then approached for slack variable when η approach 0Minimum value.
2. it is according to claim 1 based on the smooth method for distinguishing multiple harmonic sources for approaching sparse reconstruct and interior point method, it is special
Sign is, the process of the harmonic electric current of solution node are as follows:
Step1: the node harmonic voltage U of measurement is inputted, harmonic wave measures matrix A, threshold epsilon, step-length l；
Step2: initialization k=0, tk=t0, I*(t0)=0；
Step3: it is solved using interior point methodOptimal solution I*(tk)；
Step4: if | | I*(tk)-I*(tk-1)||2> ε enables k=k+1, tk=t0+ kl returns to Step3；Conversely, output I*(tk),
The as harmonic electric current of node.
3. it is according to claim 1 based on the smooth method for distinguishing multiple harmonic sources for approaching sparse reconstruct and interior point method, it is special
Sign is, further includes the supplement optimization method of harmonic wave measure configuration after the step C, and step is specific as follows:
Step a: to harmonic source suspicion node region in power grid, harmonic wave measurement node is determined using Analysis on Observability, is constituted humorous
Point set M is distributed in wave measurement rationally0, guarantee the ornamental of harmonic source suspicion node region；
Step b: will be approached node harmonic electric current that sparse restructing algorithm is estimated and sorted by amplitude size by smooth,
Amplitude is greater than given threshold IεNode, be successively denoted as N by amplitude is descending1, N2..., Nr；
Step c: judge N1Whether belong to harmonic wave measurement and distributes point set M rationally0If being not belonging to, supplement is enabled to distribute rationally a little
Set M=M0∪N1, point set M is distributed rationally according to supplement, estimates harmonic injection electric current again；If N1Belong to M0, then successively sentence
Disconnected N2~NrIf having some measuring point to be added to supplement to distribute rationally in point set M, harmonic injection electric current is estimated again；
Step d: repeating Step a~Step c, until all harmonic current amplitudes are greater than given threshold IεNode exist
Supplement is distributed rationally within point set M, and output supplement optimization measure configuration scheme and harmonic wave current estimation are as a result, accurate recognition is humorous
Wave source injects node.
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