CN106896267B - A kind of Distribution Network Harmonics resonance improvement modal analysis method - Google Patents
A kind of Distribution Network Harmonics resonance improvement modal analysis method Download PDFInfo
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- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
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Abstract
The invention discloses a kind of Distribution Network Harmonics resonance to improve modal analysis method, the following steps are included: determining resonance frequency using frequency spectrum analysis method, the eigenvalue matrix of the node admittance matrix under resonance frequency is found out again, ascending order arrangement is carried out to it by size to the characteristic value of node admittance matrix, records the position of each characteristic value；Feasible solution of the m minimal eigenvalue as mode crucial under resonance frequency before taking, determine the corresponding right feature vector of key of each feasible solution, maximum right eigenvalue and its position of these crucial right feature vector feasible solutions, position, that is, highest excitation node feasible solution can be obtained.The advantages such as computational efficiency is high, highest excitation node locating is accurate the beneficial effects of the present invention are: the present invention has, are more applicable for Distribution Network Harmonics harmonic analysis.
Description
Technical field
The present invention relates to Power System Analysis and control technology field, in particular to a kind of Distribution Network Harmonics resonance improves mould
State analysis method.
Background technique
In recent years, being continuously increased with power demand, the extensive application of converter technique, the nonlinear-load in power distribution network
Increase year by year, the harmonic problem of power grid is on the rise, and causes potential hazard to the stable operation of power grid.On the one hand, harmonic wave is deposited
In the power quality for reducing power grid, the safe and reliable operation of electrical equipment is endangered, increases plant capacity loss, or even damage is set
It is standby, cause power-off fault.On the other hand, when the harmonic frequency and close system resonance frequencies in power grid, it may induce system
Resonance generates resonance overvoltage, seriously affects the safe and reliable operation of power grid.
Harmonic resonance is an important harm caused by harmonic wave, and parallel resonance causes overvoltage, and series resonance caused electricity
Stream, causes damages to safe and stable operation of power system, thus needs to inhibit the harmonic resonance of electric system, this just needs to carry out
Harmonic resonance analysis, obtains resonance frequency and resonance range, so that corresponding measure be taken to avoid the generation of harmonic resonance, reduces humorous
Breakdown loss caused by shaking, this has important practical significance to the stable operation for ensureing electric system.
Harmonic resonance analysis method mainly has Spectral Analysis Method, modal analysis method etc., and Spectral Analysis Method can determine resonance
Frequency, but the more information of resonance cannot be provided, the influence degree such as resonance location and each element to resonance, traditional modal analysis
Method is widely noticed due to efficiently convenient, by the characteristic root of analysis node admittance matrix, so that it may obtain the various letters of resonance
Breath, such as resonance frequency, highest excitation point, highest observation point and participates in the factor, but its computational efficiency is lower, and can not accurately sentence
Highest in disconnected Distribution Network Harmonics resonance excites node.Therefore, there is an urgent need to study a kind of Distribution Network Harmonics resonance improvement mode
Analysis method determines the various information of Distribution Network Harmonics resonance with efficiently and accurately.
Summary of the invention
The present invention is directed to overcome the shortcomings of traditional modal analysis method, propose that a kind of Distribution Network Harmonics resonance improves mode point
Analysis method, the present invention analyze power distribution network node impedance extreme point position first with Spectral Analysis Method, determine resonance frequency, eliminate
The step of traditional modal analysis method interior joint admittance matrix decomposes, eigenvalue matrix is inverted, improves computational efficiency；It is right simultaneously
Traditional modal analysis method is improved, by increase judge excitation node can occur at the resonant frequency fx the condition of resonance come
It determines highest excitation node and best observer nodes, it is wrong to reduce positioning of the traditional modal analysis method for generating when power distribution network
Accidentally, it is capable of various information (such as resonance frequency, highest excitation point, the highest sight of determining Distribution Network Harmonics resonance of efficiently and accurately
Measuring point and the participation factor), which is applicable not only to power distribution network, is equally applicable to power transmission network.
In order to achieve the above-mentioned object of the invention, the present invention provides a kind of Distribution Network Harmonics resonance to improve modal analysis method,
Specifically includes the following steps:
S1, resonance frequency is determined using frequency spectrum analysis method, specifically, it is humorous to work as i-node generation in system for distribution network of power
When vibration frequency is the parallel resonance of f, i-node impedance shows maximum value, and each node maximum impedance is by formula (1) in electric system
It finds out:
In formula, ziifFor the node impedance under a certain frequency, famous value is taken；
Frequency corresponding to each node impedance maximum value can be found out according to each node maximum impedance for finding out, i.e., described
Resonance frequency；
Wherein, the frequency spectrum analysis method uses adaptive sweep frequency technique, specifically includes the following steps:
Step S101, original frequency f0, final frequency fmax, initial step length h0=0.2Hz, maximum step-length hmax=are set
10Hz (increasing step-length when frequency sweep can be improved computational efficiency, but step-length too it is big may across some unimodal sections, the section Dan Gu,
Therefore the maximum value of hmax restricted step is set)；
Step S102, h1=h2=h0, f1=f0, f2=f1+h1, f3=f2+h2 are set gradually；
Step S103, Z is node self-impedance, is calculated
Step S104, by calculating the product of the slope between twice sweep, i.e. A=k1*k2 controls the size of step-length；
Step S105, as A > 0, i.e., frequency sweep increases step-length (h1 with increasing section or in section of successively decreasing at this time twice
=h2, h2=h2+0.2), advance (f1=f2, f2=f3, f3=f2+h2, k1=k2), until encounter a unimodal section or
Until the section Dan Gu (Rule of judgment is A < 0), turn 6.；During frequency sweep, if reaching section right margin fmax, program is whole
Only.
As A < 0, i.e., frequency sweep is in unimodal section or the section Dan Gu twice, and node impedance has in frequency sweep section twice at this time
Extreme point, frequency sweep, step-length become the half (h1=h1/2, h2=h12+0.2) of original steps to the section [f1, f3] domestic demand again,
Turn 3., to continue frequency sweep and find out Impedance Peak position, that is, can determine resonance frequency.
S2, the eigenvalue matrix that the node admittance matrix under the resonance frequency that step S1 is obtained is found out using formula (2),
Y=L Λ T (2)
Wherein, Λ is diagonal eigenmatrix, and L and T are respectively left eigenvector matrix and right eigenvectors matrix, L=T-1；
Mode voltage vector U=TV, mode current vector J=TI are defined, then U=Λ-1J can be represented by the formula:
In formula, λ-1Referred to as mode impedance Zm, work as λi=0 or when very little, even if mode i Injection Current JiVery little will also generate
Very big mode i voltage Ui, claim the smallest λiFor the crucial mode of resonance, corresponding [Ti1,Ti2,…Tin]、[L1i,L2i,…Lni]T
Respectively crucial right feature vector and crucial left eigenvector；
S3, ascending order arrangement is carried out to it by size to the characteristic value of node admittance matrix, records the position of each characteristic value；Such as
Shown in lower:
S4, take preceding m minimal eigenvalue in step S3 as the feasible solution of mode crucial under resonance frequency, preferably m=10,
The corresponding right feature vector of key of each feasible solution is determined according to above-mentioned formula (2), these crucial right feature vectors can be obtained
The maximum right eigenvalue of feasible solution and its position, the position, that is, highest excitation node feasible solution；
S5, by mode electric current JiIt indicates are as follows:
Ji=Ti1I1+Ti2I2+Ti3I3+…+TinIn (4)
Work as TijWhen maximum, corresponding IjTo mode electric current JiContribution it is maximum, illustrate that j node is that mode i most easily occurs
The position of resonance, works as TijWhen=0, no matter IjIt is much all to excite resonance, therefore with crucial right feature vector [Ti1,Ti2,…
Tin] indicate each node current to the excitation degree of mode i resonance；The excitability of crucial mode can use right key feature vector
It indicates, having the node of maximum right eigenvalue is that highest excites node in mode.
Further, due to certain corresponding mode have highest can incentive node simultaneously also with highest Observable
Property, thus highest observer nodes can excite node identical with above-mentioned highest, therefore highest observation can be obtained by the above method
Node；It can determine the corresponding participation factor by formula (5):
PFbm=LbmTmb (5)
In formula, PF is to participate in the factor, and L is crucial left eigenvector, and T is crucial right feature vector, and b is bus number, and m is mould
State number.
The invention has the benefit that compared with prior art, the present invention has computational efficiency height, highest excitation node fixed
Level really etc. advantages, be more applicable for Distribution Network Harmonics harmonic analysis, by improve modal analysis method by spectrum analysis and tradition
Model analysis combines, and determines resonance frequency using Spectral Analysis Method analysis node Impedance Peak point position, has eliminated node and led
It receives matrix decomposition, eigenvalue matrix the step of inverting, improves computational efficiency；Traditional modal analysis is utilized at the resonant frequency fx
Method, while increasing judgement and node is excited the condition of resonance can to occur at the resonant frequency fx to determine that highest excites node, subtract
The positioning mistake for having lacked traditional modal analysis method is capable of the various information for determining Distribution Network Harmonics resonance of efficiently and accurately, such as
Resonance frequency, highest excitation point, highest observation point and the participation factor.
Detailed description of the invention
Fig. 1 is the flow chart of method in the embodiment of the present invention.
Fig. 2 is the flow chart of the adaptive frequency sweep of step S1 in the embodiment of the present invention.
Fig. 3 is the schematic diagram of the area comparative test of embodiment of the present invention Zhong Bonanyou electricity distribution network model.
Fig. 4 is to be corresponded in comparative test of the embodiment of the present invention using 62, No. 66 nodes that traditional modal analysis method determines
Impedance frequency characteristic curve graph.
Fig. 5 is to improve No. 62 nodes pair that modal analysis method determines using the present invention in comparative test of the embodiment of the present invention
The impedance frequency characteristic curve graph answered.
Specific embodiment
The present invention is lower for mentioning existing harmonic resonance analysis method in background technique there are efficiency, and can not be accurate
The problems such as judging the highest excitation node in Distribution Network Harmonics resonance, provides a kind of Distribution Network Harmonics resonance improvement model analysis
Method determines resonance frequency first with Spectral Analysis Method, finds out the eigenvalue matrix of resonance frequency lower node admittance matrix, and
Ascending order arrangement is carried out to it by size, records the position of each characteristic value, m minimal eigenvalue is as crucial under resonance frequency before taking
The feasible solution of mode determines the corresponding right feature vector of key of each feasible solution, obtains crucial right feature vector feasible solution most
Big right eigenvalue and its position, these positions, that is, highest excitation node feasible solution.By find out occur at the resonant frequency fx it is humorous
The feasible solution of the highest excitation node of vibration, and take the feasible solution for wherein possessing maximum impedance value (per unit value) to excite as highest and save
Point, corresponding mode are crucial mode, obtain highest observer nodes using determining crucial mode and traditional modal analysis method
And the factor is participated in accordingly.
Technical solution of the present invention is described in detail combined with specific embodiments below.
Embodiment 1
The embodiment of the invention provides a kind of Distribution Network Harmonics resonance to improve modal analysis method, specifically includes following step
It is rapid:
S1, resonance frequency is determined using frequency spectrum analysis method, specifically, it is humorous to work as i-node generation in system for distribution network of power
When vibration frequency is the parallel resonance of f, i-node impedance shows maximum value, and each node maximum impedance is by formula (1) in electric system
It finds out:
In formula, ziifFor the node impedance under a certain frequency, famous value is taken；
Frequency corresponding to each node impedance maximum value can be found out according to each node maximum impedance for finding out, i.e., described
Resonance frequency；
Wherein, the frequency spectrum analysis method uses adaptive sweep frequency technique, specifically includes the following steps:
Step S101, original frequency f0, final frequency fmax, initial step length h0=0.2Hz, maximum step-length hmax=are set
10Hz (increasing step-length when frequency sweep can be improved computational efficiency, but step-length too it is big may across some unimodal sections, the section Dan Gu,
Therefore the maximum value of hmax restricted step is set)；
Step S102, h1=h2=h0, f1=f0, f2=f1+h1, f3=f2+h2 are set gradually；
Step S103, Z is node self-impedance, is calculated
Step S104, by calculating the product of the slope between twice sweep, i.e. A=k1*k2 controls the size of step-length；
Step S105, as A > 0, i.e., frequency sweep increases step-length (h1 with increasing section or in section of successively decreasing at this time twice
=h2, h2=h2+0.2), advance (f1=f2, f2=f3, f3=f2+h2, k1=k2), until encounter a unimodal section or
Until the section Dan Gu (Rule of judgment is A < 0), turn 6.；During frequency sweep, if reaching section right margin fmax, program is whole
Only.
As A < 0, i.e., frequency sweep is in unimodal section or the section Dan Gu twice, and node impedance has in frequency sweep section twice at this time
Extreme point, frequency sweep, step-length become the half (h1=h1/2, h2=h12+0.2) of original steps to the section [f1, f3] domestic demand again,
Turn 3., to continue frequency sweep and find out Impedance Peak position, that is, can determine resonance frequency.
S2, the eigenvalue matrix that the node admittance matrix under the resonance frequency that step S1 is obtained is found out using formula (2),
Y=L Λ T (2)
Wherein, Λ is diagonal eigenmatrix, and L and T are respectively left eigenvector matrix and right eigenvectors matrix, L=T-1；
Mode voltage vector U=TV, mode current vector J=TI are defined, then U=Λ-1J can be represented by the formula:
In formula, λ-1Referred to as mode impedance Zm, work as λi=0 or when very little, even if mode i Injection Current JiVery little will also generate
Very big mode i voltage Ui, claim the smallest λiFor the crucial mode of resonance, corresponding [Ti1,Ti2,…Tin]、[L1i,L2i,…Lni]T
Respectively crucial right feature vector and crucial left eigenvector；
S3, ascending order arrangement is carried out to it by size to the characteristic value of node admittance matrix, records the position of each characteristic value；Such as
Shown in lower:
S4, take preceding m minimal eigenvalue in step S3 as the feasible solution of mode crucial under resonance frequency, preferably m=10,
The corresponding right feature vector of key of each feasible solution is determined according to above-mentioned formula (2), these crucial right feature vectors can be obtained
The maximum right eigenvalue of feasible solution and its position, the position, that is, highest excitation node feasible solution；
S5, by mode electric current JiIt indicates are as follows:
Ji=Ti1I1+Ti2I2+Ti3I3+…+TinIn (4)
Work as TijWhen maximum, corresponding IjTo mode electric current JiContribution it is maximum, illustrate that j node is that mode i most easily occurs
The position of resonance, works as TijWhen=0, no matter IjIt is much all to excite resonance, therefore with crucial right feature vector [Ti1,Ti2,…
Tin] indicate each node current to the excitation degree of mode i resonance；The excitability of crucial mode can use right key feature vector
It indicates, having the node of maximum right eigenvalue is that highest excites node in mode.
Further, due to certain corresponding mode have highest can incentive node simultaneously also with highest Observable
Property, thus highest observer nodes can excite node identical with above-mentioned highest, therefore highest observation can be obtained by the above method
Node；It can determine the corresponding participation factor by formula (5):
PFbm=LbmTmb (5)
In formula, PF is to participate in the factor, and L is crucial left eigenvector, and T is crucial right feature vector, and b is bus number, and m is mould
State number.
Comparative experiments
This comparative experiments applies traditional modal analysis method and the present invention by taking the area Shengli Oil Field Bo Nanyou power distribution network as an example respectively
Improved modal analysis method analyzes Distribution Network Harmonics resonance respectively, compares the analysis of two methods as a result, verifying improves mode point
The superiority of analysis method.
The area Bo Nanyou electricity distribution network model as shown in figure 3, wherein under every route have branched line, amount to 733 nodes,
749 branches；Two methods analyze result and simulation time is as shown in table 1.
1 area Bo Nanyou power distribution network modal analysis result of table and simulation time
By the data of table 1, it can be seen that No. 62 node on behalf Bo Nan infuse -1250 nodes, No. 66 node on behalf oil plants -
1250 nodes determine that two resonance frequencies are respectively 905.2Hz, 1545.2Hz using traditional modal analysis method, resonance frequency
It is 493, No. 625 nodes respectively that highest, which excites node, adds the frequency filtering to be at No. 493 nodes in the area Bo Nanyou electricity distribution network model
The resonance filter of 905.2Hz, it is the resonance filter of 1545.2Hz, 62, No. 66 nodes that frequency filtering is added at No. 625 nodes
Impedance frequency characteristic curve is as shown in Figure 4.
Filter deutomerite is added in 62,66 node impedance frequency characteristics when red line indicates not add filter in Fig. 4, green line
Point impedance frequency characteristic adds the resonance filter that frequency filtering is 905.2Hz not as seen from the figure at No. 493 nodes
It can inhibit harmonic resonance, it is that the resonance filter of 1545.2Hz can effectively inhibit harmonic wave that frequency filtering is added at No. 625 nodes
Resonance.Above analysis shows traditional modal analysis method may cause highest excitation node locating when analyzing Distribution Network Harmonics resonance
Mistake, traditional modal analysis method are not suitable for Distribution Network Harmonics harmonic analysis.
By the data of table 1, it can be seen that No. 62 node on behalf Bo Nan infuse -1250 nodes, No. 66 node on behalf oil plants -
1250 nodes improve the highest excitation node point that modal analysis method determines resonance frequency 905.2Hz, 1545.2Hz using the present invention
It is not 63, No. 625 nodes, highest when No. 625 nodes have verified that as 1545.2Hz excites node, in the area Bo Nanyou power distribution network mould
Adding frequency filtering in type at No. 63 nodes is the resonance filter of 905.2Hz, No. 62 node impedance frequency characteristics such as Fig. 5 institute
Show.
Filter deutomerite is added in 62,66 node impedance frequency characteristics when red line indicates not add filter in Fig. 5, green line
Point impedance frequency characteristic, as seen from the figure, it is that the resonance filter of 905.2Hz can have that frequency filtering is added at No. 63 nodes
Effect inhibits harmonic resonance.
Through above-mentioned comparison, it can be seen that compared with traditional modal analysis method, modal analysis method is improved in analysis power distribution network
Highest excitation node can be accurately positioned when harmonic resonance, and traditional modal analysis method simulation time 38120.5s is much larger than and changes
Into modal analysis method simulation time 6545.4s, show that the computational efficiency for improving modal analysis method is apparently higher than traditional modal analysis
Method computational efficiency.
In conclusion although traditional modal analysis method can determine the resonance frequency of power grid, highest excitation node, highest
Observer nodes and bus participate in the factor, but it needs to carry out node admittance matrix decomposition, and computational efficiency is lower, and applies in distribution
Highest excitation node is unable to judge accurately in the analysis of net harmonic resonance, improvement modal analysis method proposed by the present invention is by spectrum analysis
It is combined with traditional modal analysis method, while increasing judgement excitation node the item of resonance can occur at the resonant frequency fx
Part can efficiently, accurately determine that Distribution Network Harmonics resonance frequency, highest excite node.Improvement model analysis proposed by the present invention
Method is suitable for Distribution Network Harmonics harmonic analysis.
The foregoing is merely presently preferred embodiments of the present invention, is not intended to limit the invention, it is all in spirit of the invention and
Within principle, any modification, equivalent replacement, improvement and so on be should all be included in the protection scope of the present invention.
Claims (3)
1. a kind of Distribution Network Harmonics resonance improves modal analysis method, which is characterized in that specific step is as follows for the analysis method:
S1, resonance frequency is determined using frequency spectrum analysis method, specifically, when i-node generation resonance frequency in system for distribution network of power
When rate is the parallel resonance of f, i-node impedance shows maximum value, and each node maximum impedance is asked by formula (1) in electric system
Out:
In formula, ziifFor the node impedance under a certain frequency, famous value is taken；
Frequency corresponding to each node impedance maximum value, the i.e. resonance can be found out according to each node maximum impedance found out
Frequency；
S2, the eigenvalue matrix that the node admittance matrix under the resonance frequency that step S1 is obtained is found out using formula (2),
Y=L Λ T (2)
Wherein, Λ is diagonal eigenmatrix, and L and T are respectively left eigenvector matrix and right eigenvectors matrix, L=T-1；
Mode voltage vector U=TV, mode current vector J=TI are defined, then U=Λ-1J can be represented by the formula:
In formula, λ-1Referred to as mode impedance Zm, work as λi=0 or when very little, even if mode i Injection Current JiVery little will also generate very big
Mode i voltage Ui, claim the smallest λiFor the crucial mode of resonance, corresponding [Ti1,Ti2,…Tin]、[L1i,L2i,…Lni]TPoint
It Wei not crucial right feature vector and crucial left eigenvector；
S3, ascending order arrangement is carried out to it by size to the characteristic value of node admittance matrix, records the position of each characteristic value；
S4, feasible solution of the preceding m minimal eigenvalue as mode crucial under resonance frequency in step S3 is taken, according to above-mentioned formula
(2) it determines the corresponding right feature vector of key of each feasible solution, the maximum of these crucial right feature vector feasible solutions can be obtained
Right eigenvalue and its position, the position, that is, highest excitation node feasible solution；
S5, by mode electric current JiIt indicates are as follows:
Ji=Ti1I1+Ti2I2+Ti3I3+…+TinIn (4)
Work as TijWhen maximum, corresponding IjTo mode electric current JiContribution it is maximum, illustrate that j node is that mode i resonance most easily occurs
T is worked as in positionijWhen=0, no matter IjIt is much all to excite resonance, therefore with crucial right feature vector [Ti1,Ti2,…Tin] indicate
Excitation degree of each node current to mode i resonance；The excitability of crucial mode can indicate have with right key feature vector
The node of maximum right eigenvalue is highest excitation node namely highest observer nodes in mode；
Wherein, the frequency spectrum analysis method in the step S1 uses adaptive frequency sweeping method, specifically:
Step S101, original frequency f0, final frequency fmax, initial step length h0=0.2Hz, maximum step-length hmax=are set
10Hz, increasing step-length when frequency sweep can be improved computational efficiency, but step-length too it is big may across some unimodal sections, the section Dan Gu,
Therefore the maximum value of hmax restricted step is set；
Step S102, h1=h2=h0, f1=f0, f2=f1+h1, f3=f2+h2 are set gradually；
Step S103, Z is node self-impedance, is calculated
Step S104, by calculating the product of the slope between twice sweep, i.e. A=k1*k2 controls the size of step-length；
Step S105, as A > 0, i.e., frequency sweep increases step-length (h1=with increasing section or in section of successively decreasing at this time twice
H2, h2=h2+0.2), advance (f1=f2, f2=f3, f3=f2+h2, k1=k2), until encountering a unimodal section or list
Until paddy section (Rule of judgment is A < 0), S106 is gone to step；During frequency sweep, if reaching section right margin fmax, journey
Sequence terminates；
Step S106, as A < 0, i.e., frequency sweep is in unimodal section or the section Dan Gu twice, and node impedance is in frequency sweep area twice at this time
Interior to have extreme point, frequency sweep, step-length become half (h1=h1/2, the h2=h12+ of original steps to the section [f1, f3] domestic demand again
0.2) S103, is gone to step, continues frequency sweep and finds out Impedance Peak position, that is, can determine resonance frequency.
2. Distribution Network Harmonics resonance according to claim 1 improves modal analysis method, which is characterized in that pass through formula
(5) the participation factor is calculated:
In formula, PF is to participate in the factor, and L is crucial left eigenvector, and T is crucial right feature vector, and b is bus number, and m is mode
Number.
3. Distribution Network Harmonics resonance according to claim 1 or 2 improves modal analysis method, which is characterized in that the step
In rapid S4, feasible solution of the preceding m=10 minimal eigenvalue as mode crucial under resonance frequency in step S3 is taken.
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