CN106548418A - Power system small interference stability appraisal procedure - Google Patents
Power system small interference stability appraisal procedure Download PDFInfo
- Publication number
- CN106548418A CN106548418A CN201611128492.8A CN201611128492A CN106548418A CN 106548418 A CN106548418 A CN 106548418A CN 201611128492 A CN201611128492 A CN 201611128492A CN 106548418 A CN106548418 A CN 106548418A
- Authority
- CN
- China
- Prior art keywords
- random
- variable
- point
- hermite
- value
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 238000000034 method Methods 0.000 title claims abstract description 67
- 238000005286 illumination Methods 0.000 claims abstract description 72
- 239000011159 matrix material Substances 0.000 claims abstract description 39
- 238000004458 analytical method Methods 0.000 claims abstract description 33
- 238000009826 distribution Methods 0.000 claims abstract description 33
- 238000013016 damping Methods 0.000 claims abstract description 28
- 230000009466 transformation Effects 0.000 claims abstract description 9
- 238000005315 distribution function Methods 0.000 claims description 32
- 230000001186 cumulative effect Effects 0.000 claims description 30
- 230000004044 response Effects 0.000 claims description 9
- 238000000342 Monte Carlo simulation Methods 0.000 claims description 8
- 230000015572 biosynthetic process Effects 0.000 claims description 7
- 230000008859 change Effects 0.000 claims description 7
- 230000003247 decreasing effect Effects 0.000 claims description 6
- 238000003491 array Methods 0.000 claims description 4
- 238000000354 decomposition reaction Methods 0.000 claims description 4
- 230000005611 electricity Effects 0.000 claims description 4
- 230000003760 hair shine Effects 0.000 claims description 3
- 230000004069 differentiation Effects 0.000 claims description 2
- 239000004744 fabric Substances 0.000 claims description 2
- 241000229175 Calotes Species 0.000 claims 1
- 230000002902 bimodal effect Effects 0.000 abstract description 9
- 230000008569 process Effects 0.000 abstract description 7
- 238000013097 stability assessment Methods 0.000 abstract description 6
- 230000000875 corresponding effect Effects 0.000 description 21
- 238000006243 chemical reaction Methods 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 230000000694 effects Effects 0.000 description 2
- 230000011218 segmentation Effects 0.000 description 2
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 description 1
- 238000009825 accumulation Methods 0.000 description 1
- 230000009471 action Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000005540 biological transmission Effects 0.000 description 1
- 238000004364 calculation method Methods 0.000 description 1
- 230000001276 controlling effect Effects 0.000 description 1
- 230000002596 correlated effect Effects 0.000 description 1
- 238000001514 detection method Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 230000007613 environmental effect Effects 0.000 description 1
- 230000035699 permeability Effects 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
- 230000001360 synchronised effect Effects 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q50/00—Information and communication technology [ICT] specially adapted for implementation of business processes of specific business sectors, e.g. utilities or tourism
- G06Q50/06—Energy or water supply
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q10/00—Administration; Management
- G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
- G06Q10/063—Operations research, analysis or management
- G06Q10/0639—Performance analysis of employees; Performance analysis of enterprise or organisation operations
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
- Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
- Y04S10/00—Systems supporting electrical power generation, transmission or distribution
- Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications
Landscapes
- Business, Economics & Management (AREA)
- Human Resources & Organizations (AREA)
- Engineering & Computer Science (AREA)
- Economics (AREA)
- Strategic Management (AREA)
- Theoretical Computer Science (AREA)
- Entrepreneurship & Innovation (AREA)
- Educational Administration (AREA)
- Marketing (AREA)
- Development Economics (AREA)
- Health & Medical Sciences (AREA)
- Tourism & Hospitality (AREA)
- Physics & Mathematics (AREA)
- General Business, Economics & Management (AREA)
- General Physics & Mathematics (AREA)
- Public Health (AREA)
- Primary Health Care (AREA)
- Water Supply & Treatment (AREA)
- General Health & Medical Sciences (AREA)
- Game Theory and Decision Science (AREA)
- Operations Research (AREA)
- Quality & Reliability (AREA)
- Complex Calculations (AREA)
Abstract
The invention discloses a kind of power system small interference stability appraisal procedure, is related to Operation of Electric Systems analysis and control field.Methods described comprises the steps：Set up the little interference analysis model of photovoltaic system；Calculate the correlation matrix of stochastic inputs variable；Be converted to the correlation matrix of the random vector of standardized normal distribution；Hermite chaos multinomial is generated using Line independent point collocation and matches somebody with somebody point；Nataf is adopted to become the point transformation of matching somebody with somebody of changing commanders into corresponding illumination value and random load value；Obtain corresponding random input variable value；Try to achieve the coefficient of Hermite chaos polynomial expansions；Hermite chaos polynomial expansions to obtaining are emulated, and try to achieve the distribution character of random output variable using Density Estimator, assess the probability of small interference stability.Methods described can process the bimodal problem of illumination patterns, effectively estimate the projection of the bimodal and CDF of the PDF of critical mode damping ratio, obtain more preferable Stability Assessment result.
Description
Technical field
The present invention relates to the control method technical field of power system, more particularly to a kind of power system small interference stability is commented
Estimate method.
Background technology
Due to environmental constraints and energy sustainable supply demand, clean reproducible new forms of energy and greatly developed, its
Permeability in power system is improved constantly, and at present, photovoltaic generation has become the larger generation of electricity by new energy of accounting in power system
Form.
While photovoltaic generation continuously injects clean energy resource for system, the little interference of power system is also contributed to steady
Determine characteristic, increased the uncertain factor of power system.First, the interference little to power system of photovoltaic generating system internal dynamic is steady
Fixed impact be can not ignore, and should give fully modeling.Its impact shows：1) MPPT maximum power point tracking (maximum power
Point tracking, MPPT) under pattern the fluctuation of photovoltaic power output can affect the power output of synchronous generator and important
The trend of circuit.2) affected by zero inertia of photovoltaic generating system, after conventional electric generators are substituted, the total inertia of system reduces.3)
The controlling unit of photovoltaic generating system and bad parameter may reduce damping torque.Secondly, photovoltaic generating system is to power train
The Small signal stability analysis of system increased new stochastic variable.Photovoltaic generating system is generally in maximal power tracing operation mould
Formula, due to the uncertainty of illumination, is affected by illumination fluctuation, and its active exerting oneself will be chronically at dynamic tracking process, present
Go out strong randomness.Photovoltaic generating system under some illumination may cause the appearance of power system negative damping, be that little interference is steady
Surely bring threat.Then, photovoltaic generating system has very important correlation with load, should give consideration.
The assessment of power system small interference stability is to process stochastic variable and provide the effective of power system stability operation probability
Means.As power system is non-linear, complexity, the method for finding quick and precisely assessment small interference stability will be with important meaning
Justice.Method common at present has Monte Carlo simulation, point estimations, Cumulants method etc..Monte Carlo simulation is most accurate
Method, but it is time-consuming, the model analysis of a large amount of repeatability is needed, so there are more applications in detection accuracy.Point estimation
Method is proposed by Rosenblueth, by constantly improve, such as widely used 2m+1 methods, and which being capable of accurate estimated probability density
The front quadravalence of function is away from and may be without solution when m is too big.Cumulants method can be used in any distribution input, employ line
Propertyization process, more reflects local characteristicses.As seen from the above analysis, the method for occurring in prior art has necessarily
Limitation, using effect is bad.
The content of the invention
The technical problem to be solved is how to provide a kind of bimodal problem that can process illumination patterns, effectively
The PDF for estimating critical mode damping ratio bimodal and CDF projection, and the power system small interference stability of precise control
Appraisal procedure.
To solve above-mentioned technical problem, the technical solution used in the present invention is：A kind of power system small interference stability is commented
Estimate method, it is characterised in that methods described comprises the steps：
Set up the little interference analysis model of photovoltaic system；
It is stochastic inputs variable to take the illumination with correlation and random load, calculates the coefficient correlation of stochastic inputs variable
Matrix；
The correlation matrix of stochastic inputs variable is converted to the coefficient correlation square of the random vector of standardized normal distribution
Battle array；
Determine the exponent number in the random response face of the correlation matrix of the random vector of standardized normal distribution, using linear only
Vertical point collocation generates Hermite chaos multinomial and matches somebody with somebody point；
Nataf is adopted to become the point transformation of matching somebody with somebody of changing commanders into corresponding illumination value and random load value；
According to the illumination value and random load value that obtain, model analysis is carried out, critical mode damping ratio is taken for random output
Variable, obtains corresponding random input variable value；
Hermite chaos polynomial expansion will be substituted into random input variable value with point value, try to achieve Hermite chaos multinomial
The coefficient that formula is launched；
Using Monte Carlo method, the Hermite chaos polynomial expansions to obtaining are emulated, are asked using Density Estimator
The distribution character of random output variable is obtained, the probability of small interference stability is assessed.
Further technical scheme is：The described method for setting up the little interference analysis model of photovoltaic system is as follows：
The structure of photovoltaic system is that the secondary light volt for including photovoltaic array, boost, inverter, wave filter and phaselocked loop is sent out
Electric system, wherein, the output characteristics of photovoltaic cell adopts engineering calculating method, function of the battery temperature for illumination, whole photovoltaic
The stochastic inputs variable of system model is illumination and random load；
Its control model is that MPPT maximum power point tracking controls and determine inverter direct-current voltage control, wherein, all control rings
Section is controlled using PI, and, in the unity power factor method of operation, DC side voltage of converter is constant by inverter for invertor operation
Active power ring realizes that boost low-pressure side voltages size is determined by MPPT maximum power point tracking control；
Linearized in photovoltaic system operating point, set up the photovoltaic system algebraic differentiation suitable for Small signal stability analysis
Equation, the photovoltaic system algebraic differential equation are combined with generator algebraic differential equation and network algebra equation, you can contained
The power system Linearized state equations of photovoltaic system.
Further technical scheme is：Described takes the illumination with correlation and random load for stochastic inputs change
Amount, the method for calculating the correlation matrix of stochastic inputs variable are as follows：
It is stochastic inputs vector that setting tool has the illumination of correlation and random load active power:
X=[RPV,PL]T
In formula, RPV=[r1,…,ri,…,rn] for the illumination of photovoltaic system, riFor the illumination of i-th photovoltaic system, n is
The number of photovoltaic system, PL=[p1,…,pj,…,pm] for random load, pjFor j-th random load, m is the individual of random load
Number；
The analysis period is set, the history photometric data D of the period photovoltaic system is obtainedR=[Dr1,…,Drn] and random load
Historical load data DL=[DL1,…,DLm], K is the number of historical data, then DRDimension is K × n, DLDimension is K × m；
Using Density Estimator, the probability density function f of history photometric data is soughtri(ri) and cumulative distribution function Fri
(ri), i represents i-th photovoltaic system；Seek the probability density function f of historical load datapj(pj) and cumulative distribution function Fpj
(pj), j represents j-th random load, calculates the coefficient correlation between stochastic variable, and formula is as follows：
In formula, xiAnd xjFor any two stochastic variable in X,WithIt is xiAnd xjMean value, ρijIt is xiAnd xjCorrelation
Coefficient；The coefficient correlation of any two stochastic variable in calculated X is arranged according to the order of stochastic variable in X,
Obtain the correlation matrix of X
Further technical scheme is：The described correlation matrix by stochastic inputs variable is converted to standard normal
The method of the correlation matrix of the random vector of distribution is as follows：
Following implicit function is solved, the coefficient correlation between stochastic inputs variable is converted to the phase between standard normal random variable
Relation number
In formula, XiAnd XjFor any two stochastic inputs variable in X, meet Nataf distributions, YiAnd YjIt is and XiAnd XjCorrespondence
Standard normal random variable,WithIt is XiAnd XjMean value and standard deviation, Φ () be standard normal with
The cumulative distribution function of machine variable, φ2(Yi, Yj, ρ0ij) it is YiAnd YjJoint probability density function, ρij0It is YiAnd YjCorrelation
Coefficient；
By ρij0According to XiAnd XjOrder in X is arranged, obtain stochastic inputs variable standardized normal distribution with
The correlation matrix C of machine vectorY
Further technical scheme is：The correlation matrix of the random vector for calibrating really quasi normal distribution
The exponent number in random response face, generates method of the Hermite chaos multinomial with point using Line independent point collocation as follows：
The exponent number l of the Hermite chaos polynomial expansions that random response face adopts, wherein 2-5 ranks are determined as needed
Hermite chaos polynomial expansions are as follows：
In formula, ξ is random output variable,It is independent standard normal random vector, represents random defeated
Enter variable, n is the number of element in vectorial U,For n rank Hermite multinomials
When the free degree of random output variable is q, the item number of p rank Hermite chaos polynomial expansions isThe undetermined coefficient of each is set to a0, ai1, ai1i2, ai1i2i3, ai1i2,...,in, define a=[a0, ai1, ai1i2,
ai1i2i3, ai1i2,...,in]；
Then Hermite chaos polynomial expansion is expressed as ξ=Ha, and H is made up of Hermite chaos multinomials；
Using Line independent probability point collocation ask Hermite chaos polynomial expansions with point, number is
Further technical scheme is：Described employing Line independent probability point collocation seeks Hermite chaos multinomials
The method with point launched is as follows：
1) p+1 rank Hermite root of polynomials are calculated, permutation and combination goes out all possible with point；
2) form symmetrical with point group according to point with regard to the symmetry of origin；
3) according to the symmetrical order successively decreased with point group probability, check each symmetrical successively with point group, it is all until what is chosen
With a H battle array full rank for being formed, with the selected condition of a group it is：The newly-increased symmetrical H for matching somebody with somebody point group and all having matched somebody with somebody a little group formation
It is linear unrelated；
If 4) symmetrical all detect with point group, H battle arrays still not full rank, then according to the order successively decreased with a probability, successively
Check each single with point, all with a H battle array full rank for being formed until what is chosen, the single condition selected with point is：It is newly-increased
It is single linear unrelated with the H for all having matched somebody with somebody a little formation with point.
Further technical scheme is：Adopt Nataf become change commanders it is described with point transformation into corresponding illumination value with it is random
The method of load value is as follows：
Calculate the combination of stochastic inputs variable：Photometric data is divided into into bloom and shines DRHWith low illumination DRLTwo groups：
DRH={ Dr1H,…,DriH,…,DrnH},DRL={ Dr1L,…,DriL,…,DrnL}
In formula, DriHData amount check be KiH, DRiLData amount check be KiL；Using Density Estimator, bloom is asked to shine DRHWith
Low illumination DRLIn each data probability density function friH(riH)、friL(riL) and cumulative distribution function FriH(riH)、FriL
(riL)；
According to DRH、DRLAnd DL, list the data combination of all possible stochastic inputs variable：
Dg={ [DPV,DL]|DPV=[DPV1,…,DPVi,…,DPVn], DPVi∈{DriH,DriL}}
DgHave 2nIndividual element；
For DgIn each element, adopting Nataf to become, to change commanders with point transformation be corresponding illumination value and random load value, such as
For element [DPV1,…,DPVi,…,DPVn,DL], wherein, DPV1=Dr1H, { DPV2..., DPVn}∈DRL：
1) to correlation matrix CYCarry out Cholesky decomposition
CY=BBT
In formula, B is CYJing Cholesky decompose the lower triangular matrix for obtaining；
2) by independent standard normal random variable space with point UCBe transformed to the standard normal with correlation at random to
Amount YC：YC=BUC；
3) principle is converted according to equiprobability, by YCBe converted to former stochastic inputs vector；
In formula,It is [DPV1,…,DPVi,…,DPVn,DL] in arbitrary element edge cumulative distribution function anti-letter
Number, if the element is DPV1, then edge cumulative distribution function is Fr1HIf the element is DPV2,…,DPVn, then edge accumulation
Distribution function is Fr1L(r1L),…,FrnL(rnL)；XCiFor the former stochastic inputs variate-value obtained；Repeat 1) -3), you can obtain Dg
The former stochastic inputs vector of middle all elements, is designated as Xg=[Xg1,…,Xgi,…,Xgw], in formula, 1<i<2n, w=2n；
Obtain corresponding to Dg={ [DPV,DL]|DPV=[DPV1,…,DPVi,…,DPVn] illumination with random load value be
Xg。
Further technical scheme is：Illumination value and random load value that described basis is obtained, carry out model analysis,
It is random output variable to take critical mode damping ratio, and the method for obtaining corresponding random input variable value is as follows：
By the illumination value for obtaining and random load value XgBring the little interference analysis model of photovoltaic system into, carry out model analysis and obtain
To corresponding random input variable value ξg=[ξg1,…,ξgi,…,ξgw], in formula, 1<i<2n, w=2n；
Further technical scheme is：Described will be more with point value and random input variable value substitution Hermite chaos
Item formula is launched, and the method for trying to achieve the coefficient of Hermite chaos polynomial expansions is as follows：
By the illumination value for obtaining and random load value XgWith random input variable value ξgIt is multinomial that Hermite chaos is substituted into respectively
Formula is launched, by ξgAs the output of Hermite chaos polynomial expansions, using with point Hermite chaos polynomial expansion as
Input, obtains the coefficient of Hermite chaos polynomial expansions, is designated as ag=[ag1,…,agi,…,agw]。
Further technical scheme is：Described employing Monte Carlo method, the Hermite chaos multinomial exhibitions to obtaining
Drive capable emulation into, the distribution character of random output variable is tried to achieve using Density Estimator, assess the side of the probability of small interference stability
Method is as follows：
The accounting of each stochastic variable data combination is calculated, for DgMiddle element [DPV1,…,DPVi,…,DPVn,DL], its
In, DPV1=Dr1H, { DPV2..., DPVn}∈DRL, accounting is
(K1H/K)×(K2L/K)×…×(KiL/K)×…×(KnL/K),2<i<n
By calculated accounting according to the element in XgIn corresponding order arranged, obtain Tg=[Tg1,…,
Tgi,…,Tgw], in formula, 1<i<2n, w=2n；
M U vector value is generated, which is assigned to into each stochastic variable data combination according to accounting, each group will obtain Mg=
MTgIndividual U values；The U values that each group is obtained, bring the corresponding Hermite chaos polynomial expansion of the group into, try to achieve corresponding random defeated
Go out the value of variable；It is ξ to remember that all stochastic variable data combine the value of the random output variable for obtainingM, i.e. key model damping ratio
Value be ξM, its number is M；
Using Density Estimator, ξ is soughtMCumulative distribution function FξM(ξM), the FξM(ξM) it is critical mode damping ratio
Cumulative distribution function；
Small interference stability is assessed with small interference stability probability：The unstable probability of little interference is FξM(0), small interference stability
Probability be 1-FξM(0)。
Using the beneficial effect produced by above-mentioned technical proposal it is：The bimodal problem of illumination patterns can be processed；Can
Estimate well critical mode damping ratio PDF it is bimodal；Can be good at estimating critical mode damping ratio CDF it is convex
Rise；With very accurate small interference stability assessment result.
Description of the drawings
The present invention is further detailed explanation with reference to the accompanying drawings and detailed description.
Fig. 1 is the flow chart of embodiment of the present invention methods described；
Fig. 2 is the theory diagram of embodiment of the present invention photovoltaic generating system；
Fig. 3 is that the embodiment of the present invention sets up the little interference analysis model figure of photovoltaic system；
Fig. 4 is linear independent probability point collocation flow chart in embodiment of the present invention methods described；
Fig. 5 is the 39 node electricity generation system theory diagram of IEEE10 machines containing photovoltaic access in the embodiment of the present invention；
Fig. 6 a are illumination probability density function figures in the embodiment of the present invention；
Fig. 6 b are illumination cumulative distribution function figures in the embodiment of the present invention；
Fig. 6 c are Load Probability density function figures in the embodiment of the present invention；
Fig. 6 d are load cumulative distribution function figures in the embodiment of the present invention；
Fig. 7 a are segmentation illumination probability density function figures in the embodiment of the present invention；
Fig. 7 b are segmentation illumination cumulative distribution function figures in the embodiment of the present invention；
Fig. 8 a are critical mode damping ratio probability density function figures in the embodiment of the present invention；
Fig. 8 b are critical mode damping ratio cumulative distribution function figures in the embodiment of the present invention；
Wherein：1-39 represents the 1st to No. 39 bus respectively；40th, interconnect transmission line 41, electricity become station transformer 42, etc.
Effect lumped-parameter system 43, equivalent step-up transformer 44, photovoltaic plant.
Specific embodiment
With reference to the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete
Ground description, it is clear that described embodiment a part of embodiment only of the invention, rather than the embodiment of whole.It is based on
Embodiment in the present invention, it is every other that those of ordinary skill in the art are obtained under the premise of creative work is not made
Embodiment, belongs to the scope of protection of the invention.
Many details are elaborated in the following description in order to fully understand the present invention, but the present invention can be with
It is different from alternate manner described here to implement using other, those skilled in the art can be without prejudice to intension of the present invention
In the case of do similar popularization, therefore the present invention is not limited by following public specific embodiment.
Theory analysis：
A. stochastic inputs are represented
1) independent stochastic inputs
The first step is to represent input random variable vector X using standardized normal distribution stochastic variable (SRVs)
In formulaFor the inverse function of the cumulative distribution function of X, cumulative distribution letters of the Φ () for standardized normal distribution
Number.UiIt is the standard normal variable with zero-mean and unit variance, this is often random from independent identically distributed standard normal
Select in variable.
2) related stochastic inputs and Nataf conversion
I-th independent input X in formula (1)iUncertainty directly by i-th independent random input variable UiFunction
Represent.However, equation (1) might not be set up in power system, because stochastic inputs vector X is generally relative to each other.Therefore, may be used
Independent standard normal random variable U is transformed to become related non-standard stochastic variable in the vectorial X that changes commanders using Nataf.
Assume that above-mentioned related random vector X there are marginal probability density function CDF FXi(Xi), (i=1 ..., n) and phase relation
Matrix number CX
Wherein ρijWith cov (Xi,X j) it is coefficient correlation XiAnd XjIncidence coefficient and covariance,WithIt is X respectivelyi
And XjStandard deviation.First, changed according to equiprobability, XiWith standard normal variable YiCDF meetThat is phase
Close stochastic variable XiStandardized normal stochastic variable Y with zero-mean and unit norm deviation can be converted intoi
Arrangement YiOne and Matrix C will be formedYWith marginal probability density function φn(Y,CY) vector correlation n dimension standard just
State vector Y
ρ0ijIt is YiAnd YjCoefficient correlation.Matrix CYMiddle element can be obtained by solving following formula
WithIt is mean value and correlated random variables XjStandard deviation.
WhenMarginal probability distribution function and XiAnd XjCorrelation coefficient ρijWhen known, by solving shown in formula (7)
Nonlinear equation just can determine that equivalent correlation coefficient ρ0ij, work as CY, it is known that the correlation matrix to standard normal random variable
CYCarry out Cholesky decomposition
CY=BBT (8)
B is CYJing Cholesky decompose the lower triangular matrix for obtaining.Can be by relevant criterion normal random variable vector using B
Y is converted to independent standard normal random vector U.
U=B-1Y (9)
So far the direct transform process of Nataf conversion is completed, original related non-standard random variable vector X can be represented by vectorial U
B. estimate output
Output performance is estimated by using Hermite chaos polynomial expansion, can be by complication system Implicitly function relation
Replaced by simple explicit function.In this step, all of stochastic inputs need to be considered because any stochastic inputs can all affect with
Machine is exported.Output and input can be expressed as the function of identical standard normal random variable.
Random output variable can adopt following Hermite random number polynomials to launch to estimate：
It is the vector of the standard normal random variable for representing stochastic inputs, n becomes at random for standard normal
The number of amount；For n rank Hermite multinomials, its computing formula：
When random output is when the free degree in random space is n, the item number N that p rank Hermite random number polynomials launcha's
Computing formula：
C. calculate the coefficient of random number polynomial expanded expression
First, adopt probability point collocation (PCM) and provide for standard normal random vector U with point.Secondly, using formula (10) or
(1) calculate corresponding to point be originally inputted random vector X.Then, by model analysis, Z=[Z are exported accordingly1,
Z2,…,ZN]T, so, formula (11) can be replaced by：
Z=Ha (14)
Wherein, H is N × NaDimension separate space matrix, the formula can solve unknowm coefficient a.
The principle of probability point collocation is：1) what generally, p ranks random number polynomial launched is many by p+1 rank Hermite with point
The root of formula is determining the value of input stochastic variable, alternative with counting out as (p+1)n.2) choose the number with point
The number of undetermined coefficient is typically more than.3) match somebody with somebody point in prioritizing selection high probability region.4) with point as far as possible with regard to origin symmetry.5)
Matrix H full rank.
To according to these principles, the present invention provides the probability point collocation (Fig. 4) of a Line independent.It is one by one with point
Selected.When only Hermite multinomials information matrix is Line independent, should match somebody with somebody point just can be selected.First, from regard to original
Point symmetry and high probability are screened with point so that H is linear uncorrelated.Secondly, when being symmetrically insufficient to allow H battle array full ranks with point,
From high probability it is asymmetric with point in screened so that H is linear uncorrelated.Until H battle arrays reach full rank.
D. the application of stochastic response surface
After unknowm coefficient in formula (11) determines, p rank Hermite chaos multinomials can be used for small interference stability assessment.
Using Monte Carlo method (MCS), formula (11) is emulated in a large number, then using the random output (critical mode damping ratio) of estimation
PDF and CDF, finally, probability of the critical mode damping ratio more than 0, i.e., stable general of little probability of interference are obtained by CDF
Rate.
Analyze by more than, it is overall, as shown in figure 1, a kind of the invention discloses power system small interference stability assessment
Method, methods described comprise the steps：
S101：Set up consider photovoltaic generating system internal dynamics, using the light of MPPT maximum power point tracking operational mode
The little interference analysis model of volt system.
S102：Model analysis is carried out, and critical mode damping ratio is taken for random output variable；
S103：It is stochastic inputs variable to take the illumination with correlation and random load, obtains stochastic inputs variable history
Data, try to achieve the distribution character of stochastic inputs variable using Density Estimator, calculate the correlation matrix of stochastic inputs variable；
S104：The correlation matrix of stochastic inputs variable is converted to the phase relation of the random vector of standardized normal distribution
Matrix number；
S105：Determine the exponent number in random response face, Hermite chaos multinomials are generated using Line independent point collocation and is matched somebody with somebody
Point；
S106：Adopt Nataf to become to change commanders with point transformation as corresponding illumination value and random load value；
S107：According to the illumination value and random load value that obtain, carry out model analysis and obtain corresponding random output variable
Value；
S108：Hermite chaos polynomial expansion will be substituted into random input variable value with point value, and try to achieve Hermite and mix
The coefficient of ignorant polynomial expansion；
S109：Using Monte Carlo method, the Hermite chaos polynomial expansions to obtaining are emulated, using cuclear density
The distribution character of random output variable is tried to achieve in estimation, assesses the probability of small interference stability.
Specifically, described step S101 specifically includes following steps：
S1011:The little interference analysis model of photovoltaic system is set up, as Figure 2-3：
Its structure is the secondary light photovoltaic generating system for including photovoltaic array, boost, inverter, wave filter, phaselocked loop, its
In, the output characteristics of photovoltaic cell adopts engineering calculating method, and battery temperature is the function of illumination, whole photovoltaic system model
Stochastic inputs variable is illumination；
Its control model is that MPPT maximum power point tracking controls and determine inverter direct-current voltage control, wherein, all control rings
Section is controlled using PI, and, in the unity power factor method of operation, DC side voltage of converter is constant by inverter for invertor operation
Active power ring realizes that boost low-pressure side voltages size is determined by MPPT maximum power point tracking control；
Step S1012:Linearized in photovoltaic system operating point, set up the photovoltaic system suitable for Small signal stability analysis
System algebraic differential equation.The photovoltaic system algebraic differential equation is combined with generator algebraic differential equation and network algebra equation,
The power system Linearized state equations containing photovoltaic system can be obtained.
Described step S103 specifically includes following steps：
S1031:It is stochastic inputs vector that setting tool has the illumination of correlation and random load active power:
X=[RPV,PL]T (17)
In formula, RPV=[r1,…,ri,…,rn] for the illumination of photovoltaic system, riFor the illumination of i-th photovoltaic system, n is
The number of photovoltaic system, PL=[p1,…,pj,…,pm] for random load, pjFor j-th random load, m is the individual of random load
Number.
S1032:Analysis period, such as the 11 of August are set:30-12:30, obtain the history illumination number of the period photovoltaic system
According to DR=[Dr1,…,Drn] and random load historical load data DL=[DL1,…,DLm], K is the number of historical data, then DR
Dimension is K × n, DLDimension is K × m；
S1033：Using Density Estimator, the probability density function f of history photometric data is soughtri(ri) and cumulative distribution function
Fri(ri), i represents i-th photovoltaic system：Seek the probability density function f of historical load datapj(pj) and cumulative distribution function Fpj
(pj), j represents j-th random load.The coefficient correlation between stochastic variable is calculated, formula is as follows：
In formula, xiAnd xjFor any two stochastic variable in X,WithIt is xiAnd xjMean value, ρijIt is xiAnd xjCorrelation
Coefficient.The coefficient correlation of any two stochastic variable in calculated X is arranged according to the order of stochastic variable in X,
Obtain the correlation matrix of X
Step S104 specifically includes following steps：
S1041：Following implicit function is solved, the coefficient correlation between stochastic inputs variable is converted to into standard normal random variable
Between coefficient correlation
In formula, XiAnd XjAny two stochastic inputs variable in the X of position, meets Nataf distributions, YiAnd YjIt is and XiAnd XjCorrespondence
Standard normal random variable,WithIt is XiAnd XjMean value and standard deviation, Φ () is standard normal
The cumulative distribution function of stochastic variable, φ2(Yi,Yj, ρ0ij) it is YiAnd YjJoint probability density function, ρij0It is YiAnd YjPhase
Relation number.
S1042：By ρ ij0 according to XiAnd XjOrder in X is arranged, and obtains that (stochastic inputs variable is in standard normal
The correlation matrix of the random vector of distribution) CY
Step S105 specifically includes following steps：
S1051:The exponent number l of the Hermite chaos polynomial expansions that random response face adopts is determined as needed, and exponent number is got over
Height, the degree of accuracy are higher.Usual 3 rank or so can meet required precision.2-5 rank Hermite chaos polynomial expansions are given below：
In formula, ξ is random output variable,It is independent standard normal random vector, represents random defeated
Enter variable, n is the number of element in vectorial U,For n rank Hermite multinomials
When the free degree of random output variable is q, the item number of p rank Hermite chaos polynomial expansions is
The undetermined coefficient of each is set to a0, ai1, ai1i2, ai1i2i3, ai1i2,...,in, define a=[a0, ai1, ai1i2, ai1i2i3,
ai1i2,...,in]。
Then Hermite chaos polynomial expansion can be expressed as ξ=Ha, and H is made up of Hermite chaos multinomials.
S10512:Using Line independent probability point collocation (such as Fig. 4) ask Hermite chaos polynomial expansions with point, it is individual
Number is
1) p+1 rank Hermite root of polynomials are calculated, permutation and combination goes out all possible with point；
2) form symmetrical with point group according to point with regard to the symmetry of origin；
3) according to the symmetrical order successively decreased with point group probability, check each symmetrical successively with point group, it is all until what is chosen
With a H battle array full rank for being formed.With the selected condition of a group it is：The newly-increased symmetrical H for matching somebody with somebody point group and all having matched somebody with somebody a little group formation
It is linear unrelated；
If 4) symmetrical all detect with point group, H battle arrays still not full rank, then according to the order successively decreased with a probability, successively
Check each single with point, it is all with a H battle array full rank for being formed until what is chosen.It is single with putting selected condition to be：It is newly-increased
It is single linear unrelated with the H for all having matched somebody with somebody a little formation with point.So far, obtain matching somebody with somebody for U in Hermite chaos polynomial expansions
Point.
Step S106 specifically includes following steps：
S1061:Calculate the combination of stochastic variable：Generally history photometric data is presented obvious bimodal distribution, by illumination number
D is shone according to bloom is divided intoRHWith low illumination DRLTwo groups：
DRH={ Dr1H,…,DriH,…,DrnH},DRL={ Dr1L,…,DriL,…,DrnL} (27)
In formula, DriHData amount check be KiH, DRiLData amount check be KiL.Using Density Estimator, bloom is asked to shine DRHWith
Low illumination DRLIn each data probability density function friH(riH)、friL(riL) and cumulative distribution function FriH(riH)、FriL(riL)；
S1062:Shine or low illumination as illumination can take bloom, so according to DRH、DRLAnd DL, list all possible
The data combination of stochastic variable：
Dg={ [DPV,DL]|DPV=[DPV1,…,DPVi,…,DPVn], DPVi∈{DriH, DriL}} (28)
It can be seen that, DgHave 2nIndividual element.
S1063:For middle DgEach element, adopts Nataf changes to change commanders negative with random into corresponding illumination value with point transformation
Charge values.Such as element [DPV1,…,DPVi,…,DPVn,DL], wherein, DPV1=Dr1H,{DPV2,…,DPVn}∈DRL：
1) to correlation matrix CYCarry out Cholesky decomposition
CY=BBT (29)
In formula, B is CYJing Cholesky decompose the lower triangular matrix for obtaining.
2) independent standard normal random variable space (is denoted as into U with pointC) it is transformed to the standard normal with correlation
Random vector YC：YC=BUC.
3) principle is converted according to equiprobability, by YCBe converted to former stochastic inputs vector (illumination and random load)；
In formula,It is [D in step S1062PV1,…,DPVi,…,DPVn,DL] inner arbitrary element edge cumulative distribution
The inverse function of function, if the element is DPV1, then edge cumulative distribution function is Fr1HIf the element is DPV2,…,DPVn,
Then edge cumulative distribution function is Fr1L(r1L),…,FrnL(rnL)；XCiFor the former stochastic inputs variate-value obtained.So far, obtain
Corresponding to DgMiddle element [DPV1,…,DPVi,…,DPVn,DL] the vector illumination of former stochastic inputs and random load value.Repeatedly 1)-
3), you can obtain DgThe former stochastic inputs vector of middle all elements, is designated as Xg=[Xg1,…,Xgi,…,Xgw], in formula, 1<i<2n,
W=2n。
Remember corresponding to Dg={ [DPV,DL]|DPV=[DPV1,…,DPVi,…,DPVn] illumination and random load value
For Xg,
Step S107 specifically includes the illumination value and random load value X for obtaining step S106gBring system model into,
Carry out model analysis and obtain corresponding random input variable value ξg=[ξg1,…,ξgi,…,ξgw], in formula, 1<i<2n, w=2n。
Step S108 specifically includes the illumination value and random load value X for obtaining step S106 and S107gWith it is random
Input variable value ξgHermite chaos polynomial expansions are substituted into respectively, by ξgAs the output of Hermite chaos polynomial expansions,
Using with point Hermite chaos polynomial expansion as input, obtain the coefficient of Hermite chaos polynomial expansions, be designated as ag
=[ag1,…,agi,…,agw]。
Step S109 is comprised the following steps：
S1091:The accounting of each stochastic variable data combination is calculated, such as DgMiddle element [DPV1,…,DPVi,…,
DPVn,DL], wherein, DPV1=Dr1H, { DPV2..., DPVn}∈DRL, accounting is
(K1H/K)×(K2L/K)×…×(KiL/K)×…×(KnL/K),2<i<n (31)
By calculated accounting according to the element in XgIn corresponding order arranged, obtain Tg=[Tg1,…,
Tgi,…,Tgw], in formula, 1<i<2n, w=2n。
S1092:M U vector value is generated, which is assigned to into each stochastic variable data combination according to accounting, each group is incited somebody to action
To Mg=MTgIndividual U values.The U values that each group is obtained, bring the corresponding Hermite chaos polynomial expansion of the group into, try to achieve corresponding
The value of random output variable.Remember the random output variable (i.e. critical mode damping ratio) that all stochastic variable data combinations are obtained
It is worth for ξM, its number is M.
S1093：Using Density Estimator, ξ is soughtMCumulative distribution function FξM(ξM), the FξM(ξM) it is critical mode resistance
The cumulative distribution function of Buddhist nun's ratio.
S1094：Small interference stability is assessed with small interference stability probability：The unstable probability of little interference is FξM(0) it is, little dry
Stable probability is disturbed for 1-FξM(0)。
Enforcement with example to the present invention below in conjunction with the accompanying drawings is described further, but the enforcement of the present invention and comprising not limiting
In this.
By taking 10 machine, 39 node power system as an example, as shown in figure 5, No. 19 bus accesses photovoltaic system.G1-G10 in Fig. 5
Generator is represented, A1-A2 and A4-A5 represents region, BP1-BP4Represent bus.
Determine stochastic inputs vector：Illumination and positioned at the 16th bus and random 16th random load and the 20th of the 20th bus
Random load.It is determined that random output variable：When illumination takes standard 1000M/m2, when random load takes calculation of tidal current, correspondence
Critical mode be 0.46Hz, damping ratio is 0.002, takes the mode damping ratio for random output variable.Determine that stochastic inputs become
The distribution of amount and coefficient correlation：The photometric data of the photovoltaic system takes from somewhere nearest 10 year August 11:30-12:30 history
Photometric data, random load data take from the random load data of adjoining area, using Density Estimator, obtain illumination patterns and
Power load distributing as shown in figures 6 a-6d, and calculates coefficient correlation CX, it is converted into CY。
Determine that Hermite chaos polynomial expansion exponent numbers are taken as 3, ask Hermite to mix using Line independent probability point collocation
Ignorant polynomial expansion with point UC.Determine packet：Illumination is divided into into bloom and shines DrHWith low illumination DrLTwo groups of data, then at random
Variable data combines Dg={ Dg1, Dg2, Dg1=[DrH,DL16,DL20],Dg2=[DrL,DL16,DL20].Asked using Density Estimator
Respective distribution character, as shown in Fig. 7 a-7b.Converted using Nataf and calculate with point respectively corresponding to Dg1And Dg2Illumination with it is random
Load value Xg1And Xg2.By each group illumination and random load value Xg1And Xg2Bring model analysis into, obtain the damping of each group critical mode
Than ξ g1And ξg2；Bring Hermite chaos polynomial expansions into, obtain each group coefficient ag1And ag2。
The probability density function and cumulative distribution function of critical mode damping ratio are asked using Monte Carlo simulation：Calculate Dg1
And Dg2Accounting Tg1And Tg2, 1000 U values are generated, then Mg1=1000Tg1And Mg2=1000Tg2, U is substituted into into each group
Hermite chaos polynomial expansions, try to achieve all groups of critical mode damping ratio ξM.Using Density Estimator, ξ is soughtMIterated integral
Cloth function FξM(ξM), the FξM(ξM) it is the cumulative distribution function of critical mode damping ratio.As a result as shown in Figure 8 a-8b, wherein,
Monte Carlo is carried out with model analysis, for representing legitimate reading.It can be seen that, the method that the present invention is provided can process illumination
The bimodal problem of distribution；Estimate well critical mode damping ratio PDF it is bimodal；Critical mode damping is estimated well
The projection of the CDF of ratio；With very accurate small interference stability assessment result.According to Fig. 8 b, it can be estimated that obtain the system little
The probability of interference stability is 89%.The small interference stability assessment result will be provided to traffic control personnel control power system stability
Effective information.
Claims (10)
1. a kind of power system small interference stability appraisal procedure, it is characterised in that methods described comprises the steps：
Set up the little interference analysis model of photovoltaic system；
It is stochastic inputs variable to take the illumination with correlation and random load, calculates the coefficient correlation square of stochastic inputs variable
Battle array；
The correlation matrix of stochastic inputs variable is converted to the correlation matrix of the random vector of standardized normal distribution；
Determine the exponent number in the random response face of the correlation matrix of the random vector of standardized normal distribution, matched somebody with somebody using Line independent
Point method generates Hermite chaos multinomial and matches somebody with somebody point；
Nataf is adopted to become the point transformation of matching somebody with somebody of changing commanders into corresponding illumination value and random load value；
According to the illumination value and random load value that obtain, model analysis is carried out, it is random output variable to take critical mode damping ratio,
Obtain corresponding random input variable value；
Hermite chaos polynomial expansion will be substituted into random input variable value with point value, try to achieve Hermite chaos multinomial exhibitions
The coefficient opened；
Using Monte Carlo method, the Hermite chaos polynomial expansions to obtaining are emulated, using Density Estimator try to achieve with
The distribution character of machine output variable, assesses the probability of small interference stability.
2. power system small interference stability appraisal procedure as claimed in claim 1, it is characterised in that described sets up photovoltaic system
The method of the little interference analysis model of system is as follows：
The structure of photovoltaic system is to include that the secondary light volt of photovoltaic array, boost, inverter, wave filter and phaselocked loop generates electricity to be
System, wherein, the output characteristics of photovoltaic cell adopts engineering calculating method, function of the battery temperature for illumination, whole photovoltaic system
The stochastic inputs variable of model is illumination and random load；
Its control model is that MPPT maximum power point tracking controls and determine inverter direct-current voltage control, wherein, all controlling units are equal
Using PI controls, in the unity power factor method of operation, DC side voltage of converter is constant by inverter active for invertor operation
Power ring realizes that boost low-pressure side voltages size is determined by MPPT maximum power point tracking control；
Linearized in photovoltaic system operating point, set up the photovoltaic system algebraic differentiation side suitable for Small signal stability analysis
Journey, the photovoltaic system algebraic differential equation are combined with generator algebraic differential equation and network algebra equation, you can obtained containing light
The power system Linearized state equations of volt system.
3. power system small interference stability appraisal procedure as claimed in claim 1, it is characterised in that described takes with correlation
Property illumination and random load be stochastic inputs variable, calculate stochastic inputs variable correlation matrix method it is as follows：
It is stochastic inputs vector that setting tool has the illumination of correlation and random load active power:
X=[RPV,PL]T
In formula, RPV=[r1,…,ri,…,rn] for the illumination of photovoltaic system, riFor the illumination of i-th photovoltaic system, n is photovoltaic
The number of system, PL=[p1,…,pj,…,pm] for random load, pjFor j-th random load, numbers of the m for random load；
The analysis period is set, the history photometric data D of the period photovoltaic system is obtainedR=[Dr1,…,Drn] and random load go through
History load data DL=[DL1,…,DLm], K is the number of historical data, then DRDimension is K × n, DLDimension is K × m；
Using Density Estimator, the probability density function f of history photometric data is soughtri(ri) and cumulative distribution function Fri(ri), i tables
Show i-th photovoltaic system；Seek the probability density function f of historical load datapj(pj) and cumulative distribution function Fpj(pj), j is represented
J-th random load, calculates the coefficient correlation between stochastic variable, and formula is as follows：
In formula, xiAnd xjFor any two stochastic variable in X,WithIt is xiAnd xjMean value, ρijIt is xiAnd xjPhase relation
Number；The coefficient correlation of any two stochastic variable in calculated X is arranged according to the order of stochastic variable in X, is obtained
To the correlation matrix of X
4. power system small interference stability appraisal procedure as claimed in claim 3, it is characterised in that described by stochastic inputs
The method that the correlation matrix of variable is converted to the correlation matrix of the random vector of standardized normal distribution is as follows：
Following implicit function is solved, the coefficient correlation between stochastic inputs variable is converted to the phase relation between standard normal random variable
Number
In formula, XiAnd XjFor any two stochastic inputs variable in X, meet Nataf distributions, YiAnd YjIt is and XiAnd XjCorresponding mark
Quasi- normal random variable,WithIt is XiAnd XjMean value and standard deviation, Φ () is that standard normal becomes at random
The cumulative distribution function of amount, φ2(Yi,Yj,ρ0ij) it is YiAnd YjJoint probability density function, ρij0It is YiAnd YjPhase relation
Number；
By ρij0According to XiAnd XjOrder in X is arranged, obtain stochastic inputs variable standardized normal distribution it is random to
The correlation matrix C of amountY
5. power system small interference stability appraisal procedure as claimed in claim 4, it is characterised in that it is described calibrate really it is accurate just
The exponent number in the random response face of the correlation matrix of the random vector of state distribution, is generated using Line independent point collocation
The method that Hermite chaos multinomial matches somebody with somebody point is as follows：
The exponent number l, wherein 2-5 ranks Hermite of the Hermite chaos polynomial expansions that random response face adopts are determined as needed
Chaos polynomial expansion is as follows：
In formula, ξ is random output variable,It is independent standard normal random vector, represents stochastic inputs change
Amount, n is the number of element in vectorial U,For n rank Hermite multinomials
When the free degree of random output variable is q, the item number of p rank Hermite chaos polynomial expansions is
The undetermined coefficient of each is set to a0, ai1, ai1i2, ai1i2i3, ai1i2,...,in, define a=[a0, ai1, ai1i2, ai1i2i3,
ai1i2,...,in]；
Then Hermite chaos polynomial expansion is expressed as ξ=Ha, and H is made up of Hermite chaos multinomials；
Using Line independent probability point collocation ask Hermite chaos polynomial expansions with point, number is
。
6. power system small interference stability appraisal procedure as claimed in claim 5, it is characterised in that described employing is linearly only
Vertical probability point collocation asks the method with point of Hermite chaos polynomial expansions as follows：
1) p+1 rank Hermite root of polynomials are calculated, permutation and combination goes out all possible with point；
2) form symmetrical with point group according to point with regard to the symmetry of origin；
3) according to the symmetrical order successively decreased with point group probability, check each symmetrical successively with point group, it is all with point until what is chosen
The H battle array full ranks of formation, with the selected condition of a group be：The newly-increased symmetrical H fronts matched somebody with somebody point group and all matched somebody with somebody a little group formation
Property is unrelated；
If 4) symmetrical all detect with point group, H battle arrays still not full rank, then according to the order successively decreased with a probability, is checked successively
Each single with point, all with a H battle array full rank for being formed until what is chosen, the single condition selected with point is：It is newly-increased single
It is linear unrelated with the H for all having matched somebody with somebody a little formation with point.
7. power system small interference stability appraisal procedure as claimed in claim 5, it is characterised in that become using Nataf and changed commanders
Described is that corresponding illumination value is as follows with the method for random load value with point transformation：
Calculate the combination of stochastic inputs variable：Photometric data is divided into into bloom and shines DRHWith low illumination DRLTwo groups：
DRH={ Dr1H,…,DriH,…,DrnH},DRL={ Dr1L,…,DriL,…,DrnL}
In formula, DriHData amount check be KiH, DRiLData amount check be KiL；Using Density Estimator, bloom is asked to shine DRHWith low light
According to DRLIn each data probability density function friH(riH)、friL(riL) and cumulative distribution function FriH(riH)、FriL(riL)；
According to DRH、DRLAnd DL, list the data combination of all possible stochastic inputs variable：
Dg={ [DPV,DL]|DPV=[DPV1,…,DPVi,…,DPVn], DPVi∈{DriH,DriL}}
DgHave 2nIndividual element；
For DgIn each element, adopting Nataf to become, to change commanders with point transformation be corresponding illumination value and random load value, such as
Element [DPV1,…,DPVi,…,DPVn,DL], wherein, DPV1=Dr1H,{DPV2,…,DPVn}∈DRL：
1) to correlation matrix CYCarry out Cholesky decomposition
CY=BBT
In formula, B is CYJing Cholesky decompose the lower triangular matrix for obtaining；
2) by independent standard normal random variable space with point UCIt is transformed to the standard normal random vector Y with correlationC：
YC=BUC；
3) principle is converted according to equiprobability, by YCBe converted to former stochastic inputs vector；
In formula,It is [DPV1,…,DPVi,…,DPVn,DL] in arbitrary element edge cumulative distribution function inverse function, such as
Really the element is DPV1, then edge cumulative distribution function is Fr1HIf the element is DPV2,…,DPVn, then edge cumulative distribution letter
Number is Fr1L(r1L),…,FrnL(rnL)；XCiFor the former stochastic inputs variate-value obtained；Repeat 1) -3), you can obtain DgIn own
The former stochastic inputs vector of element, is designated as Xg=[Xg1,…,Xgi,…,Xgw], in formula, 1<i<2n, w=2n；
Obtain corresponding to Dg={ [DPV,DL]|DPV=[DPV1,…,DPVi,…,DPVn] illumination and random load value be Xg。
8. power system small interference stability appraisal procedure as claimed in claim 7, it is characterised in that what described basis was obtained
Illumination value and random load value, carry out model analysis, take critical mode damping ratio for random output variable, obtain it is corresponding with
The method of machine input variable value is as follows：
By the illumination value for obtaining and random load value XgBring the little interference analysis model of photovoltaic system into, carry out model analysis and obtain phase
Random input variable value ξ answeredg=[ξg1,…,ξgi,…,ξgw], in formula, 1<i<2n, w=2n。
9. power system small interference stability appraisal procedure as claimed in claim 8, it is characterised in that it is described will with point value with
Random input variable value substitutes into Hermite chaos polynomial expansions, the method for trying to achieve the coefficient of Hermite chaos polynomial expansions
It is as follows：
By the illumination value for obtaining and random load value XgWith random input variable value ξgHermite chaos multinomial exhibitions are substituted into respectively
Open, by ξgAs the output of Hermite chaos polynomial expansions, using with point Hermite chaos polynomial expansion as input,
The coefficient of Hermite chaos polynomial expansions is obtained, a is designated asg=[ag1,…,agi,…,agw]。
10. power system small interference stability appraisal procedure as claimed in claim 9, it is characterised in that described is special using covering
Calot's method, the Hermite chaos polynomial expansions to obtaining are emulated, and try to achieve random output variable using Density Estimator
Distribution character, the method for assessing the probability of small interference stability are as follows：
The accounting of each stochastic variable data combination is calculated, for DgMiddle element [DPV1,…,DPVi,…,DPVn,DL], wherein, DPV1
=Dr1H,{DPV2,…,DPVn}∈DRL, accounting is
(K1H/K)×(K2L/K)×…×(KiL/K)×…×(KnL/K),2<i<n
By calculated accounting according to the element in XgIn corresponding order arranged, obtain Tg=[Tg1,…,Tgi,…,
Tgw], in formula, 1<i<2n, w=2n；
M U vector value is generated, which is assigned to into each stochastic variable data combination according to accounting, each group will obtain Mg=MTgIndividual U
Value；The U values that each group is obtained, bring the corresponding Hermite chaos polynomial expansion of the group into, try to achieve corresponding random output variable
Value；It is ξ to remember that all stochastic variable data combine the value of the random output variable for obtainingM, i.e. the value of key model damping ratio is
ξM, its number is M；
Using Density Estimator, ξ is soughtMCumulative distribution function FξM(ξM), the FξM(ξM) it is the iterated integral of critical mode damping ratio
Cloth function；
Small interference stability is assessed with small interference stability probability：The unstable probability of little interference is FξM(0), small interference stability is general
Rate is 1-FξM(0)。
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201611128492.8A CN106548418B (en) | 2016-12-09 | 2016-12-09 | Small interference stability evaluation method for power system |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201611128492.8A CN106548418B (en) | 2016-12-09 | 2016-12-09 | Small interference stability evaluation method for power system |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN106548418A true CN106548418A (en) | 2017-03-29 |
| CN106548418B CN106548418B (en) | 2020-12-22 |
Family
ID=58396777
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201611128492.8A Active CN106548418B (en) | 2016-12-09 | 2016-12-09 | Small interference stability evaluation method for power system |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN106548418B (en) |
Cited By (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109522519A (en) * | 2018-11-06 | 2019-03-26 | 中国兵器工业第五九研究所 | A kind of dependence evaluation method between multiple performance parameters of ammunition parts |
| CN109830987A (en) * | 2019-04-11 | 2019-05-31 | 东南大学 | The active distribution network Probabilistic Stability method of meter and distributed photovoltaic randomness |
| CN109921458A (en) * | 2019-02-22 | 2019-06-21 | 中国能源建设集团甘肃省电力设计院有限公司 | The electric system small interference stability appraisal procedure of new energy access |
| CN110350529A (en) * | 2019-07-30 | 2019-10-18 | 南方电网科学研究院有限责任公司 | Electric system small interference stability method, apparatus, equipment and storage medium |
| CN111444608A (en) * | 2020-03-24 | 2020-07-24 | 成都理工大学 | Method for determining optimal truncation order in geotechnical engineering reliability analysis |
| CN112100821A (en) * | 2020-08-26 | 2020-12-18 | 西北工业大学 | Robustness optimization design method of photovoltaic cell |
| CN112467746A (en) * | 2020-11-21 | 2021-03-09 | 东南大学 | Power distribution network optimization method considering out-of-limit risk |
| CN113964857A (en) * | 2020-07-21 | 2022-01-21 | 华北电力大学（保定） | Photovoltaic power generation access method based on perturbation method damping ratio sensitivity |
| CN116611303A (en) * | 2023-07-20 | 2023-08-18 | 华东交通大学 | Random evaluation method and system for meshing mechanical characteristics, electronic equipment and storage medium |
Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103530473A (en) * | 2013-10-25 | 2014-01-22 | 国家电网公司 | Random production analog method of electric system with large-scale photovoltaic power station |
| CN104050604A (en) * | 2014-06-10 | 2014-09-17 | 上海交通大学 | Electric power system static safety assessment method based on probabilistic tide |
| CN104079003A (en) * | 2014-07-21 | 2014-10-01 | 国家电网公司 | Probability load flow calculation method for photovoltaic power contained distribution network |
| CN104504618A (en) * | 2014-12-29 | 2015-04-08 | 天津大学 | Micro-grid reliability evaluation data sampling method based on pair-copula function |
| US20150199606A1 (en) * | 2014-01-14 | 2015-07-16 | Mitsubishi Electric Research Laboratories, Inc. | System and Method for Optimal Power Flow Analysis |
| CN106126890A (en) * | 2016-06-17 | 2016-11-16 | 河海大学 | A kind of probability optimal load flow computational methods based on stochastic response surface |
-
2016
- 2016-12-09 CN CN201611128492.8A patent/CN106548418B/en active Active
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103530473A (en) * | 2013-10-25 | 2014-01-22 | 国家电网公司 | Random production analog method of electric system with large-scale photovoltaic power station |
| US20150199606A1 (en) * | 2014-01-14 | 2015-07-16 | Mitsubishi Electric Research Laboratories, Inc. | System and Method for Optimal Power Flow Analysis |
| CN104050604A (en) * | 2014-06-10 | 2014-09-17 | 上海交通大学 | Electric power system static safety assessment method based on probabilistic tide |
| CN104079003A (en) * | 2014-07-21 | 2014-10-01 | 国家电网公司 | Probability load flow calculation method for photovoltaic power contained distribution network |
| CN104504618A (en) * | 2014-12-29 | 2015-04-08 | 天津大学 | Micro-grid reliability evaluation data sampling method based on pair-copula function |
| CN106126890A (en) * | 2016-06-17 | 2016-11-16 | 河海大学 | A kind of probability optimal load flow computational methods based on stochastic response surface |
Cited By (15)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109522519A (en) * | 2018-11-06 | 2019-03-26 | 中国兵器工业第五九研究所 | A kind of dependence evaluation method between multiple performance parameters of ammunition parts |
| CN109522519B (en) * | 2018-11-06 | 2023-02-03 | 中国兵器工业第五九研究所 | Dependency evaluation method among multiple performance parameters of ammunition component |
| CN109921458A (en) * | 2019-02-22 | 2019-06-21 | 中国能源建设集团甘肃省电力设计院有限公司 | The electric system small interference stability appraisal procedure of new energy access |
| CN109830987A (en) * | 2019-04-11 | 2019-05-31 | 东南大学 | The active distribution network Probabilistic Stability method of meter and distributed photovoltaic randomness |
| CN110350529B (en) * | 2019-07-30 | 2021-01-19 | 南方电网科学研究院有限责任公司 | Small interference stabilizing method, device, equipment and storage medium for power system |
| CN110350529A (en) * | 2019-07-30 | 2019-10-18 | 南方电网科学研究院有限责任公司 | Electric system small interference stability method, apparatus, equipment and storage medium |
| CN111444608A (en) * | 2020-03-24 | 2020-07-24 | 成都理工大学 | Method for determining optimal truncation order in geotechnical engineering reliability analysis |
| CN111444608B (en) * | 2020-03-24 | 2022-04-19 | 成都理工大学 | Method for determining optimal truncation order in geotechnical engineering reliability analysis |
| CN113964857A (en) * | 2020-07-21 | 2022-01-21 | 华北电力大学（保定） | Photovoltaic power generation access method based on perturbation method damping ratio sensitivity |
| CN113964857B (en) * | 2020-07-21 | 2023-09-26 | 华北电力大学（保定） | Photovoltaic power generation access method based on perturbation method damping ratio sensitivity |
| CN112100821A (en) * | 2020-08-26 | 2020-12-18 | 西北工业大学 | Robustness optimization design method of photovoltaic cell |
| CN112467746A (en) * | 2020-11-21 | 2021-03-09 | 东南大学 | Power distribution network optimization method considering out-of-limit risk |
| CN112467746B (en) * | 2020-11-21 | 2022-11-01 | 东南大学 | Power distribution network optimization method considering out-of-limit risk |
| CN116611303A (en) * | 2023-07-20 | 2023-08-18 | 华东交通大学 | Random evaluation method and system for meshing mechanical characteristics, electronic equipment and storage medium |
| CN116611303B (en) * | 2023-07-20 | 2023-09-19 | 华东交通大学 | Random evaluation method and system for meshing mechanical characteristics, electronic equipment and storage medium |
Also Published As
| Publication number | Publication date |
|---|---|
| CN106548418B (en) | 2020-12-22 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN106548418A (en) | Power system small interference stability appraisal procedure | |
| Cao et al. | Detecting prosumer-community groups in smart grids from the multiagent perspective | |
| CN105449713B (en) | Consider the intelligent Sofe Switch planing method of active power distribution network of distributed power source characteristic | |
| CN106874630A (en) | Based on the regional power grid new energy development potential evaluation method that electricity is dissolved | |
| CN105656031B (en) | The methods of risk assessment of power system security containing wind-powered electricity generation based on Gaussian Mixture distribution characteristics | |
| CN108306303A (en) | A kind of consideration load growth and new energy are contributed random voltage stability assessment method | |
| CN104376378A (en) | Distributed-power-source-contained power distribution network reactive power optimization method based on mixed integer cone optimization | |
| CN103227467B (en) | Lyapunov stability analysis method of time delay electric system | |
| CN105069236B (en) | Consider the broad sense load joint probability modeling method of wind power plant node space correlation | |
| CN107846024A (en) | Isolated island micro-capacitance sensor Probabilistic Load Flow Analytic Calculation Method | |
| CN106849066A (en) | A kind of regional wind power prediction method | |
| CN103825272A (en) | Reliability determination method for power distribution network with distributed wind power based on analytical method | |
| CN108683214A (en) | Wind-electricity integration system self-adaption damping control method based on multiple convex polytope | |
| Bahmanifirouzi et al. | Multi-objective stochastic dynamic economic emission dispatch enhancement by fuzzy adaptive modified theta particle swarm optimization | |
| CN110516944A (en) | A kind of power distribution network multistage typical case's Run-time scenario generation method | |
| Liu et al. | Controlled islanding via weak submodularity | |
| Abdullah et al. | A noniterative method to estimate load carrying capability of generating units in a renewable energy rich power grid | |
| Zhang et al. | Data-driven sizing planning of renewable distributed generation in distribution networks with optimality guarantee | |
| CN109921458A (en) | The electric system small interference stability appraisal procedure of new energy access | |
| CN108694475B (en) | Short-time-scale photovoltaic cell power generation capacity prediction method based on hybrid model | |
| CN106655266B (en) | It is a kind of access new energy area power grid can flexible modulation power configuration method | |
| CN105488247A (en) | K-mean community structure mining method and apparatus | |
| CN110675276B (en) | Method and system for inversion droop control of direct current power transmission system | |
| Marley et al. | An AC-QP optimal power flow algorithm considering wind forecast uncertainty | |
| Shukla et al. | ATC assessment and enhancement of integrated transmission and distribution system considering the impact of active distribution network |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |