CN109921458A - The electric system small interference stability appraisal procedure of new energy access - Google Patents

The electric system small interference stability appraisal procedure of new energy access Download PDF

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Publication number
CN109921458A
CN109921458A CN201910134303.5A CN201910134303A CN109921458A CN 109921458 A CN109921458 A CN 109921458A CN 201910134303 A CN201910134303 A CN 201910134303A CN 109921458 A CN109921458 A CN 109921458A
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pcfe
small interference
variable
random
multinomial
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代海建
吴兴全
李志伟
瞿继平
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Co Ltd Of Chinese Energy Construction Group Gansu Prov Electric Power Design Inst
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Co Ltd Of Chinese Energy Construction Group Gansu Prov Electric Power Design Inst
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    • 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
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02B—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO BUILDINGS, e.g. HOUSING, HOUSE APPLIANCES OR RELATED END-USER APPLICATIONS
    • Y02B10/00—Integration of renewable energy sources in buildings
    • Y02B10/10—Photovoltaic [PV]
    • 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
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00—Energy generation through renewable energy sources
    • Y02E10/50—Photovoltaic [PV] energy
    • Y02E10/56—Power conversion systems, e.g. maximum power point trackers

Abstract

A kind of electric system small interference stability appraisal procedure of new energy access, steps are as follows: establishing the small interference analysis model of photovoltaic system；The battery temperature of photovoltaic system is the function of illumination, and illumination and random load are the stochastic inputs variable of photovoltaic system model；By illumination value and random load value, model analysis is carried out, taking the damping ratio of critical mode is random output variable, obtains corresponding random output variate-value；Stochastic inputs variable is normalized, is converted into PCFE with point；Stochastic inputs variable after the mean value and normalization of the random output variable that model analysis is obtained substitutes into PCFE multinomial, obtains PCFE coefficient using Homotopy；Sobol random sequence is generated in certain threshold range；It substitutes into obtained PCFE multinomial and carries out simulation calculation；Using kernel density estimation method, the distribution character of random output variable is obtained, assesses the probability of small interference stability.

Description

The electric system small interference stability appraisal procedure of new energy access
Technical field
The present invention relates to the electric system that the technical field of control method of electric system more particularly to a kind of new energy access Small interference stability appraisal procedure.
Background technique
Exhausted status and problems are faced for traditional fossil energy, so that in energy electric field, new energy Generation technology has become a hot topic of research one of problem and important directions.With going deep into for research, technology is also increasingly moved towards It is mature.Among this, photovoltaic power generation belongs to the hot fields of generation of electricity by new energy, meanwhile, specific gravity shared by photovoltaic power generation is entire The trend gradually increased is showed in electric system.
It is known that for traditional fossil energy, photovoltaic power generation is clean as a kind of new forms of electricity generation Renewable energy.But the access of photovoltaic power generation, certain influence is produced to the small signal stability of electric system, is not known Factor greatly increases.Firstly, the internal dynamic of photovoltaic generating system can generate electric system small interference stability, therefore for this A part, it should fully consider the modeling problem of photovoltaic generating system.Influence after photovoltaic power generation access electric system is shown as Below three aspect:
First, photovoltaic power generation uses MPPT maximum power point tracking mode, and photovoltaic power output can generate fluctuation, and then can be right The power output of synchronous generator and the trend of important line have an impact.
Second, since the inertia of photovoltaic generating system itself is zero, after instead of traditional generator, can make be Total inertia of uniting also is reduced therewith.
Third, if parameter setting is improper to may be such that damping turns when designing the controlling unit of photovoltaic generating system Square reduces.
In addition, increasing due to the randomness and fluctuation of photovoltaic generating system to the Small signal stability analysis of electric system New stochastic variable.In the case where photovoltaic generating system is generally in maximal power tracing operational mode, due to not knowing for illumination Property, it is illuminated by the light the influence of fluctuation, active power output will be chronically at dynamically track process, show strong randomness.In certain light Photovoltaic generating system according under may cause the appearance of electric system negative damping, bring threat for small interference stability.Its simultaneously, In photovoltaic generating system, illumination has certain correlation with load.The application considers these situations, makes system modelling and divides Analysis method is more in line with actual conditions.
Summary of the invention
Technical problem to be solved by the invention is to provide a kind of electric system small interference stability assessments of new energy access Method, thus effectively estimate critical mode damping ratio probability density function (PDF) and accumulative density function (CDF)；Obtain accurate small interference stability assessment result.
In order to solve the above technical problems, the technical solution used in the present invention is: a kind of electric system of new energy access Small interference stability appraisal procedure, includes the following steps:
Step (1) establishes the small interference analysis model of photovoltaic system；The battery temperature of photovoltaic system is the function of illumination, light According to the stochastic inputs variable for random load being photovoltaic system model；
Step (2), the illumination value obtained according to step (1) and random load value, progress model analysis take critical mode Damping ratio is random output variable, obtains corresponding random output variate-value；
By obtained illumination value and random load value XgBring the small interference analysis mould of photovoltaic system that step (1) is established into Type carries out model analysis and obtains corresponding random output variate-value ξg=[ξg1,…,ξgi,…,ξgw], 1 < i < 2n, w=2n；
Step (3) normalizes stochastic inputs variable, is PCFE (polynomial by stochastic inputs variables transformations Correlated function expansion, Polynomial correlation function function expansion) it is polynomial with point；
Stochastic inputs variable is normalized, since PCFE model is built upon n dimensional input vector unit hypercube [0,1]nFunction in domain, therefore to stochastic variable xi, it is normalized:
In formula (1), ximaxFor variable xiMaximum value, ximinFor variable xiMinimum value.
Step (4) determines PCFE polynomial order, the mean value of random output variable that model analysis is obtained, corresponding And the stochastic inputs variable after normalization substitutes into PCFE multinomial, and it is polynomial to obtain PCFE using Homotopy (homotopy) algorithm Coefficient matrix；PCFE method gives the multinomial of the g (x) based on stochastic variable:
In formula (2),ψ is known as by Hibert (Hilbert) definition space by the polynomial basis of X for input variable. By this principle, rewrite formula (1) are as follows:
In formula (3), g0For average response,Indicate the unknown system of base Number, g (x) is the citation form of PCFE.
When with PCFE polynomial analysis practical problem, it is generally the case that only need the multinomial of low order time to have higher Precision, so can generally pass through 2 rank PCFE polynomial analysis problems:
Formula (4) with condition should be noted high order component function need and all low order component functions two-by-two just It hands over.So multinomial coefficient α solved in formula (4) becomes particularly important under the premise of this.
The response observed by sampled pointAnd average responseDefinitionFormula (4) is changed to matrix form:
ψ α=d (5)
In formula (5), ψ is basic function, and α is PCFE multinomial coefficient.
Formula (5) is converted, multiplies ψ simultaneously at left and right both endsTTo get arrive new matrix form:
B α=C (6)
In formula (5), B=ψTψ, B=ψTd。
ψ column having the same, B row having the same, it is extra that these identical row and columns can be considered as, when removing respectively When these row and columns, available new expression matrix form:
B' α=C'(7)
In formula (7), B', C' are respectively B, and C matrix eliminates resulting matrix form after extra row and column.It utilizes Homotopy algorithm design factor α vector.Definition B' is p × q rank matrix, and p < q, then:
α (s)=(B')-1C'+(I-(B')'v(s) (8)
In formula (8), (B')-1It is the inverse matrix of B', I is q rank unit square matrix.
Consider the domain M:Searching route α (s) on s ∈ [0, ∞]:
In formula (9),
It defines P=I- (B')-1B', then formula (8) and formula (9) can be written as respectively:
α=(B')-1C'+Pv(s) (10)
It can be seen that P matrix has following two property after with up conversion:
Objective function:
In formula (13), W is weight matrix, has symmetrical and nonnegativity.
Consider:
It can be released by formula (14):
From formula (15) as can be seen that when s is intended to ∞, objective function reaches minimum.
Objective function O in alternate form (13), formula (14), obtains:
V'=-W α (s) (16)
V ' in (16) formula of replacement, obtains:
α (s)=e-sPWα0 (17)
α0All PCFE multinomial coefficients are formed, are obtained by least square regression.
Definition PW rank of matrix be r, W gusts of decomposed P:
PW=R Λ R-1 (18)
In formula (18), R is PW gusts of feature vector, and
By R and R-1Piecemeal is carried out, is obtained:
R is a square matrix, is obtained:
Therefore available:
That is, W gusts are a positive definite matrixes, P gusts are an orthogonal project operator.Therefore, PW gusts of all characteristic values are all Positive, when s is intended to ∞, the first item in formula (22) reduces, it may be assumed that
Because PW gusts be it is asymmetric, directly characteristic value and eigenvectors matrix are obtained by Eigenvalues Decomposition may cause The result of mistake；Therefore, it by W gusts of singular value decomposition (SVD) decomposed P, obtains:
Wherein,
It is recognised that Vq-rWithRespectively PW gusts of right feature vector and left eigenvector, feature vector is not unique, That is:
Consider:
If
Rq-r=Vq-r (28)
(28) formula substitution (27) formula is obtained:
Therefore:
Finally formula (28) and formula (30) are substituted into formula (23) to get arriving the polynomial coefficient vector of PCFE:
Step (5) generates Sobol sequence (low deviation sequence) in certain threshold range, polynomial as PCFE Stochastic inputs variable carries out simulation calculation to PCFE multinomial；
Sobol sequence belongs to one kind of low deviation sequence, and Sobol possesses preferable computational accuracy and computational efficiency.Below The generating principle of Sobol sequence is introduced, first, it will be assumed that under one-dimensional case, generate a sequence x1, x2, x3..., 0 < xi < 1.We need a direction number set v1, v2..., each viIt is binary fraction, and:
Here miIt is odd number, and mi< 2i。
To generate direction number vi, we choose primitive polynomial:
P=xd+a1xd-1+Λad-1x+1 (33)
Meet coefficient a hereini∈ { 0,1 }, and the freedom degree of primitive polynomial P is d.
Once we have selected multinomial, we can calculate v using his coefficienti:
In formula (34)XOR operation by turn is represented, similarly, we can calculate mi；
Finally, in order to generate sequence x1, x2, x3... formula can be used in we:
In formula (36), b1,b2, Λ is the binary representation of n；xnThe stochastic inputs Variables Sequence as generated, as PCFE Polynomial stochastic inputs variable.
Step (6) emulates PCFE multinomial using monte carlo (Monte Carlo) emulation, using cuclear density The estimation technique obtains the distribution character of random output variable, assesses the probability of small interference stability.
M U vector value is generated using Sobol sequence, it is assigned to each stochastic variable data according to accounting and is combined, respectively Group will obtain Mg=MTgA U value；The U value that each group is obtained brings the corresponding PCFE chaos polynomial expansion of the group into, acquires correspondence Random output variable value；The value for remembering the random output variable that all stochastic variable data combine is ξM, i.e., crucial mould The value of type damping ratio is ξM, 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；
Assess small interference stability with small interference stability probability: the unstable probability of small interference is FξM(0), small interference stability Probability be 1-FξM(0)。
Step (1) a further technical solution lies in: the described method for establishing the small interference analysis model of photovoltaic system is such as Under:
Its control model is that MPPT maximum power point tracking controls and determine inverter direct-current voltage control, wherein all control rings Section is all made of PI (proportional integration) control, and for invertor operation in the unity power factor method of operation, DC side voltage of converter is permanent Fixed to be realized by inverter active power ring, boost (boosting) low-pressure side voltage size is determined by MPPT maximum power point tracking control；
It is linearized in photovoltaic system operating point, establishes the photovoltaic system algebraic differentiation for being suitable for Small signal stability analysis Equation, the photovoltaic system algebraic differential equation can be obtained and contain in conjunction with generator algebraic differential equation and network algebra equation The electric system Linearized state equations of photovoltaic system.
A further technical solution lies in the illumination values and random load value that are obtained according to step (1) for step (2), carry out Model analysis, taking the damping ratio of critical mode is random output variable, obtains corresponding random output variate-value:
It brings obtained illumination value and random load value Xg into photovoltaic system small interference analysis model, carries out model analysis and obtain To corresponding random output variate-value ξ g=[ξ g1 ..., ξ gi ..., ξ gw], 1 < i < 2n, w=2n.
Step (4) a further technical solution lies in: determining the weight matrix W of Homotopy algorithm, to obtain PCFE polynomial Coefficient matrix；
The determination of weight matrix W is a step of homotopy algorithm key.In PCFE multinomial, we utilize component function Layering orthogonality as condition construct weight matrix W.
Orthogonality condition requires single order component function and g0It is mutually orthogonal, it may be assumed that
In formula (37),For xiProbability density function (PDF),For xiBasic function.Because of g0For average response, and Not equal to 0, therefore available:
It is sampled by Meng Teka, then formula (38) is writeable are as follows:
Write formula (39) as vector form:
Accordingly, with respect to the objective function of the PCFE of single order are as follows:
In formula (41), W1 i=[G1(xi)][G1(xi)]T。
Second order PCFE polynomial analysis method is identical as single order, repeats no more.
Single order PCFE obtains PCFE multinomial coefficient using homotopy algorithm according to optimal orthogonal polynomial basis representation, Least square regression ensure that the convergence of homotopy algorithm.
Such as single order PCFE multinomial:
Assuming that ψ is optimal orthogonal polynomial, then
It samples also with Monte Carlo:
It is obtained in conjunction with formula (41), (44) and (45):
W1 i=0 (46)
Formula (46) shows that there is no limit for the composition polynomial function of PCFE.
Technical solution provided by the invention, is capable of handling stochastic variable, calculates power system stability operation generally to provide The effective means of rate.In the case where electric system has non-linear, complexity, searched out can quick and precisely assess it is small dry Stable method is disturbed, the research of small interference monitoring and control is beneficial to.
The beneficial effects of the present invention are: it can handle the bimodal problem of illumination patterns；Key can be estimated well The PDF's (probability density function) of mode damping ratio is bimodal；The CDF that can be good at estimating critical mode damping ratio is (accumulative Density function) protrusion；Compared to other methods, there is very accurate small interference stability assessment result.
Detailed description of the invention
Fig. 1 is flow chart of the invention.
Specific embodiment
As shown in Figure 1, a kind of electric system small interference stability appraisal procedure of new energy access provided by the invention, including Following steps:
S101: it establishes and considers photovoltaic generating system internal dynamics and using MPPT maximum power point tracking operational mode shape The small interference analysis model of photovoltaic system under state；The photovoltaic generating system is the prior art, and structure includes five parts, It is respectively as follows: photovoltaic array, boost (boosting), inverter, filter and phaselocked loop, is second level photovoltaic generating system.It is sent out in photovoltaic In electric system, the output characteristics of photovoltaic cell is calculated using engineering calculating method, the battery temperature of photovoltaic system is illumination Function, illumination and random load are the stochastic inputs variable of photovoltaic system model.The step is the accurate of verifying proposed method Property provide model basis.
S102: it takes illumination and random load as stochastic inputs variable, carries out model analysis, take the damping ratio of critical mode For random output variable, corresponding random output variate-value is obtained；The step has determined the input quantity and output quantity of system, with reality The modal analysis result on border is as primary quantity, then brings established PCFE multinomial into, acquires multinomial coefficient.
S103: by stochastic inputs variable normalized；Being that PCFE is polynomial by stochastic inputs variables transformations matches point；It should Step has done normalized to stochastic inputs variable, is allowed to meet requirement of the PCFE multinomial to input quantity.
S104: determining the polynomial order of PCFE, after random output variable that model analysis is obtained and normalization with Machine input variable substitutes into PCFE multinomial, acquires the polynomial coefficient matrix of PCFE using Homotopy；The step utilizes mode Input quantity and output quantity after analysis, it is determined that the polynomial coefficient of PCFE.
S105: Sobol sequence is generated in certain threshold range, as the polynomial stochastic inputs variable of PCFE；It should Step produces under stochastic regime, and the stochastic inputs amount of system is allowed to meet the actual conditions of electric system.
S106: obtained PCFE multinomial is emulated to obtain random output using monte carlo (Monte Carlo) Variable；The distribution character that random output variable is then acquired using Density Estimator, assesses the probability of small interference stability.Specific packet It includes:
Stochastic inputs variable is generated using Sobol sequence, established PCFE multinomial is brought into and carries out Monte Carlo simulation It calculates and uses Density Estimator, seek ξMCumulative distribution function FξM(ξM), the FξM(ξM) be critical mode damping ratio accumulation Distribution function；Assess small interference stability with small interference stability probability: the unstable probability of small interference is FξM(0), small interference is steady Fixed probability is 1-FξM(0)。
The stochastic inputs amount that the step is generated by Sobol brings established PCFE multinomial into, it is small to acquire electric system Interference stability probability.

Claims (7)

1. a kind of electric system small interference stability appraisal procedure of new energy access, it is characterised in that include the following steps:
Step (1) establishes the small interference analysis model of photovoltaic system；The battery temperature of photovoltaic system be illumination function, illumination and Random load is the stochastic inputs variable of photovoltaic system model；
Step (2), the illumination value obtained according to step (1) and random load value, progress model analysis take the damping of critical mode Than obtaining corresponding random output variate-value for random output variable；
Step (3) normalizes stochastic inputs variable, and it is polynomial with point to be converted into PCFE；
Step (4) determines PCFE polynomial order, after the mean value and normalization of the random output variable that model analysis is obtained Stochastic inputs variable substitutes into PCFE multinomial, obtains the polynomial coefficient matrix of PCFE using Homotopy；
Step (5) generates Sobol random sequence in certain threshold range；It substitutes into obtained PCFE multinomial and is imitated It is true to calculate；
Step (6), using monte carlo emulation PCFE multinomial is emulated, and utilize kernel density estimation method, obtain with The distribution character of machine output variable assesses the probability of small interference stability.
2. a kind of electric system small interference stability appraisal procedure of new energy access according to claim 1, feature exist In: photovoltaic system described in step (1) is the second level photovoltaic generating system of the prior art, in photovoltaic generating system, using work Journey calculation method calculates the output characteristics of photovoltaic cell, and battery temperature is the function of illumination, illumination and random load is are ground Study carefully the stochastic inputs variable of photovoltaic system model.
3. a kind of electric system small interference stability appraisal procedure of new energy access according to claim 2, feature exist In: step (2) is to take key as stochastic inputs variable according to obtained illumination and random load value using modal analysis method The damping ratio of mode is random output variable, obtains corresponding random output variate-value.
4. a kind of electric system small interference stability appraisal procedure of new energy access according to claim 3, feature exist In: step (3) is to do normalized to the stochastic inputs variable that model analysis obtains, so that it is multinomial to be converted to established PCFE Formula matches point.
5. a kind of electric system small interference stability appraisal procedure of new energy access according to claim 4, feature exist In: step (4) is to determine PCFE polynomial order, random defeated after the random output variable that model analysis is obtained and normalization Enter variable and substitute into PCFE multinomial, obtains the polynomial coefficient matrix of PCFE using Homotopy algorithm.
6. a kind of electric system small interference stability appraisal procedure of new energy access according to claim 5, feature exist In: step (5) is to generate random PCFE multinomial with point using Sobol sequence.
7. a kind of electric system small interference stability appraisal procedure of new energy access according to claim 6, feature exist In step (6) is to generate stochastic inputs variable using Sobol sequence, brings established PCFE multinomial into and carries out Monte Carlo Simulation calculation uses Density Estimator, seeks ξMCumulative distribution function FξM(ξM), the FξM(ξM) it is critical mode damping ratio Cumulative distribution function；Assess small interference stability with small interference stability probability: the unstable probability of small interference is FξM(0), small dry Disturbing stable probability is 1-FξM(0)。
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CN115618171A (en) * 2022-06-06 2023-01-17 北京理工大学 Propellant combustion balance product solving method based on homotopy algorithm

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107204618A (en) * 2017-05-05 2017-09-26 郓城金河热电有限责任公司 Quasi-Monte-Carlo probabilistic loadflow computational methods based on digital interleaving technique
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CN112356033B (en) * 2020-11-09 2021-09-10 中国矿业大学 Mechanical arm path planning method integrating low-difference sequence and RRT algorithm
CN115618171A (en) * 2022-06-06 2023-01-17 北京理工大学 Propellant combustion balance product solving method based on homotopy algorithm
CN115618171B (en) * 2022-06-06 2023-10-24 北京理工大学 Method for solving propellant combustion balance product based on homotopy algorithm

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