CN105552938B - Three-phase asymmetric distribution network voltage sag evaluation method - Google Patents

Three-phase asymmetric distribution network voltage sag evaluation method Download PDF

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CN105552938B
CN105552938B CN201610105910.5A CN201610105910A CN105552938B CN 105552938 B CN105552938 B CN 105552938B CN 201610105910 A CN201610105910 A CN 201610105910A CN 105552938 B CN105552938 B CN 105552938B
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distribution network
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CN105552938A (en
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贾东梨
刘科研
盛万兴
孟晓丽
胡丽娟
何开元
叶学顺
刁赢龙
唐建岗
李雅洁
董伟杰
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State Grid Corp of China SGCC
China Electric Power Research Institute Co Ltd CEPRI
State Grid Beijing Electric Power Co Ltd
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State Grid Corp of China SGCC
China Electric Power Research Institute Co Ltd CEPRI
State Grid Beijing Electric Power Co Ltd
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/26—Arrangements for eliminating or reducing asymmetry in polyphase networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/001—Methods to deal with contingencies, e.g. abnormalities, faults or failures
    • H02J3/382—
    • 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
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/50—Arrangements for eliminating or reducing asymmetry in polyphase networks

Abstract

The invention relates to a voltage sag evaluation method of a three-phase asymmetric distribution network, which comprises the following steps: establishing a fault random model of the three-phase asymmetric distribution network; establishing a DG random model of the three-phase asymmetric power distribution network; orthogonal transformation is carried out on the fault random model to obtain an irrelevant fault random model corresponding to the fault random model; processing random variables formed by an irrelevant fault random model and a DG random model by adopting a point estimation method to obtain random variables of two groups of simulation schemes; carrying out inverse decomposition on the random variables of the two groups of simulation schemes to obtain two groups of related random variables of the simulation schemes corresponding to the random variables of the two groups of simulation schemes; respectively determining probability density functions of elements in random variables of two groups of related simulation schemes through a Cornish-Fisher series; the correlation between the fault type and the fault line in the power distribution network and various short-circuit faults in the power distribution network are comprehensively considered to simulate the characteristics of the whole power distribution network, and reference is provided for adopting measures for inhibiting voltage sag.

Description

Three-phase asymmetric distribution network voltage sag evaluation method
Technical Field
The invention relates to the technical field of power quality of power systems, in particular to a voltage sag evaluation method for a three-phase asymmetric distribution network.
Background
The voltage sag is also called voltage sag, which means that the effective value of the power frequency voltage at a certain point in the system suddenly drops to 10% -90% of a rated value and returns to normal after a short duration period of 10ms-1min later. With the popularization of high-power electronic switching equipment and the technical update of electric equipment, particularly the wide application of numerical control technology to industrial production, the harm caused by voltage sag is more and more obvious. In power distribution networks, the most severe voltage sag problem is mostly caused by short-circuit faults. The impact of voltage sag on sensitive equipment (such as adjustable speed motors, precision control equipment, etc.) can be even comparable to a power outage. The voltage sag is particularly prominent in severe impact and hazardous performance to industrial users, and can also cause casualties and equipment damage.
As with other power quality issues, the voltage sag problem is not a new problem and has been studied by a number of technical sources. The voltage sag assessment is an important aspect of power quality analysis through the query of the prior art data.
With the development of scientific technology, new methods are continuously introduced into voltage quality analysis. At present, the point estimation method has been applied in the field of power quality. Technology 1 (application of wubei, zhangyan, chenminjiang. point estimation method in voltage stability analysis [ J ]. report of chinese motor engineering, 2008,28(25):38-43.) the point estimation method is introduced into voltage stability analysis, and voltage stability analysis is performed aiming at randomness of branch faults, so that uncertainty problems of line faults and node injection power can be uniformly processed. Technology 2 (Xupeai, Xiao Xian Yong, Wang Ying, Voltage sag frequency two-point estimation random evaluation method [ J ]. electric power system protection and control, 2011,39(9):1-6.) the problem of voltage sag frequency is researched by considering the randomness of the tolerance voltage of sensitive equipment and the normal operation voltage of a system bus. Both of the techniques 1 and 2 can obtain satisfactory results in consideration of the calculation accuracy and the calculation time.
The current methods for analyzing voltage sag are mainly the critical distance method (technique 3: M.N.Moschakis, N.D.Hatziangyoriou.Analyzation and storage analysis of voltage losses [ J ]. IEEE Transactions on Power Delivery systems [ J ]. IEEE Transactions on distribution systems [ J ]. IEEE Transactions on analysis Applications,1996,32(6): 1414) 1414. technique 3: Padmanabi Thaku, evaluation K.Singh, RameC.Banpanel on analysis for storage of voltage losses [ I ]. C.M.N.Moschakis, N.D.Hatziangyoriou.Analy.A. analytical analysis and storage analysis of voltage losses [ J ]. IEEE Transactions on distribution systems [ J ]. IEEE Transactions on analysis Applications,1996,32(6): 1414. technique 1425: Padmanabi. environmental analysis for storage of voltage losses [ I.M.M.M.M.M.M.M.M.M.N.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.S. A. A. The critical distance method is a relatively classical method for evaluating voltage sags caused by symmetric faults and asymmetric faults. The point of failure method simulates the behavior of the entire power system with only specific failures at a few selected points. The monte carlo method is a method widely used to analyze random problems. The sampling times of the Monte Carlo method are irrelevant to the scale of the system, and the complexity of the system has little influence on the system, but the Monte Carlo method has the defects of statics, low calculation efficiency, long time consumption and the like. With the development of science and technology, new methods are continuously introduced into the voltage sag analysis, such as a two-point method (technology 6: a voltage sag simulation and evaluation method for an active power distribution network, china: CN 201410406537.8). The two-point method converts the random problem into the deterministic problem, and realizes the evaluation and simulation of the voltage sag. However, when the voltage sag is evaluated by using the above methods, the power distribution network is treated as a three-phase symmetric network, and the problem of three-phase asymmetry of the power distribution network is not considered, but the three-phase asymmetry phenomenon generally exists in the power distribution network. The existing literature has less research on the voltage sag problem of the three-phase asymmetric power distribution network.
Disclosure of Invention
The invention provides a voltage sag evaluation method for a three-phase asymmetric distribution network, which aims to comprehensively consider the correlation between fault types and fault lines in a distribution network and various short-circuit faults in the distribution network to simulate the characteristics of the whole distribution network, provide reference for adopting measures for inhibiting voltage sag and improve the power supply reliability of the distribution network.
The purpose of the invention is realized by adopting the following technical scheme:
in a method for evaluating voltage sag in a three-phase asymmetric power distribution network, the improvement comprising:
(1) establishing a fault random model of the three-phase asymmetric power distribution network;
(2) establishing a DG random model of the three-phase asymmetric power distribution network;
(3) carrying out orthogonal transformation on the fault random model to obtain an irrelevant fault random model corresponding to the fault random model;
(4) processing random variables formed by the uncorrelated fault random model and the DG random model by adopting a point estimation method to obtain random variables of two groups of simulation schemes;
(5) performing inverse decomposition on the random variables of the two groups of simulation schemes by adopting a Cholesky decomposition mode, and acquiring two groups of related random variables of the simulation schemes corresponding to the random variables of the two groups of simulation schemes;
(6) the probability density functions of the elements in the random variables of the two sets of related simulation solutions are determined separately by means of a Cornish-Fisher series.
Preferably, in the step (1), establishing a fault stochastic model of the three-phase asymmetric power distribution network by using a monte carlo simulation mode includes:
(1-1) establishing a fault line model of the three-phase asymmetric power distribution network according to the following formula:
Figure BDA0000929973260000031
in the formula (1), x is obedient [0,1 ]]Uniformly distributed random numbers, i.e. x-U [0,1 ]]，FLineNumbering the fault branches, wherein M is the total number of branches in the three-phase asymmetric distribution network, PLine,iFor the fault rate of the ith branch in the three-phase asymmetric distribution network, i belongs to {1, M }, and U is a uniform distribution function;
(1-2) establishing a fault location model of the three-phase asymmetric power distribution network according to the following formula:
FLoc＝y*100％ (2)
in the formula (2), y is obedient [0,1 ]]Uniformly distributed random numbers, i.e. y-U [0,1 ]]，FLocFor the faulty branch FLineBefore the fault point, the length of the branch and the fault branch FLinePercentage of total length;
(1-3) establishing a fault type model of the three-phase asymmetric power distribution network includes:
if the fault branch F of the three-phase asymmetric distribution networkLineFor three phases, a faulty branch F of the three-phase asymmetric distribution network is established according to the following formulaLineThe corresponding fault type model:
Figure BDA0000929973260000032
in the formula (3), z is obedient [0,1 ]]Uniformly distributed random numbers, i.e. z-U0, 1]，FTypeFor a faulty branch F of the three-phase asymmetric distribution networkLineCorresponding fault types, 3LG is three-phase grounding short-circuit fault type, 2L is two-phase interphase short-circuit fault type, and 2LG is two-phase connectionType of short-circuit to earth, LG type of short-circuit to single-phase earth, P3LGProbability of occurrence of three-phase ground short-circuit fault, P2LProbability of occurrence of short-circuit fault between two phases, P2LGThe two-phase grounding short circuit fault occurrence probability is obtained;
if the fault branch F of the three-phase asymmetric distribution networkLineFor two phases, a faulty branch F of the three-phase asymmetric distribution network is established according to the following formulaLineThe corresponding fault type model:
Figure BDA0000929973260000033
if the fault branch F of the three-phase asymmetric distribution networkLineFor two phases, a faulty branch F of the three-phase asymmetric distribution network is established according to the following formulaLineThe corresponding fault type model:
FType＝LG (5)。
(1-4) establishing a fault duration model of the three-phase asymmetric power distribution network according to the following formula:
FDur＝μ (6)
in the formula (6), μ is a random number following a standard normal distribution expected to be 0.06s with a standard deviation of 0.01s, i.e., μ to N [0.06,0.01 ]]，FDurFor a faulty branch F of the three-phase asymmetric distribution networkLineA corresponding fault duration;
(1-5) establishing a fault impedance model of the three-phase asymmetric power distribution network according to the following formula:
FRes＝τ (7)
in the formula (7), τ is a random number that follows a standard normal distribution expected to be 5 Ω with a standard deviation of 1 Ω, i.e., τ to N [5,1 ]]，FResFor a faulty branch F of the three-phase asymmetric distribution networkLineThe corresponding fault impedance.
Preferably, in the step (2), establishing a DG random model of the three-phase asymmetric power distribution network by using a monte carlo simulation method includes:
(2-1) the fan power generation system adopts a primary curve model, and the fanOutput power PwindThe relationship to the wind speed v is:
Figure BDA0000929973260000041
in the formula (8), the reaction mixture is,
Figure BDA0000929973260000042
are all constant, vrIs the rated wind speed, P, of the fanrIs the rated power, v, of the fanciIs the cut-in wind speed, v, of the fancoThe cut-out wind speed of the fan;
the number of the wind turbine generators is NwtgTime, wind turbine generator output power PωThe model of (a) is:
Pω＝PwindNwtg(9)
when v isci<v<vrTime, wind turbine generator output power PωThe formula of the probability density function of (a) is:
Figure BDA0000929973260000043
in the formula (10), K is the shape parameter of Weibull distribution, C is the scale parameter of Weibull distribution, and f (P)ω) Probability density function, Q, of active power output of wind turbineωIs the reactive output of the wind turbine generator,
Figure BDA0000929973260000044
is the power factor;
(2-2) photovoltaic power generation system output power PsolarThe model of (a) is:
Psolar＝rAη (11)
in the formula (11), r is the radiant emittance and has the unit of W/m2，
Figure BDA0000929973260000045
Is the total area of the solar array of the photovoltaic power generation system, AmNumber of cells of solar array of photovoltaic power generation system，
Figure BDA0000929973260000051
For the photoelectric conversion efficiency of solar arrays of photovoltaic power generation systems, ηmPhotoelectric conversion efficiency for a single cell assembly;
output power P of photovoltaic power generation systemsolarThe probability density function of (a) is:
Figure BDA0000929973260000052
in the formula (12), Rsolar＝rmaxA η is the maximum output power of the solar array of the photovoltaic power generation system, rmaxFor maximum radiance, α and β are both Beta distribution shape parameters.
Preferably, in the step (3), the performing orthogonal transformation on the fault stochastic model by using Cholesky decomposition includes:
a 5-dimensional random variable p is formed by a fault line model, a fault position model, a fault type model, a fault duration model and a fault impedance model in the fault random model [ p [ ]1,p2,…,p5]TThe desired vector of the random variable p is up＝[u1,u2,…,u5]TCovariance matrix C of said random variable ppComprises the following steps:
Figure BDA0000929973260000053
determining a partial derivative factor λ of the random variable p3The formula is as follows:
Figure BDA0000929973260000054
in the formula (14), the compound represented by the formula (I),
Figure BDA0000929973260000055
for the ith random variable p in the random variables plIs within 1,5]；
The formula for determining the uncorrelated matrix q for the random variable p is:
q＝Bp (15)
in formula (15), B is an intermediate matrix;
covariance matrix C for the random variable ppPerforming orthogonal transformation, wherein the formula is as follows:
Cp＝LLT(16)
in the formula (16), L is the covariance matrix CpThe lower triangular matrix of (2);
determining the desired vector u of said uncorrelated matrix qqThe formula of (1) is:
uq＝L-1up(17)
in the formula (17), upIs the desired vector of the random variable p;
determining the r-th element q in the uncorrelated matrix qrCoefficient of partial derivation of
Figure BDA0000929973260000056
The formula of (1) is:
Figure BDA0000929973260000061
in the formula (18), the reaction mixture,
Figure BDA0000929973260000062
is the covariance matrix CpIs the r row and L column elements of the lower triangular array L, r, L e [1,5 ]]。
Preferably, in the step (4), processing the fault stochastic model and the DG stochastic model of the three-phase asymmetric power distribution network by using a point estimation method includes:
a fault line model, a fault position model, a fault type model, a fault duration model, a fault impedance model and a DG random model in the fault random model form a 7-dimensional random variable X ═ X [ X ] composed of the output power of the wind generating set and the output power of the photovoltaic power generation system in the fault random model1,X2,…,X7]TWherein Y is h (X) is as defined aboveThe random variable X is a non-linear function of the variable,
Figure BDA0000929973260000063
is the probability density function of the ith random variable in the random variables X, i belongs to [1,7 ]]；
An ith random variable X from the random variables XiTwo estimation points are extracted, wherein the k estimation point xi,kThe calculation formula is as follows:
xi,k＝μi+ξi,kσi(19)
in the formula (19), muiIs composed of
Figure BDA0000929973260000064
Expectation of (a)iIs composed of
Figure BDA0000929973260000065
Standard deviation of (A), ξi,kIs xi,kThe corresponding position coefficient, k is 1, 2;
determining an estimate of the 3 rd moment of the nonlinear function Y ═ h (X) with the random variable X as a variable according to:
Figure BDA0000929973260000066
in the formula (20), j is 1,2,3, k is 1,2, i ∈ [1,7 ]]，ωi,kIs xi,kCorresponding weight coefficient, mui-1Is composed of
Figure BDA0000929973260000067
Expectation of (d), mui+1Is composed of
Figure BDA0000929973260000068
(iii) a desire;
wherein x isi,kCorresponding weight coefficient omegai,kAnd position coefficient ξi,kSatisfies the equation:
Figure BDA0000929973260000069
in formula (21), λi,jIs the ith random variable X in the random variables XiJ order central moment of (d);
when j is 1,2, λi,1＝0，λi,2X is 1i,kCorresponding weight coefficient omegai,kAnd position coefficient ξi,kSatisfies the equation:
Figure BDA00009299732600000610
preferably, in the step (6), Y isiFor the ith element, i e [1,14 ], in the random variables of the two sets of related simulation schemes]Then, the formula for determining the probability density function of the elements in the random variables of the two sets of related simulation schemes by the Cornish-Fisher series is:
Figure BDA0000929973260000071
in the formula (23), the compound represented by the formula,
Figure BDA0000929973260000072
is ξiStandard normal distribution probability density function of (1)%, x3Is a third-order semi-invariant;
wherein, χ3Has a value of YiCoefficient of partial derivation of ξiIs YiStandard form, the formula is:
ξi＝(x-μi)/σi(24)
in the formula (24), muiIs YiMean value of (a)iIs YiThe variance of (c).
The invention has the beneficial effects that:
the invention provides a voltage sag evaluation method of a three-phase asymmetric distribution network, which is used for researching the asymmetric problem of the distribution network, converting a random probability problem into a plurality of deterministic problems by using a Cholesky decomposition and two-point estimation method, then building a model by using the existing distribution network analysis software, carrying out voltage sag simulation on an active distribution network, counting the statistic characteristics of voltage sag, analyzing weak links in the power network, building a voltage sag probability density function of each node based on a Cornish-Fisher series, calculating a voltage sag index, realizing the voltage sag evaluation of the three-phase asymmetric distribution network, comprehensively considering the correlation between fault types and fault lines in the power network and the characteristics of various short-circuit faults in the power network to simulate the whole power distribution network, being applicable to the three-phase asymmetric distribution network and the three-phase symmetric network, and providing reference for adopting measures for inhibiting the voltage sag, and the power supply reliability of the power distribution network is improved.
Drawings
Fig. 1 is a flow chart of a voltage sag evaluation method of a three-phase asymmetric distribution network according to the present invention.
Detailed Description
The following detailed description of embodiments of the invention refers to the accompanying drawings.
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention provides a three-phase asymmetric distribution network voltage sag evaluation method, which is used for researching asymmetric problems of a distribution network, converting random probability problems into a plurality of deterministic problems by using Cholesky decomposition (Cholesky decomposition) and a two-point estimation method, then building a model by using existing distribution network analysis software, carrying out voltage sag simulation on an active distribution network, counting statistic characteristics of voltage sag, analyzing weak links in the power network, building a voltage sag probability density function of each node based on a Cornish-Fisher series, calculating a voltage sag index, realizing voltage sag evaluation on the three-phase asymmetric distribution network, providing reference for adopting measures for inhibiting voltage sag, and improving power supply reliability of the distribution network, and comprises the following steps of:
(1) establishing a fault random model of the three-phase asymmetric power distribution network;
(2) establishing a DG random model of the three-phase asymmetric power distribution network;
(3) carrying out orthogonal transformation on the fault random model to obtain an irrelevant fault random model corresponding to the fault random model;
(4) processing random variables formed by the uncorrelated fault random model and the DG random model by adopting a point estimation method to obtain random variables of two groups of simulation schemes;
(5) performing inverse decomposition on the random variables of the two groups of simulation schemes by adopting a Cholesky decomposition mode, and acquiring two groups of related random variables of the simulation schemes corresponding to the random variables of the two groups of simulation schemes;
(6) the probability density functions of the elements in the random variables of the two sets of related simulation solutions are determined separately by means of a Cornish-Fisher series.
Specifically, in the step (1), establishing a fault random model of the three-phase asymmetric power distribution network by using a monte carlo simulation mode includes:
(1-1) establishing a fault line model of the three-phase asymmetric power distribution network according to the following formula:
Figure BDA0000929973260000081
in the formula (1), x is obedient [0,1 ]]Uniformly distributed random numbers, i.e. x-U [0,1 ]]，FLineNumbering the fault branches, wherein M is the total number of branches in the three-phase asymmetric distribution network, PLine,iFor the fault rate of the ith branch in the three-phase asymmetric distribution network, i belongs to {1, M }, and U is a uniform distribution function;
(1-2) establishing a fault location model of the three-phase asymmetric power distribution network according to the following formula:
FLoc＝y*100％ (2)
in the formula (2), y is obedient [0,1 ]]Uniformly distributed random numbers, i.e. y-U [0,1 ]]，FLocFor the faulty branch FLineBefore the fault point, the length of the branch and the fault branch FLinePercentage of total length;
(1-3) establishing a fault type model of the three-phase asymmetric power distribution network includes:
if the fault branch F of the three-phase asymmetric distribution networkLineFor three phases, a faulty branch F of the three-phase asymmetric distribution network is established according to the following formulaLineThe corresponding fault type model:
Figure BDA0000929973260000091
in the formula (3), z is obedient [0,1 ]]Uniformly distributed random numbers, i.e. z-U0, 1]，FTypeFor a faulty branch F of the three-phase asymmetric distribution networkLineCorresponding fault types, 3LG is three-phase grounding short-circuit fault type, 2L is two-phase interphase short-circuit fault type, 2LG is two-phase grounding short-circuit fault type, LG is single-phase grounding short-circuit fault type, P3LGProbability of occurrence of three-phase ground short-circuit fault, P2LProbability of occurrence of short-circuit fault between two phases, P2LGThe two-phase grounding short circuit fault occurrence probability is obtained;
if the fault branch F of the three-phase asymmetric distribution networkLineFor two phases, a faulty branch F of the three-phase asymmetric distribution network is established according to the following formulaLineThe corresponding fault type model:
Figure BDA0000929973260000092
if the fault branch F of the three-phase asymmetric distribution networkLineFor two phases, a faulty branch F of the three-phase asymmetric distribution network is established according to the following formulaLineThe corresponding fault type model:
FType＝LG (5)。
(1-4) establishing a fault duration model of the three-phase asymmetric power distribution network according to the following formula:
FDur＝μ (6)
in the formula (6), μ is a random number following a standard normal distribution expected to be 0.06s with a standard deviation of 0.01s, i.e., μ to N [0.06,0.01 ]]，FDurFor a faulty branch F of the three-phase asymmetric distribution networkLineA corresponding fault duration;
(1-5) establishing a fault impedance model of the three-phase asymmetric power distribution network according to the following formula:
FRes＝τ (7)
in the formula (7), τ is a random number that follows a standard normal distribution expected to be 5 Ω with a standard deviation of 1 Ω, i.e., τ to N [5,1 ]]，FResFor a faulty branch F of the three-phase asymmetric distribution networkLineThe corresponding fault impedance.
In the step (2), establishing a DG random model of the three-phase asymmetric power distribution network by using a monte carlo simulation mode, including:
(2-1) the fan power generation system adopts a primary curve model, and the fan output power PwindThe relationship to the wind speed v is:
Figure BDA0000929973260000093
in the formula (8), the reaction mixture is,
Figure BDA0000929973260000101
are all constant, vrIs the rated wind speed, P, of the fanrIs the rated power, v, of the fanciIs the cut-in wind speed, v, of the fancoThe cut-out wind speed of the fan;
the number of the wind turbine generators is NwtgTime, wind turbine generator output power PωThe model of (a) is:
Pω＝PwindNwtg(9)
when v isci<v<vrTime, wind turbine generator output power PωThe formula of the probability density function of (a) is:
Figure BDA0000929973260000102
in the formula (10), K is the shape parameter of Weibull distribution, C is the scale parameter of Weibull distribution, and f (P)ω) Probability density function, Q, of active power output of wind turbineωIs the reactive output of the wind turbine generator,
Figure BDA0000929973260000103
is the power factor;
(2-2) photovoltaic power generation system output power PsolarThe model of (a) is:
Psolar＝rAη (11)
in the formula (11), r is the radiant emittance and has the unit of W/m2，
Figure BDA0000929973260000104
Is the total area of the solar array of the photovoltaic power generation system, AmIs the area of a single battery component, M is the number of battery components of a solar array of the photovoltaic power generation system,
Figure BDA0000929973260000105
for the photoelectric conversion efficiency of solar arrays of photovoltaic power generation systems, ηmPhotoelectric conversion efficiency for a single cell assembly;
output power P of photovoltaic power generation systemsolarThe probability density function of (a) is:
Figure BDA0000929973260000106
in the formula (12), Rsolar＝rmaxA η is the maximum output power of the solar array of the photovoltaic power generation system, rmaxFor maximum radiance, α and β are both Beta distribution shape parameters.
In the step (3), performing orthogonal transformation on the fault stochastic model by using Cholesky decomplexition includes:
a 5-dimensional random variable p is formed by a fault line model, a fault position model, a fault type model, a fault duration model and a fault impedance model in the fault random model [ p [ ]1,p2,…,p5]TThe desired vector of the random variable p is up＝[u1,u2,…,u5]TCovariance matrix C of said random variable ppComprises the following steps:
Figure BDA0000929973260000111
determining a partial derivative factor λ of the random variable p3The formula is as follows:
Figure BDA0000929973260000112
in the formula (14), the compound represented by the formula (I),
Figure BDA0000929973260000113
for the ith random variable p in the random variables plIs within 1,5]；
The formula for determining the uncorrelated matrix q for the random variable p is:
q＝Bp (15)
in formula (15), B is an intermediate matrix;
covariance matrix C for the random variable ppPerforming orthogonal transformation, wherein the formula is as follows:
Cp＝LLT(16)
in the formula (16), L is the covariance matrix CpThe lower triangular matrix of (2);
determining the desired vector u of said uncorrelated matrix qqThe formula of (1) is:
uq＝L-1up(17)
in the formula (17), upIs the desired vector of the random variable p;
determining the r-th element q in the uncorrelated matrix qrCoefficient of partial derivation of
Figure BDA0000929973260000117
The formula of (1) is:
Figure BDA0000929973260000114
in the formula (18), the reaction mixture,
Figure BDA0000929973260000115
is the covariance matrix CpIs the r row and L column elements of the lower triangular array L, r, L e [1,5 ]]。
In the step (4), the processing of the fault random model and the DG random model of the three-phase asymmetric power distribution network by using the point estimation method includes:
a fault line model, a fault position model, a fault type model, a fault duration model, a fault impedance model and a DG random model in the fault random model form a 7-dimensional random variable X ═ X [ X ] composed of the output power of the wind generating set and the output power of the photovoltaic power generation system in the fault random model1,X2,…,X7]TY ═ h (X) is a nonlinear function with the random variable X as a variable,
Figure BDA0000929973260000116
is the probability density function of the ith random variable in the random variables X, i belongs to [1,7 ]]；
An ith random variable X from the random variables XiTwo estimation points are extracted, wherein the k estimation point xi,kThe calculation formula is as follows:
xi,k＝μi+ξi,kσi(19)
in the formula (19), muiIs composed of
Figure BDA0000929973260000121
Expectation of (a)iIs composed of
Figure BDA0000929973260000122
Standard deviation of (A), ξi,kIs xi,kThe corresponding position coefficient, k is 1, 2;
determining an estimate of the 3 rd moment of the nonlinear function Y ═ h (X) with the random variable X as a variable according to:
Figure BDA0000929973260000123
in the formula (20), j is 1,2,3, k is 1,2, i ∈ [1,7 ]]，ωi,kIs xi,kCorresponding weight coefficient, mui-1Is composed of
Figure BDA0000929973260000124
Expectation of (d), mui+1Is composed of
Figure BDA0000929973260000125
(iii) a desire;
wherein x isi,kCorresponding weight coefficient omegai,kAnd position coefficient ξi,kSatisfies the equation:
Figure BDA0000929973260000126
in formula (21), λi,jIs the ith random variable X in the random variables XiJ order central moment of (d);
when j is 1,2, λi,1＝0，λi,2X is 1i,kCorresponding weight coefficient omegai,kAnd position coefficient ξi,kSatisfies the equation:
Figure BDA0000929973260000127
in the step (5), performing inverse decomposition on the random variables of the two sets of simulation schemes by adopting a Cholesky decomposition mode, and acquiring two sets of related random variables of the simulation schemes corresponding to the random variables of the two sets of simulation schemes;
the random variables of the two sets of simulation schemes are unrelated random variables, which cannot be subjected to simulation calculation, so that inverse transformation is required, and the two sets of related random variables of the simulation schemes corresponding to the random variables of the two sets of simulation schemes are, for example: only two phases, the type of fault after cholesky decomposition may be three phase earth, but this is not possible and therefore needs to be reversed.
In the step (6), Y is setiFor the ith element, i e [1,14 ], in the random variables of the two sets of related simulation schemes]Then, the formula for determining the probability density function of the elements in the random variables of the two sets of related simulation schemes by the Cornish-Fisher series is:
Figure BDA0000929973260000128
in the formula (23), the compound represented by the formula,
Figure BDA0000929973260000129
is ξiStandard normal distribution probability density function of (1)%, x3Is a third-order semi-invariant;
wherein, χ3Has a value of YiCoefficient of partial derivation of ξiIs YiStandard form, the formula is:
ξi＝(x-μi)/σi(24)
in the formula (24), muiIs YiMean value of (a)iIs YiThe variance of (c).
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.

Claims (5)

1. A three-phase asymmetric distribution network voltage sag assessment method is characterized by comprising the following steps:
(1) establishing a fault random model of the three-phase asymmetric power distribution network;
(2) establishing a DG random model of the three-phase asymmetric power distribution network;
(3) carrying out orthogonal transformation on the fault random model to obtain an irrelevant fault random model corresponding to the fault random model;
(4) processing random variables formed by the uncorrelated fault random model and the DG random model by adopting a point estimation method to obtain random variables of two groups of simulation schemes;
(5) performing inverse decomposition on the random variables of the two groups of simulation schemes by adopting a Cholesky decomposition mode, and acquiring two groups of related random variables of the simulation schemes corresponding to the random variables of the two groups of simulation schemes;
(6) respectively determining probability density functions of elements in random variables of the two groups of related simulation schemes through a Cornish-Fisher series;
in the step (1), establishing a fault random model of the three-phase asymmetric power distribution network by using a monte carlo simulation mode, including:
(1-1) establishing a fault line model of the three-phase asymmetric power distribution network according to the following formula:
Figure FDA0002354777630000011
in the formula (1), x is obedient [0,1 ]]Uniformly distributed random numbers, i.e. x-U [0,1 ]]，FLineNumbering the fault branches, wherein M is the total number of branches in the three-phase asymmetric distribution network, PLine,iFor the fault rate of the ith branch in the three-phase asymmetric distribution network, i belongs to {1, M }, and U is a uniform distribution function;
(1-2) establishing a fault location model of the three-phase asymmetric power distribution network according to the following formula:
FLoc＝y*100％ (2)
in the formula (2), y is obedient [0,1 ]]Uniformly distributed random numbers, i.e. y-U [0,1 ]]，FLocFor the faulty branch FLineBefore the fault point, the length of the branch and the fault branch FLinePercentage of total length;
(1-3) establishing a fault type model of the three-phase asymmetric power distribution network includes:
if the fault branch F of the three-phase asymmetric distribution networkLineFor three phases, a faulty branch F of the three-phase asymmetric distribution network is established according to the following formulaLineThe corresponding fault type model:
Figure FDA0002354777630000021
in the formula (3), z is obedient [0,1 ]]Uniformly distributed random numbers, i.e. z-U0, 1]，FTypeFor a faulty branch F of the three-phase asymmetric distribution networkLineCorresponding fault types, 3LG is three-phase grounding short-circuit fault type, 2L is two-phase interphase short-circuit fault type, 2LG is two-phase grounding short-circuit fault type, LG is single-phase grounding short-circuit fault type, P3LGProbability of occurrence of three-phase ground short-circuit fault, P2LProbability of occurrence of short-circuit fault between two phases, P2LGThe two-phase grounding short circuit fault occurrence probability is obtained;
if the fault branch F of the three-phase asymmetric distribution networkLineFor two phases, a faulty branch F of the three-phase asymmetric distribution network is established according to the following formulaLineThe corresponding fault type model:
Figure FDA0002354777630000022
if the fault branch F of the three-phase asymmetric distribution networkLineFor two phases, a faulty branch F of the three-phase asymmetric distribution network is established according to the following formulaLineThe corresponding fault type model:
FType＝LG (5)。
(1-4) establishing a fault duration model of the three-phase asymmetric power distribution network according to the following formula:
FDur＝μ (6)
in the formula (6), μ is a random number following a standard normal distribution expected to be 0.06s with a standard deviation of 0.01s, i.e., μ to N [0.06,0.01 ]]，FDurFor the three-phase asymmetric distribution networkBarrier branch FLineA corresponding fault duration;
(1-5) establishing a fault impedance model of the three-phase asymmetric power distribution network according to the following formula:
FRes＝τ (7)
in the formula (7), τ is a random number that follows a standard normal distribution expected to be 5 Ω with a standard deviation of 1 Ω, i.e., τ to N [5,1 ]]，FResFor a faulty branch F of the three-phase asymmetric distribution networkLineThe corresponding fault impedance.
2. The method of claim 1, wherein in step (2), the step of creating a DG stochastic model of the three-phase asymmetric power distribution network using monte carlo simulation comprises:
(2-1) the fan power generation system adopts a primary curve model, and the fan output power PwindThe relationship to the wind speed v is:
Figure FDA0002354777630000023
in the formula (8), the reaction mixture is,
Figure FDA0002354777630000031
are all constant, vrIs the rated wind speed, P, of the fanrIs the rated power, v, of the fanciIs the cut-in wind speed, v, of the fancoThe cut-out wind speed of the fan;
the number of the wind turbine generators is NwtgTime, wind turbine generator output power PωThe model of (a) is:
Pω＝PwindNwtg(9)
when v isci<v<vrTime, wind turbine generator output power PωThe formula of the probability density function of (a) is:
Figure FDA0002354777630000032
in the formula (10), K is WThe shape parameter of the eibull distribution, C is the scale parameter of the Weibull distribution, f (P)ω) Probability density function, Q, of active power output of wind turbineωIs the reactive output of the wind turbine generator,
Figure FDA0002354777630000036
is the power factor;
(2-2) photovoltaic power generation system output power PsolarThe model of (a) is:
Psolar＝rAη (11)
in the formula (11), r is the radiant emittance and has the unit of W/m2，
Figure FDA0002354777630000033
Is the total area of the solar array of the photovoltaic power generation system, AmIs the area of a single battery component, M is the number of battery components of a solar array of the photovoltaic power generation system,
Figure FDA0002354777630000034
for the photoelectric conversion efficiency of solar arrays of photovoltaic power generation systems, ηmPhotoelectric conversion efficiency for a single cell assembly;
output power P of photovoltaic power generation systemsolarThe probability density function of (a) is:
Figure FDA0002354777630000035
in the formula (12), Rsolar＝rmaxA η is the maximum output power of the solar array of the photovoltaic power generation system, rmaxFor maximum radiance, α and β are both Beta distribution shape parameters.
3. The method of claim 1, wherein the step (3) of orthogonally transforming the stochastic model of the fault using cholesky decomposition comprises:
the fault line model and the fault position model in the fault stochastic modelAnd the fault type model, the fault duration model and the fault impedance model form a 5-dimensional random variable p ═ p1,p2,…,p5]TThe desired vector of the random variable p is up＝[u1,u2,…,u5]TCovariance matrix C of said random variable ppComprises the following steps:
Figure FDA0002354777630000041
determining a partial derivative factor λ of the random variable p3The formula is as follows:
Figure FDA0002354777630000042
in the formula (14), the compound represented by the formula (I),
Figure FDA0002354777630000043
for the ith random variable p in the random variables plIs within 1,5]；
The formula for determining the uncorrelated matrix q for the random variable p is:
q＝Bp (15)
in formula (15), B is an intermediate matrix;
covariance matrix C for the random variable ppPerforming orthogonal transformation, wherein the formula is as follows:
Cp＝LLT(16)
in the formula (16), L is the covariance matrix CpThe lower triangular matrix of (2);
determining the desired vector u of said uncorrelated matrix qqThe formula of (1) is:
uq＝L-1up(17)
in the formula (17), upIs the desired vector of the random variable p;
determining the r-th element q in the uncorrelated matrix qrCoefficient of partial derivation of
Figure FDA0002354777630000044
The formula of (1) is:
Figure FDA0002354777630000045
in the formula (18), the reaction mixture,
Figure FDA0002354777630000046
is the covariance matrix CpIs the r row and L column elements of the lower triangular array L, r, L e [1,5 ]]。
4. The method of claim 1, wherein in step (4), the processing the fault stochastic model and the DG stochastic model of the three-phase asymmetric power distribution network using a point estimation method comprises:
a fault line model, a fault position model, a fault type model, a fault duration model, a fault impedance model and a DG random model in the fault random model form a 7-dimensional random variable X ═ X [ X ] composed of the output power of the wind generating set and the output power of the photovoltaic power generation system in the fault random model1,X2,…,X7]TY ═ h (X) is a nonlinear function with the random variable X as a variable,
Figure FDA0002354777630000047
is the probability density function of the ith random variable in the random variables X, i belongs to [1,7 ]]；
An ith random variable X from the random variables XiTwo estimation points are extracted, wherein the k estimation point xi,kThe calculation formula is as follows:
xi,k＝μi+ξi,kσi(19)
in the formula (19), muiIs composed of
Figure FDA0002354777630000051
Expectation of (a)iIs composed of
Figure FDA0002354777630000052
Standard deviation of (A), ξi,kIs xi,kThe corresponding position coefficient, k is 1, 2;
determining an estimate of the 3 rd moment of the nonlinear function Y ═ h (X) with the random variable X as a variable according to:
Figure FDA0002354777630000053
in the formula (20), j is 1,2,3, k is 1,2, i ∈ [1,7 ]]，ωi,kIs xi,kCorresponding weight coefficient, mui-1Is composed of
Figure FDA0002354777630000054
Expectation of (d), mui+1Is composed of
Figure FDA0002354777630000055
(iii) a desire;
wherein x isi,kCorresponding weight coefficient omegai,kAnd position coefficient ξi,kSatisfies the equation:
Figure FDA0002354777630000056
in formula (21), λi,jIs the ith random variable X in the random variables XiJ order central moment of (d);
when j is 1,2, λi,1＝0，λi,2X is 1i,kCorresponding weight coefficient omegai,kAnd position coefficient ξi,kSatisfies the equation:
Figure FDA0002354777630000057
5. the method of claim 1, wherein in step (6), Y is setiIs the ith element in the random variable of the two sets of related simulation schemes, i e [ [ alpha ] ]1,14]Then, the formula for determining the probability density function of the elements in the random variables of the two sets of related simulation schemes by the Cornish-Fisher series is:
Figure FDA0002354777630000058
in the formula (23), the compound represented by the formula,
Figure FDA0002354777630000059
is ξiStandard normal distribution probability density function of (1)%, x3Is a third-order semi-invariant;
wherein, χ3Has a value of YiCoefficient of partial derivation of ξiIs YiStandard form, the formula is:
ξi＝(x-μi)/σi(24)
in the formula (24), muiIs YiMean value of (a)iIs YiThe variance of (c).
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