CN108847673A - The Probabilistic Load Flow method based on NATAF transformation in the uncertain source of arbitrariness probability distributing is obeyed in a kind of consideration AC-DC hybrid power grid - Google Patents
The Probabilistic Load Flow method based on NATAF transformation in the uncertain source of arbitrariness probability distributing is obeyed in a kind of consideration AC-DC hybrid power grid Download PDFInfo
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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
- H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
- H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
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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
- H02J3/36—Arrangements for transfer of electric power between ac networks via a high-tension dc link
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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
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Abstract
The invention discloses a kind of Probabilistic Load Flow methods based on NATAF transformation in the uncertain source that arbitrariness probability distributing is obeyed in consideration AC-DC hybrid power grid, mainly include the following steps that：1) the stochastic inputs variable X of power flow algorithm is determined.2) it generates n and ties up stochastic variable G that is irrelevant and obeying standard gaussian distribution.3) the Gaussian Profile D with degree of correlation is calculated according to stochastic variable G and split-matrix.4) Gaussian Profile Z is sampled, obtains sample point matrix A.5) the input variable matrix R for obeying Arbitrary distribution is calculated.6) using R as in the sample point input AC/VSC-MTDC AC-DC hybrid power grid certainty tide model selected, Load flow calculation is carried out.The present invention solve the problems, such as in AC-DC hybrid power grid it is a variety of have correlation uncertainty element, thus to AC-DC hybrid power grid carry out Probabilistic Load Flow analysis, to ensure that it reliably and securely runs.
Description
Technical field
The present invention relates to new-energy grid-connected technology, any probability point is obeyed in specifically a kind of consideration AC-DC hybrid power grid
The Probabilistic Load Flow method based on NATAF transformation in the uncertain source of cloth.
Background technique
HVDC transmission system (Voltage Source Converter based based on voltage-source type converter
High Voltage Direct Current, VSC-HVDC) application in from long-range wind power plant to the transmission of electricity of city load center
Extensively, it quickly grows.Compared with VSC-HVDC, multi-terminal HVDC transmission (VSC-MTDC) technology of voltage source converter has more
High power transmission efficiency and higher safety in operation.In engineering practice, a kind of certainty trend (DPF) quilt based on sequential method
It is widely used in the steady-state analysis of general AC-DC hybrid power grid, is particularly suitable for the combined hybrid system of AC/VSC-MTDC.
There is a large amount of uncertain source in AC/VSC-MTDC serial-parallel power grid, such as wind power plant, photovoltaic power plant and some waves
Dynamic load.It, should in the modeling and analysis of electric system in order to more accurately reflect the truth of alternating current-direct current power grid
These uncertain factors are taken into account.In fact, Probabilistic Load Flow (PPF) is assessment under the influence of uncertain factor
Alternating current-direct current mixing operation of power networks state effective ways, while the potential risk in Operation of Electric Systems can also be disclosed.
There are three types of Probabilistic Load Flow analytic approach：Simulation, analytic method and approximation method.Wherein, simulation refers to Monte Carlo
(Monte Carlo Simulation, the MCS) method of emulation, this method are not needed to simplify archetype, imitated every time
Originally determined property power flow algorithm is used in very, and the correlation of input variable is not required.Generally, due to MCS's
Calculated result can be exactly accurate, therefore usually as the exact value of reference, be used to other methods result calculated into
Row comparison reference.However, MCS needs a large amount of simulation calculation that could restrain, heavy computational burden is taken a substantial amount of time.It is another
Aspect, analytic method have been able to handle common Probabilistic Load Flow problem with comparatively faster calculating speed.But most of solutions
Analysis method will all linearize archetype, it is assumed that do not have correlation between the uncertain source of input system, and these processing are all
It will lead to the accuracy decline of calculated result.
In probabilistic load flow, approximation method can preferably take into account calculating speed and precision.Unscented transform
(Unscented Transformation, UT) algorithm is that have prominent representative algorithm in approximation method, it not only calculates effect
Rate is high, and can directly handle original variable and have the problem of Pearson correlation.It is general for studying the correlation of input variable
A very important important link in rate Power Flow Problem.It is current to have and UT algorithm is applied to Probabilistic Load Flow in the prior art,
To study influence of the correlation to AC network of input variable.The program is disadvantageous in that it by all stochastic inputs
Variable is assumed to be Gaussian Profile.However, the stochastic variable for inputting power grid in reality is not so.For example, wind speed may obey
Weibull distribution, Burr distribution or Lognormal distribution, and the radiation of the sun is distributed usually using beta (beta) and carries out
Modeling.
In addition, the specific distribution of various loads also relies on actual consumer behavior, they are also possible to disobey Gauss
Distribution.That is, stochastic variable may obey arbitrary asymmetrical probability distribution, and also in modern power systems
It can have correlation (more specifically, being Pearson correlation).But traditional UT method uses symmetrical sampling policy,
Such sample mode obviously cannot be used to the accurately approximate non-gaussian random variables for obeying asymmetric distribution, if still
It is handled using symmetric sampling, then the accuracy of the result of Probabilistic Load Flow will be excessively poor.
Summary of the invention
Present invention aim to address problems of the prior art.
To realize the present invention purpose and the technical solution adopted is that such, obeyed in a kind of consideration AC-DC hybrid power grid
The Probabilistic Load Flow method based on NATAF transformation in the uncertain source of arbitrariness probability distributing, mainly includes the following steps that：
1) determine that the stochastic inputs variable X of power flow algorithm, key step are as follows：
1.1) the known stochastic inputs variable X=(X for obeying different distributions type of power flow algorithm is determined1,X2,…,
Xn) and the corresponding stochastic variable Z=(Z for obeying standardized normal distribution of stochastic inputs variable X1,Z2,…,Zn)。
Further, the data in stochastic inputs variable X are that n Uncertain Stochastic variable of AC-DC hybrid power grid is obeyed
Probability distribution.N is the quantity of the Uncertain Stochastic variable of AC-DC hybrid power grid.
The Uncertain Stochastic variable mainly includes wind speed, solar radiation and the load of AC-DC hybrid power grid.
1.2) cumulative distribution function of the known stochastic inputs variable X for obeying different distributions type is determinedAnd standard
Cumulative distribution function Φ (the Z of normally distributed random variable Zi)。
1.3) the original Pearson correlation coefficient square of the known stochastic inputs variable X for obeying different distributions type is obtained
Battle array, is denoted as CX。
Wherein matrix cXThe element of i-th row jth column is stochastic inputs variable XiWith stochastic inputs variable XjBetween phase relation
Number, is denoted as ρx(i,j)。
Stochastic inputs variable XiWith stochastic inputs variable XjBetween correlation coefficient ρx(i, j) is as follows：
In formula, XiFor stochastic inputs variable XiMean value.σiFor stochastic inputs variable XiStandard deviation.μjFor stochastic inputs change
Measure XjMean value.σjFor stochastic inputs variable XjStandard deviation.For stochastic inputs variable XiCumulative distribution function anti-letter
Number.For stochastic inputs variable XjCumulative distribution function inverse function.Φ(Zi) it is standardized normal distribution ZiCumulative distribution
Function；Φ(Zj) it is standardized normal distribution ZjCumulative distribution function；For standardized normal distribution stochastic variable
Element Z in ZiAnd ZjJoint distribution function, expression is as follows：
In formula, ρ is Pearson correlation coefficient Matrix CZThe element of i-th row jth column；ZiAnd ZjIt is in stochastic variable Z
Element；
1.4) the Pearson correlation coefficient Matrix C of stochastic variable Z is obtainedZ.Wherein Pearson correlation coefficient Matrix CZI-th
The element of row jth column is variable ZiWith variable ZjBetween correlation coefficient ρz(i, j) is abbreviated as ρ.
To Pearson correlation coefficient Matrix CZIt is decomposed using Cholesky, obtains split-matrix L.I.e.：
CZ=LLT。 (3)
In formula, CZFor Pearson correlation coefficient Matrix CZ.L is split-matrix.Subscript T is transposition.
2) it generates n and ties up stochastic variable G that is irrelevant and obeying standard gaussian distribution.
3) the Gaussian Profile D=(D with degree of correlation is calculated according to stochastic variable G and split-matrix1,D2,…,
Dn)。
D=G × L. (4)
In formula, G is that n ties up stochastic variable that is irrelevant and obeying standard gaussian distribution.L is split-matrix.
4) the weighted value W of Gaussian Profile D is calculated0, weighted value WkWith weighted value Wk+n, wherein W0For initial weight value, WkAnd Wk +nTo calculate weighted value required for obtaining sample point.Weighted value W0, weighted value WkWith weighted value Wk+nMeet following formula：
In formula, n is matrix dimension.
Weighted value W0, weighted value WkWith weighted value Wk+nCalculation formula respectively as shown in formula 6 to formula 8, i.e.,：
In formula, n is the quantity of the Uncertain Stochastic variable of matrix dimension namely AC-DC hybrid power grid.
In formula, n is the quantity of the Uncertain Stochastic variable of matrix dimension namely AC-DC hybrid power grid.W0For Gauss
It is distributed the initial weight value of Z.
In formula, n is the quantity of the Uncertain Stochastic variable of matrix dimension namely AC-DC hybrid power grid.W0For Gauss
It is distributed the initial weight value of Z.
5) Gaussian Profile Z is sampled, obtains 2n+1 sample point, obtains sample point matrix A.Sample point matrix A master
It to include three groups of samples, i.e.,：
Wherein, first group of sample α0For n-dimensional vector, including
Second group of sample α1For the matrix of n row n column, i.e. α1=(α1 1,α1 2,…,α1 n), wherein k-th of vector is as follows：
In formula,It is arranged for the kth of matrix L.AndK=1,2 ..., n.WkFor weighted value.α0For
First group of sample of sample point matrix A.
Second group of sample α2For the matrix of n row n column, i.e. α2=(α2 1,α2 2,…,α2 n), wherein k-th of vector is as follows：
In formula,It is arranged for the kth of matrix L.AndK=1,2 ..., n.Wk+nFor weighted value.α0For
First group of sample of sample point matrix A.
6) inverse transformation is utilized, according to the cumulative distribution function Φ (A) of input variable A, calculates the input for obeying Arbitrary distribution
Matrix of variables R, i.e.,：
R=F-1[Φ(A)]。 (12)
In formula, F-1Indicate inverse function.Φ (A) is the cumulative distribution function of sample point matrix A.
Matrix R is the matrix of 2n+1 row, n column, R=(R1、R2……Rn)。
Wherein：
In formula,For X1The inverse function of corresponding Cumulative Distribution Function.
In formula,For X2The inverse function of corresponding Cumulative Distribution Function.
In formula,For XnThe inverse function of corresponding Cumulative Distribution Function.
According to formula 12 to formula 14, matrix R is as follows：
7) it is inputted R as the sample point selected in AC/VSC-MTDC AC-DC hybrid power grid certainty tide model, into
Row Load flow calculation.
Assuming that the unbalanced power amount of four equations is respectively Δ d in tide modelj1, Δ dj2, Δ dj3, Δ dj4, described
AC/VSC-MTDC AC-DC hybrid power grid certainty tide model is as shown in formula 16 to formula 19：
In formula, PsjThe active power absorbed for j-th of VSC inverter from AC system.udjFor the voltage of DC node.UsjFor
The voltage magnitude for the AC node being linked with VSC inverter.ujFor DC voltage usage factor.δjFor udjAnd UsjPhase angle difference.
MjFor the adjustment ratio of pulse width modulation.YjFor the equivalent admittance of jth VSC inverter and converter power transformer.αjFor YjCorresponding resistance
Anti- impedance angle.
In formula, QsjThe reactive power absorbed for j-th of VSC inverter from AC system.udjFor the voltage of DC node.UsjFor
The voltage magnitude for the AC node being linked with VSC inverter.MjFor the adjustment ratio of pulse width modulation.ujFor DC voltage utilization
Coefficient.δjFor udjAnd UsjPhase angle difference.XfjFor the impedance of alternating current filter in j-th of VSC inverter.
In formula, udjFor the voltage of DC node.UsjFor the voltage magnitude for the AC node being linked with VSC inverter.ujIt is straight
Galvanic electricity presses usage factor.δjFor udjAnd UsjPhase angle difference.MjFor the adjustment ratio of pulse width modulation.idjFor the electric current of DC node.
In formula, idjFor the electric current of DC node.gdjbFor the corresponding element of DC network node admittance matrix.udbFor DC node electricity
Pressure.ncFor VSC inverter sum in power grid.
8) judge whether calculated result reaches preset convergence precision, the i.e. maximum value of the absolute value of unbalanced power amount
max{|Δdj1|, | Δ dj2|, | Δ dj3|, | Δ dj4| whether meet max | Δ dj1|, | Δ dj2|, | Δ dj3|, | Δ dj4|}≤
Δd.Wherein, Δ d is preset convergence precision.
If not satisfied, not restraining then, return step 1.
If satisfied, then restraining, calculation of tidal current is exported.
The solution have the advantages that unquestionable.A kind of UT based on correlation coefficient transformation method of invention is calculated
Method handles Probabilistic Load Flow problem with this algorithm.The processing method of this Probabilistic Load Flow has been used with correlation not
Same probability density function (PDF).Basic thought the present invention is based on UT technology AC-DC hybrid power grid PPF is：From input with
A series of specific sample points are chosen on the PDFs of machine variable, the AC/VSC-MTDC alternating current-direct current mixed connection electricity for being determined property
Net Load flow calculation, and estimate the probabilistic information of AC-DC hybrid power grid output state variable.It is mixed that the present invention solves alternating current-direct current
It is a variety of in connection power grid that there is the problem of correlation uncertainty element (such as wind speed, solar radiation, load), thus to alternating current-direct current
Serial-parallel power grid carries out Probabilistic Load Flow (Probabilistic Power Flow, PPF) analysis, to ensure that it is reliably and securely transported
Row.
Detailed description of the invention
Fig. 1 is the IEEE-14 meshed network after being revised as AC/VSC-MTDC power grid；
Fig. 2 is AC/VSC-MTDC AC-DC hybrid power grid certainty Load flow calculation flow chart.
Specific embodiment
Below with reference to embodiment, the invention will be further described, but should not be construed the above-mentioned subject area of the present invention only
It is limited to following embodiments.Without departing from the idea case in the present invention described above, according to ordinary skill knowledge and used
With means, various replacements and change are made, should all include within the scope of the present invention.
Embodiment 1：
Obeyed in a kind of consideration AC-DC hybrid power grid the uncertain source of arbitrariness probability distributing based on the general of NATAF transformation
Rate trend method, mainly includes the following steps that：
1) determine that the stochastic inputs variable X of power flow algorithm, key step are as follows：
1.1) an AC/VSC-MTDC serial-parallel power grid, the power grid with minor modifications to IEEE-14 node power grid, are become
As shown in Figure 1.
Determine the known stochastic inputs variable X=(X for obeying different distributions type of power flow algorithm1,X2,…,Xn) and
The corresponding stochastic variable Z=(Z for obeying standardized normal distribution of stochastic inputs variable X1,Z2,…,Zn)。
Further, the data in stochastic inputs variable X are n of AC-DC hybrid power grid (AC/VSC-MTDC) uncertain
Property stochastic variable obey probability distribution.N is the quantity of the Uncertain Stochastic variable of AC-DC hybrid power grid.
The Uncertain Stochastic variable mainly includes wind speed, solar radiation and the load of AC-DC hybrid power grid.
1.2) cumulative distribution function (CDF) of the known stochastic inputs variable X for obeying different distributions type is determinedWith
Cumulative distribution function Φ (the Z of standardized normal distribution stochastic variable Zi)。
1.3) the original Pearson correlation coefficient square of the known stochastic inputs variable X for obeying different distributions type is obtained
Battle array, is denoted as CX。
Wherein Matrix CXThe element of i-th row jth column is stochastic inputs variable XiWith stochastic inputs variable XkBetween phase relation
Number, is denoted as ρx(i,j)。
Stochastic inputs variable XiWith stochastic inputs variable XjBetween correlation coefficient ρx(i, j) is as follows：
In formula, μiFor stochastic inputs variable XiMean value.σiFor stochastic inputs variable XiStandard deviation.μjFor stochastic inputs change
Measure XjMean value.σjFor stochastic inputs variable XjStandard deviation.For stochastic inputs variable XiCumulative distribution function anti-letter
Number.For stochastic inputs variable XjCumulative distribution function inverse function.Φ(Zi) it is standardized normal distribution ZiCumulative distribution
Function.Φ(Zj) it is standardized normal distribution ZjCumulative distribution function.For standardized normal distribution stochastic variable
Element Z in ZiAnd ZjJoint distribution function.
Wherein,As follows：
In formula, ρ is Pearson correlation coefficient Matrix CZThe element of i-th row jth column.ZiAnd ZjIt is in stochastic variable Z
Element.
1.4) the Pearson correlation coefficient Matrix C of stochastic variable Z is obtainedZ.Wherein Pearson correlation coefficient Matrix CZI-th
The element of row jth column is variable ZiWith variable ZjBetween correlation coefficient ρz(i, j) is abbreviated as ρ.
To Pearson correlation coefficient Matrix CZIt is decomposed using Cholesky, obtains split-matrix L.I.e.：
CZ=LLT。 (3)
In formula, CZFor Pearson correlation coefficient Matrix CZ.L is split-matrix.Subscript T is transposition.
2) it generates n and ties up stochastic variable G that is irrelevant and obeying standard gaussian distribution.
3) the Gaussian Profile D=(D with degree of correlation is calculated according to stochastic variable G and split-matrix1,D2,…,
Dn)。
D=G × L. (4)
In formula, G is that n ties up stochastic variable that is irrelevant and obeying standard gaussian distribution.L is split-matrix.
4) the weighted value W of Gaussian Profile D is calculated0, weighted value WkWith weighted value Wk+n, wherein W0For initial weight value, WkAnd Wk +nIt is to calculate weighted value required for obtaining sample point.Weighted value W0, weighted value WkWith weighted value Wk+nMeet following formula：
In formula, n is matrix dimension.
Weighted value W0, weighted value WkWith weighted value Wk+nCalculation formula respectively as shown in formula 6 to formula 8, i.e.,：
In formula, n is the quantity of the Uncertain Stochastic variable of matrix dimension namely AC-DC hybrid power grid.
In formula, n is the quantity of the Uncertain Stochastic variable of matrix dimension namely AC-DC hybrid power grid.W0For Gauss
It is distributed the initial weight value of Z.
In formula, n is the quantity of the Uncertain Stochastic variable of matrix dimension namely AC-DC hybrid power grid.W0For Gauss
It is distributed the initial weight value of Z.
5) Gaussian Profile Z is sampled, obtains 2n+1 sample point, obtains sample point matrix A.Sample point matrix A master
It to include three groups of samples, i.e.,：
Wherein, first group of sample α0For n-dimensional vector, including
Second group of sample α1For the matrix of n row n column, i.e. α1=(α1 1,α1 2,…,α1 n), wherein k-th of vector is as follows：
In formula,It is arranged for the kth of matrix L.AndK=1,2 ..., n.WkFor weighted value.α0For
First group of sample of sample point matrix A.
Second group of sample α2For the matrix of n row n column, i.e. α2=(α2 1,α2 2,…,α2N), wherein the following institute of k-th of vector
Show：
In formula,It is arranged for the kth of matrix L.AndK=1,2 ..., n.Wk+nFor weighted value.α0For
First group of sample of sample point matrix A.
6) inverse transformation is utilized, according to the cumulative distribution function Φ (A) of input variable A, calculates the input for obeying Arbitrary distribution
Matrix of variables R, i.e.,：
R=F-1[Φ(A)]。 (12)
In formula, F-1Indicate inverse function.Φ (A) is the cumulative distribution function of sample point matrix A.
Matrix A is obtained and to sampling to standardized normal distribution variable Z, so the element in matrix A is clothes
From the sample of standardized normal distribution.According to Nataf transformation premise --- former distribution variable is general with standardized normal distribution variable
Rate cumulative function is equal, i.e.,So when sample being transformed to from gaussian variable the variable of former distribution, it is defeated
Enter be Gaussian Profile sample as input, obtain obeying the sample of former distribution according to formula 11, in formula R matrix representative with
The corresponding former distribution sample matrix of A matrix.
Matrix R is the matrix of 2n+1 row, n column, R=(R1、R2……Rn)。
Wherein：
In formula,For X1The inverse function of corresponding Cumulative Distribution Function.
In formula,For X2The inverse function of corresponding Cumulative Distribution Function.
In formula,For XnThe inverse function of corresponding Cumulative Distribution Function.
According to formula 12 to formula 14, matrix R is as follows：
The parameter of the above cumulative distribution function can be according to uncertain element (wind speed, solar irradiance, the load in power grid
Deng) historical record in estimate and acquire.Typical probability distribution such as table 1 that element is obeyed are not known in power grid：
The typical probability distribution that element is obeyed is not known in 1 power grid of table
7) it is inputted R as the sample point selected in AC/VSC-MTDC AC-DC hybrid power grid certainty tide model, into
Row Load flow calculation.
The AC/VSC-MTDC AC-DC hybrid power grid certainty tide model is as shown in formula 16 to formula 19：
In formula, PsjThe active power absorbed for j-th of VSC inverter from AC system.udjFor the voltage of DC node.UsjFor
The voltage magnitude for the AC node being linked with VSC inverter.ujFor DC voltage usage factor.δjFor udjAnd UsjPhase angle difference.
MjFor the adjustment ratio of pulse width modulation.YjFor the equivalent admittance of jth VSC inverter and converter power transformer.αjFor YjCorresponding resistance
Anti- impedance angle
In formula, QsjThe reactive power absorbed for j-th of VSC inverter from AC system.udjFor the voltage of DC node.UsjFor
The voltage magnitude for the AC node being linked with VSC inverter.ujFor DC voltage usage factor.δjFor udjAnd UsjPhase angle difference.
MjFor the adjustment ratio of pulse width modulation.XfjFor the impedance of alternating current filter in j-th of VSC inverter.
In formula, udjFor the voltage of DC node.UsjFor the voltage magnitude for the AC node being linked with VSC inverter.ujIt is straight
Galvanic electricity presses usage factor.δjFor udjAnd UsjPhase angle difference.MjFor the adjustment ratio of pulse width modulation.idjFor the electric current of DC node.
In formula, idjFor the electric current of DC node.
gdjbFor the corresponding element of DC network node admittance matrix.udbFor DC node voltage.ncFor VSC inverter in power grid
Sum.
Further, VSC inverter can independent control be active and reactive power.In order to realize automatic maintain in DC grid
Active power balance, should at least choosing a VSC inverter as the active power regulation device of DC grid, (VSC is generally adopted
With determining DC voltage udjControl).In general, the control model of VSC can be divided into following four：
I) determine DC voltage udj, determine reactive power QsjControl：(udj-Qsj)。
II) determine DC voltage udj, determine DC voltage UsjControl：(udj-Usj)。
III) determine dc power Psj, determine reactive power QsjControl：(Psj-Qsj)。
IV) determine dc power Psj, determine DC voltage UsjControl：(Psj-Usj)。
It is worth noting that the basic thought based on UT technology AC-DC hybrid power grid PPF is：From input stochastic variable
A series of specific sample points are chosen on PDFs, based on the AC/VSC-MTDC AC-DC hybrid power grid trend of being determined property
It calculates, and estimates the probabilistic information of AC-DC hybrid power grid output state variable, such as：Ac bus voltage, the branch of alternating current-direct current
The control parameter of road trend and VSC-MTDC.Fig. 2 is the alternating of AC/VSC-MTDC AC-DC hybrid power grid certainty Load flow calculation
The process of iteration.
8) judge whether calculated result reaches preset convergence precision, the i.e. maximum value of the absolute value of unbalanced power amount
max{|Δdj1|, | Δ dj2|, | Δ dj3|, | Δ dj4| whether meet max | Δ dj1|, | Δ dj2|, | Δ dj3|, | Δ dj4|}≤
Δd.Wherein, Δ d is preset convergence precision.
If not satisfied, not restraining then, return step 1.
If satisfied, then restraining, calculation of tidal current, the i.e. probability of output AC/DC serial-parallel power grid output state variable are exported
Information mainly includes alternating current-direct current busbar voltage, the control parameter of the Branch Power Flow of alternating current-direct current and VSC-MTDC.
Claims (3)
1. a kind of probability based on NATAF transformation in the uncertain source for considering to obey arbitrariness probability distributing in AC-DC hybrid power grid
Trend method, which is characterized in that mainly include the following steps that：
1) determine that the stochastic inputs variable X of the power flow algorithm, key step are as follows：
1.1) the known stochastic inputs variable X=(X for obeying different distributions type of power flow algorithm is determined1, X2..., Xn)
Stochastic variable Z=(the Z that obeys standardized normal distribution corresponding with stochastic inputs variable X1, Z2..., Zn)；
1.2) the cumulative distribution function F of the known stochastic inputs variable X for obeying different distributions type is determinedXiWith standard normal point
Cumulative distribution function Φ (the Z of cloth stochastic variable Zi)；
1.3) the original Pearson correlation coefficient matrix of the known stochastic inputs variable X for obeying different distributions type, note are obtained
For CX；
Stochastic inputs variable XiWith stochastic inputs variable XjBetween correlation coefficient ρx(i, j) is as follows：
In formula, μiFor stochastic inputs variable XiMean value；σiFor stochastic inputs variable XiStandard deviation；μjFor stochastic inputs variable Xj
Mean value；σjFor stochastic inputs variable XjStandard deviation；For stochastic inputs variable XiCumulative distribution function inverse function；For stochastic inputs variable XjCumulative distribution function inverse function；Φ(Zi) it is standardized normal distribution ZiCumulative distribution letter
Number；Φ(Zj) it is standardized normal distribution ZjCumulative distribution function；For standardized normal distribution stochastic variable Z
In element ZiAnd ZjJoint distribution function, expression is as follows：
In formula, ρ is Pearson correlation coefficient Matrix CZThe element of i-th row jth column；ZiAnd ZjIt is the element in stochastic variable Z；
1.4) the Pearson correlation coefficient Matrix C of stochastic variable Z is obtainedZ；Wherein Pearson correlation coefficient Matrix CZI-th row jth
The element of column is variable ZiWith variable ZjBetween correlation coefficient ρz(i, j) is abbreviated as ρ；
To Pearson correlation coefficient Matrix CZIt is decomposed using Cholesky, obtains split-matrix L；I.e.：
CZ=LLT； (3)
In formula, CZFor Pearson correlation coefficient Matrix CZ；L is split-matrix；Subscript T is transposition；
2) it generates n and ties up stochastic variable G that is irrelevant and obeying standard gaussian distribution；
3) the Gaussian Profile D=(D with degree of correlation is calculated according to stochastic variable G and split-matrix1, D2..., Dn)；
D=G × L； (4)
In formula, G is that n ties up stochastic variable that is irrelevant and obeying standard gaussian distribution；L is split-matrix；
4) the weighted value W of Gaussian Profile D is calculated0, weighted value WkWith weighted value Wk+n；Weighted value W0, weighted value WkWith weighted value Wk+n
Meet following formula：
In formula, n is matrix dimension；
Weighted value W0, weighted value WkWith weighted value Wk+nCalculation formula respectively as shown in formula 6 to formula 8, i.e.,：
In formula, n is the quantity of the Uncertain Stochastic variable of matrix dimension namely AC-DC hybrid power grid；
In formula, n is the quantity of the Uncertain Stochastic variable of matrix dimension namely AC-DC hybrid power grid；W0For Gaussian Profile Z
Initial weight value；
In formula, n is the quantity of the Uncertain Stochastic variable of matrix dimension namely AC-DC hybrid power grid；W0For Gaussian Profile Z
Initial weight value；
5) Gaussian Profile Z is sampled, obtains 2n+1 sample point, obtains sample point matrix A；Sample point matrix A is mainly wrapped
Three groups of samples are included, i.e.,：
Wherein, first group of sample α0For n-dimensional vector, including
Second group of sample α1For the matrix of n row n column, i.e. α1=(α1 1, α1 2..., α1 n), wherein k-th of vector is as follows：
In formula,It is arranged for the kth of matrix L；AndWkFor weighted value；α0For sample
First group of sample of this dot matrix A；
Second group of sample α2For the matrix of n row n column, i.e. α2=(α2 1, α2 2..., α2 n), wherein k-th of vector is as follows：
In formula,It is arranged for the kth of matrix L；AndWk+nFor weighted value；α0For sample
First group of sample of this dot matrix A；
6) inverse transformation is utilized, according to the cumulative distribution function Φ (A) of input variable A, calculates the input variable for obeying Arbitrary distribution
Matrix R, i.e.,：
R=F-1[Φ(A)]； (12)
In formula, F-1Indicate inverse function；Φ (A) is the cumulative distribution function of sample point matrix A；
Matrix R is the matrix of 2n+1 row, n column, R=(R1、R2……Rn)；
Wherein：
In formula,For X1The inverse function of corresponding Cumulative Distribution Function；
In formula,For X2The inverse function of corresponding Cumulative Distribution Function；
In formula,For XnThe inverse function of corresponding Cumulative Distribution Function；
According to formula 13 to formula 15, matrix R is as follows：
7) using R as in the sample point input AC/VSC-MTDC AC-DC hybrid power grid certainty tide model selected, tide is carried out
Stream calculation；
8) judge whether calculated result reaches preset convergence precision, that is, judge the maximum value of the absolute value of unbalanced power amount
max{|Δdj1|, | Δ dj2|, | Δ dj3|, | Δ dj4| whether meet max | Δ dj1|, | Δ dj2|, | Δ dj3|, | Δ dj4|}≤
Δd；
If not satisfied, not restraining then, return step 1.
If satisfied, then restraining, calculation of tidal current is exported.
2. a kind of uncertain source for considering to obey arbitrariness probability distributing in AC-DC hybrid power grid according to claim 1
Probabilistic Load Flow method based on NATAF transformation, it is characterised in that：Data in stochastic inputs variable X are AC-DC hybrid power grid
N Uncertain Stochastic variable obey probability distribution；N is the number of the Uncertain Stochastic variable of AC-DC hybrid power grid
Amount；
The Uncertain Stochastic variable mainly includes wind speed, solar radiation and the load of AC-DC hybrid power grid.
3. obeying the uncertain of arbitrariness probability distributing in a kind of consideration AC-DC hybrid power grid according to claim 1 or 2
The Probabilistic Load Flow method based on NATAF transformation in source, it is characterised in that：Assuming that in tide model four equations unbalanced power
Amount is respectively Δ dj1, Δ dj2, Δ dj3, Δ dj4, the AC/VSC-MTDC AC-DC hybrid power grid certainty tide model such as public affairs
Shown in formula 17 to formula 20：
In formula, PsjThe active power absorbed for j-th of VSC inverter from AC system；udjFor the voltage of DC node；UsjFor and VSC
The voltage magnitude for the AC node that inverter is linked；ujFor DC voltage usage factor；δjFor udjAnd UsjPhase angle difference；MjFor arteries and veins
Rush the adjustment ratio of width modulated；YjFor the equivalent admittance of jth VSC inverter and converter power transformer；αjFor YjThe resistance of counterpart impedance
Anti- angle；
In formula, QsjThe reactive power absorbed for j-th of VSC inverter from AC system；udjFor the voltage of DC node；UsjFor and VSC
The voltage magnitude for the AC node that inverter is linked；ujFor DC voltage usage factor；MjFor the adjustment ratio of pulse width modulation；
δjFor udjAnd UsjPhase angle difference；XfjFor the impedance of alternating current filter in j-th of VSC inverter；
In formula, udjFor the voltage of DC node；UsjFor the voltage magnitude for the AC node being linked with VSC inverter；ujFor direct current
Press usage factor；δjFor udjAnd UsjPhase angle difference；idjFor the electric current of DC node；MjFor the adjustment ratio of pulse width modulation；
In formula, idjFor the electric current of DC node；gdjbFor the corresponding element of DC network node admittance matrix；udbFor DC node voltage；nc
For the sum of VSC inverter in power grid.
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