CN105515001B - A kind of probability load flow calculation method containing wind power system based on minimum error originated from input criterion - Google Patents
A kind of probability load flow calculation method containing wind power system based on minimum error originated from input criterion Download PDFInfo
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Abstract
The invention discloses a kind of probability load flow calculation method containing wind power system based on minimum error originated from input criterion, comprise the following steps：Step 1：Obtain initial data；Step 2：Probabilistic Modeling is carried out to uncertain factor, obtains reference distribution function；Step 3：Based on minimum error originated from input criterion, Optimal calculation exponent number k is judgedopt；Step 4, using koptRank cumulant calculates Probabilistic Load Flow with Gram Charlier series expansions.The present invention can quickly determine the series exponent number for making error originated from input minimum, consider the influence of each uncertain factor pair distribution function fitting effect comprehensively, so as on the premise of computational accuracy is ensured, improve the computational efficiency of the Probabilistic Load Flow containing wind power system.
Description
Technical field
The present invention relates to a kind of Probabilistic Load field, specifically a kind of cumulant and Gram-
The system of selection of exponent number in Charlier series expansion probabilistic load flows.
Background technology
Wind-electricity integration brings more uncertain factors to power system, in order to describe power system uncertain factor pair
The influence of system safety and economic operation, using Probabilistic Load Flow method can effectively judge system state variables it is various it is uncertain because
Excursion under the influence of element, alternative plan is formulated for scheduler, maintain system normal operation significant.
Monte Carlo uses extensive sampling techniques, and sampling obtains system-wide stochastic regime, and each state is carried out
Load flow calculation, as a result accurate but amount of calculation is excessive.Cumulants method utilizes cumulant with Gram-Charlier Series Expansion Methods
Linear behavio(u)r, the distribution function of stochastic variable is expressed as to the multinomial series of normal distribution, eliminated the reliance on extensive random
Sampling, only logical too small amount of calculating can obtain the distribution situation of stochastic variable.
It is existing to be based in cumulant and Gram-Charlier series expansion probability load flow calculation methods, often in 3-9 ranks
Middle selection single order lacks foundation as calculating limit, so selection.In view of uncertain factor in power system diversity with
Complexity, influence of the different uncertain factor of accurate evaluation to error originated from input is difficult to using conventional probability trend method, and lacked
Weary unified error criterion assesses the fitting effect of the relatively original stochastic variable of Gram-Charlier series, so as to cause
Exponent number selection is chaotic, and computational efficiency is low.
The content of the invention
In place of the present invention is in order to overcome above-mentioned the shortcomings of the prior art, there is provided one kind is based on minimum error originated from input criterion
The probability load flow calculation method containing wind power system, to can quickly determine to make the minimum series exponent number of error originated from input, Quan Miankao
The influence of each uncertain factor pair distribution function fitting effect is considered, so as to which on the premise of computational accuracy is ensured, raising contains wind-powered electricity generation
The computational efficiency of system Probabilistic Load Flow.
In order to realize foregoing invention purpose, the present invention adopts the following technical scheme that：
A kind of probability load flow calculation method containing wind power system based on minimum error originated from input criterion of the present invention, it is described to contain wind
Electric system includes fired power generating unit, wind power plant and load；The fired power generating unit is designated as G={ G1,G2,...,Gi,...,GNG, Gi
Represent i-th fired power generating unit, i-th fired power generating unit GiActive power and reactive power be designated as P respectivelyGiAnd QGi, i=1,
2,…,NG；The wind power plant is designated as W={ W1,W2,...,Wj,...,WNW}；WjRepresent j-th of wind power plant；J-th of the wind
Electric field WjActive power note with reactive power be designated as P respectivelyWjAnd QWj, j=1,2 ..., NW；The load is designated as L={ L1,
L2,...,Lm,...,LNL, LmRepresent m-th of load, m-th of load LmActive power be designated as respectively with reactive power
PLmAnd QLm, m=1,2 ..., NL；It is characterized in, the probability load flow calculation method is to carry out as follows：
Step 1：I-th fired power generating unit G is established respectivelyiActive-power PGiReference distribution function CDFPGi, it is described
I-th fired power generating unit GiReactive power QGiReference distribution function CDFQGi, j-th of wind power plant WjActive-power PWj
Reference distribution function CDFPWj, j-th of wind power plant WjReactive power QWjReference distribution function CDFQWj, the m
Individual load LmActive-power PLmReference distribution function CDFPLmAnd m-th of load LmReactive power QLmReference
Distribution function CDFQLm；
Step 2：I-th fired power generating unit G is calculated respectivelyiActive-power PGi1-kmaxRank moment of the orignWith 1-kmaxRank cumulantInstitute
State i-th fired power generating unit GiReactive power QGi1-kmaxRank moment of the orignWith 1-
kmaxRank cumulantJ-th of wind power plant WjActive-power PWj1-kmax
Rank moment of the orignWith 1-kmaxRank cumulant
J-th of wind power plant WjReactive power QWj1-kmaxRank moment of the orignWith 1-
kmaxRank cumulantM-th of load LmActive-power PLm1-kmaxRank is former
Point squareWith 1-kmaxRank cumulantWith
And m-th of load LmReactive power QLm1-kmaxRank moment of the orignWith
1-kmaxRank cumulant
Step 3：Using minimum error originated from input criterion, it is optimal to find the Gram-Charlier series for making error of fitting minimum
Exponent number kopt；
Step 3-1：Definition test exponent number is ktest；1≤ktest≤kmax；And initialize ktest=3；
Step 3-2：I-th fired power generating unit G is extracted respectivelyiActive-power PGi1-ktestRank cumulantI-th fired power generating unit GiReactive power QGi1-ktestRank cumulantJ-th of wind power plant WjActive-power PWj1-ktestRank cumulantJ-th of wind power plant WjReactive power QWj1-ktestRank cumulantM-th of load LmActive-power PLm1-ktestRank cumulantAnd m-th of load LmActive-power PLm1-ktestRank cumulantAnd k is used respectivelytestRank A type Gram-Charlier series generates i-th fired power generating unit Gi
Active-power PGiKtestRank is fitted distribution functionI-th fired power generating unit GiReactive power QGiKtest
Rank is fitted distribution functionJ-th of wind power plant WjActive-power PWjKtestRank is fitted distribution functionJ-th of wind power plant WjReactive power QWjKtestRank is fitted distribution functionDescribed m-th negative
Lotus LmActive-power PLmKtestRank is fitted distribution functionM-th of load LmReactive power QLmKtest
Rank is fitted distribution function
Step 3-3：I-th fired power generating unit G is calculated respectivelyiActive-power PGiKtestRank is fitted distribution functionError of fitting indexI-th fired power generating unit GiReactive power QGiKtestRank fitting distribution letter
NumberError of fitting indexJ-th of wind power plant WjActive-power PWjKtestRank fitting distribution letter
NumberError of fitting indexJ-th of wind power plant WjReactive power QWjKtestRank fitting distribution letter
NumberError of fitting indexM-th of load LmActive-power PLmKtestRank is fitted distribution functionError of fitting indexAnd m-th of load LmReactive power QLmKtestRank fitting distribution letter
NumberError of fitting index
Step 3-4：Calculate ktestRank is fitted the overall error of fitting index of distribution functionAnd by ktest+ 1 is assigned to
ktest, judge ktest≤kmaxWhether set up, if so, then return to step 3-2 orders perform；Otherwise, represent to obtain overall distribution
Function Fitting error criterionInto step 3-5；
Step 3-5：From the overall distribution Function Fitting error criterionIn select minimum value institute
Corresponding exponent number is designated as k as optimal exponent numberopt；When multiple identical minimum values be present, then select corresponding to multiple minimum values
Exponent number in minimum exponent number as optimal exponent number, be designated as kopt；
Step 4：With i-th fired power generating unit GiActive-power PGi1-koptRank cumulantI-th fired power generating unit GiReactive power QGi1-koptRank cumulantJ-th of wind power plant WjActive-power PWj1-koptRank cumulantJ-th of wind power plant WjReactive power QWj1-koptRank cumulantM-th of load LmActive-power PLm1-koptRank cumulantAnd m-th of load LmReactive power QLm1-koptRank cumulantAs probabilistic load flow model input variable and carry out probabilistic load flow, saved respectively
The 1-k of point voltageoptThe 1-k of rank cumulant and branch poweroptRank cumulant；Recycle koptRank A types Gram-
The distribution function of node voltage and branch power described in Charlier series approachings.
The characteristics of probability load flow calculation method containing wind power system of the present invention based on minimum error originated from input criterion
Lie also in,
The step 3-2 is to obtain k as followstestRank is fitted distribution function：
Step 3-2-1：According to i-th fired power generating unit GiActive-power PGi1-ktestRank cumulantI-th fired power generating unit GiReactive power QGi1-ktestRank cumulantJ-th of wind power plant WjActive-power PWj1-ktestRank cumulantJ-th of wind power plant WjReactive power QWj1-ktestRank cumulantM-th of load LmActive-power PLm1-ktestRank cumulantAnd m-th of load LmActive-power PLm1-ktestRank cumulantCalculate respectively and obtain i-th fired power generating unit GiActive-power PGi1-ktestRank A types
Gram-Charlier series coefficientsI-th fired power generating unit GiReactive power QGi1-ktest
Rank A type Gram-Charlier series coefficientsJ-th of wind power plant WjActive-power PWj1-
ktestRank A type Gram-Charlier series coefficientsJ-th of wind power plant WjReactive power QWj
1-ktestRank A type Gram-Charlier series coefficientsM-th of load LmActive-power PLm
1-ktestRank A type Gram-Charlier series coefficientsAnd m-th of load LmIt is idle
Power QLm1-ktestRank A type Gram-Charlier series coefficients
Step 3-2-2：I-th fired power generating unit G is obtained according to formula (1) respectivelyiActive-power PGiKtestRank is intended
Close distribution functionI-th fired power generating unit GiReactive power QGiKtestRank is fitted distribution functionJ-th of wind power plant WjActive-power PWjKtestRank is fitted distribution functionJ-th of the wind
Electric field WjReactive power QWjKtestRank is fitted distribution functionM-th of load LmActive-power PLm's
ktestRank is fitted distribution functionM-th of load LmReactive power QLmKtestRank is fitted distribution function
In formula (1), H(k-1)(x) it is k-1 rank Hermite multinomials, Φ (x) is the distribution function of standardized normal distribution,For the density function of standardized normal distribution；temp∈{PGi,QGi,PWj,QWj,PLm,QLm}.
The step 3-3 is to calculate i-th fired power generating unit G respectively according to formula (2)iActive-power PGiKtestRank
It is fitted distribution functionError of fitting indexI-th fired power generating unit GiReactive power QGiKtest
Rank is fitted distribution functionError of fitting indexJ-th of wind power plant WjActive-power PWjKtest
Rank is fitted distribution functionError of fitting indexJ-th of wind power plant WjReactive power QWjKtest
Rank is fitted distribution functionError of fitting indexM-th of load LmActive-power PLmKtestRank
It is fitted distribution functionError of fitting indexAnd m-th of load LmReactive power QLmKtest
Rank is fitted distribution functionError of fitting index
The step 3-4 is the steps of obtaining overall error of fitting index
Step 3-4-1：With i-th fired power generating unit GiActive-power PGiAverage value, j-th of wind power plant Wj
Active-power PWjAverage value and m-th of load LmActive-power PLmAverage value respectively with containing wind power system
The ratio between total burden with power, respectively as the error of fitting indexWeight coefficient wPGi, the error of fitting indexWeight coefficient wPWjAnd the error of fitting indexWeight coefficient wPLm；With i-th fired power generating unit
GiReactive power QGiAverage value, j-th of wind power plant WjReactive power QWjAverage value and it is described m-th it is negative
Lotus LmReactive power QLmAverage value respectively with containing the ratio between total load or burden without work of wind power system, referring to respectively as the error of fitting
MarkWeight coefficient wQGi, the error of fitting indexWeight coefficient wQWjAnd the error of fitting indexWeight coefficient wPLm；
Step 3-4-2：K is calculated according to formula (3)testRank global error index
Compared with the prior art, beneficial effects of the present invention are embodied in：
1st, Integral Thought of the present invention is simply clear and definite, considers fired power generating unit, wind power plant and load active power probability comprehensively
Contribution of the factor to Gram-Charlier series error originated from inputs, for the Gram-Charlier of the Probabilistic Load containing wind-powered electricity generation
Series calculates exponent number selection, there is provided effective practical approach.
2nd, the present invention proposes the minimum error originated from input judgment criterion of Probabilistic Load Flow, for based on Cumulants method and Gram-
The Probabilistic Load Flow method of Charlier series expansions, there is provided the guidance foundation of exponent number selection, filled up ongoing research area
Vacancy, to the full extent in reservation system uncertain factor probability characteristics.
3rd, the present invention considers the influence of a variety of uncertain factors in power system, it is contemplated that the moderate heat of power system containing wind-powered electricity generation
The random fault of group of motors, wind power plant active power output and load active power random fluctuation, are more comprehensively reflected containing wind-powered electricity generation
Influence of the uncertain factor to system operation in power system.
4th, the fitting effect of present invention selection distribution function is as error judgment foundation, definition fitting distribution function and reference
The integration square in full domain of the difference of distribution function overcomes discrete variable and density is not present as error of fitting index
The problem of function, by the discrete random variable in power system and the unified consideration of continuous random variable.
5th, the present invention selects the ratio of rated active power and system installed capacity as each uncertain factor to being distributed letter
The weight coefficient of number error of fitting index, with the cumulant that this is selected and Gram-Charlier series expansion exponent numbers, Neng Gouti
The difference that now each uncertain factor pair distribution function fitting effect influences.
Brief description of the drawings
Fig. 1 is the flow chart of the present invention.
Embodiment
With reference to specific embodiment, the present invention is furture elucidated, it should be understood that these embodiments are merely to illustrate the present invention
Rather than limitation the scope of the present invention, after the present invention has been read, various equivalences of the those skilled in the art to the present invention
The modification of form falls within the application appended claims limited range.
In the present embodiment, include fired power generating unit, wind power plant and load containing wind power system；Fired power generating unit is designated as G={ G1,
G2,...,Gi,...,GNG, GiRepresent i-th fired power generating unit, i-th fired power generating unit GiActive power be designated as with reactive power
PGi、QGi, i=1,2 ..., NG；Wind power plant is designated as W={ W1,W2,...,Wj,...,WNW}；WjRepresent j-th of wind power plant；Jth
Individual wind power plant WjActive power note with reactive power be designated as PWj、QWj, j=1,2 ..., NW；Load is designated as L={ L1,
L2,...,Lm,...,LNL, LmRepresent m-th of load, m-th of load LmActive power and reactive power be designated as PLm、QLm, m
=1,2 ..., NL；
As shown in figure 1, a kind of probability load flow calculation method containing wind power system based on minimum error originated from input criterion, can
To the full extent in reservation system uncertain factor probability characteristics, it is comprehensive to embody each uncertain factor pair distribution function fitting effect
The influence of fruit.Specifically, it is to carry out as follows：
Step 1：I-th fired power generating unit G is established respectivelyiActive-power PGiReference distribution function CDFPGi, i-th fire
Group of motors GiReactive power QGiReference distribution function CDFQGi, j-th of wind power plant WjActive-power PWjReference distribution letter
Number CDFPWj, j-th of wind power plant WjReactive power QWjReference distribution function CDFQWj, m-th of load LmActive-power PLm
Reference distribution function CDFPLmAnd m-th of load LmReactive power QLmReference distribution function CDFQLm；
Step 1-1：Obtain the dependency number of fired power generating unit, wind power plant and load active power and reactive power probabilistic Modeling
According to, including fired power generating unit fault rate λGi, repair rate μGi；The historical data P of active power of wind power field and reactive powerWj,n、QWj,n,
N=1,2 ..., 8760；Load active power fluctuation standard deviation sigmaPLmWith reactive power fluctuation standard deviation sigmaQLm；
Step 1-2：According to fired power generating unit fault rate λGi, repair rate μGi, fired power generating unit forced outage is calculated according to formula (1)
Rate FORGi,
I-th fired power generating unit G is obtained using formula (2)iActive-power PGiReference distribution function CDFPGi；
I-th fired power generating unit G is obtained using formula (3)iReactive power QGiReference distribution function CDFQGi：
Step 1-3：According to active power of wind power field historical data PWj,n, calculate j-th of wind power plant WjAverage active power
PWj,aveWith maximum active-power PWj,max, j-th of wind power plant W is calculated according to formula (4)jActive-power PWjWeibull distribution shape
Shape parameter kPWjWith scale parameter cPWj,
J-th of wind power plant W is obtained using formula (5)jActive-power PWjReference distribution function CDFPWj：
According to wind power plant reactive power historical data QWj,n, calculate j-th of wind power plant WjAverage reactive power QWj,aveWith
Maximum active power QWj,max, j-th of wind power plant W is calculated according to formula (6)jReactive power QWjWeibull Distribution Form Parameter
kQWjWith scale parameter cQWj,
The reference distribution function CDF of wind power plant reactive power is obtained using formula (7)QWj：
Step 1-4：According to load fluctuation standard deviation sigmaLm, the reference distribution function of load active power is established according to formula (8)
CDFPLmWith the reference distribution function CDF of reactive powerQLm；
Step 2：I-th fired power generating unit G is calculated respectivelyiActive-power PGi1-kmaxRank moment of the orignWith 1-kmaxRank cumulantThe
I platform fired power generating units GiReactive power QGi1-kmaxRank moment of the orignWith 1-kmax
Rank cumulantJ-th of wind power plant WjActive-power PWj1-kmaxRank origin
SquareWith 1-kmaxRank cumulantJth
Individual wind power plant WjReactive power QWj1-kmaxRank moment of the orignWith 1-kmaxRank
CumulantM-th of load LmActive-power PLm1-kmaxRank moment of the orignWith 1-kmaxRank cumulantAnd
M-th of load LmReactive power QLm1-kmaxRank moment of the orignWith 1-kmaxRank
Cumulant
Step 2-1：According to fired power generating unit forced outage rate FORGi, i-th fired power generating unit G is calculated according to formula (9)iIt is active
Power PGi1-kmaxRank moment of the orignWith i-th fired power generating unit GiReactive power QGi1-kmaxRank moment of the orignK=
1,2,…,kmax；
Step 2-2：According to j-th of wind power plant WjActive-power PWjReference distribution function CDFPWjWith j-th of wind power plant
WjReactive power QWjReference distribution function CDFQWj, j-th of wind power plant W is calculated according to formula (10)jActive-power PWj1-
kmaxRank moment of the orignWith j-th of wind power plant WjReactive power QWj1-kmaxRank moment of the orign
Step 2-3：According to m-th of load LmActive-power PLmReference distribution function CDFPLmWith m-th of load Lm's
Reactive power QLmReference distribution function CDFQLm, m-th of load L is calculated according to formula (11)mActive-power PLm1-kmaxRank
Moment of the orignWith m-th of load LmReactive power QLm1-kmaxRank moment of the orign
Step 2-4：According to such as formula (12) moment of the orign and the conversion relation of cumulant, substitute into fired power generating unit, wind power plant and
The k rank moment of the origns of load active powerWithCalculate fired power generating unit, wind power plant
With the k rank cumulant of load active powerWith
In formula (12), temp ∈ { PGi, QGi, PWj, QWj, PLm, QLm }；
Step 3：Using minimum error originated from input criterion, it is optimal to find the Gram-Charlier series for making error of fitting minimum
Exponent number kopt；
Step 3-1：Definition test exponent number is ktest；1≤ktest≤kmax；And initialize ktest=3；
Step 3-2：I-th fired power generating unit G is extracted respectivelyiActive-power PGi1-ktestRank cumulantI-th fired power generating unit GiReactive power QGi1-ktestRank cumulant
J-th of wind power plant WjActive-power PWj1-ktestRank cumulantJ-th of wind power plant WjNothing
Work(power QWj1-ktestRank cumulantM-th of load LmActive-power PLm1-ktestRank
CumulantAnd m-th of load LmActive-power PLm1-ktestRank cumulantAnd k is used respectivelytestRank A type Gram-Charlier series generates i-th fired power generating unit GiHave
Work(power PGiKtestRank is fitted distribution functionI-th fired power generating unit GiReactive power QGiKtestRank is fitted
Distribution functionJ-th of wind power plant WjActive-power PWjKtestRank is fitted distribution functionJ-th of wind
Electric field WjReactive power QWjKtestRank is fitted distribution functionM-th of load LmActive-power PLmKtestRank
It is fitted distribution functionM-th of load LmReactive power QLmKtestRank is fitted distribution function
Step 3-2-1：According to i-th fired power generating unit GiActive-power PGi1-ktestRank cumulantI-th fired power generating unit GiReactive power QGi1-ktestRank cumulant
J-th of wind power plant WjActive-power PWj1-ktestRank cumulantJ-th of wind power plant WjNothing
Work(power QWj1-ktestRank cumulantM-th of load LmActive-power PLm1-ktestRank
CumulantAnd m-th of load LmActive-power PLm1-ktestRank cumulantCalculate respectively and obtain i-th fired power generating unit GiActive-power PGi1-ktestRank A types Gram-
Charlier series coefficientsI-th fired power generating unit GiReactive power QGi1-ktestRank A types Gram-
Charlier series coefficientsJ-th of wind power plant WjActive-power PWj1-ktestRank A types Gram-
Charlier series coefficientsJ-th of wind power plant WjReactive power QWj1-ktestRank A types Gram-
Charlier series coefficientsM-th of load LmActive-power PLm1-ktestRank A types Gram-
Charlier series coefficientsAnd m-th of load LmReactive power QLm1-ktestRank A types
Gram-Charlier series coefficients
Step 3-2-2：I-th fired power generating unit G is obtained according to formula (13) respectivelyiActive-power PGiKtestRank fitting point
Cloth functionI-th fired power generating unit GiReactive power QGiKtestRank is fitted distribution functionJ-th of wind
Electric field WjActive-power PWjKtestRank is fitted distribution functionJ-th of wind power plant WjReactive power QWjKtest
Rank is fitted distribution functionM-th of load LmActive-power PLmKtestRank is fitted distribution functionM
Individual load LmReactive power QLmKtestRank is fitted distribution function
In formula (1), H(k-1)(x) it is k-1 rank Hermite multinomials, Φ (x) is the distribution function of standardized normal distribution,For the density function of standardized normal distribution；temp∈{PGi,QGi,PWj,QWj,PLm,QLm}.
Step 3-3：I-th fired power generating unit G is calculated according to formula (14) respectivelyiActive-power PGiKtestRank fitting distribution
FunctionError of fitting indexI-th fired power generating unit GiReactive power QGiKtestRank fitting distribution letter
NumberError of fitting indexJ-th of wind power plant WjActive-power PWjKtestRank is fitted distribution functionError of fitting indexJ-th of wind power plant WjReactive power QWjKtestRank is fitted distribution functionError of fitting indexM-th of load LmActive-power PLmKtestRank is fitted distribution functionError of fitting indexAnd m-th of load LmReactive power QLmKtestRank is fitted distribution functionError of fitting index
Step 3-4：Calculate ktestRank is fitted the overall error of fitting index of distribution functionAnd by ktest+ 1 is assigned to
ktest, judge ktest≤kmaxWhether set up, if so, then return to step 3-2 orders perform；Otherwise, represent to obtain overall distribution
Function Fitting error criterionInto step 3-5；
Step 3-4-1：With i-th fired power generating unit GiActive-power PGiAverage value, j-th of wind power plant WjWattful power
Rate PWjAverage value and m-th of load LmActive-power PLmAverage value respectively with containing the total burden with power of wind power system it
Than respectively as error of fitting indexWeight coefficient wPGi, error of fitting indexWeight coefficient wPWjAnd
Error of fitting indexWeight coefficient wPLm；With i-th fired power generating unit GiReactive power QGiAverage value, j-th of wind-powered electricity generation
Field WjReactive power QWjAverage value and m-th of load LmReactive power QLmAverage value respectively with containing wind power system
The ratio between total load or burden without work, respectively as error of fitting indexWeight coefficient wQGi, error of fitting indexWeight
Coefficient wQWjAnd error of fitting indexWeight coefficient wPLm；
Step 3-4-2：K is calculated according to formula (15)testRank global error index
Step 3-4-3：By ktest+ 1 is assigned to ktest, judge ktest≤kmaxWhether set up, if so, then return to step 3-
2 orders perform；Otherwise, represent to obtain overall distribution Function Fitting error criterionInto step 3-
5；
Step 3-5：From overall distribution Function Fitting error criterionIn select corresponding to minimum value
Exponent number as optimal exponent number, be designated as kopt；When multiple identical minimum values be present, then the rank corresponding to multiple minimum values is selected
Minimum exponent number is designated as k as optimal exponent number in numberopt；
Step 4：With i-th fired power generating unit GiActive-power PGi1-koptRank cumulant
I-th fired power generating unit GiReactive power QGi1-koptRank cumulantJ-th of wind power plant Wj's
Active-power PWj1-koptRank cumulantJ-th of wind power plant WjReactive power QWj1-kopt
Rank cumulantM-th of load LmActive-power PLm1-koptRank cumulantAnd m-th of load LmReactive power QLm1-koptRank cumulant
As probabilistic load flow model input variable and carry out probabilistic load flow, obtain node voltage and branch power respectively
1-koptRank cumulant；Utilize koptThe distribution letter of rank A types Gram-Charlier series approachings node voltage and branch power
Number.
Step 4-1：Do not consider, containing the uncertain factor in wind power system, to calculate certainty trend, obtain node voltage pair
Sensitivity matrix Ss of the sensitivity matrix J of node injecting power with branch power to node injecting power；
Step 4-2：According to the fired power generating unit, wind power plant, load active power 1-koptRank cumulant, utilize half
The additive property of invariant, the 1-k of calculate node injecting poweroptRank cumulant；
Containing in wind power system, not each node has fired power generating unit, wind power plant or load access.Therefore section is being calculated
During the cumulant of point injecting power, should extract accessed fired power generating unit, wind power plant or load active power partly not
Variable is calculated, if not accessing the said equipment, the cumulant for taking corresponding device is zero.
Step 4-3：Utilize the linear behavio(u)r of cumulant, sensitivity matrix J of the binding site voltage to node injecting power
The 1-k of sensitivity matrix S with branch power to node injecting power, calculate node voltage and branch poweroptRank half is constant
Amount；
Step 4-4：According to the node voltage and the 1-k of branch poweroptRank cumulant, with koptRank A types Gram-
The distribution function of Charlier series, fitting nodes voltage and branch power.
Claims (4)
1. a kind of probability load flow calculation method containing wind power system based on minimum error originated from input criterion, the bag containing wind power system
Include fired power generating unit, wind power plant and load；The fired power generating unit is designated as G={ G1,G2,...,Gi,...,GNG, GiRepresent i-th
Fired power generating unit, i-th fired power generating unit GiActive power and reactive power be designated as P respectivelyGiAnd QGi, i=1,2 ..., NG；
The wind power plant is designated as W={ W1,W2,...,Wj,...,WNW}；WjRepresent j-th of wind power plant；J-th of wind power plant Wj's
Active power is designated as P respectively with reactive powerWjAnd QWj, j=1,2 ..., NW；The load is designated as L={ L1,L2,...,
Lm,...,LNL, LmRepresent m-th of load, m-th of load LmActive power and reactive power be designated as P respectivelyLmAnd QLm,
M=1,2 ..., NL；Characterized in that, the probability load flow calculation method is to carry out as follows：
Step 1：I-th fired power generating unit G is established respectivelyiActive-power PGiReference distribution function CDFPGi, described i-th
Platform fired power generating unit GiReactive power QGiReference distribution function CDFQGi, j-th of wind power plant WjActive-power PWjGinseng
Examine distribution function CDFPWj, j-th of wind power plant WjReactive power QWjReference distribution function CDFQWj, described m-th it is negative
Lotus LmActive-power PLmReference distribution function CDFPLmAnd m-th of load LmReactive power QLmReference distribution
Function CDFQLm；
Step 2：I-th fired power generating unit G is calculated respectivelyiActive-power PGi1-kmaxRank moment of the orignWith 1-kmaxRank cumulantInstitute
State i-th fired power generating unit GiReactive power QGi1-kmaxRank moment of the orignWith 1-
kmaxRank cumulantJ-th of wind power plant WjActive-power PWj1-
kmaxRank moment of the orignWith 1-kmaxRank cumulant
J-th of wind power plant WjReactive power QWj1-kmaxRank moment of the orignWith 1-
kmaxRank cumulantM-th of load LmActive-power PLm1-kmax
Rank moment of the orignWith 1-kmaxRank cumulant
And m-th of load LmReactive power QLm1-kmaxRank moment of the orignWith
1-kmaxRank cumulant
Step 3：Using minimum error originated from input criterion, the optimal exponent number of Gram-Charlier series for making error of fitting minimum is found
kopt；
Step 3-1：Definition test exponent number is ktest；1≤ktest≤kmax；And initialize ktest=3；
Step 3-2：I-th fired power generating unit G is extracted respectivelyiActive-power PGi1-ktestRank cumulantI-th fired power generating unit GiReactive power QGi1-ktestRank cumulantJ-th of wind power plant WjActive-power PWj1-ktestRank cumulantJ-th of wind power plant WjReactive power QWj1-ktestRank cumulantM-th of load LmActive-power PLm1-ktestRank cumulantAnd m-th of load LmActive-power PLm1-ktestRank cumulantAnd k is used respectivelytestRank A type Gram-Charlier series generates i-th fired power generating unit Gi
Active-power PGiKtestRank is fitted distribution functionI-th fired power generating unit GiReactive power QGiKtest
Rank is fitted distribution functionJ-th of wind power plant WjActive-power PWjKtestRank is fitted distribution functionJ-th of wind power plant WjReactive power QWjKtestRank is fitted distribution functionDescribed m-th negative
Lotus LmActive-power PLmKtestRank is fitted distribution functionM-th of load LmReactive power QLmKtest
Rank is fitted distribution function
Step 3-3：I-th fired power generating unit G is calculated respectivelyiActive-power PGiKtestRank is fitted distribution function
Error of fitting indexI-th fired power generating unit GiReactive power QGiKtestRank is fitted distribution function
Error of fitting indexJ-th of wind power plant WjActive-power PWjKtestRank is fitted distribution function's
Error of fitting indexJ-th of wind power plant WjReactive power QWjKtestRank is fitted distribution functionPlan
Close error criterionM-th of load LmActive-power PLmKtestRank is fitted distribution functionFitting miss
Poor indexAnd m-th of load LmReactive power QLmKtestRank is fitted distribution functionFitting miss
Poor index
Step 3-4：Calculate ktestRank is fitted the overall error of fitting index of distribution functionAnd by ktest+ 1 is assigned to ktest,
Judge ktest≤kmaxWhether set up, if so, then return to step 3-2 orders perform；Otherwise, represent to obtain overall distribution function
Error of fitting indexInto step 3-5；
Step 3-5：From the overall distribution Function Fitting error criterionIn select corresponding to minimum value
Exponent number as optimal exponent number, be designated as kopt；When multiple identical minimum values be present, then the rank corresponding to multiple minimum values is selected
Minimum exponent number is designated as k as optimal exponent number in numberopt；
Step 4：With i-th fired power generating unit GiActive-power PGi1-koptRank cumulant
I-th fired power generating unit GiReactive power QGi1-koptRank cumulantJ-th of the wind
Electric field WjActive-power PWj1-koptRank cumulantJ-th of wind power plant WjIdle work(
Rate QWj1-koptRank cumulantM-th of load LmActive-power PLm1-koptRank half
InvariantAnd m-th of load LmReactive power QLm1-koptRank cumulantAs probabilistic load flow model input variable and carry out probabilistic load flow, saved respectively
The 1-k of point voltageoptThe 1-k of rank cumulant and branch poweroptRank cumulant；Recycle koptRank A types Gram-
The distribution function of node voltage and branch power described in Charlier series approachings.
2. the probability load flow calculation method containing wind power system as claimed in claim 1 based on minimum error originated from input criterion, its
It is characterized in, the step 3-2 is to obtain k as followstestRank is fitted distribution function：
Step 3-2-1：According to i-th fired power generating unit GiActive-power PGi1-ktestRank cumulantI-th fired power generating unit GiReactive power QGi1-ktestRank cumulantJ-th of wind power plant WjActive-power PWj1-ktestRank cumulantJ-th of wind power plant WjReactive power QWj1-ktestRank cumulantM-th of load LmActive-power PLm1-ktestRank cumulantAnd m-th of load LmActive-power PLm1-ktestRank cumulantCalculate respectively and obtain i-th fired power generating unit GiActive-power PGi1-ktestRank A types
Gram-Charlier series coefficientsI-th fired power generating unit GiReactive power QGi1-ktest
Rank A type Gram-Charlier series coefficientsJ-th of wind power plant WjActive-power PWj1-
ktestRank A type Gram-Charlier series coefficientsJ-th of wind power plant WjReactive power QWj's
1-ktestRank A type Gram-Charlier series coefficientsM-th of load LmActive-power PLm's
1-ktestRank A type Gram-Charlier series coefficientsAnd m-th of load LmReactive power
QLm1-ktestRank A type Gram-Charlier series coefficients
Step 3-2-2：I-th fired power generating unit G is obtained according to formula (1) respectivelyiActive-power PGiKtestRank fitting distribution
FunctionI-th fired power generating unit GiReactive power QGiKtestRank is fitted distribution functionDescribed
J wind power plant WjActive-power PWjKtestRank is fitted distribution functionJ-th of wind power plant WjIdle work(
Rate QWjKtestRank is fitted distribution functionM-th of load LmActive-power PLmKtestRank fitting distribution letter
NumberM-th of load LmReactive power QLmKtestRank is fitted distribution function
In formula (1), H(k-1)(x) it is k-1 rank Hermite multinomials, Φ (x) is the distribution function of standardized normal distribution,For
The density function of standardized normal distribution；temp∈{PGi,QGi,PWj,QWj,PLm,QLm}.
3. the probability load flow calculation method containing wind power system as claimed in claim 1 based on minimum error originated from input criterion, its
It is characterized in, the step 3-3 is to calculate i-th fired power generating unit G respectively according to formula (2)iActive-power PGiKtestRank
It is fitted distribution functionError of fitting indexI-th fired power generating unit GiReactive power QGiKtestRank
It is fitted distribution functionError of fitting indexJ-th of wind power plant WjActive-power PWjKtestRank is intended
Close distribution functionError of fitting indexJ-th of wind power plant WjReactive power QWjKtestRank is fitted
Distribution functionError of fitting indexM-th of load LmActive-power PLmKtestRank fitting distribution
FunctionError of fitting indexAnd m-th of load LmReactive power QLmKtestRank fitting distribution
FunctionError of fitting index
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4. the probabilistic load flow side containing wind power system based on minimum error originated from input criterion as described in claim 1 or 2 or 3
Method, it is characterised in that the step 3-4 is the steps of obtaining overall error of fitting index
Step 3-4-1：With i-th fired power generating unit GiActive-power PGiAverage value, j-th of wind power plant WjHave
Work(power PWjAverage value and m-th of load LmActive-power PLmAverage value respectively with always having containing wind power system
The ratio between workload, respectively as the error of fitting indexWeight coefficient wPGi, the error of fitting indexPower
Weight coefficient wPWjAnd the error of fitting indexWeight coefficient wPLm；With i-th fired power generating unit GiIdle work(
Rate QGiAverage value, j-th of wind power plant WjReactive power QWjAverage value and m-th of load LmIt is idle
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Step 3-4-2：K is calculated according to formula (3)testRank global error index
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