CN106099932B - Day-ahead planning power flow analysis method considering uncertainty time-space correlation - Google Patents

Day-ahead planning power flow analysis method considering uncertainty time-space correlation Download PDF

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CN106099932B
CN106099932B CN201610586899.9A CN201610586899A CN106099932B CN 106099932 B CN106099932 B CN 106099932B CN 201610586899 A CN201610586899 A CN 201610586899A CN 106099932 B CN106099932 B CN 106099932B
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wind power
day
wind
time
prediction error
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CN106099932A (en
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丁强
翟成玮
周京阳
许丹
潘毅
戴赛
张传成
董炜
崔晖
李强
黄国栋
韩彬
蔡帜
胡晨旭
朱泽磊
李晓磊
李培军
张加力
李博
刘芳
门德月
闫翠会
燕京华
李伟刚
刘鹏
孙振
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State Grid Corp of China SGCC
State Grid Zhejiang Electric Power Co Ltd
China Electric Power Research Institute Co Ltd CEPRI
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State Grid Corp of China SGCC
State Grid Zhejiang Electric Power Co Ltd
China Electric Power Research Institute Co Ltd CEPRI
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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
    • 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
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Abstract

The invention provides a day-ahead planning load flow analysis method considering uncertainty time-space correlation, which comprises the steps of obtaining the predicted wind speed of a wind power plant in 96 time periods of 24 hours the next day; acquiring the output of the wind power plant on the next day; obtaining the next-day output prediction error distribution of each wind power plant; carrying out independence conversion on random variables with space-time correlation; calculating the semi-invariant of the power flow on each line; relevant information required for scheduling is determined. The invention carries out engineering algorithm processing on the prediction error distribution with correlation, and solves the defect that the probability distribution with correlation cannot be directly applied to a series expansion method. The method adopts Gram-Charlie series expansion method to carry out the expansion analysis of the power flow of each line in each time interval of the next day, the method is convenient and effective to solve the problem of probability power flow by applying the analytic method, has practical value, expands the series expansion method commonly used for medium-long term probability power flow analysis to short-term planning power flow analysis at present, and provides more data support for economic dispatching.

Description

Day-ahead planning power flow analysis method considering uncertainty time-space correlation
Technical Field
The invention belongs to the field of power systems, and particularly relates to a day-ahead planning power flow analysis method considering uncertainty time-space correlation.
Background
In recent years, as the share of the output of the wind turbine in the total power generation amount is continuously improved, how to perform effective power flow analysis on a power grid containing a wind power plant is always a hot problem of research. In 2014, the number of the wind generation sets 13121 is increased newly in China, the installed capacity is increased by 23196MW, and the installed capacity is increased by 44.2% on the same scale. Under the situation, the prediction of the day-ahead wind power and the power flow analysis of the power system containing the wind power have very important reference values for guaranteeing the reliability and the economy of the next-day scheduling plan.
However, in China, the data provided by the current day-ahead plan (i.e. the next day plan) containing the wind power system still has some defects, the predicted data is often only a numerical sequence, and the day-ahead plan made by the trend calculated by the numerical sequence is often not accurate enough. The existing domestic literature mainly focuses on researches on aspects such as wind power plant output prediction, wind power plant output prediction error, probability power flow calculation based on a medium-long term wind power output model, optimal scheduling and the like, and researches on aspects such as short-term power system probability power flow considering wind power plant power prediction error and correlation thereof are not sufficient. Most probability load flow articles use a series expansion method in medium-and-long-term probability load flow analysis based on Weibull distribution, and when a short-term problem is simulated and calculated by utilizing Weibull distribution, the power density spectrum distribution of the Weibull distribution is wide in distribution and is not suitable for analyzing the probability load flow in a short term.
The research related to the probability trend is mainly divided into the following directions:
first, the study was based on the monte carlo method. The Monte Carlo method is to obtain variable samples through a large number of repeated operations, and then to generalize by using a statistical method, so as to obtain a probability trend result. On the basis of the monte carlo method, there are many articles for improving the method, such as increasing the sampling precision by using hypercube sampling, increasing the speed by using an important sampling method, and the like. However, in large-scale power system analysis, the inefficiency of the monte carlo method dictates that it cannot be applied to short-term power flow analysis.
Secondly, research based on a series expansion method. In the existing large amount of documents, a series expansion method is mainly used for analyzing the probability power flow of a long-term power system, for example, a Gram-Charlier series expansion method, a Cornish-Fisher series expansion method, and the like are used. Various series expansion methods have applicability. However, the series expansion method cannot be applied to the analysis of short-term probability trend, which is limited by the existing Weibull model.
And thirdly, analyzing errors based on a probability power flow algorithm. Such studies are aimed at improving the accuracy of the existing series expansion method, such as discretizing the probability distribution, processing by Von-Mises series expansion method, and using monte carlo method as a reference group to compare the accuracy of the results.
Fourthly, the research direction is more popular in the day ahead, namely the research considering the correlation. Domestic research mainly focuses on the directions of spatial correlation, node correlation and the like of a wind power plant, and the proposed methods are various, such as Cholesky decomposition method, TPNT point estimation method and the like. While foreign countries have more researches on the autocorrelation and cross-correlation of wind speed, the correlation of prediction error distribution, and the like.
And fifthly, for the research of the wind speed model, how to establish a scientific wind speed model is the key for analyzing the whole problem. For the long-term probability power flow problem, long-term wind speed probability density distribution such as Weibull distribution and Beta distribution is generally proposed for simulation, and for the short-term problem, a time series model is generally used for researching the related problem.
And sixthly, researching the output prediction of the fan. The foundation of short-term wind power research is necessarily based on a more accurate wind speed prediction method.
Seventhly, the research on the prediction error model is a new research direction in recent years, and the influence of the prediction error distribution on the fan prediction can be effectively analyzed through researching the prediction error model.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a day-ahead planning flow analysis method considering uncertain space-time correlation, which carries out engineering algorithm processing on prediction error distribution with correlation and solves the defect that probability distribution with correlation cannot be directly applied to a series expansion method. The method adopts Gram-Charlie series expansion method to carry out the expansion analysis of the power flow of each line in each time interval of the next day, the method is convenient and effective to solve the problem of probability power flow by applying the analytic method, has practical value, expands the series expansion method commonly used for medium-long term probability power flow analysis to short-term planning power flow analysis at present, and provides more data support for economic dispatching.
In order to achieve the purpose of the invention, the invention adopts the following technical scheme:
the invention provides a day-ahead planning power flow analysis method considering uncertainty space-time correlation, which comprises the following steps:
acquiring the predicted wind speed of a wind power plant in 96 time periods of 24 hours the next day;
acquiring the output of the wind power plant on the next day;
obtaining the next-day output prediction error distribution of each wind power plant;
carrying out independence conversion on random variables with space-time correlation;
calculating the semi-invariant of the power flow on each line;
relevant information required for scheduling is determined.
And acquiring the predicted wind speed of the wind power plant at 96 time intervals of 24 hours in the next day by establishing a wind power plant wind speed prediction time series model before the day.
The obtaining of the predicted wind speed of the wind power plant in 96 periods of 24 hours the next day comprises:
a day-ahead wind power plant wind speed prediction time series model is established based on an autoregressive moving average model, and the model comprises the following components:
Figure GDA0003177152650000031
wherein i and j are sequence numbers, l is the number of time series items, stPredicting a time series, s, for the wind speed at time tt-iA time series is predicted for the wind speed at time t-i,
Figure GDA0003177152650000032
and thetajAre all self-sliding regression mean coefficients, αtAnd alphat-jAll white noise sequences conforming to a normal distribution, i.e. alphat∈NID(0,σ2)，αt-j∈NID(0,σ2) Wherein the white noise sequence has a mean value of 0 and a variance of σ2；
Let SWtThe predicted wind speed of the wind farm at time t is expressed as:
SWt＝μt+σtst
wherein, mutIs the wind power plant wind speed average value at the moment t, sigmatThe standard deviation of wind speed of the wind power plant at the moment t;
according to SWt＝μt+σtstAnd acquiring the predicted wind speed of the wind power plant in 96 periods of 24 hours the next day.
The obtaining of the next-day wind power plant output through the wind power plant wind power output model comprises the following steps:
1) let time t equal to K + t0K and t0Respectively an integer part and a decimal part of t, and predicting the wind speed at the moment t into a time sequence s by utilizing a linear interpolation methodtExpressed as:
st＝(1-t0)×sK+t0×sK+1
wherein s isKRepresenting the time sequence of time instants K, sK+1Represents a time series of the K +1 time; and if the subscript of any one of the items exceeds the time series item number n, processing the subscript value minus n;
2) assuming that the new wind speed prediction time series has the same wind speed prediction time series s as the original wind speed prediction time seriestA specified correlation coefficient, the time shift being obtained from the correlation coefficient and the time curve; the wind speed prediction time sequence of a certain wind power plant is taken as a reference sequence, time shifting of another wind power plant is considered, a plurality of wind speed prediction time sequence models of the wind power plants with specified correlation coefficients are established, and a wind power output model of the wind power plants is generated, so that the output of the wind power plants in the next day is obtained.
The step of obtaining the prediction error distribution of the daily output of each wind power plant comprises the following steps:
fitting the wind power prediction error distribution by using the nonstandard beta distribution, wherein the probability density function of the nonstandard beta distribution is expressed as:
Figure GDA0003177152650000041
wherein f (x, gamma, eta, a, b) is a probability density function of the non-standard beta distribution; x is a power prediction error of the wind power plant, and a and b are upper and lower boundary values of x; β represents a beta distribution; γ, η are shape parameters, which are respectively expressed as:
Figure GDA0003177152650000042
wherein, muxAnd σxThe mean and standard deviation of x, respectively;
and segmenting the predicted output of different wind power plants so as to obtain the predicted error distribution of the output of each wind power plant on the next day.
The independent transformation of the random variables with the space-time correlation comprises the following steps:
the method is provided with M wind power plants, and the wind power prediction error random variable of the mth wind power plant is emM1, 2, M, then wind powerThe set of prediction error random variables E is represented as:
E＝[e1,e2,...,em,...,eM]T
setting the covariance matrix of wind power prediction error distribution of each wind power plant as CEThe covariance matrix CERespectively has a feature vector and a feature value of phimAnd λmThe following orthogonal transformation relationship exists:
E*＝STE
where T denotes transpose, S is an orthogonal matrix, and has S [ [ phi ] ]1,φ2,...,φm,...,φM]T，φmIs the mth element of the orthogonal matrix S; and has the following components:
Figure GDA0003177152650000051
then the independent wind power prediction error random variable group is expressed as:
E*＝[e1 *,e2 *,...,em *,...,eM *]T
wherein E is*Representing a set of mutually independent wind power prediction error random variables, em *And T represents transposition for mutually independent wind power prediction error random variables.
Before the calculating the semi-invariant of the power flow on each line, the method comprises the following steps:
and for each independent wind power prediction error distribution, calculating each order origin moment and calculating a semi-invariant.
For each wind power prediction error random variable which is independent from each other, calculating each order origin moment and calculating a semi-invariant comprises the following steps:
k-order origin moment alpha of wind power prediction error random variable independent of each otherkExpressed as:
Figure GDA0003177152650000052
wherein f (x) represents a probability density function of the prediction error random variable;
from the origin moment alphakObtaining n-order semi-invariant gamma of wind power prediction error random variable which are mutually independentn：
Figure GDA0003177152650000053
Wherein alpha isnPredicting the n-order origin moment of the error random variable for the wind power which are independent of each other,
Figure GDA0003177152650000054
denotes a combination of gamman-kIs a semi-invariant of order n-k; 1 st order semi-invariant gamma of wind power prediction error random variable independent of each other1Is represented by gamma1＝α1。
The calculating the semi-invariant of the power flow on each line comprises:
and calculating the semi-invariants of the power flows on the lines by using the additivity of the semi-invariants.
The calculating the semi-invariant of the power flow on each line by using the additivity of the semi-invariant comprises the following steps:
let the n-order semi-invariant of the power flow on the h-th line be Pline-h,nAnd has:
Pline-h,n＝sh-1P1+sh-2P2+...+sh-mPm+sh-mPm+sh-MPM
wherein M is the number of wind power plants PmIs the output of the mth wind farm, sh-mSensitivity of the mth wind farm to the h line.
The determining of the relevant information required for scheduling includes:
the power flow probability distribution of each line in each time period can be obtained by utilizing a Gram-Charlie series expansion method combined with semi-invariants, and the wind power pre-prediction after decoupling is carried out by utilizing a covariance matrix conversion methodThe random variable xi of error measurement follows a continuous distribution and its expectation and standard deviation are respectively muxAnd σx(ii) a The probability density function and cumulative distribution function for the normalized variable (ξ -g)/σ are denoted by f (x) and F (x), respectively, and have:
Figure GDA0003177152650000061
Figure GDA0003177152650000062
wherein n is the order of the semi-invariant, cnIs a coefficient, muxIs the mean value of x, which is the wind farm power prediction error,
Figure GDA0003177152650000063
is a probability density function of standard normal distribution, phi is a standard normal distribution function;
from a normalized variable ([ xi ] -mu)x)/σxThe probability density function f (x) and the cumulative distribution function F (x) can obtain the power flow probability distribution of any line.
The relevant information required by the scheduling determination comprises a probability density curve of a 24-hour 96 time period of the other line day and the load flow out-of-limit probability of each time period of the line day.
Compared with the closest prior art, the technical scheme provided by the invention has the following beneficial effects:
1. the method starts from the establishment of a wind speed prediction model of a single wind power plant, obtains the time sequence of the day-ahead wind speed by various day-ahead wind speed prediction methods, and commonly uses an empirical prediction error statistical method, an analysis point regression method, a probability density prediction method and the like. Through the establishment of the model, expected values are provided for the semi-invariant calculation in the following.
2. The prediction error distribution model adopted by the invention is a beta distribution model, and the correlation is fully considered in the establishment of the scene model, and comprises the correlation among the prediction errors of the wind power output of a plurality of related wind power plants and the correlation between the predicted fan output and the prediction errors. The method carries out quantitative analysis on the correlation of the prediction error, and carries out qualitative analysis on the correlation between the output of the prediction fan and the prediction error. Meanwhile, the prediction error distribution with the correlation is processed by an engineering algorithm, so that the defect that the probability distribution with the correlation cannot be directly applied to a series expansion method is overcome.
3. And after obtaining the independent probability distribution of the predicted output fluctuation of each wind field in each time period, carrying out expansion analysis on the power flow of each line in each time period of the next day by utilizing a Gram-Charlier series expansion method combined with a semi-invariant. The method for solving the probability load flow problem is convenient and effective, has practical value, expands the series expansion method commonly used for medium-long term probability load flow analysis to short-term planning load flow analysis at present, and provides more data support for economic dispatching.
Drawings
FIG. 1 is a flow chart of a method for day-ahead planning trend analysis with uncertainty-based spatiotemporal correlations in an embodiment of the present invention;
FIG. 2 is a schematic diagram of a power output curve through a wind turbine generator in an embodiment of the present invention;
FIG. 3 is a graph of the probability density of a line in a period of 96 days 5-6 in accordance with an embodiment of the present invention;
FIG. 4 is a schematic diagram of the out-of-limit probability of the tidal current in each time period line 5-6 of the next day in the embodiment of the invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
The method is based on the wind speed prediction model of a single wind power plant, and the time series of the day-ahead wind speed is obtained through various day-ahead wind speed prediction methods, such as an empirical prediction error statistical method, an analysis point regression method, a probability density prediction method and the like which are frequently used. Through the establishment of the model, expected values are provided for the semi-invariant calculation in the following.
The current wind speed and fan output prediction technology is difficult to realize zero error. The probability distribution model of the prediction error can be established by counting and segmenting the errors. The prediction error distribution model adopted by the method is a beta distribution model. And fully considering the correlation in the establishment of the scene model, wherein the correlation comprises the correlation between the prediction errors of the wind power output of a plurality of related wind power plants and the correlation between the predicted fan output and the prediction errors. The method carries out quantitative analysis on the correlation of the prediction error, and carries out qualitative analysis on the correlation between the output of the prediction fan and the prediction error. Meanwhile, the prediction error distribution with the correlation is processed by an engineering algorithm, so that the defect that the probability distribution with the correlation cannot be directly applied to a series expansion method is overcome.
And finally, after the independent probability distribution of the predicted output fluctuation of each wind power plant in each time interval is obtained, the power flow of each line in each time interval of the next day is expanded and analyzed by utilizing a Gram-Charlie series expansion method combined with a semi-invariant. The method for solving the probability load flow problem is convenient and effective, has practical value, expands the series expansion method commonly used for medium-long term probability load flow analysis to short-term planning load flow analysis at present, and provides more data support for economic dispatching.
Referring to fig. 1, the method for analyzing a planning trend in the day ahead, which considers uncertainty and spatiotemporal correlation, provided by the invention comprises the following steps:
acquiring the predicted wind speed of a wind power plant in 96 time periods of 24 hours the next day;
acquiring the output of the wind power plant on the next day;
obtaining the next-day output prediction error distribution of each wind power plant;
carrying out independence conversion on random variables with space-time correlation;
calculating the semi-invariant of the power flow on each line;
relevant information required for scheduling is determined.
And acquiring the predicted wind speed of the wind power plant at 96 time intervals of 24 hours in the next day by establishing a wind power plant wind speed prediction time series model before the day.
The obtaining of the predicted wind speed of the wind power plant in 96 periods of 24 hours the next day comprises:
the autoregressive moving average model (ARMA) has time sequence and is widely applied to establishing wind speed and time series of wind speed prediction. Through statistics of a large amount of historical observation data, a first-order difference method stabilization sequence is established, zero-averaging sequence processing, mode recognition, parameter estimation, model inspection and the like are carried out, and a wind speed prediction time sequence model of a wind power plant in the day ahead is established on the basis of an autoregressive moving average model, and the method comprises the following steps:
Figure GDA0003177152650000081
wherein i and j are sequence numbers, l is the number of time series items, stPredicting a time series, s, for the wind speed at time tt-iA time series is predicted for the wind speed at time t-i,
Figure GDA0003177152650000091
and thetajAre all self-sliding regression mean coefficients, αtAnd alphat-jAll white noise sequences conforming to a normal distribution, i.e. alphat∈NID(0,σ2)，αt-j∈NID(0,σ2) Wherein the white noise sequence has a mean value of 0 and a variance of σ2；
Let SWtThe predicted wind speed of the wind farm at time t is expressed as:
SWt＝μt+σtst
wherein, mutIs the wind power plant wind speed average value at the moment t, sigmatThe standard deviation of wind speed of the wind power plant at the moment t;
according to SWt＝μt+σtstAnd acquiring the predicted wind speed of the wind power plant in 96 periods of 24 hours the next day.
The obtaining of the next-day wind power plant output through the wind power plant wind power output model comprises the following steps:
1) let time t equal to K + t0K and t0Respectively an integer part and a decimal part of t, and predicting the wind speed at the moment t into a time sequence s by utilizing a linear interpolation methodtExpressed as:
st＝(1-t0)×sK+t0×sK+1
wherein s isKRepresenting the time sequence of time instants K, sK+1Represents a time series of the K +1 time; and if the subscript of any one of the items exceeds the time series item number n, processing the subscript value minus n;
2) assuming that the new wind speed prediction time series has the same wind speed prediction time series s as the original wind speed prediction time seriestA specified correlation coefficient, the time shift being obtained from the correlation coefficient and the time curve; the wind speed prediction time sequence of a certain wind power plant is taken as a reference sequence, time shift of another wind power plant is considered, a plurality of wind speed prediction time sequence models of the wind power plants with specified correlation coefficients are established, a wind power plant wind power output model is generated, and accordingly the output of the next-day wind power plant is obtained, as shown in figure 2, wherein the ordinate PrFor the rated power of the fan, the abscissa represents the wind speed, where vciFor cutting into the wind speed, vcoTo cut out wind speed, vrRated wind speed.
The step of obtaining the prediction error distribution of the daily output of each wind power plant comprises the following steps:
the wind power prediction error distribution is fitted by utilizing the nonstandard beta distribution, and the nonstandard beta distribution has higher reliability in the prediction error fitting of the wind power plant output power subsection. The probability density function of the non-standard beta distribution is expressed as:
Figure GDA0003177152650000101
wherein f (x, gamma, eta, a, b) is a probability density function of the non-standard beta distribution; x is a power prediction error of the wind power plant, and a and b are upper and lower boundary values of x; β represents a beta distribution; γ, η are shape parameters, which are respectively expressed as:
Figure GDA0003177152650000102
wherein, muxAnd σxThe mean and standard deviation of x, respectively;
and segmenting the predicted output of different wind power plants so as to obtain the predicted error distribution of the output of each wind power plant on the next day.
In addition to the spatial correlation of wind speeds, there is in fact a similar correlation between the prediction errors of wind speeds of individual wind farms. By carrying out correlation analysis on the time sequence number series of the historical observation prediction errors of the wind power plant, specific correlation coefficients can be obtained. The prediction error correlation of the wind power plant has the following characteristics:
1) the correlation analysis of the prediction errors of the multiple wind power fields is established on a space-time model: carrying out statistical analysis on the time sequence of the prediction error to obtain the autocorrelation coefficient of a certain reference wind power plant and the reference wind power plant at the next moment and the cross-correlation coefficient among the wind power plants;
2) the magnitude of the correlation of the prediction error is related to many factors, including mainly the wind farm spacing, wind speed, and wind direction. The closer the wind power plant distance is, the larger the wind speed is, and the more the wind direction is, the higher the prediction error correlation among the wind power plants is;
3) when the wind speed is smaller, the prediction error shows higher autocorrelation, and the cross correlation among wind power plants is sharply reduced;
4) when the time delay is 0, the cross correlation of the prediction errors is only low correlation;
5) the prediction error and the predicted fan output have certain positive correlation.
Aiming at the wind power prediction error space-time correlation model, the invention makes the following settings:
1) when the predicted wind speed is not more than 10m/s, the correlation of prediction errors is small, and the wind speeds in the range are considered to be uncorrelated and are independently distributed in the modeling process;
2) when the predicted wind speed is more than 10m/s, the distribution of the wind speed in the section is considered to have medium correlation characteristics, and the correlation coefficient range is [0.4,0.7 ];
3) the sectional model source of the prediction error of the output power of the fan is sequencing sectional statistics of a large amount of time sequence data, the correlation between the prediction errors of the wind speeds of different wind speed sections has no comparability, and the sample amount is very small, so that the correlations among the distributions are set.
The covariance matrix conversion method is characterized in that under the premise that the correlation among a group of random variables is known, the characteristic value and the characteristic vector of the covariance matrix are determined, and then the original correlated random variables are converted into a group of random variables which are mutually independent in statistics by adopting orthogonal transformation. Thereby performing probabilistic power flow analysis. This method is used for decoupling of node correlation as usual, and the invention puts it into decoupling of prediction error distribution correlation.
The independent transformation of the random variables with the space-time correlation comprises the following steps:
the method is provided with M wind power plants, and the wind power prediction error random variable of the mth wind power plant is emM1, 2.. M, then the set of wind power prediction error random variables E is represented as:
E＝[e1,e2,...,em,...,eM]T
setting the covariance matrix of wind power prediction error distribution of each wind power plant as CEThe covariance matrix CERespectively has a feature vector and a feature value of phimAnd λmThe following orthogonal transformation relationship exists:
E*＝STE
where T denotes transpose, S is an orthogonal matrix, and has S [ [ phi ] ]1,φ2,...,φm,…,φM]T，φmIs the mth element of the orthogonal matrix S; and has the following components:
Figure GDA0003177152650000111
then the independent wind power prediction error random variable group is expressed as:
E*＝[e1 *,e2 *,...,em *,...,eM *]T
wherein E is*Representing a set of mutually independent wind power prediction error random variables, em *Predicting errors for mutually independent wind powerThe difference random variable, T, denotes transpose.
I.e. for the correlation distribution by using the original prediction error covariance matrix CEThe characteristic value of the random variable e is replaced by the random variable e which is independent of each other after transformationi *The variance of (a) is sufficient. The method is easy to understand and has practical value when being realized in the program. The probability trend can be analyzed by decoupling the distribution with correlation by using a series expansion method.
Before the calculating the semi-invariant of the power flow on each line, the method comprises the following steps:
and for each independent wind power prediction error distribution, calculating each order origin moment and calculating a semi-invariant.
For each wind power prediction error random variable which is independent from each other, calculating each order origin moment and calculating a semi-invariant comprises the following steps:
k-order origin moment alpha of wind power prediction error random variable independent of each otherkExpressed as:
Figure GDA0003177152650000121
wherein f (x) represents a probability density function of the prediction error random variable;
from the origin moment alphakObtaining n-order semi-invariant gamma of wind power prediction error random variable which are mutually independentn：
Figure GDA0003177152650000122
Wherein alpha isnPredicting the n-order origin moment of the error random variable for the wind power which are independent of each other,
Figure GDA0003177152650000123
denotes a combination of gamman-kIs a semi-invariant of order n-k; 1 st order semi-invariant gamma of wind power prediction error random variable independent of each other1Is represented by gamma1＝α1。
The calculating the semi-invariant of the power flow on each line comprises:
and calculating the semi-invariants of the power flows on the lines by using the additivity of the semi-invariants.
The calculating the semi-invariant of the power flow on each line by using the additivity of the semi-invariant comprises the following steps:
let the n-order semi-invariant of the power flow on the h-th line be Pline-h,nAnd has:
Pline-h,n＝sh-1P1+sh-2P2+…+sh-mPm+…+sh-MPM
wherein M is the number of wind power plants PmIs the output of the mth wind farm, sh-mSensitivity of the mth wind farm to the h line.
The determining of the relevant information required for scheduling includes:
the power flow probability distribution of each line in each time period can be obtained by utilizing a Gram-Charlier series expansion method combined with semi-invariants, the random variable xi of the wind power prediction error decoupled by utilizing a covariance matrix conversion method is subjected to continuous distribution, and the expectation and standard deviation are respectively muxAnd σx(ii) a The probability density function and cumulative distribution function for the normalized variable (ξ -g)/σ are denoted by f (x) and F (x), respectively, and have:
Figure GDA0003177152650000131
Figure GDA0003177152650000132
wherein n is the order of the semi-invariant, cnIs a coefficient, muxIs the mean value of x, which is the wind farm power prediction error,
Figure GDA0003177152650000133
is a probability density function of standard normal distribution, phi is a standard normal distribution function;
from a normalized variable ([ xi ] -mu)x)/σxThe probability density function f (x) and the cumulative distribution function F (x) can obtain the power flow probability distribution of any line.
The relevant information required for determining the scheduling includes a probability density curve of a 24-hour 96-period on the next line day and a load flow out-of-limit probability of each period on the next line day, which are respectively shown in fig. 3 and 4.
Finally, it should be noted that: the above embodiments are only intended to illustrate the technical solution of the present invention and not to limit the same, and a person of ordinary skill in the art can make modifications or equivalents to the specific embodiments of the present invention with reference to the above embodiments, and such modifications or equivalents without departing from the spirit and scope of the present invention are within the scope of the claims of the present invention as set forth in the claims.

Claims (10)

1. A day-ahead planning power flow analysis method considering uncertainty time-space correlation is characterized in that: the method comprises the following steps:
acquiring the predicted wind speed of a wind power plant in 96 time periods of 24 hours the next day;
acquiring the output of the wind power plant on the next day;
obtaining the next-day output prediction error distribution of each wind power plant;
carrying out independence conversion on random variables with space-time correlation;
calculating the semi-invariant of the power flow on each line;
determining relevant information required by scheduling;
acquiring the predicted wind speed of a wind power plant at 96 time intervals 24 hours the next day by establishing a wind power plant wind speed prediction time series model before the day;
the obtaining of the predicted wind speed of the wind power plant in 96 periods of 24 hours the next day comprises:
a day-ahead wind power plant wind speed prediction time series model is established based on an autoregressive moving average model, and the model comprises the following components:
Figure FDA0003216560270000011
wherein i and j are sequence numbers, l is the number of time series items, stPredicting a time series, s, for the wind speed at time tt-iA time series is predicted for the wind speed at time t-i,
Figure FDA0003216560270000012
and thetajAre all self-sliding regression mean coefficients, αtAnd alphat-jAll white noise sequences conforming to a normal distribution, i.e. alphat∈NID(0,σ2)，αt-j∈NID(0,σ2) Wherein the white noise sequence has a mean value of 0 and a variance of σ2；
Let SWtThe predicted wind speed of the wind farm at time t is expressed as:
SWt＝μt+σtst
wherein, mutIs the wind power plant wind speed average value at the moment t, sigmatThe standard deviation of wind speed of the wind power plant at the moment t;
according to SWt＝μt+σtstAnd acquiring the predicted wind speed of the wind power plant in 96 periods of 24 hours the next day.
2. The method for day-ahead planning flow analysis considering uncertainty-based spatiotemporal correlation according to claim 1, characterized in that: the obtaining of the next-day wind power plant output comprises the following steps:
1) let time t equal to K + t0K and t0Respectively an integer part and a decimal part of t, and predicting the wind speed at the moment t into a time sequence s by utilizing a linear interpolation methodtExpressed as:
st＝(1-t0)×sK+t0×sK+1
wherein s isKRepresenting the time sequence of time instants K, sK+1Represents a time series of the K +1 time; and if the subscript of any one of the items exceeds the time series item number n, processing the subscript value minus n;
2) assuming a new wind speed prediction timeThe sequence has a time sequence s of wind speed predictiontA specified correlation coefficient, the time shift being obtained from the correlation coefficient and the time curve; the wind speed prediction time sequence of a certain wind power plant is taken as a reference sequence, time shifting of another wind power plant is considered, a plurality of wind speed prediction time sequence models of the wind power plants with specified correlation coefficients are established, and a wind power output model of the wind power plants is generated, so that the output of the wind power plants in the next day is obtained.
3. The method for day-ahead planning flow analysis considering uncertainty-based spatiotemporal correlation according to claim 1, characterized in that: the step of obtaining the prediction error distribution of the daily output of each wind power plant comprises the following steps:
fitting the wind power prediction error distribution by using the nonstandard beta distribution, wherein the probability density function of the nonstandard beta distribution is expressed as:
Figure FDA0003216560270000021
wherein f (x, gamma, eta, a, b) is a probability density function of the non-standard beta distribution; x is a power prediction error of the wind power plant, and a and b are upper and lower boundary values of x; β represents a beta distribution; γ, η are shape parameters, which are respectively expressed as:
Figure FDA0003216560270000022
wherein, muxAnd σxThe mean and standard deviation of x, respectively;
and segmenting the predicted output of different wind power plants so as to obtain the predicted error distribution of the output of each wind power plant on the next day.
4. The method for day-ahead planning flow analysis considering uncertainty-based spatiotemporal correlation according to claim 1, characterized in that: the independent transformation of the random variables with the space-time correlation comprises the following steps:
is provided withThe wind power prediction error random variable of the mth wind power field is emM1, 2.. M, then the set of wind power prediction error random variables E is represented as:
E＝[e1,e2,...,em,...,eM]T
setting the covariance matrix of wind power prediction error distribution of each wind power plant as CEThe covariance matrix CERespectively has a feature vector and a feature value of phimAnd λmThe following orthogonal transformation relationship exists:
E*＝STE
where T denotes transpose, S is an orthogonal matrix, and has S [ [ phi ] ]1,φ2,...,φm,...,φM]T，φmIs the mth element of the orthogonal matrix S; and has the following components:
Figure FDA0003216560270000031
then the independent wind power prediction error random variable group is expressed as:
E*＝[e1 *,e2 *,...,em *,...,eM *]T
wherein E is*Representing a set of mutually independent wind power prediction error random variables, em *And T represents transposition for mutually independent wind power prediction error random variables.
5. The method for day-ahead planning flow analysis considering uncertainty-based spatiotemporal correlation according to claim 1, characterized in that: before the calculating the semi-invariant of the power flow on each line, the method comprises the following steps:
and for each independent wind power prediction error distribution, calculating each order origin moment and calculating a semi-invariant.
6. The method for day-ahead planning flow analysis considering uncertainty-based spatiotemporal correlation according to claim 5, wherein: for each independent wind power prediction error distribution, calculating each order origin moment and calculating a semi-invariant, wherein the method comprises the following steps:
k-order origin moment alpha of wind power prediction error random variable independent of each otherkExpressed as:
Figure FDA0003216560270000032
wherein f (x) represents a probability density function of the prediction error random variable;
from the origin moment alphakObtaining n-order semi-invariant gamma of wind power prediction error random variable which are mutually independentn：
Figure FDA0003216560270000041
Wherein alpha isnPredicting the n-order origin moment of the error random variable for the wind power which are independent of each other,
Figure FDA0003216560270000042
denotes a combination of gamman-kIs a semi-invariant of order n-k; 1 st order semi-invariant gamma of wind power prediction error random variable independent of each other1Is represented by gamma1＝α1。
7. The method for day-ahead planning flow analysis considering uncertainty-based spatiotemporal correlation according to claim 5, wherein: the calculating the semi-invariant of the power flow on each line comprises:
and calculating the semi-invariants of the power flows on the lines by using the additivity of the semi-invariants.
8. The method for day-ahead planning flow analysis considering uncertainty-based spatiotemporal correlation according to claim 7, wherein: the calculating the semi-invariant of the power flow on each line by using the additivity of the semi-invariant comprises the following steps:
let the n-order semi-invariant of the power flow on the h-th line be Pline-h,nAnd has:
Pline-h,n＝sh-1P1+sh-2P2+…+sh-mPm+…+sh-MPM
wherein M is the number of wind power plants PmIs the output of the mth wind farm, sh-mSensitivity of the mth wind farm to the h line.
9. The method for day-ahead planning flow analysis considering uncertainty-based spatiotemporal correlation according to claim 1, characterized in that: the determining of the relevant information required for scheduling includes:
the power flow probability distribution of each line in each time period can be obtained by utilizing a Gram-Charlier series expansion method combined with semi-invariants, the random variable xi of the wind power prediction error decoupled by utilizing a covariance matrix conversion method is subjected to continuous distribution, and the expectation and standard deviation are respectively muxAnd σx(ii) a The probability density function and cumulative distribution function for the normalized variable (ξ -g)/σ are denoted by f (x) and F (x), respectively, and have:
Figure FDA0003216560270000043
Figure FDA0003216560270000051
wherein n is the order of the semi-invariant, cnIs a coefficient, muxIs the mean value of x, which is the wind farm power prediction error,
Figure FDA0003216560270000052
is a probability density function of standard normal distribution, phi is a standard normal distribution function;
from a normalised variable(ξ-μx)/σxThe probability density function f (x) and the cumulative distribution function F (x) can obtain the power flow probability distribution of any line.
10. The method for day-ahead planning flow analysis considering uncertainty-based spatiotemporal correlation according to claim 1, characterized in that: the relevant information required by the scheduling determination comprises a probability density curve of a 24-hour 96 time period of the other line day and the load flow out-of-limit probability of each time period of the line day.
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