CN114970212A - High-precision alternating current-direct current series-parallel power grid power flow algorithm - Google Patents

High-precision alternating current-direct current series-parallel power grid power flow algorithm Download PDF

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CN114970212A
CN114970212A CN202210818181.3A CN202210818181A CN114970212A CN 114970212 A CN114970212 A CN 114970212A CN 202210818181 A CN202210818181 A CN 202210818181A CN 114970212 A CN114970212 A CN 114970212A
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彭穗
陶婧
朱自伟
徐松龄
周群臣
唐俊杰
徐婉婉
谢开贵
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Nanchang University
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Abstract

The invention discloses a high-precision alternating current-direct current series-parallel power grid load flow algorithm, which solves the probability density function of each variable by taking K-L distance minimization as a target function and fractional order moment as a constraint condition according to the principle of a maximum entropy method. And finally, performing probability load flow calculation on the AC/VSC-MTDC hybrid power grid based on a Latin hypercube sampling algorithm by combining the model. The method is used for fitting the probability density distribution of wind speed and illumination intensity in an actual power grid based on a maximum entropy model and fractional order moment, and is used for the probability load flow calculation of an AC/VSC-MTDC hybrid power grid; the low-order fractional statistical moment can contain information of a large number of integer orders, so that the problem of variation in the process of solving the high-order integer statistical moment is avoided. The method for calculating the maximum entropy of the fractional order moment can obviously improve the accuracy of the probability load flow calculation of the AC/VSC-MTDC hybrid power grid.

Description

High-precision alternating current-direct current series-parallel power grid power flow algorithm
Technical Field
The invention relates to the technical field of power systems, in particular to a high-precision alternating current-direct current series-parallel power grid power flow algorithm.
Background
With the progress of society and the development of technology, more and more new energy bases such as wind power, photovoltaic and the like are merged into a large alternating current power grid through a multi-terminal direct current system (VSC-MTDC) based on a voltage source converter. Under the influence of wind speed and illumination intensity, the wind power and photovoltaic output has strong randomness, intermittence and fluctuation. In order to further reveal the influence of the output of the new energy with strong uncertainty on the operation of a future power grid, the probability load flow calculation of the alternating-current and direct-current hybrid power grid is of great practical significance. And the determination of accurate probability density functions of random variables (such as wind speed and illumination intensity) of the power system is the key and the basis for probability power flow calculation.
Currently, when probability power flow analysis is performed, it is often assumed by artificial experience that wind speed obeys Weibull distribution and illumination intensity obeys Beta distribution, then sampling is performed on the probability distribution, and a deterministic alternating current-direct current hybrid power grid power flow model is input for probability power flow analysis. However, wind speed and light intensity in an actual grid do not necessarily obey common probability distributions. Probability modeling is carried out based on common probability distribution, so that the accuracy of probability load flow calculation is questioned.
At present, the input probability distribution is usually fitted based on an integer order moment maximum entropy model. However, its accuracy is greatly affected by higher order statistical moments. In the process of solving the integer order moment of the random variable, along with the increase of the order number of the integer order moment, the variability of the high-order statistical moment is very large and is difficult to accurately obtain. Particularly for a newly-built wind power plant or a newly-built photovoltaic power station, if the acquired wind speed and illumination intensity history are insufficient, the calculation accuracy of the high-order statistical moment is insufficient, so that the fitting probability distribution accuracy is reduced. Undoubtedly, this will further affect the accuracy of the probabilistic power flow calculation of the ac-dc hybrid grid.
Disclosure of Invention
Aiming at the problems in the prior art, the invention aims to provide a high-precision alternating current-direct current hybrid power grid power flow algorithm.
Since the historical data of wind speed and illumination intensity is less, it is difficult to accurately describe the probability density function with a complex uncertainty source according to a small amount of sample data. Aiming at the characteristic, the method solves the probability density function of each variable by taking K-L distance minimization as an objective function and fractional order moment as a constraint condition according to the principle of a maximum entropy method. And finally, performing probability load flow calculation on the AC/VSC-MTDC hybrid power grid based on a Latin hypercube sampling algorithm by combining the model. The method comprises the following steps:
a high-precision alternating current-direct current series-parallel power grid power flow algorithm comprises the following steps:
step S1: collecting a historical data set of random variables in an electrical power system, X ═ X 1 ,x 2 ,…,x n ) The number of the random variables is N, and the total number of the samples is N;
step S2: sequentially obtaining fractional order moment expressions of all random variables in the step S1 based on the definition of the fractional order moment;
step S3: establishing a K-L distance function model of each random variable based on a maximum entropy method;
step S4: taking the fractional order moment expression obtained in the step S2 as a constraint condition, and adopting the K-L distance minimization in the step S3 as optimizationTargeting to find the probability density function f of each random variable i (x i )；
Step S5: according to the probability density function f obtained in step S4 i (x i ) Generating random variable sample set in power system by Latin hypercube sampling method
Figure BDA0003743121970000021
Step S6: collecting system parameters of an alternating current power grid and a direct current power grid of a power system to form an alternating current-direct current series-parallel power grid deterministic load flow calculation module;
step S7: the random variable sample set obtained in step S5
Figure BDA0003743121970000022
And (4) inputting the results into a deterministic AC/DC hybrid power grid deterministic power flow calculation module established in the step S6 group by group for probabilistic power flow calculation, so as to output a probabilistic power flow calculation result of the AC/DC hybrid power grid.
Further, the step S2 specifically includes the following steps:
from the definition of the fractional order moment, the expression of the fractional order moment of the random variable can be obtained as follows:
Figure BDA0003743121970000023
wherein alpha is i Representing a random variable x i Order of fractional order moment, alpha i Taking the value as positive real number;
Figure BDA0003743121970000024
describing the probability characteristics of random variables by fractional order moments of one or more orders, where M denotes the describing variable x i The number of orders of the fractional order moments; f. of i (x i ) Is a random variable x i The probability density function of (1) is a function to be solved;
Figure BDA0003743121970000025
about its mean value x 0 The taylor series of (a) is expanded as:
Figure BDA0003743121970000031
wherein j is 0,1,2, …, n;
the values of the coefficients of the fractional order moment binomials are as follows:
Figure BDA0003743121970000032
therefore, the expression of the fractional order moment of each random variable in step S1 is as follows:
Figure BDA0003743121970000033
from the above features, it can be found that a single fractional order moment contains information of a large number of integer order moments.
Further, the step S3 specifically includes the following steps:
based on the maximum entropy method, a K-L distance function is adopted to measure a probability density estimation function g i (x i ) And the true probability density function f i (x i ) A deviation value therebetween; thus, K-L distance expression K [ f ] of each random variable can be obtained i (x i ),g i (x i )]The following were used:
Figure BDA0003743121970000034
wherein λ is i Representing a random variable x i Lagrange multipliers under the constraint of fractional order moments,
Figure BDA0003743121970000035
m represents a descriptive variable x i The number of orders of the fractional order moment is two in total, so that M is 2;
H[f i (x i )]representing a random variable x i The information entropy of (2) is specifically expressed as follows:
Figure BDA0003743121970000036
g i (x i ) Representing a random variable x i Has the following expression for the purpose of introducing a constraint of fractional order moments:
Figure BDA0003743121970000041
λ 0 representing a random variable x i The lagrange multiplier under normalized conditions can be expressed as follows:
Figure BDA0003743121970000042
wherein the content of the first and second substances,
Figure BDA0003743121970000043
further, the step S4 specifically includes the following steps:
if want to make random variable x i The entropy of the information of (a) is maximized, then the K-L distance function K [ f i (x i ),g i (x i )]The minimum value is required to be obtained; entropy due to true probability density H [ f ] i (x i )]For a given fractional order moment, is invariant, so that the degree of minimization of the K-L distance depends on the vector α of the parameter to be determined i And λ i Define Γ (λ) of each random variable i ,α i ) The function is as follows:
Figure BDA0003743121970000044
according to the principle of maximum entropy, it is necessary to find a condition such that Γ (λ) i ,α i ) Function minimized f i (x i ) It can be translated into the following optimization problem:
Figure BDA0003743121970000045
solving in MATLAB by using a simplex searching method to obtain a variable vector alpha to be solved i And λ i A value of (d);
therefore, the random variables x can be sequentially obtained according to the one-dimensional maximum entropy model under the constraint condition of the fractional order moment i Probability density function f i (x i )：
Figure BDA0003743121970000046
Further, the step S5 specifically includes the following steps:
probability density function f obtained from step S4 i (x i ) The random variable x can be obtained i Cumulative distribution function F i (x i ) And F is i (x i ) In [0,1 ]]The interval is uniformly distributed;
using Latin hypercube sampling method at F i (x i ) Up-sampled and passed through an inverse function
Figure BDA0003743121970000047
Obtaining a random variable x i Sample set of
Figure BDA0003743121970000048
The samples of all random variables are collected together to generate a random variable sample set in the power system
Figure BDA0003743121970000049
Further, the step S6 specifically includes the following steps:
collecting system parameters of alternating current and direct current power grids of a power system, and establishing a model for deterministic load flow calculation of an AC/VSC-MTDC alternating current and direct current synchronous/asynchronous series-parallel power grid, wherein the model can be solved by adopting an alternating iteration method.
The input quantity of the deterministic load flow calculation of the AC/VSC-MTDC hybrid power grid comprises the following input quantities: the generator outputs active and reactive power, a load value and topological parameters of an alternating current-direct current hybrid power grid; the output quantity comprises: the method comprises the following steps of (1) controlling the voltage of an alternating current-direct current hybrid power grid, the line tide of the alternating current-direct current hybrid power grid and control parameters of a VSC converter station;
the deterministic load flow calculation of the AC/VSC-MTDC hybrid power grid can look at an implicit function, which can be expressed as:
y pf ＝R pf (X sample ) (12)
if part of the input variable X sample Is a random variable, the problem becomes the problem of the probabilistic power flow analysis of the AC/VSC-MTDC hybrid power grid.
Further, the step S7 specifically includes the following steps:
the random variable sample set generated in step S5
Figure BDA0003743121970000051
And inputting the known power system parameters into the deterministic probabilistic load flow calculation model of the alternating current-direct current hybrid power grid established in the step S6, and outputting the voltage of the alternating current-direct current hybrid power grid, the line load flow of the alternating current-direct current hybrid power grid and the control parameters of the VSC converter station.
The invention has the beneficial effects that:
1) the method aims at the problem that the common probability distribution cannot accurately describe the data characteristics of the random variables. The method is used for fitting the probability density distribution of wind speed and illumination intensity in an actual power grid based on a maximum entropy model and fractional order moment, and is used for the probability load flow calculation of an AC/VSC-MTDC hybrid power grid;
2) aiming at the problem that the fitting input probability distribution of the maximum entropy method of the integer order moment is unreasonable, the maximum entropy method based on the fraction order moment is provided. The low order fractional statistical moment may contain information about a large number of integer order moments, thereby avoiding variation problems in solving the high order integer statistical moment. The method for calculating the maximum entropy of the fractional order moment can obviously improve the accuracy of the probability load flow calculation of the AC/VSC-MTDC hybrid power grid.
Drawings
FIG. 1 is a flow chart of a high-precision alternating current-direct current series-parallel power grid power flow algorithm of the invention;
FIG. 2 is a VSC converter station steady state model;
FIG. 3 is an improved IEEE-118 node system;
fig. 4 is a frequency histogram of load data of the ac/dc hybrid power grid in operation scenario 1;
FIG. 5 is a frequency histogram of illumination intensity data of an AC/DC hybrid power grid in an operation scene 1;
FIG. 6 is a frequency histogram of wind speed data of an AC/DC hybrid power grid in an operation scene 1;
fig. 7 is a frequency histogram of load data of the ac/dc hybrid power grid in operation scenario 2;
fig. 8 is a frequency histogram of illumination intensity data of the ac/dc hybrid power grid in the operation scene 2;
fig. 9 is a frequency histogram of wind speed data of the ac/dc hybrid grid in operation scene 2.
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. It is to be understood that the described embodiments are merely a few embodiments of the invention, and not all embodiments. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, belong to the scope of the present invention.
A high-precision alternating current-direct current hybrid power grid power flow algorithm is shown in figure 1 and comprises the following steps:
step S1: collecting historical data set X (X) of random variables (mainly comprising continuous random variables such as wind speed, illumination and load) in a power system 1 ,x 2 ,…,x n ) (ii) a The method comprises the following specific steps:
collecting a historical data set X ═ X (X) of random variables of the required wind power plant and photovoltaic power plant 1 ,x 2 ,…,x n ) The number of random variables is N, and the total number of samples is N.
Step S2: sequentially obtaining fractional order moment expressions of all random variables in the step S1 based on the definition of the fractional order moment; the specific process is as follows:
from the definition of the fractional order moment, the expression of the fractional order moment of the random variable can be obtained as follows:
Figure BDA0003743121970000061
wherein alpha is i Representing a random variable x i Order of fractional order moment, alpha i Taking the value as positive real number;
Figure BDA0003743121970000062
fractional order moments, usually of one or more orders, are used to describe the probability characteristics of a random variable, where M denotes the describing variable x i The number of orders of the fractional order moments; f. of i (x i ) Is a random variable x i Is the function to be solved.
Figure BDA0003743121970000071
About its mean value x 0 The Taylor series expansion is as follows:
Figure BDA0003743121970000072
where j is 0,1,2, …, n.
The values of the coefficients of the fractional order moment binomials are as follows:
Figure BDA0003743121970000073
therefore, the expression of the fractional order moments of the respective random variables in step S1 is as follows:
Figure BDA0003743121970000074
from the above features, it can be found that a single fractional order moment contains information of a large number of integer order moments.
Therefore, only two fractional orders are needed to describe the probability characteristics of random data more completely. In addition, when the historical samples of the random variables are few, the stability of the fractional order moment value is extremely high, and the insufficiency of the variability of the high order moment can be overcome.
Step S3: establishing a K-L distance function model of each random variable based on a maximum entropy method; the specific process is as follows:
based on the maximum entropy method, a K-L distance function is adopted to measure a probability density estimation function g i (x i ) And the true probability density function f i (x i ) The deviation value therebetween. Thus, K-L distance expression K [ f ] of each random variable can be obtained i (x i ),g i (x i )]The following:
Figure BDA0003743121970000075
wherein λ is i Representing a random variable x i Lagrange multipliers under the constraint of fractional order moments,
Figure BDA0003743121970000076
m represents a descriptive variable x i The number of orders of the fractional order moment is 2 because the parameters to be solved are two in total.
H[f i (x i )]Representing a random variable x i The information entropy of (2) is specifically expressed as follows:
Figure BDA0003743121970000081
g i (x i ) Representing a random variable x i Has the purpose of introducing a constraint of fractional order momentsThe following expression forms:
Figure BDA0003743121970000082
λ 0 representing a random variable x i The lagrange multiplier under normalized conditions can be expressed as follows:
Figure BDA0003743121970000083
wherein the content of the first and second substances,
Figure BDA0003743121970000084
step S4: taking the fractional order moment expression obtained in the step S2 as a constraint condition, taking the K-L distance minimization in the step S3 as an optimization target, and solving a probability density function f of each random variable i (x i ) (ii) a The specific process is as follows:
if want to make random variable x i The entropy of the information of (a) is maximized, then the K-L distance function K [ f i (x i ),g i (x i )]The minimum value is required. Entropy due to true probability density H [ f ] i (x i )]For a given fractional order moment, is invariant, so that the degree of minimization of the K-L distance depends on the vector α of the parameter to be determined i And λ i Define Γ (λ) of each random variable i ,α i ) The function is as follows:
Figure BDA0003743121970000085
according to the principle of maximum entropy, it is necessary to find a condition such that Γ (λ) i ,α i ) Function minimized f i (x i ) It can be translated into the following optimization problem:
Figure BDA0003743121970000086
solved in MATLAB using a simplex search method. Since it is a direct search method without using gradient information, calling this module can obtain the vector alpha of the variable to be solved i And λ i The value of (c).
Therefore, the random variables x can be sequentially obtained according to the one-dimensional maximum entropy model under the constraint condition of the fractional order moment i Probability density function f i (x i )：
Figure BDA0003743121970000087
Step S5: according to the probability density function f obtained in step S4 i (x i ) Generating random variable sample set in power system by adopting Latin hypercube sampling method
Figure BDA0003743121970000091
The specific process is as follows:
probability density function f obtained from step S4 i (x i ) The random variable x can be obtained i Cumulative distribution function F i (x i ) And F is i (x i ) In [0,1 ]]The distribution is uniform.
Using Latin hypercube sampling method at F i (x i ) Up-sampled and passed through an inverse function
Figure BDA0003743121970000092
Obtaining a random variable x i Sample set of
Figure BDA0003743121970000093
The samples of all random variables are collected together to generate a random variable sample set in the power system
Figure BDA0003743121970000094
Step S6: collecting system parameters of an alternating current power grid and a direct current power grid of a power system to form an alternating current-direct current series-parallel power grid deterministic load flow calculation module; the specific process is as follows:
collecting system parameters of alternating current and direct current power grids of a power system, and establishing a deterministic load flow calculation model of an AC/VSC-MTDC alternating current and direct current synchronous/asynchronous series-parallel power grid with any topological structure, wherein the model can be solved by adopting an alternating iteration method.
1) Steady-state power flow model introduction of VSC
As shown in FIG. 2, the ith VSC in the VSC-MTDC system is simplified to be a controllable voltage source, and the voltage vector of the controllable voltage source is represented as
Figure BDA0003743121970000095
Z ci ＝R ci +jX ci Representing the equivalent impedance of the converter station, B fi Is a filter, Z tfi ＝R tfi +jX tfi Representing the equivalent impedance of the converter transformer. The apparent power injected into the AC grid bus i from the VSC converter station side is respectively represented as S ci ＝P ci +jQ ci And S si ＝P si +jQ si The alternating-current bus side power flow equation is expressed as:
Figure BDA0003743121970000096
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003743121970000097
and
Figure BDA0003743121970000098
the voltage vectors at the ac bus side and the filter, respectively. The flow equation of the current transformer station bus injected into the alternating current bus is as follows:
Figure BDA0003743121970000099
the reactive power loss of the ac filter is expressed as:
Figure BDA00037431219700000910
active loss P of converter station lossi Comprises the following steps:
Figure BDA00037431219700000911
Figure BDA0003743121970000101
wherein, I ci Is the current flowing through the converter station. K A ，K B And K C The constant is obtained according to the experimental test of the operation scene of the direct current power grid.
The power flow calculation model of the dc grid may be expressed as:
Figure BDA0003743121970000102
wherein i di And u di Representing the dc network current and voltage, respectively. Y is dij And representing a direct current grid node admittance matrix.
2) Introduction to control scheme of VSC
The VSC converter station has the capability of independently controlling the active and reactive power outputs. In order to balance the active power of the VSC-MTDC system, at least one VSC converter station in the VSC-MTDC system must be selected to serve as an active balance regulator of the whole system. Generally, the VSC station is controlled as follows (where i denotes any VSC station of the VSC-MTDC):
(1) constant DC voltage u di Constant reactive power Q si Control (referred to as "u-Q" control);
(2) constant DC voltage u di Fixed bus voltage U si Control (U-U control for short);
(3) constant active power P si Constant reactive power Q si Control (P-Q control for short);
(4) is fixed withWork power P si Fixed bus voltage U si And (4) controlling (P-U controlling for short).
The calculation equation of the load flow of the node a in the alternating current power grid can be expressed as follows:
Figure BDA0003743121970000103
according to the invention, the deterministic load flow calculation of the AC/VSC-MTDC hybrid power grid is solved by adopting an alternating iteration method. The input quantity of the deterministic load flow calculation of the AC/VSC-MTDC hybrid power grid comprises the following input quantities: the generator outputs active and reactive power, a load value, topological parameters of an alternating current and direct current hybrid power grid and the like; the output quantity comprises: the voltage of the alternating current-direct current hybrid power grid and the line tide of the alternating current-direct current hybrid power grid. The deterministic load flow calculation of the AC/VSC-MTDC hybrid power grid can look at an implicit function, which can be expressed as: y is pf ＝R pf (X sample ) (19)
If part of the input variable X sample The problem becomes the problem of the probabilistic power flow analysis of the AC/VSC-MTDC hybrid grid if the stochastic variable is output by a wind power plant and the like.
Step S7: the random variable sample set obtained in step S5
Figure BDA0003743121970000111
Inputting the results into a deterministic AC/DC hybrid power grid deterministic load flow calculation module established in the step S6 group by group for probabilistic load flow calculation, and outputting a probabilistic load flow calculation result of the AC/DC hybrid power grid; the specific process is as follows:
the random variable sample set generated in step S5
Figure BDA0003743121970000112
And inputting the known power system parameters into the deterministic probabilistic load flow calculation model of the alternating current-direct current hybrid power grid established in the step S6, and outputting the voltage of the alternating current-direct current hybrid power grid, the line load flow of the alternating current-direct current hybrid power grid and the control parameters of the VSC converter station. (there is a callable module).
Example of the implementation
An improved IEEE-118 node system (as shown in fig. 3) was applied for testing the validity and superiority of the proposed probabilistic trend algorithm. The improved IEEE-118 node system comprises a five-terminal VSC-MTDC system (named DC1), a three-terminal VSC-MTDC system (named DC2), three wind farm output models (named WF1, WF2 and WF3) and two photovoltaic power stations (named PV1 and PV 2). Data for the IEEE-118 node system is derived from the MATPOWER6.0 software package. Assuming that the capacity of the photovoltaic power stations PV1 and PV2 is 50MW and 40MW, respectively, the capacity of the wind farm is 100 MW.
The improved IEEE-118 node system contains 104 uncertainty sources in total, including 99 loads, 3 wind farms, and 2 photovoltaic power plants. Note that the wind speeds at the wind farms WF1, WF2 and WF3, the light intensities at the photovoltaic power plants PV1 and PV2, and the historical data of 99 loads are all from the actual power system. The method is based on probability load flow calculation, and the probability density function with high precision is fitted based on the historical data of the random variables in the power system.
(ii) accuracy of probability density function of fitting historical data
In order to verify the effectiveness and high accuracy of the proposed method in fitting historical data, a frequency histogram based on historical data is used as a reference, which is called historical data for short. In order to verify the superiority of the proposed method, two operational scenarios were set:
operational scenario 1: in the operation scene with sufficient historical data, the historical data of wind speed, illumination and load in the AC-DC hybrid power grid are all 20000 groups;
operation scenario 2: and in an operation scene with relatively insufficient historical data, the historical data of wind speed, illumination and load in the alternating current-direct current hybrid power grid is only 2000 groups.
In the above operation scenario, the proposed method will compare the fitting accuracy with the following algorithm:
comparative method 1: assuming that random variables in the power system all obey a conventional probability density function, fitting wind speed data, Beta distribution fitting illumination intensity data and normal distribution fitting load data by utilizing Weibull distribution.
Comparative method 2: integer order moments are used in conjunction with the maximum entropy model to fit the historical data.
The method comprises the following steps: the fractional order moments are combined with a maximum entropy model for fitting the historical data. Note that for fairness of comparison, all fitting models generate the same amount of data as the historical data and participate in comparison with the frequency histogram of the data. The model fitting the historical data is the best, and the model fitting the historical data is more accurate.
Fig. 4 to 9 show frequency histograms of load, illumination intensity and wind speed data in the ac/dc hybrid power grid obtained by the historical data, the comparison method 1, the comparison method 2 and the proposed method, respectively. The method is most fit with a frequency histogram based on historical data, and the effectiveness and high precision of the method are proved. As can be seen from the frequency histogram, historical data of random variables in the power system may not follow a common distribution, and the random variable data features may not be accurately described by using the common probability distribution. Therefore, the fitting effect of the frequency histogram obtained based on the idea that the random variables obey common distribution on the historical data is not good in the comparison method 1.
When the historical data is more abundant (scenario 1), the effect of combining the integer order moments with the maximum entropy model for fitting the historical data (comparative method 2) is better than directly fitting the historical data using the common probability distribution (comparative method 1). Because the historical data of random variables in a power system may not follow a common distribution, conventional probability density functions do not accurately characterize the random variable data. In addition, in the process of solving the integer order moment of the random variable, along with the increase of the order of the integer order moment, the variability of the high-order statistical moment is very large and is difficult to obtain accurately, so that the effect of the tail characteristic of the historical data fitted by the comparison method 2 is poor. The conclusion can be visually seen from the fitting effect of the wind speed data.
When the historical data is relatively insufficient (in the operational scenario 2), the effect of the combination of the fractional order moments and the maximum entropy model for fitting the historical data (the proposed method) is significantly better than the effect of the combination of the integer order moments and the maximum entropy model for fitting the historical data (the comparative method 2). The fitting effect of the comparison method 2 in the running scene 2 (a scene with relatively insufficient data) is worse than that in the case where the historical data is sufficient. Due to insufficient acquired load, illumination intensity wind and wind speed history, the calculation accuracy of the high-order statistical moment is further insufficient, and the accuracy of the fitted probability distribution is reduced. The conclusion can be visually seen from the fitting effect of the random variable data.
The method provided by the invention can overcome the problems, and the main reasons are as follows: the method comprises the steps that random characteristics of historical data are described by using low-order fractional order moments, the fractional order statistical moments are more stable, and therefore the problem of variation in the process of solving the high-order integer statistical moments is solved; secondly, the fractional order moment contains a large amount of information of the integer order moment, and the input probability distribution can be well fitted under the condition that the historical data is insufficient, so that the probability modeling precision is further improved.
(II) precision analysis of probability power flow algorithm
In order to verify the effectiveness of the proposed probabilistic power flow calculation method, 20000 groups of historical data are input into a deterministic alternating current-direct current hybrid power grid power flow calculation model based on the idea of a Monte Carlo simulation method, and a 'reference value' of a probabilistic power flow calculation result is obtained. Meanwhile, the calculation precision of the proposed probabilistic power flow algorithm is compared with the following algorithm:
comparing probability trend method 1: artificially assuming that random variables in the power system obey common distribution, fitting wind speed data, Beta distribution fitting illumination intensity data and normal distribution fitting load data by utilizing Weibull distribution, then generating random data based on the common distribution, inputting the random data into a deterministic AC/DC hybrid power grid load flow calculation model, and performing probability load flow calculation.
The probability trend comparison method 2: and combining the integer order moment with a maximum entropy model for fitting historical data, then generating random data based on the model, inputting the random data into a deterministic alternating current-direct current hybrid power grid load flow calculation model, and performing probabilistic load flow calculation.
The proposed probabilistic power flow method: and combining the fractional order moment with the maximum entropy model to fit historical data, then generating random data based on the method, inputting the random data into a deterministic alternating current-direct current hybrid power grid load flow calculation model, and performing probabilistic load flow calculation. Note that the probabilistic power flow algorithm uses the latin hypercube to select 5000 groups of sample points on the constructed probability input distribution for probabilistic power flow calculation.
Table 1 operating scenario 1 relative errors of mean, standard deviation, third order moment and fourth order moment of voltage amplitude at bus 45
Figure BDA0003743121970000131
Table 2 operating scenario 2 relative errors of mean, standard deviation, third order moment and fourth order moment of voltage amplitude at bus 45
Figure BDA0003743121970000132
The calculation results of the operation scene 1 and the operation scene 2 can find that the probability load flow calculation accuracy of the history data is the worst based on the direct fitting of the conventional distribution (compared with the probability load flow method 1). The relative calculation error of the third moment and the fourth moment in the operation scene 2 of the comparative probabilistic power flow method 1 is up to 29.79% and 46.16%. The main reason is that the probability modeling precision in the probability load flow calculation process is reduced and the reliability of the probability load flow calculation result is directly influenced only by assuming that the wind speed obeys Weibull distribution, the illumination intensity obeys Beta distribution and the load obeys normal distribution through artificial experience.
Comparing the operation scenario 1 and the operation scenario 2, it can be found that the calculation error of the comparison probabilistic power flow method 2 is significantly increased. For example, the relative calculation errors of the third moment and the fourth moment of the comparative probabilistic power flow method 2 in the operational scenario 1 are 8.66% and 9.57%, whereas the relative calculation errors of the third moment and the fourth moment thereof in the operational scenario 2 increase to 14.66% and 19.57%. The main reason is that the history in the operation scene 2 is relatively insufficient, which results in insufficient calculation accuracy of the high-order integer statistical moment, and the effect of combining the integer order moment and the maximum entropy model for fitting the history data is further reduced, thereby reducing the probability load flow calculation accuracy.
The proposed probabilistic power flow method performs well in all operational scenarios. The relative calculation errors of the third moment and the fourth moment in the operation scene 1 of the proposed probabilistic power flow method are 3.98% and 4.56%, the relative calculation errors of the third moment and the fourth moment in the operation scene 2 are 6.58% and 8.43%, and the calculation accuracy is ideal, mainly because: 1) the low-order fractional order moment is used as a constraint condition, so that the characteristics of the historical data can be fitted more comprehensively and meticulously. 2) Based on the maximum entropy model, the problem of insufficient historical data can be solved, the probability distribution is better fitted and input, and the probability load flow calculation precision is further improved.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (7)

1. A high-precision alternating current-direct current series-parallel power grid power flow algorithm is characterized in that: the method comprises the following steps:
step S1: collecting a historical data set of random variables in an electrical power system, X ═ X 1 ,x 2 ,…,x n ) The number of the random variables is N, and the total number of the samples is N;
step S2: sequentially obtaining fractional order moment expressions of all random variables in the step S1 based on the definition of the fractional order moment;
step S3: establishing a K-L distance function model of each random variable based on a maximum entropy method;
step S4: taking the fractional order moment expression obtained in the step S2 as a constraint condition, taking the K-L distance minimization in the step S3 as an optimization target, and solving a probability density function f of each random variable i (x i )；
Step S5: according to the probability density function f obtained in step S4 i (x i ) Generating random variable sample set in power system by adopting Latin hypercube sampling method
Figure FDA0003743121960000011
Step S6: collecting system parameters of an alternating current power grid and a direct current power grid of a power system to form an alternating current-direct current series-parallel power grid deterministic load flow calculation module;
step S7: the random variable sample set obtained in step S5
Figure FDA0003743121960000012
And (4) inputting the results into a deterministic AC/DC hybrid power grid deterministic power flow calculation module established in the step S6 group by group for probabilistic power flow calculation, so as to output a probabilistic power flow calculation result of the AC/DC hybrid power grid.
2. The high-precision alternating current-direct current hybrid power grid power flow algorithm according to claim 1, characterized in that: the specific process of step S2 is as follows:
from the definition of the fractional order moment, the expression of the fractional order moment of the random variable can be obtained as follows:
Figure FDA0003743121960000013
wherein alpha is i Representing a random variable x i Order of fractional order moment, alpha i Taking the value as positive real number;
Figure FDA0003743121960000014
describing the probability characteristics of random variables by fractional order moments of one or more orders, where M denotes the describing variable x i The number of orders of the fractional order moments; f. of i (x i ) Is a random variable x i The probability density function of (1) is a function to be solved;
Figure FDA0003743121960000015
about its mean value x 0 The Taylor series expansion is as follows:
Figure FDA0003743121960000021
wherein j is 0,1,2, …, n;
the values of the coefficients of the fractional order moment binomial are as follows:
Figure FDA0003743121960000022
therefore, the expression of the fractional order moments of the respective random variables in step S1 is as follows:
Figure FDA0003743121960000023
from the above features, it can be found that a single fractional order moment contains information of a large number of integer order moments.
3. The high-precision alternating current-direct current hybrid power grid power flow algorithm according to claim 2, characterized in that: the specific process of step S3 is as follows:
based on the maximum entropy method, measuring the probability density estimation function g by adopting a K-L distance function i (x i ) And the true probability density function f i (x i ) A deviation value therebetween; thus, K-L distance expression K [ f ] of each random variable can be obtained i (x i ),g i (x i )]The following:
Figure FDA0003743121960000024
wherein λ is i Representing a random variable x i Lagrange multipliers under the constraint of fractional order moments,
Figure FDA0003743121960000025
m represents a descriptive variable x i The number of orders of the fractional order moment is two in total, so that M is 2;
H[f i (x i )]representing a random variable x i Specifically, the information entropy of (2) is expressed as follows:
Figure FDA0003743121960000026
g i (x i ) Representing a random variable x i Has the following expression for the purpose of introducing a constraint of fractional order moments:
Figure FDA0003743121960000031
λ 0 representing a random variable x i The lagrange multiplier under normalized conditions can be expressed as follows:
Figure FDA0003743121960000032
wherein the content of the first and second substances,
Figure FDA0003743121960000033
4. the high-precision alternating current-direct current hybrid power grid power flow algorithm according to claim 3, characterized in that: the specific process of step S4 is as follows:
if want to make random variable x i The entropy of the information of (a) is maximized, then the K-L distance function K [ f i (x i ),g i (x i )]The minimum value is required to be obtained; entropy due to true probability density H [ f ] i (x i )]For a given fractional order moment, is invariant, so that the degree of minimization of the K-L distance depends on the vector α of the parameter to be determined i And λ i Define Γ (λ) of each random variable i ,α i ) The function is as follows:
Figure FDA0003743121960000034
according to the principle of maximum entropy, the requirement is found to satisfy gamma (lambda) i ,α i ) Function minimized f i (x i ) It can be translated into the following optimization problem:
Figure FDA0003743121960000035
solving in MATLAB by using a simplex searching method to obtain a variable vector alpha to be solved i And λ i A value of (d);
therefore, the random variables x can be sequentially obtained according to the one-dimensional maximum entropy model under the constraint condition of the fractional order moment i Probability density function f i (x i )：
Figure FDA0003743121960000036
5. The high-precision alternating current-direct current hybrid power grid power flow algorithm according to claim 1, characterized in that: the specific process of step S5 is as follows:
probability density function f obtained from step S4 i (x i ) To obtain a random variable x i Cumulative distribution function F i (x i ) And F is i (x i ) In [0,1 ]]The interval is uniformly distributed;
using Latin hypercube sampling method at F i (x i ) Up-sampled and passed through an inverse function
Figure FDA0003743121960000041
Obtaining a random variable x i Sample set of
Figure FDA0003743121960000042
The samples of all random variables are collected together to generate a random variable sample set in the power system
Figure FDA0003743121960000043
6. The high-precision alternating current-direct current hybrid power grid power flow algorithm according to claim 1, characterized in that: the specific process of step S6 is as follows:
collecting system parameters of alternating current and direct current power grids of a power system, and establishing a model for deterministic load flow calculation of an AC/VSC-MTDC alternating current synchronous/asynchronous series-parallel power grid, wherein the model can be solved by adopting an alternating iteration method;
the input quantity of the deterministic load flow calculation of the AC/VSC-MTDC hybrid power grid comprises the following input quantities: the generator outputs active and reactive power, a load value and topological parameters of an alternating current-direct current hybrid power grid; the output quantity comprises: the voltage of the alternating current-direct current hybrid power grid and the line tide of the alternating current-direct current hybrid power grid are calculated;
the deterministic load flow calculation of the AC/VSC-MTDC hybrid power grid can look at an implicit function, which can be expressed as:
y pf ＝R pf (X sample ) (12)
if part of the input variable X sample Is a random variable, the problem becomes the problem of the probabilistic power flow analysis of the AC/VSC-MTDC hybrid power grid.
7. The high-precision alternating current-direct current hybrid power grid power flow algorithm according to claim 6, characterized in that: the specific process of step S7 is as follows:
the random variable sample set generated in step S5
Figure FDA0003743121960000044
Inputting the known parameters of the power system into the deterministic probabilistic power flow calculation model of the AC/DC hybrid power grid established in the step S6, and outputting the voltage, AC/DC of the AC/DC hybrid power gridAnd the flow of the series-parallel power grid line and the control parameters of the VSC converter station.
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