A probabilistic power flow calculation method for AC / DC hybrid systems considering the boundedness and correlation of new energy

Abstract

The application discloses a kind of AC-DC hybrid system probabilistic power flow calculation method considering new energy boundedness and correlation, comprising the following steps: 1) obtaining AC-DC hybrid system basic information, determine the scaling factor, and utilize scaling unscented transformation method to select sample points on standard normal distribution;2) calculate boundary parameter, convert the selected sample points to original probability space, obtain original probability space sample points;3) establish the power conversion model of wind farm and photovoltaic power station and the deterministic power flow model of AC-DC hybrid system;4) input wind speed, light intensity into the power conversion model of wind farm and photovoltaic power station, obtain wind power and photovoltaic output data;5) input load data, wind power and photovoltaic output data into the deterministic power flow model of AC-DC hybrid system, carry out probabilistic power flow analysis and calculation.The application can analyze high-dimensional probabilistic power flow considering new energy boundedness and correlation when large-scale new energy is accessed to AC-DC hybrid power grid.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of probabilistic power flow calculation, and particularly relates to a probabilistic power flow calculation method for AC / DC hybrid system considering boundedness and correlation of new energy. BACKGROUND

[0002] Large-scale AC / DC hybrid power grid is essentially an uncertain system. The main sources of uncertainty come from large-scale new energy (such as wind farms, photovoltaic power generation, etc.), volatile loads, etc. Probabilistic power flow (PPF) calculation has become an important tool for studying the impact of new energy and load uncertainty on AC / DC hybrid power grid.

[0003] There are mainly three kinds of probabilistic power flow algorithms: Monte Carlo simulation method, analytical method and unscented transformation method.

[0004] Monte Carlo simulation (MCS) is the most widely used simulation method at present, which has several obvious advantages, including system dimension independence, high calculation accuracy and good ability to handle correlation. The disadvantage is that the computational burden is too large. Therefore, Monte Carlo method is more suitable as a "reference algorithm".

[0005] In contrast, the analytical method is more efficient in terms of calculation speed. However, for most analytical methods, the highly nonlinear deterministic power flow (DPF) model needs to be linearized, and it is assumed that the random variables are not correlated, which will lead to unreliable results.

[0006] The traditional unscented transformation algorithm (TUT) selects 2n+1 sample points based on the symmetric sampling strategy (n represents the dimension of the input variable), which performs well in PPF analysis. However, in the high-dimensional PPF calculation of large-scale new energy connected to AC / DC hybrid power grid, the TUT algorithm will exhibit the following characteristics: as the dimension of the input random variable increases, the sampling radius of the sample points also increases, resulting in the "global sampling problem". This problem has two adverse effects: first, extreme samples may occur, leading to a decrease in the accuracy of PPF calculation results; second, sample points may continue to diverge, eventually "running out" of the reasonable physical interval, resulting in the loss of physical meaning of probabilistic power flow analysis.

[0007] Due to the highly structured sample points of the traditional Unscented Transformation algorithm, which cannot be arbitrarily increased, discarded or even moved, the prior art introduces a scaling factor to flexibly scale the sample points, thereby theoretically avoiding the global sampling problem of the Unscented Transformation algorithm. However, in actual AC-DC hybrid power grids with a large amount of new energy and loads, the boundaries of new energy and loads have great differences. When the method is used to perform probabilistic power flow calculation on the actual AC-DC hybrid power grid, it always faces the 'decision dilemma' of determining the scaling parameter, which easily leads to the local sampling problem (the definition of the local sampling problem is that a large number of sample points are distributed around the mean, resulting in a too small sampling range, thereby affecting the accuracy of the probability analysis). At the same time, it is difficult for the method to comprehensively consider and take into account all boundary values of the greatly different new energy and loads in the actual AC-DC hybrid power grid. Therefore, the boundary problem brings a severe challenge to the probabilistic power flow calculation of the AC-DC hybrid power grid based on the Scaled Unscented Transformation (SUT) algorithm.

[0008] To solve the above problems, some scholars introduce the method of mutual cooperation of Universal Transformation and Power Transformation (UPT) to solve the boundary problem of probabilistic power flow. However, the method has the following two shortcomings: (1) it ignores the correlation between input random variables, resulting in inaccurate probabilistic power flow analysis results; (2) UPT is a nonlinear function, and when the correlation coefficient is transformed by UPT, the value of the correlation coefficient will change, introducing errors into the probabilistic power flow calculation. SUMMARY

[0009] The purpose of the present application is to provide a probabilistic power flow calculation method for AC-DC hybrid systems considering the boundedness and correlation of new energy, comprising the following steps:

[0010] 1) Obtain the basic information of the AC-DC hybrid system.

[0011] The basic information of the AC-DC hybrid system includes random variables, probability density functions of random variables, cumulative distribution functions, Pearson correlation coefficient matrix ρ X , and Pearson correlation coefficient matrix ρ Z of random variables in the standard normal distribution space. The random variables include wind speed, light intensity and load.

[0012] The Pearson correlation coefficient matrix ρ Z of random variables in the standard normal distribution space is as follows:

[0013]

[0014] In the formula, ρij Z represents a standard normal distribution sample i The Pearson correlation coefficient between the standard normal distribution sample Z j i = 1, 2, …, n; j = 1, 2, …, n.

[0015] 2) Determine the scaling factor according to the basic information of the AC-DC hybrid system, select sample points on the standard normal distribution using the scaled unscented transformation method, and determine the weight coefficient, the steps including:

[0016] 2.1) Determine the scaling factor, the steps including:

[0017] 2.1.1) Generate n-dimensional uncorrelated random variables V obeying the standard normal distribution.

[0018] 2.1.2) Generate standard normal random variables Z containing the Pearson correlation coefficient matrix ρ Z .

[0019] 2.1.3) Select sample points on the n-dimensional standard normal distribution based on the traditional unscented transformation algorithm, and obtain the sample point matrix Z tut = [z 0 , z 1 , …, z k ]. The elements in the sample point matrix Z tut satisfy the following formula:

[0020]

[0021] W 0 = 1 / 3 (3)

[0022]

[0023] In the formula, z k is the sample point obtained by using the traditional unscented transformation. W 0 is the initial weight of the traditional unscented transformation, and W k is the weight coefficient corresponding to the sample point. m, P ZZ represent the mean vector and covariance matrix of the input variable. is the kth row of the matrix square root .

[0024] Wherein, the covariance matrix P ZZ is as follows:

[0025]

[0026] In the formula, cov(Z i , Z j ) is the Pearson correlation coefficient between the standard normal distribution sample Z i and the standard normal distribution sample Zj The covariance of i = 1, 2, ..., n; j = 1, 2, ..., n.

[0027] covariance cov(Z) i Z j The following equation must be satisfied:

[0028]

[0029] In the formula, σ i σ j Z represents a standard normal distribution sample. i Compared with the standard normal distribution sample Z j The standard deviation of ρ. ij Z represents a standard normal distribution sample i Compared with the standard normal distribution sample Z j The Pearson correlation coefficient between them.

[0030] 2.1.4) Calculate the scaling factor α of the scaling unscented transformation method, i.e.

[0031]

[0032] In the formula, ε emp These are empirical parameters.

[0033] Wherein, the intermediate parameter z max As shown below:

[0034] z max =max(|Z tut |) (8)

[0035] 2.2) The steps for selecting sample points on the standard normal distribution using the scaling unscented transform method include:

[0036] 2.2.1) Select sample points on the standard normal distribution using the scaling unscented transform method to obtain sample point Z. sut =[z 0 ,z 1 ,…,z k Sample point Z sut The elements in the equation satisfy the following formula:

[0037]

[0038]

[0039] In the formula, β is the weight adjustment parameter.

[0040] 2.2.2) Determine the weighting coefficients in the scaling unscented transformation method, i.e.:

[0041]

[0042]

[0043] where z 0 , z k represent the sample points obtained by the scaled unscented transformation method. n is the dimension of the random variable. P ZZ is the covariance of the input random variable. W 0 is the initial weight of the scaled unscented transformation, is the weight coefficient of the mean of the input random variable. W c 0 , W c k is the weight coefficient of the covariance matrix of the input variable.

[0044] 3) Calculate the boundary parameters and convert the selected sample points to the original probability space by using the boundary inverse transformation algorithm to obtain the original probability space sample points considering the boundary and correlation.

[0045] The step of calculating the boundary parameters includes:

[0046] 3.1) Estimate the upper and lower boundary values of each dimension variable according to the historical data X and i = 1, 2, 3, …, n. The historical data X includes the historical basic information of the AC-DC hybrid system.

[0047] 3.2) Calculate the boundary parameters and the boundary parameters i.e.:

[0048]

[0049] where F i (·) is the cumulative distribution function of the random variable X i in the actual power system. and are the minimum value and the maximum value of the random variable estimated according to the historical data, respectively. and are the boundary parameters in the boundary inverse transformation method.

[0050] The original probability space sample points X i considering the boundary and correlation satisfy the following formula:

[0051] u i = Φ(Z sut ), Z sut ∈ (-∞, +∞) (14)

[0052]

[0053]

[0054] where Z sut is a standard normal distribution variable. u i is a uniformly distributed variable in the interval (0, 1). denotes the value of the input random variable transformed to the uniform distribution space. and are the lower and upper bounds of the random variable, respectively. Φ(Z sut ) denotes the inverse cumulative distribution function of the standard normal distribution.

[0055] 4) The power conversion model of the wind farm and photovoltaic power station and the deterministic power flow model of the AC / DC hybrid system are established.

[0056] The probabilistic power flow model of the AC / DC hybrid system is as follows:

[0057] Y _output = p f (X _input ) (17)

[0058] where X _input , Y _output represent the input and output of the AC / DC hybrid system, respectively. p f represents the power flow calculation module of the AC / DC hybrid system.

[0059] 5) The wind speed and solar irradiance in the original probability space sample points are input into the power conversion model of the wind farm and photovoltaic power station to obtain the wind power and photovoltaic power output data.

[0060] The wind power output data P w is as follows:

[0061]

[0062] where v w represents the wind speed, v ci , v r , v co represent the cut-in wind speed, rated wind speed and cut-out wind speed of the wind turbine, respectively; P r represents the rated power of the wind farm.

[0063]

[0064]

[0065]

[0066] The photovoltaic power output data P sAs shown below:

[0067] P s = rArea h (22)

[0068] In the formula, r is the real-time light intensity; Area is the total light area; h is the conversion efficiency of photovoltaic power generation.

[0069] 6) Load data, wind power and photovoltaic output data are input into the deterministic power flow model of the AC-DC hybrid system for probability power flow analysis and calculation.

[0070] The input X _input and output Y _input of the AC-DC hybrid system are as follows:

[0071] X_ input = [P load , Q load , P ren , Q ren , T ac , T dc ] T (23)

[0072] In the formula, P load and Q load are the active power and reactive power of the load respectively. T ac and T dc represent the topological parameters of the AC-DC power grid respectively. P ren and Q ren represent the electric energy generated by new energy such as wind farms.

[0073] Y _output = [U ac , U dc , S ac_ij , P dc_ij , Q conver ] T (24)

[0074] In the formula, U ac and U dc represent the AC and DC grid voltages respectively. S ac_ij is the apparent power of the AC grid. P dc_ij is the active power of the DC grid. Q conver is the reactive power generated by the converter between the AC-DC power grid.

[0075] The steps of probability power flow analysis and calculation also include statistics on the probability power flow results to obtain the mean and covariance of the probability power flow calculation results.

[0076] The mean and covariance of the probability power flow are as follows:

[0077]

[0078] In the formula, P YY are the mean and covariance matrix of the probabilistic power flow.

[0079] The covariance P of the probabilistic power flow YY The relationship between the probabilistic power flow variance satisfies the following formula:

[0080]

[0081] In the formula, D(Y) is the variance of the probabilistic power flow. cov(Y n , Y1) is the covariance between the output Y n and the output Y1.

[0082] The technical effects of the present application are self-evident, and the present application has the following advantages:

[0083] 1) The present application proposes an empirical calculation formula of the scaling unscented transformation method proportional scaling coefficient, to balance the global sampling and local sampling problems.

[0084] 2) The present application fully obtains the probability information of the random input distribution, thereby improving the accuracy of the probabilistic power flow calculation considering large-scale new energy access AC-DC hybrid power grid.

[0085] 3) The present application proposes a boundary inverse transformation algorithm, based on which the high-quality sample points obtained by the scaling unscented transformation method are converted to the original probability space, ensuring that all sample points fall within a reasonable physical interval.

[0086] 4) The present application combines the scaling unscented transformation method and the boundary inverse transformation algorithm, so that the algorithm can efficiently and accurately process the probabilistic power flow problem of AC-DC hybrid power grid with different boundaries and different correlation levels of new energy and load. BRIEF DESCRIPTION OF DRAWINGS

[0087] Figure 1 is the integral interval of the standard normal distribution;

[0088] Figure 2 is the boundary inverse transformation algorithm step proposed by the present application;

[0089] Figure 3 is the general step of PPF calculation;

[0090] Figure 4 is an improved IEEE 1354 node system (PEGASE) - AC-DC hybrid power grid accessing voltage source converters (VSCs);

[0091] Figure 5Mean error (%) of DC bus voltage amplitude;

[0092] Figure 6 STD error (%) of DC bus voltage amplitude;

[0093] Figure 7 Scatter plot of wind speed of wind farms WF1 and WF2;

[0094] Figure 8 Scatter plot of loads of AC bus 3 and AC bus 2457 (the loads of AC bus 3 and AC bus 2457 belong to load type A and load type B respectively);

[0095] Figure 9 Scatter plot of loads of AC bus 6697 and AC bus 6744 (the loads of AC bus 6697 and AC bus 6744 both belong to load type C);

[0096] Figure 10 (a) Mean error (%) of DC bus voltage amplitude; Figure 10 ((b) STD error (%) of DC bus voltage amplitude; DETAILED DESCRIPTION

[0097] The application will be further described in conjunction with the examples below, but should not be understood as limiting the above-mentioned subject matter of the application to the following examples. Various substitutions and modifications can be made according to ordinary technical knowledge and conventional means without departing from the above-mentioned technical ideas of the application, and all should be included in the protection scope of the application.

[0098] Example 1:

[0099] Reference Figures 1 to 3 A probabilistic power flow calculation method for AC / DC hybrid systems considering boundedness and correlation of new energy, comprising the following steps:

[0100] 1) Obtain basic information of the AC / DC hybrid system.

[0101] The basic information of the AC / DC hybrid system includes random variables, probability density functions of random variables, cumulative distribution functions, Pearson correlation coefficient matrix ρ X of random variables in the standard normal distribution space, and Pearson correlation coefficient matrix ρ Z of random variables in the standard normal distribution space. The random variables include wind speed, light intensity and load.

[0102] The Pearson correlation coefficient matrix ρ Z of random variables in the standard normal distribution space is as follows:

[0103]

[0104] where ρ ij i j is the Pearson correlation coefficient between the standard normal distribution samples Zi = 1, 2, …, n; j = 1, 2, …, n.

[0105] 2) Determine the scaling factor according to the basic information of the AC-DC hybrid system, select sample points on the standard normal distribution using the scaled unscented transformation method, and determine the weight coefficient, the steps including:

[0106] 2.1) Determine the scaling factor, the steps including:

[0107] 2.1.1) Generate n-dimensional uncorrelated random variables V obeying the standard normal distribution.

[0108] 2.1.2) Generate standard normal random variables Z containing the Pearson correlation coefficient matrix ρ Z .

[0109] 2.1.3) Select sample points on the n-dimensional standard normal distribution based on the traditional unscented transformation algorithm, and obtain the sample point matrix Z tut = [z 0 , z 1 , …, z k ]. The elements in the sample point matrix Z tut satisfy the following formula:

[0110]

[0111] W 0 = 1 / 3 (3)

[0112]

[0113] where z k is the sample point obtained by using the traditional unscented transformation. W 0 is the initial weight of the traditional unscented transformation, and W k is the weight coefficient corresponding to the sample point. m, P ZZ represent the mean vector and covariance matrix of the input variables. is the kth row of the matrix square root .

[0114] where the covariance matrix P ZZ is as follows:

[0115]

[0116] where cov(Z i , Z j ) is the standard normal distribution sample Z​i Covariance of standard normal distribution samples Z j i = 1, 2, …, n; j = 1, 2, …, n.

[0117] Covariance cov(Z i , Z j ) satisfies the following formula:

[0118]

[0119] In the formula, σ i , σ j are standard deviations of standard normal distribution samples Z i and Z j , respectively. ρ ij represents the Pearson correlation coefficient between standard normal distribution samples Z i and Z j .

[0120] 2.1.4) Calculate the scaling factor α of the scaled unscented transformation method, that is,

[0121] z max = max(|Z tut |) (7)

[0122]

[0123] In the formula, ε emp is an empirical parameter.

[0124] 2.2) The steps of selecting sample points on the standard normal distribution using the scaled unscented transformation method include:

[0125] 2.2.1) Select sample points on the standard normal distribution using the scaled unscented transformation method to obtain sample points Z sut = [z 0 , z 1 , …, z k ]. The elements in sample points Z sut satisfy the following formula:

[0126]

[0127]

[0128] In the formula, β is a weight adjustment parameter.

[0129] 2.2.2) Determine the weight coefficient in the scaled unscented transformation method, that is:

[0130]

[0131]

[0132] where z 0 , z k denote the sample points obtained by the scaled unscented transformation method. n is the dimension of the random variable. P ZZ is the covariance of the input random variable. W 0 is the initial weight of the scaled unscented transformation, is the weight coefficient of the mean of the input random variable. W c 0 , W c k is the weight coefficient of the covariance matrix of the input variable.

[0133] 3) Calculate the boundary parameters and convert the selected sample points to the original probability space by using the boundary inverse transformation algorithm to obtain the original probability space sample points considering the boundary and correlation.

[0134] The step of calculating the boundary parameters includes:

[0135] 3.1) Estimate the upper and lower boundary values of each dimension variable according to the historical data X and i = 1, 2, 3, …, n. The historical data X includes the historical basic information of the AC-DC hybrid system.

[0136] 3.2) Calculate the boundary parameters and the boundary parameter i.e.:

[0137]

[0138] where F i (·) is the cumulative distribution function of the random variable X i in the actual power system. and X i u are the minimum and maximum values of the random variable estimated according to the historical data, respectively. and are the boundary parameters in the boundary inverse transformation method.

[0139] The original probability space sample points X i considering the boundary and correlation satisfy the following formula:

[0140] u i = Φ(Z sut ), Z sut ∈ (-∞, +∞) (14)

[0141]

[0142]

[0143] where Z sut is a standard normal distribution variable. u i is a uniformly distributed variable in the interval (0, 1). denotes the value of the input random variable transformed to the uniform distribution space. and are the lower and upper bounds of the random variable, respectively. Φ(Z sut ) denotes the function that generates a uniformly distributed variable.

[0144] 4) The power conversion model of the wind farm and photovoltaic power station and the deterministic power flow model of the AC / DC hybrid system are established.

[0145] The probabilistic power flow model of the AC / DC hybrid system is as follows:

[0146] Y _output = p f (X _input ) (17)

[0147] where X _input and Y _output represent the input and output of the AC / DC hybrid system, respectively. p f represents the power flow calculation module of the AC / DC hybrid system.

[0148] 5) The wind speed and solar irradiance in the original probability space sample points are input into the power conversion model of the wind farm and photovoltaic power station to obtain the wind power and photovoltaic output data.

[0149] The wind power output data P w is as follows:

[0150]

[0151] where v w represents the wind speed, v ci , v r , and v co represent the cut-in wind speed, rated wind speed, and cut-out wind speed of the wind turbine, respectively. P r represents the rated power of the wind farm.

[0152] The intermediate variable A, the intermediate variable B, and the intermediate variable C are as follows:

[0153]

[0154]

[0155]

[0156] Photovoltaic output data P s As shown below:

[0157] P s = rArea h (22)

[0158] In the formula, r is the real-time light intensity; Area is the total light area; h is the conversion efficiency of photovoltaic power generation.

[0159] 6) Load data, wind power and photovoltaic output data are input into the deterministic power flow model of the AC-DC hybrid system for probability power flow analysis and calculation.

[0160] The input X of the AC-DC hybrid system _input and the output Y _output are as follows:

[0161] X_ input = [P load , Q load , P ren , Q ren , T ac , T dc ] T (23)

[0162] In the formula, P load and Q load are the active power and reactive power of the load respectively. T ac and T dc represent the topological parameters of the AC-DC power grid respectively. P ren and Q ren represent the electric energy generated by new energy sources such as wind farms.

[0163] Y _output = [U ac , U dc , S ac_ij , P dc_ij , Q conver ] T (24)

[0164] In the formula, U ac and U dc represent the AC and DC grid voltages respectively. S ac_ij is the apparent power of the AC grid. P dc_ij is the active power of the DC grid. Q conver is the reactive power generated by the converter between the AC-DC power grid.

[0165] The steps of probability power flow analysis and calculation also include statistics on the probability power flow results to obtain the mean and covariance of the probability power flow calculation results.

[0166] The mean and covariance of the probabilistic power flow are shown as follows:

[0167]

[0168] where, P YY is the mean and covariance matrix of the probabilistic power flow.

[0169] The covariance P YY of the probabilistic power flow satisfies the following formula:

[0170]

[0171] where, D(Y) is the variance of the probabilistic power flow. cov(Y n ,Y1) is the covariance between the outputs Y n and Y1.

[0172] Embodiment 2:

[0173] Referring to Figures 1 to 3 , a probabilistic power flow calculation method for AC / DC hybrid systems considering the boundedness and correlation of new energy includes the following steps:

[0174] 1) Obtain the random variables in the AC / DC hybrid system, and estimate the probability density function, cumulative distribution function, and Pearson correlation coefficient matrix ρ X of the random variables.

[0175] Collect the historical data of random variables (including wind speed, light intensity, and load) X in the actual AC / DC hybrid power grid, and estimate the PDF, CDF, and Pearson correlation coefficient matrix ρ X of the input random variables.

[0176] Wind speed in new energy is usually modeled by Weibull distribution and lognormal distribution, and light intensity generally obeys beta distribution. Their PDFs are infinite and unbounded functions. However, actual wind speed and light intensity are bounded. The PDF, CDF parameters, and boundary values of wind speed and light intensity can be estimated from their historical records.

[0177] In actual power systems, the load is usually modeled by a normal distribution. According to different customer behaviors, the actual load will show different distribution ranges or boundary values, and the upper and lower boundary values may be asymmetrically distributed on both sides of the mean value. Using the historical records of the load, the data characteristics of the load can be extracted, and the load can be calculated by dividing it into different types.

[0178] 2) Calculate the Pearson correlation coefficient matrix ρ Z of the random variables in the standard normal distribution space, and deduce the covariance matrix P based on the Pearson correlation coefficient matrix ρ Z .ZZ

[0179] In AC-DC hybrid power grid, the correlation between new energy output cannot be ignored. Assuming X = [X1,..., X i ,...,X n ] T is a random input vector with Pearson correlation matrix ρ X , the inverse cumulative distribution function of variable X i is The CDF (Cumulative Distribution Function) of standard normal distribution is denoted as Φ(·), and u i represents a variable subject to uniform distribution. Based on NATAF transformation, the correlation matrix ρ Z of random variable X corresponding to standard normal space can be obtained, and based on Pearson correlation coefficient matrix ρ Z , the covariance matrix P ZZ can be derived:

[0180] The Pearson correlation matrix ρ n of standard normal distribution sample Z = [Z1,Z2,...,Z T ] Z can be expressed as:

[0181]

[0182]

[0183]

[0184] In the formula, ρ ij is the Pearson correlation coefficient between random variables Z i and Z j ; σ i and σ j are the standard deviations of random variables Z i and Z j , respectively; and P ZZ is the covariance matrix of the sample.

[0185] 3) Determine the scaling and stretching coefficient of the scaling unscented transformation method

[0186] The scaling and stretching coefficient of the SUT affects the position and weight coefficient of the sample point, and has a significant impact on the accuracy of the PPF result. Therefore, based on the characteristics of PPF analysis, it is crucial to propose an empirical formula to determine the scaling and stretching coefficient of the SUT. The steps to determine the scaling and stretching coefficient of the scaling unscented transformation method include:

[0187] 3.1) generating n-dimensional uncorrelated random variables V obeying the standard normal distribution;

[0188] 3.2) generating standard normal random variables Z containing Pearson correlation coefficient matrix ρ Z ;

[0189] 3.3) selecting sample points on the n-dimensional standard normal distribution based on the traditional unscented transformation algorithm, obtaining sample point matrix Z tut = [z0, z 1 ,..., z k ]; the elements in sample point matrix Z tut satisfy the following formula:

[0190]

[0191] W 0 = 1 / 3 (5)

[0192]

[0193] In the formula, z k is a sample point obtained by using the traditional unscented transformation; W 0 is an initial weight of the traditional unscented transformation, W k is a weight coefficient corresponding to the sample point; m, P ZZ represent a mean vector and a covariance matrix of the input variable; is the kth row of matrix square root , which can be obtained by Cholesky decomposition.

[0194] 3.4) calculating the scaling and stretching coefficient α of the scaling unscented transformation method, that is,

[0195] z max = max (|Z tut |) (7)

[0196]

[0197] In the formula, ε emp is an empirical parameter.

[0198] As Figure 1As shown, the integral interval [-3, 3] of three standard deviations can cover 99.74% of the probability information in the standard normal distribution. Since the sample points for PPF analysis are initially selected from the standard normal distribution, this invention designs the following empirical formula based on the characteristics of the standard normal distribution: find the sampling point with the largest dispersion using equation (7), and substitute it into equation (8) to obtain a reasonable scaling factor, thereby ensuring that all sample points fall within the interval [-3, 3] of the standard normal distribution. The empirical formula can alleviate the global and local sampling problems of the scaling unscented transformation method to a certain extent. The scaling unscented transformation method based on the empirical formula can make the sample points evenly distributed within a reasonable interval to obtain sufficient probability information, thereby improving the calculation accuracy of PPF in AC / DC hybrid power grids.

[0199] 4) Select sample points on the standard normal distribution using the scaling unscented transform method and determine the weighting coefficients to obtain the probability information of the random variable distribution.

[0200] This invention introduces two new parameters, α and β, into the scaling unscented transform method. Parameter α, called the scaling factor, controls the distance between the sample point and the mean; parameter β is the weight adjustment parameter, which improves the accuracy of obtaining probability information from sample points using the scaling unscented transform. After obtaining the scaling factor α, the scaling unscented transform method is used to reselect sample points and calculate the weight coefficients. This invention introduces a scaling factor into the sample point selection strategy, allowing for flexible scaling of sample points. The sample point selection steps are as follows:

[0201] 4.1) Select sample points on the standard normal distribution using the scaling unscented transform method to obtain sample point Z. sut =[z 0 ,z 1 ,…,z k ]; Sample point Z sut The elements in the equation satisfy the following formula:

[0202]

[0203]

[0204] In the formula, β is the weight adjustment parameter;

[0205] 4.2) Determine the weighting coefficients, i.e.:

[0206]

[0207]

[0208] In the formula, z 0 z kXn represents the sample points obtained by the scaled unscented transformation method; n is the dimension of the random variable; P ZZ Cov(X) is the covariance of the input random variable; W 0 is the initial weight of the scaled unscented transformation, is the weight coefficient of the mean of the input random variable.

[0209] 5) Convert the selected sample points to the original probability space based on the boundary inverse transformation algorithm

[0210] After obtaining high-quality sample points of auxiliary variables by the scaled unscented transformation method, the boundary values of the accurate physical variables need to be converted to the original probability space. The boundary inverse transformation algorithm proposed in the present application can simultaneously consider the boundary characteristics and correlation of the random variables to achieve the purpose.

[0211] Inverse transformation can construct the mapping relationship between auxiliary variables and physical variables, but the inverse transformation process cannot handle the boundary of the input random variable. The basic idea of the boundary inverse transformation algorithm is to limit the boundary of the physical variable in the inverse transformation process, which can be expressed as:

[0212] 5.1) Estimate the upper and lower boundary values of each dimension variable according to historical data X and i = 1, 2, 3, …, n;

[0213] 5.2) Calculate the boundary parameters and the boundary parameters That is:

[0214]

[0215] In the formula, F i (·) is the cumulative distribution function of the random variable X i in the actual power system; and are the minimum and maximum values of the random variable estimated according to the historical data, respectively; and are the boundary parameters in the boundary inverse transformation method.

[0216] The original probability space sample points X i satisfy the following formula:

[0217] u i = Φ(Z sut ), Z sut ∈ (-∞, +∞) (14)

[0218]

[0219]

[0220] where Z sut is a standard normal distribution variable; u i is a uniform distribution variable in the interval (0, 1); represents the value of the input random variable transformed to the uniform distribution space; and are the lower and upper bounds of the random variable, respectively.

[0221] The boundary inverse transformation algorithm proposed in the present application is shown in the following steps: Figure 2 Compared with the inverse transformation, the boundary inverse transformation algorithm designs a simple linear function in the uniform distribution space. In the PPF calculation, the uniform distribution variable in the interval (0, 1) is transformed to the actual physical interval Therefore, the sample points selected from the standard normal distribution (without any boundary) can be explicitly transformed into a reasonable physical interval with a strict mapping relationship. Based on the boundary inverse transformation method, the sample points in each dimension can be converted to the original probability space to ensure that all samples fall within a reasonable physical interval.

[0222] 6) Input the wind speed and light intensity into the power conversion model of the wind power plant and the photovoltaic power station to obtain wind power and photovoltaic output data

[0223] The sample points X i in the matrix are input into the power conversion model of the wind power plant and the photovoltaic power station to obtain the wind power plant and photovoltaic power station output data matrix.

[0224] 7) Establish a deterministic power flow model of the AC-DC hybrid system

[0225] The deterministic power flow model of the AC-DC hybrid system specifically includes:

[0226] The actual AC-DC hybrid power grid itself has uncertainties, therefore, the main purpose of PPF calculation is to estimate the state of the AC-DC hybrid power grid after large-scale new energy access, and the PPF calculation formula can be expressed as:

[0227] Y _output = p f (X _input ) (17)

[0228] where X _input and Y _output are random variables, and p f represents the implicit function of the AC-DC hybrid power grid power flow calculation. The input vector can be expressed as

[0229] X _input = [P load , Q load , Pren Q ren T ac T dc ] T (18)

[0230] P load and Q load are the active and reactive power of the load, respectively; T ac and T dc represent the topological parameters of the AC / DC grid; P ren and Q ren represent the power generated by new energy sources such as wind farms. The output vector Y _output can be expressed as

[0231] Y _output = [U ac , U dc , S ac_ij , P dc_ij , Q conver ] T (19)

[0232] U ac and U dc represent the AC and DC grid voltages, respectively; S ac_ij is the apparent power of the AC grid; P dc_ij is the active power of the DC grid. The reactive power generated by the AC / DC converter is Q conver .

[0233] 8) Input the sample points into the deterministic power flow model of the AC / DC hybrid system for probabilistic power flow analysis and calculation

[0234] In the AC / DC hybrid grid, the correlation between new energy outputs cannot be ignored. Assume that X i = [X1,...,X i ,...,X n ] T is a random input vector with Pearson correlation matrix ρ X , and the inverse cumulative distribution function of variable X i is The CDF of the standard normal distribution is denoted as Φ(·), and u i represents a variable following a uniform distribution. Based on the NATAF transformation, the correlation matrix ρ i of the random variable X Z in the standard normal space can be obtained. The PPF calculation steps considering Pearson correlation are shown in Figure 3 .

[0235] The PPF calculation process can be divided into the following four parts:

[0236] 8.1) Select sample points V = [V1,...,V2] from a uniform and independent standard normal distribution. i ,...,V n ] T Selecting sample points from a uniform standard normal distribution has two advantages: First, samples from a uniform standard normal distribution are easy to process and transform into different probability distribution spaces with correlation, which is very beneficial for dealing with correlation problems; second, it is easier to obtain high-quality sample points with sufficient probability information, especially for algorithms that use symmetric sampling strategies.

[0237] 8.2) Generate the Pearson correlation matrix ρ using Choleskey decomposition. Z A standard normal distribution sample Z = [Z1,...,Z i ,...,Z n ] T ;

[0238] 8.3) Transform the relevant variables back to the original probability space and obtain relevant samples with different distributions in the actual power system;

[0239] 8.4) Input these sample points into the deterministic AC / DC power flow module and obtain the results.

[0240] like Figure 3 As shown, this invention defines two types of variables in PPF analysis: the first type is called auxiliary variables, such as standard normal variables, which, although they do not have a clear physical meaning, play an auxiliary role in PPF calculation; the second type is called physical variables, such as wind speed, light intensity and other new energy outputs, which have clear and specific physical meanings.

[0241] Inverse transformation can bridge the gap between auxiliary variables and physical variables. It's important to note that auxiliary variables are unbounded, while physical variables are bounded. In PPF (Progressive Power Filter), physical variables are typically characterized by their uncertainty using PDF (Predicted Distribution), for example, wind speed is generally modeled using a Weibull distribution. Therefore, during the process of transforming auxiliary variables into physical variables using inverse transformation, sample points may fall outside a reasonable physical range, causing the PPF analysis to lose its physical meaning and affecting its validity.

[0242] 9) Statistical probability power flow results

[0243] Calculate the mean, variance, and covariance matrix of PPF results, such as voltage and branch power flow in AC / DC power grids.

[0244] The mean and covariance of the probabilistic power flow are shown below:

[0245]

[0246] In the formula, P YY are the mean and covariance matrix of the probabilistic power flow.

[0247] The covariance P YY of the probabilistic power flow satisfies the following formula:

[0248]

[0249] In the formula, D(Y) is the variance of the probabilistic power flow; cov(Y n , Y1) is the covariance between the outputs Y n and Y1.

[0250] Embodiment 3:

[0251] Referring to Figures 1 to 3 , a probabilistic power flow calculation method for AC / DC hybrid systems considering the boundedness and correlation of new energy output includes the following contents:

[0252] 1) Collect historical data: Collect the historical data of random variables (such as wind speed, light intensity, load) X in the actual AC / DC hybrid power grid, and estimate the PDF and CDF of the input random variables.

[0253] 2) Process the correlation coefficient matrix: Through NATAF transformation, determine the Pearson correlation coefficient matrix ρ X of the random matrix X, and obtain the Pearson correlation coefficient matrix ρ Z under the standard normal distribution space.

[0254] 3) Calculate the boundary parameters: According to the collected historical data X, estimate the upper and lower boundary values of each dimension variable and (i = 1, 2, 3, …, n), and calculate the corresponding boundary parameters and

[0255] 4) Select sample points based on the SUT algorithm:

[0256] 4.1) Generate n-dimensional uncorrelated random variables V obeying the standard normal distribution.

[0257] 4.2) Calculate the sample point value of the maximum dispersion degree according to formula (1), and substitute it into formula (2) to obtain the scaling factor α.

[0258] The embodiment proposes an empirical formula of the scaling factor, as shown below:

[0259] z max = max(|Z tut |) (1)

[0260]

[0261] In the formula, ε emp These are empirical parameters.

[0262] like Figure 3 As shown, the integral interval [-3, 3] of three standard deviations can cover 99.74% of the probability information in the standard normal distribution. Since the sample points for probabilistic power flow analysis are initially selected from the standard normal distribution, this invention designs the following empirical formula based on the characteristics of the standard normal distribution: find the sampling point with the largest dispersion using equation (1), and substitute it into equation (2) to obtain a reasonable scaling factor, thereby ensuring that all sample points fall within the interval [-3, 3] of the standard normal distribution. The above empirical formula can alleviate the global and local sampling problems of SUT to a certain extent. The SUT algorithm based on the empirical formula can make the sample points evenly distributed within a reasonable interval to obtain sufficient probability information, thereby improving the calculation accuracy of PPF of AC / DC hybrid power grids.

[0263] 4.3) Select sample points for the SUT algorithm from the standard normal distribution and calculate the relevant weight coefficients.

[0264] 5) Transform the sample points using the inverse boundary transformation algorithm: Calculate the sample points uniformly distributed within the interval (0,1) and uniformly distributed within the interval... The sample points, the sample points X on the original probability distribution i .

[0265] After obtaining high-quality sample points for auxiliary variables using the inverse boundary transformation algorithm, it is necessary to consider the boundary values ​​of the precise physical variables and transform them back to the original probability space. The BIT algorithm proposed in this invention can achieve the above objective.

[0266] Inverse transformation can construct a mapping relationship between auxiliary variables and physical variables, but the inverse transformation process cannot properly handle the boundaries of the input random variables. The basic idea of ​​the boundary inverse transformation algorithm is to restrict the boundaries of the physical variables during the inverse transformation process, which can be expressed as:

[0267] u i =Φ(Z sut ),Z sut ∈(-∞,+∞) (3)

[0268]

[0269]

[0270] Among them, Z i For a standard normally distributed variable, u iF i (·) is the CDF of the random variable X i in the actual power system. and are the lower and upper bounds of the random variable estimated according to historical data, respectively. denotes a uniformly distributed variable considering the boundary values of the input random variable, and are boundary parameters in the BIT algorithm, which can be obtained by the following formula:

[0271]

[0272] The steps of the boundary inverse transformation algorithm proposed in the present application are shown in Figure 2 Compared with the inverse transformation, the boundary inverse transformation algorithm designs a simple linear function in the uniformly distributed space. In the PPF calculation, the uniformly distributed variable in the interval (0, 1) is converted to the actual physical interval Therefore, the sample points selected from the standard normal distribution (without any boundary) can be explicitly converted into a reasonable physical interval with a strict mapping relationship.

[0273] The boundary inverse transformation algorithm has the following three advantages: first, the boundary inverse transformation algorithm can consider the boundary values of the random variable in each dimension separately, ensuring that all sample points are within a reasonable interval; second, the linear transformation does not change the Pearson correlation, and in the probability flow analysis based on the combination of the scaled unscented transformation algorithm and the boundary inverse transformation algorithm, the NATAF transformation can still be used to accurately process the Pearson correlation; third, the boundary inverse transformation algorithm is very simple and easy to implement.

[0274] 6) Probabilistic power flow calculation: according to the sample points X i , the probabilistic power flow calculation of the AC-DC hybrid power grid is performed.

[0275] 7) Statistical results: calculate the mean, variance and covariance matrix of the probabilistic power flow results, such as the voltage and branch flow of the AC-DC power grid.

[0276] The method of the present embodiment determines the scaling factor to avoid the problems of global sampling and local sampling, to obtain high-quality sample points with sufficient probability information, considers the physical boundary of each input random variable, and cleverly transforms the sample points to ensure their physical significance.

[0277] Embodiment 4:

[0278] An experiment of a method for calculating the probabilistic power flow of an AC-DC hybrid system considering the boundedness and correlation of new energy output, including the following contents:

[0279] The performance of the algorithm is evaluated by using the modified IEEE 1354 bus system (PEGASE).

[0280] To simulate the large-scale integration of new energy into AC / DC hybrid power grid, this example uses multiple wind farms and loads as representative uncertain sources for experimental simulation. As shown in FIG. 1, two VSC-based DC systems are connected to the AC power grid. The base capacity of the AC / DC hybrid power grid is set to 100 MVA. The parameters of the AC power grid are obtained in Matpower 6.0, and the parameters of the DC system are obtained in MatACDC 1.0. This example is implemented in Matlab software on an Intel i7 3.30 GHz CPU and 8 gb RAM computer. Figure 4

[0281] Wind farms WF1, WF2, and WF3 are connected to the AC power grid through a four-terminal DC power grid; wind farms WF4, WF5, and WF6 are connected to the AC power grid through a three-terminal DC system; and wind farms WF7, WF8, and WF9 are directly connected to the bus 6516 of the modified IEEE 1354 bus system. It is assumed that the capacity of all wind farms is 100 MW, and the connection, rated, and cut-off speeds are 3 m / s, 12 m / s, and 25 m / s, respectively.

[0282] Wind speed is usually modeled using Weibull distribution and lognormal distribution, whose PDFs are infinite and unbounded functions, but the wind speed of actual wind farms is bounded. In this example analysis, the historical records of southern China are used as wind speed input data, and the PDF parameters and boundary values estimated from the wind speed historical records are shown in Table I. It is assumed that the wind speed of the wind farms in this example has the same probability characteristics and boundary values as the wind speed in southern China. The wind speed of wind farms WF1, WF2, WF3, WF4, WF5, and WF6 follows Weibull distribution, and the wind speed of wind farms WF7, WF8, and WF9 follows lognormal distribution.

[0283] In actual power systems, loads are usually modeled using normal distribution. According to different customer behaviors, actual loads may exhibit different distribution ranges or boundary values, which may be asymmetrically distributed on both sides of the mean value. This invention uses the historical records of the load of China's power grid. It is worth noting that this invention extracts the data characteristics of the load and divides it into three types, as shown in Table II.

[0284] ​The improved IEEE 1354 bus system can be divided into three different power supply areas: bus 3 to bus 2432 belongs to power supply area A; power supply area B contains bus 2457 to bus 6692; power supply area C contains bus 6697 to bus 9231 (note that the bus numbers of the case 1354 system are continuous and monotonically increasing). It is assumed that the loads of the three power supply areas A, B, and C have the probability characteristics and boundary values corresponding to loads A, B, and C in Table II. Based on the above, in the research example, the uncertainties such as wind speed and load have different boundary intervals.

[0285] The correlation between random variables in AC / DC hybrid power grid has an important influence on power system operation and planning. It is assumed that the correlation coefficient between wind speeds is 0.4, the correlation coefficient between loads in power supply area A is 0.35, the correlation coefficient between loads in power supply area B is 0.3, and the correlation coefficient between loads in power supply area C is 0.2; the correlation coefficients between loads in areas A and B, B and C, and A and C are 0.25, 0.05, and 0.15, respectively; and the correlation coefficient between wind speed and load is-0.1. It is worth noting that in the improved IEEE 1354 node system, the number of uncertainty sources reaches 630.

[0286] Table I Wind speed parameters

[0287]

[0288] Table II Load parameters

[0289]

[0290] Algorithm effectiveness evaluation

[0291] In order to verify the effectiveness and accuracy of the algorithm, the test results of the MCS algorithm are used as a reference in the research example. 60,000 valid samples are selected from the input distribution, which are sufficient to produce reliable estimates of the mean and standard deviation. If the samples of MCS are within a reasonable interval, the samples are identified as valid samples for PPF analysis; otherwise, the samples will be discarded. In order to verify the superiority of the algorithm proposed in the present application, the following algorithms are used for comparison:

[0292] (1) Traditional unscented transformation method, denoted as TUT.

[0293] (2) The random variables of the actual power system can be transformed into the standard normal distribution space, so the edge values of the standard normal distribution space can be determined using the boundary values of the original probability space. The minimum boundary value of the standard normal distribution space is used to replace the empirical parameter in equation (11), and the method for obtaining the sample points of the SUT is recorded as SUT-Min according to step 4) in section IV.C. The load A has the smallest interval on the standard normal distribution space, so the scaling factor of SUT-Min is 0.47.

[0294] (3) The maximum boundary value of the standard normal distribution space can be easily found by the above method, and the sample points of the SUT algorithm are obtained, which is recorded as SUT-max. In the research example, the Weibull distribution model of wind speed has a long tail, and there is a maximum boundary on the standard normal distribution, so the scaling factor of SUT-Max is 0.74.

[0295] (4) The scaling factor of the SUT algorithm is obtained by using the average of the maximum and minimum boundary values on the standard normal space, which is denoted as SUT-Ave. According to the above analysis, the scaling factor of SUT-Ave is 0.605.

[0296] (5) The SUT algorithm with empirical formula is combined with the BIT algorithm to form the algorithm proposed in the present application, which is recorded as SUT-BIT. According to equations (10) and (11), the scaling factor of SUT-BIT in this example can be determined as 0.7. Note: first, the PPF calculation method uses NATAF transformation to transform the correlation matrix of input random variables following different probability distributions to the standard normal space; second, the error in the figures or tables of the present application refers to the percentage error relative to the results obtained by the MCS algorithm.

[0297] The mean error and standard deviation error of the DC bus voltage are shown in Figure 5 、 Figure 6 From the figure, it can be seen that the errors of the mean value and the standard deviation (STD) obtained by the algorithm (SUT-BIT) proposed in the present application are much smaller than the results obtained by using TUT, SUT-Min, SUT-Max and SUT-Ave algorithms. The average errors of the mean value of the DC bus voltage obtained by using TUT, SUT-Min, SUT-Max, SUT-Ave and SUT-BIT algorithms are within 0.54%, 0.19%, 0.21%, 0.19% and 0.06% respectively, and the average errors of the standard deviation of the DC bus voltage are 18.30%, 8.97%, 10.06%, 9.97% and 3.72% respectively.

[0298] Table III Mean error (%) of AC and DC branch power flow

[0299]

[0300] STD error (%) of AC and DC branch power flow in Table IV

[0301]

[0302] The errors of mean and STD of branch power flow in AC / DC hybrid power grid are listed in Table III and Table IV. The average errors of AC / DC branch power flow obtained by SUT-Min, SUT-Max, SUT-Ave and SUT-BIT algorithm are 2.67%, 2.09%, 1.75%, 1.53%, 0.65% (mean), 35.49%, 15.62%, 15.28%, 12.13%, 3.55% (STD), respectively. The results show that the error of result obtained by TUT algorithm is the largest; the calculation accuracy of SUT-Min, SUT-Max and SUT-Ave method is also not ideal, for example, the STD error of DC branch power flow obtained by SUT-Min, SUT-Max and SUT-Ave algorithm is all greater than 10%. The mean and STD errors of SUT-BIT algorithm are less than 0.93% and 4.23%, respectively, which indicates that the algorithm has acceptable accuracy for high-dimensional PPF analysis of large-scale new energy access AC / DC hybrid power grid. The above results verify the effectiveness of the algorithm proposed in the application.

[0303] Figure 7 、 Figure 8 、 Figure 9 are the wind speed and load scatter plots corresponding to different wind farms and AC buses. In actual power system, the physical variables such as wind speed and load have specific boundaries, and the reasonable interval of these physical quantities must be considered to ensure their correct physical meaning and the rationality of PPF analysis. Once the sample points of MCS algorithm exceed the reasonable interval, the sample points should be discarded, but the UT algorithm cannot handle the sample points in this way. Unlike the MCS algorithm, the sample points selected by the UT algorithm are highly structured and are not allowed to be added, discarded or even moved at will.

[0304] From Figure 7 、 Figure 8 and Figure 9It can be seen that the sample points of the TUT algorithm (purple square marked points) are obviously out of the reasonable range of wind speed and load. This is because the sample points of the TUT algorithm will diverge when calculating the PPF of the high-dimensional random variable AC-DC power grid, which will lead to the following consequences: 1) the PPF analysis based on the TUT algorithm will lose the correct physical meaning; 2) the global sampling problem of the TUT algorithm, the sample points of which cannot obtain probability information well, leading to the decrease of the accuracy of PPF analysis. It can be seen from the results that the maximum standard deviation error of the DC branch power flow of the TUT algorithm even reaches 40.23%.

[0305] Compared with the TUT algorithm, all sample points of the SUT-Min (black pentagram marked points) fall on the boundary, but the calculation accuracy of the SUT-Min algorithm is still not ideal. The average error of the DC voltage amplitude and the AC branch power flow standard deviation obtained by the SUT-Min algorithm is 8.97% and 15.62%, respectively. This is because when the minimum scaling factor is used, the sample points of the SUT-Min will show a very narrow sampling range. For example, the load value at the AC bus 6697 is in the range of [195.32, 423.92] MW, while the sample point value range of the SUT-Min algorithm is only [238.52, 372.45] MW (as shown in Figure 9 ). This is the so-called local sampling problem, which will lead to the lack of probability information, thereby seriously affecting the calculation accuracy.

[0306] When the scaling factor is increased from SUT-Min, the local sampling effect will be more or less affected. But this will inevitably bring a problem, that is, the sample points will deviate from the physical variable boundary of the minimum interval, similar to the load of the No. 3 AC bus. Figure 8 It can be seen that once the scaling factor (SUT-Max and SUT-Ave algorithms) is greater than SUT-Min, the sample points on the load of the AC bus 3 (cyan diamond marked and blue hexagon marked) will "run out" of the reasonable range, so that the selected sample points lose physical meaning. The maximum load at the AC bus 3 is 160.11 MW, and the maximum sample point values of the SUT-Max and SUT-Ave algorithms are 165.28 MW and 162.66 MW, respectively. The sample points of the SUT-Max and SUT-Ave algorithms all fall outside the reasonable physical boundary, and cannot obtain effective probability information, further reducing the calculation accuracy. The DC voltage standard deviation error of bus 7 obtained by using the SUT-Max and SUT-Ave algorithms is 10.23% and 10.15%, respectively.

[0307] From the result analysis of SUT-min, SUT-max and SUT-ave algorithms, it can be known that the SUT algorithm will face the "decision dilemma" of determining the proportional scaling factor when dealing with the boundary problem in PPF analysis. The key reason is that the SUT algorithm is based on a single proportional scaling factor, and it is difficult to coordinate the massive boundary values when a large-scale new energy is connected to the AC-DC hybrid power grid.

[0308] From Figure 7 、 Figure 8 、 Figure 9 It can be seen that the sampling points (red marked points) of the SUT-BIT algorithm proposed by the present application are all in the corresponding physical interval, and are reasonably distributed. Therefore, the sample points of the SUT-BIT algorithm can fully obtain the probability information of the input distribution, and are transmitted through the deterministic power flow model of the AC-DC hybrid power grid to obtain accurate results. The maximum error of the mean value and the standard deviation of the DC voltage in the SUT-BIT algorithm result is 0.13% and 4.21% respectively, which shows that even if there are hundreds of input random variables in the system, the SUT-BIT algorithm can achieve high precision when performing PPF analysis on the large and complex AC-DC hybrid power grid.

[0309] Comparison with other similar PPF technologies

[0310] In order to further verify the superiority of the SUT-BIT algorithm proposed by the present application, the calculation results are compared with the following algorithms:

[0311] (1) PEM-UPT algorithm: general transformation and power transformation (UPT) are introduced, and the point estimation method (PEM) is combined to deal with the boundary problem in PPF analysis.

[0312] (2) PEM-UPT-NF algorithm: NATAF transformation is combined with the PEM algorithm to deal with the correlated input random variables in PPF calculation.

[0313] Figure 10The mean and standard deviation error of the DC bus voltage calculated by the PEM-UPT, PEM-UPT-NF and SUT-BIT algorithms are shown. As can be seen from the figure, the SUT-BIT algorithm proposed in the present application has the highest calculation accuracy. The maximum mean and STD error of the DC bus voltage obtained by using the PEM-UPT algorithm, the PEM-UPT-NF algorithm and the SUT-BIT algorithm are 0.97%, 0.19%, 0.13% (mean) and 39.23%, 7.23%, 4.21% (standard deviation), respectively. As shown in Table V, similar conclusions can also be obtained from the standard deviation error of the active power loss of the AC-DC system. The standard deviation error of the active power loss of the AC system and the DC system obtained by using the PEM-UPT, PEM-UPT-NF and SUT-BIT algorithms are 39.22%, 7.12%, 3.98% (AC system) and 37.67%, 6.96%, 3.77% (DC system), respectively.

[0314] The main reason for the largest error of the results obtained by using the PEM-UPT algorithm is that the PEM-UPT algorithm does not consider the correlation between the input variables. In the PPF analysis, ignoring the correlation between random variables (such as wind speed and new energy output) will bring significant error. After using the NATAF transformation, the calculation accuracy of the PEM-UPT-NF algorithm is obviously better than that of the PEM-UPT algorithm, but compared with the SUT-BIT algorithm proposed in the present application, the calculation error of the PEM-UPT-NF algorithm is still large. This shows that when a nonlinear function (such as UPT) is added between the standard normal distribution and the original distribution, the NATAF transformation will not be able to accurately handle the correlation problem and will correspondingly lose the calculation accuracy. On the contrary, the algorithm proposed in the present application can solve this key problem because BIT is a linear function in the uniform distribution space and can keep the correlation matrix unchanged. Therefore, the NATAF transformation can be combined with the SUT-BIT algorithm to accurately handle the correlation problem.

[0315] Table V Mean and standard deviation error of the active power loss of the AC and DC systems (%)

[0316]

[0317] Table VI Running time of different algorithms

[0318]

[0319] Table VI shows the computation time of the PEM-UPT, PEM-UPT-NF, MCS and SUT-BIT algorithms. The results show that the SUT-BIT algorithm has almost the same computation load as the PEM-UPT-NF algorithm, and thus for large-scale AC / DC hybrid power systems, these two algorithms significantly shorten the computation time of PPF analysis compared with the MCS algorithm. It can also be noted that the PEM-UPT algorithm has the highest computation speed because it does not have the step of NATAF transformation compared with the PEM-UPT-NF and SUT-BIT algorithms. In summary, through the comprehensive comparison of computation accuracy and efficiency, the SUT-BIT algorithm can be considered as a better candidate algorithm for solving the PPF problem of large-scale AC / DC hybrid power systems.

Claims

1. A probabilistic power flow calculation method for AC / DC hybrid systems considering the boundedness and correlation of new energy sources, characterized in that, Includes the following steps: 1) Obtain basic information about the AC / DC hybrid system; 2) Determine the scaling factor based on the basic information of the AC / DC hybrid system, select sample points on the standard normal distribution using the scaling unscented transform method, and determine the weighting coefficients; 3) Calculate the boundary parameters and use the boundary inverse transformation algorithm to transform the selected sample points to the original probability space to obtain the original probability space sample points considering boundary and correlation. 4) Establish power conversion models for wind farms and photovoltaic power plants, and deterministic power flow models for AC / DC hybrid systems; 5) Input the wind speed and light intensity from the original probability space sample points into the power conversion models of wind farms and photovoltaic power plants to obtain wind power and photovoltaic output data; 6) Input the load data, wind power and photovoltaic output data into the deterministic power flow model of the AC / DC hybrid system to perform probabilistic power flow analysis and calculation; The steps to determine the scaling factor include: 2.1) Generate an n-dimensional uncorrelated random variable V that follows a standard normal distribution; 2.2) Generate the matrix ρ containing the Pearson correlation coefficient. Z Z is a standard normally distributed random variable. 2.3) Based on the traditional unscented transformation algorithm, sample points are selected on the n-dimensional standard normal distribution to obtain the sample point matrix Z. tut =[z 0 ,z 1 ,…,z k ]; Sample point matrix Z tut The elements in the equation satisfy the following formula: W 0 ＝1 / 3 (3) In the formula, z k These are sample points obtained using traditional unscented transform; W 0 W represents the initial weights for the traditional unscented transform. k For the corresponding weighting coefficients of the sample points; m, P ZZ Represents the mean vector and covariance matrix of the input variables; It is the square root of the matrix. The k-th row; Wherein, the covariance matrix P ZZ As shown below: In the formula, cov(Z) i Z j Z is a standard normally distributed sample. i Compared with the standard normal distribution sample Z j The covariance; i = 1, 2, ..., n; j = 1, 2, ..., n; covariance cov(Z) i Z j The following equation must be satisfied: In the formula, σ i σ j Z represents a standard normal distribution sample. i Compared with the standard normal distribution sample Z j Standard deviation; ρ ij Z represents a standard normal distribution sample i Compared with the standard normal distribution sample Z j The Pearson correlation coefficient between them; 2.4) Calculate the scaling factor α of the scaling unscented transformation method, i.e. In the formula, ε emp These are empirical parameters; Wherein, the intermediate parameter z max As shown below: With max =max(|Z tut |) (8) The steps for selecting sample points on a standard normal distribution using the scaling unscented transform method include: S1) Select sample points on the standard normal distribution using the scaling unscented transform method to obtain sample point Z. sut =[z 0 ,z 1 ,…,z k ]; Sample point Z sut The elements in the equation satisfy the following formula: In the formula, β is the weight adjustment parameter; S2) Determine the weight coefficients in the scaling unscented transformation method, i.e.: In the formula, z 0 z k This represents the sample points obtained by the scaling unscented transformation method; n is the dimension of the random variable; P ZZ The covariance of the input random variable; W 0 To scale the initial weights of the unscented transform, The weighting coefficients for the mean of the input random variable; These are the weighting coefficients of the input variable covariance matrix; Wind power output data P w As shown below: In the formula, v w Indicates wind speed, v ci v r v co These represent the inlet velocity, rated velocity, and outlet velocity of the fan, respectively; P r This indicates the rated power of the wind farm; The intermediate parameters A, B, and C are shown below: Photovoltaic power output data P s As shown below: P s =rAreah (26) In the formula, r is the real-time light intensity; Area is the total illuminated area; and h is the conversion efficiency of photovoltaic power generation.

2. The probabilistic power flow calculation method for an AC / DC hybrid system considering the boundedness and correlation of new energy sources according to claim 1, characterized in that, The basic information of the AC / DC hybrid system includes random variables, probability density functions of the random variables, cumulative distribution functions, and Pearson correlation coefficient matrix ρ. X The Pearson correlation coefficient matrix ρ of random variables in the standard normal distribution space Z The random variables include wind speed, light intensity, and load. Wherein, the Pearson correlation coefficient matrix ρ of the random variable in the standard normal distribution space Z As shown below: In the formula, ρ ij Z represents a standard normal distribution sample i Compared with the standard normal distribution sample Z j The Pearson correlation coefficient between them; i = 1, 2, ..., n; j = 1, 2, ..., n.

3. The probabilistic power flow calculation method for an AC / DC hybrid system considering the boundedness and correlation of new energy sources according to claim 1, characterized in that, The steps for calculating boundary parameters include: 1) Estimate the upper and lower boundary values ​​of each dimension variable based on historical data X. and 2,3,…,n; The historical data X includes basic historical information about the AC / DC hybrid system; 2) Calculate boundary parameters and boundary parameters Right now: In the formula, F i (·) represents the random variable X in the actual power system. i The cumulative distribution function; and These are the minimum and maximum values ​​of the random variable estimated based on historical data, respectively. and These are the boundary parameters in the inverse boundary transformation method.

4. The probabilistic power flow calculation method for an AC / DC hybrid system considering the boundedness and correlation of new energy sources according to claim 1, characterized in that, Considering boundary conditions and correlations, the original probability space sample points X i Satisfy the following formula: at i =Φ(Z sut ),WITH sut ∈(-∞,+∞) (14) In the formula, Z sut The variable is a standard normally distributed variable; u i Let be a uniformly distributed variable within the interval (0,1); This represents the value of the input random variable when transformed into a uniform distribution space; and These are the lower and upper bounds of the random variable, respectively; Φ(Z) sut ) represents the inverse cumulative distribution function of the standard normal distribution; and These are the boundary parameters in the inverse boundary transformation method.

5. The probabilistic power flow calculation method for an AC / DC hybrid system considering the boundedness and correlation of new energy sources according to claim 1, characterized in that, The probabilistic power flow model for an AC / DC hybrid system is shown below: Y _output =p f (X _input ) (17) In the formula, X _input Y _output These represent the input and output of the AC / DC hybrid system, respectively; p f This represents the power flow calculation module for AC / DC hybrid systems.

6. The probabilistic power flow calculation method for an AC / DC hybrid system considering the boundedness and correlation of new energy sources according to claim 5, characterized in that, Input X of AC / DC hybrid system _input and output Y _output They are shown below: X_ input =[P load ,Q load ,P ren ,Q ren ,T ac ,T dc ] T (18) In the formula, P load and Q load These represent the active power and reactive power of the load, respectively; T ac and T dc These represent the topology parameters of the AC and DC power grids, respectively; P ren and Q ren This refers to electrical energy generated by wind farms; Y_ output =[U ac ,U dc ,S ac_ij ,P dc_ij ,Q conver ] T (19) In the formula, U ac and U dc These represent AC and DC grid voltages, respectively; S ac_ij P represents the apparent power of the AC power grid. dc_ij Q represents the active power of a DC power grid. conver This refers to the reactive power generated by the converter between AC and DC power grids.

7. The probabilistic power flow calculation method for an AC / DC hybrid system considering the boundedness and correlation of new energy sources according to claim 1, characterized in that, The steps for performing probabilistic power flow analysis calculations also include statistical analysis of the probabilistic power flow results to obtain the mean and covariance of the probabilistic power flow calculation results; The mean and covariance of the probabilistic power flow are shown below: In the formula, P YY Let be the mean and covariance matrix of the probability flow; Covariance P of probability current YY The relationship between the variance of the probability flow and the variance of the power flow satisfies the following formula: In the formula, D(Y) represents the variance of the probabilistic power flow; cov(Y) n Y1) is the output Y n The covariance between the output Y1 and the output Y1.

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