CN111130117B - Probability optimal power flow calculation method based on high-dimensional data clustering - Google Patents

Abstract

The invention discloses a probabilistic optimal power flow calculation method based on high-dimensional data clustering. Aiming at the problems of slow calculation and low accuracy of traditional probability optimal power flow calculation when solving high-dimensional random data such as wind power output, photovoltaic output, load and the like in a power system, the invention provides a probability optimal power flow calculation method based on high-dimensional data clustering, which extracts a data set with the most representative characteristics in random variables of the probability optimal power flow problem by using the thought of principal component analysis and the spectral clustering algorithm of Rank-order distance, and then solves the probability optimal power flow problem by combining the obtained data set with an artificial bee colony algorithm. Therefore, the bloated data set is converted into a small data set with high value, and the calculation efficiency is improved on the basis of ensuring the accuracy of the probability optimal power flow calculation result.

Description

Probability optimal power flow calculation method based on high-dimensional data clustering

Technical Field

The invention belongs to the technical field of load flow calculation of smart power grids, particularly relates to a probabilistic optimal load flow calculation method based on high-dimensional data clustering, and aims to solve the problem that the characteristic quantity of power load data in a system is increased due to the fact that renewable new energy is connected to a power grid system in a large quantity.

Background

With the increase of the permeability of wind and light in a Power grid, uncertainty must be considered in the Optimal Power Flow calculation of a system, a traditional Power system analysis tool is no longer suitable for Power system analysis under the current random factor, and then a Probabilistic Optimal Power Flow (POPF) calculation method for a Power system is proposed. The POPF applies a probabilistic analysis of uncertainty, which can be defined as having the control variables in the system respond in an optimal way for the random variation of these uncertain variables in the system, in case the system has random variables.

The increase of the wind and light permeability in the power network causes the increase of wind and light data features required to be extracted by the POPF, which causes the occurrence of 'dimension disaster'. This results in a large number of duplicate calculations because each set of data in the wind data needs to be considered during the POPF optimization process. The method for extracting representative data by clustering analysis of the wind and light data is an effective method for solving the problem of overlarge wind and light data amount in the POPF, and in a high-dimensional space, the distances between sample points are approximately equal, so that a data processing method successfully applied to a low-dimensional space is not suitable for high-dimensional data. This requires the study of clustering methods for high dimensional data.

Disclosure of Invention

Aiming at the problem that the traditional probabilistic optimal power flow calculation shows slow calculation and low accuracy when solving high-dimensional random data such as wind power output, photovoltaic output, load and the like in an electric power system, the invention provides a probabilistic optimal power flow calculation method based on high-dimensional data clustering. The flow chart of the method steps is shown in fig. 1, and the specific steps are as follows:

step 1: obtaining data related to random variables such as wind power output, photovoltaic output and load in a power network to form an n-dimensional sample data set D ═ x₁,x₂,...,x_m}；

Step 2: processing the data set D according to a k-nearest neighbor algorithm, and calculating a nearest neighbor subset N of each data point in the data set_i(x_i) And obtaining a strong correlation neighbor set N ═ N of each data in the data set₁(x₁),N₂(x₂),...,N_m(x_m)}；

And step 3: calculate covariance matrix cov (N)_i(x_i) And performing eigenvalue decomposition on the vector set to obtain an eigenvalue vector set alpha_i＝{α_i1,α_i2,...,α_in}. Each neighbor subset N_i(x_i) The feature value vector set of (2) is sorted by size. After reducing dimensionIs generally determined by a principal component specific gravity threshold p, assuming that the m eigenvalues are λ₁≥λ₂≥...≥λ_mN' can be obtained by the following formula, and rho generally takes a value of 0.8;

and 4, step 4: forming the first n' eigenvectors into an eigenvector matrix W corresponding to each neighboring subset_i＝{α′_i1,α′_i2,...,α′_in′}. By z_i＝W_i ^Tx_iThe mapping converts the sample data set D to a new sample data set D' ═ { z ═ z₁,z₂,...,z_m}。

And 5: calculating any two data points z in the data set D' according to the information provided by the neighbor set of the data set D_j、z_kThe asymmetric Rank-order distance is calculated according to the following formula:

in the formula (I), the compound is shown in the specification,

represents z_jThe ith nearest neighbor point of (a),

represents z_kIs at z_jThe order of bits in the neighbor list. l (z)_j,z_k) Is large or small determines z_j、z_kSimilarity of nearest neighbors of two points.

Obtaining a symmetrical and normalized Rank-order distance rl (z) by using the formula (3)_j,z_k)

Thereby obtaining an adjacency matrix R as shown in formula (4):

step 6: and (4) when the adjacency matrix R is known, performing clustering analysis by using spectral clustering, wherein clustering results correspond to the clusters to which the samples in the original wind-light and load data set D belong. And (3) setting the number of clusters of the clustering result as K, extracting the central points of the clusters as representative points, wherein the formula (5) is as follows:

wherein K is 1, 2.., K; g_kRepresents the k-th cluster obtained by clustering, x_sRepresents samples in a class cluster s;

representing the number of data in the kth class cluster.

And 7: representing the point y by the wind-light load data obtained in the step 6_i∈{y₁,y₂,...,y_KEstablishing a mathematical model of probability optimal power flow by taking the minimum running cost of a generator in a power network as an optimization target as a state variable of an optimization problem;

and 8: solving optimal solution F for probability optimization problem by adopting artificial bee colony algorithm_i，F_iThe method comprises the information of the running cost of the generator, the output of the generator, the node voltage, the transformer transformation ratio and the like. Obtaining data representative of scene, load and the like { y₁,y₂,...,y_KThe corresponding probabilistic optimal solution set is { F }₁,F₂,...,F_K}。

And step 9: optimal solution set { F) for probabilistic optimal power flow calculation₁,F₂,...,F_KAnd solving probability statistical data such as expectation, variance and the like.

The method of the invention has the advantages and beneficial results that:

(1) the invention classifies the collected wind, light and load data, extracts the data with representative characteristics, plays a role of reducing data volume, greatly reduces the calculation time of probability optimal power flow, and can ensure the accuracy of the calculation result on the basis.

(2) The method not only realizes the dimensionality reduction operation on high-dimensional data, but also can realize the retention of characteristic data which has high weight influence on local data by utilizing the thought of principal component analysis and the spectral clustering algorithm of Rank-order distance, and has very strong filtering effect on the characteristic data which is not beneficial to clustering. The k nearest neighbor method is combined with principal component analysis, so that an adjacency matrix structure and cluster analysis can be better provided for spectral clustering on the premise of saving local and global information, and comprehensive information and reliable guarantee are provided. The Rank-order distance can solve the problem that the direct distance between two points in a high-dimensional space is unreliable by adding shared adjacent points between the two points and utilizing shared information of the adjacent points.

Drawings

FIG. 1 is a flow chart of the probabilistic optimal power flow calculation based on high-dimensional data clustering according to the present invention;

fig. 2 is a network topology diagram of an embodiment in a detailed implementation.

Detailed Description

The present invention will be described in detail with reference to specific embodiments, but it should not be construed that the scope of the above-described subject matter of the present invention is limited to the following examples. Various substitutions and alterations can be made without departing from the technical idea of the invention and the scope of the invention is covered by the present invention according to the common technical knowledge and the conventional means in the field.

The present example employs a modified IEEE30 power node network system, as shown in fig. 2. A wind power plant with four wind turbines is accessed at the nodes 29 and 30 of IEEE 30. The load active power in the network system is regarded as obeying normal distribution, the expected load rated active power is the load rated active power, and the standard deviation is 5% of the expected value; the reactive power of the load can be obtained by active power and power factor, and the power factor of the network system is 0.85. A wind power plant is connected to two nodes 29 and 30 in the network system respectively, and parameters are shown in the table 1. The wind speed was considered to follow a weibull distribution with the ratio and shape parameters 7.28 and 2.01, respectively. The setting conditions of the correlation among random variables in the network system are as follows:

1) the loads of all nodes in the system have correlation, and the correlation coefficient is 0.1;

2) there is also a correlation between the loads of nodes 29 and 30 and the wind farm on the same node, with a correlation coefficient of-0.2;

3) the correlation coefficient between the wind speeds at nodes 29 and 30 is 0.7.

TABLE 1 wind farm Fan parameters

The method comprises the following specific steps of calculating the probability optimal power flow of the embodiment:

step 1: acquiring data related to random variables such as wind power output, photovoltaic output, load and the like in a power network;

step 2: extracting a data set with the most representative characteristics from random variables of POPF by using the thought of principal component analysis and a spectral clustering algorithm of Rank-order distance;

and step 3: establishing an objective function of the optimal power flow, wherein the optimization objective function is the total operation cost of all generators in the network:

in the formula, F (P)_Gi) Represents the ith generator operating cost; and alpha, beta and gamma are the cost economic coefficients of the generator respectively.

The control variables are as follows: active power output P of generator_GVoltage amplitude of generator U_GAnd the tap ratio T of the transformer can be adjusted. The control variable of the objective function is 5 active power outputs of the generators and 6 active power outputsGenerator terminal voltage, 4 adjustable transformer tap positions.

The equality constraint and inequality constraint of the probability optimal power flow calculation are as follows:

(1) a set of equality constraints, i.e. power balance equations on each bus in the grid:

in the formula, P_Gi、Q_GiRespectively the active output and the reactive output of the generator at the node i in the power network; p_Li、Q_LiRespectively an active load and a reactive load at corresponding nodes; u shape_i、θ_iThe amplitude and the phase angle of the bus voltage at the node i are respectively; g_ij、B_ijRespectively, the node admittance matrix elements.

(2) Set of inequality constraints

1) Generator restraint

The generator constraint comprises generator active power output, reactive power output and node voltage constraint, and is shown in formula (4):

in the formula (I), the compound is shown in the specification,

and

the active output upper and lower limits of the ith generator are respectively set;

and

the upper limit and the lower limit of the reactive power output of the ith generator are respectively set;

and

the node voltage upper and lower limits of the ith generator are respectively set; n is_GIs the number of generators in the node system.

2) Ratio constraint for adjustable transformer

The transformation ratio of the transformer is constrained to meet the boundary of the adjustable position of a tap of the transformer when the transformation ratio of the transformer meets the following formula;

T_i ^min≤T_i≤T_i ^max,i＝1,2,...,n_T (5)

in the formula, T_i ^minAnd T_i ^maxThe upper limit and the lower limit of the adjustable transformation ratio of the ith transformer are respectively 0.9 and 1.1; n is_TIs the number of transformers in the node system.

3) Line safety restraint

The line safety constraint comprises a voltage amplitude constraint and a line capacity constraint of a PQ node in the power saving system, and is represented by the following formula (6):

in the formula (I), the compound is shown in the specification,

and

the voltage amplitude upper and lower limits of the ith PQ node are respectively;

the upper limit of the transmission capacity of the ith line in the power saving system is set; n is_PQAnd n_LnThe number of PQ nodes and the number of transmission lines in the power saving system are respectively.

And 4, step 4: and (3) solving the optimal solution of the probability optimization problem by adopting an artificial bee colony algorithm, wherein the number of employed bees of the ABC algorithm is set to be 20, the maximum non-updating times limit of the food source is 30, and the maximum iteration times is 100. And obtaining an objective function value of the optimal problem, such as the running cost of the generator and the like, and a control variable value, the output of the system generator, the node voltage, the transformation ratio of the transformer and the like. And solving probability statistical data such as expectation, variance and the like for the optimal solution set of the probability optimal power flow calculation.

Tables 2 to 3 list the solution results of the embodiment of the invention, including the optimal solution of the objective function of the probabilistic optimal power flow, the expectation and variance of the control variable values, and the consumption duration, and compare with the commonly used Point Estimation Method (PEM) and the Genetic Algorithm based on K-means clustering (Kmeans-GA).

TABLE 2 probabilistic optimal power flow calculation comparison results

TABLE 3 comparison of objective function values for probabilistic optimal power flow calculation

TABLE 4 time consuming comparison of probabilistic optimal power flow calculations

As can be seen from Table 2, the calculation results of the method provided by the invention for the examples are very close to PEM and Kmeans-GA, and the accuracy of the algorithm is proved. Table 3 gives the expected and standard values of the total operating cost of the generator, the information of which table has an indicative effect on the operation of the risk. As can be seen from the table, the expected value of the method provided by the invention is less than that of PEM and Kmeans-GA, and the method provided by the invention is proved to have high optimization performance and better optimization result than PEM and Kmeans-GA. In the aspect of standard deviation, the method provided by the invention is smaller than the other two methods, which shows that the optimization calculation result of the method is more concentrated and the fluctuation range is smaller than the other two methods. Table 4 shows the time consumption for POPF calculated by three methods, among which the time consumption of the proposed method is the shortest, only 19.06s, which is 85.58% shorter than PEM time and 74.05% shorter than Kmeans-GA time.

Claims (1)

1. A probabilistic optimal power flow calculation method based on high-dimensional data clustering is characterized by comprising the following steps:

step 1: obtaining random variable data related to wind power output, photovoltaic output and load in a power network to form an n-dimensional sample data set D ═ x₁,x₂,...,x_m}；

Step 2: processing the data set D according to a k-nearest neighbor algorithm, and calculating a nearest neighbor subset N of each data point in the data set_i(x_i) And obtaining a strong correlation neighbor set N ═ N of each data in the data set₁(x₁),N₂(x₂),...,N_m(x_m)}；

And step 3: calculate covariance matrix cov (N)_i(x_i) And performing eigenvalue decomposition on the vector set to obtain an eigenvalue vector set alpha_i＝{α_i1,α_i2,...,α_in}; each neighbor subset N_i(x_i) The feature value vector sets of (1) are sorted according to size; the dimension n' after dimension reduction is determined by a principal component proportion threshold value rho, and m characteristic values are assumed to be lambda₁≥λ₂≥...≥λ_mN' is obtained by the following formula, and rho takes a value of 0.8;

and 4, step 4: forming the first n' eigenvectors into an eigenvector matrix W corresponding to each neighboring subset_i＝{α′_i1,α′_i2,...,α′_in′}; by z_i＝W_i ^Tx_iThe mapping converts the sample data set D to a new sample data set D' ═ { z ═ z₁,z₂,...,z_m}；

And 5: calculating any two data points z in the data set D' according to the information provided by the neighbor set of the data set D_j、z_kThe asymmetric Rank-order distance is calculated according to the following formula:

in the formula (I), the compound is shown in the specification,

represents z_jThe ith nearest neighbor point of (a),

represents z_kIs at z_jThe number of bits in the neighbor list; l (z)_j,z_k) Is large or small determines z_j、z_kSimilarity of nearest adjacent points of the two points;

obtaining a symmetrical and normalized Rank-order distance rl (z) by using the formula (3)_j,z_k)

Thereby obtaining an adjacency matrix R as shown in formula (4):

step 6: if the adjacency matrix R is known, performing clustering analysis by using spectral clustering, wherein clustering results correspond to clusters to which samples in the original wind, light and load data set D belong; and (3) setting the number of clusters of the clustering result as K, extracting the central points of the clusters as representative points, wherein the formula (5) is as follows:

wherein K is 1, 2.., K; g_kRepresents the k-th cluster obtained by clustering, x_sRepresents samples in a class cluster s;

representing the number of data in the kth class cluster;

and 7: representing the point y by the wind-light load data obtained in the step 6_i∈{y₁,y₂,...,y_KEstablishing a mathematical model of probability optimal power flow by taking the minimum running cost of a generator in a power network as an optimization target as a state variable of an optimization problem;

and 8: solving optimal solution F for probability optimization problem by adopting artificial bee colony algorithm_i，F_iThe method comprises the steps of (1) including the running cost of a generator, the output of the generator, the node voltage and the transformer transformation ratio information; obtaining data representative of scene, load and the like { y₁,y₂,...,y_KThe corresponding probabilistic optimal solution set is { F }₁,F₂,...,F_K}；

And step 9: optimal solution set { F) for probabilistic optimal power flow calculation₁,F₂,...,F_KAnd solving probability statistical data such as expectation, variance and the like.

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