CN105846448B - Method for determining reactive compensation capacity of power distribution network based on random matrix theory - Google Patents

Method for determining reactive compensation capacity of power distribution network based on random matrix theory Download PDF

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CN105846448B
CN105846448B CN201610363706.3A CN201610363706A CN105846448B CN 105846448 B CN105846448 B CN 105846448B CN 201610363706 A CN201610363706 A CN 201610363706A CN 105846448 B CN105846448 B CN 105846448B
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CN105846448A (en
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贾东梨
盛万兴
刘科研
孟晓丽
胡丽娟
何开元
叶学顺
刁赢龙
唐建岗
董伟杰
李雅洁
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State Grid Corp of China SGCC
China Electric Power Research Institute Co Ltd CEPRI
State Grid Jiangsu Electric Power Co Ltd
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China Electric Power Research Institute Co Ltd CEPRI
State Grid Jiangsu Electric Power Co Ltd
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for AC mains or AC distribution networks
    • H02J3/18—Arrangements for adjusting, eliminating or compensating reactive power in networks
    • H02J3/1821—Arrangements for adjusting, eliminating or compensating reactive power in networks using shunt compensators
    • H02J3/1871—Methods for planning installation of shunt reactive power compensators
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    • Y02E40/30—Reactive power compensation

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Abstract

本发明提出一种基于随机矩阵理论的配电网无功补偿容量确定方法，其包括：通过归一化节点注入功时间序列矩阵、节点注入无功时间序列矩阵和节点电压时间序列矩阵，构建高维随机矩阵以及协方差矩阵S，获取协方差矩阵的特征根；构建包含节点无功补偿容量时间序列矩阵、节点电压偏差时间序列矩阵的高维随机矩阵，以及对应的协方差矩阵和协方差矩阵的特征根；通过计算两个协方差矩阵最大特征值比，拟合配电网无功补偿容量；从而免去了传统无功优化中冗长复杂的计算工作量。

Figure 201610363706

The present invention proposes a method for determining the reactive power compensation capacity of a distribution network based on random matrix theory, which includes: constructing a high-voltage time series matrix by normalizing the node injected power time series matrix, the node injected reactive power time series matrix and the node voltage time series matrix. dimensional random matrix and covariance matrix S, obtain the characteristic root of the covariance matrix; construct a high-dimensional random matrix including the node reactive power compensation capacity time series matrix, the node voltage deviation time series matrix, and the corresponding covariance matrix and covariance matrix The eigenvalue of the distribution network is fitted by calculating the ratio of the maximum eigenvalues of the two covariance matrices, thereby eliminating the long and complicated computational workload in traditional reactive power optimization.

Figure 201610363706

Description

Method for determining reactive compensation capacity of power distribution network based on random matrix theory
The technical field is as follows:
the invention belongs to the technical field of operation of power distribution networks, and particularly relates to a method for determining reactive compensation capacity of a power distribution network based on a random matrix theory.
Background
The reactive power optimization can improve the voltage quality and reduce the network loss, and belongs to the nonlinear programming problem by taking reactive power compensation or regulation equipment as a control means. The traditional voltage reactive power optimization has the following main problems: (1) the problem of reactive power repeatability construction exists due to the hierarchical management of the power grid, and meanwhile, due to the complex operation of the power grid, the power cost is increased, the investment of multi-stage equipment is large, the utilization rate is low, and the comprehensive effect is poor; (2) the existing reactive compensation strategy is usually limited to local reactive compensation, the problem of a global voltage stability domain cannot be considered, and the existing reactive compensation strategy is rarely related to the global reactive compensation of a power grid; (3) traditional reactive power optimization software is single in function, and voltage reactive power analysis is not considered. The power distribution network is located at the tail end of the power grid, so that the power distribution network has more nodes and complicated wiring, and the problems are more prominent. Particularly, in the reactive global optimization, when the whole network reactive optimization is performed, if all the nodes are considered, the range is too large, the optimization speed is slow, and an ideal effect cannot be achieved.
The random matrix theory can reflect the deviation degree of the actual data to the random by comparing the statistical characteristics of the random multi-dimensional time sequence and reveal the behavior characteristics of the overall correlation in the actual data. It is this specific view that makes the random matrix theory widely used in the field of optical applications such as physics, finance, mathematics, biometrics, network science, etc., and gradually applied in the field of power systems.
At present, the application of the big data technology in the technical field of reactive power optimization of the power distribution network is few.
Disclosure of Invention
In order to overcome the defects, the invention provides a method for determining the reactive compensation capacity of the power distribution network based on the random matrix theory, and the reactive compensation capacity of the power distribution network is determined through simple and convenient calculation.
The purpose of the invention is realized by adopting the following technical scheme:
a method for determining reactive compensation capacity of a power distribution network based on random matrix theory comprises the following steps:
(1) determining a node injection active time sequence matrix P, a node injection reactive time sequence matrix Q and a node voltage time sequence matrix V;
(2) performing normalization processing to construct a high-dimensional random matrix Y;
(3) defining a covariance matrix S of a high-dimensional random matrix, and acquiring a characteristic root of the covariance matrix;
(4) constructing a high-dimensional random matrix dY containing a node reactive compensation capacity time sequence matrix delta Q and a node voltage deviation time sequence matrix delta V, and defining a covariance matrix dS of the high-dimensional random matrix dY, and acquiring a characteristic root of the covariance matrix dS;
(5) calculating the ratio of the maximum eigenvalue of the covariance matrix S to the maximum eigenvalue of the matrix covariance matrix dS;
(6) and fitting the reactive compensation capacity of the power distribution network through a unitary linear function.
Preferably, the step (1) includes: acquiring historical data of a power distribution network, and injecting an active time sequence, a reactive time sequence and a node voltage time sequence into a node to generate a node injection active time sequence matrix P, a node injection reactive time sequence matrix Q and a node voltage time sequence matrix V;
both P, Q and V are M rows and N columns matrix; and N is the single-day data acquisition frequency, N is 24T, T is the data acquisition frequency of the measuring device per hour, and M is the number of the nodes of the power distribution network.
Further, the high-dimensional random matrix in the step (2) is constructed by taking 24 hours per day as a time window, and the specific steps include:
respectively carrying out normalization processing on P, Q, V before constructing the high-dimensional random matrix; the normalization of the Pjth column is performed according to equation (1):
Figure GDA0003320622120000021
wherein i is 1,2, …, N;
Figure GDA0003320622120000022
normalizing the active load of the ith row and the j column of the matrix P; p is a radical ofijIs the element of ith row and j column of the matrix P;
Figure GDA0003320622120000023
the maximum load value of the jth column of the matrix P;
the j-th columns of the matrices Q and V are normalized by equations (2) and (3), respectively, as follows:
Figure GDA0003320622120000024
Figure GDA0003320622120000025
in formula (3), i is 1,2, …, N;
Figure GDA0003320622120000026
reactive load normalized for j columns and i rows of matrix Q, QijIs the element of ith row and j column of the matrix Q;
Figure GDA0003320622120000027
the maximum load value in the jth column of the matrix Q,
Figure GDA0003320622120000028
normalized voltage, V, for ith row and j columns of matrix VijIs the element of the ith row and j column of the matrix V,
Figure GDA0003320622120000031
the maximum load value in the jth column of matrix V.
Further, let
Figure GDA0003320622120000032
The matrices obtained by performing normalization for P, Q and V, respectively;
selecting
Figure GDA0003320622120000033
As elements of the high-dimensional random matrix, the high-dimensional random matrix is constructed as follows:
Figure GDA0003320622120000034
expand Y as follows:
Figure GDA0003320622120000035
in the formula (5), Y is a matrix of 3M rows and N columns.
Preferably, the step (3) specifically includes: a covariance matrix S based on a large-dimensional stochastic matrix spectral analysis is defined by equation (6):
S＝1/N*Y'*Y (6)
obtaining the characteristic root of the covariance matrix S through calculation:
SxS＝λSxS， (7)
in the formula (7), Y' is an estimated value of a high-dimensional random matrix Y, xSIs an N-dimensional column vector; lambda [ alpha ]SIs the characteristic root of S;
obtaining lambda by solving a homogeneous system of linear equations of N unknownsSAnd recording the maximum characteristic root λmaxS。
Preferably, the step (4) specifically includes collecting historical data of the power distribution network, and injecting a time sequence of reactive compensation capacity and a node voltage deviation time sequence into the node to generate a time sequence matrix Δ Q of reactive compensation capacity and a time sequence matrix Δ V of node voltage deviation;
selecting delta Q and delta V as data sources of the high-dimensional random matrix, and constructing the high-dimensional random matrix by taking 24 hours a day as a time window;
both the delta Q and the delta V are matrixes of M rows and N columns; and N is the number of data acquisition per day, N is 24T, T is the number of data acquisition times of the measuring device per hour, and M is the number of nodes of the power distribution network.
Further, the constructing the high-dimensional random matrix may be preceded by: converting Δ V to a per unit value
Figure GDA0003320622120000047
And normalizing the delta Q by an expression (8), wherein the expression is as follows:
Figure GDA0003320622120000041
in formula (8), i is 1,2, …, N;
Figure GDA0003320622120000042
the normalized reactive compensation capacity of the ith row and j columns of the matrix delta Q is obtained; dqijIs the element of ith row and j column of the matrix delta Q;
Figure GDA0003320622120000043
the maximum load value of the jth column of the matrix P;
selecting
Figure GDA0003320622120000044
And
Figure GDA0003320622120000045
as the elements of the high-dimensional random matrix, the construction of the high-dimensional random matrix is completed as follows:
dY＝[dQ；dV] (9)
expand dY as follows:
Figure GDA0003320622120000046
where dY is a matrix of 2M rows and N columns.
Further, in the step (4), defining a covariance matrix dS of the high-dimensional random matrix dY, and acquiring a feature root of the covariance matrix dS includes:
a covariance matrix dS based on a large-dimensional stochastic matrix spectral analysis is defined by equation (11):
dS＝1/N*dY'*dY (11)
acquiring a characteristic root of the covariance matrix dS, wherein the expression is as follows:
dSxd＝λdSxd， (12)
in the formula (12), xdIs an N-dimensional column vector; lambda [ alpha ]dSIs the characteristic root of dS;
obtaining lambda by solving a homogeneous system of linear equations of N unknownsdSAnd recording the maximum characteristic root λmaxdS。
Preferably, the step (5) includes calculating a ratio of the maximum eigenvalue of the covariance matrix S to the maximum eigenvalue of the matrix covariance matrix dS:
Figure GDA0003320622120000051
preferably, in the step (6), fitting the reactive compensation capacity of the power distribution network by using a unary linear function includes:
the expression of the reactive compensation capacity y of the power grid is as follows:
y＝kx+b (14)
in the formula (14), b is a constant, and x is the sum of the active power of the distribution network.
Compared with the closest prior art, the invention has the following beneficial effects:
1. the method for determining the reactive compensation capacity of the power distribution network based on the random matrix theory introduces the high-dimensional random matrix theory into the reactive optimization analysis of the power distribution network, and provides a new analysis method for the reactive optimization of the power distribution network. Under the condition that the network topology structure is not changed, the method is not influenced by a network wiring mode, load diversity and load randomness, and therefore the calculation speed is improved.
2. Constructing a high-dimensional random matrix suitable for reactive power optimization of the power distribution network by using time sequence active power, time sequence reactive power and time sequence voltage acquired by the power distribution network in history, and calculating a characteristic value of a covariance matrix of the random matrix; constructing a target matrix by using historical time sequence reactive compensation capacity and voltage difference before and after time sequence compensation, and calculating a characteristic value of a covariance matrix of the target matrix; the ratio of the maximum eigenvalues of the two covariance matrices is used as the selection of the reactive compensation capacity, the calculation is simple, and the calculation result is accurate and effective.
Drawings
Fig. 1 is a flow chart of a method for determining reactive compensation capacity of a power distribution network based on a random matrix theory provided by the invention.
The specific implementation mode is as follows:
the invention provides a method for determining the reactive compensation capacity of a power distribution network based on a random matrix theory, which comprises the steps of constructing a high-dimensional random matrix suitable for reactive optimization of the power distribution network by utilizing time sequence active power, reactive power and voltage collected by the power distribution network, analyzing a covariance matrix of the high-dimensional random matrix, and calculating the maximum characteristic root of the covariance matrix; and according to the result after the reactive compensation, constructing a high-dimensional random matrix of the reactive compensation capacity delta Q and the voltage deviation delta V, analyzing a covariance matrix of the high-dimensional random matrix, and calculating the maximum characteristic root of the covariance matrix. And calculating the ratio of the maximum characteristic root of the two-covariance matrix so as to find out the existing regularity.
As shown in fig. 1, the method specifically comprises the following steps:
(1) determining a node power injection time sequence matrix P, a node reactive power injection time sequence matrix Q and a node voltage time sequence matrix V;
the step (1) comprises the following steps: acquiring historical data of a power distribution network, and injecting an active time sequence, a reactive time sequence and a node voltage time sequence into a node to generate a node injection active time sequence matrix P, a node injection reactive time sequence matrix Q and a node voltage time sequence matrix V;
both P, Q and V are M rows and N columns matrix; and N is the single-day data acquisition frequency, N is 24T, T is the data acquisition frequency of the measuring device per hour, and M is the number of the nodes of the power distribution network.
(2) Performing normalization processing to construct a high-dimensional random matrix Y;
the high-dimensional random matrix in the step (2) is constructed by taking 24 hours per day as a time window, and the specific steps comprise:
respectively carrying out normalization processing on P, Q, V before constructing the high-dimensional random matrix; the normalization of the Pjth column is performed according to equation (1):
Figure GDA0003320622120000061
wherein i is 1,2, …, N;
Figure GDA0003320622120000062
normalizing the active load of the ith row and the j column of the matrix P; p is a radical ofijIs the element of ith row and j column of the matrix P;
Figure GDA0003320622120000063
the maximum load value of the jth column of the matrix P;
the j-th columns of the matrices Q and V are normalized by equations (2) and (3), respectively, as follows:
Figure GDA0003320622120000071
Figure GDA0003320622120000072
in formula (3), i is 1,2, …, N;
Figure GDA0003320622120000073
reactive load normalized for ith row and j column of matrix Q，qijIs the element of ith row and j column of the matrix Q;
Figure GDA0003320622120000074
the maximum load value in the jth column of the matrix Q,
Figure GDA0003320622120000075
normalized voltage, V, for ith row and j columns of matrix VijIs the element of the ith row and j column of the matrix V,
Figure GDA0003320622120000076
the maximum load value in the jth column of matrix V.
Is provided with
Figure GDA0003320622120000077
The matrices obtained by performing normalization for P, Q and V, respectively;
selecting
Figure GDA0003320622120000078
As elements of the high-dimensional random matrix, the high-dimensional random matrix is constructed as follows:
Figure GDA0003320622120000079
expand Y as follows:
Figure GDA00033206221200000710
in the formula (5), Y is a matrix of 3M rows and N columns.
(3) Defining a covariance matrix S of a high-dimensional random matrix, and acquiring a characteristic root of the covariance matrix;
a covariance matrix S based on a large-dimensional stochastic matrix spectral analysis is defined by equation (6):
S＝1/N*Y'*Y (6)
obtaining the characteristic root of the covariance matrix S through calculation:
SxS＝λSxS， (7)
in the formula (7), Y' is an estimated value of a high-dimensional random matrix Y, xSIs an N-dimensional column vector; lambda [ alpha ]SIs the characteristic root of S;
obtaining lambda by solving a homogeneous system of linear equations of N unknownsSAnd recording the maximum characteristic root λmaxS。
(4) Constructing a high-dimensional random matrix dY containing a node reactive compensation capacity time sequence matrix delta Q and a node voltage deviation time sequence matrix delta V, and defining a covariance matrix dS of the high-dimensional random matrix dY, and acquiring a characteristic root of the covariance matrix dS;
the step (4) specifically comprises the steps of collecting historical data of the power distribution network, and injecting a time sequence of reactive compensation capacity and a node voltage deviation time sequence into nodes to generate a reactive compensation capacity time sequence matrix delta Q and a node voltage deviation time sequence matrix delta V;
selecting delta Q and delta V as data sources of the high-dimensional random matrix, and constructing the high-dimensional random matrix by taking 24 hours a day as a time window;
both the delta Q and the delta V are matrixes of M rows and N columns; and N is the number of data acquisition per day, N is 24T, T is the number of data acquisition times of the measuring device per hour, and M is the number of nodes of the power distribution network.
Before constructing the high-dimensional random matrix, converting the delta V into a per unit value
Figure GDA0003320622120000081
And normalizing the delta Q by an expression (8), wherein the expression is as follows:
Figure GDA0003320622120000082
in formula (8), i is 1,2, …, N;
Figure GDA0003320622120000083
the normalized reactive compensation capacity of the ith row and j columns of the matrix delta Q is obtained; dqijFor ith row and j columns of matrix DeltaQAn element;
Figure GDA0003320622120000084
the maximum load value of the jth column of the matrix P;
selecting
Figure GDA0003320622120000085
And
Figure GDA0003320622120000086
as the elements of the high-dimensional random matrix, the construction of the high-dimensional random matrix is completed as follows:
dY＝[dQ；dV] (9)
expand dY as follows:
Figure GDA0003320622120000091
where dY is a matrix of 2M rows and N columns.
In the step (4), defining a covariance matrix dS of the high-dimensional random matrix dY, and obtaining a feature root of the covariance matrix dS includes:
a covariance matrix dS based on a large-dimensional stochastic matrix spectral analysis is defined by equation (11):
dS＝1/N*dY'*dY (11)
acquiring a characteristic root of the covariance matrix dS, wherein the expression is as follows:
dSxd＝λdSxd， (12)
in the formula (12), xdIs an N-dimensional column vector; lambda [ alpha ]dSIs the characteristic root of dS;
obtaining lambda by solving a homogeneous system of linear equations of N unknownsdSAnd recording the maximum characteristic root λmaxdS。
(5) Calculating the ratio of the maximum eigenvalue of the covariance matrix S to the maximum eigenvalue of the matrix covariance matrix dS;
Figure GDA0003320622120000092
(6) and fitting the reactive compensation capacity of the power distribution network through a unitary linear function. It includes:
the expression of the reactive compensation capacity y of the power grid is as follows:
y＝kx+b (14)
in the formula (14), b is a constant, and x is the sum of the active power of the distribution network.
And selecting the sum of the active power of a time window in the historical data of the power distribution network and the corresponding reactive compensation capacity, and calculating the value b. And calculating reactive compensation capacity according to the values of k and b and the active power.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.

Claims (10)

1. A method for determining reactive compensation capacity of a power distribution network based on random matrix theory is characterized by comprising the following steps:
(1) determining a node injection active time sequence matrix P, a node injection reactive time sequence matrix Q and a node voltage time sequence matrix V;
(2) performing normalization processing to construct a high-dimensional random matrix Y;
(3) defining a covariance matrix S of a high-dimensional random matrix, and acquiring a characteristic root of the covariance matrix;
(4) constructing a high-dimensional random matrix dY containing a node reactive compensation capacity time sequence matrix delta Q and a node voltage deviation time sequence matrix delta V, and defining a covariance matrix dS of the high-dimensional random matrix dY, and acquiring a characteristic root of the covariance matrix dS;
(5) calculating the ratio of the maximum eigenvalue of the covariance matrix S to the maximum eigenvalue of the matrix covariance matrix dS;
(6) and fitting the reactive compensation capacity of the power distribution network through a unitary linear function.
2. The method of claim 1, wherein step (1) comprises: acquiring historical data of a power distribution network, and injecting an active time sequence, a reactive time sequence and a node voltage time sequence into a node to generate a node injection active time sequence matrix P, a node injection reactive time sequence matrix Q and a node voltage time sequence matrix V;
both P, Q and V are M rows and N columns matrix; and N is the single-day data acquisition frequency, N is 24T, T is the data acquisition frequency of the measuring device per hour, and M is the number of the nodes of the power distribution network.
3. The method as claimed in claim 1 or 2, wherein the high-dimensional random matrix in step (2) is constructed by taking 24 hours per day as a time window, and the specific steps comprise:
respectively carrying out normalization processing on P, Q, V before constructing the high-dimensional random matrix; the normalization of the Pjth column is performed according to equation (1):
Figure FDA0003320622110000011
wherein i is 1,2, …, N;
Figure FDA0003320622110000012
normalizing the active load of the ith row and the j column of the matrix P; p is a radical ofijIs the element of ith row and j column of the matrix P;
Figure FDA0003320622110000013
the maximum load value of the jth column of the matrix P;
the j-th columns of the matrices Q and V are normalized by equations (2) and (3), respectively, as follows:
Figure FDA0003320622110000014
Figure FDA0003320622110000021
in formula (3), i is 1,2, …, N;
Figure FDA0003320622110000022
reactive load normalized for j columns and i rows of matrix Q, QijIs the element of ith row and j column of the matrix Q;
Figure FDA0003320622110000023
the maximum load value in the jth column of the matrix Q,
Figure FDA0003320622110000024
normalized voltage, V, for ith row and j columns of matrix VijIs the element of the ith row and j column of the matrix V,
Figure FDA0003320622110000025
the maximum load value in the jth column of matrix V.
4. The method of claim 3, wherein let P, Q, V be P, Q and V, respectively, for the matrix obtained by performing the normalization;
p, Q, V is selected as the elements of the high-dimensional random matrix, and the high-dimensional random matrix is constructed as follows:
Figure FDA0003320622110000026
expand Y as follows:
Figure FDA0003320622110000027
in the formula (5), Y is a matrix of 3M rows and N columns.
5. The method according to claim 4, wherein the step (3) comprises in particular: a covariance matrix S based on a large-dimensional stochastic matrix spectral analysis is defined by equation (6):
S1/N Y' Y (6) the characteristic root of the covariance matrix S is obtained by calculation:
SxS＝λSxS， (7)
in the formula (7), Y' is an estimated value of a high-dimensional random matrix Y, xSIs an N-dimensional column vector; lambda [ alpha ]SIs the characteristic root of S; obtaining lambda by solving a homogeneous system of linear equations of N unknownsSAnd recording the maximum characteristic root λmaxS。
6. The method of claim 1, wherein the step (4) specifically comprises collecting historical data of the distribution network, injecting a time series of reactive compensation capacity and a time series of node voltage deviation into the nodes, and generating a time series matrix Δ Q of reactive compensation capacity and a time series matrix Δ V of node voltage deviation;
selecting delta Q and delta V as data sources of the high-dimensional random matrix, and constructing the high-dimensional random matrix by taking 24 hours a day as a time window;
both the delta Q and the delta V are matrixes of M rows and N columns; and N is the number of data acquisition per day, N is 24T, T is the number of data acquisition times of the measuring device per hour, and M is the number of nodes of the power distribution network.
7. The method of claim 6, wherein constructing the high-dimensional random matrix is preceded by: converting the Δ V into a per unit value dV, and normalizing the Δ Q by an expression (8) which is:
Figure FDA0003320622110000031
in formula (8), i is 1,2, …, N;
Figure FDA0003320622110000032
the normalized reactive compensation capacity of the ith row and j columns of the matrix delta Q is obtained; dqijIs the element of ith row and j column of the matrix delta Q;
Figure FDA0003320622110000033
the maximum load value of the jth column of the matrix P;
for delta V, converting the delta V into a per unit value dV without normalization processing; after finishing processing the delta Q and the delta V, the matrixes are dQ and dV respectively;
selecting dQ and dV as elements of the high-dimensional random matrix, and completing the construction of the high-dimensional random matrix as follows:
dY＝[dQ；dV] (9)
expand dY as follows:
Figure FDA0003320622110000034
where dY is a matrix of 2M rows and N columns.
8. The method according to claim 6 or 7, wherein in the step (4), defining a covariance matrix dS of the high-dimensional random matrix dY, and obtaining an eigenroot of the covariance matrix dS comprises:
a covariance matrix dS based on a large-dimensional stochastic matrix spectral analysis is defined by equation (11):
dS＝1/N*dY'*dY (11)
acquiring a characteristic root of the covariance matrix dS, wherein the expression is as follows:
dSxd＝λdSxd， (12)
in the formula (12), xdIs an N-dimensional column vector; lambda [ alpha ]dSIs the characteristic root of dS;
obtaining lambda by solving a homogeneous system of linear equations of N unknownsdSAnd recording the maximum characteristic root λmaxdS。
9. The method of claim 1, wherein step (5) comprises calculating a ratio of the largest eigenvalue of the covariance matrix S to the largest eigenvalue of the matrix covariance matrix dS:
Figure FDA0003320622110000041
10. the method of claim 9, wherein the step (6) of fitting the reactive compensation capacity of the distribution network through a unary linear function comprises:
the expression of the reactive compensation capacity y of the power grid is as follows:
y＝kx+b (14)
in the formula (14), b is a constant, and x is the sum of the active power of the distribution network.
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