CN108429263B

CN108429263B - System parameter optimal configuration method for multi-device integration of alternating current and direct current power grid

Info

Publication number: CN108429263B
Application number: CN201810181837.9A
Authority: CN
Inventors: 邓卫; 裴玮; 张学; 孔力; 李鲁阳; 黄强; 李强; 黄地
Original assignee: Institute of Electrical Engineering of CAS; Electric Power Research Institute of State Grid Jiangsu Electric Power Co Ltd
Current assignee: Institute of Electrical Engineering of CAS; Electric Power Research Institute of State Grid Jiangsu Electric Power Co Ltd
Priority date: 2018-03-06
Filing date: 2018-03-06
Publication date: 2020-04-24
Anticipated expiration: 2038-03-06
Also published as: CN108429263A

Abstract

The invention relates to a system parameter optimal configuration method for multi-device integration of an alternating current-direct current power grid, which is realized by the following steps: initializing parameters of a system to be optimized integrated by multiple devices of an alternating current-direct current power grid to obtain initial characteristic values, wherein the initial characteristic values are N initial characteristic roots in a matrix corresponding to the parameters to be optimized; based on the initial characteristic value, monotonically increasing or decreasing the parameter to be optimized; generating a sensitivity matrix according to the parameters to be optimized in a monotone increasing or decreasing manner; combining the characteristic roots in the sensitivity matrix, calculating the dominant distance between the characteristic roots, and providing a basis for clustering the characteristic roots with different change characteristics; forming a dominant distance matrix according to the dominant distance; and classifying all the characteristic roots through a clustering algorithm, providing a corresponding limited range for determining parameter optimization criteria, and obtaining optimized system parameters by searching for the optimal parameter optimization criteria.

Description

System parameter optimal configuration method for multi-device integration of alternating current and direct current power grid

Technical Field

The invention relates to a system parameter optimal configuration method for multi-device integration of an alternating current-direct current power grid, and belongs to the technical field of alternating current-direct current power distribution networks.

Background

The access of large-scale distributed renewable energy sources to the power grid provides new challenges and higher requirements for flexible access and effective management and control of the system. The alternating current-direct current power distribution network is flexible in networking, renewable energy sources can be integrated at multiple voltage levels, the energy utilization efficiency can be improved while the links of power conversion are reduced, the renewable energy sources are fully consumed in a larger range, the power supply capacity is enhanced, and the method becomes one of important power grid forms. Various converter devices such as an active converter, a load converter, a storage converter and the like in an alternating current and direct current power distribution network are different in operation characteristics and need to be coordinated and matched with each other. If the parameters of the multi-variable flow system are not properly coordinated, the overall operation performance is affected.

Disclosure of Invention

The invention solves the problems: the method for optimizing and configuring the system parameters facing the integration of the AC/DC power grid and the multiple devices overcomes the defects of the prior art, determines optimized system key parameters by searching for the optimal parameter optimization criterion, realizes the optimization of the integration coordination among the AC/DC source-load-storage and other multiple variable current devices, and effectively improves the overall integration operation performance of the system.

The technical scheme of the invention is as follows: a multi-device integration system parameter optimization configuration method for an alternating current-direct current power grid comprises the following steps:

initializing parameters of a system to be optimized integrated by multiple devices of an alternating current-direct current power grid, wherein the initialization result is to obtain initial characteristic values, namely N characteristic roots (the characteristic roots are initial characteristic roots) in a matrix corresponding to the parameters to be optimized; the parameters of the system to be optimized include a plurality of parameters, for example, an electrical structure corresponding to a certain system is shown in fig. 2,

the corresponding circuit satisfies the following conditions:

the corresponding small signal equation is:

the variable subscripts m, s1, s2, DC represent physical quantities of the master VSC, the slave VSC1, the slave VSC2, and the DC/DC converter, respectively. U shape_m、i_mRespectively representing the DC voltage, DC current, U of the VSC of the master station_s1、i_s1、C_s1、P_s1Respectively represents the direct current voltage, the direct current side capacitance and the actual active power of the slave VSC1, U_s2、i_s2、C_s2、P_s2Respectively representing the direct voltage, the direct current, the direct-current side capacitance and the actual active power i of the slave VSC2_dc、C_dc、P_dcThe DC current, the DC-side capacitance, and the actual active power of the DC/DC converter are shown, respectively. r is_m,r_s1,r_s2Respectively the resistance of each line impedance, L_m，L_s1，L_s2Respectively the reactance of each line impedance.

Small signal stability, also known as small interference stability, refers to the ability of a system to maintain synchronization when subjected to small disturbances. The small disturbance means that the influence caused by the disturbance is small enough, and the model of the system can be linearized without influencing the analysis accuracy, such as random fluctuation of load, slow change of partial parameters, and the like. Small signal variations are generally denoted by Δ.

Writing into a matrix form, namely, obtaining a model:

dΔx/dt＝AΔx

Δ x is the system state vector, [ △ i ]_m,△i_s1,△i_s2,△U_dc,△U_s1,△U_s2]^TAnd A is the system state matrix:

the parameters appearing in the matrix are all system parameters that can be optimized;

solving the a matrix, assuming that N feature roots can be obtained, wherein the 1 st, 2.. i.. N feature roots (in this case, initial feature values) are expressed as: lambda [ alpha ]^o _i＝σ^o _i+jω^o _iWhere the superscript o denotes the initial value, σ denotes the real part, ω denotes the imaginary part;

the result of the initialization is to obtain the 1 st, 2.. i.. N characteristic roots (in this case, initial characteristic values) λ^o _i＝σ^o _i+jω^o _i

Obtaining a parameter to be optimized which monotonically increases or decreases according to the initial characteristic value;

monotonically increasing or decreasing the parameter to be optimized refers to a parameter to be optimized, such as C in A_dcStarting from the current value, the parameter to be optimized is continuously changed by adding a fixed step size or subtracting a fixed step size.

Generating a sensitivity matrix according to the parameters to be optimized in a monotone increasing or decreasing manner;

(1) the A matrix is naturally updated after a certain parameter of the system is changed, the updated A matrix can be solved at this time, N characteristic roots can be obtained, and the 1 st, 2 nd, i. Lambda [ alpha ]_i＝σ_i+jω_i；。

Then, according to the real part and the imaginary part of each characteristic root, subtracting the real part and the imaginary part of the respective initial characteristic value to obtain a change amount:

are respectively delta sigma_i＝σ_i-σ^o _i；Δω_i＝ω_i-ω^o _i；

On the basis, the change quantity of the 1 st, 2 th_i<0 is: delta lambda_i＝-1*sqrt((Δσ_i)²+(Δω_i)²) Otherwise Δ λ_i＝sqrt((Δσ_i)²+(Δω_i)²)；

To obtain Delta lambda₁，Δλ₂..Δλ_i,Δλ_j..Δλ_NThereafter, they are divided by each other, i.e. η_ij＝Δλ_i/Δλ_jI belongs to 1 to N, j belongs to 1 to N, so that N times N numbers can be written into a table form, such as table 1 (called a sensitivity matrix); n is the total feature root number), i and j are variables that can represent any one of 1 to N;

step four, combining the characteristic roots in the sensitivity matrix, calculating the dominant distance between the characteristic roots and providing a basis for clustering the characteristic roots with different change characteristics; forming a dominant distance matrix according to the dominant distance;

the sensitivity matrix generated in the previous step, according to the formula:

Ω_ij＝sqrt((η_i1-η_j1)²+(η_i2-η_j2)²+…+(η_iN-η_jN)²) and/N, solving the dominant distance between the characteristic roots. This step is to continue calculating the index on the basis of the previous step.

And step five, classifying all the characteristic roots through K grouping clustering, providing a corresponding limited range for determining parameter optimization criteria, and determining optimized system key parameters by searching for the optimal parameter optimization criteria.

On the basis of the dominant distance matrix generated in the previous step, clustering can be performed on each feature according to a K-block clustering method. This step is continued further on the basis of the previous step.

Compared with the prior art, the invention has the advantages that: the optimal parameter optimization criterion is obtained by continuously changing the parameters to be optimized of the system and by the provided system parameter optimization configuration method facing the multi-device integration of the alternating current and direct current power grid. Wherein: calculating the dominant distance between the characteristic roots by means of the sensitivity matrix of the characteristic roots, and providing a basis for clustering the characteristic roots with different change characteristics; and classifying all the characteristic roots through K grouping clustering, and providing a corresponding limited range for determining parameter optimization criteria. By searching the optimal parameter optimization criterion, the optimized system key parameters are determined, the optimization of integration coordination among the AC/DC source-load-storage and other multi-variable-current devices is realized, and the overall integration operation performance of the system is effectively improved.

Drawings

FIG. 1 is a flow chart of the method of the present invention;

fig. 2 is an electrical structural diagram corresponding to one system of the present invention.

Detailed Description

The invention is described in detail below with reference to the accompanying drawings and examples

As shown in fig. 1, the method of the present invention is specifically implemented as follows:

1. the initialization process is as follows:

(1) establishing a small signal model d delta x/dt of the alternating current and direct current grid system as A delta x, wherein delta x is a system state vector, and A is a system state matrix;

(2) solving the A matrix to obtain N characteristic roots, wherein the 1 st, 2.. i.. N characteristic roots are expressed as: lambda [ alpha ]^o _i＝σ^o _i+jω^o _i。

2. The sensitivity matrix generation flow is as follows:

(1) after a certain parameter of the system is changed, the matrix A is updated, the matrix A is solved to obtain N characteristic roots, wherein the 1 st, 2 nd, i. Lambda [ alpha ]_i＝σ_i+jω_i；

(2) Calculating the real part and imaginary part change quantity of the 1,2.. i.. N characteristic roots, namely delta sigma_i＝σ_i-σ^o _i；Δω_i＝ω_i-ω^o _i；

(3) Calculating the change of the 1 st, 2.. i.. N characteristic roots if delta sigma_i<0 is: delta lambda_i＝-1*sqrt((Δσ_i)²+(Δω_i)²) Otherwise Δ λ_i＝sqrt((Δσ_i)²+(Δω_i)²)；

(4) According to Δ λ₁，Δλ₂...Δλ_i.Δλ_j...Δλ_NGenerating a sensitivity matrix η_N*NWherein η_ij＝Δλ_i/Δλ_j，

TABLE 1

	λ₁	λ₂	…	λ_N
					λ₁	η₁₁	η₁₂	…	η_1N
λ₂	η₂₁	η₂₂	…	η_2N
					…	…	…	…	…
λ_N	η_N1	η_N2	…	η_NN

Assuming that the system has 5 characteristic roots, after changing an optimization parameter, the change amount of the characteristic root is as follows:

Δλ₁＝-15，Δλ₂＝-15，Δλ₃＝3，Δλ₄＝10，Δλ₅＝10

according to the sensitivity matrix generation method, the sensitivity matrix at this time can be calculated as shown in table 2:

TABLE 2

	λ₁	λ₂	λ₃	λ₄	λ₅
						λ₁	η₁₁＝1	η₁₂＝1	η₁₃＝-5	η₁₄＝-1.5	η₁₅＝-1.5
λ₂	η₂₁＝1	η₂₂＝1	η₂₃＝-5	η₂₄＝-1.5	η₂₅＝-1.5
						λ₃	η₃₁＝-1/5	η₃₂＝-1/5	η₃₃＝1	η₃₄＝3/10	η₃₅＝3/10
λ₄	η₄₁＝-10/15	η₄₂＝-10/15	η₄₃＝10/3	η₄₄＝1	η₄₅＝1
						λ_N	η₅₁＝-10/15	η₅₂＝-10/15	η₅₃＝10/3	η₅₄＝1	η₅₅＝1

3. The dominant distance calculation process is as follows:

combined sensitivity matrix η_N*NCalculating the lambda-th_i、λ_j(i ∈ N, j ∈ N) dominant distance Ω between two feature roots_ij：

Ω_ij＝sqrt((η_i1-η_j1)²+(η_i2-η_j2)²+…+(η_iN-η_jN)²)/N

According to omega_ijForming a dominant distance matrix omega_N*NAs shown in table 3:

TABLE 3

	λ₁	λ₂	…	λ_N
					λ₁	Ω₁₁	Ω₁₂	…	Ω_1N
λ₂	Ω₂₁	Ω₂₂	…	Ω_2N
					…	…	…	…	…
λ_N	Ω_N1	Ω_N2	…	Ω_NN

Assume that a dominant matrix is calculated as in table 4:

TABLE 4

	λ₁	λ₂	λ₃	λ₄	λ_N
						λ₁	Ω₁₁＝0	Ω₁₂＝0	Ω₁₃＝6.58	Ω₁₄＝10.5	Ω₁₅＝10.5
λ₂	Ω₂₁＝0	Ω₂₂＝0	Ω₂₃＝6.58	Ω₂₄＝10.5	Ω₂₅＝10.5
						λ₃	Ω₃₁＝6.58	Ω₃₂＝6.58	Ω₃₃＝0	Ω₃₄＝3.31	Ω₃₅＝3.31
λ₄	Ω₄₁＝10.5	Ω₄₂＝10.5	Ω₄₃＝3.31	Ω₄₄＝0	Ω₄₅＝0
						λ_N	Ω₅₁＝10.5	Ω₅₂＝10.5	Ω₅₃＝3.31	Ω₅₄＝0	Ω₅₅＝0

4. The characteristic root clustering process is as follows:

setting K groups of the feature root clusters; k is more than or equal to 2 and less than or equal to N/2;

2.1 line by line search omega_N*NCorresponds to Ω_abAnd the position where the minimum min of non-zero values occurs for the first time, e.g. is Ω_cd：

2.2 if K is 2, determine λ_a,λ _c2 centroid characteristics when K is 2The first appearance position of the root, maximum max, is shown as Ω according to Table 4₁₄I.e. a equals 1, then λ₁Is the centroid feature root of the cluster; similarly, the position where the minimum min of the non-zero value occurs for the first time can be known as Ω according to Table 4₃₄I.e. c is 3, then λ₃Another centroid feature root for the cluster); if K is>2, dividing (K-1) between max and min equally, determining corresponding (K-2) division point values, and searching omega line by line_N*NThe leading distance omega nearest to each bisector point value in the ith characteristic root, i ≠ a, c_ijThe first position of occurrence, noted Ω_ef,…,Ω_xy(K-2 in total), determining lambda_a,λ_c,λ_e…λ_xIs k>K centroid feature roots at 2; the method mainly comprises the steps of selecting K grouping centroids for K groups, and selecting lambda along with the execution of the subsequent steps₁、λ₃Is an initial centroid feature root;

2.3 analyzing the leading distance omega between the ith feature root (i.e. i ≠ a, c, e.) of the non-centroid feature root and the K centroid feature roots respectively_ia,Ω_ic,Ω_ie…Ω_ixE.g. λ₁、λ₃When the centroid feature root is defined as a1, c 3, then λ remains for 5 feature roots₂、λ₄、λ₅To analyze the dominant distance between the two users, when i is 2, the value is taken as Ω₂₁And Ω₂₃Determine the above-mentioned omega₂₁And Ω₂₃The subscript to the minimum, assuming ic, will be λ_iClustering to lambda_c；

2.4 repeating the step 2.3 until all the characteristic roots are clustered;

2.5 for K groups, calculating the average value of the dominant distances between all the non-centroid feature roots and the centroid feature roots in each group, searching the feature root of which the dominant distance between the feature root and the centroid in each group is closest to the value, recording as a new centroid feature root of each group, and expressing as lambda_a1,λ_c1,λ_e1…λ_x1。

2.6 analysis of the i-th feature root of the non-centroid feature root (i.e., i ≠ a1, c1, e1..) the dominant distances from the K centroid feature roots, respectivelyΩ_ia1,Ω_ic1,Ω_ie1…Ω_ix1Judging the subscript corresponding to the minimum value, and assuming ie1, determining lambda_iClustering to lambda_e1；

2.7 repeating the step 2.6 until all the characteristic roots are clustered;

2.8 if the clustering result is not changed from the last clustering result, ending the feature root clustering. Otherwise, repeating the step 2.5-2.7 until the clustering result is unchanged from the last clustering result, and ending the feature root clustering. Computing sum of squared errors SSE for K packets_KI.e. the sum of the squares of the dominant distances of all non-centroid feature roots to the centroid feature root to which they belong.

2.9 in the range that K is more than or equal to 2 and less than or equal to N/2, continuously increasing the K value, and repeating the steps 2.1 to 2.8 until K exceeds the limit. At this time, the minimum value of the error square sum under different groups is determined to be SSE_MThen M packets are confirmed as the optimal packet cluster.

5. The parameter optimization criterion is calculated as follows:

the characteristic root clustering can know that the 1 st, 2 nd, i.e. N characteristic roots are clustered to different grouping groups₁..group_m..group_M，group_mThe total number of the corresponding feature roots is recorded as C_mThe ith feature root belongs to group_mCan be expressed as lambda_i∈group_m.

For group_mSetting gamma_mAs the imaginary part weight, the optimization criterion corresponding to the group is attributed to group_mIs a function F between the mean of the real part variations and the imaginary part variations of all the feature roots_m：

Wherein: if | ω_i|>|ω^o _i|,Δω^* _i＝|Δω_iElse Δ ω^* _i＝-|Δω_i|，Δσ_i＝σ_i-σ^o _i；Δω_i＝ω_i-ω^o _i；

Therefore, ω_iIs the ith characteristic root lambda_iImaginary part of, Δ ω_iIs the ith characteristic root lambda_iChange of imaginary part of, Δ ω^* _iAre intermediate variables with no specific physical meaning.

The simple optimization criterion F of the system as a whole can be described as:

F＝F₁+..+F_m+..+F_M

the complex optimization criterion of the whole system can be described as follows:

F＝F₁/β₁+..+F_m/β_m+..+F_M/β_M

wherein, the setting is 1/β_mTo be group_mβ_mTo be group_mAverage of the distances from each other group.

And n ≠ m, n represents a variable; f₁To be group₁Function of (A), F_mTo be group_mFunction F of_MTo be group_MAs a function of (c).

l_mnIs defined as group_mGrouping internal feature root and group_nThe largest dominant distance between characteristic roots in the grouping, n and m are variables, and the alternating current-direct current power distribution network can provide an effective technical means for flexible access and safe operation control of a large number of renewable energy sources in the future, and is an important development direction in the future. The integrated coordination among the multiple variable current devices such as the alternating current and direct current source, the load, the storage and the like becomes one of important functions of the operation of the alternating current and direct current power distribution network, the parameter coordination among the multiple variable current systems is optimized, and the overall operation performance is further improved. Therefore, the invention provides a system parameter optimal configuration method for multi-device integration of an alternating current-direct current power grid, fills the technical blank, and has wide development and application prospects.

The above examples are provided only for the purpose of describing the present invention, and are not intended to limit the scope of the present invention. The scope of the invention is defined by the appended claims. Various equivalent substitutions and modifications can be made without departing from the spirit and principles of the invention, and are intended to be within the scope of the invention.

Claims

1. A system parameter optimal configuration method for multi-device integration of an alternating current-direct current power grid is characterized by comprising the following steps: the method comprises the following steps:

initializing parameters of a system to be optimized integrated by multiple devices of an alternating current-direct current power grid to obtain initial characteristic values, wherein the initial characteristic values are N initial characteristic roots in a matrix corresponding to the parameters to be optimized;

based on the initial characteristic value, monotonically increasing or decreasing the parameter to be optimized;

classifying all characteristic roots through a clustering algorithm on the basis of the dominant distance matrix, providing a corresponding limited range for determining parameter optimization criteria, and obtaining optimized system parameters by searching for the optimal parameter optimization criteria;

in the third step, the sensitivity matrix is generated as follows:

(1) after a certain parameter of the system is changed, the system state matrix A is updated, the system state matrix A is solved, and N characteristic roots are obtained, wherein the 1 st, 2 nd, i. Lambda [ alpha ]_i＝σ_i+jω_i；

(2) Calculating the real part and imaginary part change quantity of the 1,2.. i.. N characteristic roots, namely delta sigma_i＝σ_i-σ^o _i；Δω_i＝ω_i-ω^o _i(ii) a Wherein the superscript o denotes the initial value, σ denotes the real part, ω denotes the imaginary part;

(3) calculating the 1,2.. i.. N characteristic rootsChange amount if Δ σ_i<0 is: delta lambda_i＝-1*sqrt((Δσ_i)²+(Δω_i)²) Otherwise Δ λ_i＝sqrt((Δσ_i)²+(Δω_i)²)；

(4) According to Δ λ₁，Δλ₂..Δλ_i，Δλ_j..Δλ_NGenerating a sensitivity matrix η_N*NWherein the sensitivity is η_ij＝Δλ_i/Δλ_j。

2. The method for optimizing and configuring system parameters for multi-device integration of the alternating current-direct current power grid according to claim 1, wherein the method comprises the following steps: in the first step, the initialization process is as follows:

(2) solving the A matrix to obtain N characteristic roots, wherein the 1 st, 2.. i.. N characteristic roots are expressed as: lambda [ alpha ]^o _i＝σ^o _i+jω^o _iWhere the superscript o denotes the initial value, σ denotes the real part and ω denotes the imaginary part.

3. The method for optimizing and configuring system parameters for multi-device integration of the alternating current-direct current power grid according to claim 1, wherein the method comprises the following steps: in the fourth step, the dominant distance omega between the characteristic roots is solved according to the following formula_ij，

Ω_ij＝sqrt((η_i1-η_j1)²+(η_i2-η_j2)²+…+(η_iN-η_jN)²)/N。

4. The method for optimizing and configuring system parameters for multi-device integration of the alternating current-direct current power grid according to claim 1, wherein the method comprises the following steps: in the fifth step, the clustering algorithm adopts a K grouping clustering algorithm, and is specifically realized as follows:

setting the needed characteristic root cluster as K groups, wherein K is more than or equal to 2 and less than or equal to N/2;

(1) searching for dominant distance matrix omega line by line_N*NCorresponds to Ω_abAnd the position where the minimum min of non-zero values occurs for the first time is Ω_cd：

(2) If K is 2, determine λ_a,λ_c2 centroid feature roots when K is 2; if K is>2, dividing max and min into K-1 equal parts, determining corresponding K-2 equal division point values, and searching omega line by line_N*NWhere i ≠ a, c is the omega nearest to the value of each bisector_ijThe first position of occurrence, noted Ω_ef,…,Ω_xyK-2 in total, determining lambda_a,λ_c,λ_e…λ_xIs k>K centroid feature roots at 2;

(3) analyzing the ith characteristic root of the non-centroid characteristic root, namely i ≠ a, c, e_ia,Ω_ic,Ω_ie…Ω_ixJudging the subscript corresponding to the minimum value, and if the subscript is ic, determining lambda_iClustering to lambda_cAnd so on;

(4) repeating the step (3) until all the characteristic root clustering is completed;

(5) for K groups, calculating the average value of the dominant distances between all the non-centroid feature roots and the centroid feature roots in each group, searching the feature root of which the dominant distance between the feature root and the centroid in each group is closest to the value, recording as a new centroid feature root of each group, and expressing as lambda_a1,λ_c1,λ_e1…λ_x1；

(6) Analyzing the ith feature root of the non-centroid feature roots, i.e. i ≠ a1, c1, e1., and respectively comparing the ith feature root with the dominant distances omega of the K centroid feature roots_ia1,Ω_ic1,Ω_ie1…Ω_ix1Judging the subscript corresponding to the minimum value, and if the subscript is ie1, then converting lambda into_iClustering to lambda_e1；

(7) Repeating the step (6) until all the characteristic root clustering is completed;

(8) if the clustering result is not changed from the last clustering result, ending the feature root clustering, otherwise, repeating the steps (5) - (7) until the clustering result is changed from the last clustering resultThe secondary clustering result is unchanged, and the feature root clustering is ended; computing sum of squared errors SSE for K packets_KThe sum of squares of the dominant distances of all the non-centroid feature roots and the centroid feature root to which the non-centroid feature roots belong;

(9) within the range that K is more than or equal to 2 and less than or equal to N/2, continuously increasing the value of K, repeating the steps (1) to (8) until K exceeds the limit, and judging the minimum value SSE of the error square sum under different groups at the moment_MThen M packets are confirmed as the optimal packet cluster.

5. The method for optimizing and configuring system parameters for multi-device integration of the alternating current-direct current power grid according to claim 1, wherein the method comprises the following steps: in the fifth step, the parameter optimization criterion is calculated as follows:

(1) feature root clustering the 1 st, 2.. i.. N feature roots are clustered into different grouping groups₁..group_m..group_M，group_mThe total number of the corresponding feature roots is recorded as C_mThe ith feature root belongs to group_mIs denoted by λ_i∈group_m，

(2) For packet group_mSetting gamma_mAs the imaginary part weight, the optimization criterion corresponding to the group is attributed to group_mIs a function F between the mean of the real part variations and the imaginary part variations of all the feature roots_m：

Wherein: if | ω_i|>|ω^o _i|,Δω^* _i＝|Δω_iElse Δ ω^* _i＝-|Δω_i|

The simple optimization criterion F of the whole system is described as follows:

F＝F₁+..+F_m+..+F_M

the complex optimization criterion of the whole system is described as follows:

F＝F₁/β₁+..+F_m/β_m+..+F_M/β_M

wherein, the setting is 1/β_mTo be group_mβ of the global weight_mTo be group_mThe average of the distances from each of the other groups,

n belongs to M and n is not equal to M

l_mnIs defined as group_mGrouping internal feature root and group_nThe largest dominant distance between feature roots within a group.