CN111327028B - Method for realizing protection constant value setting calculation under different topologies by utilizing K-Means clustering - Google Patents

Method for realizing protection constant value setting calculation under different topologies by utilizing K-Means clustering Download PDF

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CN111327028B
CN111327028B CN202010255908.2A CN202010255908A CN111327028B CN 111327028 B CN111327028 B CN 111327028B CN 202010255908 A CN202010255908 A CN 202010255908A CN 111327028 B CN111327028 B CN 111327028B
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陈朝晖
漆家炜
张静伟
张弛
郑茂然
李捷
田德良
李银红
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China Southern Power Grid Co Ltd
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Abstract

The invention discloses a method for realizing setting calculation of protection setting values under different topologies by utilizing K-Means clustering, and belongs to the field of relay protection setting calculation of power systems. The method comprises the steps of firstly, acquiring data such as load current of each branch circuit, short-circuit current of each protection outlet, general action time delay and the like under different topological operation of a power system; then, respectively clustering all protection clusters and all topologies by utilizing a K-Means algorithm to obtain the number of sets of fixed values required by each protection and the topology governed by each set of corresponding fixed values; and finally, solving by using the conventional linear programming algorithm to obtain the constant values of all the protection constant value areas. The method and the device can determine the number of the optimal constant value areas required by each protection according to the self-adaptive characteristics of the protection, and can ensure the minimum number of the constant value areas in the whole network while meeting the constant value performance requirements, thereby reducing the misoperation risk, reducing the operation and maintenance workload and ensuring the safe and economic operation of the power grid.

Description

Method for realizing protection constant value setting calculation under different topologies by utilizing K-Means clustering
Technical Field
The invention belongs to the field of relay protection setting calculation of a power system, and particularly relates to a method for realizing setting calculation of protection setting values under different topologies by utilizing K-Means clustering.
Background
The inverse time-limit overcurrent protection is widely applied to domestic and foreign power transmission and distribution networks at present due to the simple realization of the principle and low cost. In order to ensure system reliability, the overcurrent protection installed on the transmission line and the protection at the upstream of the transmission line usually form a main backup protection group. When a power grid transmission line has a fault, the main protection quickly acts on the corresponding circuit breaker to trip off the fault line, and once the main protection acts according to various reasons, the backup protection is started to replace the action of the main protection to realize effective isolation of a fault area. In order to realize the coordination, a short time delay, namely a set time level difference, is bound to exist between the main backup protection groups. Therefore, the power system relay protection setting calculation determines the main backup protection action sequence among all protection groups under the constraint of the given setting time level difference.
The power system is a real-time dynamic system, and network topology changes, that is, the operation mode changes, often occur due to steady-state operation requirements or transient system faults. The protection polarity of the new equipment is not subjected to polarity test, no reliable main protection exists, and the operation mode of the power grid is changed at multiple ends in the starting process of the new equipment, so that faults can be quickly and reliably removed in various modes. In order to adapt to different topologies of the operation of the power grid, all possible operation modes must be considered during the relay protection setting calculation, so that the protection can accurately act without errors once faults occur in various operation modes of the power grid.
Currently, protection devices are almost completely entering the era of microcomputer protection, and digital overcurrent is widely used. The digital overcurrent device allows a user to set a plurality of fixed values in advance in the device so as to adapt to different operation modes of the power grid. However, the number of sets of fixed values provided by the device is extremely limited, far from the number of different topologies of the grid. At present, the finite fixed value area provided by a microcomputer protection device is utilized to realize the protection setting coordination under different topologies of a power grid. However, the current research neglects the self-adaptive protection characteristic, the number of the total constant value areas of the whole network is large, the misoperation risk is potentially increased, the operation and maintenance workload is increased, and the safe and economic operation of the power grid is not facilitated.
Disclosure of Invention
Aiming at the defects or improvement requirements of the prior art, the invention provides a method for realizing protection constant value setting calculation under different topologies by utilizing K-Means clustering, and aims to solve the technical problems of misoperation risk increase and operation and maintenance workload increase caused by neglecting the adaptive characteristic of protection in the setting calculation under different topologies of the existing digital overcurrent protection.
In order to achieve the purpose, the invention provides a method for realizing the setting calculation of protection fixed values under different topologies by utilizing K-Means clustering, which comprises the following steps:
s1: carrying out power grid load flow calculation and three-phase symmetrical short circuit fault calculation under various topologies to be considered, and obtaining load current matrix of each branch circuit of the power system under different topological operation modes
Figure BDA0002437303920000021
Short-circuit current matrix for each protection outlet
Figure BDA0002437303920000022
And protecting the generic action delay matrix
Figure BDA0002437303920000023
And the like, wherein m is the total number of topologies, b is the total number of branches, n is the total number of protections,
Figure BDA0002437303920000024
the load current element in the ith row and the jth column of the load current matrix,
Figure BDA0002437303920000025
is a short-circuit current element of the ith row and the jth column in the short-circuit current matrix, tijFor the protection general action delay element in the ith row and jth column in the general action delay matrix,
Figure BDA0002437303920000026
representing a real space;
s2: the short-circuit current matrix I obtained according to step S1FClustering all protections by using a K-Means algorithm to obtain a protection cluster needing to be configured with K sets of definite values
Figure BDA0002437303920000027
K, K is the maximum fixed value zone number allowed to be configured by the digital overcurrent protection device;
s3: the protection general action time delay matrix T obtained according to the step S1GIn each protection cluster by using K-Means algorithm
Figure BDA0002437303920000028
Network topology clustering is carried out to obtain topology clusters which are configured with k sets of fixed values and protect the governed area of each fixed value area
Figure BDA0002437303920000029
S4: and (4) establishing an overcurrent protection optimization setting calculation model, and solving by utilizing a linear programming algorithm to obtain the constant values of all the constant value regions to be protected by combining the data obtained in the steps S1, S2 and S3.
Preferably, the obtaining of the protection general action time delay matrix T in step S1GThe method specifically comprises the following steps:
s1.1: selecting each over-current protection starting current constant value I according to the principle that the protection starting current is slightly larger than the maximum load currentPiThe expression is as follows:
Figure BDA00024373039200000210
wherein i is a protection number, KrelFor a reliability factor, KrelTaking 1.10-1.30;
s1.2: let all protection time constant value TDS be unit 1, i.e. TDSi＝1；
S1.3: and (3) calculating the general action time of each protection under each topology by combining the short circuit current matrix data to form a general action time delay matrix, wherein the calculation formula is as follows:
Figure BDA00024373039200000211
wherein TDSiAnd IPiRespectively, the time constant value and the starting current constant value of the protection i.
Preferably, the step of performing protected clustering by using the K-Means algorithm in step S2 specifically includes:
s2.1: Min-Max standardization processing is carried out on the short-circuit current matrix to ensure that the element range is [0,1 ]]The normalized formula is:
Figure BDA0002437303920000031
wherein X is the original data of the outlet short-circuit current of each protection under all topologies, namely a matrix IFIs represented as a column vector of
Figure BDA0002437303920000032
Figure BDA0002437303920000033
The column vector being formed for normalized short-circuit current data, i.e.
Figure BDA0002437303920000034
S2.2: selecting a protection adaptability index RAiTo preserve clustering index, RAiDefined as the ripple rate of the fault current flowing through each protection under all topologies, i.e.:
Figure BDA0002437303920000035
wherein
Figure BDA0002437303920000036
S2.3: data [ RA ] using K-Means algorithm1,RA2,...,RAn]Clustering is performed to protect the number of classes
Figure BDA0002437303920000037
The maximum number of constant value zones K allowed to be configured for the digital overcurrent protection device, i.e. K
Figure BDA0002437303920000038
Preferably, the step of topological clustering in step S3 specifically includes:
s3.1: selecting motion time mean MVjFor topological clustering index, MVjDefined as the mean of all protection general action delays under each topology, i.e.:
Figure BDA0002437303920000039
s3.2: at each protection cluster
Figure BDA00024373039200000310
In the method, data [ MV ] is subjected to K-Means algorithm1,MV2,...,MVm]Clustering, number of topological classes
Figure BDA00024373039200000311
The number of constant value zones k to be configured for the protection cluster, i.e.
Figure BDA00024373039200000312
Preferably, the step of establishing the overcurrent protection optimization setting calculation model in step S4 specifically includes:
s4.1: selecting an objective function as the minimum sum of the action time of all main protections of the whole network under all topologies, namely:
Figure BDA00024373039200000313
wherein t isijThe action time for protection has an action characteristic of a general inverse time-limit time-current curve, namely:
Figure BDA00024373039200000314
s4.2: determining an overcurrent protection setting matching principle under multi-topology: the upper and lower protection level difference constraints are satisfied, namely:
Figure BDA00024373039200000315
g belongs to G; wherein (t)p)g、
Figure BDA00024373039200000316
Respectively representing a main protection p and a backup protection b thereofxIn the action time under the topology g, CTI is the level difference, and is generally 0.3-0.5 s; omegagAll protection coordination group sets under the topology g are provided, and omega is the protection coordination group set under all the topologies; g is the set of all considered topologies;
s4.3: setting boundary constraints of the decision variable TDS, i.e.
Figure BDA00024373039200000317
Wherein
Figure BDA00024373039200000318
Figure BDA00024373039200000319
The lower limit and the upper limit of the time constant of protection i are respectively taken
Figure BDA00024373039200000320
S4.4: the starting current constant value of each over-current protection is selected according to the principle that the protection starting current is slightly larger than the maximum load current, namely
Figure BDA0002437303920000041
Wherein KrelTaking 1.10-1.30;
compared with the prior art, the technical scheme of the invention has the following beneficial effects: the invention considers the adaptability of each protection to the topology, obtains the optimal number of constant value areas required by each class of protection according to the self-adaptive characteristic of the protection, further realizes that the topology clustering determines the topology governed by each set of constant value of the protection, finally establishes an overcurrent protection optimization setting calculation model, and obtains the constant values of each constant value area of all the protections by utilizing the linear programming algorithm, and the solved result is more favorable for various topology operation requirements of the actual power system. The invention considers the different adaptability of the protection to the topology and can ensure that the number of the fixed value areas which are most suitable for each protection is obtained, thereby ensuring the optimal total number of the fixed value areas of the whole network, further effectively reducing the misoperation risk, reducing the operation and maintenance workload and ensuring the safe and economic operation of the power grid.
Drawings
FIG. 1 is a schematic flow chart of a method for realizing protection constant value setting calculation under different topologies by using K-Means clustering according to the present invention;
FIG. 2 is a schematic flow chart of protective clustering using a K-Means algorithm according to an embodiment of the present invention;
FIG. 3 is a schematic flow chart of topology clustering using the K-Means algorithm according to the embodiment of the present invention;
fig. 4 is a schematic diagram of a protection clustering result provided in the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features according to the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
As shown in fig. 1, the method for realizing the protection fixed value setting calculation under different topologies by using K-Means clustering specifically comprises the following steps:
s1: carrying out power grid load flow calculation and three-phase symmetrical short circuit fault calculation under various topologies to be considered, and obtaining load current matrix of each branch circuit of the power system under different topological operation modes
Figure BDA0002437303920000042
Short-circuit current matrix for each protection outlet
Figure BDA0002437303920000043
And protecting the generic action delay matrix
Figure BDA0002437303920000044
And the like, wherein m is the total number of topologies, b is the total number of branches, n is the total number of protections,
Figure BDA0002437303920000045
the load current element in the ith row and the jth column of the load current matrix,
Figure BDA0002437303920000046
is a short-circuit current element of the ith row and the jth column in the short-circuit current matrix, tij is a protection general action delay element in the ith row and the jth column in the general action delay matrix,
Figure BDA0002437303920000047
representing a real space; further, in this step, the time delay matrix T for obtaining and protecting the general action is obtainedGThe method specifically comprises the following steps:
s1.1: selecting each over-current protection starting current constant value I according to the principle that the protection starting current is slightly larger than the maximum load currentPiThe expression is as follows:
Figure BDA0002437303920000051
wherein i is a protection number, KrelFor a reliability factor, KrelTake 1.10-1.30, in this example, take Krel1.20; specifically, m times of load flow calculation are carried out on m topologies to obtain m load currents of each branch, and then the maximum load current is taken and multiplied by a reliability coefficient KrelNamely the protection starting current of the branch circuit; in addition, for directional overcurrent protection configured at two ends of the line, load current values at two ends of each branch circuit need to be respectively read according to current directions, and then starting current values for protection at two ends of the line can be obtained according to the steps.
S1.2: let all protection time constant value TDS be unit 1, i.e. TDS i1 is ═ 1; in particular, timeThe constant value itself is a protection constant value to be solved, and in order to obtain a protection action time characteristic for subsequent topological clustering, it is assumed here that all the protected time constant values all take a unit of 1.
S1.3: and (3) calculating the general action time of each protection under each topology by combining the short circuit current matrix data to form a general action time delay matrix, wherein the calculation formula is as follows:
Figure BDA0002437303920000052
wherein TDSiAnd IPiRespectively setting the time and the starting current of the protection i; specifically, according to the protection starting current fixed value and the time fixed value obtained in the steps S1.1 and S1.2, the fault current flowing through the protection at the three-phase short-circuit fault of the line outlet under all topologies is combined and substituted into the calculation formula, so that the general action delay matrix is obtained.
S2: the short-circuit current matrix I obtained according to step S1FClustering all protections by using a K-Means algorithm to obtain a protection cluster needing to be configured with K sets of definite values
Figure BDA0002437303920000053
K, K is the maximum fixed value zone number allowed to be configured by the digital overcurrent protection device; specifically, the flow chart of the protected clustering process is shown in fig. 2. Further, the step of performing protected clustering by using the K-Means algorithm in this step specifically includes:
s2.1: Min-Max standardization processing is carried out on the short-circuit current matrix to ensure that the element range is [0,1 ]]The normalized formula is:
Figure BDA0002437303920000054
wherein X is the original data of the outlet short-circuit current of each protection under all topologies, namely a matrix IFIs represented as a column vector of
Figure BDA0002437303920000055
Figure BDA0002437303920000056
Is a standardThe column vector formed by the post-conversion short-circuit current data, i.e.
Figure BDA0002437303920000057
Specifically, because the positions of different protections are different and the operation modes of power grids under different topologies are different, the fault currents measured by the protections are different in size, so that the minimax standardization is performed on the outlet fault current values of all the protections under all the topologies to facilitate the subsequent quantitative comparison and analysis under the same dimensionality, and the range of the obtained fault currents is [0,1]Internal fault current data. In addition, the Min-Max normalization belongs to one of linear transformations, and does not change the distribution characteristics of the original data.
S2.2: selecting a protection adaptability index RAiTo preserve clustering index, RAiDefined as the ripple rate of the fault current flowing through each protection under all topologies, i.e.:
Figure BDA0002437303920000061
wherein
Figure BDA0002437303920000062
In particular, RAiThe ratio of the variance to the mean value of the fault current of each protection under all topologies, namely the variation coefficient in the mathematical sense, is expressed, the fluctuation rate of the group of fault currents is measured, and the adaptability of the protection to all topologies is reflected. For different protections, RAiIs also different according to RAiAnd clustering the protection, and dividing the protection with similar adaptive characteristics into the same protection cluster. In addition, RAiSize is a depiction of protection compliance, RAiSmaller means less fault current variation in all topologies, and thus fewer fixed value regions can be configured to meet operational requirements, and conversely, for RAiThe larger the size, the more constant value regions need to be configured for protection to fully cope with the topology changes.
S2.3: data [ RA ] using K-Means algorithm1,RA2,...,RAn]Clustering is performed to protect the number of classes
Figure BDA0002437303920000063
The maximum number of constant value zones K allowed to be configured for the digital overcurrent protection device, i.e. K
Figure BDA0002437303920000064
Specifically, one-dimensional data [ RA ]1,RA2,...,RAn]And the number of classes to be clustered
Figure BDA0002437303920000065
Inputting into a K-Means solver to obtain
Figure BDA0002437303920000066
A protection cluster, i.e. [ RA ]1,RA2,...,RAn]According to data size division
Figure BDA0002437303920000067
And (4) class. In addition, for the number of classes of the cluster, the actual situation needs to be considered, that is, the maximum number of fixed value regions allowed to be configured by the protection device is considered.
S3: the protection general action time delay matrix T obtained according to the step S1GIn each protection cluster by using K-Means algorithm
Figure BDA0002437303920000068
Network topology clustering is carried out to obtain topology clusters which are configured with k sets of fixed values and protect the governed area of each fixed value area
Figure BDA0002437303920000069
Specifically, the flow chart of the protected clustering process is shown in fig. 3. Further, the step of topological clustering in this step specifically includes:
s3.1: selecting motion time mean MVjFor topological clustering index, MVjDefined as the mean of all protection general action delays under each topology, i.e.:
Figure BDA00024373039200000610
in particular, all protections under different topologiesThe action time is different. Action time mean level of all protections under different topologies describes the severity of the various topologies, more specifically the MVjThe smaller the value, the more severe the topology is, the greater the impact on the power system when a fault occurs, the shorter the protection is required to act to remove the fault, and conversely, the MVjThe larger the value is, the more slight the fault occurs in the topology, and no higher requirement is made on the protection action. Thus, MVs according to all topologiesjThe value clusters the topology, and the topology with similar severities can be regarded as one class, so that only one set of definite value can be used for protection.
S3.2: at each protection cluster
Figure BDA0002437303920000071
In the method, data [ MV ] is subjected to K-Means algorithm1,MV2,...,MVm]Clustering, number of topological classes
Figure BDA0002437303920000072
The number of constant value zones k to be configured for the protection cluster, i.e.
Figure BDA0002437303920000073
Specifically, in practical engineering, the number of constant value areas provided by the protection device is extremely limited, and it is impossible to satisfy a mode that a set of constant values corresponds to a topology, so that by adopting topology clustering, the number of selected classes in the topology clustering is equal to the set of constant values that the cluster protection needs to be configured, that is, each set of constant values corresponds to a topology cluster. After topological clustering is adopted, a protection cluster needing to be configured with k sets of definite values is obtained
Figure BDA0002437303920000074
Each constant value area of the topology cluster
Figure BDA0002437303920000075
S4: and (4) establishing an overcurrent protection optimization setting calculation model, and solving by utilizing a linear programming algorithm to obtain the constant values of all the constant value regions to be protected by combining the data obtained in the steps S1, S2 and S3. Further, the step of establishing the overcurrent protection optimization setting calculation model in this step specifically includes:
s4.1: selecting an objective function as the minimum sum of the action time of all main protections of the whole network under all topologies, namely:
Figure BDA0002437303920000076
wherein t isijThe action time for protection has an action characteristic of a general inverse time-limit time-current curve, namely:
Figure BDA0002437303920000077
specifically, in the overcurrent protection setting calculation, the protection quick-acting performance is used as a target function of a model, and the constraint of protection sensitivity and selectivity is realized through constraint conditions, so that a protection constant value meeting the actual operation requirement is calculated. In addition, referring to the common overcurrent protection characteristic of international standard, a general inverse time-current curve is selected as the overcurrent protection characteristic curve.
S4.2: determining an overcurrent protection setting matching principle under multi-topology: the upper and lower protection level difference constraints are satisfied, namely:
Figure BDA0002437303920000078
g belongs to G; wherein (t)p)g、
Figure BDA0002437303920000079
Respectively representing a main protection p and a backup protection b thereofxIn the action time under the topology g, CTI is the level difference, and is generally 0.3-0.5 s; omegagAll protection coordination group sets under the topology g are provided, and omega is the protection coordination group set under all the topologies; g is the set of all considered topologies; specifically, traversing the relation of a main backup protection group for each topology, and calculating the constraint conditions of the upper and lower stage protection action time according to the fault current flowing through the main backup protection to obtain the constraint conditions of overcurrent protection setting matching with all the stage differences under multiple topologies.
S4.3: setting boundary constraints of the decision variable TDS, i.e.
Figure BDA00024373039200000710
Wherein
Figure BDA00024373039200000711
Figure BDA00024373039200000712
The lower limit and the upper limit of the time constant of protection i are respectively taken
Figure BDA00024373039200000713
Specifically, the fixed value obtained by only solving from the mathematical theory does not necessarily meet the actual engineering requirements, so the range of the fixed value to be obtained needs to be limited reasonably, and the upper limit and the lower limit of each protected time fixed value are set respectively by combining a large amount of industry research.
S4.4: the starting current constant value of each over-current protection is selected according to the principle that the protection starting current is slightly larger than the maximum load current, namely
Figure BDA00024373039200000714
Wherein KrelTaking 1.10-1.30, in this embodiment, KrelTake 1.20. Specifically, the protection starting current fixed value and the time fixed value both belong to fixed value parameters needing setting calculation for inverse time-limited overcurrent protection, and after the starting current fixed value is selected according to the principle that the protection starting current is slightly larger than the maximum load current, the time fixed value can be taken as a decision variable to be considered, and the overcurrent protection setting calculation model is simplified into a linear programming model to be solved.
The invention solves the overcurrent protection optimization setting calculation model established from S4.1 to S4.4 by using a linear programming algorithm to obtain the constant values of all the constant value regions, and specifically comprises the following steps:
s4.5: calculating a target function coefficient vector according to the overcurrent protection optimization setting calculation model established from S4.1 to S4.4
Figure BDA0002437303920000081
WhereinNSGTo preserve the total number of constant value regions, any element f in the vector fl(1≤l≤NSG) Sequentially arranging the k-th constant value area of the ith protection according to the sequence of the k-th constant value area of the ith protection, wherein the calculation formula is
Figure BDA0002437303920000082
S4.6: according to the overcurrent protection optimization setting calculation model established from S4.1 to S4.4, an inequality constraint coefficient matrix is calculated
Figure BDA0002437303920000083
Wherein N ispbFor the total constraint number of the upper and lower protection level differences, two element calculation formulas corresponding to the main protection p and the corresponding backup protection b in any row of the matrix A are respectively
Figure BDA0002437303920000084
Figure BDA0002437303920000085
S4.7: according to the overcurrent protection optimization setting calculation model established from S4.1 to S4.4, an inequality constraint constant vector is calculated
Figure BDA0002437303920000086
Any element b in vector blThe calculation formula is bl＝-CTI。
S4.8: calculating a lower constant vector of a decision variable according to the overcurrent protection optimization setting calculation model established from S4.1 to S4.4
Figure BDA0002437303920000087
And
Figure BDA0002437303920000088
any element lb in vector lblThe calculation formula is lbl＝TDSminAny element ub in the vector ublThe calculation formula is ubl＝TDSmax。
S4.9: selecting a fixed time value to be used as the time value according to the data obtained from S4.5 to S4.8As decision variables
Figure BDA0002437303920000089
Calling the linprog function in MATLAB, i.e., using x ═ linprog (f, A, b, etc],[]The lb, ub statement finds x, where]"denotes an empty set, i.e. the respective fixed value TDS of each protected respective fixed value area.
The invention will now be described in detail with reference to specific examples as follows:
the method for realizing the Setting calculation of the protection fixed value under Different topologies by using K-Means Clustering provided by the invention carries out method verification on a modified IEEE14 node system, and a system wiring diagram and related network parameters are disclosed in the document (Ojaghi M, Mohammadi V.use of Clustering to Reduce the Number of differential Setting Groups for Adaptive coding of inverse Current claims [ J ]. IEEE Transactions on Power Delivery, 2018, 33 (3): 1204 1212.). The verification result shows that: the method for solving the overcurrent protection constant value can meet the constant value performance requirement and simultaneously can ensure the minimum number of constant value areas of the whole network, thereby reducing the misoperation risk and reducing the operation and maintenance workload.
The digital overcurrent protection multi-constant-value-region setting calculation analysis of the power grid N-1 topology is realized by utilizing K-Means clustering. The protection relays are numbered as protection devices 1 to 39, respectively, with reference to 39 protection relays installed in the IEEE14 node system of the above-mentioned document. Considering N-1 emergency analysis, the obtained topology set of possible operation of the power grid comprises 21 topologies which are respectively numbered from topology #1 to topology #21 under the conditions that 16 branches respectively fail and exit from operation, 2 transformers (T21 and T31) respectively fail and exit from operation, 2 generators (G11 and G21) respectively fail and exit from operation and all elements normally operate. Taking the maximum 4 constant value regions allowed to be configured by the protection device as an example, the steps S1-S4 according to the method of the present invention perform constant value setting calculation to obtain the clustered protection clusters and the number of the constant value regions to be configured, and the topology clusters governed by each constant value region, and the detailed results are shown in table 1.
As can be seen from table 1, after protection clustering is performed, 4 classes of protection clusters that need to be configured with 1-4 constant value regions, each class has 1, 26, 9, and 3 protections, and total 39 digital overcurrent protections. And then carrying out topology clustering in each type of protection cluster to respectively obtain the topology type governed by the constant value region configured for each protection cluster, namely the last column of data in the table 1.
In this embodiment, the clustering result of the protection using the K-Means algorithm according to the steps of the present invention is shown in fig. 4. FIG. 4 shows that the adaptability of each protection to different topologies is different, and clustering is used so that the protections with similar protection adaptability form a cluster; and for the cluster with a smaller RA value, only a few constant value areas need to be configured for protection, and as the RA value increases, the number of the configured constant value areas also increases correspondingly. According to the results shown in table 1, in this embodiment, the total protection fixed value area number of the whole network is 92.
TABLE 1 protective clustering and topological clustering results
Figure BDA0002437303920000091
Figure BDA0002437303920000101
According to the protection clustering and topological clustering results, a setting calculation model is established according to the step S4 of the invention to carry out constant value optimization calculation, and the obtained time constant values of each protection are shown in the last four columns in the table 2. The "-" in the table indicates no definite value in the definite value area.
Meanwhile, in order to further illustrate the technical superiority of the present invention, three schemes are provided in the embodiments of the present invention for comparison:
scheme a: all protection is considered to be configured with 1 constant value area for setting calculation;
scheme B: all protection considers configuring 4 constant value areas for setting calculation;
scheme C: all the protections adopt the method of the invention to determine a protection constant value area for setting calculation;
the calculation results of the protection time fixed value setting under the three schemes are shown in table 2, wherein the last two rows of the table respectively give the number of the areas after the TDS and the total fixed value under the three schemes. It should be noted that, since the schemes B and C are not a constant value area, it is meaningless to directly add all TDSs compared with the scheme a, so the TDSs protected by each of the schemes B and C are weighted and summed according to the number of topology in jurisdiction to obtain the sum of the TDSs. As can be seen from table 2, the number of each protection constant value region in the scheme C is consistent with the number of the constant value regions after the previous protection clustering. Meanwhile, compared with the scheme A, the scheme B has the advantages that after the technology of a plurality of constant value areas is adopted, the sum of the constant values of the overcurrent protection time of the whole network is greatly reduced, the reduction proportion reaches 55.434%, and the protection constant value performance is greatly improved. But the number of the fixed value areas increases with the increase of 4 times.
Further, according to the result of the scheme C, it can be seen that, by adopting the technical scheme provided by the present invention, the sum of the protection time setting values is almost equivalent to that of the scheme B in which all the protections are configured with 4 setting value regions, and is increased by only 15.47%, but the sum of the number of the setting value regions of all the protections is reduced by 69.57% compared with the scheme B. The method can ensure that the number of the fixed value areas which are most suitable for each protection is obtained, so that the optimal total number of the fixed value areas of the whole network is ensured while the protection fixed value performance is met, the misoperation risk is effectively reduced, the operation and maintenance workload is reduced, and the safe and economic operation of the power grid is ensured. The calculation result is more beneficial to various topological operation requirements of the actual power system.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
TABLE 2 fixed value setting calculation results of protection time under three schemes
Figure BDA0002437303920000102
Figure BDA0002437303920000111
。
The invention provides a method for realizing setting calculation of protection setting values under different topologies by utilizing K-Means clustering in consideration of different protection adaptability to various topologies. The method comprises the steps of firstly obtaining data such as load current of each branch circuit, short-circuit current of each protection outlet, general action time delay and the like under different topological operation of the power system. Secondly, clustering all protection clusters and all topologies respectively by utilizing a K-Means algorithm to obtain the number of sets of fixed values required by each protection and the topology governed by each set of corresponding fixed values. And finally, establishing an overcurrent protection optimization setting calculation model, and solving by using the conventional linear programming algorithm to obtain the fixed values of all the protected fixed value areas. The invention considers the different adaptability of the protection to the topology and can ensure that the number of the fixed value areas which are most suitable for each protection is obtained, thereby ensuring the optimal total number of the fixed value areas of the whole network, further effectively reducing the misoperation risk, reducing the operation and maintenance workload and ensuring the safe and economic operation of the power grid.

Claims (7)

1. A method for realizing protection constant value setting calculation under different topologies by utilizing K-Means clustering is characterized by comprising the following steps:
s1: under various topological modes considered by the power system, load flow calculation and short-circuit fault calculation are carried out on the power system, and load current matrixes of all branches of the power system under different topological operation modes are obtained
Figure FDA0003488378160000011
Short-circuit current matrix for each protection outlet
Figure FDA0003488378160000012
And protecting the generic action delay matrix
Figure FDA0003488378160000013
Data, where m is the total number of topologies, b is the total number of branches, n is the total number of protections,
Figure FDA0003488378160000014
is the load currentThe load current element in row i and column j of the matrix,
Figure FDA0003488378160000015
is a short-circuit current element of the ith row and the jth column in the short-circuit current matrix, tijFor the protection general action delay element in the ith row and jth column in the general action delay matrix,
Figure FDA0003488378160000016
representing a real space;
s2: the short-circuit current matrix I obtained according to step S1FClustering all protections by using a K-Means algorithm to obtain a protection cluster needing to be configured with K sets of definite values
Figure FDA0003488378160000017
K, K is the maximum fixed value zone number allowed to be configured by the digital overcurrent protection device;
s3: the protection general action time delay matrix T obtained according to the step S1GIn each protection cluster by using K-Means algorithm
Figure FDA0003488378160000018
Network topology clustering is carried out to obtain topology clusters which are configured with k sets of fixed values and protect the governed area of each fixed value area
Figure FDA0003488378160000019
S4: and (4) establishing an overcurrent protection optimization setting calculation model, and solving by utilizing a linear programming algorithm to obtain the constant values of all the constant value regions to be protected by combining the data obtained in the steps S1, S2 and S3.
2. The setting calculation method according to claim 1, wherein the obtaining of the protection general action delay matrix T in step S1GThe method specifically comprises the following steps:
s1.1: selecting each over-current protection starting current according to the principle that the protection starting current is slightly larger than the maximum load currentFlow constant value IPiThe expression is as follows:
Figure FDA00034883781600000110
wherein i is a protection number, KrelFor a reliability factor, KrelTaking 1.10-1.30;
s1.2: let all protection time constant value TDS be unit 1, i.e. TDSi＝1；
S1.3: and (3) calculating the general action time of each protection under each topology by combining the short circuit current matrix data to form a general action time delay matrix, wherein the calculation formula is as follows:
Figure FDA0003488378160000021
wherein TDSiAnd IPiRespectively, the time constant value and the starting current constant value of the protection i.
3. The tuning calculation method according to claim 1, wherein the step of protecting the cluster in step S2 specifically includes:
s2.1: Min-Max standardization processing is carried out on the short-circuit current matrix to ensure that the element range is [0,1 ]]The normalized formula is:
Figure FDA0003488378160000022
wherein X is the original data of the outlet short-circuit current of each protection under all topologies, namely a matrix IFIs represented as a column vector of
Figure FDA0003488378160000023
Figure FDA0003488378160000024
The column vector being formed for normalized short-circuit current data, i.e.
Figure FDA0003488378160000025
S2.2: selecting a protection adaptability index RAiTo preserve clustering index, RAiDefined as the ripple rate of the fault current flowing through each protection under all topologies, i.e.:
Figure FDA0003488378160000026
wherein
Figure FDA0003488378160000027
S2.3: data [ RA ] using K-Means algorithm1,RA2,...,RAn]Clustering is performed to protect the number of classes
Figure FDA0003488378160000028
The maximum number of constant value zones K allowed to be configured for the digital overcurrent protection device, i.e. K
Figure FDA0003488378160000029
4. The tuning calculation method according to claim 1, wherein the step of topological clustering in step S3 specifically includes:
s3.1: selecting motion time mean MVjFor topological clustering index, MVjDefined as the mean of all protection general action delays under each topology, i.e.:
Figure FDA00034883781600000210
s3.2: at each protection cluster
Figure FDA00034883781600000211
In the method, data [ MV ] is subjected to K-Means algorithm1,MV2,...,MVm]Clustering, number of topological classes
Figure FDA00034883781600000212
The number of constant value zones k to be configured for the protection cluster, i.e.
Figure FDA00034883781600000213
5. The setting calculation method according to claim 1, wherein the step of establishing the overcurrent protection optimization setting calculation model in step S4 specifically includes:
s4.1: selecting an objective function as the minimum sum of the action time of all main protections of the whole network under all topologies, namely:
Figure FDA0003488378160000031
wherein t isijThe action time for protection has an action characteristic of a general inverse time-limit time-current curve, namely:
Figure FDA0003488378160000032
s4.2: determining an overcurrent protection setting matching principle under multi-topology: the upper and lower protection level difference constraints are satisfied, namely:
Figure FDA0003488378160000033
wherein (t)p)g、
Figure FDA0003488378160000034
Respectively representing a main protection p and a backup protection b thereofxIn the action time under the topology g, CTI is the level difference, and 0.3-0.5 s is taken; omegagAll protection coordination group sets under the topology g are provided, and omega is the protection coordination group set under all the topologies; g is the set of all considered topologies;
s4.3: setting boundary constraints of the decision variable TDS, i.e.
Figure FDA0003488378160000035
Wherein
Figure FDA0003488378160000036
Respectively setting a lower limit and an upper limit of a time constant value of the protection i;
s4.4: starting current slightly larger than maximum according to protectionThe high-load current principle selects the starting current constant value of each over-current protection, i.e.
Figure FDA0003488378160000037
Wherein KrelTaking 1.10-1.30.
6. The setting calculation method according to claim 5, characterized in that, taking
Figure FDA0003488378160000038
Figure FDA0003488378160000039
7. The setting calculation method according to claim 2 or 5, characterised in that K is KrelTake 1.20.
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