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CN112103950A - Power grid partitioning method based on improved GN splitting algorithm - Google Patents

Power grid partitioning method based on improved GN splitting algorithm Download PDF

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CN112103950A
CN112103950A CN202010895055.9A CN202010895055A CN112103950A CN 112103950 A CN112103950 A CN 112103950A CN 202010895055 A CN202010895055 A CN 202010895055A CN 112103950 A CN112103950 A CN 112103950A
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node
betweenness
active power
power
line
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CN112103950B (en
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段建东
王海峰
程文姬
薛冰
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Xian University of Technology
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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
    • 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
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
    • 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
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications

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Abstract

The invention discloses a power grid partitioning method based on an improved GN splitting algorithm, which comprises the following steps: simplifying the power network to obtain a topological structure; calculating the shortest path between nodes in the topological structure to obtain the shortest line between the nodes; calculating the active power betweenness and the voltage weighted edge betweenness of the shortest line between the nodes; weighting the active power betweenness and the line voltage weighting betweenness by using an analytic hierarchy process, and obtaining a two-factor comprehensive weighting betweenness through analytical calculation; and continuously removing the edge with the maximum number of the two-factor comprehensive weighted edges until the condition of partition ending is reached, and determining the community after the partition. The accuracy of power grid expression can be improved, the problem that the calculated amount is too large due to the fact that all nodes are divided into communities is avoided, and the nondeterministic polynomial problem in the process of searching the cut sets is prevented.

Description

Power grid partitioning method based on improved GN splitting algorithm
Technical Field
The invention belongs to the technical field of power grid partitioning methods, and relates to a power grid partitioning method based on an improved GN splitting algorithm.
Background
In the development process of the power system, in order to ensure the economic requirement and the increase of the power load, the power system often needs to construct a power grid with a higher voltage level to deliver more power. At present, domestic and foreign power grids mostly present an operation mode of multi-voltage-level and partition interconnection, so that the problems of exceeding short-circuit current and the like under the existing voltage level are increasingly highlighted, and the safe and stable operation of the system is endangered. The purpose of partitioning the power grid is to facilitate control and management of the power grid of each region, the power grid after partitioning has the characteristics that the connection degree between the interiors of all the partitions is close, and the connection between the partitions is weak, so that the control on the interiors of all the partitions cannot cause great influence on the outside. Therefore, the reasonable partitioning of the power grid is a key measure for ensuring the safe operation and the effective control of the system.
At present, the method for partitioning the power grid at home and abroad mainly comprises the following steps: (1) and constructing vector type transient voltage characteristics of the nodes according to the transient voltage time sequence information of the nodes, aggregating the nodes with similar transient voltage behavior characteristics by adopting an affine propagation clustering algorithm, and evaluating a partitioning scheme by utilizing the contour coefficient to obtain an optimal partitioning scheme. (2) And introducing a local voltage stability index, constructing a partitioned inner layer and a partitioned outer layer by adopting hierarchical clustering and a complex network theory respectively, and performing layer superposition on the basis to realize power grid partitioning. (3) From the reactive voltage perspective, a reactive voltage optimization partition model based on the regional load reactive margin and a reactive voltage control partition algorithm based on the mapping partition are respectively provided, and the partition of the grid structure is completed. And (4) taking the energy information of the nodes as a starting point, constructing an energy sensitivity matrix by using the energy change trend of the nodes, and dividing a voltage control area of the matrix by adopting a fuzzy clustering analysis method. (5) In consideration of the application defects of the traditional GN algorithm, the improved GN algorithm based on the backtracking thought is provided to expand the diversity of the feasible partitioning scheme.
For (1) - (5), the current considered objects for dividing the grid frame are single, such as node transient voltage, local voltage stability, reactive voltage, node energy information, and the like, and thus the division precision is difficult to ensure.
Disclosure of Invention
The invention aims to provide a power grid partitioning method based on an improved GN splitting algorithm, which solves the problem of low partitioning precision in the prior art.
The technical scheme adopted by the invention is that a power grid partitioning method based on an improved GN splitting algorithm comprises the following steps:
step 1, simplifying a power network to obtain a topological structure;
step 2, calculating the shortest path between nodes in the topological structure to obtain the shortest path between the nodes;
step 3, calculating the active power betweenness and the voltage weighting edge betweenness of the shortest line between the nodes;
step 4, weighting is added to the active power betweenness and the line voltage weighting betweenness by utilizing an analytic hierarchy process, and the two-factor comprehensive weighting betweenness is obtained through analytical calculation;
and 5, continuously removing the edge with the maximum number of the two-factor comprehensive weighted edges until the condition of partition ending is reached, and determining the community after the partition.
The invention is also characterized in that:
in step 3, the expression of the active power betweenness is as follows:
Figure BDA0002658200560000021
in the above formula, Pl-dFor being transmitted from node d to line lijPower of Pl-mIs a warp line lijActive power, P, to load node mgRepresenting the actual output active power of the output node g, PfRepresenting the active power actually absorbed by the input node f, PlRepresenting the active power flow on the line l, PLnRepresenting the active power flow absorbed by the load node n,
Figure BDA0002658200560000031
represents the positive sequence power distribution matrix AzThe element of the g row and the f column in the inverse matrix of (1);
the expression of the voltage-weighted edge betweenness is as follows:
Figure BDA0002658200560000032
in the above formula, UijRepresenting the line voltage between node i and node j, Uij＝(Ui+Uj)/2，UBIndicates the corresponding reference voltage, omega, at that voltage levelijRepresenting the weight of the edge; dij(l) Represents the number of shortest paths between node i and node j through line l, dijRepresenting the shortest path between the node i and the node j; (ii) a Zij,dIs the modulus, P, of the equivalent impedance of node i and node jijIs the modulus of the line power between node i and node j.
The step 4 specifically comprises the following steps:
step 4.1, normalization processing is carried out on the active power betweenness:
Figure BDA0002658200560000033
in the above formula, max [ R ]]Representing the active power coefficient R in all the lines between the nodesij(l) Maximum value of (d);
step 4.2, voltage weighting edge betweenness normalization processing:
Figure BDA0002658200560000034
in the above formula, max [ H ]]Representing the voltage-weighted edge margin H in all the lines between nodesij(l) Maximum value of (d);
step 4.3, comparing the importance relationship between the active power betweenness and the line voltage weighted edge betweenness by using an analytic hierarchy process, and sequencing to obtain an importance relationship matrix C, calculating the weight mu of the active power betweenness and the weight gamma of the line voltage weighted edge betweenness by using the importance relationship matrix C, wherein mu + gamma is 1, so as to obtain the two-factor comprehensive weighted edge betweenness:
Figure BDA0002658200560000041
the partition ending conditions are as follows: and stopping partitioning if the front K lines with the maximum two-factor comprehensive weighted edge betweenness all belong to the community after partitioning.
The partition ending conditions are as follows: and stopping partitioning when less than J nodes appear in a certain community or certain communities.
The partition ending conditions are as follows: the topological structure is obviously split, but the situation that only one node is independent after the side with the maximum number of the two-factor comprehensive weighted sides is disconnected is not included.
The invention has the beneficial effects that:
according to the power grid partitioning method based on the improved GN splitting algorithm, the system electrical characteristics of a power grid are considered, the improved edge index indexes of various electrical quantities are comprehensively considered, and the accuracy of power grid expression can be improved; the partition ending condition is improved, the problem of overlarge calculation amount caused by dividing each node into communities is avoided, the nondeterministic polynomial problem in the cutting set searching process is prevented, and the method has obvious significance for accurately identifying the power transmission section of the system in the later period.
Drawings
FIG. 1 is a flow chart of a power grid partitioning method based on an improved GN splitting algorithm of the present invention;
FIG. 2 is an initial topology structure diagram of an embodiment of the grid partitioning method of the present invention based on an improved GN splitting algorithm;
FIG. 3 is a simplified topology block diagram of an embodiment of a power grid partitioning method of the present invention based on an improved GN splitting algorithm;
FIG. 4 is a simulation result diagram of the calculation of the system weight value of IEEE39 node in the power grid partitioning method based on the improved GN splitting algorithm of the present invention;
FIG. 5 is a graph of the result of the active power betweenness normalization in a power grid partitioning method based on an improved GN splitting algorithm according to the present invention;
FIG. 6 is a graph of the result of the voltage weighted edge betweenness normalization in a power grid partitioning method based on an improved GN splitting algorithm of the present invention;
FIG. 7 is a graph of the result of the two-factor integrated weighted edge betweenness in the power grid partitioning method based on the improved GN splitting algorithm of the present invention;
FIG. 8 is a diagram of the partitioning result of the IEEE39 node system in the power grid partitioning method based on the improved GN splitting algorithm.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
A power grid partitioning method based on an improved GN splitting algorithm is disclosed, as shown in FIG. 1, and comprises the following steps:
step 1, simplifying a power network to obtain a topological structure;
specifically, a power plant, a transformer substation and a load in an actual system are abstracted into nodes, a power transmission line is used as an edge, an initial topological graph is further simplified according to the principle of node contraction, and weights are defined by integrating electrical distances and active power to form a topological structure.
Step 2, calculating the shortest path between nodes in the topological structure by using a Floyd algorithm to obtain the shortest line between the nodes; when calculating the shortest path between node i and node j, there are two cases, one is from node i directly to node j, and the other is from node i via several nodes k (k ═ 1,2, 3.. once, n,), and finally reaches node j.
Further, calculating values of d (i, j) and d (i, k) + d (k, j), wherein d (i, k) and d (k, j) respectively represent the shortest distances between nodes i to k and k to j; the specific process is as follows:
1) inputting an adjacency matrix of the topological graph G;
2) if d (i, j) > d (i, k) + d (k, j), updating d (i, j) by letting d (i, j) equal to d (i, k) + d (k, j);
3) if d (i, j) <0, then there is a negative loop containing node i, terminating the update; or k ═ n ends; otherwise go to 2).
Step 3, calculating the active power betweenness and the voltage weighting edge betweenness of the shortest line between the nodes;
two factors are mainly considered in calculating the active power betweenness: the specific details of the line with a heavier power transmission proportion and the line with a larger passing frequency in the transmission process are as follows:
in a practical system, the output node g delivers active power to the input node f from a plurality of outgoing lines, and the power flow passing through the outgoing lines in this part is different due to its own parameters and system structure. In the analysis process, a line with a heavy tide is often taken as a key monitoring object, so that the line with the largest proportion of tide flow transmission can be taken as an important line.
Calculating the lines with more passing times in the transmission process, and mainly considering the transmission line lijThe active power betweenness, the expression of the active power betweenness is as follows:
Figure BDA0002658200560000061
in the above formula, Pl-dFor being transmitted from node d to line lijPower of Pl-mIs a warp line lijActive power, P, to load node mgRepresenting the actual output active power of the output node g, PfRepresenting the active power actually absorbed by the input node f, PlRepresenting the active power flow on the line l, PLnRepresenting the active power flow absorbed by the load node n,
Figure BDA0002658200560000062
represents the positive sequence power distribution matrix AzThe element of the g row and the f column in the inverse matrix of (1);
the expression of the voltage-weighted edge betweenness is as follows:
Figure BDA0002658200560000063
in the above formula, UijRepresenting the line voltage between node i and node j, Uij＝(Ui+Uj)/2，UBIndicates the corresponding reference voltage, omega, at that voltage levelijRepresenting the weight of the edge; dij(l) Represents the number of shortest paths between node i and node j through line l, dijRepresenting the shortest path between the node i and the node j; zij,dIs the modulus of the equivalent impedance of node i and node j，PijIs the modulus of the line power between node i and node j.
Step 4, weighting is added to the active power betweenness and the line voltage weighting betweenness by utilizing an analytic hierarchy process, and the two-factor comprehensive weighting betweenness is obtained through analytical calculation;
step 4.1, normalization processing is carried out on the active power betweenness:
Figure BDA0002658200560000071
in the above formula, max [ R ]]Representing the active power coefficient R in all the lines between the nodesij(l) Maximum value of (d);
step 4.2, voltage weighting edge betweenness normalization processing:
Figure BDA0002658200560000072
in the above formula, max [ H ]]Representing the voltage-weighted edge margin H in all the lines between nodesij(l) Maximum value of (d);
4.3, comparing the importance relations between the active power betweenness and the line voltage weighted edge betweenness by using an analytic hierarchy process, and sequencing to obtain an importance relation matrix C;
calculating the product Y of each row factor of the importance relation matrix Ci：
Figure BDA0002658200560000073
To obtain YiRoot of power n Mi：
Figure BDA0002658200560000074
Carrying out normalization treatment on the sample:
Figure BDA0002658200560000075
then eta is [. eta. ]1,η2,...,ηn]TRepresenting a weight factor;
where eta is [. eta. ]1,η2,...,ηn]TSelecting weights of active power betweenness mu and line voltage weighting side betweenness gamma, wherein mu + gamma is 1, and obtaining the double-factor comprehensive weighting side betweenness:
Figure BDA0002658200560000076
and 5, continuously removing the edge with the maximum number of the two-factor comprehensive weighted edges until the condition of partition ending is reached, and determining the community after the partition. The partition ending conditions are as follows:
the method comprises the following steps that under the first condition, if the first K lines with the maximum number of the two-factor comprehensive weighted edges belong to a community group behind the subarea, the subarea is stopped;
under the second condition, stopping partitioning when less than J nodes appear in a certain community or certain communities;
the condition III is that the topological structure is obviously split, but the condition that only one node is independently generated after the side with the maximum betweenness of the two-factor comprehensive weighting sides is disconnected is not included;
it should be noted that the specific value of K, J is determined by the specific study object and the actual situation, and only one of the above three conditions needs to be satisfied. Generally, the system partition has the obvious disconnection of the system as the end condition, i.e. the condition three has the highest possibility of occurrence.
Examples
An IEEE39 node system model shown in figure 2 is built on a PSASP software platform. The system contains 10 gensets, 12 double-winding transformers, 46 lines, 39 nodes (of which, 29 PQ nodes, 9 PV nodes and 1 relaxation node).
Step 1, simplifying the system into a topological structure, and numbering each side (the number marked by the line in the figure is the number of each line), as shown in fig. 3; combining system element parameters and operation data to calculate the weight values of each side of the system, the result is shown in fig. 4;
step 2, calculating the shortest path between each node in the whole system by using a Floyd algorithm;
step 3, calculating the line active power betweenness and the line voltage weighted edge betweenness, wherein the results are shown in fig. 5 and 6;
step 4, adding weights to the exponent indexes by using an analytic hierarchy process, and obtaining the exponent indexes through analysis, calculation and inspection: mu is 0.6667, gamma is 0.3333, and the final index of the two-factor integrated weighted edge betweenness is
Figure BDA0002658200560000081
The results are shown in FIG. 7;
step 5, determining a partitioning result according to a partitioning end condition;
as shown in fig. 8, the two-factor integrated weighted edge betweenness of the line 21 is the largest, 0.6974, which is taken as the edge to be removed first; then according to the idea of improving GN splitting, dynamically removing the edge with the largest number of updated net rack edges, continuously and circularly determining the final partition of the system, directly taking the split areas as partitions without area merging because the system has a smaller scale, and totally dividing into 5 partitions, wherein the partition statistical result is shown in Table 1:
TABLE 1 IEEE39 node System partitioning results
Tab.1 IEEE 39-node system initial partition result
Figure BDA0002658200560000091
The result of the comparison theoretical calculation judgment is the same as the result of the PSASP model simulation, which shows that the partition scheme can accurately divide the complex network communities.

Claims (6)

1. A power grid partitioning method based on an improved GN splitting algorithm is characterized by comprising the following steps:
step 1, simplifying a power network to obtain a topological structure;
step 2, calculating the shortest path between each node in the topological structure to obtain the shortest path between the nodes;
step 3, calculating the active power betweenness and the voltage weighting edge betweenness of the shortest line between the nodes;
step 4, adding weights to the active power medians and the line voltage weighted edge medians by utilizing an analytic hierarchy process, and obtaining a two-factor comprehensive weighted edge medians through analytical calculation;
and 5, continuously removing the edge with the maximum two-factor comprehensive weighted edge betweenness until a partition ending condition is reached, and determining the community after the partition.
2. A power grid partitioning method based on an improved GN splitting algorithm as claimed in claim 1, wherein in step 3, the expression of the active power betweenness is as follows:
Figure FDA0002658200550000011
in the above formula, Pl-dFor being transmitted from node d to line lijPower of Pl-mIs a warp line lijActive power, P, to load node mgRepresenting the actual output active power of the output node g, PfRepresenting the active power actually absorbed by the input node f, PlRepresenting the active power flow on the line l, PLnRepresenting the active power flow absorbed by the load node n,
Figure FDA0002658200550000012
represents the positive sequence power distribution matrix AzThe element of the g row and the f column in the inverse matrix of (1);
the expression of the voltage-weighted edge betweenness is as follows:
Figure FDA0002658200550000013
in the above formula, UijRepresenting the line voltage between node i and node j, Uij＝(Ui+Uj)/2，UBIndicates the corresponding reference voltage, omega, at that voltage levelijRepresenting the weight of the edge; dij(l) Represents the number of shortest paths between node i and node j through line l, dijRepresenting the shortest path between node i and node j; (ii) a Zij,dIs the modulus, P, of the equivalent impedance of node i and node jijIs the modulus of the line power between node i and node j.
3. The power grid partitioning method based on the improved GN splitting algorithm as claimed in claim 1, wherein step 4 specifically comprises the following steps:
step 4.1, normalization processing is carried out on the active power betweenness:
Figure FDA0002658200550000021
in the above formula, max [ R ]]Representing the active power coefficient R in all the lines between the nodesij(l) Maximum value of (d);
step 4.2, carrying out voltage weighting edge betweenness normalization treatment:
Figure FDA0002658200550000022
in the above formula, max [ H ]]Representing the voltage-weighted edge margin H in all the lines between nodesij(l) Maximum value of (d);
step 4.3, comparing the importance relationships between the active power betweenness and the line voltage weighted edge betweenness by using an analytic hierarchy process, and sequencing to obtain an importance relationship matrix C, calculating the weight mu of the active power betweenness and the weight gamma of the line voltage weighted edge betweenness by using the importance relationship matrix C, wherein mu + gamma is 1, so as to obtain a two-factor comprehensive weighted edge betweenness:
Figure FDA0002658200550000023
4. a power grid partitioning method based on an improved GN splitting algorithm as claimed in claim 1, wherein the partitioning end condition is: and stopping partitioning if the front K lines with the maximum two-factor comprehensive weighted edge betweenness all belong to the community after partitioning.
5. A power grid partitioning method based on an improved GN splitting algorithm as claimed in claim 1, wherein the partitioning end condition is: and stopping partitioning when less than J nodes appear in a certain community or certain communities.
6. A power grid partitioning method based on an improved GN splitting algorithm as claimed in claim 1, wherein the partitioning end condition is: the topological structure is obviously split, but the situation that only one node is independently generated after the edge with the maximum betweenness of the two-factor comprehensive weighting edges is disconnected is not included.
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