CN110138620B - Distribution network synchronous measurement and communication link configuration method facing distributed state estimation - Google Patents

Distribution network synchronous measurement and communication link configuration method facing distributed state estimation Download PDF

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CN110138620B
CN110138620B CN201910453309.9A CN201910453309A CN110138620B CN 110138620 B CN110138620 B CN 110138620B CN 201910453309 A CN201910453309 A CN 201910453309A CN 110138620 B CN110138620 B CN 110138620B
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王成山
赵志达
李鹏
宿洪智
孔祥玉
于浩
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Tianjin University
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    • H—ELECTRICITY
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    • H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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    • H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
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Abstract

A distribution network synchronous measurement and communication link configuration method for distributed state estimation comprises the following steps: for the selected power distribution system, acquiring the topological connection relation and the electrical parameters of a power distribution network, and acquiring the cost of a synchronous phasor measurement device, a phasor data concentrator and a communication link; constructing an adjacency matrix A and an inter-node communication path vector E respectivelyr,t(ii) a Aiming at a communication and calculation framework adopted by distributed state estimation, a power distribution system is divided into a plurality of areas according to a synchronous phasor measurement configuration partitioning method for power distribution network distributed state estimation; establishing a 0-1 integer linear programming model for distributed state estimation-oriented power distribution network synchronous measurement and communication link configuration; and solving the planning model to obtain a configuration scheme of the synchronous phasor measurement device, the phasor data concentrator and the communication link. The invention better accords with the increasingly obvious distributed characteristic of the current power distribution network, obviously reduces the communication burden and provides guarantee for the real-time analysis and control of the power distribution system.

Description

Distribution network synchronous measurement and communication link configuration method facing distributed state estimation
Technical Field
The invention relates to a distribution network synchronous measurement and communication link configuration method. In particular to a distribution network synchronous measurement and communication link configuration method oriented to distributed state estimation.
Background
According to the traditional centralized state estimation, measurement information which is widely distributed needs to be uploaded to a control center step by step and then estimated and calculated, along with the expansion of the scale of a power distribution system, a large number of distributed power supplies are connected in and participate at user sides, the communication burden is heavy, the state variable dimension is high, the whole time consumption is long, and the requirement for real-time analysis and control of a power distribution network is difficult to meet. In order to cope with the increasingly obvious distributed characteristics of the power distribution network, reduce communication burden and accelerate computing speed, distributed state estimation gradually becomes an effective means for solving the problem. However, most of the measurement used for state estimation comes from a data acquisition and monitoring control system and an advanced measurement system, so that the problems of low precision, poor synchronism and long acquisition period of data exist, measurement and state variables are in a nonlinear relation, iterative solution needs to be performed by an algorithm such as a weighted least square method, and even if distributed state estimation is adopted, the accuracy and the real-time performance of system state solution are difficult to guarantee. In addition, the premise of state estimation convergence is that the system is considerable, and the existing power distribution network is not strong in integral observability due to the fact that data acquisition points are multiple, the data acquisition points are widely distributed, and monitoring points are not completely covered.
Due to the introduction of the synchronous phasor measurement device, the operation monitoring level of the power distribution network is greatly improved. Compared with the traditional measuring device, the synchronous phasor measuring device can acquire amplitude measurement information of node voltage and branch current, can measure phase angles of the voltage and the current and system frequency, improves calculation speed and accuracy of applications such as model parameter verification, state estimation, system protection and operation control, and is an important ring for the technical development of the intelligent power distribution network. Particularly, in the application of state estimation, the voltage and current phasors acquired by the synchronous phasor measurement device are measured and are in linear relation with the state variable of the system, the system state can be solved by adopting algorithms such as linear state estimation and the like, the calculation time is greatly reduced, the application of the synchronous phasor measurement device can effectively solve the problems of poor measurement data quality, low synchronism and long acquisition period of the traditional power distribution system, the accuracy of state estimation is improved, and the real-time analysis control of the power distribution system is guaranteed.
If all the measurement data adopted in the distributed state estimation come from the synchronous phasor measurement device, the rapidity of state variable solving can be ensured, the communication burden can be reduced, and the accuracy and the instantaneity of the estimation result can be ensured due to high data quality and high uploading frequency. However, due to the economic cost constraint, it is necessary to consider how to reasonably configure the synchrophasor measurement apparatus and its related communication devices, and the distributed state estimation requires each sub-region to be fully observable. Therefore, it is necessary to configure a synchronous phasor measurement apparatus for each sub-region to meet observability requirements, then select a point to perform centralized and intra-region state estimation calculation of measurement data, and consider information interaction between adjacent regions. This is a problem related to how to configure the synchrophasor measurement apparatus, the data concentrator and the communication link so that the configuration scheme is at minimum cost.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a distribution network synchronous measurement and communication link configuration method oriented to distributed state estimation.
The technical scheme adopted by the invention is as follows: a distribution network synchronous measurement and communication link configuration method oriented to distributed state estimation comprises the following steps:
1) for the selected power distribution system, acquiring the topological connection relation and the electrical parameters of a power distribution network, and acquiring the cost of a synchronous phasor measurement device, a phasor data concentrator and a communication link;
2) constructing an adjacent matrix A and an inter-node communication path vector E respectively according to the topological connection relation of the power distribution network acquired in the step 1)r，t；
3) Aiming at a communication and calculation framework adopted by distributed state estimation, dividing the power distribution system into a plurality of areas according to a synchronous phasor measurement configuration partitioning method for power distribution network distributed state estimation;
4) for the power distribution system which is partitioned in the step 3), a 0-1 integer linear programming model for distributed state estimation-oriented power distribution network synchronous measurement and communication link configuration is established, and the model comprises the following steps: taking the lowest total cost of the power distribution system synchronous phasor measurement device, the phasor data concentrator and the communication link configuration scheme as an objective function, and considering the observability constraint of a subarea network, the data transmission constraint of the synchronous phasor measurement device, the decision variable constraint of the overlapped nodes of adjacent subareas, the information interaction constraint between the phasor data concentrators, the bandwidth constraint of a communication link and the configuration constraint of the communication link;
5) and solving the 0-1 integer linear programming model of the distribution network synchronous measurement and communication link configuration oriented to the distributed state estimation in the step 4) to obtain a synchronous phasor measurement device, a phasor data concentrator and a communication link configuration scheme.
The cost of the communication link in the step 1) is as follows:
Figure BDA0002075811760000021
wherein, CCLRepresenting a total cost of the power distribution system configuration communication link; k represents a branch number; lambdaBRepresenting a set formed by all branches of the power distribution system; l iskFor decision variables, L if branch k configures a communication linkkIs 1, otherwise LkIs 0; cLAnd CBUnit costs representing communication link length and bandwidth, respectively; skRepresenting the length of the communication link configured by the branch k; b iskIndicating that leg k configures the bandwidth of the communication link.
Inter-node communication path vector E described in step 2)r，tThe kth element of (2) is:
Figure BDA0002075811760000022
wherein E isr，t，kRepresenting an inter-node communication path vector Er，tThe kth element of (1); r and t both represent node numbers; k denotes a branch number.
The communication and calculation framework adopted by the distributed state estimation in the step 3) is as follows:
and a centralized control center does not exist in the power distribution network, each sub-region carries out intra-region state estimation respectively, and each sub-region only interacts with the adjacent sub-regions with the state information of the boundary nodes.
The step 4) is as follows:
(1) the method takes the lowest total cost of a synchronous phasor measurement device, a phasor data concentrator and a communication link configuration scheme of a power distribution system as an objective function, and the mathematical expression is as follows:
min(CPMU+CPDC+CCL)
Figure BDA0002075811760000023
Figure BDA0002075811760000024
Figure BDA0002075811760000031
wherein, CPMUCost of the device for synchronous phasor measurement; cPDCCost of the phasor data concentrator; cCLA cost for the communication link; cP1Represents the unit cost of the synchronous phasor measurement device; m represents the number of the sub-region; gamma-shapedZRepresenting a set formed by all sub-areas after the power distribution system is partitioned; i represents the number of nodes in the sub-region m; omegamRepresenting a set of all nodes in sub-region m; x is the number ofiFor decision variables, if node i is equipped with a synchrophasor measurement apparatus xiIs 1, otherwise xiIs 0; n is a radical ofOLRepresenting the number of repeated calculations of the synchronous phasor measurement device caused by the overlapping of adjacent region nodes; cP2Represents the unit cost of the phasor data concentrator; y isiFor decision variables, if node i is equipped with a phasor data concentrator, then yiIs 1, otherwise yiIs 0; k represents a branch number; lambdaBRepresenting a set formed by all branches of the power distribution system; l iskFor decision variables, L if branch k configures a communication linkkIs 1, otherwise LkIs 0; cLAnd CBRespectively representing the unit cost of the communication link length and the bandwidth; skRepresenting the length of the communication link configured by the branch k; b iskIndicating that the branch k configures the bandwidth of the communication link;
(2) the sub-area network observability constraint is:
Amxm≥1，m∈ΓZ
wherein A ismRepresentation sub-regionA adjacency matrix of domain m; x is the number ofmIs a column vector composed of decision variables configured for synchronous phasor measurement in the sub-region m; 1 is N with elements 1mVector of dimension, NmRepresents the number of nodes in sub-region m;
(3) the data transfer constraints of the synchrophasor measurement apparatus are:
Figure BDA0002075811760000032
Figure BDA0002075811760000033
Figure BDA0002075811760000034
wherein, the first constraint ensures that the node sending information is provided with a synchronous phasor measurement device, i and j are the serial numbers of the nodes in the sub-region m, and zi，jFor data transmission decision variables, z if the synchronous phasor measurement apparatus of node i communicates with the phasor data concentrator of node ji，jIs 1, otherwise zi，jIs 0; the second constraint ensures that the nodes receiving the measurement information are equipped with phasor data concentrators, ziSending a row vector of decision variables, y, for all data associated with node i in sub-region mmA column vector consisting of decision variables configured for all phasor data concentrators in the sub-region m; the third constraint ensures that each subregion has one and only one data concentrator;
(4) the adjacent subregion overlapping node decision variable constraint is as follows:
xi＝1，i∈Ωm∩Ωn，m∈ΓZ，n∈ΓZ
wherein m and n are both sub-region numbers; i is the number of the node overlapped by the sub-region m and the sub-region n; omegamAnd omeganRespectively representing the sets of the nodes contained in the sub-regions m and n;
(5) the information interaction constraint among the phasor data concentrators is as follows:
Figure BDA0002075811760000035
Figure BDA0002075811760000036
wherein, the first constraint ensures that the node in the sub-region m communicating with the sub-region n configures a phasor data concentrator, i is the number of the node in the sub-region m, l is the number of the node in the sub-region n, and w is the number of the node in the sub-region ni，lDeciding variables for information interaction, if the phasor data concentrator of node i communicates with the phasor data concentrator of node l, then wi，lIs 1, otherwise wi，lIs 0; the second constraint ensures that nodes in sub-area n communicating with sub-area m configure the phasor data concentrator, wiA row vector y formed by all information interaction decision variables related to the node i in the sub-region mnA column vector composed of decision variables configured for the vector data concentrator in the sub-region n;
(6) the bandwidth constraints of the communication link are:
Figure BDA0002075811760000041
wherein i and j are node numbers in the sub-region m; giRepresents the degree of node i, i.e., the number of branches associated with node i; ei，jIndicating whether the equipment of the node i passes through each branch when communicating with the equipment of the node j, and if the equipment passes through the branch k, Ei，jK element of (E)i，j，kIs 1, otherwise Ei，j，kIs 0; set ΨAEach element in (a) is a set of two adjacent sub-region numbers, i.e.
Figure BDA0002075811760000042
m and n both represent the number of the sub-region; h is the set ΨAMiddle element; omegah，1Presentation elementThe first sub-region in element h contains a set of nodes; omegah，2Representing a set of nodes contained in a second sub-region of the element h; r and t respectively represent the numbers of nodes in two adjacent sub-areas; d represents the data compression ratio when the phasor data concentrator communicates; p represents a bandwidth required for transmitting a unit phasor data frame; b represents the bandwidth of each branch configuration communication link;
(7) the configuration constraints of the communication link are:
FL≥B
L≤B
0≤L≤1
wherein F is a positive number greater than any element in B; l represents whether each branch is configured with a communication link or not, and if the branch k is configured with the communication link, L iskIs 1, otherwise LkIs 0; 0 represents an H-dimensional column vector with elements of 0, and H represents the total number of branches of the power distribution system; 1 represents an H-dimensional column vector whose elements are all 1.
The distribution network synchronous measurement and communication link configuration method for distributed state estimation divides a distribution system by utilizing a partition principle of the distributed state estimation, constructs a 0-1 integer linear programming model of distribution network synchronous measurement and communication link configuration for the distributed state estimation by taking the lowest cost of a synchronous phasor measurement device and a related communication equipment configuration scheme thereof as an objective function, and solves the model to obtain an economical and reasonable synchronous phasor measurement device and a related communication equipment configuration scheme thereof. The distributed state estimation-oriented communication method is oriented to distributed state estimation, meanwhile, the aggregation of measurement information in an area and the interaction of interval boundary information are considered, compared with a communication configuration scheme oriented to centralized state estimation, the distributed state estimation-oriented communication method is more consistent with increasingly obvious distributed characteristics of the current power distribution network, the communication burden is obviously reduced, and a guarantee is provided for real-time analysis and control of a power distribution system.
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Fig. 1 is a flow chart of a distribution network synchronous measurement and communication link configuration method for distributed state estimation according to the present invention;
FIG. 2 is a diagram of an IEEE 33 node algorithm;
FIG. 3 is a graph of the PG & E69 node calculation;
FIG. 4 is a schematic diagram of an exemplary synchrophasor measurement apparatus and related communication device configuration for an IEEE 33 node configuration;
fig. 5 is a schematic diagram of a synchrophasor measurement apparatus and related communication equipment configuration according to an example of PG & E69 node configuration.
Detailed Description
The following describes the distribution network synchronization measurement and communication link configuration method oriented to distributed state estimation in detail with reference to the embodiments and the accompanying drawings.
The invention relates to a distribution network synchronous measurement and communication link configuration method facing distributed state estimation, which comprises the following steps:
1) for the selected power distribution system, acquiring the topological connection relation and the electrical parameters of a power distribution network, and acquiring the cost of a synchronous phasor measurement device, a phasor data concentrator and a communication link; wherein, the cost of the communication link is:
Figure BDA0002075811760000051
wherein, CCLRepresenting a total cost of the power distribution system configuration communication link; k represents a branch number; lambdaBRepresenting a set formed by all branches of the power distribution system; l iskFor decision variables, L if branch k configures a communication linkkIs 1, otherwise LkIs 0; cLAnd CBUnit costs representing communication link length and bandwidth, respectively; skRepresenting the length of the communication link configured by the branch k; b iskIndicating that leg k configures the bandwidth of the communication link.
2) Constructing an adjacent matrix A and an inter-node communication path vector E respectively according to the topological connection relation of the power distribution network acquired in the step 1)r，t(ii) a Wherein said inter-node communication path vector Er，tThe kth element of (2) is:
Figure BDA0002075811760000052
wherein E isr，t，kRepresenting nodesInter-communication path vector Er，tThe kth element of (1); r and t both represent node numbers; k denotes a branch number.
3) Aiming at a communication and calculation framework adopted by distributed state estimation, dividing the power distribution system into a plurality of areas according to a synchronous phasor measurement configuration partitioning method for power distribution network distributed state estimation; wherein the following steps:
(1) the communication and computation architecture adopted by the distributed state estimation is as follows:
and a centralized control center does not exist in the power distribution network, each sub-region carries out intra-region state estimation respectively, and each sub-region only interacts with the adjacent sub-regions with the state information of the boundary nodes.
(2) A distribution network distributed state estimation oriented synchronous phasor measurement configuration partitioning method comprises the following steps:
(2.1) for the selected power distribution system, acquiring the topological connection relation of the power distribution network, constructing an adjacent matrix A, and setting the number M of sub-regions, wherein the number M of the sub-regions is as follows:
Figure BDA0002075811760000053
wherein N represents the total node number of the power distribution system to be partitioned,
Figure BDA0002075811760000054
number of representations
Figure BDA0002075811760000055
And rounding down.
(2.2) establishing a synchronous phasor measurement configuration partition model facing the power distribution network distributed state estimation, wherein the synchronous phasor measurement configuration partition model facing the power distribution network distributed state estimation takes the minimum node number difference between sub-regions as a target function, and a mathematical expression is as follows:
Figure BDA0002075811760000056
wherein N ismIndicating the number of nodes contained in the sub-region m.
(2.3) solving the synchronous phasor measurement configuration partition model facing the power distribution network distributed state estimation in the step 2) through a genetic algorithm; the method comprises the following steps:
(2.3.1) setting the length of an individual chromosome in a genetic algorithm to be equal to the number M of subregions, setting the value set of genes on the chromosome to be the set omega formed by all nodes of a power distribution system, wherein omega is {1, 2, …, N }, N represents the total number of the nodes of the power distribution system to be partitioned, randomly generating an initial population, setting the evolution generation e to be 1, and setting the cross probability pCGenetic probability pMAnd a maximum evolution algebra D;
(2.3.2) obtaining an initial center node through chromosomes of individuals in a group, partitioning the power distribution network by using a center expansion partitioning method, and further calculating the fitness of the individuals; the central extension partition method comprises the following steps:
(2.3.2.1) setting all nodes to be not partitioned, randomly acquiring M nodes as initial central nodes, and marking the initial central nodes as partitioned nodes;
(2.3.2.2) the expansion times s is 0, updating the sub-region set corresponding to the initial central node according to the initial central node and constructing a partition matrix GsThe expansion times s is s + 1; wherein the partition matrix GsIs a matrix of dimension M × N, for
Figure BDA0002075811760000061
Figure BDA0002075811760000062
l and m respectively represent a node number and a sub-region number, and G is the node l in the sub-region msRow m, column l element G s，m，l1, otherwise Gs，m，lIs 0, a sub-region set pilThe middle element is the number of the sub-region to which the node l belongs, and if the node l is in the sub-region m, m belongs to pil；
(2.3.2.3) setting the partition matrix G 'to be adjusted after the s time expansion's＝Gs-1A, A is adjacent matrix, and the partition to be adjustedMatrix G'sAll non-zero elements in the sequence are set to be 1, m is 1, n is 2, and m and n are numbers of subareas;
(2.3.2.4) if n > M, then M is M +1, n is M +1, go to step (2.3.2.5), otherwise go to step (2.3.2.6);
(2.3.2.5) if M is equal to M, entering the (2.3.2.8) th step, otherwise, entering the (2.3.2.6) th step;
(2.3.2.6) obtaining a set of overlapping nodes Ω for sub-region m and sub-region nm，nIf the node set Ω overlapsm，nIf the current is empty, n is n +1, the step (2.3.2.4) is carried out, otherwise, the step (2.3.2.7) is carried out;
(2.3.2.7) if overlapping the set of nodes Ωm，nIf there are only two nodes in the partition matrix G ', the two nodes are used as shared boundary nodes of the sub-region m and the sub-region n, the difference between the maximum region node number and the minimum region node number is compared, the boundary node is selected by taking the minimum difference as a target, and if the differences are the same, the node in the sub-region i before expansion is taken as a boundary, and the partition matrix G ' to be adjusted is adjusted 'sUpdating a sub-region set corresponding to the boundary node, wherein n is n +1, and entering the (2.3.2.4) th step;
(2.3.2.8) set the set of all partitioned nodes to ΩAZTo a
Figure BDA0002075811760000063
If m is equal to ΠlThen the partition matrix G 'is to be adjusted'sLine m of l-th element G's，m，l1, otherwise G's，m，l＝0；
(2.3.2.9) set the set of all non-partitioned overlapping nodes to ΩNZTo a
Figure BDA0002075811760000064
If the overlapped subareas have boundaries, dividing the node l into the subarea with the minimum node number, if the subarea with the minimum node number has a plurality of subareas, dividing the node l into the subarea with the minimum serial number, and adjusting the subarea matrix G 'to be adjusted'sUpdating the sub-region set corresponding to the node l;
(2.3.2.10) setting m to be 1 and n to be 2, wherein m and n are subarea numbers;
(2.3.2.11) if n > M, then M is M +1, n is M +1, go to step (2.3.2.12), otherwise go to step (2.3.2.13);
(2.3.2.12) if M is equal to M, entering the (2.3.2.15), otherwise entering the (2.3.2.13) step;
(2.3.2.13) obtaining a set omega of overlapping nodes of the sub-region m and the sub-region nm，nIf the node set Ω overlapsm，nIf the current is empty, n is n +1, the step (2.3.2.11) is carried out, otherwise, the step (2.3.2.14) is carried out;
(2.3.2.14) if overlapping the set of nodes Ωm，nThe node is not partitioned, and the sub-region m and the sub-region n are overlapped for the first time, then the node is used as a boundary node shared by the sub-region m and the sub-region n, and a partition matrix G 'to be adjusted is adjusted'sUpdating a sub-region set corresponding to the boundary node, wherein n is n +1, and entering the (2.3.2.11) th step;
(2.3.2.15) setting the adjusted partition matrix Gs＝G'sIf G iss＝Gs-1Go to step (2.3.2.16), otherwise GsMarking the nodes contained in the data packet as partitioned nodes, expanding the times s to s +1, and entering the step (2.3.2.3);
(2.3.2.16) according to the partition matrix GsOutputting a partition result;
(2.3.3) acting a selection operator on the population, and reserving the individual with the highest fitness;
(2.3.4) acting the crossover operator and the mutation operator on the selected population to generate a next generation, wherein the evolution generation e is e + 1;
(2.3.5) if the evolution algebra e is less than D, entering the step (2.3.2), otherwise, entering the step (2.3.6);
(2.3.6) outputting the individual with the highest fitness as the optimal solution.
4) For the power distribution system which is partitioned in the step 3), a 0-1 integer linear programming model for distributed state estimation-oriented power distribution network synchronous measurement and communication link configuration is established, and the model comprises the following steps: taking the lowest total cost of the power distribution system synchronous phasor measurement device, the phasor data concentrator and the communication link configuration scheme as an objective function, and considering the observability constraint of a subarea network, the data transmission constraint of the synchronous phasor measurement device, the decision variable constraint of the overlapped nodes of adjacent subareas, the information interaction constraint between the phasor data concentrators, the bandwidth constraint of a communication link and the configuration constraint of the communication link; wherein, the said:
(1) the method takes the lowest total cost of a synchronous phasor measurement device, a phasor data concentrator and a communication link configuration scheme of a power distribution system as an objective function, and the mathematical expression is as follows:
min(CPMU+CPDC+CCL)
Figure BDA0002075811760000071
Figure BDA0002075811760000072
Figure BDA0002075811760000073
wherein, CPMUCost of the device for synchronous phasor measurement; cPDCCost of the phasor data concentrator; cCLA cost for the communication link; cP1Represents the unit cost of the synchronous phasor measurement device; m represents the number of the sub-region; gamma-shapedZRepresenting a set formed by all sub-areas after the power distribution system is partitioned; i represents the number of nodes in the sub-region m; omegamRepresenting a set of all nodes in sub-region m; x is the number ofiFor decision variables, if node i is equipped with a synchrophasor measurement apparatus xiIs 1, otherwise xiIs 0; n is a radical ofOLRepresenting the number of repeated calculations of the synchronous phasor measurement device caused by the overlapping of adjacent region nodes; cP2Represents the unit cost of the phasor data concentrator; y isiFor decision variables, if node i is equipped with a phasor data concentrator, then yiIs 1, otherwise yiIs 0; k represents a branch number; lambdaBRepresenting all branch structures of a power distribution systemA set of; l iskFor decision variables, L if branch k configures a communication linkkIs 1, otherwise LkIs 0; cLAnd CBRespectively representing the unit cost of the communication link length and the bandwidth; skRepresenting the length of the communication link configured by the branch k; b iskIndicating that the branch k configures the bandwidth of the communication link;
(2) the sub-area network observability constraint is:
Amxm≥1，m∈ΓZ
wherein A ismA adjacency matrix representing a sub-region m; x is the number ofmIs a column vector composed of decision variables configured for synchronous phasor measurement in the sub-region m; 1 is N with elements 1mVector of dimension, NmRepresents the number of nodes in sub-region m;
(3) the data transfer constraints of the synchrophasor measurement apparatus are:
Figure BDA0002075811760000074
Figure BDA0002075811760000075
Figure BDA0002075811760000076
wherein, the first constraint ensures that the node sending information is provided with a synchronous phasor measurement device, i and j are the serial numbers of the nodes in the sub-region m, and zi，jFor data transmission decision variables, z if the synchronous phasor measurement apparatus of node i communicates with the phasor data concentrator of node ji，kIs 1, otherwise zi，jIs 0; the second constraint ensures that the nodes receiving the measurement information are equipped with phasor data concentrators, ziSending a row vector of decision variables, y, for all data associated with node i in sub-region mmA column vector consisting of decision variables configured for all phasor data concentrators in the sub-region m;the third constraint ensures that each subregion has one and only one data concentrator;
(4) the adjacent subregion overlapping node decision variable constraint is as follows:
xi＝1，i∈Ωm∩Ωn，m∈ΓZ，n∈ΓZ
wherein m and n are both sub-region numbers; i is the number of the node overlapped by the sub-region m and the sub-region n; omegamAnd omeganRespectively representing the sets of the nodes contained in the sub-regions m and n;
(5) the information interaction constraint among the phasor data concentrators is as follows:
Figure BDA0002075811760000081
Figure BDA0002075811760000082
wherein, the first constraint ensures that the node in the sub-region m communicating with the sub-region n configures a phasor data concentrator, i is the number of the node in the sub-region m, l is the number of the node in the sub-region n, and w is the number of the node in the sub-region ni，lDeciding variables for information interaction, if the phasor data concentrator of node i communicates with the phasor data concentrator of node l, then wi，lIs 1, otherwise wi，lIs 0; the second constraint ensures that nodes in sub-area n communicating with sub-area m configure the phasor data concentrator, wiA row vector y formed by all information interaction decision variables related to the node i in the sub-region mnA column vector composed of decision variables configured for the vector data concentrator in the sub-region n;
(6) the bandwidth constraints of the communication link are:
Figure BDA0002075811760000083
wherein i and j are node numbers in the sub-region m; giRepresenting degree of node i, i.e. AND nodei the number of associated branches; ei，jIndicating whether the equipment of the node i passes through each branch when communicating with the equipment of the node j, and if the equipment passes through the branch k, Ei，，jK element of (E)i，j，kIs 1, otherwise Ei，j，kIs 0; set ΨAEach element in (a) is a set of two adjacent sub-region numbers, i.e.
Figure BDA0002075811760000084
m and n both represent the number of the sub-region; h is the set ΨAMiddle element; omegah，1Representing that a first sub-region in element h contains a set of nodes; omegah，2Representing a set of nodes contained in a second sub-region of the element h; r and t respectively represent the numbers of nodes in two adjacent sub-areas; d represents the data compression ratio when the phasor data concentrator communicates; p represents a bandwidth required for transmitting a unit phasor data frame; b represents the bandwidth of each branch configuration communication link;
(7) the configuration constraints of the communication link are:
FL≥B
L≤B
0≤L≤1
wherein F is a positive number greater than any element in B; l represents whether each branch is configured with a communication link or not, and if the branch k is configured with the communication link, L iskIs 1, otherwise LkIs 0; 0 represents an H-dimensional column vector with elements of 0, and H represents the total number of branches of the power distribution system; 1 represents an H-dimensional column vector whose elements are all 1.
5) And solving the 0-1 integer linear programming model of the distribution network synchronous measurement and communication link configuration oriented to the distributed state estimation in the step 4) to obtain a synchronous phasor measurement device, a phasor data concentrator and a communication link configuration scheme.
Specific examples are given below:
respectively adopting IEEE 33 node calculation and PG&The E69 node algorithmically verifies the method provided by the invention, and the topological connection relationship between the two is shown in FIG. 2 and FIG. 3. The unit cost of the communication equipment is taken as: cPMU40,000.00 USD/station, CPDC7,500.00 USD/station, CB＝120.00USD/kbps，CL1,500.00USD/km, d 0.56, P25 kbps. IEEE 33 node calculation and PG&The calculated line lengths for the E69 node are shown in tables 1 and 2. Dividing an IEEE 33 node into 3 sub-regions by using a partitioning method oriented to distributed state estimation synchronous phasor measurement configuration, and PG&Dividing the E69 node example into 4 sub-regions, then applying the model provided by the invention and solving to obtain the IEEE 33 node example and PG&The scheme of the synchrophasor measurement apparatus and the related communication equipment of the E69 node algorithm is shown in fig. 4 and 5, and the specific scheme is shown in table 3.
TABLE 1 IEEE 33 node example line length
Branch numbering Head end node End node Length/km Branch numbering Head end node End node Length/km
1 1 2 0.0922 17 17 18 0.7320
2 2 3 0.4930 18 2 19 0.1640
3 3 4 0.3660 19 19 20 1.5042
4 4 5 0.3811 20 20 21 0.4095
5 5 6 0.8190 21 21 22 0.7089
6 6 7 0.1872 22 3 23 0.4512
7 7 8 0.7114 23 23 24 0.8980
8 8 9 1.0300 24 24 25 0.8960
9 9 10 1.0440 25 6 26 0.2030
10 10 11 0.1966 26 26 27 0.2842
11 11 12 0.3744 27 27 28 1.0590
12 12 13 1.4680 28 28 29 0.8042
13 13 14 0.5416 29 29 30 0.5075
14 14 15 0.5910 30 30 31 0.9744
15 15 16 0.7463 31 31 32 0.3105
16 16 17 1.2890 32 32 33 0.3410
TABLE 2 PG & E69 node arithmetic line length
Figure BDA0002075811760000091
Figure BDA0002075811760000101
TABLE 3 measurement apparatus of synchronous phasor under different calculation examples and related communication equipment configuration scheme
Figure BDA0002075811760000102
Under the same configuration scheme of the synchrophasor measurement apparatus, the bandwidth ratio of the communication link in the configuration scheme facing distributed state estimation and the configuration scheme facing centralized state estimation is shown in table 4 and table 5. As can be seen from table 4, in the IEEE 33 node calculation example, the total bandwidth required for the centralized configuration is 7075kbps, the cost is 849,000.00USD, the total bandwidth required for the distributed configuration is 3005kbps, the cost is 360,600.00USD, and the total bandwidth cost is saved by 488,400.00 USD; as can be seen from table 5, in the PG & E69 node calculation example, the total bandwidth required by the centralized configuration is 20325kbps, the cost is 2,439,000.00USD, the total bandwidth required by the distributed configuration is 9567kbps, the cost is 1,148,040.00USD, and the total bandwidth cost is 1,290,960.00 USD. In addition, for the communication links configured by the same branch, the bandwidth required by the distributed configuration scheme is less than or equal to the bandwidth required by the centralized configuration scheme, and the effectiveness of the method in reducing the communication burden is verified.
TABLE 4 communication Link Bandwidth under different configuration modes of IEEE 33 node example
Figure BDA0002075811760000111
TABLE 5 communication Link Bandwidth of PG & E69 node examples in different configuration modes
Figure BDA0002075811760000112
Figure BDA0002075811760000121

Claims (4)

1. A distribution network synchronous measurement and communication link configuration method oriented to distributed state estimation is characterized by comprising the following steps:
1) for the selected power distribution system, acquiring the topological connection relation and the electrical parameters of a power distribution network, and acquiring the cost of a synchronous phasor measurement device, a phasor data concentrator and a communication link;
2) constructing an adjacent matrix A and an inter-node communication path vector E respectively according to the topological connection relation of the power distribution network acquired in the step 1)r，t；
3) Aiming at a communication and calculation framework adopted by distributed state estimation, dividing the power distribution system into a plurality of areas according to a synchronous phasor measurement configuration partitioning method for power distribution network distributed state estimation;
4) for the power distribution system which is partitioned in the step 3), a 0-1 integer linear programming model for distributed state estimation-oriented power distribution network synchronous measurement and communication link configuration is established, and the model comprises the following steps: taking the lowest total cost of the power distribution system synchronous phasor measurement device, the phasor data concentrator and the communication link configuration scheme as an objective function, and considering the observability constraint of a subarea network, the data transmission constraint of the synchronous phasor measurement device, the decision variable constraint of the overlapped nodes of adjacent subareas, the information interaction constraint between the phasor data concentrators, the bandwidth constraint of a communication link and the configuration constraint of the communication link; wherein the following steps:
(1) the method takes the lowest total cost of a synchronous phasor measurement device, a phasor data concentrator and a communication link configuration scheme of a power distribution system as an objective function, and the mathematical expression is as follows:
min(CPMU+CPDC+CCL)
Figure FDA0002963740740000011
Figure FDA0002963740740000012
Figure FDA0002963740740000013
wherein, CPMUCost of the device for synchronous phasor measurement; cPDCCost of the phasor data concentrator; cCLA cost for the communication link; cP1Represents the unit cost of the synchronous phasor measurement device; m represents the number of the sub-region; gamma-shapedZRepresenting a set formed by all sub-areas after the power distribution system is partitioned; i represents the number of nodes in the sub-region m; omegamRepresenting a set of all nodes in sub-region m; x is the number ofiFor decision variables, if node i is equipped with a synchrophasor measurement apparatus xiIs 1, otherwise xiIs 0; n is a radical ofOLRepresenting the number of repeated calculations of the synchronous phasor measurement device caused by the overlapping of adjacent region nodes; cP2Represents the unit cost of the phasor data concentrator; y isiFor decision variables, if node i is equipped with a phasor data concentrator, then yiIs 1, otherwise yiIs 0; k represents a branch number; lambdaBRepresenting a set formed by all branches of the power distribution system; l iskFor decision variables, L if branch k configures a communication linkkIs 1, otherwise LkIs 0; cLAnd CBRespectively representing the unit cost of the communication link length and the bandwidth; skRepresenting the length of the communication link configured by the branch k; b iskIndicating that the branch k configures the bandwidth of the communication link;
(2) the sub-area network observability constraint is:
Amxm≥1 ，m∈ΓZ
wherein A ismA adjacency matrix representing a sub-region m; x is the number ofmIs a column vector composed of decision variables configured for synchronous phasor measurement in the sub-region m; 1 is N with elements 1mVector of dimension, NmRepresents the number of nodes in sub-region m;
(3) the data transfer constraints of the synchrophasor measurement apparatus are:
Figure FDA0002963740740000021
Figure FDA0002963740740000022
Figure FDA0002963740740000023
wherein, the first constraint ensures that the node sending information is provided with a synchronous phasor measurement device, i and j are the serial numbers of the nodes in the sub-region m, and zi，jFor data transmission decision variables, z if the synchronous phasor measurement apparatus of node i communicates with the phasor data concentrator of node ji，jIs 1, otherwise zi，jIs 0; the second constraint ensures that the nodes receiving the measurement information are equipped with phasor data concentrators, ziSending a row vector of decision variables, y, for all data associated with node i in sub-region mmA column vector consisting of decision variables configured for all phasor data concentrators in the sub-region m; the third constraint ensures that each subregion has one and only one data concentrator;
(4) the adjacent subregion overlapping node decision variable constraint is as follows:
xi＝1，i∈Ωm∩Ωn，m∈ΓZ，n∈Γz
wherein m and n are both sub-region numbers; i is the number of the node overlapped by the sub-region m and the sub-region n; omegamAnd omeganRespectively representing the sets of the nodes contained in the sub-regions m and n;
(5) the information interaction constraint among the phasor data concentrators is as follows:
Figure FDA0002963740740000024
Figure FDA0002963740740000025
wherein the first constraint guarantees that the node in the sub-region m communicating with the sub-region n configures a phasor numberData concentrator, i is the number of nodes in sub-region m, Ɩ is the number of nodes in sub-region n, wi，ƖFor information exchange decision variables, w if the phasor data concentrator of node i communicates with the phasor data concentrator of node Ɩi，ƖIs 1, otherwise wi，ƖIs 0; the second constraint ensures that nodes in sub-area n communicating with sub-area m configure the phasor data concentrator, wiA row vector y formed by all information interaction decision variables related to the node i in the sub-region mnA column vector composed of decision variables configured for the vector data concentrator in the sub-region n;
(6) the bandwidth constraints of the communication link are:
Figure FDA0002963740740000026
wherein i and j are node numbers in the sub-region m; giRepresents the degree of node i, i.e., the number of branches associated with node i; ei，jIndicating whether the equipment of the node i passes through each branch when communicating with the equipment of the node j, and if the equipment passes through the branch k, Ei，jK element of (E)i，j，kIs 1, otherwise Ei，j，kIs 0; set ΨAEach element in (a) is a set of two adjacent sub-region numbers, i.e.
Figure FDA0002963740740000027
m and n both represent the number of the sub-region; h is the set ΨAMiddle element; omegah，1Representing that a first sub-region in element h contains a set of nodes; omegah，2Representing a set of nodes contained in a second sub-region of the element h; r and t respectively represent the numbers of nodes in two adjacent sub-areas; d represents the data compression ratio when the phasor data concentrator communicates; p represents a bandwidth required for transmitting a unit phasor data frame; b represents the bandwidth of each branch configuration communication link;
(7) the configuration constraints of the communication link are:
FL≥B
L≤B
0≤L≤1
wherein F is a positive number greater than any element in B; l represents whether each branch is configured with a communication link or not, and if the branch k is configured with the communication link, L iskIs 1, otherwise LkIs 0; 0 represents an H-dimensional column vector with elements of 0, and H represents the total number of branches of the power distribution system; 1 represents an H-dimensional column vector whose elements are all 1;
5) and solving the 0-1 integer linear programming model of the distribution network synchronous measurement and communication link configuration oriented to the distributed state estimation in the step 4) to obtain a synchronous phasor measurement device, a phasor data concentrator and a communication link configuration scheme.
2. The distribution network synchronization measurement and communication link configuration method for distributed state estimation according to claim 1, wherein the cost of the communication link in step 1) is:
Figure FDA0002963740740000031
wherein, CCLRepresenting a total cost of the power distribution system configuration communication link; k represents a branch number; lambdaBRepresenting a set formed by all branches of the power distribution system; l iskFor decision variables, L if branch k configures a communication linkkIs 1, otherwise LkIs 0; cLAnd CBUnit costs representing communication link length and bandwidth, respectively; skRepresenting the length of the communication link configured by the branch k; b iskIndicating that leg k configures the bandwidth of the communication link.
3. The distribution network synchronization measurement and communication link configuration method for distributed state estimation according to claim 1, wherein the inter-node communication path vector E in step 2)r，tThe kth element of (2) is:
Figure FDA0002963740740000032
wherein E isr，t，kRepresenting an inter-node communication path vector Er，tThe kth element of (1); r and t both represent node numbers; k denotes a branch number.
4. The distribution network synchronous measurement and communication link configuration method oriented to distributed state estimation of claim 1, wherein the communication and computation architecture adopted by the distributed state estimation in step 3) is as follows:
and a centralized control center does not exist in the power distribution network, each sub-region carries out intra-region state estimation respectively, and each sub-region only interacts with the adjacent sub-regions with the state information of the boundary nodes.
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