CN113139288A - Power distribution network distributed robust state estimation method and device based on GPU (graphics processing Unit) secondary acceleration - Google Patents

Power distribution network distributed robust state estimation method and device based on GPU (graphics processing Unit) secondary acceleration Download PDF

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CN113139288A
CN113139288A CN202110440151.9A CN202110440151A CN113139288A CN 113139288 A CN113139288 A CN 113139288A CN 202110440151 A CN202110440151 A CN 202110440151A CN 113139288 A CN113139288 A CN 113139288A
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node
partition
state estimation
distribution network
power distribution
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曾顺奇
吴杰康
王瑞东
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Guangzhou Power Supply Bureau of Guangdong Power Grid Co Ltd
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Guangzhou Power Supply Bureau of Guangdong Power Grid Co Ltd
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • 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
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00—Details relating to the application field
    • G06F2113/04—Power grid distribution networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/06—Power analysis or power optimisation
    • 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]

Abstract

The application discloses a distributed robust state estimation method and device for a power distribution network based on GPU secondary acceleration, wherein the method comprises the following steps: partitioning the power distribution network to be estimated according to a network structure to obtain a plurality of partitions; constructing a power parameter model corresponding to each partition based on the power network parameters of each partition, wherein the power parameter model comprises: a branch power measurement model, a node voltage measurement model and a branch current amplitude measurement model; constructing a corresponding robust state estimation model according to the Jacobian matrix of the power parameter model of each partition; solving the robust state estimation model of each partition to obtain robust state estimation sub-results corresponding to each partition; and determining the robust state estimation result of the power distribution network according to all the robust state estimation sub-results, and obtaining the state of the power distribution network close to the reality by using the effective data under the condition that bad data exists.

Description

Power distribution network distributed robust state estimation method and device based on GPU (graphics processing Unit) secondary acceleration
Technical Field
The application relates to the technical field of power distribution network analysis, in particular to a distributed robust state estimation method and device for a power distribution network based on GPU secondary acceleration.
Background
The power distribution network state estimation is to combine the measured data obtained from the feeder line and the bus to supplement pseudo measured data such as bus load prediction, non-remote sensing remote measuring data and the like under the condition of acquiring the network structure of the whole network, and estimate the power distribution network state by using the measured data.
With the rapid development of the power market, the power demand is rapidly increased, the number of branches of the power distribution network is increased day by day, the scale is larger and larger, and the number and the types of the measuring equipment are more and more, so that more data are more and more during the estimation of the state of the power distribution network, more bad data can appear in the measured data, and the estimated accuracy of the state of the power distribution network is lower.
Therefore, how to obtain the state of the power distribution network close to the reality by using the valid data in the presence of the bad data is a technical problem to be solved urgently by those skilled in the art.
Disclosure of Invention
The application provides a distributed robust state estimation method and device for a power distribution network based on GPU secondary acceleration, which can obtain the state of the power distribution network close to the reality by using effective data under the condition that bad data exists.
In view of this, the first aspect of the present application provides a method for estimating a distributed robust state of a power distribution network based on GPU secondary acceleration, including:
partitioning the power distribution network to be estimated according to a network structure to obtain a plurality of partitions;
constructing a power parameter model corresponding to each partition based on the power network parameters of each partition, wherein the power parameter model comprises: a branch power measurement model, a node voltage measurement model and a branch current amplitude measurement model;
constructing a corresponding robust state estimation model according to the Jacobian matrix of the power parameter model of each partition;
solving the robust state estimation model of each partition to obtain robust state estimation sub-results corresponding to each partition;
and determining the robust state estimation result of the power distribution network according to all the robust state estimation sub-results.
Optionally, partitioning the power distribution network to be estimated according to a network structure to obtain a plurality of partitions, specifically including:
describing a directed graph representing the power distribution network to be estimated based on an adjacent matrix in a graph theory algorithm, and acquiring a path matrix of the power distribution network based on the adjacent matrix;
acquiring node information values of all nodes in the power distribution network based on the adjacency matrix and the path matrix;
acquiring the total number of nodes contained in the power distribution network and the number of partitions to be partitioned;
under the condition that the calculated amount of each partition is balanced, determining the maximum node number contained in each partition according to the total number of the nodes and the number of the partitions;
and partitioning the power distribution network according to the node information value corresponding to each node by considering the maximum node number of each partition and combining a depth-first search algorithm and a breadth-first search algorithm to obtain a plurality of partitions.
Optionally, the maximum node number of each partition is considered, the power distribution network is partitioned according to the node information value corresponding to each node by combining a depth-first search algorithm and a breadth-first search algorithm, so as to obtain a plurality of partitions, and the method specifically includes:
taking a power supply in the power distribution network as a main root node;
searching a feeder line with an end node farthest from the main root node according to the number of line segments in the node information value, wherein the number of the line segments is the number of the line segments from the corresponding node to the main root node;
searching from a terminal node of the feeder line to the main root node along the feeder line, and searching a superior node j of an i node when a node i is searched;
when the difference value between the first node number of the node j and the second node number of the corresponding partition is a numerical value above the maximum node number, stopping searching, and taking the node i as the initial root node of the partition, wherein the first node number is all subsequent node numbers of the node j, and the second node number is all subsequent node numbers connected with all terminal nodes of the partition;
and searching based on the initial root node corresponding to each partition to obtain the corresponding partition.
Optionally, constructing a corresponding robust state estimation model according to the jacobian matrix of the power parameter model of each partition, specifically including:
solving the power parameter model according to the power parameter model of each partition to obtain a corresponding Jacobian matrix;
according to the Jacobian matrix of each partition, constructing a corresponding robust state estimation model based on an exponential function of a standardized residual error, wherein the robust state estimation model is as follows:
Figure BDA0003031596220000031
wherein c (x) is a zero injection power equality constraint equation for the tie endpoint, J (x) is an objective function,
Figure BDA0003031596220000032
for the measurement values obtained by the measurement equipment, h (x) is a Jacobian matrix, and W is an exponential weight function diagonal matrix.
Optionally, solving the robust state estimation model of each partition to obtain a robust state estimation sub-result corresponding to each partition, specifically including:
introducing a Lagrange multiplier lambda into each robust state estimation model to obtain an unconstrained optimization problem of an augmented Lagrange function L (x, lambda), wherein the unconstrained optimization problem is as follows: minL (x, λ) ═ J (x) + λTc(x)；
Solving each unconstrained optimization problem by adopting a Newton method to obtain a correction equation of the robust state estimation model;
and solving each correction equation based on a minimum residual error method accelerated by the GPU to obtain an robust state estimation sub-result corresponding to each partition.
Optionally, constructing a corresponding robust state estimation model according to the jacobian matrix of the power parameter model of each partition as follows:
and in parallel, constructing a corresponding robust state estimation model according to the Jacobian matrix of the power parameter model of each partition.
Optionally, the branch power measurement model is:
Pij＝Vi 2Gij-ViVj(Gijcosδij+Bijsinδij)；
Qij＝-Vi 2Bij-ViVj(Gijsinδij-Bijcosδij)；
in the formula, PijIs the active power of the branch, QijIs the reactive power of the branch, GijFor the real part, V, of the admittance matrix of the nodes of the distribution networkiIs the voltage amplitude of node i, VjIs the voltage amplitude, delta, of node jijIs the phase angle difference between node i and node j, BijAn imaginary part of a power distribution network node admittance matrix is obtained;
the node power measurement model is as follows:
Figure BDA0003031596220000041
Figure BDA0003031596220000042
in the formula, PiIs the active power of the node, QiIs the reactive power of the node;
the branch current amplitude measurement model is as follows:
Iij＝{(Gij 2+Bij 2)[Vi 2+Vj 2-2ViVjcosδij]}1/2；
in the formula IijThe branch current magnitude between node i and node j.
The second aspect of the present application provides a distribution network distributed robust state estimation device based on GPU secondary acceleration, including:
the partition unit is used for partitioning the power distribution network to be estimated according to a network structure to obtain a plurality of partitions;
the first construction unit is used for constructing a power parameter model corresponding to each partition based on the power network parameters of each partition, wherein the power parameter model comprises: a branch power measurement model, a node voltage measurement model and a branch current amplitude measurement model;
the second construction unit is used for constructing a corresponding robust state estimation model according to the Jacobian matrix of the power parameter model of each partition;
the solving unit is used for solving the robust state estimation model of each partition to obtain robust state estimation sub-results corresponding to each partition;
and the determining unit is used for determining the robust state estimation result of the power distribution network according to all the robust state estimation sub-results.
Optionally, the partition unit specifically includes:
the first acquisition subunit is used for describing a directed graph representing the power distribution network to be estimated based on an adjacent matrix in a graph theory algorithm and acquiring a path matrix of the power distribution network based on the adjacent matrix;
the second obtaining subunit is configured to obtain a node information value of each node in the power distribution network based on the adjacency matrix and the path matrix;
the third obtaining subunit is used for obtaining the total number of nodes contained in the power distribution network and the number of partitions to be partitioned;
the determining subunit is used for determining the maximum number of nodes contained in each partition according to the total number of the nodes and the number of the partitions under the condition that the calculated amount of each partition is balanced;
and the partition subunit is used for partitioning the power distribution network according to the node information value corresponding to each node by considering the maximum node number of each partition and combining a depth-first search algorithm and a breadth-first search algorithm to obtain a plurality of partitions.
The third aspect of the application provides a distributed robust state estimation device for a power distribution network based on GPU secondary acceleration, which comprises a processor and a memory;
the memory is used for storing program codes and transmitting the program codes to the processor;
the processor is configured to execute the method for estimating the distributed robust state of the power distribution network based on GPU secondary acceleration according to instructions in the program code.
A fourth aspect of the present application provides a storage medium, where the storage medium is configured to store program codes, and the program codes are configured to execute the method for estimating a distributed robust state of a power distribution network based on GPU secondary acceleration according to the first aspect.
According to the technical scheme, the embodiment of the application has the following advantages:
the application provides a distributed robust state estimation method for a power distribution network based on GPU secondary acceleration, which comprises the following steps: partitioning the power distribution network to be estimated according to a network structure to obtain a plurality of partitions; constructing a power parameter model corresponding to each partition based on the power network parameters of each partition, wherein the power parameter model comprises: a branch power measurement model, a node voltage measurement model and a branch current amplitude measurement model; constructing a corresponding robust state estimation model according to the Jacobian matrix of the power parameter model of each partition; solving the robust state estimation model of each partition to obtain robust state estimation sub-results corresponding to each partition; and determining the robust state estimation result of the power distribution network according to all the robust state estimation sub-results. Carry out the subregion to large-scale distribution network in this application for calculated amount and redundancy in every subregion are roughly equal, with each subregion measurement error limitation in this subregion when reducing the operation dimension, have certain tolerance difference, can be under the condition that has bad data, utilize effective data to obtain the distribution network state of being close to reality.
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In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present application, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without inventive exercise.
Fig. 1 is a schematic flowchart of a first embodiment of a distributed robust state estimation method for a power distribution network based on GPU secondary acceleration in the embodiment of the present application;
fig. 2 is a schematic flowchart of a second embodiment of a distributed robust state estimation method for a power distribution network based on GPU secondary acceleration in the embodiment of the present application;
fig. 3 is a schematic structural diagram of an embodiment of a distributed robust state estimation apparatus for a power distribution network based on GPU secondary acceleration in the embodiment of the present application.
Detailed Description
The embodiment of the application provides a distributed robust state estimation method and device for a power distribution network based on GPU secondary acceleration, and the method and device can obtain the state of the power distribution network close to the reality by using effective data under the condition that bad data exist.
In order to make the technical solutions of the present application better understood, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
Referring to fig. 1, a schematic flow chart of a first embodiment of a distributed robust state estimation method for a power distribution network based on GPU secondary acceleration in the embodiment of the present application is shown.
In this embodiment, a distributed robust state estimation method for a power distribution network based on GPU secondary acceleration includes:
step 101, partitioning the power distribution network to be estimated according to a network structure to obtain a plurality of partitions.
It can be understood that a large-scale power distribution network is automatically divided into a plurality of small partitions with calculated amount and equivalent redundancy according to the processing capacity, some measurement values with larger errors can be limited in the partitions where the measurement values are located, the influence of local bad data on the whole network is prevented, the redundancy of each partition is also improved, the accuracy of state estimation is improved, and the large-scale power distribution network has certain tolerance to measurement errors.
102, constructing a power parameter model corresponding to each partition based on the power network parameters of each partition, wherein the power parameter model comprises: the system comprises a branch power measurement model, a node voltage measurement model and a branch current amplitude measurement model.
After the power distribution network is partitioned, measurement conversion and model construction of each partition are the same, node voltage amplitude and phase angle are used as state variables, and all data and variables are represented by a normalized value system. The state variable is expressed as x ═ δ, V]TAnd converting the measurement data of the system measurement equipment and the solved pseudo measurement into a corresponding node voltage representation function to obtain a corresponding measurement model.
In this embodiment, the active power measurement P of the branch is obtainedijAnd reactive power measurement QijThe corresponding branch power measurement model is:
Pij＝Vi 2Gij-ViVj(Gijcosδij+Bijsinδij)；
Qij＝-Vi 2Bij-ViVj(Gijsinδij-Bijcosδij)；
in the formula, GijFor the real part, V, of the admittance matrix of the nodes of the distribution networkjIs the voltage amplitude, delta, of node jijIs node i and node jPhase angle difference between them, BijAnd an imaginary part of the admittance matrix of the power distribution network node.
Obtaining node injection active power PiAnd reactive power measurement QiThe node power measurement model is as follows:
Figure BDA0003031596220000071
Figure BDA0003031596220000072
obtaining node voltage amplitude measurement ViAnd the phase angle is measurediThe node voltage measurement model is as follows:
Vi＝Vi；
δi＝δi。
obtaining branch current amplitude measurement IijThe corresponding branch flow amplitude measurement model is as follows:
Iij＝{(Gij 2+Bij 2)[Vi 2+Vj 2-2ViVjcosδij]}1/2。
and 103, constructing a corresponding robust state estimation model according to the Jacobian matrix of the power parameter model of each partition.
The robust state estimation is an estimation method which fully utilizes effective data, reduces the influence of available data, identifies and eliminates bad data, establishes a certain objective function and finally obtains an estimated value close to the actual running state of the power distribution network under the condition that bad data exists.
And 104, solving the robust state estimation model of each partition to obtain robust state estimation sub-results corresponding to each partition.
And after the partition decoupling is realized, each partition is subjected to robust state estimation to obtain robust state estimation sub-results corresponding to each partition.
And 105, determining the robust state estimation result of the power distribution network according to all the robust state estimation sub-results.
After the robust state estimation sub-results of each partition are obtained, all the robust state estimation sub-results are integrated, and then the robust state estimation result of the whole power distribution network can be determined. For example, after the distribution network is partitioned, a partition 1, a partition 2, a partition 3, a partition 4, and a partition 5 are obtained, and the robust state estimation sub-result corresponding to each partition is as follows: the robust state estimation sub-result 1, the robust state estimation sub-result 2, the robust state estimation sub-result 3, the robust state estimation sub-result 4 and the robust state estimation sub-result 5, and the robust state estimation result of the power distribution network can be determined by combining the 5 robust state estimation sub-results.
In this embodiment, a large-scale power distribution network is partitioned, so that the calculated amount and the redundancy in each partition are approximately equal, the measurement error of each partition is limited in the partition while the calculation dimensionality is reduced, and the method has a certain tolerance, and can obtain the state of the power distribution network close to the reality by using effective data under the condition of poor data.
The first embodiment of the method for estimating the distributed robust state of the power distribution network based on the secondary acceleration of the GPU is provided above, and the second embodiment of the method for estimating the distributed robust state of the power distribution network based on the secondary acceleration of the GPU is provided below.
Referring to fig. 2, a flowchart of a second embodiment of a distributed robust state estimation method for a power distribution network based on GPU secondary acceleration in the embodiment of the present application is shown.
In this embodiment, a distributed robust state estimation method for a power distribution network based on GPU secondary acceleration includes:
step 201, describing a directed graph representing the power distribution network to be estimated based on the adjacency matrix in the graph theory algorithm, and acquiring a path matrix of the power distribution network based on the adjacency matrix.
The distribution network generally adopts a closed-loop structure, operates in an open-loop mode, has a radiation type overall structure, takes a power supply in a power network as a main root node, processes distributed energy into common nodes, and can be abstracted into a graph when only the topological relation of the network is considered without considering the characteristics of network elements, wherein the graph is the combination of abstract nodes and branches and reflects the branches contained in the graph and the connection relation among the nodes. In graph theory, a graph can be represented as G (E, V), and when an edge in the graph has a direction, the graph becomes a directed graph.
In this embodiment, when a power distribution network is partitioned, a path problem from a root node to each feeder terminal node and a problem of upper and lower nodes of each node are considered, when two nodes are connected through a branch, the direction of the branch is a node close to the root node and flows to a node close to the feeder terminal point, and the root node is generally set as node 1.
(1) Definition of adjacency matrix
If there are n nodes in the graph, the adjacent order matrix is n × n square matrix (a)ij)n×nWhen a directed edge from i to j exists between two nodes i and j, then aij1, otherwise aij0; and when a directed edge pointing to i from j exists between the i node and the j node, aji1, otherwise aji0. The directed graph G (E, V) adjacency matrix E is represented as:
Figure BDA0003031596220000091
obviously, the adjacency matrix of the directed graph is generally not symmetric. When the topology of the distribution network can be accurately obtained, the topology of the distribution network can be represented by the adjacency matrix.
(2) Definition of Path matrix
A path is a line segment that starts from a certain starting node i and passes through a plurality of branches and nodes to reach an end point j (the branches and nodes that the path passes through cannot be repeated). The path matrix is an important concept for describing the existence of paths and the distance between any nodes, and the path matrix L of the directed graph G (E, V) is roughly expressed as:
Figure BDA0003031596220000092
in the formula: n is the distance value between two nodes.
When the adjacency matrix E is known, the path matrix L is obtained by the following steps:
(1) let L be E;
(2) starting from the end point of the feeder line, the end point node number of the feeder line with the row number corresponding to the row number with all 0 elements can be known from the adjacent matrix, and when the number is the end point of the feeder line with j and l is the end point of the feeder line with jijWhen 1, find another side node k of the branch with direction pointing to node i from the adjacency matrix, and record it as the connected superior node, and obtain lkiWhen 1, a new element l is obtainedkj＝lki+lijAnd 2, by analogy, obtaining the distance values between the terminal node and all the nodes with paths on the feeder line, and then starting to search the superior nodes, wherein the distance between the superior nodes and the nodes with paths is the distance between the terminal node and the nodes, minus 1, for example, the last four nodes of the feeder line are arranged in the sequence of i, j, k, f, and are the terminal nodes:
ljf＝2,lif＝3；
ljk＝ljf-1＝1,lik＝lif-1＝2；
and repeating the steps until judging whether paths exist among all nodes from the root node to the end node of the feeder line and calculating the distance if the paths exist.
(3) And (4) changing another feeder line, deducing from the end point, and returning to the step (2) until all the feeder lines are calculated.
(4) And obtaining a path matrix F after all elements are calculated.
Step 202, acquiring node information values of all nodes in the power distribution network based on the adjacency matrix and the path matrix.
After the adjacency matrix and the path matrix are obtained, the relevance of the node in the power distribution network and other nodes can be obtained, and the required node information value is obtained, wherein the information contained in the node information value comprises the following information:
(1) the number of the upper node connected with the node (the upper node is the node which is directly connected with the node and is close to the side of the root node), namely the opposite side node which flows to the node branch in the direction in the adjacent matrix.
(2) And the number of a lower node connected with the node (the lower node is a node which is directly connected with the node and is close to the end point side of the feeder line).
(3) The number of subordinate nodes connected to a node (a subordinate node is a node which is directly connected with the node and is close to the tail end side, so that the node is connected with a plurality of branches, and the node has a plurality of subordinate nodes).
(4) The number of all subsequent nodes connected with the node (namely the number of all nodes connected behind the node, which is used for conveniently determining whether the maximum number of the nodes contained in each partition is reached in the process of searching from the terminal node to the power supply end) is the distance value between the node and the feeder terminal.
(5) The distance of a node from the primary root node, i.e., the first row of elements in the path matrix.
And step 203, acquiring the total number of nodes contained in the power distribution network and the number of partitions to be partitioned.
And step 204, determining the maximum node number contained in each partition according to the total number of the nodes and the partition number under the condition of balanced calculated amount of each partition.
It should be noted that the computation amount of each partition should be kept substantially balanced, i.e., the number of nodes contained in each partition should be approximately equal. The partition boundary can automatically identify the boundary branch and the node, and the boundary branch and the node can be properly processed when each partition is calculated, so that communication is realized between each partition.
Under the condition of considering the factors, the total number of the nodes contained in the power distribution network and the number of the partitions to be partitioned can determine that each partition can contain the maximum number of the nodes as follows under the condition that the calculated amount of each partition is balanced and the power distribution network is given by the node connection line:
Figure BDA0003031596220000101
in the formula: f (integer variable) is the maximum number of nodes that each partition can contain; k is the number of partitions; n is the total number of nodes in the power distribution network; t is an adjustment factor, typically taking a value between 1 and 2.
Step 205, taking into account the maximum node number of each partition, partitioning the power distribution network according to the node information value corresponding to each node by combining a depth-first search algorithm and a breadth-first search algorithm to obtain a plurality of partitions.
Considering the maximum number of nodes of each partition, partitioning the power distribution network according to node information values corresponding to the nodes by combining a depth-first search algorithm and a breadth-first search algorithm to obtain a plurality of partitions, and specifically comprising the following steps:
taking a power supply in a power distribution network as a main root node;
searching a feeder line with the tail end node farthest from the main root node according to the number of line segments in the node information value, wherein the number of the line segments is the number of the line segments from the corresponding node to the main root node;
searching from a terminal node of the feeder line to a main root node along the feeder line, and searching a superior node j of an i node when a node i is searched;
when the difference value between the first node number of the node j and the second node number of the corresponding partition is a numerical value above the maximum node number, stopping searching, and taking the node i as the initial root node of the partition, wherein the first node number is all subsequent node numbers of the node j, and the second node number is all subsequent node numbers connected with all terminal nodes of the partition;
and searching based on the initial root node corresponding to each partition to obtain the corresponding partition.
The general idea of partitioning is as follows: according to the node information value, depth-first search and breadth-first search are combined, from the perspective of balance of calculated amount of each partition, from the 'line segment number from the node to the main root node' of the node information value, a feeder line with the end node farthest from the main root node is sequentially searched, partitions are searched from the end node of the feeder line to the power supply end along the feeder line, then the feeder line with the end node farthest from the root node is continuously searched, the feeder line is partitioned, and finally the main root node is connected with the nodes which are not partitioned to form the main root node partition.
Partition search stop conditions on the feeder:
(1) in the process of the partition from the end node to the previous search, when the node i is searched, the superior node of the node i is continuously searched, the node is made to be the number of all the subsequent nodes connected with j, j minus the number of all the subsequent nodes connected with the end node of the partition is larger than or equal to the maximum number F of the partition, the number of the nodes contained in the partition is indicated to reach the limit value, the search is stopped, and the node i is the initial root node of the partition.
(2) In the partition process of starting the previous search from the end node, when a node i is searched, the upper node of the node i is continuously searched, the node is made to be j, the node is found to be divided into partitions, the search is stopped, and at the moment, i is the starting node of the partition.
(3) In order to ensure that the calculated amount of the root node area is equal to that of each subsequent partition, the root node area also needs to have a certain number of nodes. When a partition close to the master root node is searched, if the judgment standard in (1) is used only, the process of searching a partition from the end node to the power supply end may occur, and a certain number of nodes cannot be left for the root node area because the maximum number of nodes F contained in each area is not reached and the partition is searched in the direction of the power supply end. In order to avoid the situation, a judgment standard is provided, namely when the number of line segments from a certain node i to a main root node is less than a certain set value O (the O value is determined by the number of feeder lines), the search is stopped, and the node i is the root node of the partition.
Processing branch lines during partitioning:
in the process of searching the subareas, for the lines without branches, the subareas are easily divided by searching from the end node to the power supply end according to the connection relation, but when the branches exist, the processing is troublesome. Therefore, the "number of nodes connected to all subsequent nodes" of the node information value is used for processing. When searching for a node from the power source end, if a node with a branch is encountered, the number of nodes on the branch line is automatically included in all the subsequent nodes connected with the node.
When the state estimation is carried out on each subarea, the connecting line and the node on the other side of the connecting line are also included, so that the state of the node on the connecting line and the load flow on the connecting line are repeatedly calculated, the error of the subarea network state estimation is reduced, and the result is more accurate.
Step 206, constructing a power parameter model corresponding to each partition based on the power network parameters of each partition, wherein the power parameter model comprises: the system comprises a branch power measurement model, a node voltage measurement model and a branch current amplitude measurement model.
Correspondingly, the electric power parameter models of all the partitions are constructed in parallel, the state estimation of all the partitions is performed simultaneously (parallel calculation) by adopting a distributed state estimation method in operation, the distributed parallel calculation time is approximately equal to the whole state estimation time divided by the number of the partitions, and under the condition that the communication of all the partitions is good, the estimation time is reduced by times, so that the state estimation is accelerated once.
And step 207, solving the power parameter model according to the power parameter model of each partition to obtain a corresponding Jacobian matrix.
It is understood that the solution of the jacobian matrix is specifically: each measurement value has a corresponding measurement model, the measurement model is derived, and the jacobian matrix can be obtained by substituting the numerical value of the corresponding power distribution network node admittance matrix and the voltage amplitude phase angle of each node.
It should be noted that, according to the jacobian matrix of the power parameter model of each partition, the corresponding robust state estimation model is constructed as follows:
and in parallel, constructing a corresponding robust state estimation model according to the Jacobian matrix of the power parameter model of each partition.
And 208, constructing a corresponding robust state estimation model based on the exponential function of the standardized residual error according to the Jacobian matrix of each partition.
In the state estimation model in this embodiment, the zero injection measurement characteristics and the influence of residuals of different measurements on the weight function are considered, and an exponential weight function based on an exponential weighted least squares (EFWLS) state estimation model is established by means of an exponential weight function of a normalized residual, and the centralized form of the state estimation model can be expressed as follows:
Figure BDA0003031596220000131
wherein c (x) is the zero injection power equality constraint equation of the contact terminal, J (x) is the objective function representing the error magnitude of the measurement function and the measurement value,
Figure BDA0003031596220000132
for the measurement values obtained by the measurement equipment, h (x) is a Jacobian matrix, and W is an exponential weight function diagonal matrix.
c (x) a zero injection power equality constraint equation for the tie endpoint, i.e. the point at which the node injection power is 0, represented by the state variable, assuming the node i injection point, the equation is:
Figure BDA0003031596220000133
Figure BDA0003031596220000134
the zero injection equality equation is simultaneously used as a virtual measurement equation and an equality constraint equation so as to improve the observability and the state estimation convergence of the system; w is an exponential weight function diagonal matrix:
Figure BDA0003031596220000135
the element calculation expression is as follows:
Figure BDA0003031596220000136
in the formula (I), the compound is shown in the specification,
Figure BDA0003031596220000137
for fixing the weight matrix R-1Measure the weight value r of iNiNormalized residual error for measurement i; the normalized residual is calculated using the internal student residuals, i.e.:
Figure BDA0003031596220000138
wherein R is the inverse of the fixed weight matrix, RiFor the ith residual value of the residual vector r, K is the residual sensitivity matrix, which is K ═ I-H (H) for the weighted least squares estimationTWH)-1HTW, wherein I is a unit matrix, and H is a Jacobian matrix; sigma is a scale parameter of the normalized residual error, and the initial value calculation formula is
Figure BDA0003031596220000141
m and n are respectively the number of measurement and the number of variables.
Solving the weight function diagonal matrix can obtain that for normal measurement with smaller residual error, the exponential weight function value is approximately equal to the prior fixed weight of the conventional least square; for bad measurement of large residual error, the EFWLS estimation model dynamically reduces the weight of the EFWLS estimation model into 0 through the exponential weight function so as to inhibit the influence of bad data on state estimation, meanwhile, the transition of the exponential weight function between normal measurement and bad measurement is smooth and continuous, the measurement is prevented from being refused or accepted, and the measurement value which is not good but still available is effectively reserved. Along with the iterative computation of the state estimation, the identification and elimination of bad data are automatically completed, so that the robust estimation of bad measurement is realized, and the state estimation precision is improved.
And 209, introducing a Lagrangian multiplier lambda into each robust state estimation model to obtain an unconstrained optimization problem of the augmented Lagrangian function L (x, lambda).
The unconstrained optimization problem is as follows: minL (x, λ) ═ J (x) + λTc(x)。
And step 210, solving each unconstrained optimization problem by adopting a Newton method to obtain a correction equation of the robust state estimation model.
And solving the optimality condition by adopting a Newton method to obtain an iterative correction equation matrix form:
Figure BDA0003031596220000142
in the formula, l is iteration times; matrix array
Figure BDA0003031596220000143
In the embodiment, the anti-differential model correction equation is obtained by the Newton method, the Newton method is used for solving the correction equation and adopts a direct method, the direct method has a better solution result for the dense linear equation with small scale, and a more accurate result can be obtained in limited steps.
After partition decoupling is realized, each sub-partition uses exponential weighted robust state estimation until a partition convergence condition is met; after adjacent partitions exchange boundary node estimation information, if the integral convergence is not met, the state estimation of each partition is carried out again after information interaction is carried out until each partition and the integral convergence condition are met.
The convergence condition of each partition is Δ x(l)< ε, ε is the convergence accuracy of each partition, and is generally set to 10-4When the power distribution network partition is divided, the boundary point is processed in this embodiment by dividing the node on the other side of the interconnection switch into the partition, that is, the state quantity of the boundary node of each partition is repeatedly calculated twice, so the overall convergence requirement is that the error of the estimated value of the overlapping node in different partitions cannot exceed the precision setting, and if the i and j nodes are the overlapping nodes of partition 2 and partition 3, the convergence requires Δ xi＝|x2,i-x3,i< ε and Δ xj＝|x2,j-x3,jIf < epsilon, the error can be given according to the precision requirement.
And step 211, solving each correction equation based on a minimum residual error method accelerated by the GPU to obtain an robust state estimation sub-result corresponding to each partition.
The mode of simultaneous calculation in each partition is based on distributed parallel primary acceleration, the distributed state estimation divides a large-scale power grid into a plurality of small-scale sub-partitions, and a parallel calculation architecture is adopted, so that the calculation scale can be effectively reduced, and the calculation efficiency is improved. In the embodiment, the operation and the processing of the partition data are transferred to the corresponding processors for parallel processing. The method and the device enable all the partitions to be processed at the same time, the used estimation time is approximately the centralized state estimation time divided by the number of the partitions, the estimation time is greatly reduced, the complexity of state estimation is reduced, and the estimation of all the partitions is simpler and faster.
In order to further reduce the computation time in this embodiment, secondary acceleration based on GPU parallelism is also performed. Solving the correction equation by using a minimum residual error method based on GPU parallel acceleration, wherein the Newton method adopts a direct method for solving the correction equation, the direct method has a better solution result for the dense linear equation with small scale, and a more accurate result can be obtained in limited steps; however, when a is a large sparse matrix, a direct method is used for carrying out element elimination simplification, a large number of non-zero filling elements are generated by the A, the sparsity of the A is broken, the space consumed in storage of the matrix A is increased, the complexity of calculation is increased, and the solution is more time-consuming.
A) GPU acceleration of minimum residual method iteration.
The modified equation is in the format of Ax ═ b, the actual power distribution network state estimation is converted into a sparse linear equation solving problem, the minimum residual error iteration method in the Krylov subspace method is adopted in the embodiment, the accurate solution of an equation set is approximated through the repeated iteration process, an approximate solution meeting a given error is obtained, the approximate solution is transplanted to a GPU for solving, the solving speed of the modified equation is greatly accelerated, the modified equation is used as a core part of the distributed robust state estimation calculation of the power distribution network based on GPU quadratic acceleration, and the optimization of the solving speed has great significance for the solving time of the whole distributed robust state estimation algorithm based on GPU quadratic acceleration.
Assuming a given sparse linear equation set of the form: and Ax is b, and the basic minimum residual error calculation process is as follows:
(1) inputs A, b and x0Calculating x ═ x0；
(2) Setting the algorithm termination precision epsilon to be more than 0, and setting the iteration number k to be 0;
(3) calculating rk＝b-Axk，
(4) If rk||∞If the epsilon is less than epsilon, outputting a result; otherwise, continuing to run downwards;
(5) computing
Figure BDA0003031596220000161
xk+1＝xk+αkrk；
(6) And k is k +1, and the step (3) is carried out.
The step of analyzing the minimum residual method can find that the coefficient matrix A is invariable in operation, and A has no injection element in a plurality of iterations before convergence.
If the coefficient matrix a is of order n and there are k non-zero elements, the minimum residual method needs to be calculated as follows:
TABLE 1
Figure BDA0003031596220000162
In the embodiment, a processing formula in each step of the minimum residual iteration method is written into a kernel function for the CUDA, the kernel function can be obtained from a table, and from the aspects of calculation amount, complexity and difficulty of program optimization, sparse matrix multiplication and vector inner product modulo are operations with large calculation amount in the algorithm, so that the performance of the whole algorithm is greatly influenced, the sparse matrix multiplication has the characteristic of row independence, and the parallel operation on the GPU has an obvious acceleration effect.
And step 212, determining the robust state estimation result of the power distribution network according to all the robust state estimation sub-results.
In this embodiment, a large-scale power distribution network is partitioned, so that the calculated amount and the redundancy in each partition are approximately equal, the measurement error of each partition is limited in the partition while the calculation dimensionality is reduced, and the method has a certain tolerance, and can obtain the state of the power distribution network close to the reality by using effective data under the condition of poor data.
In the above, for the second embodiment of the method for estimating a distributed robust state of a power distribution network based on GPU secondary acceleration provided in the embodiment of the present application, please refer to fig. 3 for the following embodiment of the device for estimating a distributed robust state of a power distribution network based on GPU secondary acceleration provided in the embodiment of the present application.
An embodiment of a distribution network distributed robust state estimation device based on GPU secondary acceleration in the embodiment of the present application includes:
the partitioning unit 301 is configured to partition the power distribution network to be estimated according to a network structure to obtain a plurality of partitions;
a first constructing unit 302, configured to construct a power parameter model corresponding to each partition based on the power network parameters of each partition, where the power parameter model includes: a branch power measurement model, a node voltage measurement model and a branch current amplitude measurement model;
a second constructing unit 303, configured to construct a corresponding robust state estimation model according to the jacobian matrix of the power parameter model of each partition;
the solving unit 304 is configured to solve the robust state estimation model of each partition to obtain a robust state estimation sub-result corresponding to each partition;
a determining unit 305, configured to determine a robust state estimation result of the power distribution network according to all robust state estimation sub-results.
Optionally, the partition unit 301 specifically includes:
the first acquisition subunit is used for describing a directed graph representing the power distribution network to be estimated based on an adjacent matrix in a graph theory algorithm and acquiring a path matrix of the power distribution network based on the adjacent matrix;
the second acquisition subunit is used for acquiring node information values of all nodes in the power distribution network based on the adjacency matrix and the path matrix;
the third acquiring subunit is used for acquiring the total number of nodes contained in the power distribution network and the number of partitions to be partitioned;
the determining subunit is used for determining the maximum node number contained in each partition according to the total number of the nodes and the partition number under the condition of balanced calculated amount of each partition;
and the partition subunit is used for partitioning the power distribution network according to the node information value corresponding to each node by considering the maximum node number of each partition and combining a depth-first search algorithm and a breadth-first search algorithm to obtain a plurality of partitions.
In this embodiment, a large-scale power distribution network is partitioned, so that the calculated amount and the redundancy in each partition are approximately equal, the measurement error of each partition is limited in the partition while the calculation dimensionality is reduced, and the method has a certain tolerance, and can obtain the state of the power distribution network close to the reality by using effective data under the condition of poor data.
The embodiment of the application also provides distribution network distributed robust state estimation equipment based on GPU secondary acceleration, and the equipment comprises a processor and a memory; the memory is used for storing the program codes and transmitting the program codes to the processor; the processor is configured to execute the distributed robust state estimation method for the power distribution network based on GPU secondary acceleration according to the first embodiment or the second embodiment.
The embodiment of the application further provides a storage medium, wherein the storage medium is used for storing program codes, and the program codes are used for executing the method for estimating the distributed robust state of the power distribution network based on the secondary acceleration of the GPU in the first embodiment or the second embodiment.
It is clear to those skilled in the art that, for convenience and brevity of description, the specific working processes of the above-described apparatuses and units may refer to the corresponding processes in the foregoing method embodiments, and are not described herein again.
In the several embodiments provided in the present application, it should be understood that the disclosed apparatus and method may be implemented in other ways. For example, the above-described apparatus embodiments are merely illustrative, and for example, the division of the units is only one logical functional division, and other divisions may be implemented, for example, a plurality of units or components may be combined or integrated into another grid network to be installed, or some features may be omitted or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection through some interfaces, devices or units, and may be in an electrical, mechanical or other form.
The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units can be selected according to the needs to achieve the purpose of the solution of the embodiment.
In addition, functional units in the embodiments of the present application may be integrated into one processing unit, or may exist alone physically, or two or more units are integrated into one unit. The integrated unit can be realized in a form of hardware, and can also be realized in a form of a software functional unit.
The integrated unit, if implemented in the form of a software functional unit and sold or used as a stand-alone product, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present application may be substantially implemented or contributed to by the prior art, or all or part of the technical solution may be embodied in a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present application. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-only memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and the like.
The above embodiments are only used for illustrating the technical solutions of the present application, and not for limiting the same; although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions in the embodiments of the present application.

Claims (10)

1. A distributed robust state estimation method for a power distribution network based on GPU secondary acceleration is characterized by comprising the following steps:
partitioning the power distribution network to be estimated according to a network structure to obtain a plurality of partitions;
constructing a power parameter model corresponding to each partition based on the power network parameters of each partition, wherein the power parameter model comprises: a branch power measurement model, a node voltage measurement model and a branch current amplitude measurement model;
constructing a corresponding robust state estimation model according to the Jacobian matrix of the power parameter model of each partition;
solving the robust state estimation model of each partition to obtain robust state estimation sub-results corresponding to each partition;
and determining the robust state estimation result of the power distribution network according to all the robust state estimation sub-results.
2. The distributed robust state estimation method for the power distribution network based on the GPU secondary acceleration according to claim 1, wherein the power distribution network to be estimated is partitioned according to a network structure to obtain a plurality of partitions, specifically comprising:
describing a directed graph representing the power distribution network to be estimated based on an adjacent matrix in a graph theory algorithm, and acquiring a path matrix of the power distribution network based on the adjacent matrix;
acquiring node information values of all nodes in the power distribution network based on the adjacency matrix and the path matrix;
acquiring the total number of nodes contained in the power distribution network and the number of partitions to be partitioned;
under the condition that the calculated amount of each partition is balanced, determining the maximum node number contained in each partition according to the total number of the nodes and the number of the partitions;
and partitioning the power distribution network according to the node information value corresponding to each node by considering the maximum node number of each partition and combining a depth-first search algorithm and a breadth-first search algorithm to obtain a plurality of partitions.
3. The distributed robust state estimation method for the power distribution network based on the GPU secondary acceleration according to claim 2, wherein the maximum number of nodes in each partition is considered, and the power distribution network is partitioned according to a node information value corresponding to each node in combination with a depth-first search algorithm and a breadth-first search algorithm to obtain a plurality of partitions, specifically comprising:
taking a power supply in the power distribution network as a main root node;
searching a feeder line with an end node farthest from the main root node according to the number of line segments in the node information value, wherein the number of the line segments is the number of the line segments from the corresponding node to the main root node;
searching from a terminal node of the feeder line to the main root node along the feeder line, and searching a superior node j of an i node when a node i is searched;
when the difference value between the first node number of the node j and the second node number of the corresponding partition is a numerical value above the maximum node number, stopping searching, and taking the node i as the initial root node of the partition, wherein the first node number is all subsequent node numbers of the node j, and the second node number is all subsequent node numbers connected with all terminal nodes of the partition;
and searching based on the initial root node corresponding to each partition to obtain the corresponding partition.
4. The distributed robust state estimation method for the power distribution network based on the GPU secondary acceleration of claim 1, wherein the building of the corresponding robust state estimation model according to the jacobian matrix of the power parameter model of each partition specifically includes:
solving the power parameter model according to the power parameter model of each partition to obtain a corresponding Jacobian matrix;
according to the Jacobian matrix of each partition, constructing a corresponding robust state estimation model based on an exponential function of a standardized residual error, wherein the robust state estimation model is as follows:
Figure FDA0003031596210000021
wherein c (x) is a zero injection power equality constraint equation for the tie endpoint, J (x) is an objective function,
Figure FDA0003031596210000022
for the measurement values obtained by the measurement equipment, h (x) is a Jacobian matrix, and W is an exponential weight function diagonal matrix.
5. The distributed robust state estimation method for the power distribution network based on the GPU secondary acceleration according to claim 4, wherein the robust state estimation model of each partition is solved to obtain the robust state estimation sub-result corresponding to each partition, and specifically comprises:
introducing a Lagrange multiplier lambda into each robust state estimation model to obtain an unconstrained optimization problem of an augmented Lagrange function L (x, lambda), wherein the unconstrained optimization problem is as follows: min L (x, λ) ═ j (x) + λTc(x)；
Solving each unconstrained optimization problem by adopting a Newton method to obtain a correction equation of the robust state estimation model;
and solving each correction equation based on a minimum residual error method accelerated by the GPU to obtain an robust state estimation sub-result corresponding to each partition.
6. The distributed robust state estimation method for the power distribution network based on the GPU secondary acceleration as recited in claim 1, characterized in that according to the Jacobian matrix of the power parameter model of each partition, the corresponding robust state estimation model is constructed as follows:
and in parallel, constructing a corresponding robust state estimation model according to the Jacobian matrix of the power parameter model of each partition.
7. The distributed robust state estimation method of power distribution network based on GPU quadratic acceleration according to claim 1,
the branch power measurement model is as follows:
Pij＝Vi 2Gij-ViVj(Gijcosδij+Bijsinδij)；
Qij＝-Vi 2Bij-ViVj(Gijsinδij-Bijcosδij)；
in the formula, PijIs the active power of the branch, QijIs the reactive power of the branch, GijFor the real part, V, of the admittance matrix of the nodes of the distribution networkiIs the voltage amplitude of node i, VjIs the voltage amplitude, delta, of node jijIs the phase angle difference between node i and node j, BijAn imaginary part of a power distribution network node admittance matrix is obtained;
the node power measurement model is as follows:
Figure FDA0003031596210000031
Figure FDA0003031596210000032
in the formula, PiIs the active power of the node, QiIs the reactive power of the node;
the branch current amplitude measurement model is as follows:
Iij＝{(Gij 2+Bij 2)[Vi 2+Vj 2-2ViVjcosδij]}1/2；
in the formula IijThe branch current magnitude between node i and node j.
8. The utility model provides a distribution network distributed robust state estimation device based on GPU secondary acceleration which characterized in that includes:
the partition unit is used for partitioning the power distribution network to be estimated according to a network structure to obtain a plurality of partitions;
the first construction unit is used for constructing a power parameter model corresponding to each partition based on the power network parameters of each partition, wherein the power parameter model comprises: a branch power measurement model, a node voltage measurement model and a branch current amplitude measurement model;
the second construction unit is used for constructing a corresponding robust state estimation model according to the Jacobian matrix of the power parameter model of each partition;
the solving unit is used for solving the robust state estimation model of each partition to obtain robust state estimation sub-results corresponding to each partition;
and the determining unit is used for determining the robust state estimation result of the power distribution network according to all the robust state estimation sub-results.
9. A distributed robust state estimation device of a power distribution network based on GPU secondary acceleration is characterized by comprising a processor and a memory;
the memory is used for storing program codes and transmitting the program codes to the processor;
the processor is used for executing the distributed robust state estimation method of the power distribution network based on the GPU secondary acceleration according to any one of claims 1 to 7 according to instructions in the program codes.
10. A storage medium for storing a program code for executing the method for estimating distributed robust state of power distribution network based on GPU quadratic acceleration according to any of claims 1 to 7.
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Application publication date: 20210720