CN114169118B - Power distribution network topological structure identification method considering distributed power output correlation - Google Patents
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Abstract
In an off-line stage, the preprocessed power grid data is used as a training set to train a neural network, in an on-line stage, a synthesized node voltage amplitude sample is obtained through the trained neural network input by a test set, and then the power distribution network topology is identified by adopting a maximum spanning tree algorithm based on a maximum information coefficient to obtain all node pairs of the power distribution network, wherein each node pair represents one side in the power distribution network topology and is used as a power distribution network topology identification result. The invention adopts a neural network to establish the relation between node voltage amplitude and node injection power, and proposes a maximum spanning tree algorithm based on a maximum information coefficient to identify the topological structure of the power distribution network.
Description
Technical Field
The invention relates to a technology for analyzing the running state of a power distribution network, in particular to a power distribution network topological structure identification method considering the output correlation of a distributed power supply.
Background
The power system topology abstracts the grid into a graph containing nodes and edges. The nodes of the graph represent nodes in a power grid and are connected with equipment such as a generator, a distributed power supply, a load and the like; the edges of the figure represent lines in the grid. The topology structure of the power system describes the connection relation among all nodes in the power grid, and is an important basis for analysis and application of power system optimization operation, fault positioning, power failure management and the like. In general, the power system operators can accurately solve the topology structure of the power transmission network, and only need to identify the errors of the topology structure according to the more complete measurement information. However, because of numerous nodes and branches of the power distribution network, measurement information is incomplete and a topology structure is frequently changed, and particularly, the topology structure of the power distribution network is difficult to accurately obtain under the background that a distributed power supply is accessed into the power distribution network in a large scale.
With the wide deployment of advanced metrology systems (ADVANCED METERING Infrastructure, AMI) and data acquisition and monitoring control systems (Supervisory Control And DataAcquisition, SCADA), node voltage amplitude and injection power measurement information can be obtained, which is of great value for topology identification. The existing power distribution network topological structure method depends on certain assumption conditions, such as known power distribution network line parameters, independent node injection power, normal distribution compliance of node voltage and the like.
Disclosure of Invention
Aiming at the defects of the prior method, the invention provides a power distribution network topological structure identification method considering the output correlation of a distributed power supply, a neural network is adopted to establish the relation between the node voltage amplitude and the node injection power, and a maximum spanning tree algorithm based on the maximum information coefficient is provided for carrying out the power distribution network topological structure identification.
The invention is realized by the following technical scheme:
The invention relates to a power distribution network topological structure identification method considering the output correlation of a distributed power supply, which is characterized in that preprocessed power grid data is used as a training set to train a neural network in an off-line stage, a synthesized node voltage amplitude sample is obtained by inputting the trained neural network through a test set in an on-line stage, and then the power distribution network topological structure identification is carried out by adopting a maximum spanning tree algorithm based on a maximum information coefficient to obtain all node pairs of the power distribution network, wherein each node pair represents one edge in the power distribution network topological structure and is used as a power distribution network topological structure identification result.
The power grid data is node injection power and node voltage amplitude measurement data of all nodes of the power grid.
The pretreatment is as follows: after the injection power measurement P i of the node i is converted into a random variable P n,i conforming to standard normal distribution, calculating a covariance matrix sigma of P n＝{pn,1,pn,2,…,pn,N, and then obtaining a lower triangular matrix L by adopting Cholesky decomposition to obtain an input sample P t＝L-1Pn T of a neural network training set, wherein: i=1, 2, …, N.
The training set refers to a set of training set input samples P t and training set output samples, namely node voltage amplitude measurement U t＝{u1,u2,…,uN.
The test set is obtained by the following steps:
1) Calculating standard deviation vector Wherein: /(I)The ith row and the kth column of matrix L -1.
2) A random variable p c,i with a mean value of 0 and a standard deviation of σ i, which obeys an independent normal distribution, is generated.
3) A test set input sample P s＝L-1Pc T is obtained, where P c＝{pc,1,pc,2,…,pc,N.
The neural network includes: preprocessing module, input layer, hidden layer and output layer, wherein: the preprocessing module converts the node voltage amplitude corresponding to the node injection power with correlation into the node voltage amplitude corresponding to the independent node injection power.
The number of neurons of the input layer is node number minus 1, the number of hidden layers is 2, the number of neurons is 1000, and the number of neurons of the output layer is node number minus 1.
The maximum spanning tree algorithm based on the maximum information coefficient specifically comprises the following steps:
i) A graph T is built containing N nodes.
Ii) calculating the maximum information coefficient of all nodes to the voltage amplitude.
Iii) All node pairs are arranged in the order of the maximum information coefficient of the voltage amplitude from large to small, and the ordered node pairs are represented by e k, k=1, 2, … and N (N-1)/2.
Iv) adding e 1 and e 2 to map T.
V) set k=3.
Vi) when the number of edges in the graph T is less than N-1, performing steps vii) to ix), otherwise going to step x):
vii) when e k is added to figure T, no ring is formed, then e k is added to figure T.
viii)k＝k+1。
Ix) when k > N (N-1)/2, go to step x), otherwise go to step vi).
X) the obtained graph T is the topology identification result.
The invention relates to a system for realizing the method, which comprises the following steps: the system comprises a data reading module, a preprocessing module, a synthesized node voltage amplitude generating module, a maximum spanning tree algorithm module and a result output module which are sequentially connected, wherein: the data reading module reads the node injection power and node voltage amplitude measurement data of the power distribution network; the preprocessing module generates a neural network training set and a test set sample according to the node injection power and the node voltage amplitude measurement data; the synthesized node voltage amplitude generating module obtains synthesized node voltage amplitude by adopting a neural network; the maximum spanning tree algorithm module obtains a maximum spanning tree according to the maximum information coefficient among the synthesized node voltage amplitudes; the result output module outputs the maximum spanning tree as a topology identification result.
Technical effects
The invention utilizes normal distribution property, transforms the neural network input set of different distributions into the input set obeying the same distribution through cumulative distribution function transformation, ensures that the coverage of the training sample input set comprises the test sample input set, improves the training precision of the neural network, and simultaneously, accurately calculates the relevance of node voltage amplitude measurement by adopting the maximum information coefficient through the maximum spanning tree algorithm based on the maximum information coefficient, and improves the precision of the topological structure identification algorithm. Compared with the prior art, the topology structure identification method effectively considers the influence of the output correlation of the distributed power supply, and obtains an accurate topology structure identification result of the power distribution network on the premise that the known power distribution network line parameters are not needed, the node injection power is not needed to be independent and the node voltage amplitude probability distribution is not needed to be assumed.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a wiring diagram of an embodiment IEEE 69 node system;
FIG. 3 is a schematic diagram of the effect of the embodiment.
Detailed Description
As shown in fig. 2, in this embodiment, an IEEE 69 node standard system is taken as an example, the node injection power measurement data disclosed by the actual power distribution network is adopted, the sampling scale is set to be 8000, the neural network adopted in this embodiment is a fully-connected neural network, the number of neurons in the hidden layer is 1000, an Adam optimizer and a root mean square loss function are adopted, and the learning rate is set to be 5e-4.
The embodiment specifically comprises the following steps:
Step 1) obtaining grid data, and obtaining a node injection power measurement sample p i (i=1, 2, …, 69) and node voltage amplitude measurement samples u i(i＝1,2,…,69).pi and u i which are vectors with dimensions of 8000.
Step 2) converting p i into a random variable p n,i conforming to a standard normal distribution, specifically comprising:
i) The cumulative distribution function value c k (k=1, 2, …, 8000) for each sample point in p i is estimated.
Ii) estimating the inverse cumulative distribution function value p n,i for the normal distribution of the standard at c k.
Step 3) calculating a covariance matrix sigma of P n＝{pn,1,pn,2,…,pn,69, and obtaining a lower triangular matrix L by adopting Cholesky decomposition.
Step 4) calculate the neural network training set input sample P t＝L-1Pn T.
Step 5) generating a neural network test set input sample P s, specifically including:
i) Calculating standard deviation vector Wherein/>The ith row and the kth column of matrix L -1.
Ii) generating a random variable p c,i with a mean value of 0 and a standard deviation of sigma i, which obeys an independent normal distribution.
Iii) A test set input sample P s＝L-1Pc T is obtained, where P c＝{pc,1,pc,2,…,pc,69.
Step 6) training the neural network by using the training set input sample and the node voltage amplitude sample.
And 7) inputting the test set input sample into a neural network to obtain a synthesized node voltage amplitude sample U s.
Step 8) calculating the maximum information coefficient between all node pairs, which specifically comprises the following steps:
i) And drawing a scatter diagram according to the node voltage amplitude samples of the two nodes i and j.
Ii) dividing the scatter diagram by grids with different rows and columns.
Iii) For a grid G with resolution of k rows and l columns, changing dividing positions of the grid, and calculating maximum mutual information I k,l((Ui,Uj),k,l)＝maxI((Ui,Uj) G of the grid based on the resolution between two node voltage amplitude samples.
Iv) calculate normalized mutual information I * k,l＝Ik,l((Ui,Uj) based on grid G with resolution k rows/columns, k, l)/logmin { k, l }.
V) forming a matrix M based on the normalized mutual information I * k,l of the grid of all resolutions, the kth row and the first column element of the matrix M being I * k,l.
Vi) the maximum information coefficient is the maximum element value in the matrix M.
Step 9) obtaining a topological structure by adopting a maximum spanning tree algorithm based on the maximum information coefficient, which comprises the following steps:
i) A graph T is built containing N nodes.
Ii) arranging all node pairs in the order of the maximum information coefficient of the voltage amplitude from large to small, wherein the ordered node pairs are represented by e k, k=1, 2, … and N (N-1)/2.
Iii) E 1 and e 2 are added to graph T.
Iv) let k=3.
V) when the number of edges in the graph T is smaller than N-1, performing steps vi) to viii), otherwise proceeding to step ix).
Vi) when e k is added to figure T, no ring is formed, then e k is added to figure T.
vii)k＝k+1。
Viii) when k > N (N-1)/2, go to step ix), otherwise go to step v).
Ix) graph T is the topology identification result.
Compared with the prior art, the topology structure identification method effectively considers the influence of the output correlation of the distributed power supply, and obtains an accurate topology structure identification result of the power distribution network on the premise that the known power distribution network line parameters are not needed, the node injection power is not needed to be independent and the node voltage amplitude probability distribution is not needed to be assumed.
The foregoing embodiments may be partially modified in numerous ways by those skilled in the art without departing from the principles and spirit of the invention, the scope of which is defined in the claims and not by the foregoing embodiments, and all such implementations are within the scope of the invention.
Claims (4)
1. The power distribution network topological structure identification method considering the distributed power supply output correlation is characterized in that the preprocessed power grid data is used as a training set to train a neural network in an off-line stage, a synthesized node voltage amplitude sample is obtained through the training neural network input by a test set in an on-line stage, then the power distribution network topological structure identification is carried out by adopting a maximum spanning tree algorithm based on a maximum information coefficient, all node pairs of the power distribution network are obtained, each node pair represents one edge in the power distribution network topological structure and is used as a power distribution network topological structure identification result;
the power grid data is node injection power and node voltage amplitude measurement data of all nodes of the power grid;
The pretreatment is as follows: after the injection power measurement P i of the node i is converted into a random variable P n,i conforming to standard normal distribution, calculating a covariance matrix sigma of P n＝{pn,1,pn,2,…,pn,N, and then obtaining a lower triangular matrix L by adopting Cholesky decomposition to obtain an input sample P t＝L-1Pn T of a neural network training set, wherein: i=1, 2, …, N;
the maximum spanning tree algorithm based on the maximum information coefficient specifically comprises the following steps:
i) Establishing a graph T containing N nodes;
ii) calculating the maximum information coefficient of all nodes to the voltage amplitude;
iii) Arranging all node pairs in the order of the maximum information coefficient of the voltage amplitude from large to small, wherein the ordered node pairs are represented by e k, k=1, 2, … and N (N-1)/2;
iv) adding e 1 and e 2 to map T;
v) set k=3;
vi) performing steps vii) to ix) when the number of edges in the graph T is less than N-1, otherwise proceeding to step x);
vii) when e k is added to graph T, no ring is formed, then e k is added to graph T;
viii)k＝k+1；
ix) when k > N (N-1)/2, go to step x), otherwise go to step vi);
x) the obtained graph T is the topology identification result;
The maximum information coefficient is obtained by the following steps:
i) Drawing a scatter diagram according to the node voltage amplitude samples of the two nodes i and j;
ii) dividing the scatter diagram by grids with different rows and columns;
iii) For a grid G with resolution of k rows and l columns, changing dividing positions of the grid, and calculating maximum mutual information I k,l((Ui,Uj),k,l)＝maxI((Ui,Uj) I G of the grid based on the resolution between two node voltage amplitude samples;
iv) calculating normalized mutual information I * k,l＝Ik,l((Ui,Uj) based on a grid G with resolution of k rows and l columns, k, l)/logmin { k, l };
v) forming a matrix M based on normalized mutual information I * k,l of grids with all resolutions, wherein the element of the kth row and the first column of the matrix M is I * k,l;
vi) the maximum information coefficient is the maximum element value in the matrix M.
2. The method for identifying the topological structure of the power distribution network by considering the output correlation of the distributed power supply according to claim 1, wherein the training set refers to a set of training set input samples P t and training set output samples, namely node voltage amplitude measurement U t＝{u1,u2,…,uN;
the test set is obtained by the following steps:
1) Calculating standard deviation vector Wherein: /(I)The ith row and the kth column of matrix L -1;
2) Generating a random variable p c,i with a mean value of 0 and a standard deviation of sigma i, which obeys independent normal distribution;
3) A test set input sample P s＝L-1Pc T is obtained, where P c＝{pc,1,pc,2,…,pc,N.
3. The method for identifying a topology of a power distribution network taking into account the correlation of distributed power output as recited in claim 1, wherein said neural network comprises: preprocessing module, input layer, hidden layer and output layer, wherein: the preprocessing module converts node voltage amplitude corresponding to the node injection power with correlation into node voltage amplitude corresponding to the independent node injection power;
the number of neurons of the input layer is node number minus 1, the number of hidden layers is 2, the number of neurons is 1000, and the number of neurons of the output layer is node number minus 1.
4. A system for implementing the method of any one of claims 1-3, comprising: the system comprises a data reading module, a preprocessing module, a synthesized node voltage amplitude generating module, a maximum spanning tree algorithm module and a result output module which are sequentially connected, wherein: the data reading module reads the node injection power and node voltage amplitude measurement data of the power distribution network; the preprocessing module generates a neural network training set and a test set sample according to the node injection power and the node voltage amplitude measurement data; the synthesized node voltage amplitude generating module obtains synthesized node voltage amplitude by adopting a neural network; the maximum spanning tree algorithm module obtains a maximum spanning tree according to the maximum information coefficient among the synthesized node voltage amplitudes; the result output module outputs the maximum spanning tree as a topology identification result.
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