CN107579516B - Method for improving state estimation calculation speed of power system - Google Patents
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Abstract
The invention discloses a method for improving the state estimation calculation speed of a power system, which realizes the rapid calculation of an active and reactive Jacobian matrix and an information matrix by using a multithread parallel algorithm based on an OpenMP shared memory programming mode, reduces the calculated amount by using a sparse technology through zero-removing operation in the matrix multiplication process, and accelerates the decomposition speed of the information matrix based on non-zero-element symbol analysis and a numerical decomposition method in the factor decomposition process, thereby improving the overall calculation speed of large-scale power grid state estimation.
Description
Technical Field
The invention relates to a method for improving the state estimation calculation speed of a power system, and belongs to the technical field of power automation.
Background
With the construction of dispatching systems and model data centers of all levels of national provinces of intelligent dispatching technical support systems (D5000) and the development of power grid scale, the state estimation calculation scale of a power system is increased day by day, the state estimation of actual production operation in the current intelligent dispatching technical support system, particularly the state estimation of the operation of the model data center, the modeling range of the state estimation calculation scale is from 1000kV to 10kV feeder outlet lines of an extra-high voltage feeder, and the state estimation calculation scale is very large, so that the calculation efficiency of the state estimation calculation scale cannot meet the requirements of real-time calculation analysis. Therefore, improving the calculation efficiency of large-scale grid state estimation becomes a focus of attention of many researchers.
At present, in the state estimation calculation of the power system, the calculation of an information matrix and the LU factorization of a coefficient matrix of a linear equation set occupy most of the state estimation time, wherein for a large-scale sparse linear system, the proportion of the factorization calculation time to the total calculation time of solving the equation set is large, and the speed of improving the information matrix and the LU factorization plays a significant role in accelerating the state of the whole power system.
Disclosure of Invention
In order to solve the technical problem, the invention provides a method for improving the calculation speed of the state estimation of the power system.
In order to achieve the purpose, the invention adopts the technical scheme that:
a method for improving the calculation speed of power system state estimation comprises the following steps,
converting a relational power grid model in a dispatching control system into a hierarchical power grid model;
reading the measurement of the SCADA in the dispatching system, and associating the measurement with an element in the hierarchical power grid model;
determining a network topology, namely a node-branch model, according to the remote signaling and the connection relation of each element;
node sorting is carried out based on the measurement number associated with the node;
forming a functional Jacobian matrix H based on OpenMP technology according to a node-branch modelpAnd a reactive Jacobian matrix Hq；
Active information matrix G calculated based on sparse matrix technology and OpenMP technologypAnd a reactive information matrix Gq，GpIs a (n-1) × (n-1) -dimensional matrix, GqThe method is characterized in that the method is an n × n-dimensional matrix, wherein n is the number of nodes calculated by a power grid;
to active information matrix GpThe analysis of the row number sets of the non-zero elements of each column of the lower triangular matrix L and the upper triangular matrix U is completed in sequence from the 1 st column to the n-1 st column according to a non-zero element symbol analysis method;
for reactive information matrix GqThe analysis of the row number sets of the non-zero elements of each column of the lower triangular matrix L and the upper triangular matrix U is completed in sequence from the 1 st column to the nth column according to a non-zero element symbol analysis method;
to active information matrix GpAccording to the Left Looking LU numerical decomposition calculation analysis method, combining the obtained non-zero row number set to sequentially perform Left Looking LU numerical decomposition from the 1 st row to the n-1 st row;
for reactive information matrix GqAccording to the Left Looking LU numerical decomposition calculation analysis method, combining the obtained non-zero row number set to sequentially carry out Left Looking LU numerical decomposition from the 1 st row to the n th row;
iteratively solving the system of equations G Δ x repeatedly during the state estimation computation processk＝HTR-1·[z-h]And correcting the state quantity until DeltaxkSatisfying a specified convergence criterion; wherein G is an active information matrix GpOr reactive information matrix Gq，xkFor the calculation of the kth iteration the node voltage amplitude or phase angle, i.e. the state quantity, xk+1＝xk+ΔxkH is a nonlinear measurement vector function, z is a measurement vector, and when G is an active information matrix GpR is then
H is HpWhen G is a reactive information matrix GqR is then
H is Hq，
And
respectively an active measurement error variance matrix and a reactive measurement error variance matrix;
when Δ xkAnd when the iteration threshold is smaller than the iteration threshold, stopping iterative computation.
The converted hierarchical network model is stored in a hierarchical database, and measurements are also stored in the hierarchical database and associated with elements in the hierarchical network model.
Remote signaling in measurement comprises a breaker state and a disconnecting link state; when the state estimation is calculated based on a new power grid model, network topology analysis is carried out based on the whole network elements; when the state of the circuit breaker and the disconnecting link exceeds the threshold value compared with the last state change number, network topology analysis is carried out based on the whole network elements; and when the current state of the circuit breaker and the disconnecting link does not exceed the threshold value compared with the last state change number, only carrying out local network topology analysis on the plant station with the changed remote signaling state according to the voltage grade.
Decoupling an active modification equation and a reactive modification equation by adopting a rapid decomposition state estimation algorithm based on the least square principle, and calculating an active Jacobian matrix H in parallelpAnd a reactive Jacobian matrix Hq。
According to the formed active Jacobian matrix HpJacobian matrix H without powerqActive power measurement error variance matrix
Sum reactive power measurement error variance matrix
Active information matrix calculation based on sparse matrix technology and OpenMP technology
And a reactive information matrix
Setting a certain column vector of the coefficient matrix A ═ LU as b, and obtaining a non-zero element structure of a column vector x by solving Lx ═ b;
let β be { i | b }i≠0}，χ＝{j|xjNot equal to 0 represents a collection of nodes of non-zero elements in b and x, respectively, where biIs the ith row element, x, in column vector bjIs the jth row element in the column vector x, where i ∈ [1, n']，j∈[1,n′]When the coefficient matrix A in the state estimation calculation is an active information matrix GpN is n-1, and the coefficient matrix A is a reactive information matrix G in the state estimation calculationq，n′＝n；
Suppose that the k' -1 column of L has been computed, and its corresponding directed graph is G (L)k′-1)；
L, U column k' is a set of non-zero nodes derived by the following criteria,
wherein lijNot equal to 0 denotes G (L)k′-1) Where there is an edge, x, from node j to node iiIs the ith row element in the column vector x;
when solving for the non-zero structure of x, the zero values produced by the numerical cancellation are ignored, since lij*xjResult in no matter biWhether or not it is 0, xiIs non-zero;
a and L are stored sparsely according to columns, the row number of a certain column of non-zero elements of A is retrieved, the non-zero elements of the column are retrieved from the corresponding column of L through the row number, and a non-zero set of x is obtained through a depth search algorithm.
The invention achieves the following beneficial effects: 1. the fast calculation of an active jacobian matrix, a reactive jacobian matrix and an information matrix is realized by using a multithreading parallel algorithm based on an OpenMP shared memory programming mode, the calculated amount is reduced by using a sparse technology through zero elimination operation in a matrix multiplication process, and the decomposition speed of the information matrix is accelerated based on non-zero element symbol analysis and a numerical decomposition method in a factor decomposition process, so that the overall calculation speed of large-scale power grid state estimation is improved; 2. based on the local topology technology, the time consumed by topology analysis during remote signaling preprocessing in large-scale power grid state estimation can be greatly reduced, and the occurrence probability of time consumed by topology analysis based on a whole network model before and after remote signaling preprocessing is effectively avoided; 3. in the LU decomposition process, a method of symbol analysis and numerical decomposition separation is adopted, so that the calculation of zero elements in the decomposition process can be effectively avoided.
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FIG. 1 is a flow chart of the present invention;
FIG. 2 is a flow of parallel computation of an information matrix;
FIG. 3 is a schematic diagram of non-zero structure analysis;
FIG. 4 is a schematic diagram of solving L, U column j.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
As shown in fig. 1, a method for increasing the calculation speed of power system state estimation includes the following steps:
Because the power grid structure of the power system has a hierarchical relationship, in order to facilitate analysis and calculation, an analysis and calculation method based on a hierarchical database is adopted in state estimation and calculation, firstly, a relational power grid model in a regulation and control system is converted into a hierarchical power grid model, the power grid model is stored in the hierarchical database, the hierarchical database stores the power grid model on a state estimation application server hard disk in a binary file mode in a disk file mapping mode, elements in the hierarchical database correspond to elements in the relational database in a scheduling and control system one by one, and calculation and analysis are carried out based on the hierarchical database during calculation and calculation.
And 2, reading the measurement of the SCADA in the dispatching system, and associating the measurement with an element in the hierarchical power grid model.
The state estimation obtains the measurement of the SCADA from the dispatching control system, wherein the remote signaling comprises a breaker state and a disconnecting link state, the remote measurement comprises line active, reactive and current, transformer active, reactive and current, gear, load active, reactive and current, generator active, reactive and current and bus voltage, and as elements of the hierarchical database and elements of the relational database in the dispatching control system are in one-to-one correspondence through keywords, the measurement acquired by the SCADA is easily related to corresponding elements in the hierarchical database.
And 3, determining a network topology, namely a node-branch model, according to the state of the circuit breaker, the state of the disconnecting link and the connection relation of each element.
When the state estimation is calculated based on a new power grid model, network topology analysis is carried out based on the whole network elements; and when the current state of the circuit breaker and the disconnecting link exceeds the threshold value compared with the last state change number, performing network topology analysis based on the whole network elements. In an actual power grid, the states of a plurality of circuit breakers and disconnecting links rarely change during normal operation, so that when the number of the state changes of the circuit breakers and the disconnecting links at this time is not more than a threshold value compared with the number of the state changes at the last time, only the plant stations with the changed remote signaling states are subjected to local network topology analysis according to the voltage levels. Based on the local topology technology, the time consumed by topology analysis during remote signaling preprocessing in large-scale power grid state estimation can be greatly reduced, and the occurrence probability of time consumed by topology analysis based on a whole network model before and after remote signaling preprocessing is effectively avoided.
Step 4, node sequencing is carried out based on the measurement number of node association, and a functional Jacobian matrix H is formed based on OpenMP (open multiprocessing) technology according to a node-branch modelpAnd a reactive Jacobian matrix Hq。
Decoupling an active modification equation and a reactive modification equation by adopting a rapid decomposition state estimation algorithm based on the least square principle, and calculating an active Jacobian matrix H in parallelpAnd a reactive Jacobian matrix Hq。
Step 5, according to the formed active Jacobian matrix HpJacobian matrix H without powerqTherein are provided withPower measurement error variance matrix
Sum reactive power measurement error variance matrix
Active information matrix calculation based on sparse matrix technology and OpenMP technology
And a reactive information matrix
GpIs a (n-1) × (n-1) -dimensional matrix, GqThe method is characterized in that the method is an n × n-dimensional matrix, wherein n is the number of nodes calculated by a power grid;
implementation of G using OpenMP techniquesp、GqBased on sparse techniques, computing Gp、GqThe specific flow of a certain column of values is shown in fig. 2.
Step 6, for the active information matrix GpThe analysis of the row number sets of the non-zero elements of each column of the lower triangular matrix L and the upper triangular matrix U is completed in sequence from the 1 st column to the n-1 st column according to a non-zero element symbol analysis method; for reactive information matrix GqAnd the analysis of the row number sets of the non-zero elements of the columns of the lower triangular matrix L and the upper triangular matrix U is completed in sequence from the 1 st column to the nth column according to a non-zero element symbol analysis method.
Setting a coefficient matrix A as LU column vector as b, and solving Lx as b to obtain a non-zero element structure of a column vector x;
let β be { i | b }i≠0}，χ＝{j|xjNot equal to 0 represents a collection of nodes of non-zero elements in b and x, respectively, where biIs the ith row element, x, in column vector bjIs the jth row element in the column vector x, where i ∈ [1, n']，j∈[1,n′]When the coefficient matrix A in the state estimation calculation is an active information matrix GpN is n-1, and the coefficient matrix A is a reactive information matrix G in the state estimation calculationq，n′＝n；
Suppose that the k' -1 column of L has been computed and the corresponding directed graph isG(Lk′-1)；
L, U column k' is a set of non-zero nodes derived by the following criteria,
wherein lijNot equal to 0 denotes G (L)k′-1) Where there is an edge, x, from node j to node iiIs the ith row element in the column vector x;
when solving for the non-zero structure of x, the zero values produced by the numerical cancellation are ignored, since lij*xjResult in no matter biWhether or not it is 0, xiA non-zero, non-zero element structural analysis diagram is shown in fig. 3;
and B, because A and L are stored sparsely according to columns, the row number of a certain column of non-zero elements of A is retrieved, the non-zero elements of the column are retrieved from the column corresponding to L through the row number, and the non-zero set of x is obtained through a depth search algorithm.
Step 7, for the active information matrix GpAccording to a Left Looking LU numerical decomposition calculation analysis method, combining the obtained non-zero row number set to sequentially perform Left Looking LU numerical decomposition from the 1 st column to the n-1 st column; for reactive information matrix GqAnd according to a Left Looking LU numerical decomposition calculation analysis method, combining the obtained non-zero row number set to sequentially perform Left Looking LU numerical decomposition from the 1 st column to the n th column.
The Left Looking LU numerical decomposition is sequentially decomposed from the 1 st column to the last column, namely, one column vector is calculated each time, and numerical calculation is carried out according to the symbol analysis result of the column, so that the numerical values of all non-zero elements of the column are obtained.
Solving L, U column j is schematically shown in FIG. 4, where matrix block L in FIG. 4 isj、L′j、UjAnd vector aj、a′j、lj、uj、x′jIs defined as follows;
aj＝(a1j,…,a(j-1)j)T
a′j＝(ajj,…,a′nj)T
lj＝(ljj,…,l′cj)T
uj＝(u1j,…,u(j-1)j)T
x′j＝(xjj,…,x′nj)T
wherein, x'jJ column j to n' th element set of x, ajjElement of j row and j column of A, ajIs the 1 st to j-1 st element set, a 'of the j column of A'jJ to n' th element set of column j of A, ujThe element sets from 1 st element to j-1 st element in the jth column of the U;
when calculating L, U column j element, first solve the lower trigonometric equation set Ljuj＝aj(Ljuj＝ajFor concrete solving expressions, and Lx ═ b above is a general expression) to obtain ujThen solve for x'j＝a′j-L′jujX'jSelecting principal element to obtain principal element ujj，ujjFor the jth element of selected jth column of U, and calculate Uj＝x′j，lj＝x′j/ujjSo that the following trigonometric equation set L is solved based on column 1, …, j-1 of Ljuj＝ajGiving L, U a value for column j.
In the LU decomposition process, a method of symbol analysis and numerical decomposition separation is adopted, so that the calculation of zero elements in the decomposition process can be effectively avoided.
Step 8, repeatedly and iteratively solving equation set G delta x in the state estimation calculation processk＝HTR-1·[z-h]And correcting the state quantity until DeltaxkSatisfying a specified convergence criterion; wherein G is an active information matrix GpOr reactive information matrix Gq，xkFor the calculation of the kth iteration the node voltage amplitude or phase angle, i.e. the state quantity, xk+1＝xk+ΔxkH is a nonlinear measurement vector function, z is a measurement vector, and when G is an active information matrix GpR is then
H is HpWhen G is a reactive information matrix GqR is then
H is Hq，
And
the error variance matrix of active measurement and the error variance matrix of reactive measurement are respectively.
Step 9, when Δ xkAnd when the iteration threshold is smaller than the iteration threshold, stopping iterative computation. And calculating the load flow values of all equipment in the power grid according to the node voltage amplitude and the phase angle obtained by state estimation calculation, wherein the load flow values comprise active and reactive values of equipment such as a line, a transformer, a load and a generator, and the reactive values and the assessment indexes of the reactive value of the capacitive reactance device.
The method realizes the rapid calculation of the active and reactive Jacobian matrixes and the information matrix by using a multithread parallel algorithm based on an OpenMP shared memory programming mode, reduces the calculated amount by using a sparse technology through zero elimination operation in the matrix multiplication process, and accelerates the decomposition speed of the information matrix based on non-zero-element symbol analysis and a numerical decomposition method in the factor decomposition process, thereby improving the overall calculation speed of large-scale power grid state estimation.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.
Claims (5)
1. A method for improving the calculation speed of state estimation of a power system is characterized in that: comprises the steps of (a) preparing a mixture of a plurality of raw materials,
converting a relational power grid model in a dispatching control system into a hierarchical power grid model;
reading the measurement of the SCADA in the dispatching system, and associating the measurement with an element in the hierarchical power grid model;
determining a network topology, namely a node-branch model, according to the state of the circuit breaker, the state of the disconnecting link and the connection relation of each element;
remote signaling in measurement comprises a breaker state and a disconnecting link state; when the state estimation is calculated based on a new power grid model, network topology analysis is carried out based on the whole network elements; when the state of the circuit breaker and the disconnecting link exceeds the threshold value compared with the last state change number, network topology analysis is carried out based on the whole network elements; when the current state change number of the circuit breaker and the disconnecting link does not exceed a threshold value compared with the last state change number, only carrying out local network topology analysis on the plant station with the changed remote signaling state according to the voltage grade;
node sorting is carried out based on the measurement number associated with the node;
forming a functional Jacobian matrix H based on OpenMP technology according to a node-branch modelpAnd a reactive Jacobian matrix Hq；
Active information matrix G calculated based on sparse matrix technology and OpenMP technologypAnd a reactive information matrix Gq，GpIs a (n-1) × (n-1) -dimensional matrix, GqThe method is characterized in that the method is an n × n-dimensional matrix, wherein n is the number of nodes calculated by a power grid;
to active information matrix GpThe analysis of the row number sets of the non-zero elements of each column of the lower triangular matrix L and the upper triangular matrix U is completed in sequence from the 1 st column to the n-1 st column according to a non-zero element symbol analysis method;
for reactive information matrix GqAccording to non-zero symbolsThe number analysis method completes the analysis of the row number sets of the non-zero elements of each column of the lower triangular matrix L and the upper triangular matrix U from the 1 st column to the nth column in sequence;
to active information matrix GpAccording to the Left Looking LU numerical decomposition calculation analysis method, combining the obtained non-zero row number set to sequentially perform Left Looking LU numerical decomposition from the 1 st row to the n-1 st row;
for reactive information matrix GqAccording to the Left Looking LU numerical decomposition calculation analysis method, combining the obtained non-zero row number set to sequentially carry out Left Looking LU numerical decomposition from the 1 st row to the n th row;
iteratively solving the system of equations G Δ x repeatedly during the state estimation computation processk＝HTR-1·[z-h]And correcting the state quantity until DeltaxkSatisfying a specified convergence criterion; wherein G is an active information matrix GpOr reactive information matrix Gq，xkFor the kth iterative calculation the node voltage amplitude or phase angle, xk+1＝xk+ΔxkH is a nonlinear measurement vector function, z is a measurement vector, and when G is an active information matrix GpR is then
H is HpWhen G is a reactive information matrix GqR is then
H is Hq，
And
respectively an active measurement error variance matrix and a reactive measurement error variance matrix;
when Δ xkAnd when the iteration threshold is smaller than the iteration threshold, stopping iterative computation.
2. The method for improving the calculation speed of the state estimation of the power system according to claim 1, wherein: the converted hierarchical network model is stored in a hierarchical database, and measurements are also stored in the hierarchical database and associated with elements in the hierarchical network model.
3. The method for improving the calculation speed of the state estimation of the power system according to claim 1, wherein: decoupling an active modification equation and a reactive modification equation by adopting a rapid decomposition state estimation algorithm based on the least square principle, and calculating an active Jacobian matrix H in parallelpAnd a reactive Jacobian matrix Hq。
4. The method for improving the calculation speed of the state estimation of the power system according to claim 1, wherein: according to the formed active Jacobian matrix HpJacobian matrix H without powerqActive power measurement error variance matrix
Sum reactive power measurement error variance matrix
Active information matrix calculation based on sparse matrix technology and OpenMP technology
And a reactive information matrix
5. The method for improving the calculation speed of the state estimation of the power system according to claim 1, wherein:
setting a certain column vector of the coefficient matrix A ═ LU as b, and obtaining a non-zero element structure of a column vector x by solving Lx ═ b;
let β be { i | b }i≠0}，χ＝{j|xjNot equal to 0, representing non-zero elements of b and x, respectivelySet of nodes, wherein biIs the ith row element, x, in column vector bjIs the jth row element in the column vector x, where i ∈ [1, n']，j∈[1,n′]When the coefficient matrix A in the state estimation calculation is an active information matrix GpN is n-1, and the coefficient matrix A is a reactive information matrix G in the state estimation calculationq，n′＝n；
Suppose that the k' -1 column of L has been computed, and its corresponding directed graph is G (L)k′-1)；
L, U column k' is a set of non-zero nodes derived by the following criteria,
wherein lijNot equal to 0 denotes G (L)k′-1) Where there is an edge, x, from node j to node iiIs the ith row element in the column vector x;
when solving for the non-zero structure of x, the zero values produced by the numerical cancellation are ignored, since lij*xjResult in no matter biWhether or not it is 0, xiIs non-zero;
a and L are stored sparsely according to columns, the row number of a certain column of non-zero elements of A is retrieved, the non-zero elements of the column are retrieved from the corresponding column of L through the row number, and a non-zero set of x is obtained through a depth search algorithm.
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