CN111695080A - Power grid state estimation method of GPU parallel acceleration preprocessing conjugate gradient iteration method - Google Patents

Power grid state estimation method of GPU parallel acceleration preprocessing conjugate gradient iteration method Download PDF

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CN111695080A
CN111695080A CN202010394592.5A CN202010394592A CN111695080A CN 111695080 A CN111695080 A CN 111695080A CN 202010394592 A CN202010394592 A CN 202010394592A CN 111695080 A CN111695080 A CN 111695080A
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杨亚洲
钱秋明
梁鸭红
胡霄
樊线
段彭圆
郭坤
杨成凡
潘飞飞
魏桥所
杨小景
王秋菊
尹昭舜
周欢
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Puer Supply Power Bureau of Yunnan Power Grid Co Ltd
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Abstract

The invention provides a power grid state estimation method of a GPU parallel acceleration preprocessing conjugate gradient iterative method, which adopts a preprocessing conjugate gradient iterative method by utilizing the symmetrical positive characteristic of a coefficient matrix A of a linear equation set in the state estimation of a weighted least square method, wherein the preprocessing conjugate gradient method is characterized in that on the basis of the conjugate gradient method, a coefficient matrix M after preprocessing is used for replacing an original coefficient matrix A so as to reduce the condition number of the coefficient matrix and accelerate the convergence speed of the algorithm, and meanwhile, an incomplete LU decomposition preprocessing method is adopted, and a GPU parallel computing framework is adopted, so that the computing speed and the computing efficiency of the state estimation of a power system are improved, the occupancy rates of an internal memory and a display memory are reduced, and the real-time requirement of the state estimation of a large-scale power system is met.

Description

Power grid state estimation method of GPU parallel acceleration preprocessing conjugate gradient iteration method
Technical Field
The invention relates to the field of power systems, in particular to a power grid state estimation method of a GPU parallel acceleration preprocessing conjugate gradient iteration method.
Background
Power system state estimation is the basis of modern energy management systems, providing underlying support for advanced applications in modern energy management systems. Currently, the most widely used state estimation algorithm in power systems is the Weighted Least Squares (WLS) method. The method assumes that the measurement quantity is subject to normal distribution, the mathematical model is simpler, the iteration times are less, the calculation speed is high, and the estimation effect is better when no bad data exist in the measurement point set. In the solving process of the WLS state estimation method, a large amount of time is consumed for solving the high-dimensional sparse matrix multiplication and the high-dimensional sparse linear equation set, and most of calculation time is occupied. The main methods for solving the large-scale sparse linear equation set can be divided into a direct method and an iterative method. The direct method is to eliminate the original linear equation set by using matrix decomposition and transformation techniques, and representative methods include a gaussian elimination method, an LU decomposition method and the like. The method has the characteristics that the selection of the principal elements is harsh, the direct method occupies more memory, parallel calculation is difficult, the solution efficiency is low after the equation scale reaches a certain order of magnitude, and the method is not suitable for calculating a large sparse linear equation set. Compared with a direct method, the iterative method has great advantages for the calculation of a large sparse linear equation set. The iterative method has low memory occupation during each calculation, is very suitable for parallel operation, and has no influence on the calculation efficiency when the matrix size is increased. But its convergence is greatly affected by the condition number of the matrix. With the development of provincial and regional integration and transmission and distribution integration of the power system, the calculation dimensionality of the power system is higher and higher, the calculation time is increased rapidly, and the traditional state estimation algorithm is difficult to meet the rapidly-increasing calculation requirement.
Therefore, a method for calculating the state of the power system is needed to improve the calculation speed and efficiency of the state estimation of the power system, reduce the occupancy rates of the memory and the video memory, and meet the real-time requirement of the state estimation of the large-scale power system.
Disclosure of Invention
In view of this, the present invention provides an electrical network state estimation method of a GPU parallel acceleration preprocessing conjugate gradient iterative method, which is characterized in that: the method comprises the following steps:
s1: initializing, forming node admittance matrix, and giving initial value to state variable
Figure BDA0002487109680000021
S2: setting an iteration variable k to 0 and a maximum iteration number kmax；
S3: according to the current state variable
Figure BDA0002487109680000022
Computing jacobian matrices
Figure BDA0002487109680000023
S4: calculating a matrix A and a vector b by utilizing a cubarse library on a GPU:
Figure BDA0002487109680000024
wherein A representsThe matrix is a matrix of a plurality of matrices,
Figure BDA0002487109680000025
representing a measured Jacobian matrix under the state variables, R representing a measured variance matrix, b representing a vector, Z representing a system measurement vector,
Figure BDA0002487109680000026
a measurement function representing a state variable;
s5: solving a system of linear equations on a GPU
Ax＝b (2)
Wherein A represents a matrix, b represents a vector, and x represents a system state variable;
s6: determining a correction amount for Newton' S iteration based on x solved in step S5
Figure BDA0002487109680000027
And determining the state variable
Figure BDA0002487109680000028
wherein ,
Figure BDA0002487109680000029
the state variable is represented by a number of variables,
Figure BDA00024871096800000210
the correction amount for the kth iteration is indicated,
Figure BDA00024871096800000213
state variables representing the kth iteration;
s7: let k equal to k +1, determine whether or not to satisfy
Figure BDA00024871096800000211
wherein ,
Figure BDA00024871096800000212
representing the correction of the ith dimensional state variable at the Kth iteration, representing the iteration convergence precision value, K representing the iteration variable, KmaxIndicating the maximum iteration number, if not, then turning toStep (3), if yes, the state estimation process is exited;
wherein, step S5 specifically includes the following steps:
by utilizing the characteristic of positive symmetry and definite symmetry of the matrix A, iterative solution is carried out by using a pretreatment conjugate gradient method, and the specific method is as follows:
s51: ILU (0) decomposition is performed on matrix a, which is a form of incomplete LU decomposition, forming a preprocessor of matrix a:
M＝LU (3)
wherein M represents the preprocessing factor of the matrix A, L represents the upper triangular matrix decomposed by ILU (0), and U represents the lower triangular matrix decomposed by ILU (0);
s52: setting the iteration number i to be 0 and the maximum iteration number imaxMeanwhile, let the initial guess of x be x0Calculating an initial residual r0And its 2-norm r0||；
S53: solving the system of equations Mz r from L and UiWhere M represents the preprocessing factor of matrix A, Z represents the systematic measurement vector, riRepresenting the calculated residual;
s54: determining ρi＝(riZ); wherein Z represents a system measurement vector, riRepresenting the calculated residual;
s55: judging whether i is zero, if so, adding piZ represents a system measurement vector, and if not, β is made to be ρi/ρi-1；
S56: determination of pi＝z+βpi-1；
S56: determining q ═ Api、α＝ρi/(pi,q)、xi+1＝xi+αpi、ri+1＝ri-αq；
S57: judging whether one of the following two conditions is met, | | ri+1||/||r0||≤ORi＜imaxIf yes, exiting iteration; if not, the process proceeds to step S53, where i is equal to i + 1.
Further, the jacobian matrix of the step S3
Figure BDA0002487109680000031
The following method is adopted for determination:
Figure BDA0002487109680000032
wherein ,
Figure BDA0002487109680000033
represents a jacobian matrix, h (x) represents a measured function of the state variables, and x represents the state variables.
The invention has the beneficial technical effects that: the invention adopts an ILU (0) preprocessing method to ensure that the residual matrix meets the decomposition condition of the ILU (0). This preprocessing method produces preconditioners that are not injected into non-zero elements. After pretreatment, the sparsity of the pretreatment seeds can be ensured. In a large sparse matrix, on one hand, the sparsity of the preprocessing son is ensured, so that the calculation amount and the memory can be saved in the matrix operation, and meanwhile, the calculation of the iterative method can be accelerated more quickly by utilizing the sparsity of the preprocessing son, which is the same as that of the original matrix. The method adopts a conjugate gradient method, and harsh applicable conditions of the conjugate gradient method are met by the symmetrical positive definite characteristic of a coefficient matrix A of a linear equation set in WLS state estimation. In the process of solving the large sparse linear equation set, the calculation efficiency of the iterative method is higher, and meanwhile, the conjugate gradient method is used as the simplest method in the calculation steps of the iterative method and has the least calculation amount and the highest calculation efficiency. The invention adopts a GPU parallel computing framework, fully utilizes the high-performance matrix vector computing technology of CUDA, and utilizes the multiplication operation of a CuSparse library to accelerate the formation of the matrix A and the vector b. Meanwhile, in the iterative process of the conjugate gradient method, each intermediate variable is quickly calculated by using the GPU, so that the quick calculation of the iterative method is ensured.
Detailed Description
The invention is further illustrated below:
state Estimation (SE) of the power system is that according to a power grid model, the device operation and switching value change conditions of a power grid are combined, bad data are removed based on the quantity measurement acquired by the SCADA system in real time, and the voltage amplitude and the phase angle of the system operation State are estimated, so that the real-time quasi-steady State operation current situation of the power system is obtained.
The invention provides a power grid state estimation method of a GPU parallel acceleration preprocessing conjugate gradient iteration method, which is characterized by comprising the following steps: the method comprises the following steps:
s1: initializing, forming node admittance matrix, and giving initial value to state variable
Figure BDA0002487109680000041
Obtaining each node admittance value of a target power grid through a power grid SCADA system, and obtaining a node admittance matrix;
s2: setting an iteration variable k to 0 and a maximum iteration number kmax；
S3: according to the current state variable
Figure BDA0002487109680000042
Computing jacobian matrices
Figure BDA0002487109680000043
S4: calculating a matrix A and a vector b by utilizing a cubarse library on a GPU:
Figure BDA0002487109680000051
wherein, A represents a matrix,
Figure BDA0002487109680000052
representing a measured Jacobian matrix under the state variables, R representing a measured variance matrix, b representing a vector, Z representing a system measurement vector,
Figure BDA0002487109680000053
a measurement function representing a state variable;
s5: solving a system of linear equations on a GPU
Ax＝b (2)
Wherein A represents a matrix, b represents a vector, and x represents a system state variable;
the time-consuming part of the WLS state estimation is mainly two steps of matrix multiplication and linear equation system solution. In each iteration of the newton method, it is necessary to solve matrix multiplication and linear equation system, which involves a large number of operations and occupies most of the time.
Due to the matrix
Figure BDA0002487109680000054
Is a high-dimensional sparse matrix, so the matrix A is still a high-dimensional sparse matrix after matrix multiplication. In the vector b, since the vector
Figure BDA0002487109680000055
Is a dense vector, so b is also a high-dimensional dense vector. In the step, the result of the matrix A and the vector b can be efficiently calculated in parallel by adopting an operation library cusaprse in the CUDA, and the calculation speed is 2-5 times faster than that of a pure CPU substitute product according to the description of the CUDA.
On the other hand, the matrix linear equation system calculation part is the most time consuming part. As can be seen from equation (1), the matrix a is a product between the matrix transpose, the identity matrix, and the matrix itself, and is a symmetric positive definite matrix. When the system scale is small, the matrix scale is small, and the method is suitable for calculating the linear equation set by using a direct method such as LU decomposition and the like. The SuperLU of the common high-performance linear equation system solving base is highly optimized, belongs to a direct method, and is high in efficiency. However, for a large-scale sparse linear equation set, the matrix condition number is large, the calculation efficiency of the direct method cannot meet the requirement, and the method is suitable for parallel calculation on a GPU by using an iterative method. The invention adopts a GPU parallel computing framework, fully utilizes the high-performance matrix vector computing technology of CUDA, and utilizes the multiplication operation of a CuSparse library to accelerate the formation of the matrix A and the vector b. Meanwhile, in the iterative process of the conjugate gradient method, each intermediate variable is quickly calculated by using the GPU, so that the quick calculation of the iterative method is ensured.
S6: determining a correction amount for Newton' S iteration based on x solved in step S5
Figure BDA0002487109680000056
And determining the state variable
Figure BDA0002487109680000057
wherein ,
Figure BDA0002487109680000058
the state variable is represented by a number of variables,
Figure BDA0002487109680000059
the correction amount for the kth iteration is indicated,
Figure BDA0002487109680000061
state variables representing the kth iteration;
s7: let k equal to k +1, determine whether or not to satisfy
Figure BDA0002487109680000062
wherein ,
Figure BDA0002487109680000063
representing the correction of the ith dimensional state variable at the Kth iteration, representing the iteration convergence precision value, K representing the iteration variable, KmaxRepresenting the maximum iteration times, if not, turning to the step (3), and if so, exiting the state estimation process;
wherein, step S5 specifically includes the following steps:
by utilizing the characteristic of positive symmetry and definite symmetry of the matrix A, iterative solution is carried out by using a pretreatment conjugate gradient method, and the specific method is as follows:
s51: ILU (0) decomposition is performed on matrix a, which is a form of incomplete LU decomposition, forming a preprocessor of matrix a:
M＝LU (3)
wherein M represents the preprocessing factor of the matrix A, L represents the upper triangular matrix decomposed by ILU (0), and U represents the lower triangular matrix decomposed by ILU (0); the invention adopts an ILU (0) preprocessing method to ensure that the residual error matrix meets the decomposition condition of the ILU (0). This preprocessing method produces preconditioners that do not inject non-zero elements. After pretreatment, the sparsity of the pretreatment seeds can be ensured. In a large sparse matrix, on one hand, the sparsity of the preprocessing son is ensured, so that the calculation amount and the memory can be saved in the matrix operation, and meanwhile, the calculation of the iterative method can be accelerated more quickly by utilizing the sparsity of the preprocessing son, which is the same as that of the original matrix.
S52: setting the iteration number i to be 0 and the maximum iteration number imaxMeanwhile, let the initial guess of x be x0Calculating an initial residual r0And its 2-norm r0||；
S53: solving the system of equations Mz r from L and UiWhere M represents the preprocessing factor of matrix A, Z represents the systematic measurement vector, riRepresenting the calculated residual;
s54: determining ρi＝(riZ); wherein Z represents a system measurement vector, riRepresenting the calculated residual;
s55: judging whether i is zero, if so, adding piZ represents a system measurement vector, and if not, β is made to be ρi/ρi-1；
S56: determination of pi＝z+βpi-1；
S56: determining q ═ Api、α＝ρi/(pi,q)、xi+1＝xi+αpi、ri+1＝ri-αq；
S57: judging whether one of the following two conditions is met, | | ri+1||/||r0||≤ORi＜imaxIf yes, exiting iteration; if not, the process proceeds to step S53, where i is equal to i + 1.
And solving the large-scale sparse linear equation set by adopting a Krylov subspace method. The Krylov space-time method is a numerical iteration method proposed in the 90 s of the 20 th century, is one of projection calculation methods, and has the advantages of less storage and calculation. Solving a general system of linear equations:
Figure BDA0002487109680000071
wherein A represents a matrix, b represents a vector, and x represents a system state variable，
The basic idea of the projection method is to derive a subspace K of smaller dimensionsmAn approximate solution is sought. This subspace KmReferred to as the search space, with dimension m.
At this time, m constraints are set, and the residual vector r is required to meet m orthogonal conditions, namely, a Petrov-Galerkin condition that r is b-Ax ⊥ LmWherein r represents a residual vector, b represents, A represents, x represents, and L representsmIs another m-dimensional subspace, called constraint space, when L is selectedm＝KmThe method is orthogonal projection method, otherwise, it is oblique projection method.
When an initial value x of iteration is given0Using affine space x0+KmIt is possible to obtain:
Figure BDA0002487109680000072
wherein: initial residual r0＝b-Ax0。
In the Krylov subspace approach, the search space KmIs Krylov subspace, defined as:
Figure BDA0002487109680000073
wherein: r can be chosen as the initial residual r0The Krylov subspace approach is to find an approximate solution in the Krylov subspace.
Different constraint spaces L are selectedmIn time, the iteration process is greatly influenced. Considering that the matrix A is a symmetrical positive definite matrix, a conjugate gradient method is adopted to select a constrained space L in a Krylove subspace methodm。
However, if the Krylov subspace method is directly used for iteration, the original matrix condition number is too high, and problems of poor convergence, multiple iteration times and the like may occur. By adopting a proper preprocessing method, the condition number of the matrix can be reduced, the iteration times are reduced, and the problem solving is easy. The incomplete LU decomposition preprocessing method has wide application range, adopts the incomplete LU decomposition preprocessing method, and provides a power system state estimation algorithm based on a preprocessing conjugate gradient method iteration method. The method adopts a conjugate gradient method, and harsh application conditions of the conjugate gradient method are met by the symmetrical positive determination characteristic of a coefficient matrix A of a linear equation set in WLS state estimation. In the process of solving the large sparse linear equation set, the calculation efficiency of the iterative method is higher, and meanwhile, the conjugate gradient method is used as the simplest method in the calculation steps of the iterative method and has the least calculation amount and the highest calculation efficiency.
In this embodiment, the jacobian matrix of step S3
Figure BDA0002487109680000081
The following method is adopted for determination:
Figure BDA0002487109680000082
wherein ,
Figure BDA0002487109680000083
represents a jacobian matrix, h (x) represents a measured function of the state variables, and x represents the state variables.
The nonlinear metrology state estimation equation for the power system may be expressed as:
z ═ h (x) + v where z represents the system measurement vector and x represents the system state variable; h (x) represents the measurement function at state x, and v represents the measurement error; z ═ h (x) + v is the core of state estimation, and is a nonlinear equation where the number m of equations is greater than the number n of state variables. According to the meaning of the existence of the solution of the nonlinear equation, if n equations in the measurement equations are independent and the measurement is assumed to have no error, namely v ═ O, m-n equations in m measurement equations are redundant equations, and if the equation set has the solution, the redundant m-n equations are required to be compatible equations, namely x obtained by the n independent equations naturally meets the other m-n equations. In fact, since measurement errors always exist, a set of x satisfying both n equations in the z ═ h (x) + v formula and m-n redundant equations cannot be found, which is a set of contradictory equations, and it is difficult to find solutions that strictly satisfy these equations, and an optimal estimated solution that satisfies the equation set must be found by a special method.
Therefore, solving the state estimation problem becomes an extension of solving the tidal current problem, and is converted into solving the problem of an over-determined equation set, and the state variable with the minimum weighted residual sum of squares is expected to be obtained
Figure BDA0002487109680000084
Thus, an optimization model can be established:
min J(x)＝[z-h(x)]TR-1[z-h(x)](5)
wherein j (x) represents the sum of squared residuals of the system measurements, z represents the system measurement vector, and x represents the system state variable; h (x) represents the measurement function in state x, and R represents the measurement error variance matrix, which represents the accuracy of each measurement.
For equation (5), in order to minimize the objective function value, there are:
Figure BDA0002487109680000091
since h (x) is a nonlinear function about the state variable x, the iterative correction quantity can be obtained by performing linear expansion on the state variable x and solving by using a Newton method:
Figure BDA0002487109680000092
in the formula ：
Figure BDA0002487109680000093
as state variables
Figure BDA0002487109680000094
The measured jacobian matrix of the following is,
Figure BDA0002487109680000095
thus, the iterative equation can be found as:
Figure BDA0002487109680000096
in the formula ：
Figure BDA0002487109680000097
and
Figure BDA0002487109680000098
the state variable and the correction amount of the kth iteration are respectively.
Finally, the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting, although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all of them should be covered in the claims of the present invention.

Claims (2)

1. A power grid state estimation method of a GPU parallel acceleration preprocessing conjugate gradient iterative method is characterized by comprising the following steps: the method comprises the following steps:
s1: initializing, forming node admittance matrix, and giving initial value to state variable
Figure FDA0002487109670000011
S2: setting an iteration variable k to 0 and a maximum iteration number kmax；
S3: according to the current state variable
Figure FDA0002487109670000012
Computing jacobian matrices
Figure FDA0002487109670000013
S4: calculating a matrix A and a vector b by utilizing a cubarse library on a GPU:
Figure FDA0002487109670000014
wherein, A represents a matrix,
Figure FDA0002487109670000015
representing a measured Jacobian matrix under the state variables, R representing a measured variance matrix, b representing a vector, Z representing a system measurement vector,
Figure FDA0002487109670000016
a measurement function representing a state variable;
s5: solving a system of linear equations on a GPU
Ax＝b (2)
Wherein A represents a matrix, b represents a vector, and x represents a system state variable;
s6: determining a correction amount for Newton' S iteration based on x solved in step S5
Figure FDA0002487109670000017
And determining the state variable
Figure FDA0002487109670000018
wherein ,
Figure FDA0002487109670000019
the state variable is represented by a number of variables,
Figure FDA00024871096700000110
the correction amount for the kth iteration is indicated,
Figure FDA00024871096700000111
state variables representing the kth iteration;
s7: let k equal to k +1, determine whether or not to satisfy
Figure FDA00024871096700000112
wherein ,
Figure FDA00024871096700000113
Representing the correction of the ith dimensional state variable at the Kth iteration, representing the iteration convergence precision value, K representing the iteration variable, KmaxRepresenting the maximum iteration times, if not, turning to the step (3), and if so, exiting the state estimation process;
wherein, step S5 specifically includes the following steps:
by utilizing the characteristic of positive symmetry and definite symmetry of the matrix A, iterative solution is carried out by using a pretreatment conjugate gradient method, and the specific method is as follows:
s51: ILU (0) decomposition is performed on matrix a, which is a form of incomplete LU decomposition, forming a preprocessor of matrix a:
M＝LU (3)
wherein M represents the preprocessing factor of the matrix A, L represents the upper triangular matrix decomposed by ILU (0), and U represents the lower triangular matrix decomposed by ILU (0);
s52: setting the iteration number i to be 0 and the maximum iteration number imaxMeanwhile, let the initial guess of x be x0Calculating an initial residual r0And its 2-norm r0||；
S53: solving the system of equations Mz r from L and UiWhere M represents the preprocessing factor of matrix A, Z represents the systematic measurement vector, riRepresenting the calculated residual;
s54: determining ρi＝(riZ); wherein Z represents a system measurement vector, riRepresenting the calculated residual;
s55: judging whether i is zero, if so, adding piZ represents a system measurement vector, and if not, β is made to be ρi/ρi-1；
S56: determination of pi＝z+βpi-1；
S56: determining q ═ Api、α＝ρi/(pi,q)、xi+1＝xi+αpi、ri+1＝ri-αq；
S57: judging whether the following two conditions are metOne of (1), (r)i+1||/||r0||≤ORi＜imaxIf yes, exiting iteration; if not, the process proceeds to step S53, where i is equal to i + 1.
2. The power grid state estimation method based on the GPU parallel acceleration preprocessing conjugate gradient iterative method as claimed in claim 1, characterized in that: the Jacobian matrix of the step S3
Figure FDA0002487109670000021
The following method is adopted for determination:
Figure FDA0002487109670000022
wherein ,
Figure FDA0002487109670000023
represents a jacobian matrix, h (x) represents a measured function of the state variables, and x represents the state variables.
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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106296469A (en) * 2016-09-12 2017-01-04 东南大学 A kind of pretreatment sub-optimized choice method of N 1 Fault load flow update equation group
CN107069696A (en) * 2016-09-23 2017-08-18 四川大学 A kind of parallel calculating method of Power system state estimation
CN108804386A (en) * 2018-07-09 2018-11-13 东北电力大学 A kind of parallelization computational methods of power system load nargin

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106296469A (en) * 2016-09-12 2017-01-04 东南大学 A kind of pretreatment sub-optimized choice method of N 1 Fault load flow update equation group
CN107069696A (en) * 2016-09-23 2017-08-18 四川大学 A kind of parallel calculating method of Power system state estimation
CN108804386A (en) * 2018-07-09 2018-11-13 东北电力大学 A kind of parallelization computational methods of power system load nargin

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