CN111695080B - Power grid state estimation method of GPU parallel acceleration preprocessing conjugate gradient iteration method - Google Patents
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- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
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Abstract
The invention provides a power grid state estimation method of a GPU parallel acceleration preprocessing conjugate gradient iteration method, which adopts a preprocessing conjugate gradient iteration method by utilizing the symmetrical positive characteristic of a linear equation set coefficient matrix A in the state estimation of a weighted least square method, wherein the preprocessing conjugate gradient method is based on the conjugate gradient method, and the preprocessed coefficient matrix M is used for replacing the original coefficient matrix A so as to reduce the condition number of the coefficient matrix, accelerate the convergence rate of an algorithm, and meanwhile, an incomplete LU decomposition preprocessing method is adopted, so that the GPU parallel computing architecture is adopted, the computing speed and the computing efficiency of the state estimation of a power system are improved, the occupancy rate of a memory and a video memory are reduced, and the real-time requirement of the state estimation of the large-scale power system is met.
Description
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 the 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 (Weighted Least Squares, WLS) method. The method assumes that the measurement of the quantity is subject to normal distribution, the mathematical model is simpler, the iteration number is less, the calculation speed is high, and the estimation effect is better when no bad data exists in the measuring point set. In the solving process of the WLS state estimating method, a large amount of time is consumed to solve the high-dimensional sparse matrix multiplication and the high-dimensional sparse linear equation set, and most of the computing time is occupied. The main method 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 matrix decomposition and transformation technology, and the representative methods include Gaussian elimination method, LU decomposition method and the like. The method is characterized in that principal elements are selected more strictly, meanwhile, the direct method occupies more memory, parallel calculation is difficult, the solving efficiency is lower 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 the direct method, the iterative method has great advantages for the calculation of a large sparse linear equation set. The iteration method has low memory occupation during each calculation, is very suitable for parallelism, and the calculation efficiency of the iteration method is not affected when the matrix scale is increased. But its convergence is greatly affected by the condition number of the matrix. With the development of power system province and ground integration and transmission and distribution integration, the calculation dimension of the power system is higher and higher, the calculation time is increased sharply, and the rapid increase of the calculation requirement is difficult to meet by the traditional state estimation algorithm.
Therefore, there is a need for a power system state estimation method that increases the calculation speed and calculation efficiency of power system state estimation, reduces the occupancy rate of memory and video memory, and meets the real-time requirement of large-scale power system state estimation.
Disclosure of Invention
In view of this, the present invention provides a method for estimating the state of a grid by using a GPU parallel acceleration preprocessing conjugate gradient iteration method, which is characterized in that: the method comprises the following steps:
s1: initializing to form a node admittance matrix, and endowing state variables with initial values to form
S2: setting an iteration variable k=0 and a maximum iteration number k max ；
S3: according to the current state variable
Computing jacobian matrix->
S4: using a custarse library on the GPU, a matrix a and a vector b are calculated:
wherein A represents a matrix,
representing a measurement jacobian matrix under state variables, R representing a measurement variance matrix, b representing a vector, Z representing a system measurement vector,>
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 cattle according to the x solved in the step S5Correction of iteration of the ton method
And determining state variables
wherein ,/>
Representing state variables +.>
Correction representing the kth iteration, +.>
A state variable representing the kth iteration;
s7: let k=k+1, determine whether or not the condition is satisfied
wherein ,/>
Represents the correction amount of the ith dimension state variable in the kth iteration, epsilon represents the iteration convergence precision value, K represents the iteration variable, and K max Representing the maximum iteration times, if not, turning to the step (3), and if so, exiting the state estimation process;
the step S5 specifically includes the following steps:
by utilizing the characteristic of symmetrical positive determination of the matrix A, the pretreatment conjugate gradient method is used for carrying out iterative solution, and the specific method is as follows:
s51: performing an ILU (0) decomposition on the matrix A, wherein the ILU (0) decomposition is a form of incomplete LU decomposition, and forms a preprocessing sub-of the matrix A:
M＝LU (3)
wherein M represents the preprocessing factor of 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 iterationsNumber i=0 and maximum number i of iterations max At the same time, let the initial guess of x be x 0 Calculating an initial residual r 0 And its 2-norm r 0 ||；
S53: solving the system of equations mz=r from L and U i Wherein M represents the preprocessing factor of matrix A, Z represents the system measurement vector, r i Representing a calculated residual;
s54: determining ρ i ＝(r i Z); wherein Z represents a system measurement vector, r i Representing a calculated residual;
s55: judging whether i is zero, if so, then p is the other i Let β=ρ if not, Z represents the system measurement vector i /ρ i-1 ；
S56: determination of p i ＝z+βp i-1 ；
S56: determining q=ap i 、α＝ρ i /(p i ,q)、x i+1 ＝x i +αp i 、r i+1 ＝r i -αq；
S57: judging whether one of the following two conditions is satisfied i+1 ||/||r 0 ||≤εORi＜i max If yes, exiting iteration; if not, let i=i+1 go to step S53.
Further, the jacobian matrix of step S3
The method is adopted for determination as follows:
wherein ,
representing a jacobian matrix, h (x) represents a measurement function of a state variable, and x represents a state variable.
The beneficial technical effects of the invention are as follows: the invention adopts the ILU (0) pretreatment method, and ensures that the residual error matrix meets the decomposition condition of the ILU (0). The pretreatment sub-generated by this pretreatment method does not inject non-zero elements. After pretreatment, the sparsity of the pretreatment sub can be ensured. In a large sparse matrix, the sparsity of the preprocessing sub is guaranteed, on one hand, the calculated amount and the memory can be saved in matrix operation, and meanwhile, the calculation of an iterative method is accelerated more quickly by utilizing the same sparsity of the preprocessing sub and the original matrix. The invention adopts the conjugate gradient method, and the characteristic that the linear equation set coefficient matrix A is symmetrically and positively determined in WLS state estimation enables the harsh adaptation condition of the conjugate gradient method to be satisfied. In the solving process of 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 method with the simplest calculation steps in the iterative method, so that the method has the least calculation amount and the highest calculation efficiency. The invention adopts a GPU parallel computing architecture, fully utilizes the high-performance matrix vector computing technology of CUDA, and accelerates the formation of matrix A and vector b by utilizing multiplication operation of a cuspark library. Meanwhile, in the iteration process of the conjugate gradient method, the GPU is used for rapidly calculating each intermediate variable, so that the rapid calculation of the iteration method is ensured.
Detailed Description
The invention is further illustrated below:
the State Estimation (SE) of the power system is to combine the equipment operation and the switching value change condition of the power grid according to the power grid model, remove bad data based on the quantity measurement acquired by the SCADA system in real time, and estimate the voltage amplitude and the phase angle of the system operation State, thereby obtaining the real-time quasi-steady State operation current situation of the power system.
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 of: the method comprises the following steps:
s1: initializing to form a node admittance matrix, and endowing state variables with initial values to form
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=0 and a maximum iteration number k max ；
S3: according to the current state variable
Computing jacobian matrix->
S4: using a custarse library on the GPU, a matrix a and a vector b are calculated:
wherein A represents a matrix,
representing a measurement jacobian matrix under state variables, R representing a measurement variance matrix, b representing a vector, Z representing a system measurement vector,>
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 in WLS state estimation is mainly two steps of matrix multiplication and linear equation system solving. In each iteration of newton's method, a system of matrix multiplications and linear equations needs to be solved, which involves a large number of operations, taking up a significant portion of the time.
Due to the matrix
Is a high-dimensional sparse matrix, so that the matrix A is still a high-dimensional sparse matrix after matrix multiplication. In vector b, due to vector +.>
Is a dense vector and thus b is also a high-dimensional dense vector. The result of the matrix A and the vector b can be calculated in parallel and high efficiency by adopting an operation library cuSPARSE in the CUDA, and the calculation speed is 2-5 times faster than that of a pure CPU substitution product according to the description of the CUDA.
On the other hand, the matrix linear equation set calculation part is the most time-consuming part. As can be seen from equation (1), matrix a is the product of the matrix transpose, the identity matrix, and the matrix itself, and is a symmetric positive definite matrix. When the system scale is smaller, the matrix scale is smaller, and the linear equation set is suitable for calculation by using a direct method such as LU decomposition. The common high-performance linear equation system solving library SuperLU is highly optimized, belongs to a direct method, and has higher efficiency. However, for a large-scale sparse linear equation set, the number of matrix conditions is large, the calculation efficiency of a direct method is difficult to 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 architecture, fully utilizes the high-performance matrix vector computing technology of CUDA, and accelerates the formation of matrix A and vector b by utilizing multiplication operation of a cuspark library. Meanwhile, in the iteration process of the conjugate gradient method, the GPU is used for rapidly calculating each intermediate variable, so that the rapid calculation of the iteration method is guaranteed.
S6: determining the correction amount of Newton iteration according to the x solved in the step S5
And determining state variables
wherein ,/>
Representing state variables +.>
Correction representing the kth iteration, +.>
A state variable representing the kth iteration;
s7: let k=k+1, determine whether or not the condition is satisfied
wherein ,/>
Represents the correction amount of the ith dimension state variable in the kth iteration, epsilon represents the iteration convergence precision value, K represents the iteration variable, and K max Representing the maximum iteration times, if not, turning to the step (3), and if so, exiting the state estimation process;
the step S5 specifically includes the following steps:
by utilizing the characteristic of symmetrical positive determination of the matrix A, the pretreatment conjugate gradient method is used for carrying out iterative solution, and the specific method is as follows:
s51: performing an ILU (0) decomposition on the matrix A, wherein the ILU (0) decomposition is a form of incomplete LU decomposition, and forms a preprocessing sub-of the matrix A:
M＝LU (3)
wherein M represents the preprocessing factor of 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 the ILU (0) preprocessing method, and ensures that the residual matrix meets the decomposition condition of the ILU (0). The pretreatment sub-generated by this pretreatment method does not inject non-zero elements. After pretreatment, the sparsity of the pretreatment sub can be ensured. In a large sparse matrix, the sparsity of the preprocessing sub is guaranteed, on one hand, the calculated amount and the memory can be saved in matrix operation, and meanwhile, the calculation of an iterative method is accelerated more quickly by utilizing the same sparsity of the preprocessing sub and the original matrix.
S52: setting the iteration number i=0 and the maximum iteration number i max At the same time, let the initial guess of x be x 0 Calculating an initial residual r 0 And its 2-norm r 0 ||；
S53: solving the system of equations mz=r from L and U i Wherein M represents the preprocessing factor of matrix A, and Z represents the system quantity direction findingQuantity, r i Representing a calculated residual;
s54: determining ρ i ＝(r i Z); wherein Z represents a system measurement vector, r i Representing a calculated residual;
s55: judging whether i is zero, if so, then p is the other i Let β=ρ if not, Z represents the system measurement vector i /ρ i-1 ；
S56: determination of p i ＝z+βp i-1 ；
S56: determining q=ap i 、α＝ρ i /(p i ,q)、x i+1 ＝x i +αp i 、r i+1 ＝r i -αq；
S57: judging whether one of the following two conditions is satisfied i+1 ||/||r 0 ||≤εORi＜i max If yes, exiting iteration; if not, let i=i+1 go to step S53.
And solving by using a Krylov subspace method aiming at a large-scale sparse linear equation set. The Krylov sub-space method is a numerical iteration method proposed in the 90 th century of the 20 th century, is one of projection calculation methods, and has the advantages of less storage and calculation. Solving a general linear equation set:
the basic idea of the projection method is to extract a subspace K from a smaller dimension m An approximate solution is found inside. This subspace K m Referred to as a search space, which has a dimension m.
At this time, m constraints are set, and the residual vector r is required to satisfy m orthogonal conditions, namely, petrov-Galerkin conditions: r=b-Ax ζl m Wherein r represents a residual vector, b represents, A represents, x represents, L m Is another m-dimensional subspace, called constraint space, L is selected m ＝K m The method is orthogonal projection method, otherwise oblique projection method.
When given an iteration initial value x 0 When affine space x is adopted 0 +K m It is possible to obtain:
wherein: initial residual r 0 ＝b-Ax 0 。
In the Krylov subspace method, the search space K m The Krylov subspace, defined as:
wherein: r can be chosen as the initial residual r 0 The Krylov subspace method is to find an approximate solution in the Krylov subspace.
Selecting a different constraint space L m There is a relatively large impact on the iterative process. Considering that the matrix A is a symmetrical positive definite matrix, adopting a conjugate gradient method to select a constraint space L in a Krylove subspace method m 。
However, if the Krylov subspace method is directly used for iteration, the problems of poor convergence, multiple iterations and the like may occur if the condition number of the original matrix is too high. The proper preprocessing method can reduce the condition number of the matrix, reduce the iteration times and facilitate problem solving. The incomplete LU decomposition pretreatment method is wide in application range, and the invention adopts the incomplete LU decomposition pretreatment method and provides an electric power system state estimation algorithm based on a pretreatment conjugate gradient method iteration method. The invention adopts the conjugate gradient method, and the symmetrical positive characteristic of the linear equation set coefficient matrix A in WLS state estimation enables the harsh application conditions of the conjugate gradient method to be satisfied. In the solving process of 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 method with the simplest calculation steps in the iterative method, so that the method has the least calculation amount and the highest calculation efficiency.
In this embodiment, the steps ofJacobian matrix of step S3
The method is adopted for determination as follows:
wherein ,
representing a jacobian matrix, h (x) represents a measurement function of a state variable, and x represents a state variable.
The nonlinear metrology state estimation equation for a power system can be expressed as:
z=h (x) +v, where z represents a system measurement vector and x represents a system state variable; h (x) represents a measurement function in state x, v represents a measurement error; z=h (x) +v is the core of the state estimation and is a nonlinear equation, where the number of equations m is greater than the number of state variables n. Analyzing according to the meaning of whether the nonlinear equation is solved or not, if n equations in the measurement equations are independent, and assuming that the measurement is free of errors, namely v=o, then m-n equations in the m measurement equations are redundant equations, and if the equation set is solved, 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 n equations in the formula of z=h (x) +v cannot be found, and another m-n redundant equations are also satisfied, which is a set of contradictory equations, and it is difficult to find a solution that strictly satisfies these equations, and an optimal estimated solution that satisfies the set of equations must be found by a special method.
Therefore, solving the state estimation problem becomes an extension of solving the power flow problem, converting into solving the problem of solving the overdetermined equation set, and expecting to obtain the state variable with the minimum weighted residual square sum
Thus, an optimization model can be built:
min J(x)＝[z-h(x)] T R -1 [z-h(x)] (5)
wherein J (x) represents the sum of squares of residuals of system measurements, z represents a system measurement vector, and x represents a system state variable; h (x) represents the measurement function in state x, R represents the measurement error variance matrix, and represents the accuracy of each measurement.
In order to minimize the objective function value, equation (5) includes:
since h (x) is a nonlinear function related to the state variable x, the state variable x is linearly developed, and the iteration correction amount can be obtained by solving the state variable x by adopting the newton method:
in the formula ：
is a state variable +.>
The underlying measured jacobian matrix is used,
thus, an iterative equation can be derived as:
in the formula ：
and />
The state variable and the correction amount for the kth iteration, respectively.
Finally, it is noted that the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and 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 and equivalents may be made thereto without departing from the spirit and scope of the technical solution of the present invention, which is intended to be covered by the scope of the claims of the present invention.
Claims (2)
1. A power grid state estimation method of a GPU parallel acceleration preprocessing conjugate gradient iteration method is characterized by comprising the following steps of: the method comprises the following steps:
s1: initializing to form a node admittance matrix, and endowing state variables with initial values to form
S2: setting an iteration variable k=0 and a maximum iteration number k max ；
S3: according to the current state variable
Computing jacobian matrix->
S4: using a custarse library on the GPU, a matrix a and a vector b are calculated:
wherein A represents a matrix,
representing measurements under state variablesJacobian matrix, R represents a measurement variance matrix, b represents a vector, Z represents a system measurement vector,/->
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 the correction amount of Newton iteration according to the x solved in the step S5
And determining state variables
wherein ,/>
Representing state variables +.>
Correction representing the kth iteration, +.>
A state variable representing the kth iteration;
s7: let k=k+1, determine whether or not the condition is satisfied
wherein ,/>
Represents the correction amount of the ith dimension state variable in the kth iteration, epsilon represents the iteration convergence precision value, K represents the iteration variable, and K max Indicating the maximum iteration number, if not, turning to the step (3), if so, exiting the state estimation processA program;
the step S5 specifically includes the following steps:
by utilizing the characteristic of symmetrical positive determination of the matrix A, the pretreatment conjugate gradient method is used for carrying out iterative solution, and the specific method is as follows:
s51: performing an ILU (0) decomposition on the matrix A, wherein the ILU (0) decomposition is a form of incomplete LU decomposition, and forms a preprocessing sub-of the matrix A:
M＝LU (3)
wherein M represents the preprocessing factor of 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=0 and the maximum iteration number i max At the same time, let the initial guess of x be x 0 Calculating an initial residual r 0 And its 2-norm r 0 ||；
S53: solving the system of equations mz=r from L and U i Wherein M represents the preprocessing factor of matrix A, Z represents the system measurement vector, r i Representing a calculated residual;
s54: determining ρ i ＝(r i Z); wherein Z represents a system measurement vector, r i Representing a calculated residual;
s55: judging whether i is zero, if so, then p is the other i Let β=ρ if not, Z represents the system measurement vector i /ρ i-1 ；
S56: determination of p i ＝z+βp i-1 ；
S56: determining q=ap i 、α＝ρ i /(p i ,q)、x i+1 ＝x i +αp i 、r i+1 ＝r i -αq；
S57: judging whether one of the following two conditions is satisfied i+1 ||/||r 0 ||≤εORi＜i max If yes, exiting the iteration; if not, let i=i+1 go to step S53.
2. The power grid state estimation method based on the GPU parallel acceleration preprocessing conjugate gradient iteration method of claim 1, wherein the method is characterized by comprising the following steps of: the steps ofJacobian matrix of step S3
The method is adopted for determination as follows:
wherein ,
representing a jacobian matrix, h (x) represents a measurement function of a state variable, and x represents a state variable.
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| 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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| 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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