CN103488610A - Method of solving power grid equations based no non-zero element traversal of sparse storage - Google Patents

Abstract

The invention relates to a method of solving power grid equations based no non-zero element traversal of sparse storage. The method includes the steps of 1, before analog time-step solution, forming a power system grid equation according to power grid structural parameters and failure disturbance information to be calculated; 2, factoring an equation coefficient matrix in the power system grid equation to obtain a post-factoring factor table matrix; 3, performing analog time-step solution. The method has the advantages that non-zero element retrieval and double cycle of the equation coefficient matrix and redundant operations and calculations in conditional judgment during application of the conventional solution methods of high-dimensional sparse linear equations can be eliminated as far as possible, the novel, utility method and process of solving the high-dimensional sparse linear equation sets is obtained, the efficiency of the method of solving the high-dimensional linear equation sets based on sparse storage and forward and back substitutions is improved, and the solution bottleneck of large-scale power systems and linear power network and circuit parts in efficient analog calculation and real-time (super real-time) simulation for large-scale power systems can be eliminated effectively.

Description

A kind of electrical network network equation method for solving of the non-zero entry traversal based on sparse storage

Technical field

The present invention relates to a kind of electrical network network equation method for solving of the non-zero entry traversal based on sparse storage, the present invention, for large-scale electrical power system electromechanical transient (surpassing) real-time simulation network equation rapid solving, belongs to the electric digital simulation technique of large net field.

Background technology

Relate generally to the calculating of the parts such as matrix, vector correlation computing, particularly linear electric power networks, circuit in electric system computational analysis and emulation, essence is that the linear equation that voltage, electric current are relevant solves.To large-scale electrical power system, the equation dimension is higher, usually reaches dimensions up to ten thousand, and its operand proportion is larger, thereby the High-dimensional Linear equation solution is one of principal element affected large-scale electrical power system computational analysis and simulated program and software operation efficiency.

How the linear equation matrix is carried out to Factorization in engineering, then based on factor table, by former generation, backward steps, solve linear equation.In addition, due to the design feature of electric power networks self, the matrix of describing above-mentioned linear equation adopts the sparsity structure storage more, in matrix, only contains a small amount of non-zero entry.Matrix is through Factorization, and packing factor table matrix also only contains a small amount of non-zero entry.

In electric system simulation, particularly, in strict real-time simulation, solve and the network equation of the whole network dynamic element solves alternately iteration to carry out.Wherein, dynamic element is discrete component access electric network, and each dynamic element is relatively independent in single solves, and the process of resolving can automatically decouple; can divide into groups is run simultaneously resolves, and dynamic element comprises the primary equipment such as motor, dynamic load and controls the secondary device such as protection.Yet, the electric network close-coupled that electric system is complete, network equation solves and is difficult to automatically decouple, thereby run simultaneously, resolves.Therefore, can network equation solves link becomes the Main Bottleneck that determines large-scale electrical power system simulation calculation efficiency, particularly, in (surpassing) real-time simulation, become the key factor that guarantee the emulation real-time.

Conventional higher-dimension sparse linear solving equations method, although effectively saved the calculator memory storage space, but in the former generation and backward steps of Solving Linear, except necessary floating number algebraic operation, also need by dual circulation, system of linear equations matrix of coefficients non-zero entry to be retrieved, wherein comprise some redundant operations, thereby reduced equation solution efficiency.Therefore, in (surpassing) real-time simulation, be necessary to eliminate as much as possible redundant operation and the computing in conventional High-dimensional Linear solving equations method flow, effectively improve High-dimensional Linear solving equations efficiency.

Summary of the invention

The electrical network network equation method for solving that the object of the invention is to consider the problems referred to above and provide a kind of non-zero entry based on sparse storage to travel through.The present invention can eliminate operation and the computing of redundancy in the retrieval of equation coefficient matrix non-zero entry in conventional higher-dimension sparse linear equation solution method and dual circulation, condition judgment as much as possible, form higher-dimension sparse linear solving equations method and the flow process of new practicality, the efficiency of lifting based on sparse storage and former generation C＋＋ language High-dimensional Linear equation method, effectively eliminate the calculating of large-scale electrical power system efficient emulation and (surpassing) real-time simulation neutral line electric network and circuit part and solve bottleneck.

Technical scheme of the present invention is: the present invention is based on the electrical network network equation method for solving of the non-zero entry traversal of sparse storage, comprise the following steps:

1) before step solves when entering emulation, according to electric network composition parameter and fault disturbance information to be calculated, form the power system network equation, equation can be described as

$\stackrel{\·}{I}=Y\stackrel{\·}{U}---\left(1\right)$

Wherein for electric system node Injection Current fundamental phasors,

for the Electric Power System Node Voltage fundamental phasors, Y is power system network node admittance battle array, and the equation dimension is designated as n;

2) before when entering emulation, step solves, equation coefficient matrix Y carries out Factorization in formula (1), obtains the factor table matrix after Factorization, is designated as

A=L+D+U (2)

Be wherein triangular portions under L factor table matrix, the main diagonal element part that D is the factor table matrix, the upper triangular portions that U is the factor table matrix;

Above-mentioned matrix all adopts sparse form to be stored, and non-zero entry by rows;

Record matrix L, U non-zero entry sum k _l, k _u;

Record matrix L, U non-zero entry place line number R _l, R _u, and record matrix L, U non-zero entry column C _l, C _u, in matrix L, i non-zero entry place row, column is designated as

in matrix U, i non-zero entry place row, column is designated as

While 3) entering emulation, step solves.

During during emulation above-mentioned steps 3), step solves, each simulation step length need be carried out network equation and be solved, and specifically comprises the steps:

31) be equation solution former generation procedure initialization intermediate variable x, x is n-dimensional vector, order

$x=\stackrel{\·}{I}---\left(3\right);$

32) according to matrix L non-zero entry quantity, substance loops following computing

$x\left(R_L^i\right)=x\left(R_L^i\right)-L(R_L^i,C_L^i)\×x\left(C_L^i\right),i=2,...,k_L---\left(4\right);$

33) according to the whole diagonal elements of matrix D, substance loops following computing

x(i)=x(i)/D(i,i),i=1,…,n (5)；

34) according to matrix U non-zero entry quantity, substance loops following computing

$x\left(R_L^i\right)=x\left(R_L^i\right)-U(R_L^i,C_L^i)\×x\left(C_L^i\right),i=k_U-1,...,1---\left(6\right)$

35) equation solution finishes, and the intermediate variable assignment is given

$\stackrel{\·}{U}=x---\left(7\right).$

The Large Scale Sparse Solving Linear that the electric system computational analysis is relevant with circuit with generally relating to electric network in emulation, the system of equations dimension is often very high, and operand proportion is larger; Relatively the electrical network dynamic element calculates, and the system of linear equations that electric network is relevant with circuit resolves and is difficult to the subnetting parallelization and synchronously carries out, so the relevant linear equation of network solves the bottleneck that link becomes electric system calculating and simulation efficiency.In the former generation and backward steps of conventional higher-dimension sparse linear solving equations method, need to system of linear equations matrix of coefficients non-zero entry, be retrieved by dual circulation, wherein comprise some redundant operations.Therefore, in (surpassing) real-time simulation, be necessary to eliminate as much as possible redundant operation and the computing in conventional High-dimensional Linear solving equations method flow.The present invention is based on the electrical network network equation method for solving of the non-zero entry traversal of sparse storage, eliminate as much as possible operation and the computing of redundancy in the retrieval of equation coefficient matrix non-zero entry in conventional higher-dimension sparse linear equation solution method and dual circulation, condition judgment, form higher-dimension sparse linear solving equations method and the flow process of new practicality, promote the efficiency based on sparse storage and former generation C＋＋ language High-dimensional Linear equation method.The present invention is the electrical network network equation method for solving that a kind of convenient and practical non-zero entry based on sparse storage travels through.

Embodiment

The present invention proposes a kind of electrical network network equation method for solving of the non-zero entry traversal based on sparse storage, the method comprises the following steps:

1) before step solves when entering emulation, according to electric network composition parameter and fault disturbance information to be calculated, form the power system network equation, equation can be described as

$\stackrel{\·}{I}=Y\stackrel{\·}{U}---\left(1\right)$

Wherein

for electric system node Injection Current fundamental phasors,

for the Electric Power System Node Voltage fundamental phasors, be equation unknown quantity to be solved, Y is power system network node admittance battle array, the equation dimension is designated as n.

2) before when entering emulation, step solves, equation coefficient matrix Y carries out Factorization in formula (1), obtains the factor table matrix after Factorization, is designated as

A=L+D+U (2)

Be wherein triangular portions under L factor table matrix, the main diagonal element part that D is the factor table matrix, the upper triangular portions that U is the factor table matrix.

Above-mentioned matrix all adopts sparse form to be stored, and non-zero entry is by the row close-packed arrays, in computing machine with real part and the imaginary part of two type double precision array variable Coutinuous store A matrixes.

Record matrix L, U non-zero entry sum k _l, k _u, in computing machine with the long variable storage.

Record matrix L, U non-zero entry place line number R _l, R _u, and record matrix L, U non-zero entry column C _l, C _u, in computing machine with long array variable Coutinuous store; In matrix L, i non-zero entry place row, column is designated as

in matrix U, i non-zero entry place row, column is designated as

While 3) entering emulation, step solves, and each simulation step length need be carried out network equation and be solved, and adopts following steps.

31) be equation solution former generation procedure initialization intermediate variable x, x is n-dimensional vector, in computing machine, with real part and the imaginary part of two double-precision array variable Coutinuous store x, makes

$x=\stackrel{\·}{I}---\left(3\right)$

32) according to matrix L non-zero entry quantity, substance loops following computing

$x\left(R_L^i\right)=x\left(R_L^i\right)-L(R_L^i,C_L^i)\×x\left(C_L^i\right),i=2,...,k_L---\left(4\right)$

Above-mentioned computing is complex operation.

33) according to the whole diagonal elements of matrix D, substance loops following computing

x(i)=x(i)/D(i,i),i=1,…,n (5)

Above-mentioned computing is complex operation.

34) according to matrix U non-zero entry quantity, substance loops following computing

$x\left(R_L^i\right)=x\left(R_L^i\right)-U(R_L^i,C_L^i)\×x\left(C_L^i\right),i=k_U-1,...,1---\left(6\right)$

Above-mentioned computing is complex operation.

35) equation solution finishes, and the intermediate variable assignment is given

$\stackrel{\·}{U}=x---\left(7\right)$

On the computing machine that is configured to processor i72720m, internal memory 4g, tested, more conventional sparse linear solving equations method, this method efficiency improves approximately 3 times, be solved to example with 13 years rich large system electrical network network equations of south electric network, single solve the time by approximately 0.32 millisecond reduce to approximately 0.12 millisecond.

Claims (2)

1. the electrical network network equation method for solving of non-zero entry based on a sparse storage traversal is characterized in that comprising the following steps:

1) before step solves when entering emulation, according to electric network composition parameter and fault disturbance information to be calculated, form the power system network equation, equation can be described as

$\stackrel{\·}{I}=Y\stackrel{\·}{U}---\left(1\right)$

Wherein

for electric system node Injection Current fundamental phasors,

for the Electric Power System Node Voltage fundamental phasors, Y is power system network node admittance battle array, and the equation dimension is designated as n;

2) before when entering emulation, step solves, equation coefficient matrix Y carries out Factorization in formula (1), obtains the factor table matrix after Factorization, is designated as

A=L+D+U (2)

Be wherein triangular portions under L factor table matrix, the main diagonal element part that D is the factor table matrix, the upper triangular portions that U is the factor table matrix;

Above-mentioned matrix all adopts sparse form to be stored, and non-zero entry by rows;

Record matrix L, U non-zero entry sum k _l, k _u;

Record matrix L, U non-zero entry place line number R _l, R _u, and record matrix L, U non-zero entry column C _l, C _u, in matrix L, i non-zero entry place row, column is designated as

in matrix U, i non-zero entry place row, column is designated as

While 3) entering emulation, step solves.

2. the electrical network network equation method for solving of non-zero entry based on sparse storage traversal according to claim 1, is characterized in that above-mentioned steps 3) emulation the time during step solves, each simulation step length need be carried out network equation and be solved, and specifically comprises the steps:

31) be equation solution former generation procedure initialization intermediate variable x, x is n-dimensional vector, order

$x=\stackrel{\·}{I}---\left(3\right);$

32) according to matrix L non-zero entry quantity, substance loops following computing

$x\left(R_L^i\right)=x\left(R_L^i\right)-L(R_L^i,C_L^i)\×x\left(C_L^i\right),i=2,...,k_L---\left(4\right);$

33) according to the whole diagonal elements of matrix D, substance loops following computing

x(i)=x(i)/D(i,i),i=1,…,n (5)；

34) according to matrix U non-zero entry quantity, substance loops following computing

$x\left(R_L^i\right)=x\left(R_L^i\right)-U(R_L^i,C_L^i)\×x\left(C_L^i\right),i=k_U-1,...,1---\left(6\right);$

35) equation solution finishes, and the intermediate variable assignment is given

$\stackrel{\·}{U}=x---\left(7\right).$