CN104158182A - Large-scale power grid flow correction equation parallel solving method - Google Patents

Abstract

The invention provides a large-scale power grid flow correction equation parallel solving method. According to the characteristic of a factor table solving linear equation operation process and the sparsity of a flow correction equation coefficient matrix, rows which can be normalized at the same time are grouped, parallel normalization operation and elimination operation are completed. Row grouping information acquired in a factor table solving process, parallel former generation operation is completed. The efficiency of large-scale power grid flow solving is improved. The flow calculation real-time requirement of flow, security analysis, AVC and other online analysis applications of a power grid dispatcher can be met. The dispatcher can find potential risks of power grid operation soon, so as to ensure safe and stable operation of a power grid.

Description

The parallel method for solving of a kind of large scale electric network trend update equation

Technical field

The present invention relates to a kind of method for solving, be specifically related to the parallel method for solving of a kind of large scale electric network trend update equation.

Background technology

Current, under the leader of State Grid Corporation of China, the practical work of intelligent grid Dispatching Control System on-line analysis software has obtained phasic results, and promote and try out in the supporting system technology of scheduling institutions at different levels, for routine analysis and the traffic control of each control centre have played very important supporting role.On-line analysis software computational speed, need parallel computing and the means of the applicable large electrical network on-line analysis software of research, be further lifted at the computational speed of line analysis software, meet the requirement of real-time that large electrical network full model real-time analysis is calculated.And trend calculating is the critical function of large electrical network on-line analysis software, along with the development of electric power system and the expansion of electrical network scale, the calculating scale of online power flow software is increasing, simultaneously the intelligent grid requirement of real-time that scheduling calculates scale grid line trend that becomes more meticulous is more and more higher, makes conventional serial trend software not be well positioned to meet following intelligent grid dispatching requirement.For improving the computational speed of scale grid line trend software, except adopting high-performance server and advanced algorithm, can also adopt distributed computing technology and parallel computing to promote software calculated performance.The dispatch automated system at current each regulation and control center is generally used high-performance server, CPU number more than 4, single cpu be generally 6 cores and more than, internal memory is generally greater than 16G, has good parallel processing capability.Therefore, by the existing application software of intelligent grid Dispatching Control System is carried out to parallelization transformation, hardware resource is fully used, can improves system-computed performance.

In shared drive model, a concurrent program is made up of the parallel task of multiple shared drives, and the exchange of data is by impliedly completing by shared data.This programming mode generally only needs to specify circulation that can executed in parallel, and does not need to consider to calculate how to divide with data, and how to carry out intertask communication, and compiler can complete above-mentioned functions automatically.Popular shared drive model development standard is OpenMP at present.OpenMP has defined a set of compiling and has instructed statement, is used to specify the information such as the sharing of concurrency, data of program/privately owned, and OpenMP provides one to support function library simultaneously.OpenMP has obtained supporting widely and using at present.The VC of Microsoft, in linux operating system, widely used GCC compiler is all supported OpenMP programming model, in addition, the hardware vendors such as IBM, HP, Sun, SGI, Intel all have the compiler product of supporting OpenMP.OpenMP is a kind of parallel schema fork/join formula parallel schema of standard, its basic thought is, when starting, program only has a main thread, serial part in program is all carried out by main thread, parallel part is to carry out by deriving from other threads, if but be to carry out serial part when parallel section does not finish.Utilizing compiling to instruct statement program can be divided into multiple thread parallels carries out.

C++ has defined an abundant in content abstract data type java standard library.Wherein most important java standard library type is string, vector and map, and they have defined respectively the right set of character string, set and the key of variable size-be worth.String and vector often by iterator as supporting type, for accessing the element in character or the vector of string.Map type is Associate array, can obtain a value as subscript with key, as built-in array type.The essence of its association is that the value of element is associated with certain specific key, and not by element, the position in array obtains.Map container provides begin and end computing, to produce the iterator for traveling through whole container.These java standard library types are the abstract of those data types (as array and pointer) more basic in language part.

In prior art, Solving Linear mainly comprises three steps: Factorization generates factor table, former generation, back substitution.The solution procedure of linear equation Bx=z is as described below:

(1) Factorization generates factor table

Factorization process comprises normalization operations and two key steps of cancellation computing.

1. normalization operations: for n × n rank matrix, the normalization that i is capable only need to be calculated the capable non-zero entry of i in upper triangular portions, if the capable j column element of i is non-zero entry, the capable diagonal element b of i _ii=1/b _ii, the capable non-zero diagonal element of i b _ij=b _ij× b _ii.

2. cancellation computing: utilized the i of normalization operations capable, capable to i on triangle non-zero entry row number corresponding row carry out cancellation computing, to capable cancellation computing, the cancellation row diagonal element b of carrying out of j _jj=b _jj-b _ij× b _ij÷ b _ii.If b _ilfor non-zero entry, also need element b _jlcarry out cancellation computing, b _jl=b _jl-b _il× b _ij÷ b _ii.In normalization process, have injection element, need to sort and be optimized by node optimization.

(2) former generation computing

By independent vector z assignment in work vector x.Former generation calculates and carries out successively to large size node from small size node, utilizes triangle on factor table to participate in cancellation computing, if upper triangle i is capable, k column element is non-zero entry, 0～(i-1) row has completed cancellation computing, x _k=x _k-b _ikx _i, the serial program of former generation computing can represent by following false code:

Standardized algorithm can represent by following false code:

For i=0to n//cyclic node, from 0 to n-1

Iter ← B[i] .begin () // initialization iterator

X[i]=iter->second*x[i] // to non-zero entry x _ithe calculating of standardizing

(3) back substitution computing.

Back substitution computing is from large node number to trifle period, if i～(n-1) row has completed cancellation computing, and the capable k that is designated as of i-1, the j column element that k is capable is non-zero entry, x _k=x _k-b _kjx _j, the serial program of back substitution computing can represent by following false code:

Wherein: i, j, k ∈ { 0,1,2 ... n}.B is symmetric coefficient matrix, and b is symmetrical matrix non-zero entry, and x is for separating vector, and z is independent vector.

Summary of the invention

In order to overcome above-mentioned the deficiencies in the prior art, the invention provides the parallel method for solving of a kind of large scale electric network trend update equation, solve the feature of thread equation calculating process and the sparse property of trend update equation coefficient matrix according to factor table, can carry out normalized row grouping simultaneously, the normalization operations that walked abreast and cancellation computing, simultaneously, the row grouping information obtaining in factor table process is asked in utilization, complete parallel former generation computing, thereby improve large scale electric network Load Flow Solution efficiency, meet dispatching of power netwoks person's trend, safety analysis, the requirement of real-time that the on-line analysis application such as AVC are calculated trend, be convenient to the potential risk that dispatcher finds operation of power networks sooner, thereby ensure the safe and stable operation of electrical network.

In order to realize foregoing invention object, the present invention takes following technical scheme:

The invention provides the parallel method for solving of a kind of large scale electric network trend update equation, said method comprising the steps of:

Step 1: sparse matrix storage;

Step 2: parallel Factorization generates factor table;

Step 3: former generation computing walks abreast;

Step 4: back substitution computing;

Step 5: trend interative computation.

In described step 1, in the parallel solution procedure of electric network swim update equation of P-Q decomposition method, complete node admittance matrix, update equation coefficient matrix B ' and B ", and B ' and the B " storage of the factor table generating after Factorization; Update equation coefficient matrix B ' and B " are sparse matrix.

Adopt the electric network swim update equation of P-Q decomposition method to be expressed as:

ΔP/U＝-B′UΔθ (1)

ΔQ/U＝-B″ΔU (2)

Wherein, Δ P is the meritorious correction vector of computing node, and Δ Q is the idle correction vector of computing node, and Δ θ is phase angle correction vector, Δ U is voltage increment vector, U is node voltage amplitude, and θ is node voltage phase angle, and P is that node injects active power, Q is that node injects reactive power, it is negative that sparse matrix B ' element is that corresponding branch road reactance inverse is got, and " element is corresponding node admittance matrix imaginary part to sparse matrix B, and i, j are node serial number.

Described step 1 specifically comprises the following steps:

Step 1-1: utilize sequence container vector that C++ abstract data type java standard library provides and associated container map to realize the storage of the electric network swim update equation coefficient matrix of P-Q decomposition method;

Defining objects vector<map<int, double>>B1, B2, Y preserves respectively sparse matrix B ', B " and node admittance matrix; Wherein map<int, double> is used for preserving row element, and row number represent by the key index of int type, and sparse matrix nonzero element is represented by the relating value of double type;

Step 1-2: node optimization sequence;

Statistics node relative branch number, props up way by node and from less to more node is carried out to static ordering; And the order according to PQ node, PV node, balance node sorts successively; In sequence, form internal node and calculate the table of comparisons that bus is numbered;

Step 1-3: computing node admittance matrix;

According to node admittance matrix dimension initialization vector object Y dimension; Node i self-admittance is the summation that diagonal element element equals the direct-connected all branch road admittance of this node, and the transadmittance between node i, j equals the negative value of connected node i, the admittance of j branch road; The node admittance array element element having calculated is saved in object Y, completes the sparse matrix storage of node admittance matrix, and only preserve triangle on node admittance matrix;

Step 1-4: sparse matrix B ' and B " are saved in object B 1 and B2.

Described step 2 comprises the following steps:

Step 2-1: specify parallel processing process number;

Step 2-2: first, by the traversal of sparse matrix nonzero element, add up every row element and be eliminated number of times, k row element is eliminated number of times and is kept at integer array variable count[k] in; At map<int, in double>>B, increase the first numerical digit of injection and put simultaneously, maximum is eliminated to number of times and is designated as max; Defined variable vector<int>muster and vector<vector<intGreatT.GreaT. GT>vec_muster (muster, max) are eliminated for collecting the row that number of times is identical; Vec_muster[m] in preserve that to be eliminated number of times be all line numbers of m time; Deposit the row that is eliminated 0 time in vec_master[0] in;

Step 2-3: according to concurrent process number by vec_muster[m] in line number be divided into N group, be eliminated number of times m=m+1;

Step 2-4: utilize compiling to instruct statement #pragma omp parallel for num_threads (N) that host process is divided into N line process, with multiple threads walk abreast normalization operations and cancellation computing, being eliminated row is eliminated number of times and subtracts 1, be count[k]-1, collection is eliminated number of times and becomes 0 line number, and is kept at vec_muster[m] in;

Step 2-5: judge vec_muster[m] whether array be empty, parallel Factorization finishes if it is empty; Otherwise return to step 2-3, continue parallel normalization operations and cancellation computing.

Described step 3 comprises the following steps:

Step 3-1: can be calculated meritorious correction vector Δ P and idle correction vector Δ Q according to the meritorious residual equation of trend and the idle residual equation of trend;

The meritorious residual equation of trend and the idle residual equation of trend are expressed as:

$\mathrm{\&Delta;}{P}_i=P_i-U_i\underset{j=1}{\overset{j=n}{\mathrm{\&Sigma;}}}{U}_j(G_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}})---\left(3\right)$

$\mathrm{\&Delta;}{Q}_i=Q_i-U_i\underset{j=1}{\overset{j=n}{\mathrm{\&Sigma;}}}{U}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}})---\left(4\right)$

Wherein, Δ P _ifor the meritorious correction of node i, Δ Q _ifor the idle correction of node i; Δ θ is phase angle correction vector, and Δ U is voltage increment vector; U _iand U _jbe respectively node i and j voltage magnitude; θ _ijfor the phase difference of node i and j is θ _ij=θ _i-θ _j; P _ifor node i is injected active power, Q _ifor node i is injected reactive power; G _ijfor node admittance matrix real part, B _ijnode admittance matrix imaginary part;

Step 3-2: in work vector x, the process of appointment is counted N by independent vector z assignment;

Independent vector z represents constant term Δ P/U and the Δ Q/U of equation group (1), (2), and what work vector x represented equation group (1), (2) waits to ask a Δ θ and Δ U;

Step 3-3: initialization is eliminated number of times m=0;

Step 3-4: peek group vec_muster[m] in row, count N and be divided into N group if line number is greater than process, otherwise do not divide into groups, the former generation cancellation computing that walks abreast, is eliminated number of times m=m+1;

Step 3-5: former generation calculates and carries out successively to large size node from small size node, utilize triangle on factor table to participate in parallel former generation cancellation computing, if upper triangle i is capable, k column element is nonzero element, 0～(i-1) row has completed parallel former generation cancellation computing, x _k=x _k-b _ikx _i; The cancellation process of former generation is with to generate the cancellation process of factor table consistent, utilizes the former generation cancellation computing that walks abreast of row grouping information in vector<vector<intGreatT.GreaT. GT>vec_muster;

Step 3-6: be eliminated number of times m=m+1, judgement is eliminated number of times and whether equals maximum cancellation number of times, if equate, former generation cancellation computing finishes, and returns to step 3-4 proceed parallel former generation cancellation computing if be less than;

Step 3-7: former generation normalization operations;

I the element x of work vector x _i=x _i/ b _ii, former generation normalization operations instructs statement #pragma omp parallel for to complete the former generation normalization operations that for circulates with compiling, according to the maximum parallel processing Thread Count of CPU former generation normalization operations.

In described step 4, back substitution computing is from large node number to trifle period, if i～(n-1) row has completed back substitution cancellation computing, and the capable k that is designated as of i-1, the j column element that k is capable is nonzero element, x _k=x _k-b _kjx _j; By formula x _k=x _k-b _kjx _j, k is descending to be solved the element of work vector one by one, the final solution to equation group (1), (2).

Described step 5 comprises the following steps:

Step 5-1: according to the phase angle correction vector Δ θ obtaining and voltage increment vector Δ U, node voltage amplitude U and node voltage phase angle theta are revised i.e. θ=θ+Δ θ, U=U+ Δ U;

Step 5-2: meritorious correction and the idle correction of calculating each node by formula (3), (4);

Step 5-3: if meritorious correction is less than meritorious convergence precision, and idle correction is less than idle convergence precision, calculated; Otherwise, return to step 3 and 4 and re-start parallel former generation computing and back substitution computing, and solve formula (1), (2).

Compared with prior art, beneficial effect of the present invention is:

1, utilize sequence container vector that C++ abstract data type java standard library provides and associated container map to realize the storage of linear equation coefficient matrix.Can access easily and quote, save internal memory, can retrieve easily and access again, can also consider that the variation of network configuration modifies to canned data easily simultaneously;

2, generating in factor table process, utilize the independence of partial row normalization and cancellation computing, row is divided into groups, parallel normalization and cancellation computing, has improved the solution efficiency of trend linear equation.

Brief description of the drawings

Fig. 1 is row normalization operations and cancellation operational flowchart in the embodiment of the present invention;

Fig. 2 is that in the embodiment of the present invention, parallel Factorization generates factor table solution flow chart;

Fig. 3 is parallel former generation cancellation operational flowchart in the embodiment of the present invention;

Fig. 4 is that in the embodiment of the present invention, certain province's electrical network 383 calculates comparative graph consuming time;

Fig. 5 is that in the embodiment of the present invention, certain network regulation and interconnection region electrical network calculate comparative graph consuming time.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described in further detail.

The invention provides the parallel method for solving of a kind of large scale electric network trend update equation, improve large scale electric network linear equation and solve computational speed, solve electrical network scale and increase the huge amount of calculation problem of bringing.In addition, the present invention also provides a kind of sparse matrix storage means, can access easily and quote, save internal memory, can retrieve easily and access again, can also consider that the variation of network configuration modifies to canned data easily, high efficiency sparse matrix storage means can improve linear equation and solve speed simultaneously.Usage factor table solution, by the computational process of normalization operations, cancellation computing and former generation back substitution in analysis factor decomposable process, utilize the sparse property of update equation coefficient matrix, can carry out normalized row grouping, the normalization operations that walked abreast and cancellation computing simultaneously.Meanwhile, utilize and ask the row grouping information obtaining in factor table process, complete parallel former generation computing.The method has effectively improved large scale electric network trend update equation solution efficiency, thereby improves the calculating real-time of the on-line analysis softwares such as trend.By Quick tidal current calculation, find in time the potential risk of operation of power networks, improve operation of power networks stability.

Sparse matrix storage, can access easily and quote, save internal memory, can retrieve easily and access again, can also consider that the variation of network configuration modifies to canned data easily, high efficiency sparse matrix storage means can improve linear equation and solve speed simultaneously.By the computational process of normalization operations, cancellation computing and former generation back substitution in analysis factor decomposable process, utilize the sparse property of update equation coefficient matrix, can carry out normalized row grouping, the normalization operations that walked abreast and cancellation computing simultaneously.Meanwhile, utilize and ask the row grouping information obtaining in factor table process, complete parallel former generation computing.The method has effectively improved large scale electric network trend update equation solution efficiency, thereby improves the calculating real-time of the on-line analysis softwares such as trend.

The invention provides the parallel method for solving of a kind of large scale electric network trend update equation, said method comprising the steps of:

Step 1: sparse matrix storage;

Step 2: parallel Factorization generates factor table;

Step 3: former generation computing walks abreast;

Step 4: back substitution computing;

Step 5: trend interative computation.

In described step 1, in the parallel solution procedure of electric network swim update equation of P-Q decomposition method, complete node admittance matrix, update equation coefficient matrix B ' and B ", and B ' and the B " storage of the factor table generating after Factorization; Update equation coefficient matrix B ' and B " are sparse matrix.

Adopt the electric network swim update equation of P-Q decomposition method to be expressed as:

ΔP/U＝-B′UΔθ (1)

ΔQ/U＝-B″ΔU (2)

Wherein, Δ P is the meritorious correction vector of computing node, Δ Q is the idle correction vector of computing node, Δ θ is phase angle correction vector, Δ U is voltage increment vector, U is node voltage amplitude, θ is node voltage phase angle, P is that node injects active power, Q is that node injects reactive power, sparse matrix B ' element is that corresponding branch road reactance inverse is got negative (not comprising balance node), sparse matrix B " element is corresponding node admittance matrix imaginary part (not comprising PV node and balance node), and i, j are node serial number.

Described step 1 specifically comprises the following steps:

Step 1-1: utilize sequence container vector that C++ abstract data type java standard library provides and associated container map to realize the storage of the electric network swim update equation coefficient matrix of P-Q decomposition method;

Defining objects vector<map<int, double>>B1, B2, Y preserves respectively sparse matrix B ', B " and node admittance matrix; Wherein map<int, double> is used for preserving row element, and row number represent by the key index of int type, and sparse matrix nonzero element is represented by the relating value of double type;

Step 1-2: node optimization sequence;

Statistics node relative branch number, props up way by node and from less to more node is carried out to static ordering; And the order according to PQ node, PV node, balance node sorts successively; In sequence, form internal node and calculate the table of comparisons that bus is numbered;

Step 1-3: computing node admittance matrix;

According to node admittance matrix dimension initialization vector object Y dimension; Node i self-admittance is the summation that diagonal element element equals the direct-connected all branch road admittance of this node, and the transadmittance between node i, j equals the negative value of connected node i, the admittance of j branch road; The node admittance array element element having calculated is saved in object Y, completes the sparse matrix storage of node admittance matrix, and only preserve triangle on node admittance matrix;

Step 1-4: sparse matrix B ' and B " are saved in object B 1 and B2.

Observing the whole cancellation process of trend coefficient matrix can find, because trend coefficient matrix is to have sparse property, every row element non-zero entry is little, and therefore, capable needs of i is eliminated i time.In cancellation process, there are many row that were never eliminated and do not need the row being eliminated again, these row can directly carry out other row of normalization operations cancellation, and the calculating of these row can parallel computation.The number of times that the every row of department of statistic's matrix number is eliminated, by parallel line number of passes, residue being eliminated to number of times is that 0 node is divided into N group, completes parallel normalization operations and cancellation computing.Complete after computing, the 2nd group of the row composition that only needed to be eliminated 1 time and to be eliminated can normalization operations and the row set of cancellation computing, again completes parallel normalization operations and cancellation computing.By that analogy, until all provisional capitals complete normalization operations.Observe former generation cancellation process, be not difficult to find, former generation cancellation process is consistent with the cancellation process that factor table generates, and i is capable all only needs triangle non-zero entry on this row of cancellation to be listed as number corresponding row, can use equally parallel computation again.Row normalization operations and cancellation computing flow process are as shown in Figure 1.

Economize and adjust the B ' matrix of 383 node systems as example taking certain, utilize static optimization method to sort to node serial number, upper triangle the 0th row element b _0,199, the 1st row b _1,200, the 2nd row b _2,201for non-zero entry, the normalization of first three rows and cancellation process are as follows: the 0th professional etiquette is formatted, cancellation 199 row, the 1st professional etiquette cancellation 200 row of formatting, the 2nd professional etiquette cancellation 201 row of formatting.Be not difficult to find, first three rows element all needn't carry out cancellation computing, can directly carry out normalization operations, then cancellation corresponding line, and can carry out parallel computation.Order by each row normalization operations and cancellation computing in observation factor table generative process can be divided into row: be eliminated the directly row set A of normalization operations 0 time, after row cancellation in set A, can be carried out the row set B of normalization operations, after row cancellation in set A and B, can be carried out the row set C of normalization operations, by that analogy, by all row groupings.Observe former generation cancellation process, be not difficult to find, the 0th row only needs cancellation 199 row, and the 1st row only needs cancellation 200 row, and the 2nd row only needs cancellation the 201st row.Therefore, can utilize the row set forming in the factor table generative process cancellation that walks abreast, the row set A cancellation corresponding row that walks abreast, the then parallel cancellation corresponding row of row set B, by that analogy, until complete the cancellation computing of all row.

Adopt the parallel method for solving of shared drive programming model OpenMP and above-mentioned system of linear equations, carry out conceptual design and realization.Parallel Factorization generates factor table solution flow process as shown in Figure 2, comprises the following steps:

Step 2-1: specify parallel processing process number;

Step 2-2: first, by the traversal of sparse matrix nonzero element, add up every row element and be eliminated number of times, k row element is eliminated number of times and is kept at integer array variable count[k] in; At map<int, in double>>B, increase the first numerical digit of injection and put simultaneously, maximum is eliminated to number of times and is designated as max; Defined variable vector<int>muster and vector<vector<intGreatT.GreaT. GT>vec_muster (muster, max) are eliminated for collecting the row that number of times is identical; Vec_muster[m] in preserve that to be eliminated number of times be all line numbers of m time; Deposit the row that is eliminated 0 time in vec_master[0] in;

Step 2-3: according to concurrent process number by vec_muster[m] in line number be divided into N group, be eliminated number of times m=m+1;

Step 2-4: utilize compiling to instruct statement #pragma omp parallel for num_threads (N) that host process is divided into N line process, with multiple threads walk abreast normalization operations and cancellation computing, being eliminated row is eliminated number of times and subtracts 1, be count[k]-1, collection is eliminated number of times and becomes 0 line number, and is kept at vec_muster[m] in;

Step 2-5: judge vec_muster[m] whether array be empty, parallel Factorization finishes if it is empty; Otherwise return to step 2-3, continue parallel normalization operations and cancellation computing.

Described step 3 comprises the following steps:

Step 3-1: can be calculated meritorious correction vector Δ P and idle correction vector Δ Q according to the meritorious residual equation of trend and the idle residual equation of trend; (illustrating: equation group (1), (2) solution procedure are equal to system of linear equations Bx=z)

The meritorious residual equation of trend and the idle residual equation of trend are expressed as:

$\mathrm{\&Delta;}{P}_i=P_i-U_i\underset{j=1}{\overset{j=n}{\mathrm{\&Sigma;}}}{U}_j(G_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}})---\left(3\right)$

$\mathrm{\&Delta;}{Q}_i=Q_i-U_i\underset{j=1}{\overset{j=n}{\mathrm{\&Sigma;}}}{U}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}})---\left(4\right)$

Wherein, Δ P _ifor the meritorious correction of node i, Δ Q _ifor the idle correction of node i; Δ θ is phase angle correction vector, and Δ U is voltage increment vector; U _iand U _jbe respectively node i and j voltage magnitude; θ _ijfor the phase difference of node i and j is θ _ij=θ _i-θ _j; P _ifor node i is injected active power, Q _ifor node i is injected reactive power; G _ijfor node admittance matrix real part, B _ijnode admittance matrix imaginary part;

Step 3-2: in work vector x, the process of appointment is counted N by independent vector z assignment;

Independent vector z represents constant term Δ P/U and the Δ Q/U of equation group (1), (2), and what work vector x represented equation group (1), (2) waits to ask a Δ θ and Δ U;

Step 3-3: initialization is eliminated number of times m=0;

Step 3-4: peek group vec_muster[m] in row, count N and be divided into N group if line number is greater than process, otherwise do not divide into groups, the former generation cancellation computing that walks abreast, is eliminated number of times m=m+1;

Step 3-5: former generation calculates and carries out successively to large size node from small size node, utilize triangle on factor table to participate in parallel former generation cancellation computing, if upper triangle i is capable, k column element is nonzero element, 0～(i-1) row has completed parallel former generation cancellation computing, x _k=x _k-b _ikx _i; The cancellation process of former generation is with to generate the cancellation process of factor table consistent, utilizes the former generation cancellation computing that walks abreast of row grouping information in vector<vector<intGreatT.GreaT. GT>vec_muster;

Step 3-6: be eliminated number of times m=m+1, judgement is eliminated number of times and whether equals maximum cancellation number of times, if equate, former generation cancellation computing finishes, and returns to step 3-4 proceed parallel former generation cancellation computing if be less than;

Step 3-7: former generation normalization operations;

I the element x of work vector x _i=x _i/ b _ii, former generation normalization operations instructs statement #pragma omp parallel for to complete the former generation normalization operations that for circulates with compiling, according to the maximum parallel processing Thread Count of CPU former generation normalization operations.

Former generation normalization operations can represent by following false code:

#pragma omp parallel for//support that by system maximum thread carries out parallel computation

For i=0to n//cyclic node, from 0 to n-1

Iter ← B[i] .begin () // initialization iterator

X[i]=iter->second*x[i] // to non-zero entry x _ithe calculating of standardizing

In parallel cancellation process, should be noted that multiple threads can not carry out cancellation computing to same non-zero entry, therefore, the latching operation function that can utilize OpenMp to provide, operation when preventing concurrent program to same internal memory.Because each thread not necessarily can be carried out the row that calls lock function simultaneously, therefore, adopt latching operation can significantly not reduce concurrent program execution efficiency, but can not cancellation its impact on Parallel Computing Performance.

In described step 4, back substitution computing is from large node number to trifle period, if i～(n-1) row has completed back substitution cancellation computing, and the capable k that is designated as of i-1, the j column element that k is capable is nonzero element, x _k=x _k-b _kjx _j; By formula x _k=x _k-b _kjx _j, k is descending to be solved the element of work vector one by one, the final solution to equation group (1), (2).

The serial program of back substitution computing can represent by following false code:

Described step 5 comprises the following steps:

Step 5-1: according to the phase angle correction vector Δ θ obtaining and voltage increment vector Δ U, node voltage amplitude U and node voltage phase angle theta are revised i.e. θ=θ+Δ θ, U=U+ Δ U;

Step 5-2: meritorious correction and the idle correction of calculating each node by formula (3), (4);

Step 5-3: if meritorious correction is less than meritorious convergence precision, and idle correction is less than idle convergence precision, calculated; Otherwise, return to step 3 and 4 and re-start parallel former generation computing and back substitution computing, and solve formula (1), (2).

Embodiment

Use respectively conventional serial computing method and parallel calculating method of the present invention, on totally 32 core servers, the P-Q decomposition trend update equation of certain provincial power network, certain net level electrical network and certain ultra high voltage interconnection region electrical network is solved and tested at two CPU, shown in the following list of test result and curve, table 1 is on average (second) consuming time of conventional serial approach, table 2 is that 383 nodes province mode transfer types are on average consuming time, table 3 is that 1265 node network regulation models are on average consuming time, and table 4 is that 6251 node network regulation models are on average consuming time; Illustrate: below table in all calculating consuming time be ten times calculate on average consuming time.

Table 1

383 node electrical networks	1265 node electrical networks	6251 node electrical networks
			0.000675182	0.010096	0.051957

Table 2

Concurrent process number (individual)	Running time (second)	Concurrent process number (individual)	Running time (second)
				1	0.001045	21	0.000802
2	0.001063	22	0.000672
				3	0.000952	23	0.000647
4	0.000768	24	0.000679
				5	0.000899	25	0.00059
6	0.000673	26	0.000733
				7	0.000796	27	0.000701
8	0.000722	28	0.000772
				9	0.000759	29	0.000789
10	0.00079	30	0.000685
				11	0.000644	31	0.000752
12	0.000689	32	0.000602
				13	0.000634	33	0.000747
14	0.000795	34	0.000651
				15	0.000697	35	0.000748
16	0.00068	36	0.000852
				17	0.000687	37	0.000662
18	0.000566	38	0.00064
				19	0.000827	39	0.000673
20	0.000604	40	0.000678

Table 3

Concurrent process number	Running time (second)	Concurrent process number	Running time (second)
				1	0.010813	21	0.008122
2	0.010311	22	0.008395
				3	0.009867	23	0.008321
4	0.009396	24	0.008867
				5	0.009124	25	0.007991
6	0.008741	26	0.00819
				7	0.008269	27	0.008209
8	0.00835	28	0.008287
				9	0.008154	29	0.008274
10	0.008213	30	0.008475

Concurrent process number	Running time (second)	Concurrent process number	Running time (second)
				11	0.008323	31	0.008052
12	0.008462	32	0.008147
				13	0.008344	33	0.008122
14	0.008307	34	0.008364
				15	0.008239	35	0.008899
16	0.008338	36	0.008118
				17	0.00895	37	0.009212
18	0.008572	38	0.00825
				19	0.008511	39	0.009029
20	0.008082	40	0.008132

Table 4

Concurrent process number	Running time (second)	Concurrent process number	Running time (second)
				1	0.025429083	21	0.025429083
2	0.0261324	22	0.0261324
				3	0.027618333	23	0.027618333
4	0.026501875	24	0.026501875
				5	0.028920375	25	0.028920375
6	0.028323364	26	0.028323364
				7	0.0262508	27	0.0262508
8	0.025908143	28	0.025908143
				9	0.027811444	29	0.027811444
10	0.0259772	30	0.0259772
				11	0.025123	31	0.025123
12	0.0272584	32	0.0272584
				13	0.036839	33	0.036839
14	0.028983444	34	0.028983444
				15	0.0280598	35	0.0280598
16	0.038933	36	0.038933
				17	0.032823125	37	0.032823125
18	0.0415146	38	0.0415146
				19	0.034480833	39	0.034480833
20	0.0418955	40	0.0418955

Can find by analyzing above data, 383 node electrical networks can not play acceleration effect in the time that the factor table that walks abreast generates, although in the time that parallel processing process number increases, calculate and consuming timely decline to some extent, but still to decompose difference consuming time little with serial factor table.In the time that factor table that 1265 nodes are walked abreast generates, the acceleration effect that can play, computational speed slightly generates faster than serial factor table, but promotes not obvious to computational speed.Curve can significantly be seen from the graph, when parallel factor table is processed the electrical network of 6251 nodes, and speed-raising successful.From test effect, be not difficult to find, this paper method solves and has good acceleration effect large scale electric network trend update equation.

The parallel method for solving of large scale electric network trend update equation and the program based on OpenMP that propose herein realize, improve the utilization rate of computer CPU resource, in the time solving the trend update equation of large scale electric network, can promote computational speed, and, along with the increase of electrical network computing node number, the acceleration effect obtaining also will be better.The method can have good acceleration effect on many cpu servers, and along with increasing of concurrent process number, computational speed is also promoting, but when approaching maximum process that CPU can process and count along with concurrent process number, computational speed promotes and is tending towards saturated.Therefore,, in the time processing the trend update equation of different node scales, how according to server performance, it is a problem requiring study that choose reasonable Optimal Parallel process number is appointed.

In addition, also propose a kind of sparse matrix storage means based on C++ java standard library container vector and map herein, can complete efficiently the traversal of sparse matrix nonzero element and search, and injected first increase, make program more succinct efficient, promoted the solution efficiency of trend linear equation.。

Finally should be noted that: above embodiment is only in order to illustrate that technical scheme of the present invention is not intended to limit; those of ordinary skill in the field still can modify or be equal to replacement the specific embodiment of the present invention with reference to above-described embodiment; these do not depart from any amendment of spirit and scope of the invention or are equal to replacement, within the claim protection range of the present invention all awaiting the reply in application.

Claims (8)

1. the parallel method for solving of large scale electric network trend update equation, is characterized in that: said method comprising the steps of:

Step 1: sparse matrix storage;

Step 2: parallel Factorization generates factor table;

Step 3: former generation computing walks abreast;

Step 4: back substitution computing;

Step 5: trend interative computation.

2. the parallel method for solving of large scale electric network trend update equation according to claim 1, it is characterized in that: in described step 1, in the parallel solution procedure of electric network swim update equation of P-Q decomposition method, complete node admittance matrix, update equation coefficient matrix B ' and B ", and B ' and the B " storage of the factor table generating after Factorization; Update equation coefficient matrix B ' and B " are sparse matrix.

3. the parallel method for solving of large scale electric network trend update equation according to claim 2, is characterized in that: adopt the electric network swim update equation of P-Q decomposition method to be expressed as:

ΔP/U＝-B′UΔθ (1)

ΔQ/U＝-B″ΔU (2)

Wherein, Δ P is the meritorious correction vector of computing node, and Δ Q is the idle correction vector of computing node, and Δ θ is phase angle correction vector, Δ U is voltage increment vector, U is node voltage amplitude, and θ is node voltage phase angle, and P is that node injects active power, Q is that node injects reactive power, it is negative that sparse matrix B ' element is that corresponding branch road reactance inverse is got, and " element is corresponding node admittance matrix imaginary part to sparse matrix B, and i, j are node serial number.

4. the parallel method for solving of large scale electric network trend update equation according to claim 2, is characterized in that: described step 1 specifically comprises the following steps:

Step 1-1: utilize sequence container vector that C++ abstract data type java standard library provides and associated container map to realize the storage of the electric network swim update equation coefficient matrix of P-Q decomposition method;

Defining objects vector<map<int, double>>B1, B2, Y preserves respectively sparse matrix B ', B " and node admittance matrix; Wherein map<int, double> is used for preserving row element, and row number represent by the key index of int type, and sparse matrix nonzero element is represented by the relating value of double type;

Step 1-2: node optimization sequence;

Statistics node relative branch number, props up way by node and from less to more node is carried out to static ordering; And the order according to PQ node, PV node, balance node sorts successively; In sequence, form internal node and calculate the table of comparisons that bus is numbered;

Step 1-3: computing node admittance matrix;

According to node admittance matrix dimension initialization vector object Y dimension; Node i self-admittance is the summation that diagonal element element equals the direct-connected all branch road admittance of this node, and the transadmittance between node i, j equals the negative value of connected node i, the admittance of j branch road; The node admittance array element element having calculated is saved in object Y, completes the sparse matrix storage of node admittance matrix, and only preserve triangle on node admittance matrix;

Step 1-4: sparse matrix B ' and B " are saved in object B 1 and B2.

5. the parallel method for solving of large scale electric network trend update equation according to claim 1, is characterized in that: described step 2 comprises the following steps:

Step 2-1: specify parallel processing process number;

Step 2-2: first, by the traversal of sparse matrix nonzero element, add up every row element and be eliminated number of times, k row element is eliminated number of times and is kept at integer array variable count[k] in; At map<int, in double>>B, increase the first numerical digit of injection and put simultaneously, maximum is eliminated to number of times and is designated as max; Defined variable vector<int>muster and vector<vector<intGreatT.GreaT. GT>vec_muster (muster, max) are eliminated for collecting the row that number of times is identical; Vec_muster[m] in preserve that to be eliminated number of times be all line numbers of m time; Deposit the row that is eliminated 0 time in vec_master[0] in;

Step 2-3: according to concurrent process number by vec_muster[m] in line number be divided into N group, be eliminated number of times m=m+1;

Step 2-4: utilize compiling to instruct statement #pragma omp parallel for num_threads (N) that host process is divided into N line process, with multiple threads walk abreast normalization operations and cancellation computing, being eliminated row is eliminated number of times and subtracts 1, be count[k]-1, collection is eliminated number of times and becomes 0 line number, and is kept at vec_muster[m] in;

Step 2-5: judge vec_muster[m] whether array be empty, parallel Factorization finishes if it is empty; Otherwise return to step 2-3, continue parallel normalization operations and cancellation computing.

6. the parallel method for solving of large scale electric network trend update equation according to claim 1, is characterized in that: described step 3 comprises the following steps:

Step 3-1: can be calculated meritorious correction vector Δ P and idle correction vector Δ Q according to the meritorious residual equation of trend and the idle residual equation of trend;

The meritorious residual equation of trend and the idle residual equation of trend are expressed as:

$\mathrm{\&Delta;}{P}_i=P_i-U_i\underset{j=1}{\overset{j=n}{\mathrm{\&Sigma;}}}{U}_j(G_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}})---\left(3\right)$

$\mathrm{\&Delta;}{Q}_i=Q_i-U_i\underset{j=1}{\overset{j=n}{\mathrm{\&Sigma;}}}{U}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}})---\left(4\right)$

Wherein, Δ P _ifor the meritorious correction of node i, Δ Q _ifor the idle correction of node i; Δ θ is phase angle correction vector, and Δ U is voltage increment vector; U _iand U _jbe respectively node i and j voltage magnitude; θ _ijfor the phase difference of node i and j is θ _ij=θ _i-θ _j; P _ifor node i is injected active power, Q _ifor node i is injected reactive power; G _ijfor node admittance matrix real part, B _ijnode admittance matrix imaginary part;

Step 3-2: in work vector x, the process of appointment is counted N by independent vector z assignment;

Independent vector z represents constant term Δ P/U and the Δ Q/U of equation group (1), (2), and what work vector x represented equation group (1), (2) waits to ask a Δ θ and Δ U;

Step 3-3: initialization is eliminated number of times m=0;

Step 3-4: peek group vec_muster[m] in row, count N and be divided into N group if line number is greater than process, otherwise do not divide into groups, the former generation cancellation computing that walks abreast, is eliminated number of times m=m+1;

Step 3-5: former generation calculates and carries out successively to large size node from small size node, utilize triangle on factor table to participate in parallel former generation cancellation computing, if upper triangle i is capable, k column element is nonzero element, 0～(i-1) row has completed parallel former generation cancellation computing, x _k=x _k-b _ikx _i; The cancellation process of former generation is with to generate the cancellation process of factor table consistent, utilizes the former generation cancellation computing that walks abreast of row grouping information in vector<vector<intGreatT.GreaT. GT>vec_muster;

Step 3-6: be eliminated number of times m=m+1, judgement is eliminated number of times and whether equals maximum cancellation number of times, if equate, former generation cancellation computing finishes, and returns to step 3-4 proceed parallel former generation cancellation computing if be less than;

Step 3-7: former generation normalization operations;

I the element x of work vector x _i=x _i/ b _ii, former generation normalization operations instructs statement #pragma omp parallel for to complete the former generation normalization operations that for circulates with compiling, according to the maximum parallel processing Thread Count of CPU former generation normalization operations.

7. the parallel method for solving of large scale electric network trend update equation according to claim 1, it is characterized in that: in described step 4, back substitution computing is from large node number to trifle period, if i～(n-1) row has completed back substitution cancellation computing, the capable k that is designated as of i-1, the j column element that k is capable is nonzero element, x _k=x _k-b _kjx _j; By formula x _k=x _k-b _kjx _j, k is descending to be solved the element of work vector one by one, the final solution to equation group (1), (2).

8. the parallel method for solving of large scale electric network trend update equation according to claim 1, is characterized in that: described step 5 comprises the following steps:

Step 5-1: according to the phase angle correction vector Δ θ obtaining and voltage increment vector Δ U, node voltage amplitude U and node voltage phase angle theta are revised i.e. θ=θ+Δ θ, U=U+ Δ U;

Step 5-2: meritorious correction and the idle correction of calculating each node by formula (3), (4);

Step 5-3: if meritorious correction is less than meritorious convergence precision, and idle correction is less than idle convergence precision, calculated; Otherwise, return to step 3 and 4 and re-start parallel former generation computing and back substitution computing, and solve formula (1), (2).