CN104699898B - Simulating method for electric power system based on compression and piecemeal frequency dependent network equivalence - Google Patents

Simulating method for electric power system based on compression and piecemeal frequency dependent network equivalence Download PDF

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CN104699898B
CN104699898B CN201510097332.0A CN201510097332A CN104699898B CN 104699898 B CN104699898 B CN 104699898B CN 201510097332 A CN201510097332 A CN 201510097332A CN 104699898 B CN104699898 B CN 104699898B
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吴文传
张伯明
孙宏斌
胡中
胡一中
郭庆来
王彬
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Tsinghua University
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Abstract

The present invention relates to a kind of simulating method for electric power system based on compression and piecemeal frequency dependent network equivalence, belong to dispatching automation of electric power systems and grid simulation technical field.This method by compressing the redundancy handled in the mathematical modeling for removing frequency dependent network equivalence, to reduce overall amount of calculation, recycles piecemeal to handle frequency dependent network equivalence, builds up some sub-blocks to realize parallel computation first.The inventive method can effectively solve the problem that frequency dependent network equivalence is applied to caused single frequency network of relation equivalence module amount of calculation problems of too during electromagnetic transient in power system emulation.The inventive method, electric system simulation speed, engineering practice good results can be dramatically speeded up.

Description

Simulating method for electric power system based on compression and piecemeal frequency dependent network equivalence
Technical field
The present invention relates to a kind of simulating method for electric power system based on compression and piecemeal frequency dependent network equivalence, belong to electricity Force system dispatching automation and grid simulation technical field.
Background technology
Electric system simulation is one of important method for studying electrical power system transient characteristic.According to the dynamic process of investigation Difference, electric system simulation can be divided into electromagnetic transient simulation, electromechanical transient simulation and long term dynamics emulation.Wherein electromagnetism is temporary State simulation accuracy highest, it is mainly used in studying the transient process of power system network element Microsecond grade, such as thunder and lighting process, wave process With direct-current commutation failure process etc..But high accuracy is using intensive as cost, because amount of calculation is too big, electro-magnetic transient is imitated Really be not suitable for being directly used in the emulation of large-scale electrical power system.Generally for whole big system, retain and be concerned about that part (refers to wishing Hope in detail understand transient process part) network element, other parts network element is represented with Equivalent Network, then carries out electricity Magnetic emulates, and reaches the purpose for reducing amount of calculation.
Traditional Equivalent Network uses promise Equivalent Model to represent, as shown in Figure 1.Right side square frame is care subnetwork; Left side square frame is using the Equivalent Network of promise Equivalent Model, i.e., with a promise equal currents IabcWith the equivalent section of a promise Point admittance matrix YabcTo represent the Equivalent Network of other parts network element.
Bus admittance matrix in promise equivalent circuit is formed under fundamental frequency, therefore can only represent network element fundamental frequency Characteristic.In order to relatively accurately represent the frequency characteristic of network element at respective frequencies, pull-in frequency network of relation equivalence (FDNE, Frequency Dependent Network Equivalent) represents network of other parts network element etc. Value.
Equivalent Network method based on FDNE, as shown in Figure 2.Right side square frame is care subnetwork;Left side square frame is base In FDNE Equivalent Network, i.e., with a promise equal currents IabcIt is used as the Equivalent Network of other parts with a FDNE.
FDNE essence is a bus admittance matrix using frequency as function.N × N-dimensional FDNE mathematical modeling is:
Wherein, s=j2 π f, f are frequencies, and j is imaginary unit, similarly hereinafter;
Either element in FDNE is expressed as a frequency-domain function:
Wherein, limit { aiAnd residual { ciOr it is real number, and or respectively with complex conjugate to occurring, constant term d and once Item h is real number, and n is limit number.
In engineering in use, typically taking first order h=0, and one group of common limit of FDNE each element {ai, then N × N-dimensional FDNE matrix Y (s) can be expressed as:
Above formula is written as to the form of transmission function:
Y (s)=C (sE-A)-1B+D,
Wherein, E is unit matrix, and its dimension is identical with matrix A,
A=diag (A1 … Ak … An),
Ak=diag ((ak ak … ak)(1×N)),
B=diag (B1 … Bk … Bn),
Bk=diag ((1 1 ... 1)(1×N)),
C=[R1 … Rk … Rn],
Fig. 3 is the matrix in block form schematic diagram of FDNE mathematic(al) representations.(not including D)
Above-mentioned FDNE mathematical modeling may apply in electromagnetic transient in power system simulated program.In each of emulation Time step, the amount of calculation O that a FDNE module needs is (being weighed with floating number multiplication number)
O=2nN2+N2+2nN。
Compared to other power system component modules, the amount of calculation of a FDNE module is very big, is briefly described as follows. The limit number that n in above formula is FDNE, in engineer applied, to ensure simulation accuracy, usual value is 50~100;Above formula In N be FDNE dimension because being triphase flow, thus N values be 3,6,9,12 etc..So in actual use, one The amount of calculation of FDNE modules can reach 104The order of magnitude, and conventional power system component module amount of calculation is general all 103Quantity Level is following.
Direct FDNE described above is applied in electromagnetic transient in power system emulation, and single FDNE modules can be caused to calculate Measure excessive, influence overall simulation efficiency.And currently without the solution for this problem.
The content of the invention
The purpose of the present invention is to propose to a kind of electric system simulation side based on compression and piecemeal frequency dependent network equivalence Method, first by compressing the redundancy in the mathematical modeling for removing frequency dependent network equivalence, to reduce overall amount of calculation, then profit Frequency dependent network equivalence is built up into some sub-blocks to realize parallel computation with piecemeal.
Simulating method for electric power system proposed by the present invention based on frequency dependent network equivalence, comprises the following steps:
(1) the mathematical modeling Y (s) for the frequency dependent network equivalence of electric system simulation is:
Wherein, N is Y (s) dimension, and s=j2 π f, f are networks, and j is imaginary unit, { aiIt is limit, { ciIt is to stay Number, d is constant term, and n is limit number;
(2) mathematical modeling of the frequency dependent network equivalence of above-mentioned steps (1) is compressed, detailed process is:
Above-mentioned Y (s) is rewritten as formula form by (2-1):
Y (s)=C (sE-A)-1B+D,
Wherein, A=diag (A1 … Ak … An), Ak=diag ((ak ak … ak)(1×N)),
B=diag (B1 … Bk … Bn), Bk=diag ((1 1 ... 1)(1×N)),
C=[R1 … Rk … Rn],
E is unit matrix, and E dimension is identical with matrix A;
(2-2) solves above-mentioned C=[R1 … Rk … Rn] in each submatrix block order, process is:
To RkSingular value decomposition is carried out, makes Rk=U Σ VT,
Wherein, Σ=diag (σ12,…,σN),σ1≥σ2≥…≥σN>=0, σ1, σ2..., σNFor RkIt is N number of unusual Value, U=(u1,u2,...,uN) and V=(v1,v2,...,vN)TRespectively RkThe unusual phasor in left and right,
A judgment threshold λ is set, matrix R is determined using judgment threshold λkOrder, i.e., be incremented by parameter r since 1, until Following formula is set up:
Then trip current RkOrder be r;
(2-3) is to matrix RkIt is compressed, detailed process is:To matrix RkOrder r judged, if r meets following bar Part,Then make the R in Matrix Ck, A in matrix AkWith the B in matrix BkBoil down to R' respectivelyk、A'kAnd B'k
R'k=(u1,u2,...,ur),
A'k=diag ((ak ak … ak)(1×r)),
B'k=(v1,v2,...,vr)T
If r meets following condition,The then R in Matrix Ck, A in matrix AkWith the B in matrix BkKeep not Become;
All submatrix block R in (2-4) Ergodic Matrices Ck, repeat the above steps (2-2) and (2-3), realizes frequency phase Close the compression of Equivalent Network mathematical modeling;
(3) piecemeal is carried out to the mathematical modeling of the frequency dependent network equivalence of above-mentioned steps (1), detailed process is:
The equivalent mathematical modeling Y (s) of said frequencies network of relation is divided into some as follows:
(4) by the frequency dependent network equivalence after above-mentioned steps (2) compress processing and the processing of above-mentioned steps (3) piecemeal Mathematical modeling for electric system simulation calculate.
Simulating method for electric power system proposed by the present invention based on frequency dependent network equivalence, its advantage It is that the inventive method can effectively solve the problem that frequency dependent network equivalence is applied to caused list during electromagnetic transient in power system emulation Individual frequency dependent network equivalence module amount of calculation problems of too, the compression process in the inventive method, reduces frequency phase The amount of calculation of Equivalent Network mathematical modeling is closed, piecemeal processing procedure therein, frequency dependent network equivalence mathematical modeling is divided into Some pieces of progress parallel computations, so as to finally dramatically speed up electric system simulation speed, engineering practice good results.
Brief description of the drawings
Fig. 1 is the existing Equivalent Network method schematic diagram using promise Equivalent Model.
Fig. 2 is the existing Equivalent Network method schematic diagram based on frequency dependent network equivalence.
Fig. 3 is the schematic diagram for the frequency dependent network equivalence mathematical modeling being related in the inventive method.
Fig. 4 is the mathematical modeling schematic diagram of the frequency dependent network equivalence after the compression processing in the inventive method.
Fig. 5 is the piecemeal schematic diagram of frequency dependent network equivalence in the inventive method.
Embodiment
Simulating method for electric power system proposed by the present invention based on frequency dependent network equivalence, comprises the following steps:
(1) the mathematical modeling Y (s) for the frequency dependent network equivalence of electric system simulation is
Wherein, N is Y (s) dimension, and s=j2 π f, f are networks, and j is imaginary unit, { aiIt is limit, { ciIt is to stay Number, d is constant term, and n is limit number;The limit of Y (s) all elements is identical, and residual is different with constant term.
(2) mathematical modeling of the frequency dependent network equivalence of above-mentioned steps (1) is compressed, detailed process is:
Above-mentioned Y (s) is rewritten as formula form by (2-1):
Y (s)=C (sE-A)-1B+D,
Wherein, A=diag (A1 … Ak … An), Ak=diag ((ak ak … ak)(1×N)),
B=diag (B1 … Bk … Bn), Bk=diag ((1 1 ... 1)(1×N)),
C=[R1 … Rk … Rn],
E is unit matrix, and E dimension is identical with matrix A;As shown in Figure 3.
(2-2) solves above-mentioned C=[R1 … Rk … Rn] in each submatrix block order, process is:
To RkSingular value decomposition is carried out, makes Rk=U Σ VT,
Wherein, Σ=diag (σ12,…,σN),σ1≥σ2≥…≥σN>=0, σ1, σ2..., σNFor RkIt is N number of unusual Value, U=(u1,u2,...,uN) and V=(v1,v2,...,vN)TRespectively RkThe unusual phasor in left and right,
A judgment threshold λ is set, threshold value λ is usually chosen to 0.9999, can be adjusted according to the required accuracy.Using sentencing Disconnected threshold value λ determines matrix RkOrder, i.e., be incremented by parameter r since 1, until following formula is set up:
Then trip current RkOrder be r;
(2-3) is to matrix RkIt is compressed, detailed process is:To matrix RkOrder r judged, if r meets following bar Part,Then make the R in Matrix Ck, A in matrix AkWith the B in matrix BkBoil down to R' respectivelyk、A'kAnd B'k
R'k=(u1,u2,...,ur),
A'k=diag ((ak ak … ak)(1×r)),
B'k=(v1,v2,...,vr)T
Frequency dependent network equivalence mathematical modeling after compression is as shown in figure 4, to RkCompression, it is possible to reduce amount of calculation is OReduce=2N2+ 2N-4rN, and almost there is no loss of accuracy;
If r meets following condition,The then R in Matrix Ck, A in matrix AkWith the B in matrix BkKeep not Become;
All submatrix block R in (2-4) Ergodic Matrices Ck, repeat the above steps (2-2) and (2-3), realizes frequency phase Close the compression of Equivalent Network mathematical modeling;
(3) piecemeal is carried out to the mathematical modeling of the frequency dependent network equivalence of above-mentioned steps (1), detailed process is:
The equivalent mathematical modeling Y (s) of said frequencies network of relation is divided into some as follows:
Because the physical meaning of of frequency dependent network equivalence itself is admittance, the addition of admittance mathematically is equivalent to physics On parallel connection, therefore according to above formula, frequency dependent network equivalence can be created as multiple parts in parallel, be illustrated in figure 5 this hair Bright one embodiment, frequency dependent network equivalence be divide into two parts, the computationally intensive of each part is approximately originally The half of frequency dependent network equivalence module, can be according to required determinant number of modules during practical application.
(4) by the frequency dependent network equivalence after above-mentioned steps (2) compress processing and the processing of above-mentioned steps (3) piecemeal Mathematical modeling for electric system simulation calculate.

Claims (1)

1. a kind of simulating method for electric power system based on frequency dependent network equivalence, it is characterised in that this method includes following step Suddenly:
(1) the mathematical modeling Y (s) for the frequency dependent network equivalence of electric system simulation is:
Wherein, N is Y (s) dimension, and s=j2 π f, f are networks, and j is imaginary unit, { aiIt is limit, { ciIt is residual, d For constant term, n is limit number;
(2) mathematical modeling of the frequency dependent network equivalence of above-mentioned steps (1) is compressed, detailed process is:
Above-mentioned Y (s) is rewritten as formula form by (2-1):
Y (s)=C (sE-A)-1B+D,
Wherein, A=diag (A1 … Ak … An), Ak=diag ((ak ak … ak)(1×N)),
B=diag (B1 … Bk … Bn), Bk=diag ((1 1 ... 1)(1×N)),
E is unit matrix, and E dimension is identical with matrix A;
(2-2) solves above-mentioned C=[R1 … Rk … Rn] in each submatrix block order, process is:
To RkSingular value decomposition is carried out, makes Rk=U Σ VT,
Wherein, ∑=diag (σ12,…,σN),σ1≥σ2≥…≥σN>=0, σ1, σ2..., σNFor RkN number of singular value, U= (u1,u2,...,uN) and V=(v1,v2,...,vN)TRespectively RkLeft and right singular vector,
A judgment threshold λ is set, matrix R is determined using judgment threshold λkOrder, i.e., be incremented by parameter r since 1, until following formula Set up:
<mrow> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <msup> <msub> <mi>&amp;sigma;</mi> <mn>1</mn> </msub> <mn>2</mn> </msup> <mo>+</mo> <msup> <msub> <mi>&amp;sigma;</mi> <mn>2</mn> </msub> <mn>2</mn> </msup> <mo>+</mo> <mn>...</mn> <mo>+</mo> <msup> <msub> <mi>&amp;sigma;</mi> <mrow> <mi>r</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mn>2</mn> </msup> </mrow> <mrow> <msup> <msub> <mi>&amp;sigma;</mi> <mn>1</mn> </msub> <mn>2</mn> </msup> <mo>+</mo> <msup> <msub> <mi>&amp;sigma;</mi> <mn>2</mn> </msub> <mn>2</mn> </msup> <mo>+</mo> <mn>...</mn> <mo>+</mo> <msup> <msub> <mi>&amp;sigma;</mi> <mi>N</mi> </msub> <mn>2</mn> </msup> </mrow> </mfrac> <mo>)</mo> </mrow> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mo>&lt;</mo> <mi>&amp;lambda;</mi> <mo>&lt;</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <msup> <msub> <mi>&amp;sigma;</mi> <mn>1</mn> </msub> <mn>2</mn> </msup> <mo>+</mo> <msup> <msub> <mi>&amp;sigma;</mi> <mn>2</mn> </msub> <mn>2</mn> </msup> <mo>+</mo> <mn>...</mn> <mo>+</mo> <msup> <msub> <mi>&amp;sigma;</mi> <mi>r</mi> </msub> <mn>2</mn> </msup> </mrow> <mrow> <msup> <msub> <mi>&amp;sigma;</mi> <mn>1</mn> </msub> <mn>2</mn> </msup> <mo>+</mo> <msup> <msub> <mi>&amp;sigma;</mi> <mn>2</mn> </msub> <mn>2</mn> </msup> <mo>+</mo> <mn>...</mn> <mo>+</mo> <msup> <msub> <mi>&amp;sigma;</mi> <mi>N</mi> </msub> <mn>2</mn> </msup> </mrow> </mfrac> <mo>)</mo> </mrow> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mo>,</mo> </mrow>
Then trip current RkOrder be r;
(2-3) is to matrix RkIt is compressed, detailed process is:To matrix RkOrder r judged, if r meets following condition,Then make the R in Matrix Ck, A in matrix AkWith the B in matrix BkBoil down to R' respectivelyk、A'kAnd B'k
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>R</mi> <mi>k</mi> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>u</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>u</mi> <mn>2</mn> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>u</mi> <mi>r</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>A</mi> <mi>k</mi> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <mi>d</mi> <mi>i</mi> <mi>a</mi> <mi>g</mi> <mrow> <mo>(</mo> <msub> <mfenced open = "(" close = ")"> <mtable> <mtr> <mtd> <msub> <mi>a</mi> <mi>k</mi> </msub> </mtd> <mtd> <msub> <mi>a</mi> <mi>k</mi> </msub> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <msub> <mi>a</mi> <mi>k</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mrow> <mo>(</mo> <mn>1</mn> <mo>&amp;times;</mo> <mi>r</mi> <mo>)</mo> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>B</mi> <mi>k</mi> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>v</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>v</mi> <mn>2</mn> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>v</mi> <mi>r</mi> </msub> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mo>;</mo> </mrow> </mtd> </mtr> </mtable> </mfenced>
If r meets following condition,The then R in Matrix Ck, A in matrix AkWith the B in matrix BkKeep constant;
All submatrix block R in (2-4) Ergodic Matrices Ck, repeat the above steps (2-2) and (2-3), realizes port with frequency-dependent network The compression of equivalent mathematical modeling;
(3) piecemeal is carried out to the mathematical modeling of the frequency dependent network equivalence of above-mentioned steps (1), detailed process is:
The equivalent mathematical modeling Y (s) of said frequencies network of relation is divided into some as follows:
<mrow> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mfrac> <msub> <mi>c</mi> <mi>i</mi> </msub> <mrow> <mi>s</mi> <mo>-</mo> <msub> <mi>a</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>+</mo> <mi>d</mi> <mo>=</mo> <mrow> <mo>(</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>m</mi> <mn>1</mn> </mrow> </munderover> <mfrac> <msub> <mi>c</mi> <mi>i</mi> </msub> <mrow> <mi>s</mi> <mo>-</mo> <msub> <mi>a</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>+</mo> <mi>d</mi> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mi>m</mi> <mn>1</mn> <mo>+</mo> <mn>1</mn> </mrow> <mrow> <mi>m</mi> <mn>2</mn> </mrow> </munderover> <mfrac> <msub> <mi>c</mi> <mi>i</mi> </msub> <mrow> <mi>s</mi> <mo>-</mo> <msub> <mi>a</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>+</mo> <mn>...</mn> <mo>+</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mi>m</mi> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mfrac> <msub> <mi>c</mi> <mi>i</mi> </msub> <mrow> <mi>s</mi> <mo>-</mo> <msub> <mi>a</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>,</mo> </mrow>
(4) by the number of the frequency dependent network equivalence after above-mentioned steps (2) compress processing and the processing of above-mentioned steps (3) piecemeal Model is learned to calculate for electric system simulation.
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