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CN113675841A - Excitation mode analysis method and system based on minimum characteristic trajectory method - Google Patents

Excitation mode analysis method and system based on minimum characteristic trajectory method Download PDF

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Publication number
CN113675841A
CN113675841A CN202110838101.6A CN202110838101A CN113675841A CN 113675841 A CN113675841 A CN 113675841A CN 202110838101 A CN202110838101 A CN 202110838101A CN 113675841 A CN113675841 A CN 113675841A
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matrix
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pss
excitation mode
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CN113675841B (en
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黄伟
黄润
甘德强
张�杰
吴琛
张丹
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Yunnan Power Grid Co Ltd
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for AC mains or AC distribution networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for AC mains or AC distribution networks
    • H02J3/002—Flicker reduction, e.g. compensation of flicker introduced by non-linear load
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]

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  • Power Engineering (AREA)
  • Physics & Mathematics (AREA)
  • Nonlinear Science (AREA)
  • Control Of Eletrric Generators (AREA)
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Abstract

The invention relates to an excitation mode analysis method and system based on a minimum characteristic trajectory method, which are used for giving the oscillation frequency of an excitation mode of a power system and determining the critical gain of a power system stabilizer PSS (power system stabilizer) so as to maximize the performance parameters of the system and ensure that the system meets the requirement of stable operation, and belong to the technical field of power grid safety. The method comprises the following steps: selecting a rotor loop as a forward channel link to obtain a compact Heffron-Phillips model; giving a system excitation mode critical instability condition according to a minimum characteristic trajectory method; analyzing the diagonal dominance characteristic of the rotor loop open-loop transfer function matrix L; simplifying a critical instability equation of an excitation mode by using matrix properties; solving an excitation mode critical instability equation; and selecting the parameters of the controller according to the frequency domain stability margin.

Description

Excitation mode analysis method and system based on minimum characteristic trajectory method
Technical Field
The invention belongs to the technical field of power grid safety, relates to a method and a system for analyzing an excitation pattern of a power system, and particularly relates to a method and a system for analyzing an excitation pattern of a multi-input-multi-output system based on a minimum characteristic trajectory method.
Background
The power system stabilizer PSS can effectively suppress low-frequency oscillation of the system, has an indispensable effect on ensuring small interference stability of the system, and is widely applied to a power grid at present. The effect of PSS is closely related to its gain. The gain of the stabilizer is the direct current or static gain, which does not include the effect of the isolation element, and is defined as the ratio of the percentage of the voltage change of the generator to the percentage of the rotation speed or frequency change. Generally, the larger the PSS gain, the better the effect on low frequency oscillations. However, the gain of the PSS cannot be increased without limitation. Research shows that when a certain value is reached, the excitation voltage is unstable, namely the aforementioned excitation mode, and the gain value is the critical gain of the PSS. This requires us to maximize the PSS gain with satisfactory excitation system stability when timing the parameters of the PSS.
The PSS gain setting method adopted in engineering is as follows: the stabilizer is put into operation, the output and terminal voltage of the stabilizer are recorded simultaneously, the gain of the stabilizer is gradually and slowly increased until continuous excitation voltage oscillation is generated, the oscillation frequency is usually 1-3 Hz, the fast excitation system may be 4-8 Hz, the gain is recorded, and the generally optimal gain value is 1/3 of the value.
The method can only give a critical gain value according to experience in practical application, cannot generally lead the excitation voltage to have complete instability, and can only give a rough critical gain, and the critical gain solving method lacks theoretical support.
In general, an engineering practical method should have a strict mathematical basis, and a good excitation pattern analysis method can not only provide a mathematical background and a theoretical basis existing in an excitation pattern, but also accurately solve the excitation pattern frequency and the PSS critical gain of any system, thereby obtaining the answer to the above-mentioned problems.
The information disclosed in this background section is only for enhancement of understanding of the general background of the invention and should not be taken as an acknowledgement or any form of suggestion that this information forms the prior art already known to a person skilled in the art.
Disclosure of Invention
The invention aims to solve the defects of the prior art and provides an excitation mode analysis method and system based on a minimum characteristic trajectory method.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
the excitation pattern analysis method based on the minimum characteristic trajectory method comprises the following steps:
1) selecting a rotor loop as a forward channel link to obtain a compact Heffron-Phillips model;
2) giving a system excitation mode critical instability condition according to a minimum characteristic trajectory method;
3) analyzing the diagonal dominance characteristic of the rotor loop open-loop transfer function matrix L;
4) simplifying a critical instability equation of an excitation mode by using matrix properties;
5) solving an excitation mode critical instability equation;
6) and selecting the parameters of the controller according to the frequency domain stability margin.
Further, it is preferable that the specific method of step 1) is:
extracting a rotor loop in a Heffron-Phillips model, and enabling a rotor channel (sM + K)D)-1The other links are combined together to be used as a feedback channel to obtain a compact Heffron-Phillips model;
defined in the compact form of the Heffron-Phillips model described above:
GQ(s)＝GQ1(s)+GQ2(s), formula (1);
wherein G isQ1(s)＝-K2[(K3+sT′d0)+GEX(s)K6]-1(GEX(s)K5+K4) Formula (2):
Figure BDA0003177867610000021
in the formula, matrix K2、K3、K4、K5、K6Is a linearized model coefficient matrix; diagonal matrix T'd0The transient time constant of the d axis of each generator is contained; the diagonal matrix M contains a generator rotor motion inertia constant; diagonal matrix KDThe damping coefficient of the rotor motion is contained; diagonal matrix GEXIs an excitation system transfer function matrix; diagonal matrix HPSS(s) is the PSS transfer function matrix; omega0For system synchronous speed, s is the generalized frequency.
Further, preferably, the step 2) of providing a system excitation mode critical instability condition according to a minimum feature trajectory method specifically includes:
vis (sM + K)D)-1And (3) transmitting a matrix for a forward channel, and taking other links as feedback channels to obtain a return difference matrix I + L of the closed-loop system:
Figure BDA0003177867610000022
wherein, the matrix K1Is a linearized model coefficient matrix; diagonal matrix GMIs a governor-prime mover system transfer function matrix;
when the system is in critical instability, the frequency response curve of the return difference matrix determinant firstly passes through a (-1, 0) point, and the concrete expression corresponding to the characteristic track is that the minimum characteristic track of the system just passes through the (-1, 0) point;
therefore, critical instability is satisfied
λmin(I + L) ═ 0, formula (5);
wherein λmin(I + L) tableThe minimum eigenvalue of the difference matrix I + L is shown back.
Further, preferably, the analyzing the diagonal dominance characteristic of the rotor loop open-loop transfer function matrix l(s) in step 3) specifically includes:
ignoring G in the L(s) expressionQ1(s) and GM(s) two terms related, the approximate expression of L(s) when combining equation (4) is as follows:
Figure BDA0003177867610000031
according to formula (2) wherein GQ2And(s) analyzing to obtain the diagonal dominance characteristic of the rotor loop open-loop transfer function matrix L(s).
Further, preferably, the simplifying the excitation mode critical instability equation by using the matrix property in the step 4) specifically includes:
according toTheorem of Geer's circleFrom L(s)Diagonal elementTo approximate the eigenvalues of L(s), equation (5) is equivalent to
1+Lii0, formula (7);
wherein L isiiRepresents the minimum modulo diagonal of L(s), L assuming the gain of the i-th PSS is studiediiNecessarily corresponding to the smallest modulo diagonal of L(s);
substituting s ═ j ω into the expression of L, and writing equation (5) in elemental form
Figure BDA0003177867610000032
Where ω denotes the angular frequency, MiIs the ith of the diagonal matrix MAnDiagonal element, KD，iIs a diagonal matrix KDI th of (1)AnDiagonal element, K1，iiIs K1The (i, i) th of the matrixAnElement gQ2，iiIs GQ2(j ω) th (i, i) of the matrixAnAn element;
then L is represented by the elements of each matrixiiThe value of (c):
Figure BDA0003177867610000033
thus, the formula (7) is further written as
Figure BDA0003177867610000041
According to GQ2Diagonal dominant property of (j ω) matrix, g in equation (9)Q2，iiIs expressed as
Figure BDA0003177867610000042
Wherein K2，iiIs K2The (i, i) th of the matrixAnElement, K6，iiIs K6The (i, i) th of the matrixAnElement gEX，iIs GEXIth of (j ω) matrixAnDiagonal element, hPSS，iIs HPSSIth of (j ω) matrixAnDiagonal element, T'd0，iIs T'd0Ith of matrixAnA diagonal element;
the belt-in type (10) is
Figure BDA0003177867610000043
Equation (12) is the simplified excitation mode critical instability equation.
Further, preferably, the step 5) of solving the excitation pattern critical instability equation specifically includes:
extracting the gain K of the PSS link, i.e. setting
hPSS，i＝KhPSS0，iFormula (13);
wherein h isPSS0，iRepresents a transfer function when the gain of the PSS is 1;
the left side of the equal sign of the formula (12) is a complex function f (omega, K), that is
Figure BDA0003177867610000044
The complex function f (ω, K) contains two variables ω and K,respectively orderThe real and imaginary parts of f (ω, K) are equal to 0 to obtain a system of equations:
Figure BDA0003177867610000045
wherein, Re represents a real part, Im represents an imaginary part;
solving the equation (15) can obtain the critical instability frequency ω of the excitation mode and the critical gain K of the PSS.
Further, preferably, the step 6) selects the controller parameter according to the frequency domain stability margin, specifically:
according to the critical gain K obtained in the step 5), 1/3 times of K is taken as the final gain of the power system stabilizer PSS.
The invention also provides an excitation pattern analysis system based on the minimum characteristic trajectory method, which comprises the following steps:
the model construction module is used for selecting a rotor loop as a forward channel link to obtain a compact Heffron-Phillips model;
the excitation mode critical instability condition calculation module is used for providing a system excitation mode critical instability condition according to a minimum characteristic trajectory method;
the diagonal dominance characteristic analysis module is used for analyzing the diagonal dominance characteristic of the rotor loop open-loop transfer function matrix L;
the critical instability equation simplification module is used for simplifying the critical instability equation of the excitation mode by utilizing matrix properties;
the first calculation module is used for solving an excitation mode critical instability equation;
and the controller parameter selection module is used for selecting the controller parameters according to the frequency domain stability margin.
The invention also provides an electronic device, which comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, and is characterized in that the processor implements the steps of the excitation pattern analysis method based on the minimum characteristic locus method when executing the program.
The present invention additionally provides a non-transitory computer-readable storage medium having stored thereon a computer program which, when executed by a processor, implements the steps of the excitation pattern analysis method based on the minimum feature trajectory method as described above.
The method provided by the invention adopts a forward channel function of the rotor loop, simplifies the function according to the property of the diagonal dominance of the matrix, can provide an excitation mode instability equation based on a minimum characteristic trajectory method, can obtain the excitation mode instability frequency and the critical gain of the power system stabilizer PSS by solving the equation, is a powerful tool for analyzing the excitation mode instability of the system, and is never applied to the analysis of the excitation mode stability problem.
Compared with the prior art, the invention has the beneficial effects that:
the method provided by the invention can obtain the resolved excitation mode critical instability equation and realize simple analysis of the excitation mode. Solving the excitation mode critical instability equation provided by the invention can obtain the instability frequency of the excitation mode and the critical gain of the power system stabilizer PSS, thereby providing guidance for parameter setting of the controller and converting the electromechanical transient small interference stability problem of a multi-input-multi-output system into a simple and feasible bivariate function analysis problem. Compared with the existing method for determining the PSS critical gain by observing the excitation voltage oscillation by raising the gain, the method provided by the invention is safer, simpler in analysis and more rigorous in theoretical basis.
Drawings
FIG. 1 is a flow chart of an excitation pattern analysis method based on a minimum feature trajectory method according to the present invention;
FIG. 2 is a Heffron-Phillips model of a conventional small interference stability analysis provided by the present invention;
FIG. 3 is a compact form of the transformed Heffron-Phillips model provided by the present invention;
FIG. 4 is a schematic structural diagram of an excitation pattern analysis system based on a minimum feature trajectory method according to the present invention;
fig. 5 is a schematic structural diagram of an electronic device according to the present invention.
Detailed Description
The present invention will be described in further detail with reference to examples.
It will be appreciated by those skilled in the art that the following examples are illustrative of the invention only and should not be taken as limiting the scope of the invention. The examples do not specify particular techniques or conditions, and are performed according to the techniques or conditions described in the literature in the art or according to the product specifications. The materials or equipment used are not indicated by manufacturers, and all are conventional products available by purchase.
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the following embodiments and accompanying drawings. The exemplary embodiments and descriptions of the present invention are provided to explain the present invention, but not to limit the present invention.
An excitation pattern analysis method based on a minimum characteristic trajectory method comprises the following steps:
1) selecting a rotor loop as a forward channel link to obtain a compact Heffron-Phillips model;
2) giving a system excitation mode critical instability condition according to a minimum characteristic trajectory method;
3) analyzing the diagonal dominance characteristic of the rotor loop open-loop transfer function matrix L;
4) simplifying a critical instability equation of an excitation mode by using matrix properties;
5) solving an excitation mode critical instability equation;
6) and selecting the parameters of the controller according to the frequency domain stability margin.
Selecting a rotor loop as a forward channel link in the step 1) to obtain a compact Heffron-Phillips model;
as shown in FIG. 2, the column vector in the conventional Heffron-Phillips modelΔPmOutputting mechanical power for the prime mover; column vector Δ Pe1And Δ Pe2Electromagnetic power of unit eΔPA component of (a); column vector dΔPIs the system power disturbance; column vectorΔωThe rotating speed of each generator; column vectorΔδThe angular displacement of each generator rotor relative to a synchronous reference shaft, namely a power angle; column vectorΔ qE′Is one by oneGenerator quadrature axis transientElectromotive force; column vector fdΔE′For the automatic voltage regulator output voltage: column vector PSSΔuOutputting the signal for the PSS; omega0Synchronizing the rotation speed of the system; the diagonal matrix M contains a generator rotor motion inertia constant; diagonal matrix KDThe damping coefficient of the rotor motion is contained; diagonal matrix T'd0The transient time constant of the d axis of each generator is contained; matrix K1、K2、K3、K4、K5、K6The method is a linear model coefficient matrix, and reflects network structure, element parameters, operation conditions and load characteristics; diagonal matrix GM(s) is a governor-prime mover system transfer function matrix; diagonal matrix GEX(s) is an excitation system transfer function matrix; diagonal matrix HPSS(s) is the PSS transfer function matrix; s is a generalized frequency.
Extracting the rotor loop, passing the rotor channel (sM + K)D)-1The other links are combined together to be used as a feedback channel, and a more compact Heffron-Phillips model is obtained as shown in figure 3.
Defined in the compact model
GQ1(s)＝-K2[(K3+sT′d0)+GEX(s)K6]-1(GEX(s)K5+K4) Formula (1);
Figure BDA0003177867610000071
GQ(s)＝GQ1(s)+GQ2(s), formula (3);
the step 2) of providing the critical instability condition of the system excitation mode according to the minimum characteristic trajectory method specifically comprises the following steps:
vis (sM + K)D)-1For forward channel transferThe matrix and other links are feedback channels to obtain a return difference matrix I + L of the closed-loop system
Figure BDA0003177867610000072
Wherein, the matrix K1Is a linearized model coefficient matrix; diagonal matrix GMIs a governor-prime mover system transfer function matrix;
when the system is in critical instability, the frequency response curve of the return difference matrix determinant firstly passes through the (-1, 0) point, and the concrete expression corresponding to the characteristic track is that the minimum characteristic track of the system just passes through the (-1, 0) point.
Therefore, critical instability is satisfied
λmin(I + L) ═ 0, formula (5);
wherein λmin(I + L) represents the minimum eigenvalue of the return difference matrix I + L.
Analyzing the diagonal dominance characteristic of the rotor loop open-loop transfer function matrix L(s) in the step 3), specifically:
the calculation experience shows that G is in the high frequency range (1-10Hz)Q1(s) and GMThe value of(s) is small, and G in the expression of L(s) can be ignoredQ1(s) and GM(s) two related terms. Binding equation (4) the approximate expression for L(s) at this time is as follows:
Figure BDA0003177867610000073
according to formula (2) wherein GQ2Expression of(s), combined with computational experience we found:
①K2is/are as followsDiagonal elementAre usually large and exhibit some diagonal dominance; ② T'd0And GEX(s) are all diagonal matrices, and K3And K6The elements are very small, so [ K ]3+sT′d0+GEX(s)K6]-1The method has the obvious diagonal dominance characteristic, and the non-diagonal element is almost 0; ③ GEX(s) and HPSS(s) is a pairAngular array, given by the aboveO2(s) have a pronounced diagonal predominance.
(sM+KD)-1Is a diagonal matrix, and GQ2(s) exhibits a relatively pronounced diagonal predominance, with elements in the first column being significantly larger than the remaining units, K1The matrix value is not large, so K1+GQ2(s) is also presentDiagonal element and the firstOne column of elements is a large property. Thus (sM + K)D)-1And K1+GQ2The result of the multiplication(s) also exhibits a relatively pronounced diagonal dominance and the elements of the first column are significantly larger than the remaining units. So that l(s) diagonal dominance can be demonstrated.
The simplification of the excitation mode critical instability equation by using the matrix property in the step 4) is specifically as follows:
in step 3), it has been demonstrated that L(s) has obvious diagonal dominance property, and according to the Gehr's circle theorem, the characteristic value of L(s) can be approximated by the diagonal elements of L(s), so that the formula (5) is equivalent to
1+Lii0, formula (7);
wherein L isiiThe minimum modulo diagonal of L(s) is expressed, assuming we are studying the gain of the i-th PSSiiNecessarily corresponding to the smallest modulo diagonal of l(s).
Substituting s ═ j ω into the expression of L, and writing equation (5) in elemental form
Figure BDA0003177867610000081
Where ω denotes the angular frequency, MiIs the ith of the diagonal matrix MAnDiagonal element, KD，iIs a diagonal matrix KDI th of (1)AnDiagonal element, K1，iiIs K1The (i, i) th of the matrixAnElement gQ2，iiIs GQ2(j ω) th (i, i) of the matrixAnAnd (4) elements.
Then we can represent L by the elements of each matrixiiThe value of (c):
Figure BDA0003177867610000082
thus, the formula (7) can be further written as
Figure BDA0003177867610000083
According to GQ2Diagonal dominant property of (j ω) matrix, g in equation (9)Q2，iiIs expressed as
Figure BDA0003177867610000091
Wherein K2，iiIs K2The (i, i) th of the matrixAnElement, K6，iiIs K6The (i, i) th of the matrixAnElement gEX，iIs GEXIth of (j ω) matrixAnDiagonal element, hPSS，iIs HPSSIth of (j ω) matrixAnDiagonal element, T'd0，iIs T'd0Ith of matrixAnAnd (4) a diagonal element.
The belt-in type (10) is
Figure BDA0003177867610000092
Equation (12) is the simplified excitation mode critical instability equation.
The step 5) of solving the excitation mode critical instability equation specifically comprises the following steps:
extracting the gain K of the PSS link, i.e. setting
hPSS，i＝KhPSS0，iFormula (13);
wherein h isPSS0，iRepresents a transfer function when the gain of the PSS is 1.
The left side of the equal sign of the formula (12) is a complex function f (omega, K), that is
Figure BDA0003177867610000093
The complex function f (ω, K) contains two variables ω and K,respectively makeThe real and imaginary parts of f (ω, K) are equal to 0 to obtain a system of equations:
Figure BDA0003177867610000094
where Re represents the real part and Im represents the imaginary part.
Solving the equation (15) can obtain the critical instability frequency ω of the excitation mode and the critical gain K of the PSS.
The step 6) of selecting the controller parameters according to the frequency domain stability margin specifically comprises the following steps:
according to the critical gain K obtained in the step 5), 1/3 times of K is taken as the final gain of the power system stabilizer PSS.
As shown in fig. 4, the excitation pattern analysis system based on the minimum feature trajectory method includes:
the model construction module 101 is used for selecting a rotor loop as a forward channel link to obtain a compact Heffron-Phillips model;
the excitation mode critical instability condition calculation module 102 is used for providing a system excitation mode critical instability condition according to a minimum feature trajectory method;
the diagonal dominance characteristic analysis module 103 is used for analyzing the diagonal dominance characteristic of the rotor loop open-loop transfer function matrix L;
a critical instability equation simplification module 104 for simplifying the excitation mode critical instability equation by using the matrix property;
the first calculation module 105 is used for solving an excitation mode critical instability equation;
and a controller parameter selecting module 106, configured to select a controller parameter according to the frequency domain stability margin.
In the embodiment of the invention, the model construction module 101 selects a rotor loop as a forward channel link to obtain a compact Heffron-Phillips model; the excitation mode critical instability condition calculation module 102 provides a system excitation mode critical instability condition according to a minimum feature trajectory method; the diagonal dominance characteristic analysis module 103 analyzes the diagonal dominance characteristic of the rotor loop open-loop transfer function matrix L; the critical instability equation simplification module 104 utilizes matrix properties to simplify excitation mode critical instability equations; the first calculation module 105 solves an excitation mode critical instability equation; the controller parameter selection module 106 selects a controller parameter according to the frequency domain stability margin.
According to the excitation mode analysis system based on the minimum characteristic trajectory method, the instability frequency of the excitation mode and the critical gain of the power system stabilizer PSS can be obtained, and therefore guidance is provided for parameter setting of the controller.
The system provided by the embodiment of the present invention is used for executing the above method embodiments, and for details of the process and the details, reference is made to the above embodiments, which are not described herein again.
Fig. 5 is a schematic structural diagram of an electronic device according to an embodiment of the present invention, and referring to fig. 5, the electronic device may include: a processor (processor)201, a communication Interface (communication Interface)202, a memory (memory)203 and a communication bus 204, wherein the processor 201, the communication Interface 202 and the memory 203 complete communication with each other through the communication bus 204. The processor 201 may call logic instructions in the memory 203 to perform the following method: selecting a rotor loop as a forward channel link to obtain a compact Heffron-Phillips model; giving a system excitation mode critical instability condition according to a minimum characteristic trajectory method; analyzing the diagonal dominance characteristic of the rotor loop open-loop transfer function matrix L; simplifying a critical instability equation of an excitation mode by using matrix properties; solving an excitation mode critical instability equation; and selecting the parameters of the controller according to the frequency domain stability margin.
In addition, the logic instructions in the memory 203 may be implemented in the form of software functional units and stored in a computer readable storage medium when the logic instructions are sold or used as independent products. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
In another aspect, an embodiment of the present invention further provides a non-transitory computer-readable storage medium, on which a computer program is stored, where the computer program is implemented to, when executed by a processor, perform the excitation pattern analysis method based on the minimum feature trajectory method provided in the foregoing embodiments, for example, including: selecting a rotor loop as a forward channel link to obtain a compact Heffron-Phillips model; giving a system excitation mode critical instability condition according to a minimum characteristic trajectory method; analyzing the diagonal dominance characteristic of the rotor loop open-loop transfer function matrix L; simplifying a critical instability equation of an excitation mode by using matrix properties; solving an excitation mode critical instability equation; and selecting the parameters of the controller according to the frequency domain stability margin.
The above-described embodiments of the apparatus are merely illustrative, and the units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment. One of ordinary skill in the art can understand and implement it without inventive effort.
Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware. With this understanding in mind, the above-described technical solutions may be embodied in the form of a software product, which can be stored in a computer-readable storage medium such as ROM/RAM, magnetic disk, optical disk, etc., and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the methods described in the embodiments or some parts of the embodiments.
Examples of the applications
In an application example of the present invention, a method for analyzing electromechanical transient small interference stability of a multiple-input multiple-output system based on a minimum feature trajectory method is provided, as shown in fig. 1, the method includes:
step 101: selecting a rotor loop as a forward channel link to obtain a compact Heffron-Phillips model;
step 102: giving a system excitation mode critical instability condition according to a minimum characteristic trajectory method;
step 103: analyzing the diagonal dominance characteristic of the rotor loop open-loop transfer function matrix L;
step 104: simplifying a critical instability equation of an excitation mode by using matrix properties;
step 105: solving an excitation mode critical instability equation;
step 106: selecting controller parameters according to the frequency domain stability margin;
in specific implementation, in a Heffron-Phillips model of a conventional small interference stability analysis as shown in FIG. 2, a rotor loop (sM + K) is selectedD)-1As a forward path transfer matrix, to a compact form as shown in fig. 3.
In specific implementation, a system excitation mode critical instability condition is given according to a minimum characteristic trajectory method:
vis (sM + K)D)-1A forward channel transfer matrix is adopted, and the other links are feedback channels, so that a return difference matrix I + L of the closed-loop system is obtained
Figure BDA0003177867610000121
According to the nature of the matrix eigenvalues:
λ(I+L)＝I+λ(L)
following the convention of single input-single output (SISO) system stability analysis, we take the feature trajectory λminThe distance of (I + L) from the origin is taken as the stability margin. Therefore, critical instability is satisfied
λmin(I+L)＝0
In specific implementation, the diagonal dominance characteristic of the rotor loop open-loop transfer function matrix L is analyzed:
the calculation experience shows that G is in the high frequency range (1-10Hz)Q1(s) and GMThe value of(s) is small, and G in the expression of L(s) can be ignoredQ1(s) and GM(s) two related terms. Binding equation (4) the approximate expression for L(s) at this time is as follows:
Figure BDA0003177867610000122
according to formula (2) wherein GQ2Expression of(s), combined with computational experience we found:
①K2is/are as followsDiagonal elementAre usually large and exhibit some diagonal dominance; ② T'd0And GEX(s) are all diagonal matrices, and K3And K6The elements are very small, so [ K ]3+sT′d0+GEX(s)K6]-1Exhibit a pronounced diagonal predominance characteristic, notDiagonal element Almost all of which areIs 0; ③ GEX(s) and HPSS(s) is a diagonal matrix, given in summary GQ2(s) have a pronounced diagonal predominance.
(sM+KD)-1Is a diagonal matrix, and GQ2(s) exhibits a relatively pronounced diagonal predominance, with elements in the first column being significantly larger than the remaining units, K1The matrix value is not large, so K1+GQ2(s) is also presentDiagonal element and the firstOne column of elements is a large property. Thus (sM + K)D)-1And K1+GQ2The result of the multiplication(s) also exhibits a relatively pronounced diagonal dominance and the elements of the first column are significantly larger than the remaining units. Thus, L(s) can be provedThe diagonal is dominant.
In specific implementation, a matrix property is used for simplifying an excitation mode critical instability equation:
according to the Geller's theorem, the characteristic value of L(s) can be approximated by the diagonal elements of L(s), so equation (5) is equivalent to
1+Lii＝0；
Wherein L isiiThe minimum modulo diagonal of L(s) is expressed, assuming we are studying the gain of the i-th PSSiiNecessarily corresponding to the smallest modulo diagonal of l(s).
Substituting s ═ j ω into the expression of L, and writing equation (5) in elemental form
Figure BDA0003177867610000131
Where ω denotes the angular frequency, MiIs the ith of the diagonal matrix MAnDiagonal element, KD，iIs a diagonal matrix KDI th of (1)AnDiagonal element, K1，iiIs K1The (i, i) th of the matrixAnElement gQ2，iiIs GQ2(j ω) th (i, i) of the matrixAnAnd (4) elements.
Then we can represent L by the elements of each matrixiiThe value of (c):
Figure BDA0003177867610000132
thus, the formula (7) can be further written as
Figure BDA0003177867610000133
According to GQ2Diagonal dominant property of (j ω) matrix, g in equation (9)Q2，iiIs expressed as
Figure BDA0003177867610000134
The belt-in type (10) is
Figure BDA0003177867610000135
The above equation is the simplified excitation mode critical instability equation.
In specific implementation, solving an excitation mode critical instability equation:
extracting the gain K of the PSS link, i.e. setting
hPSS，i＝KhPSS0，i；
Wherein h isPSS0，iRepresents a transfer function when the gain of the PSS is 1.
The left side of the equal sign of the formula (12) is a complex function f (omega, K), that is
Figure BDA0003177867610000141
The complex function f (ω, K) contains two variables ω and K,respectively orderThe real and imaginary parts of f (ω, K) are equal to 0 to obtain a system of equations:
Figure BDA0003177867610000142
where Re represents the real part and Im represents the imaginary part.
In specific implementation, the controller parameters are selected according to the frequency domain stability margin:
solving an equation to obtain a critical gain K, and taking 1/3 times of K as the final gain of the power system stabilizer PSS.
Therefore, the excitation mode stability problem of the multi-input and multi-output system can be completely analyzed.
For example, the method is used in a system of IEEE 162 nodes (also referred to as IEEE 17 machine system) to set the gain of a PSS installed in a unit number 1 therein.
Known parameters of a system of IEEE 162 nodes include: linearized model coefficient matrix K1～K6And a diagonal matrix T 'containing d-axis transient time constants of the generators'd0Diagonal matrix M containing generator rotor motion inertia constant and diagonal matrix K containing rotor motion damping coefficientDExcitation system transfer function matrix GEXPSS transfer function matrix HPSSAnd(s) the excitation pattern is carried into an equation (12), the real part and the imaginary part are respectively made equal to 0 to obtain a binary equation set equation (15), the frequency of the excitation pattern is 3.7Hz by solving, and the critical gain of the installed PSS is 24.5.
According to the calculation result, the PSS gain of the first unit is set to be 8.17, so that the system can be found out that the low-frequency oscillation is restrained and the stability of the excitation voltage is guaranteed.
As can be seen from the above examples, the analysis method obtained by the present invention analyzes the excitation pattern stability of the mimo system well.
It will be apparent to those skilled in the art that the modules or steps of the embodiments of the invention described above may be implemented by a general purpose computing device, they may be centralized on a single computing device or distributed across a network of multiple computing devices, and alternatively, they may be implemented by program code executable by a computing device, such that they may be stored in a storage device and executed by a computing device, and in some cases, the steps shown or described may be performed in an order different than that described herein, or they may be separately fabricated into individual integrated circuit modules, or multiple ones of them may be fabricated into a single integrated circuit module. Thus, embodiments of the invention are not limited to any specific combination of hardware and software.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and various modifications and changes may be made to the embodiment of the present invention by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (10)

1. The excitation pattern analysis method based on the minimum characteristic trajectory method is characterized by comprising the following steps of:
1) selecting a rotor loop as a forward channel link to obtain a compact Heffron-Phillips model;
2) giving a system excitation mode critical instability condition according to a minimum characteristic trajectory method;
3) analyzing the diagonal dominance characteristic of the rotor loop open-loop transfer function matrix L;
4) simplifying a critical instability equation of an excitation mode by using matrix properties;
5) solving an excitation mode critical instability equation;
6) and selecting the parameters of the controller according to the frequency domain stability margin.
2. The excitation pattern analysis method based on the minimum feature trajectory method according to claim 1, wherein the specific method in step 1) is as follows:
extracting a rotor loop in a Heffron-Phillips model, and enabling a rotor channel (sM + K)D)-1The other links are combined together to be used as a feedback channel to obtain a compact Heffron-Phillips model;
defined in the compact form of the Heffron-Phillips model described above:
GQ(s)＝GQ1(s)+GQ2(s), formula (1);
wherein G isQ1(s)＝-K2[(K3+sT′d0)+GEX(s)K6]-1(GEX(s)K5+K4) Formula (2);
Figure FDA0003177867600000011
in the formula, matrix K2、K3、K4、K5、K6Is a linearized model coefficient matrix; diagonal matrix T'd0The transient time constant of the d axis of each generator is contained; the diagonal matrix M contains a generator rotor motion inertia constant; diagonal matrix KDThe damping coefficient of the rotor motion is contained;diagonal matrix GEXIs an excitation system transfer function matrix; diagonal matrix HPSS(s) is the PSS transfer function matrix; omega0For system synchronous speed, s is the generalized frequency.
3. The excitation pattern analysis method based on the minimum feature trajectory method according to claim 2, wherein the step 2) of providing a critical instability condition of the system excitation pattern according to the minimum feature trajectory method specifically comprises:
vis (sM + K)D)-1And (3) transmitting a matrix for a forward channel, and taking other links as feedback channels to obtain a return difference matrix I + L of the closed-loop system:
Figure FDA0003177867600000012
wherein, the matrix K1Is a linearized model coefficient matrix; diagonal matrix GMIs a governor-prime mover system transfer function matrix;
when the system is in critical instability, the frequency response curve of the return difference matrix determinant firstly passes through a (-1, 0) point, and the concrete expression corresponding to the characteristic track is that the minimum characteristic track of the system just passes through the (-1, 0) point;
therefore, critical instability is satisfied
λmin(I + L) ═ 0, formula (5);
wherein λmin(I + L) represents the minimum eigenvalue of the return difference matrix I + L.
4. The excitation pattern analysis method based on the minimum feature trajectory method according to claim 3, wherein the analysis of the diagonal dominance characteristic of the rotor loop open-loop transfer function matrix L(s) in step 3) specifically comprises:
ignoring G in the L(s) expressionQ1(s) and GM(s) two terms related, the approximate expression of L(s) when combining equation (4) is as follows:
Figure FDA0003177867600000021
according to formula (2) wherein GQ2And(s) analyzing to obtain the diagonal dominance characteristic of the rotor loop open-loop transfer function matrix L(s).
5. The excitation pattern analysis method based on the minimum feature trajectory method according to claim 4, wherein the simplification of the excitation pattern critical instability equation by using the matrix property in the step 4) is specifically as follows:
approximating the eigenvalues of L(s) by the diagonal elements of L(s) according to the Gehr's theorem, equation (5) being equivalent to
1+Lii0, formula (7);
wherein L isiiRepresents the minimum modulo diagonal of L(s), L assuming the gain of the i-th PSS is studiediiNecessarily corresponding to the smallest modulo diagonal of L(s);
substituting s ═ j ω into the expression of L, and writing equation (5) in elemental form
Figure FDA0003177867600000022
Where ω denotes the angular frequency, MiIs the ith diagonal element, K, of the diagonal matrix MD，iIs a diagonal matrix KDThe ith diagonal element of (1)1，iiIs K1The (i, i) th element, g, of the matrixQ2，iiIs GQ2The (i, i) th element of the (j ω) matrix;
then L is represented by the elements of each matrixiiThe value of (c):
Figure FDA0003177867600000031
thus, the formula (7) is further written as
Figure FDA0003177867600000032
Limit according to GQ2Diagonal dominant property of (j ω) matrix, g in equation (9)Q2，iiIs expressed as
Figure FDA0003177867600000033
Wherein K2，iiIs K2The (i, i) th element, K, of the matrix6，iiIs K6The (i, i) th element, g, of the matrixEX，iIs GEXThe ith diagonal element, h, of the (j ω) matrixPSS，iIs HPSSThe ith diagonal element, T 'of the (j ω) matrix'd0，iIs T'd0The ith diagonal element of the matrix;
the belt-in type (10) is
Figure FDA0003177867600000034
Equation (12) is the simplified excitation mode critical instability equation.
6. The excitation pattern analysis method based on the minimum feature trajectory method according to claim 5, wherein the step 5) of solving an excitation pattern critical instability equation specifically comprises:
extracting the gain K of the PSS link, i.e. setting
hPSS，i＝KhPSS0，iFormula (13);
wherein h isPSS0，iRepresents a transfer function when the gain of the PSS is 1;
the left side of the equal sign of the formula (12) is a complex function f (omega, K), that is
Figure FDA0003177867600000035
The complex function f (ω, K) contains two variables ω and K,respectively order f(ω，K)The real part and the imaginary part of (A) are equal to 0, so that a binary equation system can be obtained:
Figure FDA0003177867600000036
wherein, Re represents a real part, Im represents an imaginary part;
solving the equation (15) can obtain the critical instability frequency ω of the excitation mode and the critical gain K of the PSS.
7. The excitation pattern analysis method based on the minimum feature trajectory method according to claim 6, wherein the step 6) selects the controller parameters according to the frequency domain stability margin, and specifically comprises the following steps:
according to the critical gain K obtained in the step 5), 1/3 times of K is taken as the final gain of the power system stabilizer PSS.
8. Excitation pattern analysis system based on minimum characteristic trajectory method, its characterized in that includes:
the model construction module (101) is used for selecting a rotor loop as a forward channel link to obtain a compact Heffron-Phillips model;
the excitation mode critical instability condition calculation module (102) is used for providing a system excitation mode critical instability condition according to a minimum characteristic trajectory method;
a diagonal dominance characteristic analysis module (103) for analyzing the diagonal dominance characteristics of the rotor loop open-loop transfer function matrix L;
a critical instability equation simplification module (104) for simplifying the excitation mode critical instability equation by using matrix properties;
a first calculation module (105) for solving an excitation mode critical instability equation;
and the controller parameter selection module (106) is used for selecting the controller parameters according to the frequency domain stability margin.
9. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the steps of the excitation pattern analysis method based on the minimum feature trajectory method according to any one of claims 1 to 7 when executing the program.
10. A non-transitory computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, implements the steps of the excitation pattern analysis method based on the minimum feature trajectory method according to any one of claims 1 to 7.
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