CN113675841B - Excitation mode analysis method and system based on minimum feature trajectory method - Google Patents
Excitation mode analysis method and system based on minimum feature trajectory method Download PDFInfo
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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
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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
- H02J3/002—Flicker reduction, e.g. compensation of flicker introduced by non-linear load
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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
- 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
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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
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
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Abstract
The invention relates to an excitation mode analysis method and system based on a minimum characteristic track method, which are used for giving the oscillation frequency of an excitation mode of a power system, determining the critical gain of a stabilizer PSS of the power system, maximizing the performance parameters of the system and ensuring that the system meets the stable operation requirement, 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; providing critical instability conditions of a system excitation mode according to a minimum characteristic track method; analyzing the diagonal dominant characteristic of a rotor loop open-loop transfer function matrix L; simplifying an excitation mode critical instability equation by utilizing matrix properties; solving an excitation mode critical instability equation; and selecting the controller parameters according to the frequency domain stability margin.
Description
Technical Field
The invention belongs to the technical field of power grid safety, relates to a method and a system for analyzing an excitation mode of an electric power system, and particularly relates to a method and a system for analyzing an excitation mode of a multi-input-multi-output system based on a minimum characteristic track method.
Background
The power system stabilizer PSS can effectively suppress the system low-frequency oscillation, has an indispensable effect in ensuring the stability of the system with small interference, and has been widely used in the power grid at present. The effect of PSS is closely related to its gain. The gain of a stabilizer refers to a direct current or static gain, which excludes the effect of an isolation link, and is defined as the ratio of the percent change in generator voltage to the percent change in rotational speed or frequency. Generally, the larger the PSS gain, the better the effect on low frequency oscillations. However, the gain of PSS cannot be increased without limitation. Research shows that when the voltage reaches a certain value, the excitation voltage is unstable, namely the excitation mode, and the gain value is the critical gain of the PSS. This requires us to maximize the PSS gain while satisfying the excitation system stability when the parameters of the PSS are set.
The PSS gain setting method adopted in engineering is as follows: the stabilizer is put into operation while the output and terminal voltage of the stabilizer are recorded, and the stabilizer gain is gradually and slowly increased until a continuous excitation voltage oscillation is generated, typically at a frequency of 1-3 Hz, and the fast excitation system may record the gain at 4-8 Hz, with a generally optimum gain value of about 1/3 of this value.
The method can only give a critical gain value according to experience in practical application, and generally cannot lead the excitation voltage to be completely unstable, 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 foundation and a good excitation pattern analysis method, so that not only can the mathematical background and theoretical basis of the existence of an excitation pattern be given, but also the excitation pattern frequency and PSS critical gain of any system can be accurately solved, thereby obtaining the answer of the problem.
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 of ordinary skill 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 track method.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
the excitation mode analysis method based on the minimum characteristic track method comprises the following steps:
1) Selecting a rotor loop as a forward channel link to obtain a compact Heffron-Phillips model;
2) Providing critical instability conditions of a system excitation mode according to a minimum characteristic track method;
3) Analyzing the diagonal dominant characteristic of a rotor loop open-loop transfer function matrix L;
4) Simplifying an excitation mode critical instability equation by utilizing matrix properties;
5) Solving an excitation mode critical instability equation;
6) And selecting the controller parameters according to the frequency domain stability margin.
Further, it is preferable that the specific method of step 1) is:
rotor circuit is extracted in the Heffron-Phillips model, and rotor channels (sM+K D ) -1 The method is characterized in that the method is regarded as a forward channel, and other links are combined together to be regarded as a feedback channel, so that a Heffron-Phillips model in a compact form is obtained;
defined in the above compact form of the Heffron-Phillips model:
G Q (s)＝G Q1 (s)+G Q2 (s) formula (1);
wherein G is Q1 (s)＝-K 2 [(K 3 +sT′ d0 )+G EX (s)K 6 ] -1 (G EX (s)K 5 +K 4 ) Formula (2):
in the matrix K 2 、K 3 、K 4 、K 5 、K 6 Is a linear model coefficient matrix; diagonal matrix T' d0 The transient time constant of the d axis of each generator is contained; the diagonal matrix M contains the generator rotor motion inertia constant; diagonal matrix K D The rotor motion damping coefficient is contained; diagonal matrix G EX A transfer function matrix of the excitation system; diagonal matrix H PSS (s) is a PSS transfer function matrix; omega 0 For system synchronous speed s is the generalized frequency.
Further, it is preferable that the critical destabilization condition of the excitation mode of the system is given according to the minimum feature trajectory method in the step 2), specifically:
view (sM+K) D ) -1 For the forward channel transfer matrix, the rest links are feedback channels, so that a return difference matrix I+L of the closed-loop system is obtained:
wherein matrix K 1 Is a linear model coefficient matrix; diagonal matrix G M A transfer function matrix for a speed regulator-prime motor system;
when the system is critically unstable, the frequency response curve of the return difference matrix determinant passes through (-1, 0) points for the first time, and the specific expression on the characteristic track is that the minimum characteristic track of the system exactly passes through (-1, 0) points;
therefore, when critical instability is caused, the method satisfies
λ min (i+l) =0, formula (5);
wherein lambda is min (I+L) represents the minimum eigenvalue of the return difference matrix I+L.
Further, it is preferable that the analyzing the diagonal dominant characteristic of the rotor loop open loop transfer function matrix L(s) in the step 3) specifically includes:
ignoring G in the L(s) expression Q1 (s) and G M (s) related terms, the approximate expression of L(s) at this time in combination with formula (4) is as follows:
according to formula (2) G Q2 The expression of(s) is analyzed to obtain the diagonal occupation of the rotor loop open-loop transfer function matrix L(s)Excellent characteristics.
Further, it is preferable that the matrix property in the step 4) is used to simplify the excitation mode critical destabilization equation, specifically:
according toGalois theorem of circleBy L(s)Diagonal elementTo approximate the eigenvalue of L(s), equation (5) is equivalent to
1+L ii =0, formula (7);
wherein L is ii Representing the minimum modulus diagonal of L(s), L is assumed to be the gain of the i-th PSS under investigation ii Necessarily corresponds to the smallest modular diagonal element of L(s);
bringing s=jω into the expression of L, writing formula (5) as element form
Wherein ω represents angular frequency, M i Ith as diagonal matrix MPersonal (S)Diagonal element, K D，i For diagonal matrix K D Is the ith of (2)Personal (S)Diagonal element, K 1，ii For K 1 Matrix (i, i)Personal (S)Element g Q2，ii Is G Q2 (j omega) th matrix (i, i)Personal (S)An element;
then the elements of each matrix are used to represent L ii Is the value of (1):
thus formula (7) is further written as
According to G Q2 Diagonal dominance of (jω) matrix, g in equation (9) Q2，ii The expression of (2) is
Wherein K is 2，ii For K 2 Matrix (i, i)Personal (S)Elements, K 6，ii For K 6 Matrix (i, i)Personal (S)Element g EX，i Is G EX Ith matrix of (jω)Personal (S)Diagonal element, h PSS，i Is H PSS Ith matrix of (jω)Personal (S)Diagonal element, T' d0，i Is T' d0 Ith of matrixPersonal (S)Diagonal members;
is carried into (10) and has
Equation (12) is the simplified excitation mode critical instability equation.
Further, preferably, the step 5) solves an excitation mode critical destabilization equation, specifically:
extracting gain K of PSS link, namely setting
h PSS，i ＝Kh PSS0，i Formula (13);
wherein h is PSS0，i Representing the transfer function when the gain of the PSS is 1;
the left side of the sign of (12) is the complex function f (omega, K), i.e
The complex function f (ω, K) comprises two variables ω and K,respectively orderThe real part and the imaginary part of f (omega, K) are equal to 0, so that a binary equation set can be obtained:
wherein Re represents a real part and Im represents an imaginary part;
the solution (15) can obtain the critical instability frequency omega of the excitation mode and the critical gain K of the PSS.
Further, preferably, the step 6) selects the controller parameters according to the frequency domain stability margin, specifically:
taking 1/3 times K as the final gain of the power system stabilizer PSS according to the critical gain K obtained in the step 5).
The invention also provides an excitation pattern analysis system based on the minimum characteristic track 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 Heffron-Phillips model in a compact form;
the excitation mode critical instability condition calculation module is used for giving out the critical instability condition of the system excitation mode according to the minimum characteristic track method;
the diagonal dominant characteristic analysis module is used for analyzing the diagonal dominant characteristic of the rotor loop open-loop transfer function matrix L;
the critical destabilization equation simplifying module is used for simplifying the critical destabilization 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 comprising a memory, a processor and a computer program stored on the memory and running on the processor, characterized in that the processor implements the steps of the excitation pattern analysis method based on the minimum feature trajectory method as described above when executing the program.
The present invention further 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 rotor loop forward channel function, simplifies according to the characteristic of the dominant angle of the matrix, can give an excitation mode instability equation based on a minimum characteristic track method, solves the equation to obtain excitation mode instability frequency and critical gain of a power system stabilizer PSS, is a powerful tool for analyzing the excitation mode instability of the system, and is not applied to analysis for solving the problem of the excitation mode stability.
Compared with the prior art, the invention has the beneficial effects that:
the method provided by the invention can obtain the analyzed excitation mode critical instability equation, and realizes the simple analysis of the excitation mode. The critical instability equation of the excitation mode provided by the invention can be solved to obtain the instability frequency of the excitation mode and the critical gain of the power system stabilizer PSS, so that guidance is provided for parameter setting of a controller, and the problem of small transient interference stability of the multi-input-multi-output system electromechanical transient can be converted into a simple and feasible double-variable function analysis problem. Compared with the existing method for determining the PSS critical gain by observing the excitation voltage oscillation through the elevation gain, the method provided by the invention is safer, the analysis is simpler, and the theoretical basis is more strict.
Drawings
FIG. 1 is a flow chart of an excitation pattern analysis method based on a minimum feature trajectory method of 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 version 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 of 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 present invention and should not be construed as limiting the scope of the invention. The specific techniques or conditions are not identified in the examples and are performed according to techniques or conditions described in the literature in this field or according to the product specifications. The materials or equipment used are conventional products available from commercial sources, not identified to the manufacturer.
The present invention will be described in further detail with reference to the following embodiments and the accompanying drawings, in order to make the objects, technical solutions and advantages of the present invention more apparent. The exemplary embodiments of the present invention and the descriptions thereof are used herein to explain the present invention, but are not intended to limit the invention.
An excitation pattern analysis method based on a minimum feature trajectory method comprises the following steps:
1) Selecting a rotor loop as a forward channel link to obtain a compact Heffron-Phillips model;
2) Providing critical instability conditions of a system excitation mode according to a minimum characteristic track method;
3) Analyzing the diagonal dominant characteristic of a rotor loop open-loop transfer function matrix L;
4) Simplifying an excitation mode critical instability equation by utilizing matrix properties;
5) Solving an excitation mode critical instability equation;
6) And selecting the controller parameters according to the frequency domain stability margin.
The rotor loop in the step 1) is selected as a forward channel link to obtain a compact Heffron-Phillips model;
as shown in FIG. 2, column vectors in the conventional Heffron-Phillips modelΔPmOutputting mechanical power for the prime mover; column vector Δp e1 And DeltaP e2 For the electromagnetic power of the unit e ΔPComponents of (2); column vector d ΔPIs a system power disturbance; column vectorΔωThe rotational speed of each generator; column vectorΔδAngular displacement, i.e., the power angle, of each generator rotor relative to a synchronous reference shaft; column vectorΔ q E′For each ofCross axis transient state of generatorAn electromotive force; column vector fd ΔE′Output voltage for the automatic voltage regulator: column vector PSS ΔuOutputting a signal for the PSS; omega 0 Synchronizing the rotation speed for the system; the diagonal matrix M contains the generator rotor motion inertia constant; diagonal matrix K D The rotor motion damping coefficient is contained; diagonal matrix T' d0 The transient time constant of the d axis of each generator is contained; matrix K 1 、K 2 、K 3 、K 4 、K 5 、K 6 For linearizing modelsThe coefficient matrix reflects the network structure, element parameters, operation conditions and load characteristics; diagonal matrix G M (s) is a governor-prime mover system transfer function matrix; diagonal matrix G EX (s) is an excitation system transfer function matrix; diagonal matrix H PSS (s) is a PSS transfer function matrix; s is the generalized frequency.
Extracting the rotor circuit, and connecting the rotor channels (sM+K) D ) -1 The remaining links are combined together as a feedback path, which is considered as a forward path, resulting in a more compact Heffron-Phillips model as shown in fig. 3.
Definition in the compact model
G Q1 (s)＝-K 2 [(K 3 +sT′ d0 )+G EX (s)K 6 ] -1 (G EX (s)K 5 +K 4 ) Formula (1);
G Q (s)＝G Q1 (s)+G Q2 (s) formula (3);
the critical destabilization condition of the system excitation mode is given according to the minimum characteristic track method in the step 2), and specifically comprises the following steps:
view (sM+K) D ) -1 The feedback matrix I+L of the closed loop system is obtained by using the forward channel transmission matrix and the feedback channels as the rest links
Wherein matrix K 1 Is a linear model coefficient matrix; diagonal matrix G M A transfer function matrix for a speed regulator-prime motor system;
when the system is critically unstable, the frequency response curve of the return difference matrix determinant passes through the (-1, 0) point for the first time, and the characteristic trace corresponding to the characteristic trace is embodied as the minimum characteristic trace of the system passes through the (-1, 0) point exactly.
Therefore, when critical instability is caused, the method satisfies
λ min (i+l) =0, formula (5);
wherein lambda is min (I+L) represents the minimum eigenvalue of the return difference matrix I+L.
The diagonal dominant characteristic of the open loop transfer function matrix L(s) of the analysis rotor circuit in the step 3) is specifically:
the calculation experience shows that in the high frequency band (1-10 Hz), G Q1 (s) and G M The value of(s) is small and G in the expression of L(s) can be ignored Q1 (s) and G M (s) two related terms. The approximate expression of L(s) at this time in combination with formula (4) is as follows:
according to formula (2) G Q2 The expression of(s), in combination with computational experience, we find:
①K 2 a kind of electronic deviceDiagonal elementIs usually large and exhibits certain diagonal dominant characteristics; (2) t'. d0 And G EX (s) are diagonal matrices, and K 3 And K 6 The elements are very small, and therefore [ K ] 3 +sT′ d0 +G EX (s)K 6 ] -1 The characteristic of obvious diagonal dominance is presented, and the non-diagonal element is almost 0; (3) g EX (s) and H PSS (s) is a diagonal array, and the above-mentioned known G is synthesized O2 (s) has a pronounced diagonal dominance characteristic.
(sM+K D ) -1 Is a diagonal matrix, and G Q2 (s) exhibit relatively pronounced diagonal dominance characteristics, the elements of the first column being significantly larger than the remaining units, K 1 The matrix value is not large, therefore K 1 +G Q2 (s) also presentDiagonal element and the firstA large array of elements. Thus (sM+K) D ) -1 And K is equal to 1 +G Q2 The result of the multiplication(s) also exhibits a relatively pronounced diagonal dominance characteristic, and the elements of the first column are significantly larger than the remaining units. So that it can be demonstrated that L(s) is diagonally dominant.
The critical instability equation of the excitation mode is simplified by utilizing matrix properties in the step 4), specifically:
in step 3) it has been shown that L(s) has a pronounced diagonal dominance, and that the eigenvalues of L(s) can be approximated by diagonal elements of L(s) according to the Gell's circle theorem, so that formula (5) is equivalent to
1+L ii =0, formula (7);
wherein L is ii Representing the minimum modulus diagonal of L(s), let us study the gain of the i-th PSS, L ii Necessarily corresponds to the smallest modular diagonal element of L(s).
Bringing s=jω into the expression of L, writing formula (5) as element form
Wherein ω represents angular frequency, M i Ith as diagonal matrix MPersonal (S)Diagonal element, K D，i For diagonal matrix K D Is the ith of (2)Personal (S)Diagonal element, K 1，ii For K 1 Matrix (i, i)Personal (S)Element g Q2，ii Is G Q2 (j omega) th matrix (i, i)Personal (S)An element.
We can represent L by the elements of each matrix ii Is the value of (1):
thus formula (7) can be further written as
According to G Q2 Diagonal dominance of (jω) matrix, g in equation (9) Q2，ii The expression of (2) is
Wherein K is 2，ii For K 2 Matrix (i, i)Personal (S)Elements, K 6，ii For K 6 Matrix (i, i)Personal (S)Element g EX，i Is G EX Ith matrix of (jω)Personal (S)Diagonal element, h PSS，i Is H PSS Ith matrix of (jω)Personal (S)Diagonal element, T' d0，i Is T' d0 Ith of matrixPersonal (S)Diagonal elements.
Is carried into (10) and has
Equation (12) is the simplified excitation mode critical instability equation.
The step 5) solves the critical instability equation of the excitation mode, and is specifically as follows:
extracting gain K of PSS link, namely setting
h PSS，i ＝Kh PSS0，i Formula (13);
wherein h is PSS0，i The transfer function at a gain of 1 for PSS is shown.
The left side of the sign of (12) is the complex function f (omega, K), i.e
The complex function f (ω, K) comprises two variables ω and K,respectively, orderThe real part and the imaginary part of f (omega, K) are equal to 0, so that a binary equation set can be obtained:
where Re represents the real part and Im represents the imaginary part.
The solution (15) can obtain the critical instability frequency omega of the excitation mode and the critical gain K of the PSS.
And 6) selecting controller parameters according to the frequency domain stability margin, wherein the controller parameters specifically comprise:
taking 1/3 times K as the final gain of the power system stabilizer PSS according to the critical gain K obtained in the step 5).
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 Heffron-Phillips model in a compact form;
the excitation mode critical instability condition calculation module 102 is used for giving out a system excitation mode critical instability condition according to a minimum characteristic track method;
the diagonal dominant characteristic analysis module 103 is used for analyzing the diagonal dominant characteristic of the rotor loop open-loop transfer function matrix L;
the critical destabilization equation simplifying module 104 is configured to simplify the excitation mode critical destabilization equation by using matrix properties;
a first calculation module 105, configured to solve an excitation mode critical instability equation;
the controller parameter selection module 106 is 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 Heffron-Phillips model in a compact form; the excitation mode critical instability condition calculation module 102 gives the system excitation mode critical instability condition according to the minimum characteristic track method; the diagonal dominant characteristic analysis module 103 analyzes the diagonal dominant characteristic of the rotor loop open-loop transfer function matrix L; the critical destabilization equation simplification module 104 utilizes the matrix property to simplify the excitation mode critical destabilization equation; the first calculation module 105 solves the excitation pattern critical instability equation; the controller parameter selection module 106 selects the controller parameters according to the frequency domain stability margin.
The excitation pattern analysis system based on the minimum characteristic track method provided by the embodiment of the invention can obtain the destabilization frequency of the excitation pattern and the critical gain of the power system stabilizer PSS, thereby providing guidance for parameter setting of a controller.
The system provided in the embodiment of the present invention is used for executing the above method embodiments, and specific flow and details refer to the above embodiments, which are not repeated herein.
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: processor (processor) 201, communication interface (Communications Interface) 202, memory (memory) 203, and communication bus 204, wherein processor 201, communication interface 202, memory 203 accomplish communication with each other through 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; providing critical instability conditions of a system excitation mode according to a minimum characteristic track method; analyzing the diagonal dominant characteristic of a rotor loop open-loop transfer function matrix L; simplifying an excitation mode critical instability equation by utilizing matrix properties; solving an excitation mode critical instability equation; and selecting the controller parameters according to the frequency domain stability margin.
Further, the logic instructions in the memory 203 may be implemented in the form of software functional units and may be stored in a computer readable storage medium when sold or used as a stand alone product. Based on this understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art or in a part of the technical solution, in the form of a software product stored in a storage medium, comprising several instructions for causing a computer device (which may be a personal computer, a server, a network device, etc.) to perform 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, random Access Memory), a magnetic disk, or an optical disk, or 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 having stored thereon a computer program that is implemented when executed by a processor to perform the excitation pattern analysis method based on the minimum feature trajectory method provided in the above embodiments, for example, including: selecting a rotor loop as a forward channel link to obtain a compact Heffron-Phillips model; providing critical instability conditions of a system excitation mode according to a minimum characteristic track method; analyzing the diagonal dominant characteristic of a rotor loop open-loop transfer function matrix L; simplifying an excitation mode critical instability equation by utilizing matrix properties; solving an excitation mode critical instability equation; and selecting the controller parameters according to the frequency domain stability margin.
The apparatus embodiments described above are merely illustrative, wherein the elements illustrated as separate elements may or may not be physically separate, and the elements shown as elements may or may not be physical elements, may be located in one place, or may be distributed over a plurality of network elements. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art will understand and implement the present invention without undue burden.
From the above description of the embodiments, it will be apparent to those skilled in the art that the embodiments may be implemented by means of software plus necessary general hardware platforms, or of course may be implemented by means of hardware. Based on this understanding, the foregoing technical solution may be embodied essentially or in a part contributing to the prior art in the form of a software product, which may be stored in a computer readable storage medium, such as ROM/RAM, a magnetic disk, an optical disk, etc., including several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method described in the respective embodiments or some parts of the embodiments.
Application instance
In an application example of the present invention, a method for stabilizing and analyzing electromechanical transient small interference 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: providing critical instability conditions of a system excitation mode according to a minimum characteristic track method;
step 103: analyzing the diagonal dominant characteristic of a rotor loop open-loop transfer function matrix L;
step 104: simplifying an excitation mode critical instability equation by utilizing matrix properties;
step 105: solving an excitation mode critical instability equation;
step 106: selecting controller parameters according to the frequency domain stability margin;
in practice, in the Heffron-Phillips model of a conventional small-disturbance stability analysis as shown in FIG. 2, the rotor loop (sM+K is chosen D ) -1 As a forward channel transfer matrix, into a compact form as shown in fig. 3.
In specific implementation, a critical instability condition of a system excitation mode is given according to a minimum characteristic track method:
view (sM+K) D ) -1 The feedback matrix I+L of the closed loop system is obtained by using the forward channel transmission matrix and the feedback channels as the rest links
According to the nature of matrix eigenvalues:
λ(I+L)＝I+λ(L)
following the convention of single input-single output (SISO) system stability analysis, we take the characteristic trace λ min The distance of (i+l) from the origin is taken as a stability margin. Therefore, when critical instability is caused, the method satisfies
λ min (I+L)＝0
In specific implementation, the diagonal dominant characteristic of the rotor loop open-loop transfer function matrix L is analyzed:
the calculation experience shows that in the high frequency band (1-10 Hz), G Q1 (s) and G M The value of(s) is small and G in the expression of L(s) can be ignored Q1 (s) and G M (s) two related terms. The approximate expression of L(s) at this time in combination with formula (4) is as follows:
according to formula (2) G Q2 The expression of(s), in combination with computational experience, we find:
①K 2 a kind of electronic deviceDiagonal elementIs usually large and exhibits certain diagonal dominant characteristics; (2) t'. d0 And G EX (s) are diagonal matrices, and K 3 And K 6 The elements are very small, and therefore [ K ] 3 +sT′ d0 +G EX (s)K 6 ] -1 Exhibit a distinct diagonal dominance, notDiagonal element Almost allIs 0; (3) g EX (s) and H PSS (s) is a diagonal array, and the above-mentioned known G is synthesized Q2 (s) has a pronounced diagonal dominance characteristic.
(sM+K D ) -1 Is a diagonal matrix, and G Q2 (s) exhibit relatively pronounced diagonal dominance characteristics, the elements of the first column being significantly larger than the remaining units, K 1 The matrix value is not large, therefore K 1 +G Q2 (s) also presentDiagonal element and the firstA large array of elements. Thus (sM+K) D ) -1 And K is equal to 1 +G Q2 The result of the multiplication(s) also exhibits a relatively pronounced diagonal dominance characteristic, and the elements of the first column are significantly larger than the remaining units. So that it can be demonstrated that L(s) is diagonally dominant.
In specific implementation, the matrix property is utilized to simplify the critical instability equation of the excitation mode:
according to the rule of the Gerr circle, the eigenvalues of L(s) can be approximated by diagonal elements of L(s), so that the formula (5) is equivalent to
1+L ii ＝0；
Wherein L is ii Representing the minimum modulus diagonal of L(s), let us study the gain of the i-th PSS, L ii Necessarily corresponds to the smallest modular diagonal element of L(s).
Bringing s=jω into the expression of L, writing formula (5) as element form
Wherein ω represents angular frequency, M i Ith as diagonal matrix MPersonal (S)Diagonal element, K D，i For diagonal matrix K D Is the ith of (2)Personal (S)Diagonal element, K 1，ii For K 1 Matrix (i, i)Personal (S)Element g Q2，ii Is G Q2 (j omega) th matrix (i, i)Personal (S)An element.
We can represent L by the elements of each matrix ii Is the value of (1):
thus formula (7) can be further written as
According to G Q2 Diagonal dominance of (jω) matrix, g in equation (9) Q2，ii The expression of (2) is
Is carried into (10) and has
The above equation is the simplified excitation mode critical instability equation.
In specific implementation, solving an excitation mode critical instability equation:
extracting gain K of PSS link, namely setting
h PSS，i ＝Kh PSS0，i ；
Wherein h is PSS0，i The transfer function at a gain of 1 for PSS is shown.
The left side of the sign of (12) is the complex function f (omega, K), i.e
The complex function f (ω, K) comprises two variables ω and K,respectively orderThe real part and the imaginary part of f (omega, K) are equal to 0, so that a binary equation set can be obtained:
where Re represents the real part and Im represents the imaginary part.
In specific implementation, selecting controller parameters according to the frequency domain stability margin:
solving the equation to obtain a critical gain K, and taking 1/3 times K as the final gain of the power system stabilizer PSS.
So far, the problem of stable excitation mode of the multi-input-multi-output system can be completely analyzed.
For example, the method is utilized in a system of IEEE 162 nodes (also referred to as IEEE 17 machine system) to set the gain of PSS installed in a set number 1 therein.
Known parameters of the system of IEEE 162 nodes include: linearization model coefficient matrix K 1 ～K 6 Diagonal matrix T 'containing d-axis transient time constants of each generator' d0 Diagonal matrix M containing generator rotor motion inertia constant and diagonal matrix K containing rotor motion damping coefficient D Transfer function matrix G of excitation system EX PSS transfer function matrix H PSS And(s) carrying out the process in the formula (12), and respectively enabling the real part and the imaginary part to be equal to 0 to obtain a binary equation set formula (15), solving the obtained excitation mode frequency to be 3.7Hz, and setting the installed PSS critical gain to be 24.5.
According to the calculation result, the PSS gain of the first unit is set to be 8.17, and the system can be found that the stability of exciting voltage is ensured while the low-frequency oscillation is restrained.
From the above examples, it is apparent that the analysis method according to the present invention well analyzes the excitation pattern stability of the multiple input-multiple output system.
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 in a general purpose computing device, they may be concentrated on a single computing device, or distributed across a network of computing devices, they may alternatively be implemented in program code executable by computing devices, so that they may be stored in a storage device for execution by computing devices, and in some cases, the steps shown or described may be performed in a different order than what is shown or described, or they may be separately fabricated into individual integrated circuit modules, or a plurality of modules or steps in 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 of the preferred embodiments of the present invention and is not intended to limit the present invention, and various modifications and variations can be made to the embodiments of the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (5)
1. The excitation mode analysis method based on the minimum characteristic track 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) Providing critical instability conditions of a system excitation mode according to a minimum characteristic track method;
3) Analyzing the diagonal dominant characteristic of a rotor loop open-loop transfer function matrix L;
4) Simplifying an excitation mode critical instability equation by utilizing matrix properties;
5) Solving an excitation mode critical instability equation;
6) Selecting controller parameters according to the frequency domain stability margin;
the specific method of the step 1) is as follows:
rotor circuit is extracted in the Heffron-Phillips model, and rotor channels (sM+K D ) -1 The method is characterized in that the method is regarded as a forward channel, and other links are combined together to be regarded as a feedback channel, so that a Heffron-Phillips model in a compact form is obtained;
defined in the above compact form of the Heffron-Phillips model:
G Q (s)＝G Q1 (s)+G Q2 (s) formula (1);
wherein G is Q1 (s)＝-K 2 [(K 3 +sT′ d0 )+G EX (s)K 6 ] -1 (G EX (s)K 5 +K 4 ) Formula (2);
in the matrix K 2 、K 3 、K 4 、K 5 、K 6 Is a linear model coefficient matrix; diagonal matrix T' d0 The transient time constant of the d axis of each generator is contained; the diagonal matrix M contains the generator rotor motion inertia constant; diagonal matrix K D The rotor motion damping coefficient is contained; diagonal matrix G EX A transfer function matrix of the excitation system; diagonal matrix H PSS (s) is a PSS transfer function matrix; omega 0 For the synchronous rotation speed of the system, s is the generalized frequency;
the critical destabilization condition of the system excitation mode is given according to the minimum characteristic track method in the step 2), and specifically comprises the following steps:
view (sM+K) D ) -1 For the forward channel transfer matrix, the rest links are feedback channels, so that a return difference matrix I+L of the closed-loop system is obtained:
wherein matrix K 1 Is a linear model coefficient matrix; diagonal matrix G M For transmission of speed-regulator-prime mover systemA transfer function matrix;
when the system is critically unstable, the frequency response curve of the return difference matrix determinant passes through (-1, 0) points for the first time, and the specific expression on the characteristic track is that the minimum characteristic track of the system exactly passes through (-1, 0) points;
therefore, when critical instability is caused, the method satisfies
λ min (i+l) =0, formula (5);
wherein lambda is min (I+L) represents the minimum eigenvalue of the return difference matrix I+L;
the diagonal dominant characteristic of the open loop transfer function matrix L(s) of the analysis rotor circuit in the step 3) is specifically:
ignoring G in the L(s) expression Q1 (s) and G M (s) related terms, the approximate expression of L(s) at this time in combination with formula (4) is as follows:
according to formula (2) G Q2 The expression of(s) is analyzed to obtain the diagonal dominant characteristic of the rotor loop open-loop transfer function matrix L(s);
the critical instability equation of the excitation mode is simplified by utilizing matrix properties in the step 4), specifically:
approximating the eigenvalues of L(s) with diagonal elements of L(s) according to the Galois circle theorem, equation (5) is equivalent to
1+L ii =0, formula (7);
wherein L is ii Representing the minimum modulus diagonal of L(s), L is assumed to be the gain of the i-th PSS under investigation ii Necessarily corresponds to the smallest modular diagonal element of L(s);
bringing s=jω into the expression of L, writing formula (5) as element form
Wherein ω represents angular frequency, M i Is the ith of the diagonal matrix MDiagonal element, K D,i For diagonal matrix K D Is the ith diagonal element, K 1,ii For K 1 The (i, i) th element of the matrix, g Q2,ii Is G Q2 (i, i) th element of the (jω) matrix;
then the elements of each matrix are used to represent L ii Is the value of (1):
thus formula (7) is further written as
According to G Q2 Diagonal dominance of (jω) matrix, g in equation (9) Q2,ii The expression of (2) is
Wherein K is 2,ii For K 2 The (i, i) th element of the matrix, K 6,ii For K 6 The (i, i) th element of the matrix, g EX,i Is G EX The ith diagonal element, h, of the (jω) matrix PSS,i Is H PSS The ith diagonal element, T, of the (jω) matrix d ′ 0,i Is T' d0 The ith diagonal element of the matrix;
is carried into (10) and has
The formula (12) is a simplified excitation mode critical instability equation;
the step 5) solves the critical instability equation of the excitation mode, and is specifically as follows:
extracting gain K of PSS link, namely setting
h PSS,i ＝Kh PSS0,i Formula (13);
wherein h is PSS0,i Representing the transfer function when the gain of the PSS is 1;
the left side of the sign of (12) is the complex function f (omega, K), i.e
The complex function f (omega, K) comprises two variables omega and K, and a binary equation system can be obtained by respectively enabling the real part and the imaginary part of f (omega, K) to be equal to 0:
wherein Re represents a real part and Im represents an imaginary part;
the solution (15) can obtain the critical instability frequency omega of the excitation mode and the critical gain K of the PSS.
2. The excitation pattern analysis method based on the minimum feature trajectory method according to claim 1, wherein the step 6) selects the controller parameters according to the frequency domain stability margin, specifically:
taking 1/3 times K as the final gain of the power system stabilizer PSS according to the critical gain K obtained in the step 5).
3. An excitation pattern analysis system based on a minimum feature trajectory method, which adopts the excitation pattern analysis method based on the minimum feature trajectory method according to claim 1, is characterized by comprising:
the model construction module (101) is used for selecting a rotor loop as a forward channel link to obtain a Heffron-Phillips model in a compact form;
the excitation mode critical instability condition calculation module (102) is used for giving out the system excitation mode critical instability condition according to the minimum characteristic track method;
the diagonal dominant characteristic analysis module (103) is used for analyzing the diagonal dominant characteristic of the rotor loop open-loop transfer function matrix L;
a critical destabilization equation simplification module (104) for simplifying the excitation mode critical destabilization equation by utilizing the matrix property;
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.
4. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that 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 2 when the program is executed by the processor.
5. 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 claimed in any one of claims 1 to 2.
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| CN110365026A (en) * | 2019-05-29 | 2019-10-22 | 云南电网有限责任公司 | Design method based on frequency domain margin index adjusting PSS4B parameter power oscillation damping |
| CN110707727A (en) * | 2019-06-06 | 2020-01-17 | 国网浙江省电力有限公司电力科学研究院 | Reactive damping controller based on flexible excitation system and parameter setting method |
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