CN114744625B - Wind turbine generator model order reduction method and system - Google Patents

Wind turbine generator model order reduction method and system Download PDF

Info

Publication number
CN114744625B
CN114744625B CN202210658777.1A CN202210658777A CN114744625B CN 114744625 B CN114744625 B CN 114744625B CN 202210658777 A CN202210658777 A CN 202210658777A CN 114744625 B CN114744625 B CN 114744625B
Authority
CN
China
Prior art keywords
model
state
linearization
wind turbine
turbine generator
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202210658777.1A
Other languages
Chinese (zh)
Other versions
CN114744625A (en
Inventor
王彤
李永达
王增平
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
North China Electric Power University
Original Assignee
North China Electric Power University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by North China Electric Power University filed Critical North China Electric Power University
Priority to CN202210658777.1A priority Critical patent/CN114744625B/en
Publication of CN114744625A publication Critical patent/CN114744625A/en
Application granted granted Critical
Publication of CN114744625B publication Critical patent/CN114744625B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • 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
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G06F17/12—Simultaneous equations, e.g. systems of linear equations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G06F17/13—Differential equations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • 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
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/381—Dispersed generators
    • 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]
    • 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
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/20—The dispersed energy generation being of renewable origin
    • H02J2300/28—The renewable source being wind energy
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00—Energy generation through renewable energy sources
    • Y02E10/70—Wind energy
    • Y02E10/76—Power conversion electric or electronic aspects

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Data Mining & Analysis (AREA)
  • Theoretical Computer Science (AREA)
  • Software Systems (AREA)
  • Databases & Information Systems (AREA)
  • Algebra (AREA)
  • General Engineering & Computer Science (AREA)
  • Operations Research (AREA)
  • Power Engineering (AREA)
  • Computing Systems (AREA)
  • Control Of Eletrric Generators (AREA)
  • Wind Motors (AREA)

Abstract

The invention relates to a wind turbine generator model order reduction method and system suitable for a large disturbance scene, and belongs to the field of wind turbine systems.

Description

Wind turbine generator model order reduction method and system
Technical Field
The invention relates to the field of wind power systems, in particular to a wind turbine generator model order reduction method and system.
Background
In recent years, the demand for power generation by renewable energy sources is increasing, and wind power is developed and utilized on a large scale. With the development of large-scale new energy, the grid-connected proportion of power electronic equipment is gradually increased, so that the transient behavior of a wind power grid-connected system is remarkably changed, and a severe challenge is brought to the safe and stable operation of a power grid. In order to correctly evaluate the influence of wind power integration on a power grid, deep research needs to be performed on the transient response characteristics of a wind power integration system in different large-interference scenes. If a detailed mathematical model is adopted for simulation analysis of the wind power grid-connected system, the matrix order is high, the calculation amount is large, and the simulation calculation is difficult to cause dimension disaster, so that the accuracy and the effectiveness of the dynamic characteristic analysis of the system are severely limited. Therefore, in order to improve the system analysis and calculation efficiency, it is necessary to research the wind turbine generator order reduction model.
In the power system, the model order reduction method mainly includes a modal order reduction method, a balanced truncation method and a Krylov subspace method. The corresponding model order reduction principle can be summarized as follows: a low-dimensional projection space is searched in a high-dimensional space where an original large-scale system is located, and then an original dynamic system model is projected to a corresponding low-dimensional space, so that a corresponding reduced-order model can be obtained. The method is generally based on the theory analysis of a small interference model of the system at a balance point, so that the reduced-order system can approach the transfer function (input-output relationship) of the original system as much as possible, some dynamic characteristics of the original system are kept, and the method is only suitable for small disturbance simulation analysis near the balance point of the power system. With the continuous improvement of the wind power proportion, the nonlinearity of a wind power system is not negligible, and the methods are difficult to depict the nonlinear characteristic of the wind turbine generator under large disturbance and have certain limitations.
Disclosure of Invention
The invention aims to provide a wind turbine model order reduction method and system to realize nonlinear characteristic characterization of a wind turbine under large disturbance.
In order to achieve the purpose, the invention provides the following scheme:
a wind turbine generator model order reduction method comprises the following steps:
selecting a plurality of linearization points on a state track of the wind power grid-connected system subjected to large disturbance;
linearizing the full-order model of the wind turbine generator at each linearization point to obtain a local linearization model at each linearization point;
calculating an orthogonal base and a Heisenberg matrix of each local linearization model when all leading feature roots of each local linearization model are larger than zero by adopting a Block Arnoldi algorithm;
the orthogonal base of each local linearization model and the participation matrix of the Heisenberg matrix are simultaneously established, and the generalized participation matrix of each local linearization model is obtained;
dividing all state variables into a fast variable and a slow variable according to the generalized participation factors in the generalized participation matrix of each local linearized model;
performing singular perturbation order reduction on the full-order model of the wind turbine generator according to the fast variable and the slow variable to obtain a wind turbine generator order reduction model of the wind turbine grid-connected system under large disturbance;
and analyzing the transient response characteristics of the wind power grid-connected system under different large interference scenes by using the wind turbine generator order reduction model.
Optionally, the selecting a plurality of linearization points on the state trajectory of the wind power grid-connected system after suffering from the large disturbance specifically includes:
simulating the nonlinear response of the full-order model of the wind turbine generator after suffering from large disturbance, and obtaining state vector sequences at all time steps;
selecting a first state vector in the state vector sequence as an ith linearization point, and initializing i to 1;
selecting state vectors from left to right in the state vector sequence in sequence until the first requirement is met: if the Euclidean distance between the selected state vector and each linearization point is larger than the Euclidean distance threshold, increasing the value of i by 1, and taking the state vector which meets the selection for the first time as the ith linearization point;
judging whether the numerical value of the i is smaller than the number of the selected points or not to obtain a judgment result;
if the judgment result shows yes, returning to the step of selecting the state vectors from left to right in the state vector sequence until the first requirement is met: the Euclidean distance between the selected state vector and each linearization point is larger than the Euclidean distance threshold, the value of i is increased by 1, and the state vector meeting the selection for the first time is used as the ith linearization point;
and if the judgment result shows that the point is not the linear point, all the linearization points are obtained.
Optionally, the linearizing the full-order model of the wind turbine at each linearization point to obtain a local linearization model at each linearization point specifically includes:
determining a full-order model of the wind turbine generator as
Figure GDA0003729603960000031
Wherein X is a state vector of the wind turbine generator, U is a node voltage vector of the wind turbine generator, f (X, U) is a state equation of the wind turbine generator, g (X, U) is an output equation of the wind turbine generator, and y is an output quantity;
using a formula
Figure GDA0003729603960000032
And
Figure GDA0003729603960000033
linearizing the full-order model of the wind turbine generator at each linearization point to obtain a state matrix and an input matrix at each linearization point, and forming the state matrix and the input matrix into a local linearization model at each linearization point; wherein, A i To linearize point X i State matrix of (A), B i To linearize point X i Input matrix of (X Δ) i m And U Delta i m Small disturbances of the mth component of the state vector and the input vector respectively, X is the state vector of the direct-drive permanent magnet synchronous generator, U is the node voltage vector of the direct-drive permanent magnet synchronous generator, U i To linearize point X i Node voltage vector of direct-drive permanent magnet synchronous generator, A i (: m) is the m-th component of the state matrix, B i (: m) is the mth component of the input matrix.
Optionally, the method includes, by simultaneously establishing the orthogonal basis of each local linearization model and the participation matrix of the heisenberg matrix, obtaining the generalized participation matrix of each local linearization model, and specifically includes:
performing participation factor analysis on the Heisenberg matrix to obtain a participation matrix and a dominant characteristic root of the Heisenberg matrix;
using a formula
Figure GDA0003729603960000041
Figure GDA0003729603960000044
The orthogonal base of each local linearization model and the participation matrix of the Heisenberg matrix are simultaneously established, and the generalized participation matrix of each local linearization model is obtained;
wherein, W s Is the generalized participation matrix of the s-th local linearization model,
Figure GDA0003729603960000042
is the orthogonal basis for the s-th locally linearized model,
Figure GDA0003729603960000043
is the participation matrix, ξ, of the Heisenberg matrix of the s-th local linearization model 1 、ξ m And xi n 1 x 2q order transverse vectors, p, corresponding to the 1 st, mth and nth state variables in the orthogonal basis of the s-th local linearization model 1 、p r And p 2q Column vectors, w, corresponding to the 1 st, r th and 2q leading feature roots in the participation matrix of the Heisenberg matrix of the s-th local linearization model respectively rm ＝ξ m *p r ，w rm The generalized participation factor is a generalized participation factor corresponding to the mth state variable, and the generalized participation factor represents the participation degree of the mth state variable of the full-order model of the wind turbine generator and the mth dominant characteristic root of the local linear model.
Optionally, the dividing, according to the generalized participation factor in the generalized participation matrix of each local linearization model, all the state variables into a fast variable and a slow variable specifically includes:
and determining the state variables of which the generalized participation factors are larger than 0.1 in the generalized participation matrix as slow variables, and determining the state variables of which the generalized participation factors are smaller than or equal to 0.1 as fast variables.
Optionally, performing singular perturbation order reduction on the full-order model of the wind turbine generator according to the fast variable and the slow variable to obtain a wind turbine generator order reduction model of the wind turbine grid-connected system under large disturbance, specifically including:
the full-order model of the wind turbine generator is converted into a singular perturbation equation of a fast variable and a slow variable as
Figure GDA0003729603960000051
Wherein, X I For a slowly varying set, X II Is a fast variable set, U is a node voltage vector of the wind turbine generator, f 1 (X I ,X II U) is an equation of state relating to a slow variable, f 2 (X I ,X II U) is a state equation related to the fast variables, and epsilon is a singular perturbation parameter;
making the singular perturbation parameter epsilon equal to 0, determining the quasi-steady-state expression of the fast variable as X II ＝h(X I U); wherein, h (X) I U) is a quasi-steady state expression equation of a fast variable;
combining a quasi-steady-state expression of a fast variable and the singular perturbation equation, determining a wind turbine generator reduction model of the wind power grid-connected system under large disturbance as
Figure GDA0003729603960000052
Wherein f is 1 (X I , h(X I U) is a wind turbine generator order reduction equation.
A wind turbine generator model order reduction system comprising:
the linearization point selection module is used for selecting a plurality of linearization points on a state track of the wind power grid-connected system subjected to large disturbance;
the linearization module is used for linearizing the wind turbine generator full-order model at each linearization point to obtain a local linearization model at each linearization point;
the calculation module is used for calculating the orthogonal basis and the Heisenberg matrix of each local linearization model when all leading feature roots of each local linearization model are larger than zero by adopting a Block Arnoldi algorithm;
the generalized participation matrix obtaining module is used for simultaneously establishing the orthogonal base of each local linearization model and the participation matrix of the Heisenberg matrix to obtain the generalized participation matrix of each local linearization model;
the state variable dividing module is used for dividing all state variables into fast variables and slow variables according to the generalized participation factors in the generalized participation matrix of each local linear model;
the order reduction module is used for carrying out singular perturbation order reduction on the full-order model of the wind turbine generator according to the fast variable and the slow variable to obtain a wind turbine generator order reduction model of the wind power grid-connected system under large disturbance;
and the transient response analysis module is used for analyzing the transient response characteristics of the wind power grid-connected system in different large interference scenes by utilizing the wind turbine generator order reduction model.
Optionally, the linearization point selection module specifically includes:
the disturbance simulation unit is used for simulating the nonlinear response of the full-order model of the wind turbine generator after encountering large disturbance and obtaining state vector sequences on all time steps;
the initialization unit is used for selecting a first state vector in the state vector sequence as an ith linearization point and initializing i to 1;
the linearization point selecting unit is used for sequentially selecting the state vectors from left to right in the state vector sequence until the first requirement is met: if the Euclidean distance between the selected state vector and each linearization point is greater than the Euclidean distance threshold, increasing the value of i by 1, and taking the state vector which meets the selection for the first time as the ith linearization point;
the judging unit is used for judging whether the numerical value of i is smaller than the number of the selected points or not to obtain a judging result;
and the circulating unit is used for returning to the step of selecting the state vectors from left to right in the state vector sequence if the judgment result shows that the state vectors meet the following conditions for the first time: increasing the value of i by 1 if the Euclidean distance between the selected state vector and each linearization point is larger than the Euclidean distance threshold, and taking the state vector which meets the selection for the first time as the ith linearization point;
and the output unit is used for obtaining all linearization points if the judgment result shows no.
Optionally, the state variable partitioning module specifically includes:
and the state variable definition unit is used for determining the state variables of which the generalized participation factors are larger than 0.1 in the generalized participation matrix as slow variables, and determining the state variables of which the generalized participation factors are smaller than or equal to 0.1 as fast variables.
Optionally, the order reduction module specifically includes:
the model conversion unit is used for converting the full-order model of the wind turbine generator into a singular perturbation equation of a fast variable and a slow variable
Figure GDA0003729603960000071
Wherein, X I For a slowly varying set, X II Is a fast variable set, U is a node voltage vector of the wind turbine generator, f 1 (X I ,X II U) is an equation of state relating to slow variables, f 2 (X I ,X II U) is a state equation related to the fast variables, and epsilon is a singular perturbation parameter;
a quasi-steady-state expression determining unit for making singular perturbation parameter epsilon equal to 0, and determining the quasi-steady-state expression of the fast variable as X II ＝h(X I U); wherein, h (X) I U) is a quasi-steady state expression equation of the fast variable;
the order reduction model determining unit is used for determining the order reduction model of the wind turbine generator set under the condition of large disturbance of the wind power grid-connected system by combining the quasi-steady-state expression of the fast variable and the singular perturbation equation
Figure GDA0003729603960000072
Wherein f is 1 (X I ,h(X I U), U) is a wind turbine generator order reduction equation.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention discloses a wind turbine generator model order reduction method and system suitable for a large disturbance scene, which comprises the steps of firstly selecting linearization points, linearizing a wind turbine generator full-order model at each linearization point, then dividing all state variables into fast variables and slow variables according to generalized participation factors in generalized participation matrixes of each local linearization model, and finally conducting singular perturbation order reduction on the wind turbine generator full-order model to obtain a wind turbine generator order reduction model of a wind turbine grid-connected system under the large disturbance.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to these drawings without creative efforts.
Fig. 1 is an exemplary structural diagram of a wind turbine generator model order reduction system according to an embodiment of the present invention;
FIG. 2 is a flowchart of a wind turbine generator model order reduction method according to an embodiment of the present invention;
FIG. 3 is an equivalent schematic diagram of a simulation system according to an embodiment of the present invention;
fig. 4 is a state trajectory diagram of the nonlinear response of the D-PMSG full-order system according to the embodiment of the present invention;
fig. 5 is a comparison graph of the grid-connected point voltages of the D-PMSG full-order system and the reduced-order system according to the embodiment of the present invention;
fig. 6 is a comparison diagram of dc capacitor voltages of a D-PMSG full-order system and a reduced-order system according to an embodiment of the present invention;
fig. 7 is a comparison graph of the D-axis components of the network side currents of the D-PMSG full-order system and the reduced-order system according to the embodiment of the present invention;
fig. 8 is a diagram comparing q-axis components of network side currents of a D-PMSG full-order system and a reduced-order system according to an embodiment of the present invention;
fig. 9 is a grid-connected active power comparison diagram of a D-PMSG full-order system and a reduced-order system according to an embodiment of the present invention;
fig. 10 is a comparison diagram of power-angle difference of the first synchronous set of the D-PMSG full-order system and the reduced-order system according to the embodiment of the present invention;
fig. 11 is a comparison diagram of power-angle difference of a second synchronous unit of the D-PMSG full-order system and the reduced-order system according to the embodiment of the present invention;
fig. 12 is a power-angle difference comparison diagram of a third synchronous machine set of the D-PMSG full-order system and the reduced-order system according to the embodiment of the present invention;
fig. 13 is a comparison diagram of the voltages of the grid-connected point when the transient state of the D-PMSG full-order system and the reduced-order system is unstable according to the embodiment of the present invention;
fig. 14 is a comparison diagram of voltages of dc capacitors in transient instability of a D-PMSG full-stage system and a reduced-stage system according to an embodiment of the present invention;
fig. 15 is a comparison graph of the D-axis components of the grid-side current during transient instability of the D-PMSG full-order system and the reduced-order system according to the embodiment of the present invention;
fig. 16 is a graph comparing q-axis components of the network side current during transient instability of the D-PMSG full-order system and the reduced-order system according to the embodiment of the present invention;
fig. 17 is a comparison diagram of grid-connected active power when transient instability occurs between a D-PMSG full-order system and a reduced-order system according to an embodiment of the present invention;
fig. 18 is a comparison diagram of power-angle difference of the first synchronous generator set when transient instability occurs between the D-PMSG full-order system and the reduced-order system according to the embodiment of the present invention;
fig. 19 is a comparison diagram of power-angle difference of the second synchronous machine set during transient instability of the D-PMSG full-order system and the reduced-order system according to the embodiment of the present invention;
fig. 20 is a comparison diagram of power-angle difference of the third synchronous machine set during transient instability of the D-PMSG full-order system and the reduced-order system according to the embodiment of the present invention;
fig. 21 is a graph comparing frequency response results of a D-PMSG full-order system and a reduced-order system according to an embodiment of the present invention;
fig. 22 is a frequency response error curve of the reduced-order system according to the embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
The invention aims to provide a wind turbine model order reduction method and system to realize nonlinear characteristic characterization of a wind turbine under large disturbance.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Considering that the traditional order reduction method is difficult to be applied to a large disturbance scene of a novel power system, the embodiment of the invention provides a wind turbine generator model order reduction method and system suitable for large disturbance analysis.
Referring to fig. 1, a wind turbine generator model order reduction system suitable for large disturbance analysis according to an embodiment of the present invention includes: the device comprises a linearization point selection module 1, a linearization module 2, a calculation module 3, a generalized participation matrix obtaining module 4, a state variable dividing module 5, a reduced order module 6 and a transient response analysis module 7.
In other embodiments of the present invention, the linearization point selection module 1 comprises: the device comprises a disturbance simulation unit, an initialization unit, a linearization point selection unit, a judgment unit, a circulation unit and an output unit.
In other embodiments of the present invention, the order reduction module 6 comprises: the model conversion unit, the quasi-steady-state expression determination unit and the reduced order model determination unit.
The functions of the modules and the units are further described in the following by combining a wind turbine generator model order reduction method.
Each module and each unit in the wind turbine generator model order reduction system may be deployed on the same server (for example, a data analysis server) or a computer in the form of software or a component, or each module included in the wind turbine generator model order reduction system may be an independent server.
Fig. 3 shows an exemplary application scenario of the wind turbine generator model order reduction system: an improved 4-machine two-zone test system is designed under an MATLAB platform, wherein a node 12 is connected with a direct-drive permanent magnet synchronous generator (D-PMSG) through a transformer, and a wind turbine generator model reduction system can correspondingly analyze the transient state of the 4-machine two-zone test system.
The embodiments of the present invention will be described in further detail below based on the above general description.
Referring to fig. 2, a wind turbine generator model order reduction method suitable for large disturbance analysis according to an embodiment of the present invention includes:
and step S1, selecting a plurality of linearization points on the state track of the wind power grid-connected system subjected to large disturbance.
First, the basic contents of the trajectory piecewise linearization method are described. The track piecewise linearization method basically comprises the steps of selecting a plurality of linearization points along the state track of the wind turbine generator to perform piecewise linearization on a full-order model to obtain a local linearization model of the full-order model of the wind turbine generator at the linearization points.
The wind turbine state model may be mathematically represented in the form:
Figure GDA0003729603960000101
in the formula, f (X, U) and g (X, U) are a state equation and an output equation of the wind power generation set respectively; x is a state vector of the wind turbine, which comprises I gd 、I gq 、x 4 、x 6 、x 7 、x 5 、I sd 、I sq 、ω s 、V dc 、x 1 、x 2 、 x 3 These 13 state variables, I sd 、I sq D, q-axis components, omega, of the stator current, respectively s As angular speed of the rotor, I gd 、I gq D-and q-axis components, x, of AC-side current of the grid-side converter 1 、x 2 、x 3 Intermediate variable, x, introduced for PI link in machine side converter 4 、x 5 、x 6 、x 7 Intermediate variables are introduced into a PI link in the network side converter; u is a node voltage vector of the wind turbine generator, V dc Is a dc capacitor voltage.
Linearization Point X i The detailed procedure of (i ═ 0,1, …, l-1) sampling is as follows:
1) simulating the nonlinear response of the full-order model of the wind turbine generator after suffering from large disturbance to obtain state information on all time steps, and storing the state vectors { X } 0 ,…,X N N +1 is the number of state vectors;
2) will be in the initial state X 0 Selecting a first linearization point, and making i equal to 0;
3) predetermining Euclidean distance threshold value sigma>0, state vector { X) stored from step 1) 0 ,…,X N Calculating from left to right in turn, if a certain state vector X satisfies min | | X-X j || 0≤j≤i σ, i.e. (current state vector X and all previous linearization points X i Having a euclidean distance between them greater than σ), the (i + 1) th linearization point X is selected i+1 X, i is i + 1.
4) If i is less than l-1, returning to the third step; otherwise, the algorithm ends.
Where l is the maximum number of points selected given in advance and σ specifically controls the interval of selection of the linearization points.
Step S1 can be performed by the aforementioned linearization point selection module 1. The disturbance simulation unit simulates the nonlinear response of the full-order model of the wind turbine generator after encountering large disturbance and obtains a state vector sequence at all time steps. The initialization unit selects the first state vector in the state vector sequence as the ith linearization point, and initializes i to 1. The linearization point selection unit sequentially selects the state vectors from left to right in the state vector sequence until the first requirement is met: and if the Euclidean distance between the selected state vector and each linearization point is greater than the Euclidean distance threshold, increasing the value of i by 1, and taking the state vector which meets the selection for the first time as the ith linearization point. The judging unit judges whether the value of i is less than the number of the selected points or not to obtain a judging result. If the judgment result shows yes, the circulation unit returns to the step of selecting the state vectors from left to right in the state vector sequence until the first requirement is met: and (3) if the Euclidean distance between the selected state vector and each linearization point is greater than the Euclidean distance threshold, increasing the value of i by 1, and taking the state vector which meets the selection for the first time as the ith linearization point ". And if the judgment result shows that the point is not the point, the output unit obtains all linearization points.
And step S2, linearizing the wind turbine generator full-order model at each linearization point to obtain a local linearization model at each linearization point.
Linearization point X on state track of wind turbine generator i After the position of (i is 0,1, …, l-1), linearizing the wind turbine system at the selected linearization point according to the following formula to obtain a state matrix and an input matrix [ A ] of a local linearization model i ,B i ](i-0, 1, …, l-1). The matrix is obtained by applying the operating conditions X i And U i The surrounding states and inputs provide small perturbations to compute. Thus, the elements of the system matrix may be obtained as follows:
Figure GDA0003729603960000121
Figure GDA0003729603960000122
in the formula, A i To linearize point X i State matrix of (A), B i To linearize point X i Input matrix of X.DELTA. i m And U.DELTA. i m Small perturbations, X, of the m-th component of the state vector and the input vector, respectivelyIs the state vector of the D-PMSG, U is the voltage vector of the node of the D-PMSG, U i To linearize point X i The D-PMSG node voltage vector of (A) i (m) is the m-th component of the state matrix, B i (: m) is the mth component of the input matrix.
Step S2 may be performed by the aforementioned linearizing module 2.
And step S3, calculating the orthogonal basis and the Heisenberg matrix of each local linearization model when all dominant feature roots of each local linearization model are larger than zero by adopting a BlockArnoldi algorithm.
Then, performing orthogonalization treatment on the state matrix of the local linearization model of the wind turbine generator based on a BlockArnoldi algorithm, and sequentially generating q-order orthogonal bases V q ∈C n×2q And Hessenberg (Hessenberg) matrix H q ∈C 2q×2q 。C n×2q Is a matrix of dimensions n x 2q, H q ∈C 2q×2q Is a 2q x 2q dimensional matrix.
The steps of a q-step Block Arnoldi algorithm are as follows:
Function[A]＝BlockArnoldi(A,B,q)
[v 1 ,r]＝QR(B)
let ω be Av 1 ,α 1 ＝v 1 H ω。
Let f 1 ←ω-v 1 α 1 ,V 1 ←v 1 ，H 1 ←α 1 。
Forj＝1,2,3,...,(q-1)
(1)β j ＝║f j ║,v j+1 ＝f j /β j ；
(2)V j+1 ←[V j ,v j+1 ],
Figure GDA0003729603960000131
(3)ω←Av 1 ,h←V j+1 H ω,f j+1 ←ω-V j+1 h；
(4)H j+1 ←[H j ,h]
end
Output V q ,H q 。 (3)
Wherein v is 1 Representing the orthogonal base column 1 component, QR () representing a QR decomposition, f 1 Representing the residual vector of step 1, v j+1 A sub-matrix of elements of the first j columns representing orthogonal bases, V j+1 A submatrix of elements of the first j +1 columns representing orthogonal bases, H j A sub-matrix of the first j columns of elements representing the heisenberg. r, omega, alpha 1 、β j 、h、V j+1 H Respectively representing a first, a second, a third, a fourth, a fifth and a sixth intermediate variable.
Substrate V q Numerically, this can be expressed as:
V q ＝[ξ 1 …ξ m … ξ n ] T (4)
in the formula, xi m Is a transverse vector of order 1 × 2 q.
To H q Performing participatory factor analysis to obtain H q Of (2) a participation matrix P q And if the dominant characteristic root is less than or equal to zero, changing the q value, and recalculating until the dominant characteristic root of the local linearized model is greater than zero. And when the leading feature roots of the local linearization models all meet the condition that the leading feature roots are larger than zero, obtaining the orthogonal base and the Heisenberg matrix of each local linearization model.
Step S3 may be performed by the aforementioned calculation module 3.
And step S4, simultaneously establishing the orthogonal basis of each local linearization model and the participation matrix of the Heisenberg matrix to obtain the generalized participation matrix of each local linearization model.
Simultaneous H q Of (2) a participation matrix P q With the base V of the state matrix A q And obtaining the generalized participation matrix W of the dominant eigenvalue of A to each state variable.
Figure GDA0003729603960000141
Figure GDA0003729603960000142
In the formula, W s For the generalized participation matrix of the s-th locally linearized model,
Figure GDA0003729603960000143
is the orthogonal basis for the s-th locally linearized model,
Figure GDA0003729603960000144
the participation matrix, ξ, of the Heisenberg matrix for the s-th locally linearized model 1 、ξ m And xi n 1 x 2q order transverse vectors, p, corresponding to the 1 st, mth and nth state variables in the orthogonal basis of the s-th local linearization model 1 、p r And p 2q And column vectors corresponding to the 1 st, the r th and the 2q leading feature roots in the participation matrix of the Heisenberg matrix of the s-th local linearization model respectively.
Generalized participation factor w rm ＝ξ m *p r The participation degree of the mth state variable of the wind turbine generator system and the ith dominant characteristic root of the local linear model is represented, and all w are calculated i A certain dominant feature root lambda can be obtained i For the participation degree of all the state variables, the greater the participation degree is, the higher the correlation degree between the two is.
Step S4 may be performed by the generalized participation matrix obtaining module 4 described above.
And step S5, dividing all state variables into fast variables and slow variables according to the generalized participation factors in the generalized participation matrix of each local linearized model.
According to the generalized participation matrix W, the root lambda generalized participation factor is related to any dominant feature>And determining the state variable of 0.1 as a slow variable, and determining the other state variables as fast variables to realize the division of the fast and slow variables. Calculating the generalized participation matrix W of each local linearization model in sequence, and dividing all state variables of the full-order system of the wind turbine generator into a slow variable set X respectively I And fast variable set X II 。
Step S5 can be performed by the state variable dividing module 5 and the state variable defining unit.
And step S6, performing singular perturbation order reduction on the full-order model of the wind turbine generator according to the fast variable and the slow variable to obtain a wind turbine generator order reduction model of the wind power grid-connected system under large disturbance.
The differential equations associated with all fast variables are written in singular perturbation form.
Figure GDA0003729603960000151
Figure GDA0003729603960000152
In the formula, epsilon is a singular perturbation parameter.
Let ε equal to 0, equation (8) is reduced from a differential equation to an algebraic equation (5) and a fast variable set X II Differential equations related to the medium variables are converted into steady-state equations, and the wind power full-order system achieves order reduction.
0＝f 2 (X I ,X II ,U) (9)
When equation (9) has a solution, a quasi-steady state expression of the fast variable can be obtained:
X II ＝h(X I ,U) (10)
when epsilon is small, the fast variables can quickly converge to the steady state solution of equation (10), which is described only by the slow variables in the system, thus filtering out the transient processes in the wind turbine generator set full-order system fast variables. The steady state solution is the equilibrium solution corresponding to equation of state (8). The reduced order model of the original system can be obtained by substituting formula (10) for formula (7):
Figure GDA0003729603960000161
step S6 may be performed by the foregoing order reduction module 6. The model conversion unit converts the wind turbine generatorThe singular perturbation equation of the full-order model converted into the fast variable and the slow variable is
Figure GDA0003729603960000162
Wherein, X I Is a slowly varying set of variables, X II Is a fast variable set, U is a node voltage vector of the wind turbine generator, f 1 (X I ,X II U) is an equation of state relating to a slow variable, f 2 (X I ,X II U) is a state equation related to the fast variables, and epsilon is a singular perturbation parameter. The quasi-steady-state expression determining unit makes the singular perturbation parameter epsilon equal to 0, and then determines the quasi-steady-state expression of the fast variable as X II ＝h(X I U); wherein, h (X) I U) is a quasi-steady state expression equation of a fast variable. The order-reduced model determining unit combines a quasi-steady-state expression of a fast variable and the singular perturbation equation to determine a wind turbine generator order-reduced model of the wind power grid-connected system under large disturbance as
Figure GDA0003729603960000163
Wherein, f 1 (X I ,h(X I U), U) is a wind turbine generator order reduction equation.
And step S7, analyzing transient response characteristics of the wind power grid-connected system in different large interference scenes by using the wind turbine generator order reduction model.
Step S7 may be performed by the transient response analysis module 7.
Referring to fig. 3, in the embodiment of the present invention, based on an improved 4-machine two-zone test system under an MATLAB platform, a node 12 is connected to a direct-drive permanent magnet synchronous generator (D-PMSG) through a transformer, so as to verify the order reduction effect of the proposed wind turbine generator model based on the track piecewise linear technology. In fig. 3, reference numerals 1 to 12 denote nodes, G1, G2, G3, and G4 denote 4 synchronous machines, respectively, and L1 and L2 denote first and second loads.
Firstly, applying different disturbances at a D-PMSG grid-connected point of a test system to respectively obtain a state track of nonlinear response of a D-PMSG full-order system, representing the state track of the D-PMSG system by adopting a D-PMSG input, and enabling a linearization point to be linearIn the third step of the sampling process, sigma is 0.001, and the state track of the D-PMSG system is screened, so that l is 6, and six linearization points are obtained in total, wherein t is 0.001s, 1.242s and 5.127s respectively; the second trajectory t is 1.117s and the third trajectory t is 1.109s and t is 1.705s, as shown in fig. 4. Linearization is carried out at the six linearization points to obtain a state matrix and an input matrix [ A ] of the local linearization model i ,B i ](i＝0,1,…,5)。
And finally determining that when q is 3, the dominant characteristic root of each local linearization model is greater than zero, and the order of the Heisenberg matrix of each local linearization model is 6 at the moment. According to the value of the generalized participation factor corresponding to each state variable, completing the division of all the state variables of the D-PMSG full-order system into fast and slow variables, performing singular perturbation order reduction on the D-PMSG full-order system, and establishing the D-PMSG order reduction system, wherein a slow variable set X is used for reducing the order of the D-PMSG full-order system I Having a total of 6 state variables, i.e. I gd 、I gq 、x 4 、x 7 、V dc 、x 6 Therefore, the order of the D-PMSG order-reduced system is 6.
Transient response conditions of a D-PMSG full-order system and a reduced-order system are adopted in the test system through comparative analysis. Setting the total simulation duration as 6s, when 1s, generating three-phase grounding short circuit at the No. 3 node of the test system, setting the fault duration as 100ms, and removing the fault when 1.1 s. FIGS. 5-9 compare the DC capacitor voltage V of the D-PMSG full-order system and the reduced-order system respectively dc (ii) a Net side current dq axis component i gd 、i gq (ii) a Transient response curves of variables such as grid-connected point voltage U and grid-connected active power P are shown in FIGS. 10-12, which respectively compare the transient response curves of the power angle difference of the synchronous unit when the testing system adopts a D-PMSG full-order system and a reduced-order system. Fig. 10 shows the power angle difference between the synchronous machine 1(G1) and the synchronous machine 2(G2) (G1 and G2 constitute the first synchronous machine group), fig. 11 shows the power angle difference between the synchronous machine 1(G1) and the synchronous machine 3(G3) (G1 and G3 constitute the second synchronous machine group), and fig. 12 shows the power angle difference between the synchronous machine 1(G1) and the synchronous machine 4(G4) (G1 and G4 constitute the third synchronous machine group).
In fig. 5 to 12, the black solid line represents the transient response curve of the power angle difference between each variable of the D-PMSG full-order system and the testing system synchronous unit, and the dotted line represents the transient response curve of the power angle difference between each variable of the D-PMSG reduced-order system and the testing system synchronous unit. As can be seen from fig. 5 to fig. 9, the transient response variation processes of the variables in the D-PMSG order-reducing system are well consistent with those of the full-order system, so that the research effect that the fixed slow dynamic variables should achieve is achieved. From the transient response process of each variable, the oscillation change processes of the D-PMSG full-order system and the reduced-order system are highly similar in the process that the three-phase grounding short circuit occurs in the test system. In the D-PMSG order-reducing system, after the oscillation process of the corresponding variable is finished, the steady state value can be kept consistent with the steady state value of the corresponding variable of the full-order system. As can be seen from fig. 10 to 12, when the D-PMSG full-order system and the reduced-order system are adopted in the test system, respectively, and a transient fault occurs, the power-angle difference oscillation change process of the synchronous machine is kept consistent.
The transient response characteristic analysis is to re-stabilize the test system after the transient process, and then compare and analyze the response condition of the test system when the transient instability of the D-PMSG full-order system and the reduced-order system is adopted. Setting the total simulation time length to be 6s, when 1s, accessing a three-phase grounding short-circuit fault at the node No. 3 of the test system, wherein the fault duration is 300ms, and when 1.3s, removing the fault, and the transient response condition is shown in fig. 13-20. Fig. 18 shows the power angle difference between the synchronous machine 1(G1) and the synchronous machine 2(G2), fig. 19 shows the power angle difference between the synchronous machine 1(G1) and the synchronous machine 3(G3), and fig. 20 shows the power angle difference between the synchronous machine 1(G1) and the synchronous machine 4 (G4).
The transient analysis generally focuses on the first swing process, and as can be seen from fig. 13 to 20, in the fault process of the test system, the transient response change process of each variable in the D-PMSG order-reduced system adopted by the test system keeps a good fit effect with the full-order system. As can be seen from fig. 13 to 17, after the fault is removed, the test system has already been unstable, and the oscillation processes of the D-PMSG full-order system and the reduced-order system have some errors in time, but the oscillation waveforms are highly similar. As can be seen from fig. 18 to 20, when the D-PMSG full-order system and the reduced-order system are used in the test system, respectively, to cause transient instability, the power-angle difference oscillation processes of the synchronous machine are kept consistent.
And calculating a small signal model of the D-PMSG reduced-order system, and comparing the frequency domain response with the small signal model of the D-PMSG full-order system, wherein the comparison result is shown in figure 21.
In fig. 21, the solid line and the dotted line respectively show the frequency domain response curves of the D-PMSG full-order system and the reduced-order system. As can be seen from fig. 21, the full-order system and the reduced-order system have highly similar multi-band frequency response results, and the small-signal models of the low-band full-order system and the reduced-order system maintain the same input and output characteristics.
In order to further compare the time-frequency domain response situations of the test system adopting the D-PMSG full-order system and the reduced-order system, an error curve of the frequency domain response of the reduced-order system is shown in fig. 22. It can be seen that, due to model information reduction caused by dimension reduction and simplification, certain errors exist in the frequency domain response of the reduced-order system, and the error amount increases with the reduction of the frequency band.
The invention provides a wind turbine generator model order reduction method suitable for a large disturbance scene, which is a nonlinear system singular perturbation order reduction algorithm based on a track piecewise linear technology, is suitable for large disturbance analysis of a wind power grid-connected system, reserves state variables of the wind turbine generator, and provides a solution for mechanism analysis of the wind power grid-connected system in the large disturbance scene. Taking an improved 4-machine two-zone test system as an example, transient simulation is performed on the system under different fault clearing times. The result proves that under the condition that the system is stable or even unstable, the low-order model of the wind turbine generator obtained by the method fully retains the transient characteristic and the frequency domain characteristic of the detailed model, and ensures high precision and adaptability.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the foregoing, the description is not to be taken in a limiting sense.

Claims (10)

1. A wind turbine generator model order reduction method is characterized by comprising the following steps:
selecting a plurality of linearization points on a state track of a wind power grid-connected system subjected to large disturbance;
linearizing the full-order model of the wind turbine generator at each linearization point to obtain a local linearization model at each linearization point;
calculating the orthogonal basis and the Heisenberg matrix of each local linearization model when all dominant feature roots of each local linearization model are larger than zero by adopting a BlockArnoldi algorithm;
simultaneously establishing an orthogonal base of each local linearization model and a participation matrix of a Heisenberg matrix to obtain a generalized participation matrix of each local linearization model;
dividing all state variables into fast variables and slow variables according to the generalized participation factors in the generalized participation matrix of each local linearization model;
performing singular perturbation order reduction on the full-order model of the wind turbine generator according to the fast variable and the slow variable to obtain a wind turbine generator order reduction model of the wind turbine grid-connected system under large disturbance;
and analyzing the transient response characteristics of the wind power grid-connected system in different large-interference scenes by using the wind turbine generator reduced-order model.
2. The wind turbine generator model order reduction method according to claim 1, wherein the selecting a plurality of linearization points on the state trajectory of the wind power grid-connected system after suffering from large disturbance specifically comprises:
simulating the nonlinear response of the full-order model of the wind turbine generator after suffering from large disturbance, and obtaining state vector sequences at all time steps;
selecting a first state vector in the state vector sequence as an ith linearization point, and initializing i to be 1;
selecting state vectors from left to right in the state vector sequence in sequence until the first requirement is met: if the Euclidean distance between the selected state vector and each linearization point is greater than the Euclidean distance threshold, increasing the value of i by 1, and taking the state vector which meets the selection for the first time as the ith linearization point;
judging whether the numerical value of i is smaller than the number of the selected points or not to obtain a judgment result;
if the judgment result shows yes, returning to the step of selecting the state vectors from left to right in the state vector sequence until the first requirement is met: increasing the value of i by 1 if the Euclidean distance between the selected state vector and each linearization point is larger than the Euclidean distance threshold, and taking the state vector which meets the selection for the first time as the ith linearization point;
and if the judgment result shows no, obtaining all linearization points.
3. The wind turbine generator model order reduction method according to claim 1, wherein the wind turbine generator full-order model is linearized at each linearization point to obtain a local linearization model at each linearization point, and specifically comprises:
determining a full-order model of the wind turbine generator as
Figure FDA0003729603950000021
Wherein f (X, U) is a state equation of the wind turbine generator, g (X, U) is an output equation of the wind turbine generator, and y is an output quantity;
using formulas
Figure FDA0003729603950000022
And
Figure FDA0003729603950000023
at each linearization pointLinearizing the full-order model of the wind turbine generator to obtain a state matrix and an input matrix at each linearization point, and forming the state matrix and the input matrix into a local linearization model at each linearization point; wherein, A i To linearize point X i State matrix of (B) i To linearize point X i Input matrix of (X Δ) i m And U Delta i m Small disturbances of the mth component of the state vector and the input vector respectively, X is the state vector of the direct-drive permanent magnet synchronous generator, U is the node voltage vector of the direct-drive permanent magnet synchronous generator, U i To linearize point X i Node voltage vector of direct-drive permanent magnet synchronous generator, A i (m) is the m-th component of the state matrix, B i (: m) is the mth component of the input matrix.
4. The wind turbine generator model order reduction method according to claim 1, wherein the orthogonal basis of each local linearization model and the participation matrix of the Heisenberg matrix are simultaneously established to obtain the generalized participation matrix of each local linearization model, and specifically comprises:
performing participation factor analysis on the Heisenberg matrix to obtain a participation matrix and a dominant characteristic root of the Heisenberg matrix;
using formulas
Figure FDA0003729603950000031
Figure FDA0003729603950000032
The orthogonal base of each local linearization model and the participation matrix of the Heisenberg matrix are simultaneously established, and the generalized participation matrix of each local linearization model is obtained;
wherein, W s Is the generalized participation matrix of the s-th local linearization model,
Figure FDA0003729603950000033
is the orthogonal basis for the s-th locally linearized model,
Figure FDA0003729603950000034
is the participation matrix, ξ, of the Heisenberg matrix of the s-th local linearization model 1 、ξ m And xi n 1 x 2q order transverse vectors, p, corresponding to the 1 st, mth and nth state variables in the orthogonal basis of the s-th local linearization model 1 、p r And p 2q Column vectors, w, corresponding to the 1 st, r th and 2q leading feature roots in the participation matrix of the Heisenberg matrix of the s-th local linearization model respectively rm ＝ξ m *pr，w rm The generalized participation factor is a generalized participation factor corresponding to the mth state variable, and the generalized participation factor represents the participation degree of the mth state variable of the full-order model of the wind turbine generator and the mth dominant characteristic root of the local linear model.
5. The wind turbine generator model order reduction method according to claim 4, wherein the dividing of all state variables into fast variables and slow variables according to the generalized participation factors in the generalized participation matrix of each local linearization model specifically comprises:
and determining the state variable of which the generalized participation factor is greater than 0.1 in the generalized participation matrix as a slow variable, and determining the state variable of which the generalized participation factor is less than or equal to 0.1 as a fast variable.
6. The wind turbine generator model order reduction method according to claim 1, wherein the singular perturbation order reduction is performed on the full-order wind turbine generator model according to the fast variable and the slow variable to obtain a wind turbine generator order reduction model of a wind turbine grid-connected system under large disturbance, and the method specifically comprises the following steps:
the full-order model of the wind turbine generator is converted into a singular perturbation equation of a fast variable and a slow variable as
Figure FDA0003729603950000041
Wherein, X I For a slowly varying set, X II Is a fast variable set, U is a node voltage vector of the direct-drive permanent magnet synchronous generator,f 1 (X I ,X II u) is an equation of state relating to a slow variable, f 2 (X I ,X II U) is a state equation related to the fast variables, and epsilon is a singular perturbation parameter;
making the singular perturbation parameter epsilon equal to 0, determining the quasi-steady-state expression of the fast variable as X II ＝h(X I U); wherein, h (X) I U) is a quasi-steady state expression equation of the fast variable;
combining a quasi-steady-state expression of a fast variable and the singular perturbation equation, determining a wind turbine generator reduction model of the wind power grid-connected system under large disturbance as
Figure FDA0003729603950000042
Wherein f is 1 (X I ,h(X I U), U) is a wind turbine generator order reduction equation.
7. A wind turbine generator model order reduction system is characterized by comprising:
the linearization point selection module is used for selecting a plurality of linearization points on a state track of the wind power grid-connected system subjected to large disturbance;
the linearization module is used for linearizing the full-order model of the wind turbine generator at each linearization point to obtain a local linearization model at each linearization point;
the calculation module is used for calculating the orthogonal basis and the Heisenberg matrix of each local linearization model when all leading feature roots of each local linearization model are larger than zero by adopting a Block Arnoldi algorithm;
the generalized participation matrix obtaining module is used for simultaneously establishing the orthogonal base of each local linearization model and the participation matrix of the Heisenberg matrix to obtain the generalized participation matrix of each local linearization model;
the state variable dividing module is used for dividing all state variables into fast variables and slow variables according to the generalized participation factors in the generalized participation matrix of each local linearization model;
the order reduction module is used for carrying out singular perturbation order reduction on the full-order model of the wind turbine generator according to the fast variable and the slow variable to obtain a wind turbine generator order reduction model of the wind power grid-connected system under large disturbance;
and the transient response analysis module is used for analyzing the transient response characteristics of the wind power grid-connected system in different large interference scenes by utilizing the wind turbine generator order reduction model.
8. The wind turbine generator model order reduction system according to claim 7, wherein the linearization point selection module specifically includes:
the disturbance simulation unit is used for simulating the nonlinear response of the full-order model of the wind turbine generator after encountering large disturbance to obtain a state vector sequence on all time steps;
the initialization unit is used for selecting a first state vector in the state vector sequence as an ith linearization point and initializing i to be 1;
a linearization point selecting unit, configured to sequentially select a state vector from left to right in the state vector sequence until first satisfying: if the Euclidean distance between the selected state vector and each linearization point is greater than the Euclidean distance threshold, increasing the value of i by 1, and taking the state vector which meets the selection for the first time as the ith linearization point;
the judging unit is used for judging whether the numerical value of i is smaller than the number of the selected points or not to obtain a judging result;
and the circulating unit is used for returning to the step of selecting the state vectors from left to right in the state vector sequence if the judgment result shows that the state vectors are correct, until the conditions are met for the first time: the Euclidean distance between the selected state vector and each linearization point is larger than the Euclidean distance threshold, the value of i is increased by 1, and the state vector meeting the selection for the first time is used as the ith linearization point;
and the output unit is used for obtaining all linearization points if the judgment result shows no.
9. The wind turbine generator model order reduction system of claim 7, wherein the state variable partitioning module specifically comprises:
and the state variable definition unit is used for determining the state variables of which the generalized participation factors are larger than 0.1 in the generalized participation matrix as slow variables, and determining the state variables of which the generalized participation factors are smaller than or equal to 0.1 as fast variables.
10. The wind turbine generator model order reduction system according to claim 7, wherein the order reduction module specifically comprises:
the model conversion unit is used for converting the full-order model of the wind turbine generator into a singular perturbation equation of a fast variable and a slow variable
Figure FDA0003729603950000061
Wherein, X I For a slowly varying set, X II Is a fast variable set, U is a direct-drive permanent magnet synchronous generator node voltage vector, f 1 (X I ,X II U) is an equation of state relating to a slow variable, f 2 (X I ,X II U) is a state equation related to the fast variables, and epsilon is a singular perturbation parameter;
a quasi-steady-state expression determining unit for making singular perturbation parameter epsilon equal to 0, and determining the quasi-steady-state expression of the fast variable as X II ＝h(X I U); wherein, h (X) I U) is a quasi-steady state expression equation of a fast variable;
the order reduction model determining unit is used for determining the order reduction model of the wind turbine generator set under the condition of large disturbance of the wind power grid-connected system by combining the quasi-steady-state expression of the fast variable and the singular perturbation equation
Figure FDA0003729603950000062
Wherein, f 1 (X I ,h(X I U), U) is a wind turbine generator order reduction equation.
CN202210658777.1A 2022-06-13 2022-06-13 Wind turbine generator model order reduction method and system Active CN114744625B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202210658777.1A CN114744625B (en) 2022-06-13 2022-06-13 Wind turbine generator model order reduction method and system

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202210658777.1A CN114744625B (en) 2022-06-13 2022-06-13 Wind turbine generator model order reduction method and system

Publications (2)

Publication Number Publication Date
CN114744625A CN114744625A (en) 2022-07-12
CN114744625B true CN114744625B (en) 2022-08-19

Family

ID=82287977

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202210658777.1A Active CN114744625B (en) 2022-06-13 2022-06-13 Wind turbine generator model order reduction method and system

Country Status (1)

Country Link
CN (1) CN114744625B (en)

Families Citing this family (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115758672B (en) * 2022-10-26 2023-07-28 广东工业大学 Method for constructing power electronic new energy power system reduced order small signal model
CN116070471B (en) * 2023-04-06 2023-06-20 浙江远算科技有限公司 Wind driven generator simulation acceleration method and system based on reduced order decomposition processing
CN117559528A (en) * 2023-11-15 2024-02-13 兰州理工大学 Micro-grid stability domain determining method and system based on micro-grid reduced order model

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111740440A (en) * 2020-06-30 2020-10-02 湖北工业大学 Inter-station coupling discrimination and internal model decoupling control method for flexible direct current transmission system
CN112018783A (en) * 2020-07-27 2020-12-01 华北电力大学 Model reduced order feedback control method for direct-drive fan subsynchronous oscillation suppression

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111740440A (en) * 2020-06-30 2020-10-02 湖北工业大学 Inter-station coupling discrimination and internal model decoupling control method for flexible direct current transmission system
CN112018783A (en) * 2020-07-27 2020-12-01 华北电力大学 Model reduced order feedback control method for direct-drive fan subsynchronous oscillation suppression

Non-Patent Citations (4)

* Cited by examiner, † Cited by third party
Title
Dissipativity-Preserving Model Reduction for Large-Scale Distributed Control Systems;Takayuki Ishizaki 等;《IEEE Transactions on Automatic Control》;20141112;第60卷(第4期);1023-1037 *
Study on linear dynamic model and analysis of operating characteristics of high-power VSCF wind energy conversion system;Dafeng Fu 等;《2009 World Non-Grid-Connected Wind Power and Energy Conference》;20091113;全文 *
基于主导度分析的直驱风电场奇异摄动降阶方法;高本锋 等;《中国电机工程学报》;20220405;第42卷(第7期);2449-2461 *
基于奇异摄动理论的微电网降阶建模方法与对比研究;谈赢杰 等;《电网技术》;20200531;第44卷(第5期);1914-1921 *

Also Published As

Publication number Publication date
CN114744625A (en) 2022-07-12

Similar Documents

Publication Publication Date Title
CN114744625B (en) Wind turbine generator model order reduction method and system
Kakimoto et al. Transient stability analysis of large-scale power system by Lyapunov's direct method
CN108448635B (en) Photovoltaic power generation system asymmetric voltage drop fault ride-through overall process modeling method
CN110135031A (en) Electric power system transient stability calculation method based on half implicit runge kutta method
CN103810646B (en) Improved projection integral algorithm based active power distribution system dynamic simulation method
CN110429648B (en) Small interference stability margin probability evaluation method considering wind speed random fluctuation
CN112149280B (en) Method for obtaining power grid strength of multi-feed-in system of new energy containing SVG
CN107968409A (en) A kind of probability load flow calculation method and system for considering imbalance power distribution
CN104156542A (en) Implicit-projection-based method for simulating stability of active power distribution system
US11569682B2 (en) System and method for a fast power network simulator
Kontis et al. Dynamic equivalencing of active distribution grids
CN113987781A (en) Equipment symbolization modeling facing transient simulation of power system and application method thereof
CN106991229B (en) Wind power plant equivalent modeling method for complex topology
CN113221064B (en) Model processing method, device, computer equipment and storage medium
CN112910006B (en) Universal electromagnetic transient modeling method for direct-drive wind turbine generator
CN111639463B (en) XGboost algorithm-based frequency characteristic prediction method for power system after disturbance
Bian et al. Identification and improvement of probabilistic voltage instability modes of power system with wind power integration
CN115149582A (en) Voltage stability analysis method for photovoltaic grid-connected power system based on monotonic system theory
CN114912300A (en) Rapid time domain simulation method for electric power system
CN104679937B (en) A kind of estimation error and parameter adaptive adjusting method suitable for implicit projection algorithm
CN109842113B (en) Power system simplified equivalence method based on generator group dynamic feature analysis
Sedaghati et al. Transient stability study of power systems with high-order models based on hybridizing loop solving and vector computation
Zou et al. Modeling for large-scale offshore wind farm using multi-thread parallel computing
CN116522043B (en) Short circuit current calculation method and device
CN115102232A (en) Method and system for judging low voltage ride through performance of wind power plant

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant