CN108347058B - Stability judgment method and device for grid-connected subsynchronous oscillation of doubly-fed wind turbine generator - Google Patents

Stability judgment method and device for grid-connected subsynchronous oscillation of doubly-fed wind turbine generator Download PDF

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CN108347058B
CN108347058B CN201711422699.0A CN201711422699A CN108347058B CN 108347058 B CN108347058 B CN 108347058B CN 201711422699 A CN201711422699 A CN 201711422699A CN 108347058 B CN108347058 B CN 108347058B
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doubly
wind turbine
current
fed wind
positive sequence
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CN108347058A (en
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葛维春
张艳军
高凯
葛延峰
李铁
刘凯
钱华东
梁新艳
赵伟华
毕天姝
张鹏
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Beijing Sifang Automation Co Ltd
North China Electric Power University
State Grid Liaoning Electric Power Co Ltd
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Beijing Sifang Automation Co Ltd
North China Electric Power University
State Grid Liaoning Electric Power Co Ltd
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
    • H02J3/386—
    • 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]
    • 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

Abstract

The invention relates to a method and a device for judging the stability of grid-connected subsynchronous oscillation of a doubly-fed wind turbine generator, wherein the method comprises the following steps: setting positive sequence harmonic voltage and positive sequence harmonic current of the stator of the doubly-fed wind turbine generator according to the stator a-phase voltage, the stator a-phase current and the rotor a-phase current of the doubly-fed wind turbine generator; determining an output voltage expression of a current regulation link according to the positive sequence harmonic voltage and the positive sequence harmonic current; establishing a stator side impedance analytical expression of the doubly-fed wind turbine generator according to the positive sequence harmonic voltage, the positive sequence harmonic current and the output voltage expression so as to obtain the side impedance characteristic of the doubly-fed wind turbine generator; establishing a power grid side impedance model to obtain a power grid side impedance characteristic; establishing a characteristic function equation of the side impedance characteristic of the doubly-fed wind turbine generator and the side impedance characteristic of the power grid; and solving a characteristic function equation to quantitatively judge the oscillation frequency and the damping level of the doubly-fed wind turbine generator. According to the method and the device, the oscillation frequency and the damping level can be quantitatively judged.

Description

Stability judgment method and device for grid-connected subsynchronous oscillation of doubly-fed wind turbine generator
Technical Field
The invention relates to the field of analysis of sub-synchronous oscillation of a new energy power system, in particular to a method and a device for judging stability of grid-connected sub-synchronous oscillation of a double-fed wind turbine generator.
Background
doubly-Fed Induction generators (DFIGs) are widely applied as a clean energy power generation technology, and after the DFIGs are incorporated into a power grid, subsynchronous power oscillation occurs under some special working conditions, which seriously threatens the safety of the power grid and the wind turbine, and the accident frequently occurs at home and abroad.
In order to solve the above problems, the following methods have been studied.
The state space analysis method is based on a small signal state space model of the interconnected system in a time domain, and the root track of the model is analyzed, so that the stability of the interconnected system is judged.
The impedance analysis method is characterized in that an interconnection system is simplified into a Thevenin circuit model with an ideal voltage source and a port equivalent impedance connected in series and a Norton circuit model with an ideal current source and a port equivalent impedance connected in parallel, and then stability and stability margin analysis are carried out according to the output impedance relation between interconnection subsystems. This impedance-based analysis method only requires that the equivalent impedance characteristics at both ends of the interconnect system port are known and can be calculated or measured. Compared with the information requirement of a complex state space analysis method, the stability judgment by using the impedance analysis method is simpler and more convenient, and the method is more suitable for controlling a complex wind turbine grid-connected system.
The stability of the interconnection system can be judged by utilizing a Nyquist criterion on the basis of an equivalent impedance model of the three-phase alternating-current interconnection system. The interconnection subsystem can be equivalent to a voltage source subsystem and a current source subsystem respectively, so that the equivalent output impedance of each subsystem and the ratio of the output impedance of the voltage source subsystem to the output impedance of the current source subsystem are obtained. If the output impedance ratio meets the Nyquist criterion, namely the Nyquist curve locus of the output impedance ratio does not bypass a point (-1,0) on the complex plane, the three-phase alternating-current interconnection system is stable; if the Nyquist curve locus of the output impedance ratio is farther from the point (-1,0), the larger the stability margin is, the more difficult the instability is; the closer the parts are to the point (-1,0), the more unstable the parts are, and harmonic resonance is likely to occur at the coupling point of the three-phase ac interconnection system. The existing Nyquist criterion is only suitable for stability analysis of simplified systems (equivalent single-machine infinite systems) and can only give qualitative results (stable or unstable) but not quantitative stability indicators.
Disclosure of Invention
In view of the above, the invention provides a method and a device for judging the stability of grid-connected subsynchronous oscillation of a doubly-fed wind turbine generator.
According to one aspect of the invention, a method for judging the stability of grid-connected subsynchronous oscillation of a doubly-fed wind turbine generator is provided, which comprises the following steps: setting positive sequence harmonic voltage and positive sequence harmonic current of the stator of the doubly-fed wind turbine generator according to the stator a-phase voltage, the stator a-phase current and the rotor a-phase current of the doubly-fed wind turbine generator; determining an output voltage expression of a current regulation link according to the positive sequence harmonic voltage and the positive sequence harmonic current; establishing a side impedance analytical expression of the doubly-fed wind turbine generator according to the positive sequence harmonic voltage, the positive sequence harmonic current and the output voltage expression so as to obtain the side impedance characteristic of the doubly-fed wind turbine generator; establishing a power grid side impedance model to obtain a power grid side impedance characteristic; establishing a characteristic function equation of the side impedance characteristic of the doubly-fed wind turbine generator and the side impedance characteristic of the power grid; and solving the characteristic function equation to quantitatively judge the oscillation frequency and the damping level of the doubly-fed wind turbine generator.
With the above method, in one possible implementation, the stator-a phase voltage, the stator-a phase current, and the rotor-a phase current are determined according to the following equations (1-1), (1-2), and (1-3), respectively,
Figure GDA0002329325140000021
Figure GDA0002329325140000022
Figure GDA0002329325140000023
wherein, Vsa(f) Representing the stator a phase voltage, f representing the frequency,
Figure GDA0002329325140000024
V1representing the positive sequence fundamental voltage amplitude, V, of the point of common couplingpRepresents a voltage magnitude of the positive sequence harmonic voltage,
Figure GDA0002329325140000025
respectively representing the initial phase angles, f, of the corresponding components1、fpRespectively representing the corresponding fundamental frequency and harmonic frequency,
Isa(f) showing the phase a current of the stator,
Figure GDA0002329325140000031
I1representing the positive sequence fundamental current amplitude, I, of the point of common couplingpRepresents the current magnitude of the positive sequence harmonic current,
Figure GDA0002329325140000032
respectively represent the initial phase angles of the corresponding components,
Ira(f) showing the phase a current of the rotor,
Figure GDA0002329325140000033
Ir1、Irprespectively representing the rotor current amplitude corresponding to positive sequence fundamental wave and harmonic wave,
Figure GDA0002329325140000034
respectively representing the initial phase angles, f, of the corresponding componentsrRepresenting the rotor rotation frequency, fsRepresenting slip frequency.
For the above method, in one possible implementation, the output voltage expression is determined according to the following equations (1-4),
Figure GDA0002329325140000035
where v(s) represents the output voltage, s-j 2 pi f, Hri(s) ═ kip + kii/s, kip and kii denote the proportionality and integral coefficients, respectively, of the current regulator, Krd(s) represents the decoupling coefficient in the rotor-side dq control strategy, Vp(s) represents the positive sequence harmonic voltage,
Figure GDA0002329325140000036
HPLL(s) represents the transfer function of a phase locked loop comprising a PI regulator and an integrator, Vr0Representing the magnitude of the steady-state component of the rotor voltage, VdcRepresenting the dc capacitor voltage magnitude.
For the method, in one possible implementation, the doubly-fed wind turbine side impedance analytical expression is established according to the following formula (1-5),
Figure GDA0002329325140000037
wherein Z istp(s) representing the doubly-fed wind turbine side impedance characteristic, LlsIndicating leakage inductance of the stator winding, Ll′rIndicating leakage inductance of the rotor winding, RsRepresenting the resistance of the stator winding, Rr' denotes the resistance of the rotor winding, and σ(s) denotes the rotor slip system of the doubly-fed asynchronous induction generatorThe number of the first and second groups is,
Figure GDA0002329325140000038
representing the equivalent turn ratio, ω, of the stator-side winding to the rotor-side winding of a doubly-fed asynchronous induction generator1Representing the fundamental angular velocity.
For the above method, in one possible implementation, the grid-side impedance model is established according to the following equations (1-6),
Figure GDA0002329325140000041
wherein Z issp(s) represents the grid side impedance characteristic, R represents the equivalent resistance in the grid, L represents the equivalent inductance in the grid, and C represents the equivalent series capacitance in the grid.
For the above method, in one possible implementation, the characteristic function equations of the doubly-fed wind turbine side impedance characteristic and the grid side impedance characteristic are established according to the following equations (1-7),
Zsp(s)+Ztp(s)＝0 (1-7)。
for the method, in a possible implementation manner, solving the characteristic function equation to quantitatively judge the oscillation frequency and the damping level of the doubly-fed wind turbine generator includes:
solving equations (1-7) to obtain the conjugate root λ of the eigenfunction equation1,2＝α±jβ，
The imaginary part β determines the oscillation frequency of the doubly-fed wind turbine, and the real part α determines the damping level of the doubly-fed wind turbine.
According to another aspect of the present invention, there is provided a device for determining stability of grid-connected subsynchronous oscillation of a doubly-fed wind turbine generator, including: the positive sequence harmonic voltage and current setting unit is used for setting the positive sequence harmonic voltage and the positive sequence harmonic current of the stator of the doubly-fed wind turbine generator according to the stator a-phase voltage, the stator a-phase current and the rotor a-phase current of the doubly-fed wind turbine generator; the output voltage expression determining unit is used for determining an output voltage expression of the current regulating link according to the positive sequence harmonic voltage and the positive sequence harmonic current; the stator side impedance analytical expression establishing unit is used for establishing a side impedance analytical expression of the doubly-fed wind turbine generator according to the positive sequence harmonic voltage, the positive sequence harmonic current and the output voltage expression so as to obtain the side impedance characteristic of the doubly-fed wind turbine generator; the power grid side impedance model establishing unit is used for establishing a power grid side impedance model so as to obtain the power grid side impedance characteristic; the characteristic function equation establishing unit is used for establishing a characteristic function equation of the side impedance characteristic of the doubly-fed wind turbine generator and the side impedance characteristic of the power grid; and the oscillation frequency and damping level judging unit is used for solving the characteristic function equation so as to quantitatively judge the oscillation frequency and the damping level of the double-fed wind turbine generator.
With the above arrangement, in one possible implementation, the positive sequence harmonic voltage and current setting unit determines the stator-a phase voltage, the stator-a phase current, and the rotor-a phase current according to the following equations (1-1), (1-2), and (1-3), respectively,
Figure GDA0002329325140000051
Figure GDA0002329325140000052
Figure GDA0002329325140000053
wherein, Vsa(f) Representing the stator a phase voltage, f representing the frequency,
Figure GDA0002329325140000054
V1representing the positive sequence fundamental voltage amplitude, V, of the point of common couplingpRepresents a voltage magnitude of the positive sequence harmonic voltage,
Figure GDA0002329325140000055
respectively representing corresponding componentsInitial phase angle, f1、fpRespectively representing the corresponding fundamental frequency and harmonic frequency,
Isa(f) showing the phase a current of the stator,
Figure GDA0002329325140000056
I1representing the positive sequence fundamental current amplitude, I, of the point of common couplingpRepresents the current magnitude of the positive sequence harmonic current,
Figure GDA0002329325140000057
respectively represent the initial phase angles of the corresponding components,
Ira(f) showing the phase a current of the rotor,
Figure GDA0002329325140000058
Ir1、Irprespectively representing the rotor current amplitude corresponding to positive sequence fundamental wave and harmonic wave,
Figure GDA0002329325140000059
respectively representing the initial phase angles, f, of the corresponding componentsrRepresenting the rotor rotation frequency, fsRepresenting slip frequency.
With the above apparatus, in one possible implementation, the output voltage expression determination unit determines the output voltage expression according to the following equations (1-4),
Figure GDA00023293251400000510
where v(s) represents the output voltage, s-j 2 pi f, Hri(s) ═ kip + kii/s, kip and kii denote the proportionality and integral coefficients, respectively, of the current regulator, Krd(s) represents the decoupling coefficient in the rotor-side dq control strategy, Vp(s) represents the positive sequence harmonic voltage,
Figure GDA00023293251400000511
HPLL(s) represents the transfer function of a phase locked loop comprising a PI regulator and an integrator, Vr0Representing the magnitude of the steady-state component of the rotor voltage, VdcRepresenting the dc capacitor voltage magnitude.
For the above device, in a possible implementation manner, the stator side impedance analytical expression establishing unit establishes the doubly-fed wind turbine generator side impedance analytical expression according to the following formula (1-5),
Figure GDA0002329325140000061
wherein Z istp(s) representing the doubly-fed wind turbine side impedance characteristic, LlsIndicating leakage inductance of the stator winding, Ll′rIndicating leakage inductance of the rotor winding, RsRepresenting the resistance of the stator winding, Rr' represents the resistance of the rotor winding, sigma(s) represents the rotor slip coefficient of the doubly-fed asynchronous induction generator,
Figure GDA0002329325140000062
representing the equivalent turn ratio, ω, of the stator-side winding to the rotor-side winding of a doubly-fed asynchronous induction generator1Representing the fundamental angular velocity.
With the above apparatus, in one possible implementation, the grid-side impedance model establishing unit establishes the grid-side impedance model according to the following equations (1-6),
Figure GDA0002329325140000063
wherein Z issp(s) represents the grid side impedance characteristic, R represents the equivalent resistance in the grid, L represents the equivalent inductance in the grid, and C represents the equivalent series capacitance in the grid.
For the above device, in a possible implementation manner, the characteristic function equation establishing unit establishes characteristic function equations of the doubly-fed wind turbine generator side impedance characteristic and the grid side impedance characteristic according to the following equations (1-7),
Zsp(s)+Ztp(s)＝0 (1-7)。
for the above apparatus, in a possible implementation manner, the oscillation frequency and damping level determining unit is configured to:
solving equations (1-7) to obtain the conjugate root λ of the eigenfunction equation1,2＝α±jβ，
The imaginary part β determines the oscillation frequency of the doubly-fed wind turbine, and the real part α determines the damping level of the doubly-fed wind turbine.
According to the method and the device for judging the stability of the grid-connected subsynchronous oscillation of the doubly-fed wind turbine generator, a detailed generator-end impedance model of the doubly-fed wind turbine generator can be established, the links such as dq/abc coordinate transformation, dq-axis inner and outer loop control, direct-current capacitor voltage change and the like are considered, and the method for quantitatively judging the stability of the grid-connected subsynchronous oscillation of the doubly-fed wind turbine generator is provided based on the characteristic function equation root of the side impedance characteristic of the doubly-fed wind turbine generator and the side impedance characteristic of a power grid, and the oscillation frequency and the damping level can be quantitatively judged.
Other features and aspects of the present invention will become apparent from the following detailed description of exemplary embodiments, which proceeds with reference to the accompanying drawings.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate exemplary embodiments, features, and aspects of the invention and, together with the description, serve to explain the principles of the invention.
Fig. 1 shows a flowchart of a method for determining stability of grid-connected subsynchronous oscillation of a doubly-fed wind turbine generator according to an embodiment of the present invention.
Fig. 2 shows a schematic diagram of the basic structure of a conventional rotor current closed-loop control of a doubly-fed induction wind power plant.
Fig. 3 shows a schematic diagram of grid-tied grid port impedance.
Fig. 4 shows a schematic diagram of a grid-connected equivalent impedance model of a doubly-fed wind turbine.
FIG. 5 shows a schematic diagram of PSCAD/ETMDC-based time-domain simulation calculations.
Fig. 6 shows a schematic diagram of the results of a spectral analysis of a time domain waveform.
Fig. 7 shows a block diagram of a stability determination device for grid-connected subsynchronous oscillation of a doubly-fed wind turbine generator according to an embodiment of the present invention.
Detailed Description
Various exemplary embodiments, features and aspects of the present invention will be described in detail below with reference to the accompanying drawings. In the drawings, like reference numbers can indicate functionally identical or similar elements. While the various aspects of the embodiments are presented in drawings, the drawings are not necessarily drawn to scale unless specifically indicated.
The word "exemplary" is used exclusively herein to mean "serving as an example, embodiment, or illustration. Any embodiment described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments.
Furthermore, in the following detailed description, numerous specific details are set forth in order to provide a better understanding of the present invention. It will be understood by those skilled in the art that the present invention may be practiced without some of these specific details. In some instances, methods, procedures, components, and circuits that are well known to those skilled in the art have not been described in detail so as not to obscure the present invention.
Generally, a stator side of a doubly-fed wind turbine generator is directly connected to a power grid, and a rotor-side converter is used for controlling electric quantities such as torque, power, output current and the like of the stator side, so that the wind turbine generator meets the operation requirement. Therefore, the control of the rotor-side converter has a large influence on the output impedance of the stator-side of the generator. Meanwhile, in order to simplify the impedance modeling process and highlight the focus of attention, the direct-current voltage of the rotor-side converter is assumed to be stable and free of fluctuation, namely the two converters of the double-fed motor are decoupled from each other, and the output voltage is consistent with the command voltage. The impedance modeling of the present invention is performed under this assumption. The main process of the present invention will be described in detail below.
Fig. 1 shows a flowchart of a method for determining stability of grid-connected subsynchronous oscillation of a doubly-fed wind turbine generator according to an embodiment of the present invention. As shown in fig. 1, the method comprises the steps of:
step S100, setting positive sequence harmonic voltage and positive sequence harmonic current of a stator of the doubly-fed wind turbine generator according to a phase voltage of the stator a, phase current of the stator a and phase current of a rotor a of the doubly-fed wind turbine generator;
step S110, determining an output voltage expression of a current regulation link according to the positive sequence harmonic voltage and the positive sequence harmonic current;
step S120, establishing a doubly-fed wind turbine generator side impedance analytical expression according to the positive sequence harmonic voltage, the positive sequence harmonic current and the output voltage expression so as to obtain the doubly-fed wind turbine generator side impedance characteristic;
step S130, establishing a power grid side impedance model to obtain a power grid side impedance characteristic;
step S140, establishing a characteristic function equation of the side impedance characteristic of the double-fed wind turbine generator and the side impedance characteristic of the power grid; and
and S150, solving a characteristic function equation to quantitatively judge the oscillation frequency and the damping level of the doubly-fed wind turbine generator.
First, the basic structure of the doubly-fed wind turbine system is explained.
Fig. 2 shows a schematic diagram of the basic structure of a conventional rotor current closed-loop control of a doubly-fed induction wind power plant. Wherein u issabc＝[usausbusc]T，usa、usb、uscVoltage of a three-phase static coordinate system of the stator abc; i.e. isabc＝[isaisbisc]T，isa、isb、iscIs stator abc three-phase stationary coordinate system current; u. ofsa、usb、uscFor point voltage v of common coupling in grid-side invertera、vb、vc。usdq＝[usdusq]T，usd、usqIs the stator voltage in the synchronously rotating d/q coordinate system; i.e. isdq＝[isdisq]T，isd、isqIs the stator current in a synchronously rotating d/q coordinate system. u. ofrabc＝[uraurburc]T，ura、urb、urcThe voltage in the rotor three-phase coordinate system is used as the reference voltage; i.e. irabc＝[irairbirc]T，ira、irb、ircThe current in a rotor three-phase coordinate system is used as the current; u. ofrdq＝[urdurq]T，urd、urqIs the rotor voltage in the synchronously rotating d/q coordinate system; i.e. irdq＝[irdirq]T，ird、irqThe rotor currents in the d/q coordinate system are rotated synchronously. OmegarIs the rotor angular velocity; thetaPLL、ωPLLThe phase angle of the mains voltage and the angular frequency of the mains voltage.
According to the characteristics of the double-fed wind turbine generator, the following basic circuit relationship of the system under the phase coordinate can be obtained.
Figure GDA0002329325140000091
Figure GDA0002329325140000092
Figure GDA0002329325140000093
Figure GDA0002329325140000094
Wherein psisabc＝[ψsaψsaψsa]T，ψrabc＝[ψraψraψra]T，ψsa、ψsb、ψscAnd psira、ψrb、ψrcThree-phase winding flux linkage, K, for stator and rotor of doubly-fed induction generator respectivelyeIs the ratio of the turns of the stator to the turns of the rotor, Rs、Rr、Lss、Lsr、Lrs、LrrFor the stator and rotor circuit parameters translated to the stator side, and Lss、Lsr、Lrs、LrrFor the stator and rotor of a generatorSelf-inductance and mutual inductance.
Based on the description of the above basic structure, the above steps S100 to S150 will be specifically described below.
For the step S100, the positive sequence harmonic voltage Vp and the positive sequence harmonic current Ip of the stator end stator of the doubly-fed wind turbine generator are set according to the stator a-phase voltage, the stator a-phase current and the rotor a-phase current, and a reference system is established.
Specifically, impedance of the doubly-fed wind turbine is modeled based on a harmonic linearization method, a small disturbance is superimposed on a three-phase generator-side voltage of the wind turbine, output current is calculated, and then generator-side impedance characteristics are obtained through a ratio of the small voltage disturbance to the output current.
When the doubly-fed fan system operates at a given working Point, in order to derive the rotor-side output impedance, a Point of Common Coupling (PCC) voltage is assumed to contain a fundamental positive sequence voltage and a positive sequence harmonic voltage. At this time, in one possible implementation, the expression of the stator a-phase voltage in the frequency domain may be as shown in equation (1-1).
Figure GDA0002329325140000095
In the formula, Vsa(f) The stator a phase voltage, f the frequency,
Figure GDA0002329325140000096
respectively, representing the corresponding frequency impulse components converted from the sinusoidal quantities in the time domain to the frequency domain, which is consistent with the components in the inverter. V1Positive sequence fundamental voltage amplitude, V, for point of common couplingpIs the voltage amplitude of the positive sequence harmonic voltage,
Figure GDA0002329325140000097
initial phase angles, f, of the corresponding components, respectively1、fpRespectively corresponding fundamental frequency and harmonic frequency.
Under the action of the positive sequence harmonic voltage Vp of the stator, the current of the stator generates a positive sequence harmonic current Ip with the same frequency. The expression of the phase a current of the stator in the frequency domain is shown in the formula (1-2).
Figure GDA0002329325140000098
Wherein, Isa(f) For the stator phase a current to be,
Figure GDA0002329325140000099
I1positive sequence fundamental current amplitude, I, for point of common couplingpIs the current magnitude of the positive sequence harmonic current,
Figure GDA0002329325140000101
respectively, the initial phase angles of the corresponding components.
Accordingly, the expression of the rotor a-phase current in the frequency domain can be shown as equation (1-3).
Figure GDA0002329325140000102
Wherein, Ira(f) For the rotor phase a current,
Figure GDA0002329325140000103
Ir1、Irpcorresponding to the rotor current amplitude of positive sequence fundamental wave and harmonic wave,
Figure GDA0002329325140000104
initial phase angles, f, of the corresponding components, respectivelyrIs the rotor rotation frequency, fsIs the slip frequency.
Therefore, the stator a-phase voltage, the stator a-phase current and the rotor a-phase current of the doubly-fed wind turbine generator set can be determined according to the formulas (1-1), (1-2) and (1-3), and therefore the positive sequence harmonic voltage Vp and the positive sequence harmonic current Ip are further set according to the stator a-phase voltage, the stator a-phase current and the rotor a-phase current.
For the step S110, a current regulation element output voltage expression is derived according to the positive sequence harmonic voltage Vp and the positive sequence harmonic current Ip.
Specifically, first, from the positive sequence harmonic voltage Vp and the positive sequence harmonic current Ip on the stator side, a current expression on the rotor side can be derived from the following formula.
Figure GDA0002329325140000105
Figure GDA0002329325140000106
Wherein, Vp(s) is the positive sequence harmonic voltage of the stator, which is a function of the variable s, where s is j2 π f. Further, the following expression holds.
Figure GDA0002329325140000107
Wherein the content of the first and second substances,
Figure GDA0002329325140000108
HPLL(s) represents the transfer function of a phase locked loop comprising a PI regulator and an integrator, and it can be expressed as
Figure GDA0002329325140000109
Wherein k ispp、kpiThe phase-locked loop proportionality coefficient and the integral coefficient are respectively. The angle used by each component of the rotor in converting the coordinate system is thetaPLL-θrWherein thetaPLLIs the phase angle, theta, of the mains voltagerIs the rotor position angle.
And after the d/q control of the rotor side passes through a current regulation link, obtaining an output voltage d/q axis instruction value of the rotor side converter, wherein expressions are shown as formulas (1-15) and (1-16).
Udr＝-Hri(s)ird-Krdirq(1-15)
Uqr＝-Hri(s)irq+Krdird(1-16)
In the formula, Hri(s) kip + kii/s, which is a rotor current regulation transfer function, using Proportional Integral (PI) controlKip and kii are respectively the proportionality coefficient and integral coefficient of the current regulator, KrdIs a decoupling factor in the rotor side dq control strategy.
The command value d/q of the rotor voltage output from the rotor current regulator is then coordinate-converted to the abc phase by the following expression (1-17).
Figure GDA0002329325140000111
Wherein, Ud0、Uq0The direct current steady state value is the direct current steady state value output by the current regulator of the doubly-fed wind turbine generator under the rated working state, and is related to the rated working point of the system.
Wherein:
Figure GDA0002329325140000112
from this, the positive sequence components of the output voltage of the rotor-side converter in the abc phase coordinate system can be finally derived:
Figure GDA0002329325140000113
wherein U can be represented by V(s)ra、UrbAnd UrcA value of any one of them. In addition, Vr0Amplitude of steady-state component of rotor voltage, VdcIs the dc capacitor voltage amplitude (dc bus voltage amplitude).
In addition, in the formula (1-4), the first term component is a positive sequence slip frequency, and mainly plays a role in enabling the doubly-fed wind turbine to output current and power to the outside; the second term is the output voltage harmonic output of the rotor side converter due to the presence of the positive sequence harmonic component, the frequency being the positive sequence harmonic frequency minus the rotational speed, which is related to the phase-locked loop parameters, current loop parameters, nominal operating point, and stator side voltage harmonic component, etc.
Therefore, the output voltage expression of the current regulation link can be deduced through the positive sequence harmonic voltage Vp and the positive sequence harmonic current Ip.
For the step S120, a doubly-fed wind turbine generator side impedance analytical expression (a doubly-fed asynchronous induction generator stator/rotor frequency conversion and impedance analytical expression) may be established according to the positive sequence harmonic voltage Vp, the positive sequence harmonic current Ip, and the output voltage expression v (S) to obtain a doubly-fed wind turbine generator side impedance characteristic.
The specific derivation procedure is set forth below.
Based on the relation between the stator side and the rotor side of the asynchronous induction generator represented by a single phase, the slip coefficient of a generator rotor is as follows:
Figure GDA0002329325140000121
Figure GDA0002329325140000122
wherein isa、isb、iscIs a three-phase current of stator abc, usa、usb、uscIs the stator abc three-phase voltage, ira、irb、ircFor three-phase currents of the rotor ura、urb、urcL for three-phase voltage of rotorlsIs the leakage inductance of the stator winding, Ll′rIs the leakage inductance, R, of the rotor winding after conversionsIs the resistance of the stator winding, Rr' is the converted resistance of the rotor winding, sigma(s) is the rotor slip coefficient of the doubly-fed asynchronous induction generator,
Figure GDA0002329325140000123
the equivalent turn ratio of the stator side winding and the rotor side winding of the induction generator.
Since the rotor-side impedance and the stator-side impedance are connected in parallel, they are uniformly reduced to the stator side. When the doubly-fed wind turbine generator is normally connected to the grid under the rated voltage, if the power grid contains positive sequence voltage harmonics, corresponding positive sequence current harmonics exist at a port, and at the moment, the voltage harmonic ratio current harmonic phasor obtains the positive sequence impedance characteristic (namely, the doubly-fed wind turbine generator side impedance characteristic) under the frequency:
Figure GDA0002329325140000124
wherein Z istp(s) doubly-fed wind turbine side impedance characteristic, LlsIndicating leakage inductance of the stator winding, Ll′rIndicating leakage inductance of the rotor winding, RsRepresenting the resistance of the stator winding, Rr' represents the resistance of the rotor winding, sigma(s) represents the rotor slip coefficient of the doubly-fed asynchronous induction generator,
Figure GDA0002329325140000125
representing the equivalent turn ratio, ω, of the stator-side winding to the rotor-side winding of a doubly-fed asynchronous induction generator1Representing the fundamental angular velocity.
Therefore, by the step S120, the doubly-fed wind turbine side impedance analytical expression can be established to obtain the doubly-fed wind turbine side impedance characteristic Ztp(s)。
For the above step S130, a grid side impedance model is established.
For the sake of generality, the grid side is assumed to be a series fed out system, as shown in fig. 3, which shows a schematic diagram of the grid-tied grid port impedance.
In one possible implementation, the grid-side impedance model may be established according to the following equations (1-6), so as to finally obtain the grid impedance characteristics (i.e., grid-connected grid port impedance characteristics).
Figure GDA0002329325140000131
Wherein Z issp(s) represents the grid side impedance characteristic, R represents the equivalent resistance in the grid, L represents the equivalent inductance in the grid, and C represents the equivalent series capacitance in the grid.
For the above steps S140 and S150, the above equations (1-5) and (1-6) may be used to establish a characteristic function equation, and the root of the characteristic function equation may be solved to implement the stability quantization criterion based on the root of the impedance characteristic function of the stationary coordinate system.
Fig. 4 shows a schematic diagram of a grid-connected equivalent impedance model of a doubly-fed wind turbine. When the doubly-fed wind turbine generator is incorporated into the grid, the grid impedance model is represented by Z, as shown in FIG. 4sp(s) a representation of the grid side impedance characteristics (i.e. the grid is connected with an ideal voltage source series equivalent impedance); the impedance model of the doubly-fed wind turbine generator consists of ZtpAnd(s) represents the doubly-fed wind turbine side impedance characteristic (i.e., the doubly-fed wind turbine side is generally connected with an ideal current source in parallel with an equivalent impedance). In addition, in FIG. 4, an ammeter I is also showns(s) and voltmeter Vs(s) to measure the current I(s) and the voltage V(s). Then, a characteristic function equation is established according to the following equations (1-7).
Zsp(s)+Ztp(s)＝0 (1-7)
Next, in step S150, a stability quantization determination is performed based on the stationary coordinate system impedance characteristic function root.
Specifically, the equations (1-7) are solved to obtain the root of the characteristic function equation, and the stability of the system can be judged according to the root of the characteristic function equation. The specific criterion is as follows:
◆ obtaining the conjugate root of the impedance characteristic equation lambda1,2＝α±jβ；
◆ where the imaginary part β determines the oscillation frequency ω and the real part α determines the oscillation divergence or convergence and damping levels, with the oscillations diverging more rapidly with α greater with α >0 and converging more rapidly with α greater with α < 0.
Therefore, according to the stability judgment method for grid-connected subsynchronous oscillation of the doubly-fed wind turbine generator, a detailed generator-end impedance model of the doubly-fed wind turbine generator can be established, the links such as dq/abc coordinate transformation, dq-axis inner and outer loop control, direct-current capacitor voltage change and the like are considered, and the method for quantitatively judging the grid-connected subsynchronous oscillation stability of the doubly-fed wind turbine generator is provided based on the characteristic function equation root of the side impedance characteristic of the doubly-fed wind turbine generator and the impedance characteristic of the power grid side, and the oscillation frequency and the damping level can be quantitatively judged.
The calculation analysis of the set doubly-fed wind turbine generator is performed by applying the method for quantitatively judging the grid-connected subsynchronous oscillation stability of the doubly-fed wind turbine generator. The parameters of a main circuit, a phase-locked loop and a controller of the doubly-fed wind turbine generator are shown in table 1.
In addition, the output of the doubly-fed wind turbine generator is set to be 1.0 MW. Substituting the basic parameters of the double-fed wind turbine generator into a formula (1-5) to obtain the side impedance characteristic Z of the double-fed wind turbine generatortp(s). Assuming that the equivalent inductance of the grid-connected alternating current power grid is 0.0011H and the series compensation capacitance is 100uF, obtaining the impedance characteristic Z of the power grid sidesp(s). Finally, the impedance characteristic Z of the double-fed wind turbine generator side is measuredtp(s) and grid side impedance characteristics Zsp(s) into Ztp(s)+Zsp(s) 0. calculating the root of the characteristic function equation yields an oscillation frequency ω of 4.1Hz and a damping α of 0.1s-1。
TABLE 1 basic parameters of a doubly-fed wind generator set
Figure GDA0002329325140000141
In order to verify the correctness of the method for quantitatively judging the grid-connected subsynchronous oscillation stability of the doubly-fed wind turbine generator, a time domain simulation model is established on PSCAD software or ETMDC software. Internal circuit parameters and rotor side phase locking and control parameters (namely basic parameters of the doubly-fed wind turbine generator) of the doubly-fed wind turbine generator are consistent with those in table 1. When the output of the fan is 1.0MW, the grid-side inverter and the doubly-fed fan rotor-side converter share a phase-locked loop, and corresponding parameters in the impedance analysis expression refer to phase-locked loop parameters in the table 1. Under the system parameters, simulation is carried out on PSCAD, time domain comparative analysis is carried out, and subsynchronous oscillation can occur due to the fact that a series compensation capacitor with the size of 100uF is put into the PSCAD at the time of 3s through a breaker. FIG. 5 shows a schematic diagram of PSCAD/ETMDC-based time-domain simulation calculations. Among them, fig. 5 (a) shows a time-domain waveform of a current, and fig. 5 (b) shows a time-domain waveform of a power. Fig. 6 shows a schematic diagram of the results of a spectral analysis of a time domain waveform. Among them, fig. 6 (a) shows a spectral analysis of a current, and fig. 6 (b) shows a spectral analysis of a power. From the spectrum analysis of fig. 6, it can be seen that the harmonic component at 3Hz is large, and is basically consistent with the theoretical analysis.
Therefore, the method for quantitatively judging the grid-connected subsynchronous oscillation stability of the doubly-fed wind turbine generator is proper.
Fig. 7 shows a block diagram of a stability determination device for grid-connected subsynchronous oscillation of a doubly-fed wind turbine generator according to an embodiment of the present invention. As shown in fig. 7, the stability determination device 1 for grid-connected subsynchronous oscillation of a doubly-fed wind turbine generator includes: the positive sequence harmonic voltage and current setting unit 10 is used for setting the positive sequence harmonic voltage and the positive sequence harmonic current of the stator of the doubly-fed wind turbine generator according to the stator a-phase voltage, the stator a-phase current and the rotor a-phase current of the doubly-fed wind turbine generator; an output voltage expression determining unit 11, configured to determine an output voltage expression of a current regulation link according to the positive sequence harmonic voltage and the positive sequence harmonic current; the stator side impedance analytical expression establishing unit 12 is configured to establish a side impedance analytical expression of the doubly-fed wind turbine generator according to the positive sequence harmonic voltage, the positive sequence harmonic current, and the output voltage expression, so as to obtain a side impedance characteristic of the doubly-fed wind turbine generator; the power grid side impedance model establishing unit 13 is used for establishing a power grid side impedance model so as to obtain a power grid side impedance characteristic; the characteristic function equation establishing unit 14 is configured to establish a characteristic function equation of the impedance characteristics of the doubly-fed wind turbine generator side and the impedance characteristics of the power grid side; and the oscillation frequency and damping level judging unit 15 is used for solving the characteristic function equation so as to quantitatively judge the oscillation frequency and the damping level of the double-fed wind turbine generator.
In one possible implementation, the positive sequence harmonic voltage and current setting unit 10 determines the stator-a phase voltage, the stator-a phase current, and the rotor-a phase current according to the following equations (1-1), (1-2), and (1-3), respectively,
Figure GDA0002329325140000151
Figure GDA0002329325140000152
Figure GDA0002329325140000153
wherein, Vsa(f) Representing the stator a phase voltage, f representing the frequency,
Figure GDA0002329325140000154
V1representing the positive sequence fundamental voltage amplitude, V, of the point of common couplingpRepresents a voltage magnitude of the positive sequence harmonic voltage,
Figure GDA0002329325140000155
respectively representing the initial phase angles, f, of the corresponding components1、fpRespectively representing the corresponding fundamental frequency and harmonic frequency,
Isa(f) showing the phase a current of the stator,
Figure GDA0002329325140000156
I1representing the positive sequence fundamental current amplitude, I, of the point of common couplingpRepresents the current magnitude of the positive sequence harmonic current,
Figure GDA0002329325140000157
respectively represent the initial phase angles of the corresponding components,
Ira(f) showing the phase a current of the rotor,
Figure GDA0002329325140000158
Ir1、Irprespectively representing the rotor current amplitude corresponding to positive sequence fundamental wave and harmonic wave,
Figure GDA0002329325140000159
respectively representing the initial phase angles, f, of the corresponding componentsrRepresenting the rotor rotation frequency, fsRepresenting slip frequency.
In one possible implementation, the output voltage expression determination unit 11 determines the output voltage expression according to the following formula (1-4),
Figure GDA0002329325140000161
where v(s) represents the output voltage, s-j 2 pi f, Hri(s) ═ kip + kii/s, kip and kii denote the proportionality and integral coefficients, respectively, of the current regulator, Krd(s) represents the decoupling coefficient in the rotor-side dq control strategy, Vp(s) represents the positive sequence harmonic voltage,
Figure GDA0002329325140000162
HPLL(s) represents the transfer function of a phase locked loop comprising a PI regulator and an integrator, Vr0Representing the magnitude of the steady-state component of the rotor voltage, VdcRepresenting the dc capacitor voltage magnitude.
In a possible implementation manner, the stator side impedance analytical expression establishing unit 12 establishes the doubly-fed wind turbine side impedance analytical expression according to the following formulas (1-5),
Figure GDA0002329325140000163
wherein Z istp(s) representing the doubly-fed wind turbine side impedance characteristic, LlsIndicating leakage inductance of the stator winding, Ll′rIndicating leakage inductance of the rotor winding, RsRepresenting the resistance of the stator winding, Rr' represents the resistance of the rotor winding, sigma(s) represents the rotor slip coefficient of the doubly-fed asynchronous induction generator,
Figure GDA0002329325140000164
representing the equivalent turn ratio, ω, of the stator-side winding to the rotor-side winding of a doubly-fed asynchronous induction generator1Representing the fundamental angular velocity.
In one possible implementation, the grid-side impedance model establishing unit 13 establishes the grid-side impedance model according to the following equations (1-6),
Figure GDA0002329325140000165
wherein Z issp(s) represents the grid side impedance characteristic, R represents the equivalent resistance in the grid, L represents the equivalent inductance in the grid, and C represents the equivalent series capacitance in the grid.
In one possible implementation, the characteristic function equation establishing unit 14 establishes characteristic function equations of the doubly-fed wind turbine generator side impedance characteristic and the grid side impedance characteristic according to the following formulas (1-7),
Zsp(s)+Ztp(s)＝0 (1-7)。
in one possible implementation, the oscillation frequency and damping level determination unit 15 is configured to:
solving equations (1-7) to obtain the conjugate root λ of the eigenfunction equation1,2＝α±jβ，
The imaginary part β determines the oscillation frequency of the doubly-fed wind turbine, and the real part α determines the damping level of the doubly-fed wind turbine.
The specific functions and implementation of the stability determination device 1 for grid-connected subsynchronous oscillation of a doubly-fed wind turbine generator according to the embodiment of the present invention are described in the above embodiments, and will not be described in detail here.
Therefore, according to the stability judgment device for grid-connected subsynchronous oscillation of the doubly-fed wind turbine generator, a detailed generator-end impedance model of the doubly-fed wind turbine generator can be established, the links such as dq/abc coordinate transformation, dq-axis inner and outer loop control, direct-current capacitor voltage change and the like are considered, a quantitative judgment method for grid-connected subsynchronous oscillation stability of the doubly-fed wind turbine generator is provided based on a characteristic function equation root of the side impedance characteristic of the doubly-fed wind turbine generator and the side impedance characteristic of a power grid, and the oscillation frequency and the damping level can be quantitatively judged.
Having described embodiments of the present invention, the foregoing description is intended to be exemplary, not exhaustive, and not limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terms used herein were chosen in order to best explain the principles of the embodiments, the practical application, or technical improvements to the techniques in the marketplace, or to enable others of ordinary skill in the art to understand the embodiments disclosed herein.

Claims (12)

1. A method for judging stability of grid-connected subsynchronous oscillation of a doubly-fed wind turbine generator is characterized by comprising the following steps:
setting positive sequence harmonic voltage and positive sequence harmonic current of the stator of the doubly-fed wind turbine generator according to the stator a-phase voltage, the stator a-phase current and the rotor a-phase current of the doubly-fed wind turbine generator;
determining an output voltage expression of a current regulation link according to the positive sequence harmonic voltage and the positive sequence harmonic current;
establishing a side impedance analytical expression of the doubly-fed wind turbine generator according to the positive sequence harmonic voltage, the positive sequence harmonic current and the output voltage expression so as to obtain the side impedance characteristic of the doubly-fed wind turbine generator;
establishing a power grid side impedance model to obtain a power grid side impedance characteristic;
establishing a characteristic function equation of the side impedance characteristic of the doubly-fed wind turbine generator and the side impedance characteristic of the power grid; and
solving the characteristic function equation to quantitatively judge the oscillation frequency and the damping level of the doubly-fed wind turbine generator;
wherein the stator-a phase voltage, the stator-a phase current, and the rotor-a phase current are determined according to the following equations (1-1), (1-2), and (1-3), respectively,
Figure FDA0002329325130000011
Figure FDA0002329325130000012
Figure FDA0002329325130000013
wherein, Vsa(f) Representing the stator a phase voltage, f representing the frequency,
Figure FDA0002329325130000014
V1representing the positive sequence fundamental voltage amplitude, V, of the point of common couplingpRepresents a voltage magnitude of the positive sequence harmonic voltage,
Figure FDA0002329325130000015
respectively representing the initial phase angles, f, of the corresponding components1、fpRespectively representing the corresponding fundamental frequency and harmonic frequency,
Isa(f) showing the phase a current of the stator,
Figure FDA0002329325130000016
I1representing the positive sequence fundamental current amplitude, I, of the point of common couplingpRepresents the current magnitude of the positive sequence harmonic current,
Figure FDA0002329325130000017
respectively represent the initial phase angles of the corresponding components,
Ira(f) showing the phase a current of the rotor,
Figure FDA0002329325130000018
Ir1、Irprespectively representing the rotor current amplitude corresponding to positive sequence fundamental wave and harmonic wave,
Figure FDA0002329325130000019
respectively representing the initial phase angles, f, of the corresponding componentsrRepresenting the rotor rotation frequency, fsRepresenting slip frequency.
2. The method according to claim 1, characterized in that the output voltage expression is determined according to the following equations (1-4),
Figure FDA0002329325130000021
where v(s) represents the output voltage, s-j 2 pi f, Hri(s) ═ kip + kii/s, kip and kii denote the proportionality and integral coefficients, respectively, of the current regulator, Krd(s) represents the decoupling coefficient in the rotor-side dq control strategy, Vp(s) represents the positive sequence harmonic voltage,
Figure FDA0002329325130000022
HPLL(s) represents the transfer function of a phase locked loop comprising a PI regulator and an integrator, Vr0Representing the magnitude of the steady-state component of the rotor voltage, VdcRepresenting the dc capacitor voltage magnitude.
3. The method according to claim 2, characterized in that the doubly-fed wind turbine side impedance analytical expression is established according to the following equations (1-5),
Figure FDA0002329325130000023
wherein Z istp(s) representing the doubly-fed wind turbine side impedance characteristic, LlsIndicating the leakage inductance of the stator winding, L'lrIndicating leakage inductance of the rotor winding, RsDenotes the resistance, R ', of the stator winding'rRepresents the resistance of the rotor winding, sigma(s) represents the rotor slip coefficient of the doubly-fed asynchronous induction generator,
Figure FDA0002329325130000024
representing the equivalent turn ratio, ω, of the stator-side winding to the rotor-side winding of a doubly-fed asynchronous induction generator1Representing the fundamental angular velocity.
4. A method according to claim 3, characterized in that the grid-side impedance model is established according to the following equations (1-6),
Figure FDA0002329325130000025
wherein Z issp(s) represents the grid side impedance characteristic, R represents the equivalent resistance in the grid, L represents the equivalent inductance in the grid, and C represents the equivalent series capacitance in the grid.
5. The method according to claim 4, characterized in that the characteristic function equations of the doubly-fed wind turbine side impedance characteristic and the grid side impedance characteristic are established according to the following equations (1-7),
Zsp(s)+Ztp(s)＝0 (1-7)。
6. the method of claim 5, wherein solving the eigenfunction equation to quantitatively judge the oscillation frequency and the damping level of the doubly-fed wind turbine generator comprises:
solving equations (1-7) to obtain the conjugate root λ of the eigenfunction equation1,2＝α±jβ，
The imaginary part β determines the oscillation frequency of the doubly-fed wind turbine, and the real part α determines the damping level of the doubly-fed wind turbine.
7. The utility model provides a doubly-fed wind turbine generator system's stability of sub-synchronous oscillation that is incorporated into power networks judges device which characterized in that includes:
the positive sequence harmonic voltage and current setting unit is used for setting the positive sequence harmonic voltage and the positive sequence harmonic current of the stator of the doubly-fed wind turbine generator according to the stator a-phase voltage, the stator a-phase current and the rotor a-phase current of the doubly-fed wind turbine generator;
the output voltage expression determining unit is used for determining an output voltage expression of the current regulating link according to the positive sequence harmonic voltage and the positive sequence harmonic current;
the stator side impedance analytical expression establishing unit is used for establishing a side impedance analytical expression of the doubly-fed wind turbine generator according to the positive sequence harmonic voltage, the positive sequence harmonic current and the output voltage expression so as to obtain the side impedance characteristic of the doubly-fed wind turbine generator;
the power grid side impedance model establishing unit is used for establishing a power grid side impedance model so as to obtain the power grid side impedance characteristic;
the characteristic function equation establishing unit is used for establishing a characteristic function equation of the side impedance characteristic of the doubly-fed wind turbine generator and the side impedance characteristic of the power grid; the oscillation frequency and damping level judging unit is used for solving the characteristic function equation so as to quantitatively judge the oscillation frequency and damping level of the double-fed wind turbine generator;
wherein the positive sequence harmonic voltage and current setting unit determines the stator-a phase voltage, the stator-a phase current, and the rotor-a phase current according to the following equations (1-1), (1-2), and (1-3), respectively,
Figure FDA0002329325130000031
Figure FDA0002329325130000032
Figure FDA0002329325130000033
wherein, Vsa(f) Representing the stator a phase voltage, f representing the frequency,
Figure FDA0002329325130000041
V1representing the positive sequence fundamental voltage amplitude, V, of the point of common couplingpRepresents a voltage magnitude of the positive sequence harmonic voltage,
Figure FDA0002329325130000042
respectively representing the initial phase angles, f, of the corresponding components1、fpRespectively representing the corresponding fundamental frequency and harmonic frequency,
Isa(f) showing the phase a current of the stator,
Figure FDA0002329325130000043
I1representing the positive sequence fundamental current amplitude, I, of the point of common couplingpRepresents the current magnitude of the positive sequence harmonic current,
Figure FDA0002329325130000044
respectively represent the initial phase angles of the corresponding components,
Ira(f) showing the phase a current of the rotor,
Figure FDA0002329325130000045
Ir1、Irprespectively representing the rotor current amplitude corresponding to positive sequence fundamental wave and harmonic wave,
Figure FDA0002329325130000046
respectively representing the initial phase angles, f, of the corresponding componentsrRepresenting the rotor rotation frequency, fsRepresenting slip frequency.
8. The apparatus according to claim 7, wherein the output voltage expression determination unit determines the output voltage expression according to the following equations (1-4),
Figure FDA0002329325130000047
where v(s) represents the output voltage, s-j 2 pi f, Hri(s) ═ kip + kii/s, kip and kii denote the proportionality and integral coefficients, respectively, of the current regulator, Krd(s) represents the decoupling coefficient in the rotor-side dq control strategy, Vp(s) represents the positive sequence harmonic voltage,
Figure FDA0002329325130000048
HPLL(s) denotes the transmission of a phase locked loop comprising a PI regulator and an integratorTransfer function, Vr0Representing the magnitude of the steady-state component of the rotor voltage, VdcRepresenting the dc capacitor voltage magnitude.
9. The apparatus of claim 8, wherein the stator side impedance analytical expression establishing unit establishes the doubly-fed wind turbine generator side impedance analytical expression according to the following equations (1-5),
Figure FDA0002329325130000049
wherein Z istp(s) representing the doubly-fed wind turbine side impedance characteristic, LlsIndicating the leakage inductance of the stator winding, L'lrIndicating leakage inductance of the rotor winding, RsDenotes the resistance, R ', of the stator winding'rRepresents the resistance of the rotor winding, sigma(s) represents the rotor slip coefficient of the doubly-fed asynchronous induction generator,
Figure FDA0002329325130000051
representing the equivalent turn ratio, ω, of the stator-side winding to the rotor-side winding of a doubly-fed asynchronous induction generator1Representing the fundamental angular velocity.
10. The apparatus according to claim 9, wherein the grid-side impedance model establishing unit establishes the grid-side impedance model according to the following equations (1-6),
Figure FDA0002329325130000052
wherein Z issp(s) represents the grid side impedance characteristic, R represents the equivalent resistance in the grid, L represents the equivalent inductance in the grid, and C represents the equivalent series capacitance in the grid.
11. The apparatus according to claim 10, wherein the characteristic function equation establishing unit establishes characteristic function equations of the doubly-fed wind turbine side impedance characteristic and the grid side impedance characteristic according to the following equations (1-7),
Zsp(s)+Ztp(s)＝0 (1-7)。
12. the apparatus of claim 11, wherein the oscillation frequency and damping level determination unit is configured to:
solving equations (1-7) to obtain the conjugate root λ of the eigenfunction equation1,2＝α±jβ，
The imaginary part β determines the oscillation frequency of the doubly-fed wind turbine, and the real part α determines the damping level of the doubly-fed wind turbine.
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