CN112217236A - Virtual impedance control method for double-fed wind power grid-connected system under asymmetric fault - Google Patents

Virtual impedance control method for double-fed wind power grid-connected system under asymmetric fault Download PDF

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CN112217236A
CN112217236A CN202011147980.XA CN202011147980A CN112217236A CN 112217236 A CN112217236 A CN 112217236A CN 202011147980 A CN202011147980 A CN 202011147980A CN 112217236 A CN112217236 A CN 112217236A
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power grid
wind power
fed wind
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CN112217236B (en
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宋祉明
李智玲
姚骏
戴建华
黄森
曹斌
陈诗玥
李伟光
孙鹏
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Baotou Power Supply Bureau Of Inner Mongolia Power Group Co ltd
Chongqing University
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Chongqing University
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    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/381Dispersed generators
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00Circuit arrangements for ac mains or ac distribution networks
    • H02J3/001Methods to deal with contingencies, e.g. abnormalities, faults or failures
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00Circuit arrangements for ac mains or ac distribution networks
    • H02J3/01Arrangements for reducing harmonics or ripples
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00Circuit arrangements for ac mains or ac distribution networks
    • H02J3/24Arrangements for preventing or reducing oscillations of power in networks
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2300/00Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/20The dispersed energy generation being of renewable origin
    • H02J2300/28The renewable source being wind energy
    • YGENERAL 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
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02EREDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00Energy generation through renewable energy sources
    • Y02E10/70Wind energy
    • Y02E10/76Power conversion electric or electronic aspects
    • YGENERAL 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
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02EREDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/40Arrangements for reducing harmonics

Abstract

The invention discloses a virtual impedance control method of a double-fed wind power grid-connected system under an asymmetric fault, which is characterized in that the damping level of the system is increased by introducing virtual impedance, which is equivalent to reducing the electrical distance between the double-fed wind power grid-connected system and a fault point and increasing the short-circuit ratio, so that the interaction between high line impedance and a phase-locked loop of the double-fed wind power grid-connected system during the asymmetric short-circuit fault of a power grid is weakened, and the small signal stability of the double-fed wind power grid-connected system during the asymmetric fault is improved. According to the invention, on the basis of not increasing equipment hardware and not changing parameters of an internal controller, the small signal stability of the doubly-fed wind power grid-connected system during the asymmetric fault can be obviously improved by introducing a control strategy based on the virtual impedance.

Description

Virtual impedance control method for double-fed wind power grid-connected system under asymmetric fault
Technical Field
The invention relates to a virtual impedance control method for a double-fed wind power grid-connected system, which is suitable for the double-fed wind power grid-connected system under the asymmetric short-circuit fault of an alternating current power grid.
Background
With the rapid development of renewable energy sources, the installed capacity of wind power is also increasing continuously, but wind power and load are often in a reverse distribution characteristic, and a large wind farm is usually located in a remote area and has weak grid-connected strength. When the weak grid has an asymmetric fault, under the influence of high impedance of a power transmission line, under a typical low voltage ride through control strategy of a wind turbine generator, a double-fed wind power grid-connected system may have small signal instability, and the safe and stable operation capability of the system is seriously influenced. Therefore, the key problem of the current wind power development is to improve the small signal stability of the doubly-fed wind power grid-connected system during the asymmetric fault of the power grid. At present, relevant research performed by scholars at home and abroad mainly aims at analyzing the stability of small interference under a symmetric fault, such as the published following documents:
[1] liu Ju, Yao Wei, Wen Jing Yu, double-fed fan small interference stability analysis and control considering the influence of PLL and access power grid strength [ J ] China Motor engineering reports, 2017,37(11): 3162-.
[2]H.Nian,and B.Pang,“Stability and Power Quality Enhancement Strategy for DFIG System Connected to Harmonic Grid with Parallel Compensation,”IEEE Trans.Energy Conversion,vol.34,no.2,pp.1010-1022,Jun.2019.
The document [1] analyzes that the phase-locked loop oscillation is the main reason causing the small signal instability of the wind power system incorporated into the weak grid from the perspective of the dynamic characteristic of the phase-locked loop by using a characteristic value analysis method. The wind turbine generator damping controller based on the phase compensation principle effectively improves the damping level of a phase-locked loop oscillation mode by improving the phase of the phase-locked loop in an oscillation frequency section of the phase-locked loop, so that the oscillation phenomenon is suppressed. Document [2] analyzes the cause of small-signal instability of the doubly-fed wind power from the perspective of electrical resonance by using an impedance method, and provides a doubly-fed wind power grid-connected system control strategy based on impedance remodeling. None of the above documents address the problem of small signals generated during an asymmetric fault due to the interaction of the controller with high line impedance, and therefore the phase compensated damping controller and impedance reshaping control strategy proposed by the above documents has a limitation in solving the problem of small signal instability during an asymmetric fault.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a virtual impedance control method of a double-fed wind power grid-connected system under an asymmetric fault, and the method can obviously improve the small signal stability margin of the double-fed wind power grid-connected system during the asymmetric fault.
The technical scheme of the invention is realized as follows:
a virtual impedance control method of a double-fed wind power grid-connected system under an asymmetric fault is characterized in that a system damping level is increased by introducing virtual impedance, which is equivalent to reducing the electrical distance between the double-fed wind power grid-connected system and a fault point and increasing a short-circuit ratio, so that the interaction between high line impedance and a phase-locked loop of the double-fed wind power grid-connected system during the asymmetric short-circuit fault of a power grid is weakened, and the small signal stability of the double-fed wind power grid-connected system during the asymmetric fault is improved.
The specific control steps are as follows;
A1) electric powerDuring the asymmetric short circuit fault of the grid, the double-fed wind power grid-connected system adopts a positive sequence phase-locked loop and a negative sequence phase-locked loop to acquire positive sequence components and negative sequence components of the voltage of the grid-connected point, and after virtual impedance is introduced, the positive sequence components and the negative sequence components U of the input voltage of the positive sequence phase-locked loop and the negative sequence phase-locked loop of the double-fed wind power grid-connected system are calculated accordingPv、UNv
Figure BDA0002740262530000021
In the formula of UP、UNThe positive and negative sequence components of the grid-connected point voltage; i isPg、INgThe positive sequence component and the negative sequence component of the current output to the power grid by the double-fed wind power grid-connected system during the asymmetric fault period; zPv、ZNvAre virtual impedance positive and negative sequence components;
A2) calculating the positive and negative sequence components Z of the virtual impedance of the doubly-fed wind power grid-connected system according to the following formulaPv、ZNv
Figure BDA0002740262530000022
Wherein R isPv=RNv=RL,RLThe line resistance value from the grid-connected point to the fault point; s is a laplace operator;
Figure BDA0002740262530000023
ω0is the resonant frequency, LLThe line inductance value from the grid-connected point to the fault point;
A3) on the basis of the step A1) and the step A2), when the power grid has the asymmetric short-circuit fault, the U is connectedPv、UNvInputting the virtual impedance Z into a phase-locked loop of a doubly-fed wind power grid-connected systemPv、ZNvDouble-fed wind power grid-connected system is introduced, and positive and negative sequence remodeling impedance Z of double-fed wind power grid-connected systemDFIG_PNvThe following formula is satisfied:
Figure BDA0002740262530000024
the virtual impedance control of the doubly-fed wind power grid-connected system during the asymmetric fault is realized, so that the small interference stability of the system during the asymmetric fault is improved; the remodelling impedance satisfies the following equation:
Figure BDA0002740262530000031
wherein, each element of the remolding impedance matrix is respectively:
Figure BDA0002740262530000032
Figure BDA0002740262530000033
Figure BDA0002740262530000034
Figure BDA0002740262530000035
Figure BDA0002740262530000036
Figure BDA0002740262530000041
wherein
Figure BDA0002740262530000042
Figure BDA0002740262530000043
NP(s)=GNPLL(s)GNPLL(s±j4πf1);
Figure BDA0002740262530000044
NN(s)=GPPLL(s)GPPLL(s±j4πf1);GPPLL、GNPLLRespectively the transfer functions between the positive and negative sequence phase-locked loop voltage and the output angle; i is1、I2Respectively are positive sequence fundamental frequency components and negative sequence fundamental frequency components of the output current of the doubly-fed wind power system; i1L is the corresponding fundamental frequency positive sequence current amplitude; i is* 1、I* 2Is I1、I2The conjugate component of (a); hi(s) is the transfer function of the current loop controller; f. of1=50Hz;
Figure BDA0002740262530000045
Is the angle between the positive sequence fundamental frequency voltage and the fundamental frequency current; u shape1、U2Respectively corresponding positive and negative sequence components of the fundamental frequency voltage; i U1|、|U2L is respectively the corresponding fundamental frequency positive and negative sequence voltage amplitudes; u shape* 1、U* 2Is U1、U2The conjugate component of (a); u shapeP、UNRespectively positive and negative sequence components of the grid-connected point voltage; i isP、INIs the current positive and negative sequence harmonic components; l isa、Lb、LcThe filter inductor is a filter inductor of the network side converter; kdqIs a cross decoupling coefficient; a ═ ej2/3π(ii) a j is the imaginary unit.
Compared with the prior art, the invention has the following beneficial effects:
on the basis of not increasing equipment hardware and not changing parameters of an internal controller, the method is equivalent to reducing the electrical distance between the wind power system and a fault point, increasing the short-circuit ratio, equivalently enhancing the power grid strength, weakening the interaction of high line impedance and a phase-locked loop of the double-fed wind power grid-connected system during the asymmetric short-circuit fault of the power grid and remarkably improving the small-signal stability of the double-fed wind power grid-connected system during the asymmetric fault by introducing a control strategy based on virtual impedance.
Drawings
Fig. 1 is a schematic structural diagram of a doubly-fed wind power grid-connected system after impedance is reshaped.
FIG. 2 is a diagram of a decoupled double-synchronous positive and negative sequence phase-locked loop topology.
Fig. 3 is a simulation waveform diagram of a double-phase short circuit ground fault occurring in the power grid, the voltage of the power grid drops to 0.2pu, and the double-fed wind power grid-connected system respectively adopts a traditional control method and an impedance remodeling control method.
Detailed Description
The following detailed description of specific embodiments of the invention refers to the accompanying drawings.
Fig. 1 is a schematic structural diagram of a 2MW doubly-fed wind power grid-connected system after impedance is reshaped. FIG. 2 is a diagram of a decoupled double-synchronous positive and negative sequence phase-locked loop topology.
According to the invention, the system damping level is increased by introducing the virtual impedance, which is equivalent to reducing the electrical distance between the double-fed wind power grid-connected system and a fault point, and increasing the short-circuit ratio, so that the interaction between the high line impedance of the double-fed wind power grid-connected system and a phase-locked loop during the asymmetric short-circuit fault of a power grid is weakened, and the small-signal stability of the double-fed wind power grid-connected system during the asymmetric fault is improved.
The specific implementation steps are as follows:
A1) during the asymmetric short circuit fault of the power grid, the double-fed wind power grid-connected system adopts a positive sequence phase-locked loop and a negative sequence phase-locked loop to acquire positive sequence components and negative sequence components of the voltage of a grid-connected point, and after virtual impedance is introduced, the positive sequence components and the negative sequence components U of the input voltage of the positive sequence phase-locked loop and the negative sequence phase-locked loop of the double-fed wind power grid-connected system are calculatedPv、UNv
Figure BDA0002740262530000051
In the formula of UP、UNThe positive and negative sequence components of the grid-connected point voltage; i isPg、INgThe positive sequence component and the negative sequence component of the current output to the power grid by the double-fed wind power grid-connected system during the asymmetric fault period; zPv、ZNvAre virtual impedance positive and negative sequence components;
A2) push buttonVirtual impedance positive and negative sequence components Z of doubly-fed wind power grid-connected system are calculated through following formulaPv、ZNv
Figure BDA0002740262530000052
Wherein R isPv=RNv=RL,RLThe line resistance value from the grid-connected point to the fault point; s is a laplace operator;
Figure BDA0002740262530000053
ω0is the resonant frequency, LLThe line inductance value from the grid-connected point to the fault point;
A3) on the basis of the step A1) and the step A2), when the power grid has the asymmetric short-circuit fault, the U is connectedPv、UNvInputting the virtual impedance Z into a phase-locked loop of a doubly-fed wind power grid-connected systemPv、ZNvDouble-fed wind power grid-connected system is introduced, and positive and negative sequence remodeling impedance Z of double-fed wind power grid-connected systemDFIG_PNvThe following formula is satisfied:
Figure BDA0002740262530000054
the virtual impedance control of the double-fed wind power grid-connected system during the asymmetric fault can be realized, so that the small interference stability of the system during the asymmetric fault is improved. The remodelling impedance satisfies the following equation:
Figure BDA0002740262530000061
wherein, each element of the remolding impedance matrix is respectively:
Figure BDA0002740262530000062
Figure BDA0002740262530000063
Figure BDA0002740262530000064
Figure BDA0002740262530000065
Figure BDA0002740262530000066
Figure BDA0002740262530000071
wherein
Figure BDA0002740262530000072
Figure BDA0002740262530000075
NP(s)=GNPLL(s)GNPLL(s±j4πf1);
Figure BDA0002740262530000073
NN(s)=GPPLL(s)GPPLL(s±j4πf1);GPPLL、GNPLLRespectively the transfer functions between the positive and negative sequence phase-locked loop voltage and the output angle; i is1、I2Respectively are positive sequence fundamental frequency components and negative sequence fundamental frequency components of the output current of the doubly-fed wind power system; i1L is the corresponding fundamental frequency positive sequence current amplitude; i is* 1、I* 2Is I1、I2The conjugate component of (a); hi(s) is the transfer function of the current loop controller; f. of1=50Hz;
Figure BDA0002740262530000074
Is the angle between the positive sequence fundamental frequency voltage and the fundamental frequency current; u shape1、U2Respectively corresponding positive and negative sequence components of the fundamental frequency voltage; i U1|、|U2L is respectively the corresponding fundamental frequency positive and negative sequence voltage amplitudes; u shape* 1、U* 2Is U1、U2The conjugate component of (a); u shapeP、UNRespectively positive and negative sequence components of the grid-connected point voltage; i isP、INIs the current positive and negative sequence harmonic components; l isa、Lb、LcThe filter inductor is a filter inductor of the network side converter; kdqIs a cross decoupling coefficient; a ═ ej2/3π(ii) a j is the imaginary unit.
Description of the effects of the invention:
fig. 3 shows a simulation waveform diagram of A, B two-phase voltage dropping to 0.2pu, using the conventional control strategy and the virtual impedance control strategy proposed by the present invention, respectively. Wherein, two-phase asymmetric short circuit fault occurs in the power grid at the moment of 1s, 1 s-2 s are the fault duration, and U isabcIs a grid-connected point three-phase voltage. It can be known from fig. three (a) that when the doubly-fed wind power system adopts the conventional low-voltage control strategy, it can be seen that the system has a small-interference instability phenomenon at this time, the oscillation amplitudes of the positive and negative sequence components of the voltage and current of the grid-connected point are continuously increased, and meanwhile, it can be seen from the result of Fast Fourier Transform (FFT) analysis that the system has a frequency coupling phenomenon, the Harmonic Distortion rate (THD) of the voltage of the grid-connected point reaches 11.21%, and the voltage waveform Distortion is serious. As can be seen from the third (b) of the figure, after the virtual impedance control strategy provided by the invention is adopted by the doubly-fed wind power system, the small-interference stability of the doubly-fed system is remarkably improved, the oscillation amplitude of the system is remarkably reduced, corresponding harmonic components in the voltage are all suppressed, and the THD is only 2.31%.
Therefore, the virtual impedance control method of the double-fed wind power grid-connected system can improve the low-voltage ride through capability of the double-fed wind power system during the asymmetric fault period and enhance the safe and stable operation capability of a power grid. Finally, it should be noted that the above-mentioned examples of the present invention are only examples for illustrating the present invention, and are not intended to limit the embodiments of the present invention. Although the present invention has been described in detail with reference to preferred embodiments, it will be apparent to those skilled in the art that other variations and modifications can be made based on the above description. Not all embodiments are exhaustive. All obvious changes and modifications of the present invention are within the scope of the present invention.

Claims (2)

1. A virtual impedance control method of a double-fed wind power grid-connected system under an asymmetric fault is characterized by comprising the following steps: the damping level of the system is increased by introducing the virtual impedance, which is equivalent to reducing the electrical distance between a double-fed wind power grid-connected system and a fault point, and increasing the short-circuit ratio, so that the interaction between the high line impedance of the double-fed wind power grid-connected system and a phase-locked loop during the asymmetric short-circuit fault of a power grid is weakened, and the small-signal stability of the double-fed wind power grid-connected system during the asymmetric fault is improved.
2. The method for controlling the virtual impedance of the doubly-fed wind power grid-connected system under the asymmetric fault according to claim 1, is characterized in that: the specific control steps are as follows;
A1) during the asymmetric short circuit fault of the power grid, the double-fed wind power grid-connected system adopts a positive sequence phase-locked loop and a negative sequence phase-locked loop to acquire positive sequence components and negative sequence components of the voltage of a grid-connected point, and after virtual impedance is introduced, the positive sequence components and the negative sequence components U of the input voltage of the positive sequence phase-locked loop and the negative sequence phase-locked loop of the double-fed wind power grid-connected system are calculatedPv、UNv
Figure FDA0002740262520000011
In the formula of UP、UNThe positive and negative sequence components of the grid-connected point voltage; i isPg、INgThe positive sequence component and the negative sequence component of the current output to the power grid by the double-fed wind power grid-connected system during the asymmetric fault period; zPv、ZNvAre virtual impedance positive and negative sequence components;
A2) calculating virtual resistance of doubly-fed wind power grid-connected system according to formulaResistance to positive and negative sequence components ZPv、ZNv
Figure FDA0002740262520000012
Wherein R isPv=RNv=RL,RLThe line resistance value from the grid-connected point to the fault point; s is a laplace operator;
Figure FDA0002740262520000013
ω0is the resonant frequency, LLThe line inductance value from the grid-connected point to the fault point;
A3) on the basis of the step A1) and the step A2), when the power grid has the asymmetric short-circuit fault, the U is connectedPv、UNvInputting the virtual impedance Z into a phase-locked loop of a doubly-fed wind power grid-connected systemPv、ZNvDouble-fed wind power grid-connected system is introduced, and positive and negative sequence remodeling impedance Z of double-fed wind power grid-connected systemDFIG_PNvThe following formula is satisfied:
Figure FDA0002740262520000014
the virtual impedance control of the doubly-fed wind power grid-connected system during the asymmetric fault is realized, so that the small interference stability of the system during the asymmetric fault is improved; the remodelling impedance satisfies the following equation:
Figure FDA0002740262520000021
wherein, each element of the remolding impedance matrix is respectively:
Figure FDA0002740262520000022
Figure FDA0002740262520000023
Figure FDA0002740262520000024
Figure FDA0002740262520000025
Figure FDA0002740262520000026
Figure FDA0002740262520000031
wherein
Figure FDA0002740262520000032
Figure FDA0002740262520000033
NN(s)=GPPLL(s)GPPLL(s±j4πf1);GPPLL、GNPLLRespectively the transfer functions between the positive and negative sequence phase-locked loop voltage and the output angle; i is1、I2Respectively are positive sequence fundamental frequency components and negative sequence fundamental frequency components of the output current of the doubly-fed wind power system; i1L is the corresponding fundamental frequency positive sequence current amplitude; i is* 1、I* 2Is I1、I2The conjugate component of (a); hi(s) is the transfer function of the current loop controller; f. of1=50Hz;
Figure FDA0002740262520000034
Is a positive sequence fundamental frequencyThe angle between the voltage and the fundamental current; u shape1、U2Respectively corresponding positive and negative sequence components of the fundamental frequency voltage; i U1|、|U2L is respectively the corresponding fundamental frequency positive and negative sequence voltage amplitudes; u shape* 1、U* 2Is U1、U2The conjugate component of (a); u shapeP、UNRespectively positive and negative sequence components of the grid-connected point voltage; i isP、INIs the current positive and negative sequence harmonic components; l isa、Lb、LcThe filter inductor is a filter inductor of the network side converter; kdqIs a cross decoupling coefficient; a ═ ej2/3π(ii) a j is the imaginary unit.
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CN113162120A (en) * 2021-05-31 2021-07-23 重庆大学 Wind power grid-connected system transient stability control method based on automatic virtual resistance compensation
CN113162120B (en) * 2021-05-31 2022-11-01 重庆大学 Wind power grid-connected system transient stability control method based on automatic virtual resistance compensation
CN115173409A (en) * 2022-07-27 2022-10-11 重庆大学 Asymmetric low-voltage ride-through control strategy of double-fed wind generating set based on improved phase-locked loop
CN115207912A (en) * 2022-07-27 2022-10-18 重庆大学 Small signal stability enhancement control strategy for grid-connected converter under weak grid asymmetric voltage drop fault
CN115173409B (en) * 2022-07-27 2024-03-26 重庆大学 Asymmetric low-voltage ride-through control strategy of doubly-fed wind generator set based on improved phase-locked loop
CN115207912B (en) * 2022-07-27 2024-03-29 重庆大学 Small signal stability enhancement control strategy for grid-connected converter under asymmetric voltage drop fault of weak power grid
CN115395569A (en) * 2022-09-16 2022-11-25 山东大学 Method and system for controlling asymmetric fault of double-fed fan based on equivalent negative sequence reactance

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