CN110380432B - Sub-synchronous oscillation suppression method and system for direct-drive wind power plant - Google Patents
Sub-synchronous oscillation suppression method and system for direct-drive wind power plant Download PDFInfo
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Abstract
The invention relates to a method and a system for restraining subsynchronous oscillation of a direct-drive wind power plant, belongs to the technical field of wind power integration, and solves the problem of unstable performance of the wind power plant caused by the fact that the prior art fails to perform collaborative optimization on all fan parameters in the wind power plant. The method comprises the following steps: collecting operation data of a direct-drive wind power plant grid-connected system under power grid disturbance; obtaining subsynchronous oscillation quantization criterion according to a response process of a direct-drive wind power plant grid-connected system under power grid disturbance and a subsynchronous oscillation divergence mechanism of the direct-drive wind power plant, judging the subsynchronous oscillation quantization criterion according to the operation data, and judging whether subsynchronous oscillation occurs; and if subsynchronous oscillation is judged to occur, establishing a multi-objective multi-constraint minimum optimization model, and performing collaborative optimization on the PI parameters of a phase-locked loop and a converter in the direct-drive wind power plant grid-connected system so as to suppress the subsynchronous oscillation. The method realizes the cooperative optimization of all the fans of the wind power plant, and further effectively inhibits subsynchronous oscillation.
Description
Technical Field
The invention relates to the technical field of wind power grid connection, in particular to a method and a system for restraining subsynchronous oscillation of a direct-driven wind power plant.
Background
With the continuous expansion of the wind power access scale and density, the problem of subsynchronous oscillation related to a wind power plant in a power system occurs more and more frequently, and even the safe and stable operation of the power system is seriously threatened, so that the subsynchronous oscillation becomes an important factor for restricting the development of wind power. At present, an effective inhibition measure is needed to solve the stability problem caused by the wind power system being incorporated into the power system.
Since 2009 a double-fed wind power plant in texas in usa has attracted attention due to subsynchronous oscillation, scholars at home and abroad propose various subsynchronous oscillation suppression measures which can be divided into passive suppression measures and active suppression measures in principle, wherein the active suppression measures are further divided into three types, namely optimizing controller parameters, changing controller structures and adding suppression devices.
However, the suppression measures are all to realize the suppression of subsynchronous oscillation by adjusting the control parameter of one wind turbine, that is, parameter optimization is performed on a single wind turbine, and collaborative optimization of parameters of all wind turbines in a wind power plant is not involved. However, in actual operation, the generated subsynchronous oscillation is under the combined action of all the fans of the wind power plant, and the adjustment of the parameter of only one fan is insufficient, so that the phenomenon that the adjustment amplitude is insufficient or the loss of the adjustment amplitude is caused easily is generated.
Disclosure of Invention
In view of the foregoing analysis, the embodiment of the present invention aims to provide a method and a system for suppressing subsynchronous oscillation of a direct-drive wind farm, so as to solve the problem that in the prior art, the performance of the wind farm is unstable due to failure of collaborative optimization of all fan parameters in the wind farm.
On one hand, the embodiment of the invention provides a method for suppressing subsynchronous oscillation of a direct-drive wind power plant, which comprises the following steps:
collecting operation data of a direct-drive wind power plant grid-connected system under power grid disturbance;
obtaining subsynchronous oscillation quantization criterion according to a response process of a direct-drive wind power plant grid-connected system under power grid disturbance and a subsynchronous oscillation divergence mechanism of the direct-drive wind power plant, judging the subsynchronous oscillation quantization criterion according to the operation data, and judging whether subsynchronous oscillation occurs;
and if subsynchronous oscillation is judged to occur, establishing a multi-objective multi-constraint minimum optimization model, and performing collaborative optimization on the PI parameters of a phase-locked loop and a converter in the direct-drive wind power plant grid-connected system so as to suppress the subsynchronous oscillation.
The beneficial effects of the above technical scheme are as follows: in the existing research, parameter optimization is carried out on a single wind turbine generator, and parameter collaborative optimization on all fans in a wind power plant is not involved. However, in actual operation, the generated subsynchronous oscillation is due to the combined action of all the fans of the wind power plant, and the adjustment of the parameter of one fan is not enough, which easily causes the phenomenon of insufficient adjustment amplitude or the phenomenon of considering the loss of the adjustment amplitude. Therefore, the application aims at the control parameters of all the fans in the wind field to be optimized in a coordinated mode, and the control parameters are not limited to one fan. A large number of experiments prove that the technical scheme can correctly and effectively carry out cooperative optimization on all fan parameters in the wind power plant and effectively inhibit the subsynchronous oscillation of the direct-drive wind power plant.
Based on further improvement of the method, the operation data of the direct-drive wind power plant grid-connected system comprises the following steps: phase angles of voltage phasor U at the outlet of the fan, useful work P at the outlet of the fan, useless work Q at the outlet of the fan and voltage phasor U at the outlet of the fan;
the phase-locked loop and converter PI parameters comprise: proportional gain coefficient k of phase-locked looppIntegral gain coefficient kiCurrent inner loop proportional gain coefficient K of grid-side converterp1Integral gain coefficient Ki1。
The beneficial effects of the above further improved scheme are: the method fully considers the control parameters (namely the PI parameters of the converter) of the phase-locked loop and the network side converter which influence the subsynchronous oscillation, and simultaneously omits the control parameters of the outer rings of the machine side converter and the network side converter which do not influence the subsynchronous oscillation, thereby reducing the cooperative optimization operation amount on the whole and improving the operation speed. A large number of experiments prove that the subsynchronous oscillation of the direct-drive wind power plant can be effectively inhibited.
Further, determining whether subsynchronous oscillation occurs, further comprising the steps of:
according to a response process of a direct-drive wind power plant grid-connected system under power grid disturbance and a direct-drive wind power plant subsynchronous oscillation divergence mechanism, obtaining an amplitude criterion and a phase angle criterion of subsynchronous oscillation at a fan outlet;
carrying out harmonic decomposition on voltage phasor U at the outlet of the fan to obtain amplitude U of a fundamental frequency signal0Frequency f0Initial phase angleAnd the amplitude u of the disturbance componentsFrequency fsInitial phase
According to the proportional gain coefficient k of a phase-locked loop in a direct-drive wind power plant grid-connected systempAnd integral gain coefficient kiIn combination with f obtained as described above0、fs、usThe amplitude A and the initial phase of the phase angle disturbance component are obtained by the following formula
Wherein
M=ki-(ω0-ωs),N=kp-(ω0-ωs)
ω0=2πf0,ωs=2πfs
The amplitude A and the initial phase of the obtained disturbance componentSubstituting the amplitude criterion and the phase angle criterion to judge whether subsynchronous oscillation occurs; and judging that subsynchronous oscillation occurs if any one of the amplitude criterion and the phase angle criterion is established, otherwise, judging that subsynchronous oscillation does not occur.
The beneficial effects of the above further improved scheme are: the transient response process of the phase-locked loop under the power grid disturbance and the proportional gain coefficient k of the phase-locked loop are fully consideredpAnd integral gain coefficient kiFor the influence of subsynchronous oscillation, the accurate amplitude and phase angle criterion of subsynchronous oscillation at the fan outlet can be obtained.
Further, the amplitude criterion of subsynchronous oscillation at the outlet of the fan is
Wherein
Wherein t is time, Kp1、Ki1Respectively a current inner loop proportional gain coefficient and an integral gain coefficient of the grid-side converter, wherein L is a line reactance;
the phase angle criterion of subsynchronous oscillation at the outlet of the fan is
Wherein
The beneficial effects of the above further improved scheme are: the amplitude criterion and the phase angle criterion are a set of effective criteria summarized by the inventor through a large number of tests, and the criterion is simple and feasible and can accurately and effectively judge whether subsynchronous oscillation occurs. And the stability degree of the system can be further judged according to the phase angle criterion, specifically, the smaller the gamma which meets the phase angle criterion is, the more serious the subsynchronous oscillation of the system is, otherwise, the larger the gamma which does not meet the phase angle criterion is, the higher the stability degree of the system is.
Further, the multi-objective multi-constraint minimum optimization model comprises: optimizing an objective function of wind power plant parameters and optimizing constraint conditions of the wind power plant parameters; wherein the content of the first and second substances,
the wind power plant parameter optimization objective function is
f(lect,K)=min{w1,w2,…wn}
In the formula IectFor excitation parameters, K is an operating parameter, { w }1,w2,…wnEach element in the set represents the dissipated energy of a fan corresponding to the wind power plant; the excitation parameter comprises wind speed; the operation parameters comprise voltage phasor U at the outlet of the fan, useful work P at the outlet of the fan, useless work Q at the outlet of the fan, phase angle of the voltage phasor U at the outlet of the fan and fundamental frequency f0And disturbance component frequency fs;
The wind power plant parameter optimization constraint condition is
In the formula, PiFor useful work of the ith fan, PwfThe total useful work output for the wind field; h is system variable including voltage phasor U at outlet of fan, useful work P at outlet of fan, useless work Q at outlet of fan, phase angle of voltage phasor U at outlet of fan and frequency f of fundamental frequency signal0Frequency f of the disturbance components;hmax、hminUpper and lower limits for system variables; k is a control variable to be adjusted and comprises a phase-locked loop proportional gain coefficient KpIntegral gain coefficient kiCurrent inner loop proportional gain coefficient K of grid-side converterp1Integral gain coefficient Ki1;Kmax、KminThe upper and lower limits of the control variable.
The beneficial effects of the above further improved scheme are: compared with the prior art that only the parameter of one fan is optimized, the technical scheme is that the control parameters (phase-locked loop and converter PI parameters) of all the fans in the wind power plant are cooperatively optimized, so that the output total dissipated energy and the dissipated energy of each fan are minimized, the system stability is improved, the oscillation can be quickly inhibited, and the practical application value is high.
Further, the cooperative optimization of the phase-locked loop and the converter PI parameter in the direct-drive wind power plant grid-connected system further comprises the following steps:
establishing a decision set by taking a control variable to be adjusted as a set element;
obtaining a decision set initial value, and judging whether the wind power plant parameter optimization constraint condition is met; if the wind power plant parameter optimization constraint condition is not met, changing the initial value of the decision set according to a preset rule, judging again, and obtaining all decision set values meeting the wind power plant parameter optimization constraint condition;
optimizing objective function according to wind power plant parameters and optimizing constraints of wind power plant parametersThe conditions are established as follows for a generalized objective function Li
Li=F(wi)+λ∑G
Wherein
∑G=[max{0,h-hmax}]2+[max{0,-h+hmin}]2+[max{0,K-Kmax}]2+
[max{0,-K+Kmin}]2+[max{0,γc+γ}]2+[max{0,-γ+γc}]2
In the formula, lambda is a penalty factor, k is a decreasing coefficient, n is the iteration number, a1Is a lagrange multiplier;
and sequentially inputting all decision set values meeting the optimization constraint conditions of the parameters of the wind power plant into the generalized objective function to obtain a decision set corresponding value which enables the generalized objective function to be minimum, and using the decision set corresponding value as the PI parameters of the phase-locked loop and the converter to be solved.
The beneficial effects of the above further improved scheme are: a penalty function (a part lambda sigma G where a penalty factor is located) is introduced into the generalized objective function so as to solve the problem that constraint conditions are difficult to process in the multi-objective optimization problem, and an accurate optimization result can be obtained through rapid convergence. Moreover, the method can be realized through programming design without manual intervention, and has a series of advantages of simplicity, intuition, easy realization and the like.
On the other hand, the embodiment of the invention provides a direct-drive wind power plant subsynchronous oscillation suppression system, which comprises:
the data acquisition module is used for acquiring the operation data of the direct-drive wind power plant grid-connected system under the power grid disturbance and respectively transmitting the acquired operation data to the damping analysis module and the parameter optimization module;
the damping analysis module is used for obtaining subsynchronous oscillation quantization criteria according to a response process of a direct-drive wind power plant grid-connected system under power grid disturbance and a subsynchronous oscillation divergence mechanism of the direct-drive wind power plant, judging whether subsynchronous oscillation occurs or not according to the operation data, and transmitting a judgment result to the parameter optimization module;
and the parameter optimization module is used for establishing a multi-target multi-constraint minimum optimization model when the judgment result is that subsynchronous oscillation occurs, and performing collaborative optimization on the PI parameters of the phase-locked loop and the converter in the direct-drive wind power plant grid-connected system by combining the operation data.
The beneficial effects of the above technical scheme are: in the operation of a direct-drive wind power plant grid-connected system, the generated subsynchronous oscillation is due to the combined action of all fans in the wind power plant, and the subsynchronous oscillation cannot be effectively inhibited by only adjusting the parameter of one fan in the prior art, so that the phenomenon that the adjustment amplitude is insufficient or the loss of the subsynchronous oscillation is caused easily. Therefore, the technical scheme carries out cooperative optimization on the control parameters of all the fans in the wind field, is not limited to one fan, and can effectively inhibit the subsynchronous oscillation adverse effect generated after a direct-drive wind power plant is connected into a power grid through a large number of tests.
Based on a further improvement of the above system, the damping analysis module further comprises:
a harmonic decomposition module for carrying out harmonic decomposition on the voltage phasor U at the outlet of the fan to obtain the frequency f of the fundamental frequency signal0And the amplitude u of the disturbance componentsFrequency fsInitial phaseTransmitting the obtained result to a disturbance component analysis module;
a disturbance component analysis module for analyzing the proportional gain coefficient k of the phase-locked loop in the direct-drive wind power plant grid-connected systempAnd integral gain coefficient kiIn combination with f obtained as described above0、fs、usThe amplitude A and the initial phase of the phase angle disturbance component are obtained by the following formulaA and A are addedTransmitting to a subsynchronous oscillation judging module
Wherein
M=ki-(ω0-ωs),N=kp-(ω0-ωs)
ω0=2πf0,ωs=2πfs
The subsynchronous oscillation judging module is used for obtaining an amplitude criterion and a phase angle criterion of subsynchronous oscillation at the outlet of the fan according to the response process of a direct-drive wind power plant grid-connected system under power grid disturbance and a subsynchronous oscillation dispersion mechanism of the direct-drive wind power plant, and obtaining a disturbance component amplitude A and an initial phaseSubstituting the amplitude criterion and the phase angle criterion to judge whether subsynchronous oscillation occurs; and judging that subsynchronous oscillation occurs if any one of the amplitude criterion and the phase angle criterion is established, otherwise, judging that subsynchronous oscillation does not occur.
The beneficial effects of the above further improved scheme are: the transient response process of the phase-locked loop under the power grid disturbance and the proportional gain coefficient k of the phase-locked loop are fully consideredpAnd integral gain coefficient kiFor the influence of subsynchronous oscillation, the accurate amplitude and phase angle criterion of subsynchronous oscillation at the fan outlet can be obtained.
Further, the subsynchronous oscillation determination module further includes:
an amplitude judgment submodule for obtaining amplitude criterion of subsynchronous oscillation at the outlet of the fan through the following formula
Wherein
Wherein t is time, Kp1、Ki1Respectively is a current inner loop proportional gain coefficient and an integral gain coefficient of the grid-side converter, L is a line reactance,
the amplitude criterion is used for obtaining the amplitude A and the initial phase of the disturbance componentJudging whether the current amplitude | u | meets the amplitude requirement or not, and sending an obtained judgment result I to a comprehensive judgment submodule;
a phase judgment submodule for obtaining the phase angle criterion of subsynchronous oscillation at the outlet of the fan according to the following formula
Wherein
The phase angle criterion is used for obtaining the amplitude A and the initial phase of the disturbance componentJudging whether the current phase angle gamma meets the phase angle requirement or not, and sending an obtained judgment result II to a comprehensive judgment submodule;
the comprehensive judgment submodule is used for judging whether subsynchronous oscillation occurs according to the first judgment result and the second judgment result; and when any one of the amplitude criterion and the phase angle criterion is established, judging that subsynchronous oscillation occurs, executing the next step, and if not, ending.
The beneficial effects of the above further improved scheme are: the amplitude criterion and the phase angle criterion are a set of effective criteria summarized by the inventor through a large number of tests, and the criterion is simple and feasible and can accurately and effectively judge whether subsynchronous oscillation occurs. And the stability degree of the system can be further judged according to the phase angle criterion, specifically, the smaller the gamma which meets the phase angle criterion is, the more serious the subsynchronous oscillation of the system is, otherwise, the larger the gamma which does not meet the phase angle criterion is, the higher the stability degree of the system is.
Further, the parameter optimization module further comprises:
the decision set generating module is used for establishing a decision set by taking the control variable to be adjusted as a set element, then obtaining a decision set initial value according to the received operation data, and transmitting the decision set initial value to the primary screening module;
the preliminary screening module is used for obtaining a decision set initial value and judging whether the wind power plant parameter optimization constraint condition of the multi-target multi-constraint minimum value optimization model is met or not; if the wind power plant parameter optimization constraint condition is not met, changing the initial value of the decision set according to a preset rule, judging again to obtain all decision set values meeting the wind power plant parameter optimization constraint condition, and transmitting the decision set values to the optimal parameter obtaining module;
the optimal parameter module is used for establishing the following generalized objective function L according to the wind power plant parameter optimization objective function and the wind power plant parameter optimization constraint conditionsi
Li=F(wi)+λ∑G
Wherein
∑G=[max{0,h-hmax}]2+[max{0,-h+hmin}]2+[max{0,K-Kmax}]2+
[max{0,-K+Kmin}]2+[max{0,γc+γ}]2+[max{0,-γ+γc}]2
In the formula, lambda is a penalty factor, k is a decreasing coefficient, n is the iteration number, a1And sequentially inputting all decision set values meeting the optimization constraint conditions of the parameters of the wind power plant into the generalized objective function for a Lagrange multiplier to obtain a decision set corresponding value which enables the generalized objective function to be minimum, and using the decision set corresponding value as the PI parameters of the phase-locked loop and the converter to be solved.
The beneficial effects of the above further improved scheme are: a penalty function (a part lambda sigma G where a penalty factor is located) is introduced into the generalized objective function so as to solve the problem that constraint conditions are difficult to process in the multi-objective optimization problem, and an accurate optimization result can be obtained through rapid convergence. Moreover, the method can be realized through programming design without manual intervention, and has a series of advantages of simplicity, intuition, easy realization and the like.
In the invention, the technical schemes can be combined with each other to realize more preferable combination schemes. Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and drawings.
Drawings
The drawings are only for purposes of illustrating particular embodiments and are not to be construed as limiting the invention, wherein like reference numerals are used to designate like parts throughout.
FIG. 1 is a schematic structural diagram of a direct-drive wind power plant grid-connected system;
FIG. 2 is a schematic step diagram of a sub-synchronous oscillation suppression method for a direct-drive wind power plant in embodiment 1 of the present invention;
FIG. 3 is a schematic diagram of the sub-synchronous oscillation suppression system of the direct-drive wind power plant in embodiment 3 of the present invention;
FIG. 4 is a schematic diagram of the damping analysis module according to embodiment 4 of the present invention;
fig. 5 is a schematic diagram of a parameter optimization module according to embodiment 4 of the present invention.
Reference numerals:
PMSG-a generator; an RSC-machine side converter; GSC-grid side converter; l is1,L2,Lg-an inductance; u. ofg-an infinite system (power supply); PLL-phase locked loop, MSC-machine side controller; NSC-network side controller; WM-wind motor.
Detailed Description
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate preferred embodiments of the invention and together with the description, serve to explain the principles of the invention and not to limit the scope of the invention.
Taking the direct-drive wind power plant grid-connected system shown in fig. 1 as an example, the direct-drive wind power plant grid-connected system comprises two sets of fan control systems with the same composition. Each fan control system comprises a wind motor WM, a generator PMSG, a machine side converter RSC, a network side converter GSC, an inductor L, a phase-locked loop PLL, a machine side controller MSC and a network side controller NSC.
The subsynchronous oscillation divergence mechanism of the direct-drive wind power plant is as follows: under the condition that the WM of the direct-drive wind motor is connected into a power grid, the operation control between the fans in the wind power plant passes through a wind power plant grid-connected point (inductance L)1Right side) voltage dynamic mutual coupling and influence, under the power grid disturbance, the disturbance component is superposed with the original disturbance in the phase-locked loop and the response component generated by the grid-side converter, and the response component and the original disturbance are continuously entered into the grid-side controller as the disturbance through a feedback channel in the phase-locked loop control, and finally the response components generated by all fans are superposed with the original disturbance together.
The role of the machine side converter is as follows: the alternating current generated by the generator is rectified into direct current.
The role of the grid-side converter is as follows: the grid-side converter is used for inverting the direct current into alternating current.
The phase-locked loop has the following functions: in order to keep the output voltage of the direct-drive wind turbine generator and the voltage of a power grid in the same phase constantly, the fan acquires the position of a shaft and the rotation angular frequency of the shaft through power grid voltage phase angle information provided by a phase-locked loop for coordinate transformation.
The phase-locked loop takes the network side voltage as an input variable, and can not completely track the phase information of the power grid and output the phase under the action of the network side voltage disturbance componentA disturbance component delta theta is generated in the azimuth anglePLL
In the formula, the meanings of the variables are as described in example 2.
Example 1
The invention discloses a method for suppressing subsynchronous oscillation of a direct-drive wind power plant, which comprises the following steps as shown in figure 1:
s1, collecting operation data of a direct-drive wind power plant grid-connected system under power grid disturbance;
s2, obtaining subsynchronous oscillation quantization criterion according to a response process of a direct-drive wind power plant grid-connected system under power grid disturbance and a subsynchronous oscillation divergence mechanism of the direct-drive wind power plant, judging the subsynchronous oscillation quantization criterion according to the operation data, and judging whether subsynchronous oscillation occurs or not;
and S3, if subsynchronous oscillation is judged to occur, establishing a multi-target multi-constraint minimum optimization model, and performing collaborative optimization on the parameters of a phase-locked loop and a converter PI in the direct-drive wind power plant grid-connected system so as to suppress the subsynchronous oscillation.
Compared with the prior art, the method provided by the embodiment aims at performing collaborative optimization on the control parameters of all the fans in the wind field, and further can effectively inhibit the subsynchronous oscillation adverse effect generated after the direct-drive wind power plant is connected into the power grid. In the existing research, parameter optimization is carried out on a single wind turbine generator, and parameter collaborative optimization on all fans in a wind power plant is not involved. However, in actual operation, the generated subsynchronous oscillation is due to the combined action of all the fans of the wind power plant, and the adjustment of the parameter of one fan is not enough, which easily causes the phenomenon of insufficient adjustment amplitude or the phenomenon of considering the loss of the adjustment amplitude. A large number of experiments prove that the method provided by the embodiment can correctly and effectively carry out collaborative optimization on all fan parameters in the wind power plant, and effectively inhibit the direct-drive wind power plant from generating subsynchronous oscillation.
Example 2
Optimization is performed on the basis of the embodiment 1, and the operation data of the direct-drive wind power plant grid-connected system comprises the following steps: the phase angle of the voltage phasor U at the outlet of the fan, the useful work P at the outlet of the fan, the useless work Q at the outlet of the fan and the voltage phasor U at the outlet of the fan.
The phase-locked loop and converter PI parameters include: proportional gain coefficient k of phase-locked looppIntegral gain coefficient kiCurrent inner loop proportional gain coefficient K of grid-side converterp1Integral gain coefficient Ki1。
Preferably, in step S2, the determining whether subsynchronous oscillation occurs further includes:
s21, obtaining an amplitude criterion and a phase angle criterion of subsynchronous oscillation at the outlet of the fan according to a response process of a direct-drive wind power plant grid-connected system under power grid disturbance and a subsynchronous oscillation divergence mechanism of the direct-drive wind power plant.
S22, carrying out harmonic decomposition on voltage phasor U at the outlet of the fan to obtain frequency f of a fundamental frequency signal0And the amplitude u of the disturbance componentsFrequency fsInitial phase
Illustratively, U is decomposed by a harmonic analysis prony algorithm
The amplitude u of the fundamental frequency signal can be obtained0Frequency f0Initial phaseAnd the amplitude u of the disturbance componentsFrequency fsInitial phase
S23, according to a proportional gain coefficient k of a phase-locked loop in a direct-drive wind power plant grid-connected systempAnd integral gain coefficient kiIn combination with f obtained as described above0、fs、usThe phase angle disturbance component Δ θ is obtained by the following equationPLLAmplitude A and initial phase of
Wherein
M=ki-(ω0-ωs),N=kp-(ω0-ωs)
ω0=2πf0,ωs=2πfs
S24, obtaining the amplitude A and the initial phase of the disturbance componentSubstituting the amplitude criterion and the phase angle criterion to judge whether subsynchronous oscillation occurs; and judging that subsynchronous oscillation occurs if any one of the amplitude criterion and the phase angle criterion is established, otherwise, judging that subsynchronous oscillation does not occur.
Preferably, in step S23, the amplitude criterion of the subsynchronous oscillation at the outlet of the fan is
Wherein
Wherein t is time, Kp1、Ki1Are respectively net side converterAnd the current inner loop of the device has a proportional gain coefficient and an integral gain coefficient, and L is the line reactance.
The phase angle criterion of subsynchronous oscillation at the outlet of the fan is
Wherein
The gamma can also judge the stability degree of the system, specifically, the smaller the gamma which meets the phase angle criterion, the more serious the subsynchronous oscillation of the system is, and conversely, the larger the gamma which does not meet the phase angle criterion, the higher the stability degree of the system is.
Preferably, the multi-objective multi-constraint minimum optimization model comprises: a wind power plant parameter optimization objective function and a wind power plant parameter optimization constraint condition.
Wind farm parameter optimization objective function of
f(lect,K)=min{w1,w2,…wn}
In the formula IectFor excitation parameters, K is an operating parameter, { w }1,w2,…wnEach element in the set represents the dissipated energy of a fan corresponding to the wind power plant; the excitation parameter comprises wind speed; the operation parameters comprise voltage phasor U at the outlet of the fan, useful work P at the outlet of the fan, useless work Q at the outlet of the fan, phase angle of the voltage phasor U at the outlet of the fan and fundamental frequency f0And disturbance component frequency fs。
The optimization constraint conditions of the parameters of the wind power plant are as follows
In the formula, PiFor useful work of the ith fan, PwfThe total useful work output for the wind field; h is a system variable, including a voltage phasor U at the outlet of the fan and a voltage phasor U at the outlet of the fanWork P, idle work Q at the outlet of the fan, phase angle of voltage phasor U at the outlet of the fan, and frequency f of fundamental frequency signal0Frequency f of the disturbance components;hmax、hminUpper and lower limits for system variables; k is the control variable to be set, Kmax、KminFor controlling the upper and lower limits of variable, the controlled variable includes proportional gain coefficient k of phase-locked looppIntegral gain coefficient kiCurrent inner loop proportional gain coefficient K of grid-side converterp1Integral gain coefficient Ki1。
In particular, the dissipated energy wiCan be further calculated by
Wherein
In the formula, ωwAnd ωgAngular velocity of wind turbine and generator, Dg、DωSelf-damping coefficient of wind turbine and generator, respectively, DsIs the mutual damping coefficient between the fan and the generator,the initial phases of the fan control system 1 and the fan control system 2 are shown, respectively.
Preferably, in step S3, the performing cooperative optimization on PI parameters of a phase-locked loop and a converter in the direct-drive wind farm grid-connected system further includes the following steps:
s31, establishing a decision set by taking a control variable to be adjusted as a set element;
s32, obtaining an initial value of the decision set, and judging whether the optimal constraint condition of the parameters of the wind power plant is met; if the wind power plant parameter optimization constraint condition is not met, changing the initial value of the decision set according to a preset rule, judging again, and obtaining all decision set values meeting the wind power plant parameter optimization constraint condition;
s33, establishing the following generalized objective function L according to the wind power plant parameter optimization objective function and the wind power plant parameter optimization constraint conditionsi
Li=F(wi)+λ∑G
Wherein
∑G=[max{0,h-hmax}]2+[max{0,-h+hmin}]2+[max{0,K-Kmax}]2+
[max{0,-K+Kmin}]2+[max{0,γc+γ}]2+[max{0,-γ+γc}]2
In the formula, lambda is a penalty factor, k is a decreasing coefficient, n is the iteration number, a1Is a lagrange multiplier.
And S34, sequentially inputting all decision set values meeting the parameter optimization constraint conditions of the wind power plant into the generalized objective function to obtain a decision set corresponding value enabling the generalized objective function to be minimum, and using the decision set corresponding value as a phase-locked loop and a converter PI parameter to be solved.
Compared with the embodiment 1, the method provided by the embodiment fully considers the transient response process of the phase-locked loop under the power grid disturbance and the proportional gain coefficient k of the phase-locked looppAnd integral gain coefficient kiFor the influence of subsynchronous oscillation, the accurate amplitude and phase angle criterion of subsynchronous oscillation at the fan outlet can be obtained. Compared with parameter optimization of one fan in the prior art, the method carries out collaborative optimization based on the control parameters of all fans in the wind power plant, introduces a penalty function into the objective function to solve the problem that constraint conditions are difficult to process in the multi-objective optimization problem, minimizes the dissipated energy and the total dissipated energy output by each fan of the wind power plant, and further effectively inhibits subsynchronous vibration generated after the direct-drive wind power plant is connected into a power gridRinging undesirable effects.
Example 3
The invention also provides a direct-drive wind power plant subsynchronous oscillation suppression system using the method of embodiment 1, and as shown in fig. 3, the system comprises a data acquisition module, a damping analysis module and a parameter optimization module. The output end of the data acquisition module is respectively connected with the input end of the damping analysis module and the input end of the parameter optimization module, and the output end of the damping analysis module is connected with the input end of the parameter optimization module.
And the data acquisition module is used for acquiring the operation data of the direct-drive wind power plant grid-connected system under the power grid disturbance and respectively transmitting the acquired operation data to the damping analysis module and the parameter optimization module.
And the damping analysis module is used for obtaining subsynchronous oscillation quantization criterion according to a response process of a direct-drive wind power plant grid-connected system under power grid disturbance and a subsynchronous oscillation divergence mechanism of the direct-drive wind power plant, judging whether subsynchronous oscillation occurs according to the operation data, and transmitting a judgment result to the parameter optimization module.
And the parameter optimization module is used for establishing a multi-target multi-constraint minimum optimization model when the judgment result is that subsynchronous oscillation occurs, and carrying out collaborative optimization on the PI parameters of the phase-locked loop and the converter in the direct-drive wind power plant grid-connected system by combining the operation data.
Compared with the prior art, the system provided by the embodiment is used for carrying out collaborative optimization on the control parameters of all the fans in the wind field, and is not limited to one fan. In the operation of a direct-drive wind power plant grid-connected system, the generated subsynchronous oscillation is due to the combined action of all fans in the wind power plant, and the subsynchronous oscillation cannot be effectively inhibited by only adjusting the parameter of one fan in the prior art, so that the phenomenon that the adjustment amplitude is insufficient or the loss of the subsynchronous oscillation is caused easily. A large number of experiments prove that the system provided by the embodiment can effectively inhibit the subsynchronous oscillation adverse effect generated after the direct-drive wind power plant is connected into the power grid.
Example 4
Optimization is performed on the basis of embodiment 3, and as shown in fig. 4, the damping analysis module further includes a harmonic decomposition module, a disturbance component analysis module, and a subsynchronous oscillation determination module, which are connected in sequence.
A harmonic decomposition module for carrying out harmonic decomposition on the voltage phasor U at the outlet of the fan to obtain the frequency f of the fundamental frequency signal0And the amplitude u of the disturbance componentsFrequency fsInitial phaseAnd transmitting the obtained result to a disturbance component analysis module.
A disturbance component analysis module for analyzing the proportional gain coefficient k of the phase-locked loop in the direct-drive wind power plant grid-connected systempAnd integral gain coefficient kiIn combination with f obtained as described above0、fs、usThe amplitude A and the initial phase of the phase angle disturbance component are obtained by the following formulaA and A are addedTransmitting to a subsynchronous oscillation judging module
Wherein
M=ki-(ω0-ωs),N=kp-(ω0-ωs)
ω0=2πf0,ωs=2πfs
The subsynchronous oscillation judging module is used for obtaining the occurrence frequency of the fan outlet according to the response process of the direct-drive wind power plant grid-connected system under the power grid disturbance and the subsynchronous oscillation divergence mechanism of the direct-drive wind power plantAmplitude criterion and phase angle criterion of step oscillation, and amplitude A and initial phase of obtained disturbance componentSubstituting the amplitude criterion and the phase angle criterion to judge whether subsynchronous oscillation occurs; and judging that subsynchronous oscillation occurs if any one of the amplitude criterion and the phase angle criterion is established, otherwise, judging that subsynchronous oscillation does not occur.
Preferably, the subsynchronous oscillation determination module further includes an amplitude determination submodule, a phase determination submodule, and a comprehensive determination submodule.
An amplitude judgment submodule for obtaining the amplitude A and the initial phase of the disturbance componentObtaining an amplitude criterion of subsynchronous oscillation at the outlet of the fan through the following formula, judging whether the current amplitude | u | meets the amplitude requirement according to the amplitude criterion, and sending an obtained judgment result I to the comprehensive judgment submodule. The amplitude criterion is
Wherein
Wherein t is time, Kp1、Ki1The current inner loop of the grid-side converter is a proportional gain coefficient and an integral gain coefficient respectively, and L is a line reactance.
A phase judgment submodule for obtaining the amplitude A and initial phase of the disturbance componentThe fan is obtained by the following formulaAnd judging whether the current phase angle gamma meets the phase angle requirement according to the phase angle criterion, and sending an obtained judgment result II to the comprehensive judgment submodule. The phase angle criterion is
Wherein
The comprehensive judgment submodule is used for judging whether subsynchronous oscillation occurs according to the first judgment result and the second judgment result; and when any one of the amplitude criterion and the phase angle criterion is established, judging that subsynchronous oscillation occurs, executing the next step (namely, parameter optimization is needed, and the parameter optimization module works), and otherwise, ending (namely, parameter optimization is not needed, and the parameter optimization module does not work).
Preferably, as shown in fig. 5, the parameter optimization module further includes a decision set generation module, a preliminary screening module, and an optimal parameter module, which are connected in sequence.
And the decision set generating module is used for establishing a decision set by taking the control variable to be adjusted as a set element, then obtaining a decision set initial value according to the received operation data, and transmitting the decision set initial value to the primary screening module.
The preliminary screening module is used for obtaining a decision set initial value and judging whether the wind power plant parameter optimization constraint condition of the multi-target multi-constraint minimum value optimization model is met or not; if the optimal parameter is not met, changing the initial value of the decision set according to a preset rule, judging again, obtaining all decision set numerical values meeting the optimization constraint conditions of the parameters of the wind power plant, and transmitting the decision set numerical values to the module for obtaining the optimal parameters.
The optimal parameter module is used for establishing the following generalized objective function L according to the wind power plant parameter optimization objective function and the wind power plant parameter optimization constraint conditionsiSequentially inputting all decision set values meeting the optimization constraint conditions of the wind power plant parameters into the generalized objective functionAnd obtaining a value corresponding to the decision set which enables the generalized objective function to be minimum, and using the value as a phase-locked loop and a converter PI parameter to be solved. The generalized objective function LiCan be calculated by the following formula
Li=F(wi)+λ∑G
Wherein
∑G=[max{0,h-hmax}]2+[max{0,-h+hmin}]2+[max{0,K-Kmax}]2+
[max{0,-K+Kmin}]2+[max{0,γc+γ}]2+[max{0,-γ+γc}]2
In the formula, lambda is a penalty factor, k is a decreasing coefficient, n is the iteration number, a1Is a lagrange multiplier.
Compared with the system in the embodiment 3, the system provided by the embodiment sufficiently considers the transient response process of the phase-locked loop under the power grid disturbance and the proportional gain coefficient k of the phase-locked looppAnd integral gain coefficient kiFor the influence of subsynchronous oscillation, the accurate amplitude and phase angle criterion of subsynchronous oscillation at the fan outlet can be obtained. Compared with parameter optimization of one fan in the prior art, the method carries out collaborative optimization based on the control parameters of all fans in the wind power plant, introduces a penalty function into a target function, solves the problem that constraint conditions are difficult to process in the multi-objective optimization problem, enables the dissipated energy and the total dissipated energy output by each fan of the wind power plant to be minimum, and further can effectively inhibit the subsynchronous oscillation adverse effect generated after the direct-drive wind power plant is connected into a power grid.
Those skilled in the art will appreciate that all or part of the flow of the method implementing the above embodiments may be implemented by a computer program, which is stored in a computer readable storage medium, to instruct related hardware. The computer readable storage medium is a magnetic disk, an optical disk, a read-only memory or a random access memory.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.
Claims (10)
1. A subsynchronous oscillation suppression method for a direct-driven wind power plant is characterized by comprising the following steps:
collecting operation data of a direct-drive wind power plant grid-connected system under power grid disturbance;
obtaining subsynchronous oscillation quantization criterion according to a response process of a direct-drive wind power plant grid-connected system under power grid disturbance and a subsynchronous oscillation divergence mechanism of the direct-drive wind power plant, judging the subsynchronous oscillation quantization criterion according to the operation data, and judging whether subsynchronous oscillation occurs;
and if subsynchronous oscillation is judged to occur, establishing a multi-objective multi-constraint minimum optimization model, and performing collaborative optimization on the PI parameters of a phase-locked loop and a converter in the direct-drive wind power plant grid-connected system so as to suppress the subsynchronous oscillation.
2. The method for suppressing subsynchronous oscillation of the direct-drive wind power plant according to claim 1, wherein the operation data of the grid-connected system of the direct-drive wind power plant comprises: phase angles of voltage phasor U at the outlet of the fan, useful work P at the outlet of the fan, useless work Q at the outlet of the fan and voltage phasor U at the outlet of the fan;
the phase-locked loop and converter PI parameters comprise: proportional gain coefficient k of phase-locked looppIntegral gain coefficient kiCurrent inner loop proportional gain coefficient K of grid-side converterp1Integral gain coefficient Ki1。
3. The method for suppressing subsynchronous oscillation of the direct-driven wind power plant according to claim 2, wherein the step of judging whether subsynchronous oscillation occurs comprises the following steps:
according to a response process of a direct-drive wind power plant grid-connected system under power grid disturbance and a direct-drive wind power plant subsynchronous oscillation divergence mechanism, obtaining an amplitude criterion and a phase angle criterion of subsynchronous oscillation at a fan outlet;
carrying out harmonic decomposition on voltage phasor U at the outlet of the fan to obtain frequency f of a fundamental frequency signal0And the amplitude u of the disturbance componentsFrequency fsInitial phase
According to a proportional gain coefficient k of a phase-locked loop in a direct-drive wind power plant grid-connected systempAnd integral gain coefficient kiIn combination with f obtained as described above0、fs、usThe amplitude A and the initial phase of the phase angle disturbance component are obtained by the following formula
Wherein
M=ki-(ω0-ωs),N=kp-(ω0-ωs)
ω0=2πf0,ωs=2πfs
The amplitude A and the initial phase of the obtained disturbance componentAnd substituting the amplitude criterion and the phase angle criterion to judge whether subsynchronous oscillation occurs, wherein any one of the amplitude criterion and the phase angle criterion is established, judging that subsynchronous oscillation occurs, and otherwise, judging that subsynchronous oscillation does not occur.
4. The method for suppressing subsynchronous oscillation of a direct-driven wind power plant as recited in claim 3, wherein the amplitude criterion of subsynchronous oscillation at the outlet of the wind turbine is
Wherein
Wherein t is time, Kp1、Ki1Respectively a current inner loop proportional gain coefficient and an integral gain coefficient of the grid-side converter, wherein L is a line reactance;
the phase angle criterion of subsynchronous oscillation at the outlet of the fan is
Wherein
5. The direct-drive wind power plant subsynchronous oscillation suppression method according to claim 4, wherein the multi-objective multi-constraint minimum optimization model comprises: optimizing an objective function of wind power plant parameters and optimizing constraint conditions of the wind power plant parameters; wherein the content of the first and second substances,
the wind power plant parameter optimization objective function is
f(lect,K)=min {w1,w2,…wn}
In the formula IectFor excitation parameters, K is an operating parameter, { w }1,w2,…wnEach element in the set represents the dissipated energy of a fan corresponding to the wind power plant; the excitation parameter comprises wind speed; the operation parameters comprise voltage phasor U at the outlet of the fan, useful work P at the outlet of the fan, useless work Q at the outlet of the fan, phase angle of the voltage phasor U at the outlet of the fan and fundamental frequency f0And disturbance component frequency fs;
The wind power plant parameter optimization constraint condition is
In the formula, PiFor useful work of the ith fan, PwfThe total useful work output for the wind field; h is system variable including voltage phasor U at outlet of fan, useful work P at outlet of fan, useless work Q at outlet of fan, phase angle of voltage phasor U at outlet of fan and frequency f of fundamental frequency signal0Frequency f of the disturbance components;hmax、hminUpper and lower limits for system variables; k is a control variable to be adjusted and comprises a phase-locked loop proportional gain coefficient KpIntegral gain coefficient kiCurrent inner loop proportional gain coefficient K of grid-side converterp1Integral gain coefficient Ki1,Kmax、KminThe upper and lower limits of the control variable.
6. The method for suppressing subsynchronous oscillation of the direct-driven wind farm according to claim 5, wherein the cooperative optimization of the PI parameters of the phase-locked loop and the converter in the grid-connected system of the direct-driven wind farm further comprises the following steps:
establishing a decision set by taking a control variable to be adjusted as a set element;
obtaining a decision set initial value, and judging whether the wind power plant parameter optimization constraint condition is met; if the wind power plant parameter optimization constraint condition is not met, changing the initial value of the decision set according to a preset rule, judging again, and obtaining all decision set values meeting the wind power plant parameter optimization constraint condition;
optimization objective according to wind power plant parametersThe generalized objective function L is established according to the standard function and the optimization constraint condition of the wind power plant parametersi
Li=F(wi)+λ∑G
Wherein
λ=1-kn
∑G=[max{0,h-hmax}]2+[max{0,-h+hmin}]2+[max{0,K-Kmax}]2+[max{0,-K+Kmin}]2+[max{0,γc+γ}]2+[max{0,-γ+γc}]2
In the formula, lambda is a penalty factor, k is a decreasing coefficient, n is the iteration number, a1Is a lagrange multiplier;
and sequentially inputting all decision set values meeting the optimization constraint conditions of the parameters of the wind power plant into the generalized objective function to obtain a decision set corresponding value which enables the generalized objective function to be minimum, and using the decision set corresponding value as the PI parameters of the phase-locked loop and the converter to be solved.
7. The utility model provides a directly drive wind power plant subsynchronous oscillation suppression system which characterized in that includes:
the data acquisition module is used for acquiring the operation data of the direct-drive wind power plant grid-connected system under the power grid disturbance and respectively transmitting the acquired operation data to the damping analysis module and the parameter optimization module;
the damping analysis module is used for obtaining subsynchronous oscillation quantization criteria according to a response process of a direct-drive wind power plant grid-connected system under power grid disturbance and a subsynchronous oscillation divergence mechanism of the direct-drive wind power plant, judging whether subsynchronous oscillation occurs or not according to the operation data, and transmitting a judgment result to the parameter optimization module;
and the parameter optimization module is used for establishing a multi-target multi-constraint minimum optimization model when the judgment result is that subsynchronous oscillation occurs, and performing collaborative optimization on the PI parameters of the phase-locked loop and the converter in the direct-drive wind power plant grid-connected system by combining the operation data.
8. The direct-drive wind farm subsynchronous oscillation suppression system according to claim 7, wherein the damping analysis module further comprises:
a harmonic decomposition module for carrying out harmonic decomposition on the voltage phasor U at the outlet of the fan to obtain the frequency f of the fundamental frequency signal0And the amplitude u of the disturbance componentsFrequency fsInitial phaseTransmitting the obtained result to a disturbance component analysis module;
a disturbance component analysis module for analyzing the proportional gain coefficient k of the phase-locked loop in the direct-drive wind power plant grid-connected systempAnd integral gain coefficient kiIn combination with f obtained as described above0、fs、usThe amplitude A and the initial phase of the phase angle disturbance component are obtained by the following formulaA and A are addedTransmitting to a subsynchronous oscillation judging module
Wherein
M=ki-(ω0-ωs),N=kp-(ω0-ωs)
ω0=2πf0,ωs=2πfs
Subsynchronous vibrationThe oscillation judgment module is used for obtaining an amplitude criterion and a phase angle criterion of subsynchronous oscillation at the outlet of the fan according to the response process of a direct-drive wind power plant grid-connected system under power grid disturbance and a subsynchronous oscillation divergence mechanism of the direct-drive wind power plant, and obtaining the amplitude A and the initial phase of the disturbance componentSubstituting the amplitude criterion and the phase angle criterion to judge whether subsynchronous oscillation occurs; and judging that subsynchronous oscillation occurs if any one of the amplitude criterion and the phase angle criterion is established, otherwise, judging that subsynchronous oscillation does not occur.
9. The direct-drive wind power plant subsynchronous oscillation suppression system according to claim 8, wherein the subsynchronous oscillation determination module further comprises:
an amplitude judgment submodule for obtaining amplitude criterion of subsynchronous oscillation at the outlet of the fan through the following formula
Wherein
Wherein t is time, Kp1、Ki1Respectively is a current inner loop proportional gain coefficient and an integral gain coefficient of the grid-side converter, L is a line reactance,
the amplitude criterion is used for obtaining the amplitude A and the initial phase of the disturbance componentJudging whether the current amplitude value | u | meets the amplitude value criterion or not, and sending the obtained judgment result I to the receiverA comprehensive judgment submodule;
a phase judgment submodule for obtaining the phase angle criterion of subsynchronous oscillation at the outlet of the fan by the following formula
Wherein
The phase angle criterion is used for obtaining the amplitude A and the initial phase of the disturbance componentJudging whether the current phase angle gamma meets the phase angle criterion or not, and sending an obtained judgment result II to a comprehensive judgment submodule;
the comprehensive judgment submodule is used for judging whether subsynchronous oscillation occurs according to the first judgment result and the second judgment result; and when any one of the amplitude criterion and the phase angle criterion is established, judging that subsynchronous oscillation occurs, executing the next step, and if not, ending.
10. The direct-drive wind farm subsynchronous oscillation suppression system according to claim 9, wherein the parameter optimization module further comprises:
the decision set generating module is used for establishing a decision set by taking the control variable to be adjusted as a set element, then obtaining a decision set initial value according to the received operation data, and transmitting the decision set initial value to the primary screening module;
the preliminary screening module is used for obtaining a decision set initial value and judging whether the wind power plant parameter optimization constraint condition of the multi-target multi-constraint minimum value optimization model is met or not; if the wind power plant parameter optimization constraint condition is not met, changing the initial value of the decision set according to a preset rule, judging again to obtain all decision set values meeting the wind power plant parameter optimization constraint condition, and transmitting the decision set values to the optimal parameter obtaining module; the multi-objective multi-constraint minimum optimization model comprises the following steps: optimizing an objective function of wind power plant parameters and optimizing constraint conditions of the wind power plant parameters; wherein the wind power plant parameter optimization objective function is
f(lect,K)=min {w1,w2,…wn}
In the formula IectFor excitation parameters, K is an operating parameter, { w }1,w2,…wnEach element in the set represents the dissipated energy of a fan corresponding to the wind power plant; the excitation parameter comprises wind speed; the operation parameters comprise voltage phasor U at the outlet of the fan, useful work P at the outlet of the fan, useless work Q at the outlet of the fan, phase angle of the voltage phasor U at the outlet of the fan and fundamental frequency f0And disturbance component frequency fs;
The wind power plant parameter optimization constraint condition is
In the formula, PiFor useful work of the ith fan, PwfThe total useful work output for the wind field; h is system variable including voltage phasor U at outlet of fan, useful work P at outlet of fan, useless work Q at outlet of fan, phase angle of voltage phasor U at outlet of fan and frequency f of fundamental frequency signal0Frequency f of the disturbance components;hmax、hminUpper and lower limits for system variables; k is a control variable to be adjusted and comprises a phase-locked loop proportional gain coefficient KpIntegral gain coefficient kiCurrent inner loop proportional gain coefficient K of grid-side converterp1Integral gain coefficient Ki1;Kmax、KminThe upper limit and the lower limit of the control variable are set;
the optimal parameter module is used for establishing the following generalized objective function L according to the wind power plant parameter optimization objective function and the wind power plant parameter optimization constraint conditionsi
Li=F(wi)+λ∑G
Wherein
λ=1-kn
∑G=[max{0,h-hmax}]2+[max{0,-h+hmin}]2+[max{0,K-Kmax}]2+[max{0,-K+Kmin}]2+[max{0,γc+γ}]2+[max{0,-γ+γc}]2
In the formula, lambda is a penalty factor, k is a decreasing coefficient, n is the iteration number, a1And sequentially inputting all decision set values meeting the optimization constraint conditions of the parameters of the wind power plant into the generalized objective function for a Lagrange multiplier to obtain a decision set corresponding value which enables the generalized objective function to be minimum, and using the decision set corresponding value as the PI parameters of the phase-locked loop and the converter to be solved.
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