CN109347097B - Doubly-fed wind power system subsynchronous oscillation suppression strategy based on improved particle swarm optimization algorithm - Google Patents

Doubly-fed wind power system subsynchronous oscillation suppression strategy based on improved particle swarm optimization algorithm Download PDF

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CN109347097B
CN109347097B CN201811278022.9A CN201811278022A CN109347097B CN 109347097 B CN109347097 B CN 109347097B CN 201811278022 A CN201811278022 A CN 201811278022A CN 109347097 B CN109347097 B CN 109347097B
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doubly
fed wind
wind power
subsynchronous oscillation
additional damping
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CN109347097A (en
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姚骏
曾德银
王雪微
张田
孙鹏
郭小龙
王衡
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Chongqing University
State Grid Xinjiang Electric Power Co Ltd
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State Grid Xinjiang Electric Power Co Ltd
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/386—
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/002—Flicker reduction, e.g. compensation of flicker introduced by non-linear load
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00—Energy generation through renewable energy sources
    • Y02E10/70—Wind energy
    • Y02E10/76—Power conversion electric or electronic aspects

Abstract

The invention discloses a particle based on improvementAccording to the sub-synchronous oscillation suppression strategy of the doubly-fed wind power system of the group optimization algorithm, A1) when sub-synchronous oscillation occurs, rotating speed pulses are generated through a rotating speed sensor installed at the tail of a shaft system of the doubly-fed wind power generator, and rotating speed pulse signals are demodulated, so that the instantaneous rotating speed deviation of a rotor of the doubly-fed wind power generator is obtained; A2) inputting the obtained deviation value of the rotor speed into an additional damping controller, and outputting the output delta u of the additional damping controllerdamp_rdAnd Δ udamp_rqAnd the amplitude-limited control signals are superposed in an RSC control link of the doubly-fed wind generating set. The method can effectively improve the subsynchronous oscillation modal damping of the doubly-fed wind power system and realize the subsynchronous oscillation suppression of the system; and the method has good adaptability under the full-operation working condition, and can realize the optimal distribution of the subsynchronous oscillation damping of the system under various working conditions, thereby realizing the global optimal subsynchronous oscillation suppression effect.

Description

Doubly-fed wind power system subsynchronous oscillation suppression strategy based on improved particle swarm optimization algorithm
Technical Field
The invention relates to a method for suppressing subsynchronous oscillation of a doubly-fed wind power plant caused by series compensation grid connection, in particular to a strategy for suppressing the subsynchronous oscillation of a doubly-fed wind power system based on an improved particle swarm optimization algorithm, and belongs to the technical field of new energy power generation.
Background
With the increasing severity of global energy crisis and environmental pollution, in order to vigorously advance the development of renewable new energy technologies and realize sustainable development, wind energy has received high attention and great development from governments and industries. The double-fed wind turbine generator set has become one of the mainstream models of the wind power plant because of the advantages of wide operation range, small converter capacity, small motor size, variable-speed constant-frequency operation and the like. Because wind energy resources and load centers in China are reversely distributed, large-scale wind power consumption is always transmitted in a long distance, and therefore, in order to improve transmission capacity of a power transmission line, reduce transmission loss and effectively improve system stability, a series compensation technology is widely applied to a large-scale wind power delivery system. However, in a large-scale wind power series compensation power transmission system, there is a risk of subsynchronous oscillation, which may damage equipment such as a series compensation capacitor and a main transformer, and seriously threatens safe and stable operation of an adjacent power grid.
Aiming at the problem of subsynchronous oscillation caused by series compensation grid connection of a doubly-fed wind power plant, the main suppression method is an additional damping controller, and the method is mainly divided into two types of subsynchronous oscillation additional damping control based on a converter of a wind generating set and Flexible Alternating Current Transmission Systems (FACTS). However, the use of FACTS devices for additional damping control requires additional economic investment and maintenance cost, and therefore, considering economic cost and reliability together, additional damping control based on the converter of the wind turbine generator is more widely researched and applied.
At present, some design implementation schemes exist for the additional damping suppression strategy based on the self converter of the doubly-fed wind turbine generator, such as the following published documents:
(1)Lingling Fan and Zhixin.Miao.Mitigating SSR using DFIG-based wind generation[J].IEEE Transactions on Sustainable Energy,2012,3(3):349-358.
(2)Hossein Ali Mohammadpour and Enrico Santi.SSR damping controller design and optimal placement in rotor-side and grid-side converters of series-compensated DFIG-based wind farm[J].IEEE Transactions on Sustainable Energy,2015,6(2):388-399.
(3)Hossein Ali Mohammadpour and Enrico Santi.Analysis of Sub-synchronous control interactions in DFIG-base wind farms:EROCT case study[C]//Proc.2015 IEEE Energy Conversion.Congress and Exposition(ECCE).Montreal,QC,Canada:IEEE,2015,500-505.
documents (1) - (2) and (3) introduce an additional damping controller in a Grid-side Converter (GSC) and a Rotor-side Converter (RSC) control link of the doubly-fed wind turbine generator, so as to suppress subsynchronous oscillation of the doubly-fed wind power series compensation system. The lead/lag time parameter T of the additional damping controller based on phase compensation designed in the above document is determined in advance and cannot be modified in real time, when the external structure of the system is changed, the parameter needs to be re-set, and the gain coefficient K lacks an optimization design, so that the additional damping controller based on phase compensation can only be applied to certain specific scenes and cannot realize subsynchronous oscillation suppression under all working conditions.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a double-fed wind power system subsynchronous oscillation suppression strategy based on an improved particle swarm optimization algorithm, an additional damping controller for simultaneously adding active power and reactive power in RSC control of a double-fed wind power unit is used, and the improved particle swarm optimization algorithm is used for optimizing a gain coefficient K, so that the double-fed wind power system subsynchronous oscillation suppression strategy has higher adaptability, and the purpose of effectively suppressing subsynchronous oscillation under all working conditions is realized.
The technical scheme of the invention is realized as follows:
a doubly-fed wind power system subsynchronous oscillation suppression strategy based on an improved particle swarm optimization algorithm comprises the following steps:
A1) when subsynchronous oscillation occurs, generating rotating speed pulses through a rotating speed sensor arranged at the tail part of a shaft system of the doubly-fed wind driven generator, and demodulating rotating speed pulse signals so as to obtain the instantaneous rotating speed deviation quantity delta omega of the rotor of the doubly-fed wind driven generator;
A2) inputting the rotor speed deviation quantity delta omega obtained in the step A1) into an additional damping controller, and outputting delta u of a d shaft and a q shaft of the additional damping controllerdamp_rdAnd Δ udamp_rqAfter amplitude limiting, the obtained signals are superposed in an RSC control link of the doubly-fed wind generating set;
wherein, the additional damping controller in the step A2) is designed according to the following steps:
a2.1) establishing a time domain simulation model of the doubly-fed wind power generation system without additional damping control link, and further obtaining initial values of all physical quantities and the subsynchronous oscillation frequency f of the systemssr；
A2.2) subsynchronous oscillation frequency f obtained according to step A2.1)ssrDetermining a bandpass filter GBPFParameter of (1), band-pass filter GBPFThe transfer function of (d) can be expressed as:
Figure BDA0001847452630000021
wherein
Figure BDA0001847452630000022
Wherein f isH、fLThe upper and lower cut-off frequencies of the band-pass filter are respectively; and epsilon is the damping coefficient of the filter.
A2.3) establishing the electromagnetic torque increment delta T of the rotor of the wind turbineerIncrement of rotor speed by delta omegarA transfer function between;
a2.4) determining the subsynchronous oscillation frequency f from the transfer functionssrNearby phase characteristics, and further obtaining the compensation phase angle of the additional damping controller
Figure BDA0001847452630000024
A2.5) determining the compensated phase angle according to step A2.4)
Figure BDA0001847452630000025
Determining a lead/lag time parameter T of the additional damping controller;
a2.6) combining the lead/lag time parameter T determined in the step A2.5), and establishing a full-system small signal model taking the additional damping controller into account under the operation condition of the typical double-fed wind power system;
a2.7) based on the full-system small signal model established in the step A2.6), optimizing a gain coefficient K of the additional damping controller by applying an improved PSO algorithm;
according to the compensation phase angle in step A2.5)
Figure BDA0001847452630000023
The formula for calculating the lead/lag time parameter T is as follows:
Figure BDA0001847452630000031
wherein, ω isxIs a sub-synchronous oscillation angular frequency;
Figure BDA0001847452630000032
compensating the phase for the desired lead/lag; t is1To compensate for lead time constant of the link, T2To compensate for the lag time constant of the link.
The improved design scheme of the particle swarm optimization algorithm adopted in the step A2.7) and the determination of the target function and the constraint condition thereof are as follows:
a2.7.1) using a chaotic mapping equation to produce an initial population of particles as shown below:
Figure BDA0001847452630000033
where τ is the mapping parameter, z(i)Is a chaotic sequence.
A2.7.2) incorporates inertial weights and learning factors as shown below:
Figure BDA0001847452630000034
c1＝c1s+(c1e-c1s)·cos(ω)
c2＝c2e+(c2e-c2s)·cos(ω)
in the formula, ωstartAnd ωendInitial inertia weight and final inertia weight respectivelyWeighing; k is the current iteration number; t ismaxIs the maximum number of iterations; c. C1sAnd c1eAre the first learning factor c respectively1A start value and an end value of; c. C2sAnd c2eRespectively, a second learning factor c2A start value and an end value of;
a2.7.3) incorporates a convergence factor C into the velocity and position update equation, the improved velocity and position update equation being as follows:
Figure BDA0001847452630000035
Figure BDA0001847452630000036
in the formula, VidIs the particle velocity; xidIs the particle position; r is1、r2Is [0,1 ]]A random number in between; pidThe current individual extreme value of the particle is; pgdThe extreme values of all the current particle groups are obtained; ω is 2.7.3).
A2.7.4) improving the objective function of the particle swarm optimization algorithm as follows:
Figure BDA0001847452630000037
wherein J is an objective function of the improved particle swarm optimization algorithm, xii,jRepresenting the damping ratio of the ith oscillation mode of the system under the jth operation condition; min { xii,jThe method comprises the following steps that (1) the minimum damping ratio of a closed-loop system under a certain control parameter under the j operating condition is represented; alpha is alphajRepresenting the weighting coefficient under the j operating condition; r1Representing all additional damping control gain coefficients K1/K2A set of possible values.
A2.7.5) the improved particle swarm optimization constraint equation is as follows:
Figure BDA0001847452630000041
in the formula, K1,min，K2,minIs-20; k1,max，K2,maxIs 20.
Compared with the prior art, the invention has the following beneficial effects:
the method can effectively improve the subsynchronous oscillation modal damping of the doubly-fed wind power system and realize the subsynchronous oscillation suppression of the system; and the method has good adaptability under the full-operation working condition, and can realize the optimal distribution of the subsynchronous oscillation damping of the system under various working conditions, thereby realizing the overall optimal subsynchronous oscillation suppression effect and effectively improving the stability of the doubly-fed wind power series compensation power transmission system.
Drawings
FIG. 1 is a control block diagram of a rear rotor side inverter incorporating an additional damping controller.
Fig. 2 is a structural block diagram of an additional active damping controller.
FIG. 3 is a general design flow diagram of the system additive damping control strategy.
FIG. 4 is a comparison diagram of electromagnetic torque simulation waveforms with and without additional damping controllers under different wind speed conditions.
FIG. 5 is a comparison diagram of electromagnetic torque simulation waveforms with and without additional damping controllers under different line series compensation working conditions.
Detailed Description
The following detailed description of specific embodiments of the invention refers to the accompanying drawings.
As shown in figure 1, an additional damping controller is introduced into the rotor-side converter control of the doubly-fed wind turbine generator, so that the output delta u of the additional damping controllerdamp_rdAnd Δ udamp_rqAfter amplitude limiting, and urd、urqAnd superposing the voltage signals to be output as control voltage.
As can be seen from fig. 2, the structure of the additional damping controller includes a band-pass filter, a lead/lag phase compensation element, a gain element, and a limiting element.
FIG. 3 is a general design flow chart of a system additional damping control strategy based on an improved particle swarm optimization algorithm.
The method comprises the following specific implementation steps:
A1) when subsynchronous oscillation occurs, generating rotating speed pulses through a rotating speed sensor arranged at the tail part of a shaft system of the doubly-fed wind driven generator, and demodulating rotating speed pulse signals so as to obtain the instantaneous rotating speed deviation quantity delta omega of the rotor of the doubly-fed wind driven generator;
A2) inputting the rotor speed deviation quantity delta omega obtained in the step A1) into an additional damping controller, and outputting delta u of a d shaft and a q shaft of the additional damping controllerdamp_rdAnd Δ udamp_rqAfter amplitude limiting, the obtained signals are superposed in an RSC control link of the doubly-fed wind generating set;
wherein, the additional damping controller in the step A2) is designed according to the following steps:
a2.1) establishing a time domain simulation model of the doubly-fed wind power generation system without additional damping control link, and further obtaining initial values of all physical quantities and the subsynchronous oscillation frequency f of the systemssr；
A2.2) subsynchronous oscillation frequency f obtained according to step A2.1)ssrDetermining a bandpass filter GBPFParameter of (1), band-pass filter GBPFThe transfer function of (d) can be expressed as:
Figure BDA0001847452630000051
wherein
Figure BDA0001847452630000052
Wherein f isH、fLThe upper and lower cut-off frequencies of the band-pass filter are respectively; and epsilon is the damping coefficient of the filter.
A2.3) establishing the electromagnetic torque increment delta T of the rotor of the wind turbineerIncrement of rotor speed by delta omegarA transfer function between;
a2.4) determining the subsynchronous oscillation frequency f from the transfer functionssrNearby phase characteristics, and further obtaining the compensation phase angle of the additional damping controller
Figure BDA0001847452630000057
A2.5) determining the compensated phase angle according to step A2.4)
Figure BDA0001847452630000058
Determining a lead/lag time parameter T of the additional damping controller;
a2.6) combining the lead/lag time parameter T determined in the step A2.5), and establishing a full-system small signal model taking the additional damping controller into account under the operation condition of the typical double-fed wind power system;
a2.7) based on the full-system small signal model established in the step A2.6), optimizing a gain coefficient K of the additional damping controller by applying an improved PSO algorithm;
according to the compensation phase angle in step A2.5)
Figure BDA0001847452630000059
The formula for calculating the lead/lag time parameter T is as follows:
Figure BDA0001847452630000053
wherein, ω isxIs a sub-synchronous oscillation angular frequency;
Figure BDA0001847452630000054
compensating the phase for the desired lead/lag; t is1To compensate for lead time constant of the link, T2To compensate for the lag time constant of the link.
The improved design scheme of the particle swarm optimization algorithm adopted in the step A2.7) and the determination of the target function and the constraint condition thereof are as follows:
a2.7.1) using a chaotic mapping equation to produce an initial population of particles as shown below:
Figure BDA0001847452630000055
where τ is the mapping parameter, z(i)Is a chaotic sequence.
A2.7.2) incorporates inertial weights and learning factors as shown below:
Figure BDA0001847452630000056
c1＝c1s+(c1e-c1s)·cos(ω)
c2＝c2e+(c2e-c2s)·cos(ω)
in the formula, ωstartAnd ωendRespectively an initial inertia weight and a final inertia weight; k is the current iteration number; t ismaxIs the maximum number of iterations; c. C1sAnd c1eAre the first learning factor c respectively1A start value and an end value of; c. C2sAnd c2eRespectively, a second learning factor c2A start value and an end value of;
a2.7.3) incorporates a convergence factor C into the velocity and position update equation, the improved velocity and position update equation being as follows:
Figure BDA0001847452630000061
Figure BDA0001847452630000062
in the formula, VidIs the particle velocity; xidIs the particle position; r is1、r2Is [0,1 ]]A random number in between; pidThe current individual extreme value of the particle is; pgdThe extreme values of all the current particle groups are obtained; ω is 2.7.3).
A2.7.4) improving the objective function of the particle swarm optimization algorithm as follows:
Figure BDA0001847452630000063
wherein J is an objective function of the improved particle swarm optimization algorithm, xii,jRepresenting the damping ratio of the ith oscillation mode of the system under the jth operation condition; min { xii,jThe method comprises the following steps that (1) the minimum damping ratio of a closed-loop system under a certain control parameter under the j operating condition is represented; alpha is alphajRepresenting the weighting coefficient under the j operating condition; r1Representing all additional damping control gain coefficients K1/K2A set of possible values.
A2.7.5) the improved particle swarm optimization constraint equation is as follows:
Figure BDA0001847452630000064
in the formula, K1,minAnd K2,minIs-20; k1,maxAnd K2,maxIs 20.
Description of the effects of the invention:
FIG. 4 shows the electromagnetic torque T before and after the additional damping controller is added under different wind speed conditionseAnd (5) simulating a waveform comparison graph. As can be seen from fig. 4, after the damping controller provided by the invention is adopted, the subsynchronous oscillation phenomenon of the doubly-fed wind power series compensation power transmission system can be effectively suppressed according to different wind speed operation conditions, and the stability of the system is effectively improved; meanwhile, compared with the additional damping controller optimized by adopting a standard particle swarm optimization algorithm, the additional damping controller optimized by adopting the improved particle swarm optimization algorithm can play a better inhibiting role under the worse subsynchronous oscillation condition; FIG. 5 shows the electromagnetic torque T with or without additional damping controller under different line series compensation conditions (30%, 40%, 50%)eAnd (5) simulating a waveform comparison graph. As can be seen from FIG. 5, after the additional damping controller provided by the invention is added, the subsynchronous oscillation phenomenon of the wind power system is effectively inhibited aiming at different line series compensation degree working conditions, and the additional damping controller based on the improved particle swarm optimization algorithm can be adoptedAnd the subsynchronous oscillation suppression effect is better.
To sum up, the invention provides that the damping controller is added in the active power and reactive power control loop of the RSC of the double-fed wind generating set at the same time, and the parameters of the additional damping controller are optimized by applying the improved particle swarm optimization algorithm, and the invention has the following beneficial effects: the subsynchronous oscillation modal damping of the doubly-fed wind power system is remarkably improved, and the subsynchronous oscillation of the system is effectively inhibited; the suppression strategy has good adaptability under the full-operation working condition, and the optimal distribution of the subsynchronous oscillation damping of the system under different working conditions can be realized, so that the optimal subsynchronous oscillation suppression effect can be realized when the full-operation working condition is considered, the stability of the doubly-fed wind power series compensation system is effectively improved, and the safe and stable operation capability of the doubly-fed wind power generator set is enhanced.
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 (3)

1. A doubly-fed wind power system subsynchronous oscillation suppression strategy based on an improved particle swarm optimization algorithm is characterized by comprising the following steps:
A1) when subsynchronous oscillation occurs, generating rotating speed pulses through a rotating speed sensor arranged at the tail part of a shaft system of the doubly-fed wind driven generator, and demodulating rotating speed pulse signals so as to obtain the instantaneous rotating speed deviation quantity delta omega of the rotor of the doubly-fed wind driven generator;
A2) inputting the instantaneous speed deviation quantity delta omega of the rotor of the doubly-fed wind generator obtained in the step A1) into an additional damping controller, and outputting delta u of a d axis and a q axis of the additional damping controllerdamp_rdAnd Δ udamp_rqAfter amplitude limiting, the obtained signals are superposed in an RSC control link of the doubly-fed wind generating set;
wherein, the additional damping controller in the step A2) is designed according to the following steps:
a2.1) establishing a time domain simulation model of the doubly-fed wind power generation system without additional damping control link, and further obtaining initial values of all physical quantities and the subsynchronous oscillation frequency f of the systemssr；
A2.2) subsynchronous oscillation frequency f obtained according to step A2.1)ssrDetermining a bandpass filter GBPFParameter of (1), band-pass filter GBPFThe transfer function of (d) can be expressed as:
Figure FDA0002717889820000011
wherein
Figure FDA0002717889820000012
Wherein f isH、fLThe upper and lower cut-off frequencies of the band-pass filter are respectively; epsilon is the damping coefficient of the filter;
a2.3) establishing the electromagnetic torque increment delta T of the rotor of the wind turbineerIncrement of rotor speed by delta omegarA transfer function between;
a2.4) determining the subsynchronous oscillation frequency f from the transfer functionssrNearby phase characteristics, and further obtaining the compensation phase angle of the additional damping controller
Figure FDA0002717889820000014
A2.5) determining the compensated phase angle according to step A2.4)
Figure FDA0002717889820000015
Determining a lead/lag time parameter T of the additional damping controller;
a2.6) combining the lead/lag time parameter T determined in the step A2.5), and establishing a full-system small signal model taking the additional damping controller into account under the operation condition of the typical double-fed wind power system;
a2.7) based on the full-system small signal model established in the step A2.6), the gain coefficient K of the additional damping controller is optimized by applying an improved PSO algorithm.
2. The improved particle swarm optimization algorithm-based doubly-fed wind power system subsynchronous oscillation suppression strategy according to claim 1, wherein the step A2.5) is performed according to the compensation phase angle
Figure FDA0002717889820000016
The formula for calculating the lead/lag time parameter T is as follows:
Figure FDA0002717889820000013
wherein, ω isxIs a sub-synchronous oscillation angular frequency;
Figure FDA0002717889820000027
compensating the phase for the desired lead/lag; t is1To compensate for lead time constant of the link, T2To compensate for the lag time constant of the link.
3. The improved particle swarm optimization algorithm-based doubly-fed wind power system subsynchronous oscillation suppression strategy according to claim 1, wherein the improved design scheme of the particle swarm optimization algorithm adopted in the step A2.7) and the determination of the objective function and the constraint condition thereof are as follows:
a2.7.1) using a chaotic mapping equation to produce an initial population of particles as shown below:
Figure FDA0002717889820000021
where τ is the mapping parameter, z(i)Is a chaotic sequence;
a2.7.2) incorporates inertial weights and learning factors as shown below:
Figure FDA0002717889820000022
c1＝c1s+(c1e-c1s)·cos(ω)
c2＝c2e+(c2e-c2s)·cos(ω)
in the formula, ωstartAnd ωendRespectively an initial inertia weight and a final inertia weight; k is the current iteration number; t ismaxIs the maximum number of iterations; c. C1sAnd c1eAre the first learning factor c respectively1A start value and an end value of; c. C2sAnd c2eRespectively, a second learning factor c2A start value and an end value of;
a2.7.3) incorporates a convergence factor C into the velocity and position update equation, the improved velocity and position update equation being as follows:
Figure FDA0002717889820000023
Figure FDA0002717889820000024
φ＝c1+c2＞4
in the formula, VidIs the particle velocity; xidIs the particle position; r is1、r2Is [0,1 ]]A random number in between; pidThe current individual extreme value of the particle is; pgdThe extreme values of all the current particle groups are obtained; ω is the inertial weight obtained in step A2.7.2);
a2.7.4) improving the objective function of the particle swarm optimization algorithm as follows:
Figure FDA0002717889820000025
wherein J is an improved particle groupOptimization of the algorithm objective function ξi,jRepresenting the damping ratio of the ith oscillation mode of the system under the jth operation condition; min { xii,jThe method comprises the following steps that (1) the minimum damping ratio of a closed-loop system under a certain control parameter under the j operating condition is represented; alpha is alphajRepresenting the weighting coefficient under the j operating condition; r1Representing all additional damping control gain coefficients K1/K2A set of possible values;
a2.7.5) the improved particle swarm optimization constraint equation is as follows:
Figure FDA0002717889820000026
in the formula, K1,minAnd K2,minIs-20; k1,maxAnd K2,maxIs 20.
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