CN108539759A - Improve the application method of PSO algorithm configuration novel electric power system stabilizers PSS4B - Google Patents

Abstract

The present invention provides the application method for improving PSO algorithm configuration novel electric power system stabilizers PSS4B, include being improved to basic PSO algorithms with the method that crossover operation is combined using random weight, simplified partial is carried out to the transmission function of PSS4B again, optimizing, one machine infinity bus system and 3 machine, 9 node system are carried out using the parameter optimization emulation for improving PSO algorithms progress PSS4B to parameter to be optimized in PSS4B using PSO algorithms are improved.The present invention overcomes under the classical parameter that IEEE gives, due to the use of the phase compensation link of three branches, the problem of failing to be optimal inhibition, can the effects that inhibit to low-frequency oscillation of quantitative analysis PSS4B by using PSO algorithm configuration novel electric power system stabilizers PSS4B is improved.

Description

Improve the application method of PSO algorithm configuration novel electric power system stabilizers PSS4B

Technical field

The invention belongs to technical field of power systems, more particularly to improve PSO algorithm configuration novel electric power system stabilizers The application method of PSS4B.

Background technology

With transferring electricity from the west to the east, the implementation of north and south interconnection, China's power grid scale is gradually expanded, and will form the huge of national network Electric system.Although hair transmission of electricity economy can be improved in Power System Interconnection, but also bring problem to the stabilization of power grid simultaneously.It is generating electricity Machine heavy load, long distance power transmission, using quick response excitation system excitation in the case of, the total damping of system may be made to become smaller even It is negative, easily causes low-frequency oscillation problem.Low-frequency oscillation can influence the stability of system, and off-the-line may occur when serious, cause Large-scale blackout.Therefore, low-frequency oscillation problem brings great challenge to modern power systems stable operation.

When underdamping even negative damping system in there are when microvariations or undisturbed, system may be caused unstable, into And lead to fault spread, it does great damage to system.The low-frequency oscillation of electric system appears in diesel generation earliest When machine is grid-connected, it was referred to as " to shake " at that time, which is addressed substantially by installing Damper Winding on generator amature.But It is the networking between big region as power system load is continuously increased, electric power networks are gradually complicated so that low-frequency oscillation It happens occasionally, threatens the normal operation of system.

Currently, using more PSS for single branching type power system stabilizer, PSS, such as PSS1A, PSS2A, PSS2B.With The extensive interconnection of regional power grid, the oscillation mode of low-frequency oscillation increases and frequency of oscillation is lower and lower, single branching type electric power System stabilizes to not good enough to the inhibition of low-frequency oscillation, and Quebec, CAN power office proposed multiband electric power in 2000 System stabilizer PSS4B, and input signal is divided into basic, normal, high three frequency ranges by PSS4B, can adjust phase, gain respectively Etc. parameters, provide suitable compensation phase angle for different frequency range, parameter setting has higher flexibility.

However PSS4B is complicated and parameter is numerous, parameter tuning is more flexible and difficulty is larger.Ieee standard provides The advanced limited extent of phase that is provided within the scope of 0.1-2HZ of PSS4B canonical parameters, do not have universal adaptability.For normal Self-shunt excitation system and the larger three-machine excitation system of hysteresis characteristic are advised, the lead-lag phase for adjusting 3 frequency ranges is needed to mend Link is repaid, to provide enough phase lead compensations.

Currently, the theoretical research of PSS4B is more short of in China with parameter tuning method, and put into the example of practical application Son is considerably less, it is therefore desirable to research is further analyzed to it.

Invention content

It is an object of the invention to solve the problems of the above-mentioned prior art, provides and improve PSO algorithm configuration Novel electrics The application method of Force system stabilizer PSS4B can overcome under the classical parameter that IEEE gives, since three branches are not used Phase compensation link, the problem of inhibition cannot be optimal.

The present invention adopts the following technical scheme that：

1, the application method of PSO algorithm configuration novel electric power system stabilizers PSS4B is improved, including：

S1. using random weight in such a way that crossover operation is combined, PSO algorithms are improved；

S2. simplify PSS4B parameters

S3. using eigenvalue Method emulate under Nonlinear Simulation and Simulink, quantitative analysis PSS4B is to low frequency Vibrate the effect inhibited.

The present invention in such a way that crossover operation is combined, is improved PSO algorithms, in simplification using random weight Determine that the parameter for needing to optimize is bandpass filter, phase compensation and the gain of each branch on the basis of PSS4B models Link, and random weight is improved basic PSO algorithms with the method that crossover operation is combined, utilize improvement PSO algorithms Optimizing is carried out to parameter to be optimized in PSS4B, parameter optimization is carried out in two steps, bandpass filtering and gain link are carried out first Secondly optimization optimizes the phase compensation link of each branch, improved using one machine infinity bus system and 3 machine, 9 node system PSO algorithms carry out PSS4B parameter optimization emulation, overcome under the classical parameter that IEEE gives, since three branches are not used Phase compensation link fails the inhibition being optimal.

Description of the drawings

Fig. 1 is the structure diagram of the present invention；

Fig. 2 is low frequency transducer frequency response chart；

Fig. 3 is high-frequency converter frequency response chart；

Fig. 4 is the PSS4B transfer function model figures after structure simplifies；

Fig. 5 is PSO algorithm optimization PSS4B parametric procedure schematic diagrames；

Fig. 6 is one machine infinity bus system schematic diagram；

Fig. 7 (a), Fig. 7 (b) are object function group adaptive optimal control angle value change curve；

Fig. 8 (a), 8 (b), 8 (c) be microvariations when three kinds of operating modes under generator speed deviation and electromagnetic power variation diagram；

Fig. 9 (a), 9 (b), 9 (c) be large disturbances when three kinds of operating modes under generator speed deviation and electromagnetic power variation diagram；

Figure 10 is 3 machine, 9 node simulation model；

Figure 11 (a), 11 (b) group adaptive optimal control angle value change curve；

Figure 12 (a), 12 (b) are canonical parameter PSS4B generator G2 rotor speeds deviation and electromagnetic work under base regime Rate curvilinear motion figure；

Figure 13 (a), 13 (b) are canonical parameter PSS4B generator G2 rotor speeds deviation and electromagnetic power under heavy loading Curvilinear motion figure；

Figure 14 (a), 14 (b) are canonical parameter PSS4B generator G2 rotor speeds deviation and electromagnetic power under light load Curvilinear motion figure；

Figure 15 (a), 15 (b) be optimization GPSO-PSS4B under base regime generator G2 rotor speeds deviation and electromagnetism Power curve variation diagram；

Figure 16 (a), 16 (b) are GPSO-PSS4B generator G2 rotor speeds deviation and the electromagnetic work under heavy loading of optimization Rate curvilinear motion figure；

Figure 17 (a), 17 (b) be optimization GPSO-PSS4B under light load generator G2 rotor speeds deviation and electromagnetic work Rate curvilinear motion figure.

Specific implementation mode

To make the object, technical solutions and advantages of the present invention clearer, the technical solution below in the present invention carries out clear Chu is fully described by, it is clear that described embodiments are some of the embodiments of the present invention, instead of all the embodiments.It is based on Embodiment in the present invention, those of ordinary skill in the art are obtained every other without creative efforts Embodiment shall fall within the protection scope of the present invention.

Under the classical parameter that IEEE gives, the unfavorable result caused by the phase compensation link of three branches is not used It is：The advanced limited extent of phase that the PSS4B canonical parameters that ieee standard provides provide within the scope of 0.1-2HZ does not have general All over adaptability.For the three-machine excitation system that conventional self-shunt excitation system and hysteresis characteristic are larger, need to adjust 3 frequency ranges Lead-lag phase compensation link, to provide enough phase lead compensations.

As shown in Figure 1, the application method for improving PSO algorithm configuration novel electric power system stabilizers PSS4B of the present invention, packet It includes：

First, is improved PSO algorithms with the method that crossover operation is combined using random weight；

Basic PSO algorithms belong to swarm intelligence algorithm, principle is simple by finding individual extreme value and group's extreme value optimizing solution And easily programmable realization, genetic algorithm is compared, convergence rate is very fast but with the progress of iterative process, and each particle similarity is gradual Increase, possibly can not jump out local optimum, basic PSO algorithms are due to a lack of regional area fine search ability, in the algorithm later stage It is likely to occur misconvergence, the not high disadvantage of search precision.

Iteration starts inertia weight ω value maximums, and as iterations increase, ω linearly reduces.This linear decrease power Weight method mainly for PSO algorithms are easily precocious and the algorithm later stage generates the phenomenon that vibrating easily at optimal solution, suitable weight with pass Deceleration can improve algorithm performance to a certain extent.

But for different problems, the proportionate relationship that each iteration needs is different, therefore linear decrease weight can only be directed to Certain specific problems.Meanwhile if optimizing initial stage cannot find optimum point, with the reduction of ω, local search ability enhances, then It is easily trapped into local optimum；If optimizing initial stage finds time advantage, at this moment relatively small ω can make algorithm search quickly Optimum point, but since the linear reduction of ω makes algorithm the convergence speed slow down, increase search time, therefore introduce random weight：

In formula, ω is inertia weight, and randn (0,1) is the random number of 0 to 1 normal distribution, and rand (0,1) is 0 to 1 Between equally distributed random number, μ_max、μ_min, μ be respectively random weighted mean maximum value, minimum value and average value；If Relatively optimum point can accelerate algorithm the convergence speed, be conducive to if the weighted value randomly generated is smaller iteration initial stage Globe optimum is searched out, if not finding optimum point at iteration initial stage, if using linear decrease weight at this time, the reduction of ω can Algorithm can be made finally to can not find advantage and be absorbed in local optimum, and the random elongation of weight can overcome the limitation.

Introduce compressibility factor

To enable algorithm to reach effective balance between overall situation detection is exploited part, Clerc construct containing compress because Effectively to control flying speed of partcles, speed more new formula is the PSO algorithms of son：

In formula,Referred to as compressibility factor, typical case follow the example of as c=4.1,

Introduced cross link

PSO algorithms are improved on the basis of above-mentioned several improved methods, have introduced the hybridization link in genetic algorithm, every time In iterative calculation, according to given probability of crossover, the particle of specified quantity is selected to be put into hybridization pond, particle is random in pond Hybridize two-by-two, generate the filial generation particle (child) of invariable number, and replaces parental generation particle (parent), generation of neutrons particle position Setting can obtain according to parent particle position arithmetic crossover, i.e.,

Child (x)=pparent₁(x)+(1-p)·parent₂(x)

Wherein, p is the random number between 0 to 1；

The speed of filial generation particle according to can obtain as follows：

After experience hybridizes link, the advantages of filial generation particle of generation will inherit parent；Assuming that parent particle is located at not In same local optimum region, after carrying out hybridization link and generating filial generation particle, it can usually help particle to overcome and be absorbed in part Optimal problem, and then search capability of the particle in region is made to be highly improved.

Improved PSO algorithm flows are obtained, the flow for improving PSO algorithms is as follows：

The position and speed of Step1 each particles in initialization population in prescribed limit, time counter t=0；

Step2 evaluates the fitness value of each particle, and storing the currently position of each particle and adaptive value, will in Pbest The position of adaptive value optimum individual and adaptive value are stored in Gbest in Pbest；

Step3 is according to formulaUpdate inertia weight value；

Step4 is according to formulaWithUpdate The speed of particle and displacement；

Step5 calculates the fitness value of particle；

Step6 is to each particle, by current fitness value compared with the fitness value of its desired positions undergone, if compared with It is good, then using the corresponding position of current fitness value as current desired positions, update Pbest；

The relatively more current all Pbest of Step7 and Gbest values, update Gbest；

The particle obtained by Step4 that Step8 chooses certain amount according to probability of crossover carries out at random two-by-two in hybridization pond The filial generation of the numbers such as hybridization generation, according to formula child (x)=pparent₁(x)+(1-p)·parent₂(x) andThe position and speed of filial generation particle is calculated, the position of parent particle is replaced It sets and speed, while keeping Pbest and Gbest constant；

Step9 time counters t adds 1, and judges whether to meet stop condition (iterations search precision), if full Foot, stops search, and output continues search for as a result, otherwise returning to Step3.

2nd, simplifies PSS4B parameters

In the step S1, simplify PSS4B models, bandpass filtering parameter, the phase compensation ginseng of each branch need to be optimized Number, gain link parameter.

1. the transmission function of couple PSS4B carries out simplified partial：

First, ignore amplitude limit link；

Then carries out abbreviation to low frequency transducer and high-frequency converter：

In low frequency transducer, -1.759 × 10^-4、-1.759×10^-3Much smaller than 1, transmission function can be simplified as follows：

High-frequency converter transmission function is simplified as：

It is as shown in Figure 2 and Figure 3 low frequency transducer and high-frequency converter exact transfer function and abbreviation transmission function Bode schemes.

Each frequency range of PSS4B is regarded as and is made of gain link, bandpass filtering link and phase compensation link.

As shown in figure 4, the process of simplification only considers a phase compensation link, the PSS4B transmission functions after being simplified.

PSS4B under the given classical parameters of IEEE can inhibit low-frequency oscillation in most cases, but not up to most Excellent inhibition, it is therefore desirable to optimizing be carried out to PSS4B parameters, be based on PSS4B parameters to be optimized are simplified：

Low-frequency range：K_L1、K_L2、T_L1、T_L2、T_L7、T_L8、T_L5、T_L6、K_L

Mid Frequency：K_I1、K_I2、T_I1、T_I2、T_I7、T_I8、T_I5、T_I6、K_I

High band：K_H1、K_H2、T_H1、T_H2、T_H7、T_H8、T_H5、T_H6、K_H

Need the parameter that optimizes numerous since each branches of PSS4B are made of bandpass filtering, gain and phase compensation link, Therefore the link of the 1st suboptimization is bandpass filtering and gain link：

Bandpass filtering parameter and gain link parameter are optimized：

It is 1.2 to take R, and bandpass filtering link parameter to be optimized is only each branch hub frequency F_L、F_IWith F_H, gain link Parameter to be optimized is K_L、K_IWith K_H, the 1st suboptimization can be converted into the optimization problem of following belt restraining：

The phase compensation link parameter of each branch is optimized：

Based on the 1st suboptimization as a result, the 2nd phase compensation link that will optimize each branch, the parameter of required optimization is T_L5、 T_I5、 T_H5、T_L6、T_I6、T_H6, and

The process such as attached drawing 5 of optimizing is carried out to PSS4B parameters using improved PSO algorithms.

It improves the particle that PSO algorithm optimizations obtain and is assigned to PSS4B parameters to be optimized, by running Simulink moulds Type, calculates performance indicator, then using performance indicator as the fitness value of particle, finally by judging whether to meet termination condition To determine whether terminating optimizing.

Further technical solution is to select ITAE as the performance indicator of PSS4B parameter tunings；

According to optimal control theory mesh is controlled to Constrained optimization problem by means of Pontryagin minimal principles It is designated as the ability that system output is tracked given value by minimal error, thus considers integrated performance index, realizes and inhibits power generation The oscillation of electromechanical magnetic power, rotor velocity equivalent makes it keep steady-state value.When due to low-frequency oscillation and system lacks damping, It not only will produce the opposite of rotor to wave, energy can be transmitted by electromechanics contact, and the power on power transmission line can also occur persistently to shake It swings, therefore | e (t) | for each inclined absolute value of the difference of generator amature angular speed and the inclined absolute value of the difference of each generator electromagnetic power.

Consider optimization after PSS4B have robustness, that is, ensure optimization after PSS4B can running situation change with System structure variation etc. is in most cases robust, provides suitable damping, and it is as follows to choose object function：

Selection target function

In formula, m is operation of power networks operating mode number；N is generator number in system；I is i-th generator；J is jth kind Operating mode；Δω_i,j(t) the rotor speed deviation for being the generator i under jth kind operating mode；ΔP_ei,j(t) it is to generate electricity under jth kind operating mode The electromagnetic power deviation of machine i；a_i,jAnd b_i,jThe adjustable weight factor for being generator i at operating mode j.

According to PSS4B Parametric optimization problems, population dimension D=6, the population scale S=30 chosen in two suboptimization, repeatedly In generation number T=100, GPSO algorithm, Studying factors c₁=c₂=2, random weight maximum value μ_max=0.9, minimum value μ_min= 0.4, random weight weight variances sigma=0.4 hybridizes the probability of crossover P of link_c=0.9, hybridize pond size S_p=0.2, target letter Weight factor a in number_i,j=b_i,j=1.

Parameter K in optimization problem_L、K_I、K_HRestriction range be set as [0.1,100], F_LRestriction range be set as [0.01, 0.1], the restriction range of FI is set as [0.1,1], and the restriction range of FH is set as [1,10].

According to document 1, to phase compensation link T_L5、T_L6、T_I5、T_I6、T_H5、T_H6Restriction range be set as [0.001, 0.6]。

One machine infinity bus system or 3 machine, 9 node system is added in PSS4B after optimizing in step S2 by the 3rd, utilizes feature Value analytic approach emulated under Nonlinear Simulation and Simulink, and the PSS4B after verification optimization inhibits low frequency under different operating modes The effect of oscillation.

Verify the anti-low-frequency oscillation effect of the PSS4B after one machine infinity bus system verification optimization：

Establish one machine infinity bus system

The effect that PSS4B power oscillation dampings after PSO algorithm performances and optimization are improved for the ease of analysis, in Simulink In build one machine infinity bus system, simulation result is as shown in fig. 6, system a reference value is：S_B=100MVA, U_B=230kV；It does not examine Consider governor, Infinite bus system is replaced with three-phase voltage source module.Generator is three-phase synchronous generator, generator parameter：Depending on It is 192MVA, x in power_d*=0.8958, x '_d*=0.1198, x_q*=0.8645, T '_d0=7.8s；Excitation system is single order High-speed excitation, parameters of excitation system K_A=300, T_R=0.02s；Transformer only considers winding reactance x_1*=j0.0625, no-load voltage ratio It is 18/232；Generator terminal load is constant-impedance model z_*=2；Line parameter circuit value：z_l*=0.0001+j0.28017.

In order to realize the PSS4B parameter optimization methods with robustness proposed, the different service condition of power grid is considered, Respectively represent the basic operating condition of power grid (Case 1), light load conditions (Case 2) and heavy load operating mode (Case 3).Make PSS4B can provide good damping, generator operating conditions such as table 1 under different power grid typical case's operation conditions for system.

System features root and damping such as table 2 when system is withouyt PSS.It can be obtained by table 2, under three kinds of operation conditions, The frequency of oscillation of system is different from, and its damping ratio also difference.When system is under base load operation operating mode, system hinders Buddhist nun's ratio is 0.012, and when light(-duty) service operating mode run, damping ratio 0.044, when heavy load, damping ratio is less than 0, for negative resistance Buddhist nun's state.Think that damping ratio is 0.03 rim condition for just reaching stability to system under normal operating conditions in engineering.Therefore Under base regime and heavy load operating mode, system is all in unstable state.

Generator operating condition under the different service conditions of table 1

System electromechanical modes characteristic root and damping ratio under the different service conditions of table 2

The parameter of PSS4B is optimized using PSO optimization algorithms after improvement, n=1, m=3, Fig. 7 (a), Fig. 7 (b) are Using improving PSO algorithms, under conditions of randomly selecting initial solution, the group that is obtained to the optimizing twice of PSS4B parameters to be optimized The change curve of adaptive optimal control angle value, as seen from the figure, fitness value declines comparatively fast early period in search in two suboptimization, illustrates to improve Mixing PSO algorithms has faster speed of searching optimization.

It using Philips-Heffron models, is obtained by calculation under base regime, frequency of oscillation 1.438Hz；Power generation Machine model K₁~K₆Each parameter：K₁=1.84, K₂=2.40, K₃=0.38, K₄=1.57, K₅=0.0023, K₆=0.53.According to Document 2 is to PSS4B parameter tunings, and using the method for exploration, parameter setting is carried out to PSS4B high band phase compensation links, System oscillation frequency nearby carries out phase compensation, and the power system stabilizer, PSS after note is adjusted is H-PSS4B.

It is that PSS4B takes H-PSS4B and the present invention to the inhibition and robustness of low-frequency oscillation after the verification present invention optimizes Optimization method compare, note the application optimization after PSS4B be GPSO-PSS4B.Table 3 is the value of two kinds of parameter tuning methods.

Table 3PSS4B parameter values

According to the one machine infinity bus system state matrix of listed 16 ranks write, can seek respectively under 3 kinds of typical conditions of system, Characteristic value and damping ratio after PSS4B under two kinds of setting methods of installation under system electromechanical modes, such as table 4.It can be obtained by table 4, when After installing PSS additional, the characteristic value of system is moved to Left half-plane, and system damping gets a promotion.System is electromechanical in the case of comparing 3 kinds Mode damping ratio, under the conditions of base regime and light load, the more classical parameter PSS4B of system damping for installing H-PSS4B additional has one Fixed enhancing, but damp under heavy load conditions and slightly deteriorate, since H-PSS4B is the parameter tuning carried out under base regime, Other operating conditions are not considered, so when service condition changes, H-PSS4B performances are not necessarily completely superior to classical parameter PSS4B.And GPSO-PSS4B considers the different operating condition of system, after installation system damping in basic, light load, again It is respectively 0.27,0.31,0.28 under load condition, is more than the system damping for installing H-PSS4B additional, illustrates that the PSS4B after optimization has Lifting system damping is imitated, the stability of system is enhanced.

State matrix A added with PSS4B one machine infinity bus systems is the square formation of 16 ranks, a_i,jI-th row jth in representing matrix The nonzero element of row, wherein state variable are：

X=[Δ δ, Δ ω_r,ΔE_q′,ΔE_fd,Δv₁,Δv₂,Δv₃,Δx₁,Δx₂,Δx₃,Δx₄,Δx₅,Δx₆,Δ u₁,Δu₂,Δu₃]

Nonzero element is in state matrix A：

a_1,2=2 π f₀；a_2,1=-K₁/T_J；a_2,3=-K₂/T_J；a_3,1=-K₃K₄/T₃；a_3,3=-1/T₃；a_3,4=K₃/T₃； a_4,1=-K₅K_A/T_R；a_4,3=-K₆K_A/T_R；a_4,4=-1/T_R；a_4,14=K_A/T_R；a_4,15=K_A/T_R；a_4,16=K_A/T_R；a_5,2=1/ T_M； a₅,₅=-1/T_M；a_6,1=-K₁/T_J；a_6,3=-K₂/T_J；a_6,6=-1；a_7,1=-K₁/T_J；a_7,3=-K₂/T_J；a_7,6=-1； a_7,7=-1； a₈,₂=T_L1K_L1/(T_L2T_M)；a_8,5=K_L1/T_L2-T_L1K_L1/(T_L2T_M)；a_8,8=-1/T_L2；a_9,2=T_L7K_L1/ (T_L8T_M)； a_9,5=K_L1/T_L8-T_L7K_L1/(T_L8T_M)；a_9,9=-1/T_L8；a_10,2=T_I1K_I1/(T_I2T_M)；a_10,5=K_I1/T_I2- T_I1K_I1/(T_I2T_M)； a_10,10=-1/T_I2；a_11,2=T_I7K_I1/(T_I8T_M)；a_11,5=K_I1/T_I8-T_I7K_I1/(T_I8T_M)；a_11,11=- 1/T_I8；a_12,1=-K_H1T_H1K₁/(T_H2T_J)；a_12,3=-K_H1T_H1K₂/(T_H2T_J)；a_12,6=-K_H1T_H1/T_H2；a_12,7=K_H1/T_H2- K_H1T_H1/T_H2； a_12,12=-1/T_H2；a_13,1=-K_H1T_H7K₁/(T_H8T_J)；a_13,3=-K_H1T_H7K₂/(T_H8T_J)；a_13,6=-K_H1T_H7/ T_H8； a_13,7=K_H1/T_H8-K_H1T_H7/T_H8；a_13,13=-1/T_H8；

T_M=0.017823, T₃=K₃T′_d0。

System features value after table 4PSS4B optimizations

The dynamic simulation of one machine infinity bus system is verified

The robustness of GPSO-PSS4B after optimization and the validity of power oscillation damping run work in system difference respectively Nonlinear Simulation is carried out under condition and disturbed conditions, and compared with the simulation result of canonical parameter PSS4B, H-PSS4B, the fortune of system Row operating mode and disturbed conditions such as table 5

5 system difference operating condition of table is arranged with disturbance

Fig. 8 (a), Fig. 8 (b) are under different system operating condition, and microvariations, power generation occur for generator mechanical power when 0.8s Machine rotor rotating speed deviation and electromagnetic power curve graph.

Fig. 8 (a) is indicated, under base regime when system does not add PSS, low-frequency oscillation, generator electromagnetic work occur for system Rate is apparent with rotor speed deviation amplitude and oscillatory extinction is slow, and system plays pendulum；As addition canonical parameter PSS4B When, speed oscillation amplitude attenuation is apparent, restores to stablize after 6s；When H-PSS4B is added, rotor speed is shaken in 4s or so stoppings It swings；When GPSO-PSS4B is added, system oscillation number significantly reduces, only 2 times, and rotor speed oscillation is flat in 2.3s or so Breath, regulating time shorten 1.6s compared with H-PSS4B.The electromagnetic power oscillation of generator also has similar decaying.

Fig. 8 (b) indicates also there is similar decaying under light load conditions.When heavy load such as suppression to oscillation of Fig. 8 (c), H-PSS4B Effect processed is not so good as the PSS4B of classical parameter, and the GPSO-PSS4B after present invention optimization remains to the oscillation of inhibition quickly, keeps system extensive It is multiple to stablize.

Fig. 9 (a), 9 (b), 9 (c) are that three-phase shortcircuit occurs for generator end busbar 0.8s, continue reclosing success after 0.1s When, the generator amature rotating speed deviation under different system operating condition and electromagnetic power curve graph.It can by 9 (a), 9 (b), 9 (c) , the GPSO-PSS4B of optimization can full out inhibit oscillation that system is made to restore under the conditions of large disturbances occur for three kinds of typical conditions Stablize, and the number of oscillation is minimum；In base regime and light hours, more classical parameter faster inhibits to vibrate H-PSS4B, but in weight When load, performance is not so good as classical parameter.Thus the GPSO-PSS4B after present invention optimization adapts to different system service condition, increases Strong system transient stability.

In order to illustrate the robustness of the GPSO-PSS4B after parameter optimization of the present invention, compared using ITAE indexs such as following formula Compared with

The numerical value of TAE is smaller, illustrates that the inhibition in time-domain-simulation to low-frequency oscillation is better.Under different operating modes and disturbance It is as shown in table 6 to install the performance index value that different parameters PSS4B is obtained additional.It can obtain from table 6, under various operating modes and disturbance, install additional The ITAE performance indicators of GPSO-PSS4B both less than install PSS4B and two kinds of situations of H-PSS4B additional, illustrate to install GPSO-PSS4B additional Afterwards, the departure of the overshoot of low-frequency oscillation, regulating time, rotor speed and electromagnetic power is reduced, and robustness is good.

The above emulation explanation, the GPSO-PSS4B after the present invention optimizes is under different system disturbances and operating condition Can more typical parameter PSS4B and H-PSS4B quickly damped oscillations, reduce the number of oscillation, enhance system dynamic stability, test Having demonstrate,proved the PSS4B after optimization proposed by the present invention has good robustness.

The lower ITAE performance index values of the different operating mode disturbances of table 6

The anti-low-frequency oscillation effect of PSS4B after the verification optimization of 3 machine, 9 node system

Establish 3 machine, 9 node system

Effectively power oscillation damping and there can be certain robustness further to verify the improved PSS4B of the present invention, It is S using 9 node system wiring diagram of US West's power grid WSCC3 machines, such as Figure 10 a reference values_B=100MVA, U_B=230kV.System Frequency is 60Hz, and the apparent energy of three generators G1, G2, G3 are respectively 247.5MVA, 192MVA, 128MVA, generator G1 Balance nodes are set as, G2, G3 are set as PV node.Three generators are high-speed excitation, excitation parameter：K_A=200, T_R=0.02, Remaining parameter is shown in document 3.

In order to realize the PSS4B parameter optimization methods with robustness proposed in text, 3 kinds of different power grid fortune are considered Row condition respectively represents the basic operation conditions of power grid (Case 1), heavy service situation (Case 2), light(-duty) service situation (Case 3).The actual operating condition of system is intricate, and the heavy load and light load of selection are all system operation most serious Operating mode, therefore can provide sufficient system stability margin by the PSS4B that these three operating condition designs come out.3 kinds of operation works of generator Condition such as table 6, load condition such as table 7.

Generator operating condition under the different service conditions of table 6

Load condition under the different service conditions of table 7

The theory analysis of 3 machine, 9 node system is to be based on multi-computer system inearized model, is realized by computer programming. Since program is complex, it is related to multiple variables and expression formula in system, 3 machines of installation PSS4B and list branch PSS to be studied 9 node system state matrixes are 26 ranks (wherein every 3 rank of generator, 1 rank of excitation system, single branch PSS2 ranks, PSS4B12 Rank), to ensure the correctness of eigenvalue Method, will to theoretical linear result of calculation and Simulink simulation datas result into Row compares.

Pass through generator voltage u under the system dq coordinate systems of Simulink simulation datas_Di、u_QiIt can evidence with admittance matrix Y FormulaAcquire generator end electric current i under system dq coordinate systems_Di、i_Qi, convolution δ can be calculated_i, finally according to formulaEach generator generator terminal can be calculated separately at itself U under dq coordinate systems_di、 U_qi、I_di、I_qi, these values can also be obtained by Simulink Straight simulations.The system for taking base regime It is verified, Comparative result is as shown in table 8.

8 calculation and programming result of table and Simulink simulation result contrast tables

As shown in Table 8, program calculation result differs very small with simulation result, in tolerance interval.Therefore it demonstrates The correctness of power train linearisation of the present invention.

Element in the state matrix of 3 machine, 9 node system for 0 is as follows, wherein a_i,jIndicate the i-th row in state matrix A, The element of jth row,I-th in representing matrix A₁It goes to i-th₂Row, jth₁It arranges to jth₂Matrix-block.

a_1:3,4:6=diag (ω₀),a_4:6,1:3=-diag (1/T_Ji)K₁,a_4:6,7:9=-diag (1/T_Ji)K₂,a_7:9,1:3=- diag(1/T′_d0i)K₄, a_7:9,7:9=-diag (1/T '_d0i)/K₃,a_7:9,10:12=diag (1/T '_d0i),a_10:12,1:3=-diag (1/T_Ri)diag(K_Ai)K₅, a_10:12,7:9=-diag (1/T_Ri)diag(K_Ai)K₆,a_10:12,10:12=-diag (1/T_Ri),a_11,22 =a_11,23=a_11,24=K_A2/T_R2,a_11,26=K_A3/T_R3, a_13,5=1/T_M,a_13,13=-a_13,5,a_15,1=a_14,1=a_5,1,a_15,2 =a_14,2=a_5,2,a_15,3=a_14,3=a_5,3,a_15,7=a_14,7=a_5,7, a_15,8=a_14,8=a_5,8,a_15,9=a_14,9=a_5,9, a_15,14=a_14,14=-1, a_15,15=-1, a_16,5=T_L1K_L1/(T_L2T_M),a_16,13=K_L1/T_L2-a_16,5, a_16,16=-1/T_L2, a_17,5=T_L7K_L1/(T_L8T_M),a_17,13=K_L1/T_L8-a_17,5,a_17,17=-1/T_L8,a_18,5=T_I1K_I1/(T_I2T_M), a_18,13= K_I1/T_I2-a_18,5,a_18,18=-1/T_I2,a_19,5=T_I7K_I1/(T_I8T_M),a_19,13=K_I1/T_I8-a_19,5,a_19,19=-1/T_I8,

System linearization rank rear writes system-wide state matrix, finds out total system characteristic value, by calculating electromechanical circuit phase It closes ratio and selects electromechanical modes, and find out the participation factor for reflecting characteristic value and state variable relationship under electromechanical modes.Under 3 kinds of operating modes Result such as table 9 to 14.

Table 9 participates in factor result of calculation (base regime)

10 system electromechanical oscillations mode (base regime) of table

Table 11 participates in factor result of calculation (heavy load operating mode)

12 system electromechanical oscillations mode (heavy load operating mode) of table

Table 13 participates in factor result of calculation (light load conditions)

14 system electromechanical oscillations mode (light load conditions) of table

According to the above analysis, the corresponding two characteristic value real parts of electromechanical oscillations mode are all closer to the complex plane imaginary axis, corresponding Damping ratio it is all smaller, under some operating modes be less than 0.03, present underdamping state.When there is disturbance in system, easily cause The low-frequency oscillation of system is unfavorable for the dynamic stability of system.It can be obtained according to the result of calculation for participating in the factor, be generated electricity under three kinds of operating modes The generator rotor angle of machine G2 and G3 are with rotating speed respectively to λ_9,10With λ_7,8The participation of two oscillation modes is higher, therefore need to be in generator G2 Enhance system damping with PSS is installed on G3 additional.Therefore plan to install common PSS additional on generator G3, be installed additional on generator G2 PSS4B, PSS4B and the transmission function difference of common PSS are as shown in Figure 2.

The method that common PSS parameter setting is set using multi-computer system PSS parameter.The parameter optimization of PSS4B is utilized and is changed Into rear PSO algorithms, n=3, m=3, Figure 11 (a), 11 (b) are to be sought twice to PSS4B parameters to be optimized using improvement PSO algorithms The change curve of excellent obtained group's adaptive optimal control angle value.Parameter such as table 15 after PSS4B optimizations.

15 PSS4B parameter values of table

H-PSS4B setting methods are as follows：According to the method for document 4 to PSS4B parameter tunings, multi-computer system K1 is initially set up Unit to be ground and remaining unit approximately equivalent are one machine infinity bus system, obtain unit to be ground by~K6 inearized models Phillips-heffron models, are then based on phase compensation principle, and carrying out parameter to PSS4B high band phase compensation links sets It sets, phase compensation is carried out near system oscillation frequency, the power system stabilizer, PSS after note is adjusted is H-PSS4B.

It is that PSS4B takes H-PSS4B and the present invention to the inhibition and robustness of low-frequency oscillation after the verification present invention optimizes Optimization method compare, remember the present invention optimization after PSS4B be GPSO-PSS4B.Table 15 is taking for two kinds of parameter tuning methods Value.

It is 3 kinds of PSS4B values of quantitative comparison to low-frequency oscillation inhibiting effect, the premise of common PSS is installed additional in generator G3 Under, sought under different operation of power networks operating modes using eigenvalue Method, generator G2 install additional canonical parameter PSS4B, H-PSS4B with System electromechanical oscillations mode characteristic values and corresponding damping ratio in the case of tri- kinds of GPSO-PSS4B, such as table 16.

The front and back system features value of table 16 PSS4B optimizations

For system in no PSS, the damping ratio of two electromechanical modes characteristic values is all in underdamping, after installing PSS, according to table 16, the characteristic value under electromechanical modes is moved to Left half-plane, and under 3 kinds of different operation of power networks situations under two oscillation modes System damping ratio be both greater than 0.1.Base regime is taken to analyze, generator G3 has been obviously improved corresponding spy after installing common PSS additional Value indicative λ_7,8Damping ratio, when on generator G2 install additional GPSO-PSS4B when, the electromechanic oscillation mode λ with G2 strong correlations_9,10It is right The damping ratio answered increases to 0.348, when installing H-PSS4B and canonical parameter PSS4B additional, λ_9,10Corresponding damping ratio increases respectively To 0.202 and 0.148；After installing GPSO-PSS4B additional, with the weak relevant eigenvalue λs of G2_7,8Corresponding damping ratio slightly reduces, System stability is influenced can be ignored, it is this in multi-computer system, increase the damping of certain unit while but deteriorating other and shakes There is the reason of negative damping phenomenon to 3 machine, 9 node system simultaneously in the phenomenon that swinging mode damping, referred to as negative damping phenomenon, document 5 It is analyzed, and points out that negative damping phenomenon is the intrinsic propesties of multi-computer system, root does not lie in the reasonability of PSS designs.Explanation System damping promotion becomes apparent after installing GPSO-PSS4B additional, illustrates that the PSS4B after optimization can enhance the stability of system, improves The damping characteristic of electromechanical modes.

The dynamic simulation of 3 machine, 9 node system is verified

GPSO-PSS4B after optimizing for evaluation adds the inhibition of low-frequency oscillation in generator excitation voltage respectively Under conditions of 10% disturbance and three phase short circuit fault, simulation analysis is carried out.

(1) small disturbed stability is analyzed

10% square wave step, duration 0.1s, comparison occur in 1s for the excitation voltage reference value of generator G2 The dynamic stability of GPSO-PSS4B, H-PSS4B and canonical parameter PSS4B under three kinds of typical conditions.Choosing generator G2 is Example, change of the analysis system in basic operational mode, heavy load, light(-duty) service pattern lower rotor part rotating speed deviation and electromagnetic power Change, such as Figure 12 (a), 12 (b) and Figure 13 (a), Figure 13 (b).

Base regime is taken to be analyzed, when system does not add PSS, low-frequency oscillation, generator amature rotating speed and electricity occur for system Magnetic power amplitude is apparent and oscillatory extinction is slow；After PSS is added, low-frequency oscillation is inhibited.It can be seen that, improve from figure GPSO-PSS4B after PSO optimizations more typically parameter PSS4B faster can inhibit to vibrate under three kinds of typical conditions, and reduction is shaken It swings number and shortens regulating time, system is made to restore to stablize.

(2) large disturbance stability is analyzed

For transient stability of the evaluation system under large disturbances, apply three phase short circuit fault in circuit 5-7 when passing through 0.8s, Duration 0.1s is realized, GPSO-PSS4B is compared with the simulation result of canonical parameter PSS4B, H-PSS4B, takes hair For motor G2.Figure 14 (a), Figure 14 (b), Figure 15 (a), Figure 15 (b), Figure 16 (a), Figure 16 (b), Figure 17 (a), Figure 17 (b) Respectively system is under basic operational mode, heavy load, light(-duty) service pattern, the rotor speed and electromagnetic power of generator G2 Change curve.

Shown in Figure 14 (a), Figure 14 (b), Figure 15 (a), Figure 15 (b), Figure 16 (a), Figure 16 (b), Figure 17 (a), Figure 17 (b), The GPSO-PSS4B that the present invention optimizes can most inhibit oscillation that system is made to reach soon under the conditions of large disturbances occur for three kinds of typical conditions To stabilization, the number of oscillation is minimum.And the GPSO-PSS4B after present invention optimization adapts to different system service condition, enhances system Transient stability.

There is robustness in order to illustrate the GPSO-PSS4B power oscillation dampings after parameter optimization of the present invention, saved according to 3 machines 9 Dot system is compared using ITAE indexs such as formula following formula

The numerical value of ITAE is smaller, illustrates that the inhibition in time-domain-simulation to low-frequency oscillation is better.Different operating modes and disturbance The performance index value that lower installation different parameters PSS4B is obtained is as shown in table 17.It can be obtained from table 17, under various operating modes and disturbance, The ITAE performance indicators for installing GPSO-PSS4B additional both less than install PSS4B and two kinds of situations of H-PSS4B additional, illustrate to install GPSO- additional After PSS4B, the rotor speed of low-frequency oscillation and the departure of electromagnetic power are reduced, and robustness is good.

The lower ITAE performance index values of 17 3 machine of table, 9 node system difference operating mode disturbance

Document 1.Abido M A.Optimal design of power-system stabilizers using Particle swarm optimization [J] .IEEE Power Engineering Review, 2002,17 (3)：406-413

2. Zhao Xiao of document is big, Xie Huan, Lv Sixin, waits the parameter tuning and field test of power system stabilizers 4B [J] electric power network techniques, 2016 (2)：508-513.

Document 3.Anderson P, Fouad A.Power System Control and Stability [M] //Power System control and stability.Iowa State University Press, 1977：1177-1178.

Document 4. is gone into business after Hao, the multi-computer system PSS designs of Ma Lili, Liu Xian woodss based on equivalent one machine infinity bus system [J] electric power system protection and controls, 2009,37 (23)：70-74.

5. Zhao's book of document is strong, Chang Xianrong, He Renmu, waits Borrow damping phenomena and Negative damping effect Damping during .PSS controls [J] Proceedings of the CSEEs, 2004,24 (5)：7-11.

Finally it should be noted that：The above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations；Although Present invention has been described in detail with reference to the aforementioned embodiments, it will be understood by those of ordinary skill in the art that：It still may be used To modify to the technical solution recorded in aforementioned each example or equivalent replacement of some of the technical features；This A little modification or replacements, the spirit and scope for each case technology scheme of the present invention that it does not separate the essence of the corresponding technical solution.

Claims (6)

1. improving the application method of PSO algorithm configuration novel electric power system stabilizers PSS4B, which is characterized in that including：

S1. using random weight in such a way that crossover operation is combined, PSO algorithms are improved；

S11. it is balance local improving and ability of searching optimum, using the following formula of random weight：

Wherein, ω is inertia weight, and randn (0,1) is the random number of 0 to 1 normal distribution, and rand (0,1) is equal between being 0 to 1 The random number of even distribution, μ_max、μ_min, μ be respectively random weighted mean maximum value, minimum value and average value；

S12. it is that algorithm is enable to reach effective balance between overall situation detection and part exploitation, constructs the PSO containing compressibility factor Effectively to control flying speed of partcles, speed formula is algorithm：

In formula,Referred to as compressibility factor is followed the example of as c=4.1,c₁、c₂For Studying factors；r₁、r₂Between being 0 to 1 The random number of even distribution；P_id、P_gdRespectively individual optimal and global optimum, X_idFor a body position；

S13. the hybridization link being introduced into genetic algorithm, i.e., in each iterative calculation, according to given probability of crossover, choosing The particle for selecting specified quantity is put into hybridization pond, and particle hybridizes two-by-two at random in pond, generates the filial generation particle of invariable number, and takes For parental generation particle, filial generation particle position can be obtained according to parent particle position arithmetic crossover, i.e.,

Child (x)=pparent₁(x)+(1-p)·parent₂(x)

Wherein, p is the random number between 0 to 1；

The speed of filial generation particle is obtained according to following formula：

After experience hybridization link, the advantages of filial generation particle of generation will inherit parent；

S2. simplify PSS4B parameters

S21. optimize bandpass filtering and gain link；

Bandpass filtering link setting formula be：

In formula, T_L1、T_L2、T_L7、T_L8For the time constant of transmission function in low-frequency range mixing module；K_L1、K_L2It is mixed for low-frequency range The yield value of the positive and negative branch of module；F_LFor the centre frequency of low frequency filtering link；

It is 1.2 to take R, then bandpass filtering link parameter to be optimized is only each branch hub frequency F_L、F_IWith F_H, gain link waits for Optimal Parameters are K_L、K_IWith K_H；

The bandpass filtering link optimization problem to be optimized for being converted into following belt restraining：

In formula, K_L、K_I、K_HRespectively gain link parameter to be optimized；F_L、F_I、F_HRespectively low frequency, intermediate frequency and high-frequency band pass filter The centre frequency of link；

S22. optimize the phase compensation link of each branch；

The parameter of required optimization is T_L5、T_I5、T_H5、T_L6、T_I6、T_H6, phase compensation link, which optimizes, can be converted into following optimization problem：

S23. by running Simulink models, performance indicator is calculated, then using performance indicator as the fitness value of particle, most After judge whether to meet termination condition to determine whether terminate optimizing；

S3. using eigenvalue Method emulate under Nonlinear Simulation and Simulink, quantitative analysis PSS4B is to low-frequency oscillation The effect of inhibition.

2. the application method according to claim 1 for improving PSO algorithm configuration novel electric power system stabilizers PSS4B, It is characterized in that：Error in the step S2 takes each inclined absolute value of the difference of generator amature angular speed and each generator electromagnetic work The sum of inclined absolute value of the difference of rate.

3. the application method according to claim 1 for improving PSO algorithm configuration novel electric power system stabilizers PSS4B, It is characterized in that：Consider that the PSS4B after optimization has robustness in the step 2, suitable damping is provided, object function is chosen It is as follows：

In formula, m is operation of power networks operating mode number；N is generator number in system；I is i-th generator；J is jth kind operating mode； Δω_i,j(t) the rotor speed deviation for being the generator i under jth kind operating mode；ΔP_ei,j(t) it is generator i under jth kind operating mode Electromagnetic power deviation；a_i,jAnd b_i,jThe adjustable weight factor for being generator i at operating mode j.

4. the application method according to claim 1 for improving PSO algorithm configuration novel electric power system stabilizers PSS4B, It is characterized in that：Population dimension D=6, population scale S=30, the iterations T=100 chosen in the step S1, study Factor c₁=c₂=2, random weight maximum value μ_max=0.9, minimum value μ_min=0.4, random weight weight variances sigma=0.4 hybridizes ring The probability of crossover P of section_c=0.9, hybridize pond size S_p=0.2.

5. the application method according to claim 1 for improving PSO algorithm configuration novel electric power system stabilizers PSS4B, It is characterized in that：Weight factor a in the step S2 object functions_i,j=b_i,j=1, parameter K_L、K_I、K_HRestriction range be set as [0.1,100], F_LRestriction range be set as [0.01,0.1], F_IRestriction range be set as [0.1,1], F_HRestriction range be set as [1,10]。

6. the application method according to claim 1 for improving PSO algorithm configuration novel electric power system stabilizers PSS4B, It is characterized in that：The step S3 includes that one machine infinity bus system carries out parameter optimization and 3 machine, 9 node system pair to PSS4B PSS4B carries out parameter optimization.