CN109854437A - A kind of governor pid parameter optimization method based on particle swarm algorithm - Google Patents
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Abstract
The embodiment of the present application shows a kind of governor pid parameter optimization method based on particle swarm algorithm, successively optimizes the parameter using particle group optimizing method, obtains Optimal Parameters array, includes at least one set of Optimal Parameters in the Optimal Parameters array；The disturbance quantity of every group of Optimal Parameters is calculated separately, determines that the Optimal Parameters for generating minimal disturbances amount are objective optimization parameter.Technical solution shown in the embodiment of the present application is optimized pid parameter using particle swarm optimization algorithm, and one-of-a-kind system damping coefficient increases to 1.8958 by -0.7074 after optimization, and damping ratio increases to 0.6 by -0.0013；System damping ratio is increased to 0.1297 by 0 after the method using additional controller, it is seen that ultra-low frequency oscillation can be effectively suppressed in the technical solution that application is implemented to exemplify, and inhibiting ultra-low frequency oscillation is actually the negative damping of reduction system, increases system positive damping effect.
Description
Technical field
The present invention relates to electric power system stability control technical field, in particular to a kind of governor based on particle swarm algorithm
Pid parameter optimization method.
Background technique
The hydraulic power potentials of China occupies first place in the world, and with the development and utilization continued to increase to hydroelectric resources, China is
As the maximum country of hydropower installed capacity in the world.Relative to thermal power generation, hydroelectric generation more clean and environmental protection meets China
The national strategy of sustainable development；And compared to other clean energy resourcies, cost is relatively low for water power, and the relevant technologies are mature, and construction is big
Type Hydropower Unit is the principal mode of China's development and utilization water power, and keeping Hydropower Unit stable operation in power grid is China Power
The inevitable requirement of development.
Yunnan main force hydro turbine governor is all made of microcomputer governor, and based on PID type governor.Hydropower Unit
The stability and dynamic characteristic of governor depend on governor parameter, and regulation quality difference is larger when parameter difference, unreasonable
Parameter setting may cause unit and adjust slowly or generate big overshoot or anti-tune.Consider that " water hammer effect " influences, anti-tune effect
It is larger not have the support of due frequency not only, other units can be offset instead and are correctly contributed variation, can also be caused when serious
System oscillation.Thus, for the ultra-low frequency oscillation phenomenon for inhibiting Yunnan Power System, developing a kind of suitable governor parameter seems especially heavy
It wants.
Summary of the invention
The application's is designed to provide a kind of governor pid parameter optimization method based on particle swarm algorithm, the side
Method inhibits the ultra-low frequency oscillation phenomenon of Yunnan Power System.
According to an embodiment of the present application, a kind of governor pid parameter optimization method based on particle swarm algorithm is provided, is wrapped
It includes:
The initiation parameter of the hydraulic turbine is set；
The parameter is successively optimized using particle group optimizing method, obtains Optimal Parameters array, in the Optimal Parameters array
Including at least one set of Optimal Parameters；
The disturbance quantity of every group of Optimal Parameters is calculated separately, determines that the Optimal Parameters for generating minimal disturbances amount are objective optimization ginseng
Number.
It is selectable, the calculating process of the disturbance quantity specifically:
MinJ=α JITAE+(1-α)JDamping, wherein J is disturbance quantity JITAFFor revolving speed impact factor, JDampingFor damping
Torque impact factor；
Wherein, Δ ω revolving speed deviation；
In formula,
Selectable, if enabling Dmd=0, frequency of oscillation ω is can be obtained in solutiond, and ωd=2 π fd；
fdFor boundary frequency, speed-regulating system provides corresponding frequency of oscillation when damping is zero；As frequency of oscillation f > fdWhen, water
Turbine speed-regulating system generates negative damping torque；f<fdWhen, Turbine Governor System generates positive damping torque.
Selectable, described the step of successively optimizing the parameter using particle group optimizing method, includes:
Wherein, wherein vidFor the step-length that parameter changes every time, xid' be optimization after parameter, xid' be optimization before parameter；
wiFor weight coefficient, c1And c2For Studying factors, r1And r2For the random number between [0,1], vidFor the flight of particle i
Speed, xidFor the position of particle i, pidFor the individual extreme value of particle i, pgdFor the global extremum of particle i.
It is selectable, the wiRandom number of=(1+r)/2, the r between [0,1].
From the above technical scheme, the embodiment of the present application shows a kind of governor pid parameter based on particle swarm algorithm
Optimization method successively optimizes the parameter using particle group optimizing method, obtains Optimal Parameters array, in the Optimal Parameters array
Including at least one set of Optimal Parameters；The disturbance quantity of every group of Optimal Parameters is calculated separately, determines the optimization ginseng for generating minimal disturbances amount
Number is objective optimization parameter.Technical solution shown in the embodiment of the present application carries out pid parameter using particle swarm optimization algorithm
Optimization, one-of-a-kind system damping coefficient increases to 1.8958 by -0.7074 after optimization, and damping ratio is increased to by -0.0013
0.6；System damping ratio is increased to 0.1297 by 0 after the method using additional controller, it is seen that the skill exemplified is implemented in application
Ultra-low frequency oscillation can be effectively suppressed in art scheme, and inhibiting ultra-low frequency oscillation is actually the negative damping of reduction system, increases system
Positive damping effect.
Detailed description of the invention
In order to illustrate the technical solutions in the embodiments of the present application or in the prior art more clearly, below will be to institute in embodiment
Attached drawing to be used is needed to be briefly described, it should be apparent that, the accompanying drawings in the following description is only some implementations of the application
Example, for those of ordinary skill in the art, without creative efforts, can also obtain according to these attached drawings
Obtain other attached drawings.
Fig. 1 is PID type governor model；
Fig. 2 is that a kind of governor pid parameter optimization method based on particle swarm algorithm exemplified is preferably implemented according to one
Flow chart；
Fig. 3 is that the K exemplified is preferably implemented according to oneP、KIThe comparison of test results figure of influence to damping coefficient；
Fig. 4 is that the B exemplified is preferably implemented according to oneP、KDThe comparison of test results figure of influence to damping coefficient；
Fig. 5 is the schematic diagram that damping coefficient comparison before and after the parameter optimization exemplified is preferably implemented according to one；
Fig. 6 is the schematic diagram that revolving speed deviation comparison before and after the parameter optimization exemplified is preferably implemented according to one；
Fig. 7 is the schematic diagram that the additional controller system model exemplified is preferably implemented according to one；
Fig. 8 is that the additional controller system frequency change curve exemplified is preferably implemented according to one.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Whole description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other
Embodiment shall fall within the protection scope of the present invention.
Formula used by herein:
1) Turbine Governor System damping characteristic:
The governor model of water turbine set is typical PID type governor, relationship is as schemed using electric tune type speed-regulating system
Shown in 1, transmission function are as follows:
In formula, Δ μ is guide vane opening deviation, and Δ ω is revolving speed deviation, KP、KI、KDThe respectively ratio of governor, integral
And differential coefficient, BPFor difference coefficient, TGFor executing agency's time constant.
Hydraulic turbine transmission function are as follows:
In formula, Δ PmFor the mechanical output deviation of generator；TWFor water hammer effect time constant, the general value of full load exists
0.5-4.0s。
If water turbine set speed-regulating system transmission function is G (s), as system input signal Δ ω, according to Phillips-
Heffron model, the mechanical deflection Δ P that prime mover generatesmFor
ΔPm=-G (s) Δ ω (3)；
In formula, G (s)=Ggov(s)GW(s).By s=j ωdSubstitution formula (3), obtains:
ΔPm=-DmdΔω-KmsΔδ (4)；
In formula, DmdAnd KmsThe damping provided for Turbine Governor System and synchronizing torque coefficient, and
In formula,
If enabling Dmd=0, frequency of oscillation ω can be obtained in solutiond, and ωd=2 π fd.Define fdFor boundary frequency, i.e. speed regulation system
System provides corresponding frequency of oscillation when damping is zero.As frequency of oscillation f > fdWhen, Turbine Governor System generates negative damping torque；
f<fdWhen, Turbine Governor System generates positive damping torque.
Damping torque specificity analysis is carried out to the control parameter of governor, is changing KP、KI、KD、BPIn the case where parameter,
Analyze the damping coefficient of hydrogovernor with frequency situation of change, as shown in Figure 3 and Figure 4.
In Fig. 3, in the ultralow frequency range of 0.01-0.1Hz, work as KPWhen increase, damping gradually weakens, or even negative resistance occurs
Buddhist nun；KIIt is significant in ultralow frequency range negative resistance character, and KI is bigger, the amplitude of negative damping is bigger.Fig. 4 illustrates in ultralow frequency range, BPSubtract
Hour damping change very little；KDIt is basic that positive damping is provided.
(2) unit Kinematic:
The generator equation of motion are as follows:
In formula, TJFor the inertia time constant of generator, Δ PeFor electromagnetic power deviation, D is Generator Damping coefficient, ω0
For benchmark angular speed.
Based on complex torque coefficients, Δ PeIt is writeable are as follows:
ΔPe=DedΔω+KesΔδ (7)；
In formula, DedFor damping torque component, KesFor synchronizing torque component.Formula (4) and formula (7) are substituted into formula (6), and neglected
Slightly network loss, obtains the damping ratio of system are as follows:
In formula, the electromagnetic power variable quantity of generator is approximately the active variable quantity of load, i.e. Δ Pe=KLΔ ω, wherein
KLFor load frequency regulation coefficient.
In order to facilitate analysis, system electromagnetic power variable quantity only considers part related with Δ ω.It can be obtained by formula (8), Ded
It is approximately equal to KL, do not consider KesIt is enabled to be equal to zero, then formula (8) simplifies are as follows:
The damping characteristic that can analyze computing system using damping torque method, works as DmdWhen > 0, speed-regulating system is provided to system
Positive damping；Work as DmdWhen < 0, speed-regulating system provides negative damping to system.
Referring to Fig. 2, the embodiment of the present application provides a kind of governor pid parameter optimization side based on particle swarm algorithm
Method, comprising:
The initiation parameter of the S101 setting hydraulic turbine；
Wherein, it includes: proportional gain K that parameter, which includes Optimal Parameters,P, integral gain KI, and, differential gain KD, adjust difference system
Number BP；
Damping torque specificity analysis is carried out to the control parameter of governor, is changing KP、KI、KD、BPIn the case where parameter,
The damping coefficient for analyzing hydrogovernor is as shown in Figure 3 and Figure 4 with frequency situation of change.
In Fig. 3, in the ultralow frequency range of 0.01-0.1Hz, work as KPWhen increase, damping gradually weakens, or even negative resistance occurs
Buddhist nun；KI is significant in ultralow frequency range negative resistance character, and KIBigger, the amplitude of negative damping is bigger.Fig. 4 illustrates in ultralow frequency range, BP
Damping change very little when reduction；KDIt is basic that positive damping is provided.
S102 successively optimizes the parameter using particle group optimizing method, obtains Optimal Parameters array, the Optimal Parameters number
It include at least one set of Optimal Parameters in group；
Wherein, particle group optimizing (PSO) algorithm is one kind of evolution algorithm, and PSO is initialized as the random parameter of a group, is led to
It crosses continuous iteration and finds optimal solution parameter.In an iterative process, each parameter by follow individual extreme value and global extremum come
Update oneself.All parameters have the adaptive value of oneself, and the step-length in the optimization direction and optimization of each parameter is determined according to speed,
Each odd number follows current optimized parameter to scan in solution space.According to the step-length of the optimization of following Policy Updates parameter.
It is described using particle group optimizing method successively optimize the parameter the step of include:
Wherein, wherein vidFor the step-length that parameter changes every time, xid' be optimization after parameter, xid' be optimization before parameter；
wiFor weight coefficient, c1And c2For Studying factors, r1And r2For the random number between [0,1], vidFor the flight of particle i
Speed, xidFor the position of particle i, pidFor the individual extreme value of particle i, pgdFor the global extremum of particle i.
It is selectable, wi=(1+r)/2 (11)；
Random number of the r between [0,1].
Technical solution w shown in the embodiment of the present applicationi=(1+r)/2.It can guarantee the diversity in parameter optimisation procedure,
Help to find optimal solution in optimization process.
S103 calculates separately the disturbance quantity of every group of Optimal Parameters, determines that the Optimal Parameters for generating minimal disturbances amount are that target is excellent
Change parameter.
Wherein, the calculating process of the disturbance quantity specifically:
MinJ=α JITAE+(1-α)JDamping, wherein J is disturbance quantity JITAFFor revolving speed impact factor, JDampingFor damping
Torque impact factor；
Wherein, Δ ω revolving speed deviation.
This paper presents a kind of using the damping torque that speed-regulating system provides as the method for objective function, it may be assumed that
In formula, n=(fmax-fmin)/f, fmaxAnd fminRespectively the maximum and minimum value of frequency of oscillation, f=0.005Hz are
Frequency point step size has f to i-th of Frequency pointi=fmin+(i-1) f, by Dmd(fi) make with down conversion:
In formula, Dmd(fi) it be frequency of oscillation is fiWhen speed-regulating system damping coefficient, according to formula
In formula, It is available.
It is selectable, if enabling Dmd=0, frequency of oscillation ω can be obtained in solutiond, and ωd=2 π fd；fdFor boundary frequency, speed regulation
System provides corresponding frequency of oscillation when damping is zero；As frequency of oscillation f > fdWhen, Turbine Governor System generates negative damping and turns
Square；f<fdWhen, Turbine Governor System generates positive damping torque.
After considering Turbine Governor System damping torque, the objective function of particle swarm optimization algorithm is writeable are as follows:
MinJ=α JITAE+(1-α)JDamping(15)；.
Embodiment 1:
The basic parameter of system in one-of-a-kind system model are as follows: TJ=10s, KP=0.49, KI=1.0, KD=0.7, BP=
0.04, TG=0.2s, TW=1.0s.There is ultra-low frequency oscillation phenomenon in system under initial disturbance effect, is computed system features value
For 0.0004 ± j0.3072.
Governor pid parameter is optimized using PSO algorithm, initial setting up are as follows: population scale 20, greatest iteration time
Number is 50, c1=c2=1.425, α=0.5.Initial disturbance is 5% frequency disturbance and 10% load disturbance, pid parameter after optimization
For KP=2.77, KI=0.58, KD=0.24.The damping coefficient D of speed-regulating system before and after parameter optimizationmdVariation such as Fig. 5.
Fig. 6 gives corresponding revolving speed change of error.
In Fig. 5, within the scope of the ultra low frequency of 0.01-0.1Hz, the damping torque characteristic before pid parameter optimization is poor,
D in the range of 0.03-0.1HzmdRespectively less than 0, illustrate that speed-regulating system at this time provides negative damping to system.Pid parameter optimization
Damping torque characteristic is obviously improved afterwards, DmdIt is all larger than 0 within the scope of the ultra low frequency of 0.01-0.1Hz, illustrates to mention herein
The validity of optimization method out.
From fig. 6, it can be seen that governor pid parameter exists when disturbance is set as 5% frequency disturbance and 10% load disturbance
System frequency is obviously stablized after optimization, illustrates that optimization method is effective.Thus illustrate, due to frequency disturbance and negative in one-of-a-kind system
The ultra-low frequency oscillation phenomenon that lotus disturbance occurs, is optimized, system frequency is gradually by pid parameter of the PSO algorithm to governor
Stablize, has achieved the purpose that inhibit ultra-low frequency oscillation.
Embodiment 2:
Damping characteristic analysis and verifying in one-of-a-kind system:
The pid parameter of optimization front and back is substituted into formula respectively
In formula,
The boundary frequency of one-of-a-kind system, actual oscillation frequency, damping coefficient, damping ratio calculated result are as shown in table 1.
1 damping torque calculated result of table:
In table 1, pid parameter is K before optimizingP=0.49, KI=1.0, KD=0.7, there is ultra-low frequency oscillation in system.It is practical
Frequency of oscillation f=0.0489Hz, boundary frequency fd=0.0290Hz, frequency of oscillation is higher than boundary frequency at this time, and speed-regulating system mentions
Negative damping torque, D are suppliedmd=-0.7074 illustrates that governor shows as effect of negative damping when ultra-low frequency oscillation occurs in system.
K after optimizationP=2.77, KI=0.58, KD=0.24, system is stablized.Actual oscillation frequency f=0.0428Hz, system boundary frequency
fd=0.1641Hz, frequency of oscillation is lower than boundary frequency at this time, and speed-regulating system provides positive damping torque, Dmd=1.8958, it says
By bearing just, corresponding system damping ratio increases to 0.6 for the damping that bright governor provides a system to after pid parameter optimization.
There is the mechanism of negative damping in system when damping torque analytic approach explains ultra-low frequency oscillation.Above-mentioned analytic process is to list
The damping characteristic of machine system governor pid parameter optimization front and back has carried out deep analysis, and calculated result shows ultralow in generation
When frequency vibration is swung, the damping coefficient of speed-regulating system is negative value, provides negative damping oscillation source for ultra-low frequency oscillation.Changing
After pid parameter, speed-regulating system no longer generates negative damping, and system damping becomes larger, and oscillatory occurences disappears therewith, illustrates through speed regulation system
The damping coefficient D of systemmdIt can judge the damping size that governor is provided to system.
Compare D according to formula (9)mdIn the case of 3 different parameters, system damping that method of characteristic and damping torque method obtain
Than calculated result is as shown in table 2, the validity of result verification damping torque method analysis system damping.
2 system damping ratio calculated result of table:
By formula (9) it is found that the damping of system oscillation mode mostlys come from the damping torque of Generator Governor and bears
The damping that lotus generates, the provided damping of load is typically greater than zero, and the damping of Generator Governor is prolonged by driving system
When or delayed phase effect, be easy to produce negative damping.It is substantially exactly to adjust for the ultra-low frequency oscillation phenomenon that system occurs
The negative damping that fast device generates is greater than the positive damping that load generates, and system presents negative resistance character.
If not changing the damping torque of governor offer, increase the positive damping of system, can use a kind of for the hydraulic turbine
The method of the lead-lag compensator of design is analyzed, controller transfer function are as follows:
In formula, K is the gain of controller, and T1 is measurement links time constant, and T2-T5 is that lead-lag link time is normal
Number.Generally take T2=T4, T3=T5.
Fig. 7 is the system model of additional controller.Under 5% frequency disturbance, additional controller and non-additional controller
System revolving speed deviation is as shown in Figure 8.
In Fig. 8, after additional controller, is calculated by characteristic value and know that system damping ratio is increased to 0.1297 by 0, it is positive to hinder
Buddhist nun obviously becomes larger.Under conditions of no change system friction in governor, additional controller is provided equivalent to increase load
Positive damping, and positive damping be greater than governor provided by negative damping, the total damping of system is positive, so that system frequency is gradually
Stablize.By above-mentioned analytic explanation, ultra-low frequency oscillation is can be effectively suppressed in Optimize Multivariable PID Controller and additional controller, is inhibited ultralow
Frequency vibration swings the negative damping for actually reducing system, increases system positive damping effect.
Technical solution shown in the embodiment of the present application in summary:
(1) derived damping coefficient of the Adaptive System of Water-Turbine Engine in the case where considering pid parameter, can by frequency of oscillation and
The relationship of boundary frequency judges the damping characteristic of system；
(2) in one-of-a-kind system, pid parameter is optimized using particle swarm optimization algorithm, one-of-a-kind system hinders after optimization
Buddhist nun's torque coefficient increases to 1.8958 by -0.7074, and damping ratio increases to 0.6 by -0.0013；In the side using additional controller
System damping ratio is increased to 0.1297 by 0 after method.
Those skilled in the art will readily occur to its of the application after considering specification and practicing application disclosed herein
Its embodiment.This application is intended to cover any variations, uses, or adaptations of the application, these modifications, purposes or
Person's adaptive change follows the general principle of the application and including the undocumented common knowledge in the art of the application
Or conventional techniques.The description and examples are only to be considered as illustrative, and the true scope and spirit of the application are by following
Claim is pointed out.
It should be understood that the application is not limited to the precise structure that has been described above and shown in the drawings, and
And various modifications and changes may be made without departing from the scope thereof.Scope of the present application is only limited by the accompanying claims.
Claims (5)
1. a kind of governor pid parameter optimization method based on particle swarm algorithm characterized by comprising
The initiation parameter of the hydraulic turbine is set；
The parameter is successively optimized using particle group optimizing method, Optimal Parameters array is obtained, includes in the Optimal Parameters array
At least one set of Optimal Parameters；
The disturbance quantity of every group of Optimal Parameters is calculated separately, determines that the Optimal Parameters for generating minimal disturbances amount are objective optimization parameter.
2. pid parameter optimization method according to claim 1, which is characterized in that the calculating process of the disturbance quantity is specific
Are as follows:
MinJ=α JITAE+(1-α)JDamping, wherein J is disturbance quantity JITAFFor revolving speed impact factor, JDampingFor damping torque shadow
Ring the factor；
Wherein, Δ ω revolving speed deviation；
In formula,
3. pid parameter optimization method according to claim 2, which is characterized in that if enabling Dmd=0, solution can be vibrated
Frequencies omegad, and ωd=2 π fd；
fdFor boundary frequency, speed-regulating system provides corresponding frequency of oscillation when damping is zero；As frequency of oscillation f > fdWhen, the hydraulic turbine
Speed-regulating system generates negative damping torque；f<fdWhen, Turbine Governor System generates positive damping torque.
4. pid parameter optimization method according to claim 1, which is characterized in that described using using particle group optimizing method
The step of successively optimizing the parameter include:
Wherein, wherein vidFor the step-length that parameter changes every time, xid' be optimization after parameter, xid' be optimization before parameter；
wiFor weight coefficient, c1And c2For Studying factors, r1And r2For the random number between [0,1], vidFor the flying speed of particle i,
xidFor the position of particle i, pidFor the individual extreme value of particle i, pgdFor the global extremum of particle i.
5. pid parameter optimization method according to claim 4, which is characterized in that the wi=(1+r)/2, r be [0,1] it
Between random number.
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| CN110377970A (en) * | 2019-06-27 | 2019-10-25 | 中国南方电网有限责任公司 | The hydrogovernor parameter optimization method and system of underdamping low frequency oscillation mode |
| CN113013894A (en) * | 2021-02-25 | 2021-06-22 | 云南电网有限责任公司电力科学研究院 | Control method for speed regulator of water turbine |
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Application publication date: 20190607 |