CN104300568B - A kind of frequency stable control method of alternating current-direct current combined hybrid system - Google Patents
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Abstract
The invention discloses the frequency stable control method of a kind of alternating current-direct current combined hybrid system, devise a UFLS Optimized model considering that Emergency electric generation controls and HVDC power is supported, and propose and a kind of take into account consideration frequency retrieval performance and the object function of cutting load amount size, choose the operating frequency of UFLS program and every round cut loading as control variable, utilize the cloud APSO algorithm containing dimension mutation that scheme is optimized, it is achieved the Based Intelligent Control of alternating current-direct current combined hybrid system frequency.The control method of the present invention, solve the hunting of frequency that occurs after alternating current-direct current combined hybrid system fault and system unstability and system frequency may be made to recover economy between coordination optimization problem;Optimize UFLS scheme, intelligent search Optimal tunning scheme, it is considered to frequency retrieval performance, minimize institute's cutting load amount, improve alternating current-direct current combined hybrid system transient performance and steady-state behaviour.
Description
Technical field
The present invention relates to modern power systems protection and control field, particularly to the frequency of a kind of alternating current-direct current combined hybrid system
Stable control method.
Background technology
Frequency is as one of important indicator weighing the quality of power supply, and the exception of frequency can be brought many bad to power system
Impact, system stability can be endangered time serious, affect system run economy.
Power system occurs gain merit more greatly vacancy time, UFLS (UFLS) be recover frequency stable most important means
One of.At present, low frequency deloading method mainly has traditional low-frequency off-load and self adaptation UFLS two class.The most traditional low frequency
Off-load scheme, mainly by operations staff according to the operation operating experience of real system, simulation analysis of computer conclusion is adjusted.
Tradition UFLS scheme takes constant time lag to fix resection, off-line setting calculation, and real-time is poor, was likely to result in and cuts or owe to cut.
Take the self adaptation UFLS of frequency change rate, although movement time and load resection can be flexibly set, but most of
Do not account for system topology, the frequency modulation characteristic of electromotor and the frequency characteristic of load, unnecessary load may be caused to damage
Lose.Additionally, when the frequency of occurrences is vibrated, be likely to result in the inaccurate of measurement only with frequency instantaneous rate of change as signal.
Along with extra-high voltage grid and the development of super high voltage direct current electricity transmission, the grid structure become increasingly complex and changeable operation
Mode will make FREQUENCY CONTROL more complicated.The model shorter mention direct current transportation that the improvement project of recent domestic is studied
The FREQUENCY CONTROL effect of system, and consider that it controls with Emergency electric generation to coordinate UFLS in the case of (EAGC) coordinates mutually,
To further enhance system frequency stability.Consider AC/DC interconnected system Emergency electric generation control action for this reason, it may be necessary to a kind of, examine
Consider the UFLS optimization coordinating to increase generator output and straight-flow system emergency DC power support to adjust model, to improve system fortune
The stability of row and economy.
Summary of the invention
It is an object of the invention to the shortcoming overcoming prior art with not enough, it is provided that the frequency of a kind of alternating current-direct current combined hybrid system
Stable control method.
The purpose of the present invention is realized by following technical scheme:
The frequency stable control method of a kind of alternating current-direct current combined hybrid system, comprises the step of following sequence:
S1. the optimization aim of the UFLS scheme of design one reflection alternating current-direct current combined hybrid system, described optimization aim is held concurrently
Turn round and look at frequency retrieval performance and the size of cutting load amount;
S2. design Emergency electric generation Controlling model and HVDC power support controller, and both are attached to low frequency subtract
In the computation model carried, optimize UFLS scheme;
S3. the setting parameter optimizing UFLS scheme is determined, including each operating frequency and each round cut loading of taking turns, and will
Each wheel operating frequency and each round cut loading, as control variable, determine setting program;Determine that UFLS scheme is correlated with simultaneously
Parameter;
S4. in optimized algorithm, embedded in time-domain simulation program emulate, with optimization aim as criterion, obtain in optimizing
Optimal tunning value in feasible zone, obtains the prioritization scheme of UFLS.
In step S1, the described optimization aim taking into account frequency retrieval performance and cutting load amount is as follows:
Wherein, FobjFor optimization object function value, forMinima;Δ P is at f-t respectively
Rated frequency and the enclosed area of actual frequency track, total cutting load amount under coordinate system;λ1、λ2It is respectivelyThe weights of Δ P,
And λ1+λ2=1.0;fNFor rated frequency, fkInstantaneous value for actual frequency, i.e. frequency.
DescribedComputational methods be:Wherein, n is the action wheel of UFLS
Number, t'kActual time for kth wheel action;
The computational methods of Δ P are:Wherein, Δ PlkCutting load amount for kth wheel action.
Described step S2 is specific as follows: in alternating current-direct current combined hybrid system, increases self adaptation contragradience sliding formwork and control in the i of region
The frequency control model of device particularly as follows:
Based on WAMS, design a self adaptation considering that Emergency electric generation controls and HVDC power is supported anti-
Step sliding mode controller model is specific as follows:
A, Emergency electric generation Controlling model:
B, HVDC Controlling model:
Wherein, Δ ωCOI,iFor the increment of the center of inertia angular frequency in region,For angular acceleration,
For the equivalent inertia time constant of region i, Mu.iFor the inertia time constant of the u unit in region, niGenerating for region i
Unit quantity, Δ PM,i,uFor the increment of the u unit output of region i,For Δ PM,i,uRate of change, Δ PL,iFor district
The increment of the load of territory i, Δ Pout,iFor the increment of the power that the alternating current circuit of region i transfers out, Δ PdcFor direct current transmission merit
Rate,For Δ PdcRate of change;DG, iFor the equivalent damping of region i, Δ PiFor the power shortage of region i, TT,i,uFor region i
The time constant of u power generator turbine, Δ μi,uFor the u power generator turbine valve opening of region i,For Δ μi,u
Rate of change, TG,i,uFor the time constant of the u machine unit speed regulating device of region i, Ri,uSpeed regulator for the u unit of region i
Speed droop, uG,i,uFor the urgent power input of the u unit of region i, TdcTime constant, u is controlled for dc powerdc
Control signal for hvdc transmission line.
In step S3, described respectively take turns operating frequency, each round cut loading as control variable, enter according to engineering experience
Row limits:
The operating frequency that the first round takes turns substantially: f1<49.5Hz;
Last takes turns the operating frequency of basic wheel: flast>47.5Hz;
Institute's cutting load amount:
Wherein, Δ PsPower shortage for system.
Described Δ PsDetermined by following formula:Wherein MT,sysFor the inertia time constant of system,Rate of change for the center of inertia frequency of system.
Described step S4 specifically comprises the steps of
S41. simulated program is utilized to set up optimization object function and consider that Emergency electric generation controls and HVDC power is supported
UFLS computation model, and initialize;
S42. give certain disturbance to the model set up, produce certain power shortage, carry out simulation calculation;
S43. the power shortage of estimating system, and select to tackle the measure of disturbance;
S44. give and control parameter and emulate, calculate initial target functional value;
S45. use optimized algorithm gradually to produce control parameter, again carry out simulation calculation, calculating target function value, and more
New optimal solution;
S46. judging whether iterations reaches default number of times, if meeting, stopping emulation, current optimal solution is the party
The optimal solution of case;Otherwise, step S45 is performed.
In step S4, described optimized algorithm is the cloud APSO algorithm containing dimension mutation, specific as follows:
(1) according to Clouds theory, the strategy of molecular group self-adaptative adjustment, the Changing Pattern of inertia weight ω such as formula:
Wherein, Ex=fav, En=(fav-fmin)/m1, He=En/m2, m1, m2 are for controlling parameter, at normal cloud model
In, En determines the steep of normal cloud model, and He determines the dispersion degree of water dust, En '=normrnd (En, He) produce
Probability is the random number of normal distribution;
ε is the current global optimum ratio with the current fitness value of certain particle in population kth generation;fiFor kth time repeatedly
Particle X in DaiiFitness value, favMeansigma methods for all particle fitness value summations;fminAdaptation for global optimum's particle
Angle value;
(2) the optimizing later stage introduces dimension Variation mechanism, and its strategy is such as following formula:
Xid_min=Xidmin+rand×(Xidmax-Xidmin)rand<pm;
Wherein, id_min represents the dimension needing variation, the dimension that i.e. degree of convergence is the highest;Xid_minFor particle at the i-th d_min
Position in dimension;Rand is for [0,1] upper equally distributed random number;Aberration rate pmFor the constant on [0,1], dimension variation makes grain
Son is evenly distributed on the area of feasible solutions [X of this dimension againidmin,XidmaxOn].
The present invention compared with prior art, has the advantage that and beneficial effect:
1, the present invention sets up the computation model of optimization object function and optimal control by simulated program, and feasible in optimizing
Minimum optimization object function, to optimize UFLS scheme, intelligent search Optimal tunning scheme, it is considered to frequency is extensive is obtained in territory
Renaturation energy, minimizes institute's cutting load amount, improves alternating current-direct current combined hybrid system transient performance and steady-state behaviour.
2, this method is suitable for DG, iUncertain, Δ PiThe unfavorable factors such as the modeling error of limited change and system, and
Ensure that system has Lyapunov stability.
Accompanying drawing explanation
Fig. 1 is the flow process of step S4 of the frequency stable control method of a kind of alternating current-direct current combined hybrid system of the present invention
Figure;
Fig. 2 is the flow process of the optimized algorithm of the frequency stable control method of a kind of alternating current-direct current combined hybrid system of the present invention
Figure;
Fig. 3 is that UFLS optimization control scheme is moved with traditional scheme after meritorious vacancy occurs in alternating current-direct current combined hybrid system
The frequency curve chart of the emulation of state response.
Detailed description of the invention
Below in conjunction with embodiment and accompanying drawing, the present invention is described in further detail, but embodiments of the present invention do not limit
In this.
The frequency stable control method of a kind of alternating current-direct current combined hybrid system, increases by one in traditional low-frequency off-load (UFLS) scheme
Self adaptation contragradience sliding mode controller based on WAMS, this controller comprises Emergency electric generation control (EAGC) and high straightening
Stream (HVDC) power is supported, and takes into account frequency retrieval performance and reduce cutting load amount, and it comprises the following steps:
S1. the optimization aim of the UFLS scheme of design one reflection alternating current-direct current combined hybrid system, described optimization aim is held concurrently
Turn round and look at frequency retrieval performance and the size of cutting load amount;Specific as follows:
A, optimization aim have taken into account frequency retrieval performance and the size of cutting load amount, which includes description frequency retrieval
Energy and the quantitative indices of cutting load amount;
Design optimization object function as follows:
Wherein,Δ P is rated frequency and the enclosed area of actual frequency track and always cut under f-t coordinate system respectively
Loading;λ1、λ2It is respectivelyThe weights of Δ P, and λ1+λ2=1.0;N is the action wheel number of UFLS, fNFor specified frequency
Rate, fkFor the instantaneous value of frequency, t'kActual time for kth wheel action;
B, employing sub-goalPortray frequency retrieval performance:
After increasing self adaptation contragradience sliding mode controller, f in above formulakRelation and finger when only considering adjustment effect of load
Number some difference of relational expression, but find to represent by Segment Index relational expression equally after over-fitting;Therefore emulating
Journey obtains the frequency values of each simulation step length in real time, is used under f-t coordinate system and is enclosed with rated frequency and actual frequency track
Area represent its size, and with this area of trapezoidal integration numerical computations;
C, sub-goal Δ P is used to portray the size of cutting load amount:
ΔPlkCutting load amount for kth wheel action;
S2. design Emergency electric generation Controlling model and HVDC power support controller, and both are attached to low frequency subtract
In the computation model carried, optimize UFLS scheme;The UFLS model of described optimal control, that includes Emergency electric generation
Controlling model and HVDC power support controller, specific as follows shown:
A, set up Emergency electric generation Controlling model:
Wherein, Δ PM,i,uFor the increment of the u unit output of region i, TT,i,uU power generator turbine for region i
Time constant, Δ μi,uFor the u power generator turbine valve opening of region i, TG,i,uU machine unit speed regulating device for region i
Time constant, Ri,uFor the speed regulator speed droop of the u unit of region i, uG,i,uU unit tight for region i
Anxious power input;
B, set up HVDC Controlling model:
Wherein, Δ PdcFor direct current transmission power, TdcTime constant, u is controlled for dc powerdcFor hvdc transmission line
Control signal;In the middle of, uG,i,uAnd udcControl law asked for by self adaptation contragradience Sliding Mode Control Design Method;
C, set up the computation model of UFLS prioritization scheme:
Wherein, Δ ωCOI, iFor the increment of the center of inertia angular frequency of region i,Equivalent inertia for region i
Time constant, Mu.iFor the inertia time constant of the u unit of region i, niFor the generating set quantity of region i, PL, iFor district
The load of territory i, Pout,iThe power transferred out for the alternating current circuit of region i, DG, iFor the equivalent damping of region i, Δ PiFor region
The power shortage of i;
S3. the setting parameter optimizing UFLS scheme is determined, including each operating frequency and each round cut loading of taking turns, and will
Each wheel operating frequency and each round cut loading, as control variable, determine setting program;Determine that UFLS scheme is correlated with simultaneously
Parameter;
Operating frequency that the setting parameter of the UFLS prioritization scheme in this step is taken turns by each, cutting load amount, time delay, level
Difference, the steady frequency scope allowed and transient frequency scope composition, and take turns each operating frequency, cutting load amount the two variable
As control variable, it is defined according to engineering experience:
The operating frequency that the first round takes turns substantially: f1<49.5Hz;
Last takes turns the operating frequency of basic wheel: flast>47.5Hz;
Institute's cutting load amount:
For the power shortage of system, MT,sysFor the inertia time constant of system,For system
The rate of change of center of inertia frequency;
Again its dependent variable is defined:
Time delay: Δ t=0.2s;
Differential: Δ f=0.2~0.3Hz;
Steady frequency: fss≥49.5Hz;
Transient frequency: fts≥45Hz;
S4. in optimized algorithm, embedded in time-domain simulation program emulate, with optimization aim as criterion, obtain in optimizing
Optimal tunning value in feasible zone, obtains the prioritization scheme of UFLS;
The simulated program of UFLS prioritization scheme, its program circuit schematic diagram is as it is shown in figure 1, it specifically includes:
A, utilize MATLAB environment to write simulated program, set up optimization object function and consider that Emergency electric generation controls and high pressure
The UFLS computation model that dc power is supported, user can the parameter of free initialization system and failure condition, and at the beginning of carrying out
Beginningization;
B, utilizing the computation model in previous step and given in program group to control parameter, the power of estimating system lacks
Volume, and judge the counter-measure that disturbance is used by system;Specific as follows:
(1) for Δ Ps≤ΔPp1Contingent (Δ Pp1The criterion started for controller), do not start and comprise controller
UFLS program, manual load-shedding equipment should be at armed state;
(2) for Δ Ps>ΔPp1Contingent, start and comprise the UFLS program of controller, as follows:
A. for Δ Pp1<ΔPs≤ΔPp2Contingent (Δ Pp2=10%PLThe criterion started as UFLS, PLIt is to be
The load of system, Δ Pp2>ΔPp1> 0), start Emergency electric generation and control and the support of HVDC power, do not start removal of load program, but
Manual load-shedding equipment should be at armed state;
B. for Δ Ps>ΔPp2Contingent, start controller and automatic removal of load program simultaneously;
C, using the control parameter of "current" model as the control parameter of UFLS prioritization scheme, system is carried out emulation meter
Calculate;
D, according to the simulation result calculating target function value in previous step, and with last target function value value of calculation
Compare, as more excellent in current goal function, then current solution is updated to optimal solution;
Judge whether simulated program iterations reaches default number of times, if meeting, then terminate simulated program, otherwise, hold
Row step C;
Such as Fig. 2, described optimized algorithm is the cloud APSO algorithm containing dimension mutation, specific as follows:
(1) according to Clouds theory, the strategy of molecular group self-adaptative adjustment, the Changing Pattern of inertia weight ω such as formula:
Wherein, Ex=fav, En=(fav-fmin)/m1, He=En/m2, m1, m2 are for controlling parameter, at normal cloud model
In, En determines the steep of normal cloud model, and He determines the dispersion degree of water dust, En '=normrnd (En, He) produce
Probability is the random number of normal distribution;
ε is the current global optimum ratio with the current fitness value of certain particle in population kth generation;fiFor kth time repeatedly
Particle X in DaiiFitness value, favMeansigma methods for all particle fitness value summations;fminAdaptation for global optimum's particle
Angle value;
(2) the optimizing later stage introduces dimension Variation mechanism, and its strategy is such as following formula:
Xid_min=Xidmin+rand×(Xidmax-Xidmin)rand<pm;
Wherein, id_min represents the dimension needing variation, the dimension that i.e. degree of convergence is the highest;Xid_minFor particle at the i-th d_min
Position in dimension;Rand is for [0,1] upper equally distributed random number;Aberration rate pmFor the constant on [0,1], dimension variation makes grain
Son is evenly distributed on the area of feasible solutions [X of this dimension againidmin,XidmaxOn];
S5. the UFLS scheme of optimal control is obtained by emulation bent with the frequency of the dynamic response of traditional UFLS scheme
Line, such as Fig. 3, the feasibility of checking optimum results.
Below by way of example, the present invention is further remarked additionally:
MATLAB is as emulation platform, according to step S1 of the present invention~step S5, to two region-4 machines in selection
Alternating current-direct current combined hybrid system carries out the optimization of UFLS scheme and adjusts;To system parameter selection it is: total generator capacity in region 1
For 1800MW, load is 876MW.Total generator capacity in region 2 is 1000MW, and load is 1420MW.The transmission of DC line
Rated power is 200MW, and interregional Power Exchange contracted quantity is 420MW.Failure condition is No. 14 1s when in region 2
There is the power shortage of 45% in bus;And choose λ1=0.4, λ2=0.6;
The UFLS prioritization scheme of gained contrasts such as following table with the setting parameter of traditional UFLS scheme:
Table 1 is taken turns substantially
Table 2 is special takes turns
From table 1, table 2 it can be seen that the UFLS setting program after the control method of the present invention optimizes is with traditional
The difference of UFLS scheme essentially consists in adjusting of basic wheel.By table 1, optimize the basic wheel first run operating frequency of UFLS scheme and cut
Loading is all high than traditional scheme, according to engineering experience, after first run action, uses the frequency of the system optimizing UFLS scheme
Fall off rate can be less than using system during traditional scheme, is more beneficial for the recovery of system frequency, and, because prioritization scheme
Each round cut loading by wheel successively decrease, it is known that the most several take turns action after, the frequency of system can ratio use tradition side
Frequency during case has better performance, and therefore, system is likely to be due to frequency and does not reaches the operating frequency of next round and pass than using
The system of system scheme has less action to take turns number, thus reaches the effect of few cutting load.
As it is shown on figure 3, the frequency curve that the optimization UFLS scheme adding self adaptation contragradience sliding mode controller obtains is than passing
Curve obtained by system UFLS scheme is more smooth.By Fig. 3 it is recognised that use the system frequency change optimizing UFLS scheme more flat
Slow, and steady frequency also can be higher, it addition, the recovery time of frequency is the most shorter.Consider and can obtain, optimize when using
During UFLS scheme, system has more preferable frequency retrieval performance and the economy of frequency retrieval.In Fig. 3, abscissa express time, vertical
Coordinate representation frequency.
Above-described embodiment is the present invention preferably embodiment, but embodiments of the present invention are not by above-described embodiment
Limit, the change made under other any spirit without departing from the present invention and principle, modify, substitute, combine, simplify,
All should be the substitute mode of equivalence, within being included in protection scope of the present invention.
Claims (7)
1. the frequency stable control method of an alternating current-direct current combined hybrid system, it is characterised in that comprise the step of following sequence:
S1. the optimization aim of the UFLS scheme of design one reflection alternating current-direct current combined hybrid system, described optimization aim takes into account frequency
Rate restorability and the size of cutting load amount;
S2. design Emergency electric generation Controlling model and HVDC power support controller, and both are attached to UFLS
In computation model, optimize UFLS scheme;
S3. determine the setting parameter optimizing UFLS scheme, take turns operating frequency and each round cut loading including each, and take turns each
Operating frequency and each round cut loading, as control variable, determine setting program;Determine UFLS scheme relevant parameter simultaneously;
S4. in optimized algorithm, embedded in time-domain simulation program emulate, with optimization aim as criterion, obtain feasible in optimizing
Optimal tunning value in territory, obtains the prioritization scheme of UFLS;
In step S1, the described optimization aim taking into account frequency retrieval performance and cutting load amount is as follows:
Wherein, FobjFor optimization object function value, forMinima;Δ P is in f-t coordinate system respectively
Lower rated frequency and the enclosed area of actual frequency track, total cutting load amount;λ1、λ2It is respectivelyThe weights of Δ P, and λ1+λ2
=1.0;fNFor rated frequency, fkInstantaneous value for actual frequency, i.e. frequency.
The frequency stable control method of alternating current-direct current combined hybrid system the most according to claim 1, it is characterised in that describedComputational methods be:Wherein, n is the action wheel number of UFLS, t'kMove in turn for kth
The actual time made;
The computational methods of Δ P are:Wherein, Δ PlkCutting load amount for kth wheel action.
The frequency stable control method of alternating current-direct current combined hybrid system the most according to claim 1, it is characterised in that described step
Rapid S2 is specific as follows: in alternating current-direct current combined hybrid system, increases the frequency control model of self adaptation contragradience sliding mode controller in the i of region
Particularly as follows:
Based on WAMS, devise a self adaptation contragradience considering that Emergency electric generation controls and HVDC power is supported
Sliding mode controller model is specific as follows:
A, Emergency electric generation Controlling model:
B, HVDC Controlling model:
Wherein, Δ ωCOI,iFor the increment of the center of inertia angular frequency in region,For angular acceleration,For
The equivalent inertia time constant of region i, Mu.iFor the inertia time constant of the u unit in region, niElectromotor for region i
Group quantity, Δ PM,i,uFor the increment of the u unit output of region i,For Δ PM,i,uRate of change, Δ PL,iFor region
The increment of the load of i, Δ Pout,iFor the increment of the power that the alternating current circuit of region i transfers out, Δ PdcFor direct current transmission merit
Rate,For Δ PdcRate of change;DG,iFor the equivalent damping of region i, Δ PiFor the power shortage of region i, TT,i,uFor region i
The time constant of u power generator turbine, Δ μi,uFor the u power generator turbine valve opening of region i,For Δ μi,u
Rate of change, TG,i,uFor the time constant of the u machine unit speed regulating device of region i, Ri,uSpeed regulator for the u unit of region i
Speed droop, uG,i,uFor the urgent power input of the u unit of region i, TdcTime constant, u is controlled for dc powerdc
Control signal for hvdc transmission line.
The frequency stable control method of alternating current-direct current combined hybrid system the most according to claim 1, it is characterised in that step S3
In, described respectively take turns operating frequency, each round cut loading as control variable, be defined according to engineering experience:
The operating frequency that the first round takes turns substantially: f1<49.5Hz;
Last takes turns the operating frequency of basic wheel: flast>47.5Hz;
Institute's cutting load amount:
Wherein, Δ PsPower shortage for system.
The frequency stable control method of alternating current-direct current combined hybrid system the most according to claim 4, it is characterised in that described Δ
PsDetermined by following formula:Wherein MT,sysFor the inertia time constant of system,For in the inertia of system
The rate of change of frequency of heart.
The frequency stable control method of alternating current-direct current combined hybrid system the most according to claim 1, it is characterised in that described step
Rapid S4 specifically comprises the steps of
S41. simulated program is utilized to set up optimization object function and consider that Emergency electric generation control is low with what HVDC power was supported
Frequently off-load computation model, and initialize;
S42. give certain disturbance to the model set up, produce certain power shortage, carry out simulation calculation;
S43. the power shortage of estimating system, and select to tackle the measure of disturbance;
S44. give and control parameter and emulate, calculate initial target functional value;
S45. use optimized algorithm gradually to produce control parameter, again carry out simulation calculation, calculating target function value, and update
Excellent solution;
S46. judging whether iterations reaches default number of times, if meeting, stopping emulation, current optimal solution is the program
Optimal solution;Otherwise, step S45 is performed.
The frequency stable control method of alternating current-direct current combined hybrid system the most according to claim 1, it is characterised in that step S4
In, described optimized algorithm is the cloud APSO algorithm containing dimension mutation, specific as follows:
(1) according to Clouds theory, the strategy of molecular group self-adaptative adjustment, the Changing Pattern of inertia weight ω such as formula:
Wherein, Ex=fav, En=(fav-fmin)/m1, He=En/m2, m1, m2 are for controlling parameter, and in normal cloud model, En is certainly
Determining the steep of normal cloud model, He determines the dispersion degree of water dust, En '=normrnd (En, He) producing probability is just
The random number of state distribution;
ε is the current global optimum ratio with the current fitness value of certain particle in population kth generation;fiFor grain in kth time iteration
Sub-XiFitness value, favMeansigma methods for all particle fitness value summations;fminFitness value for global optimum's particle;
(2) the optimizing later stage introduces dimension Variation mechanism, and its strategy is such as following formula:
Xid_min=Xidmin+rand×(Xidmax-Xidmin) rand<pm;
Wherein, id_min represents the dimension needing variation, the dimension that i.e. degree of convergence is the highest;Xid_minFor particle in the i-th d_min dimension
Position;Rand is for [0,1] upper equally distributed random number;Aberration rate pmFor the constant on [0,1], dimension variation makes particle weight
Newly it is evenly distributed on the area of feasible solutions [X of this dimensionidmin,XidmaxOn].
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