CN105720597B - For optimizing the method that electric vehicle fills the integrated power station charge-discharge electric power of storage - Google Patents

For optimizing the method that electric vehicle fills the integrated power station charge-discharge electric power of storage Download PDF

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CN105720597B
CN105720597B CN201410735513.7A CN201410735513A CN105720597B CN 105720597 B CN105720597 B CN 105720597B CN 201410735513 A CN201410735513 A CN 201410735513A CN 105720597 B CN105720597 B CN 105720597B
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power station
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integrated power
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CN105720597A (en
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史乐峰
刘正发
何国军
侯兴哲
周孔均
周全
郑可
汪会财
刘永相
赵杰
李辉
陈文礼
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Chongqing University
Electric Power Research Institute of State Grid Chongqing Electric Power Co Ltd
State Grid Corp of China SGCC
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Chongqing University
Electric Power Research Institute of State Grid Chongqing Electric Power Co Ltd
State Grid Corp of China SGCC
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Abstract

For optimizing the method that electric vehicle fills the integrated power station charge-discharge electric power of storage, pass through particle algorithm optimization integration power station and power grid interaction power, the peak-valley difference of network load can be significantly reduced, integrated power station participates in the ability of power grid assistant service and power station energy storage system capacity is positively correlated relation, i.e. capacity is bigger, the ability that integrated power station participates in power grid assistant service is stronger, the effect of peak load shifting is more notable, and the present invention can also further reduce the battery loss cost for filling the integrated power station of storage.

Description

For optimizing the method that electric vehicle fills the integrated power station charge-discharge electric power of storage
Technical field
The present invention relates to a kind of electric vehicle and power grid interaction technique field, particularly a kind of integrated power station of optimization and electricity The method of the interactive power of net.
Background technology
Electric vehicle is the research hotspot of auto industry, has become national governments, energy manufacturer and automobile vendor at present Focus, as the U.S. EV Project plan and China " ten thousand, cities " plan.It is anticipated that future is with battery The continuous progress of technology, petroleum resources are petered out, and electric vehicle will be popularized gradually.As following electric vehicle is large-scale Popularization, accesses grid charging on a large scale, due to the randomness and dispersiveness of charging load, will to grid generation, transmit electricity, match somebody with somebody Electricity, electricity consumption, scheduling etc. bring very important influence.Such as cause new load peak, increase network loss, some node voltages are horizontal Reduction etc..Therefore, how by rationally controlling the charging behavior of electric vehicle, reduce scale electric vehicle and charge to power grid The adverse effect brought becomes major issue urgently to be resolved hurrily.
The research of electric vehicle and power grid interaction technique at present is stored up electric vehicle as the distribution in power grid Energy unit, the effect of power grid frequency modulation, peak regulation is participated according to dispatch command.Part has studied battery to power grid centrally connected power supply (Battery to grid, B2G) pattern.B2G patterns open new approaches for the development & construction of electric automobile charging station, that is, build If fill the integrated power station of storage.However, to filling in the correlative study in the integrated power station of storage, relevant optimization method is often only Consider that power station provides the assessment of the assistant services ability such as peak-frequency regulation for power grid, have ignored the frequent charge and discharge of battery to battery life Influence.In fact, since current battery is expensive, battery cost accounts for that power station cost proportion is larger, and frequent charge and discharge certainly will Battery loss can be increased, make shorter battery life, and then influence to fill storage power station economy operation, increase the operation in power station into This, while influence the effect of power grid assistant service.Therefore, it is unfavorable to bring to evade electric vehicle scale application to power grid It influences, realizes the economy operation in power station, it is ensured that the effect of power grid assistant service, it is necessary to considering that battery loss cost is filled The integrated power station running optimizatin method of storage optimizes research.
The content of the invention
It is an object of the invention to provide a kind of the integrated power station charge-discharge electric power of storage is filled for optimizing electric vehicle Method, it can not only stabilize the load fluctuation of power grid well, reduce network load peak-valley difference, while can also efficiently reduce electricity Electrical automobile fills the cost depletions of storage power station battery.
It realizes, is as follows the purpose of the present invention is technical solution in this way:
1) object function of the integrated power station using power grid peak-valley difference and battery loss cost minimization as optimization aim is determined;
2) constraints of the charge-discharge electric power in the integrated power station of structure, battery capacity and spare capacity;
3) object function described in step 1) and the constraints described in step 2) are combined, structure optimizes mathematical modulo Type, and seek the mathematical model of optimization using particle cluster algorithm obtains interactive optimal of each period integration power station and power grid Charge-discharge electric power;
Using power grid peak-valley difference and battery loss cost minimization as the calculating of the object function of optimization aim described in step 1) Method is:
Plx(t)=Ply(t)+Plc(t)+P(t)
F=min [α (maxPlx(t)-minPlx(t))+βC]
In formula, Ply(t) it is the daily load of regional power grid, Plx(t) load for power grid after integrated power station is adjusted, C are Integrated battery loss cost, rdFor the battery loss rate converted by unit discharge power, 0.4 is taken, α, β are respectively load song The weight of line peak-valley difference and battery loss cost shared by optimization aim, and alpha+beta=1, P (t) being integrated power station and power grid Interactive charge-discharge electric power, Plc(t) the day charging and conversion electric load of electric vehicle in region is represented.
Further, the constraints described in step 2) is:
2-1) integrated power station and the constraints of the charge-discharge electric power P (t) of power grid interaction are:
-Pmax≤P(t)≤Pmax
In formula, PmaxRepresent the maximum power that power grid charges to integrated power station ,-PmaxRepresent that integrated power station is put to power grid The maximum power of electricity;
2-2) the battery capacity constraints in integrated power station is:
kQmax≤Q(t)≤Qmax
In formula, QmaxThe maximum stored energy capacitance in being integrated power station, k are spare capacity coefficient;
2-3) constraints of spare capacity is:
Qb=kQmax
In formula, QbFor spare capacity, QmaxThe maximum stored energy capacitance in being integrated power station, k are spare capacity coefficient;
2-4) integrated power station and the charge-discharge electric power P (t) and battery capacity Q (t) in integrated power station of power grid interaction are full Sufficient the following formula:
Δ Q=P (t) × t
Q (t+1)=Q (t)+Δ Q-Plc(t)
In formula, Plc(t) the day charging and conversion electric load of electric vehicle in region is represented.
Further, spare capacity coefficient k value is 20%.
Further, the specific method for seeking mathematical model of optimization using particle cluster algorithm described in step 3) is:
Known conditions and algorithm basic parameter 3-1) are inputted, initializes position and the speed of particle;Known conditions includes area The charging and conversion electric load of power distribution network daily load and electric vehicle in domain;
Particle position 3-2) is changed according to constraints;
The fitness of population, i.e. object function 3-3) are calculated, records particle individual desired positions and group's desired positions;
3-4) according to the particle rapidity of particle cluster algorithm and location update formula update particle rapidity and position;
3-5) check whether particle position is more than limit value, is then return to step 3-2), on the contrary then be transferred to step 3-6);
The fitness of population 3-6) is calculated, updates and records particle optimal location and group most optimal location;
3-7) judge whether to reach default termination condition, be to stop calculating, and export particle position at this time, i.e., it is integrated Power station and the charge-discharge electric power P (t), on the contrary then return to step 3-4 of power grid interaction).
Further, step 3-4) described in particle rapidity and location update formula be specially:
In formula, vId kIt is that v is the particle I speed that d is tieed up in kth time iteration;ω is inertia weight;c1、c2Be study because Son empirically often takes c1=c2=2;rand1 k,rand2 kIt is the random number between [0,1];xId kIt is particle I in kth time iteration In d tie up position;pbestId kIt is the coordinate that particle I individuals extreme point is tieed up in d;gbestId kIt is entire group's global extremum O'clock d dimension coordinate.
By adopting the above-described technical solution, the present invention has the advantage that:
The present invention can significantly reduce the peak of network load by particle algorithm optimization integration power station and power grid interaction power Paddy is poor, and integrated power station participates in the ability of power grid assistant service and power station energy storage system capacity is positively correlated relation, i.e. capacity is got over Greatly, integrated power station participate in power grid assistant service ability it is stronger, the effect of peak load shifting is more notable, and the present invention can also be into The battery loss cost in the integrated power station of storage is filled in the reduction of one step.
Other advantages, target and the feature of the present invention will be illustrated in the following description to a certain extent, and And to a certain extent, based on will be apparent to those skilled in the art to investigating hereafter, Huo Zheke To be instructed from the practice of the present invention.The target and other advantages of the present invention can be wanted by following specification and right Book is sought to realize and obtain.
Description of the drawings
The description of the drawings of the present invention is as follows.
Fig. 1 is the flow diagram of the present invention;
Fig. 2 is a certain regional distribution network daily load curve figure;
Fig. 3 is the day charging and conversion electric load chart of electric vehicle in region;
Fig. 4 is power distribution network daily load curve figure before and after optimization;
Fig. 5 is station capacity-power grid peak-valley difference slip graph;
Fig. 6 is power station cost depletions figure under different capabilities.
Specific embodiment
The invention will be further described with reference to the accompanying drawings and examples.
It is a kind of for optimizing the method that electric vehicle fills the integrated power station charge-discharge electric power of storage, as shown in Figure 1, including with Lower step:
1) object function of the integrated power station using power grid peak-valley difference and battery loss cost minimization as optimization aim is determined;
2) constraints of the charge-discharge electric power in the integrated power station of structure, battery capacity and spare capacity;
3) object function described in step 1) and the constraints described in step 2) are combined, structure optimizes mathematical modulo Type, and seek the mathematical model of optimization using particle cluster algorithm obtains interactive optimal of each period integration power station and power grid Charge-discharge electric power.
Using power grid peak-valley difference and battery loss cost minimization as the calculating of the object function of optimization aim described in step 1) Method is
Plx(t)=Ply(t)+Plc(t)+P(t)
F=min [α (maxPlx(t)-minPlx(t))+βC]
In formula, Ply(t) it is the daily load of regional power grid, Plx(t) load for power grid after integrated power station is adjusted, C are Integrated battery loss cost, rdFor the battery loss rate converted by unit discharge power, 0.4 is taken, α, β are respectively load song The weight of line peak-valley difference and battery loss cost shared by optimization aim, and alpha+beta=1, P (t) being integrated power station and power grid Interactive charge-discharge electric power, Plc(t) the day charging and conversion electric load of electric vehicle in region is represented.
Constraints described in step 2) is:
2-1) integrated power station and the constraints of the charge-discharge electric power P (t) of power grid interaction are:
-Pmax≤P(t)≤Pmax
In formula, PmaxRepresent the maximum power that power grid charges to integrated power station ,-PmaxRepresent that integrated power station is put to power grid The maximum power of electricity;
2-2) the battery capacity constraints in integrated power station is:
kQmax≤Q(t)≤Qmax
In formula, QmaxThe maximum stored energy capacitance in being integrated power station, k are spare capacity coefficient;
2-3) constraints of spare capacity is:
Qb=kQmax
In formula, QbFor spare capacity, QmaxThe maximum stored energy capacitance in being integrated power station, k are spare capacity coefficient;
2-4) integrated power station and the charge-discharge electric power P (t) and battery capacity Q (t) in integrated power station of power grid interaction are full Sufficient the following formula:
Δ Q=P (t) × t
Q (t+1)=Q (t)+Δ Q-Plc(t)
In formula, Plc(t) the day charging and conversion electric load of electric vehicle in region is represented.
The specific method for seeking mathematical model of optimization using particle cluster algorithm described in step 3) is:
Known conditions and algorithm basic parameter 3-1) are inputted, initializes position and the speed of particle;Known conditions includes area The charging and conversion electric load of power distribution network daily load and electric vehicle in domain;
Particle position 3-2) is changed according to constraints;
The fitness of population, i.e. object function 3-3) are calculated, records particle individual desired positions and group's desired positions;
3-4) according to the particle rapidity of particle cluster algorithm and location update formula update particle rapidity and position;
3-5) check whether particle position is more than limit value, is then return to step 3-2), on the contrary then be transferred to step 3-6);
The fitness of population 3-6) is calculated, updates and records particle optimal location and group most optimal location;
3-7) judge whether to reach default termination condition, be to stop calculating, and export particle position at this time, i.e., it is integrated Power station and the charge-discharge electric power P (t), on the contrary then return to step 3-4 of power grid interaction).
Further, step 3-4) described in particle rapidity and location update formula be specially:
In formula, vId kIt is that v is the particle I speed that d is tieed up in kth time iteration;ω is inertia weight;c1、c2Be study because Son empirically often takes c1=c2=2;rand1 k,rand2 kIt is the random number between [0,1];xId kIt is particle I in kth time iteration In d tie up position;pbestId kIt is the coordinate that particle I individuals extreme point is tieed up in d;gbestId kIt is entire group's global extremum O'clock d dimension coordinate.
By taking the daily load of somewhere power distribution network as an example, as shown in Figure 2.A maximum energy-storage battery capacity has been accessed in region The integrated power station of storage is filled for 8MWh, the day charging and conversion electric load of electric vehicle is as shown in Figure 3.
It can be obtained according to Fig. 2 and Fig. 3, the peak load period of the power grid daily load of this area is 11:00-15:00, the paddy load period For 04:00-07:00;And the charging and conversion electric peak load period 10 of electric vehicle:00-14:00, the paddy load period is 03:00-06:00, The two variation tendency is substantially uniform.Such variation tendency can cause peak load to be overlapped, and increase power grid peak-valley difference, go out Existing " on peak plus peak " phenomenon, reduces load rate of grid so that network load fluctuation further increases, and it is steady to be unfavorable for power grid security Fixed operation.
Daily load is superimposed for power distribution network daily load with electric vehicle day charging and conversion electric load before optimizing in region.Fig. 4 is shown After optimization method, the contrast curve with power distribution network daily load before optimization.As shown in Figure 4, regional power grid considers electronic The period that peak load occurs in daily load after automobile charging and conversion electric load is about 12:00-14:00, the period of paddy load is about 05:00-07:00.In addition, compared with not considering the optimization method in power station, optimization method using the present invention formulates integration electricity It stands after charge and discharge plan, power grid daily load is significantly improved, and is reduced power grid peak load, is increased power grid paddy load, can have Effect evades scale electric vehicle and charges the load fluctuation brought to power grid, stabilizes power grid peak-valley difference.
In order to which without loss of generality, the present invention is respectively also 4MWh, 5MWh, 5.5MWh, 6MWh, 7MWh to energy-storage battery capacity The integrated power station of different capabilities is waited to be emulated, further studies the variation of integrated power station energy-storage battery capacity to excellent Change the influence of Policy Result.Fig. 5 is relation of the network load peak-valley difference slip with integrated station capacity.
From figure 5 it can be seen that when stored energy capacitance is 4MWh, 5MWh, 5.5MWh, 6MWh, 7MWh, 8MWh, power grid peak valley Poor slip is respectively:5.4%th, 9.4%, 10.5%, 13.1%, 15.1%.Network load peak-valley difference slip changes with filling The variation positive correlation of the integrated power station energy storage system capacity of storage, gradually increases with the increase of capacity, when capacity is 4MW, Network load peak-valley difference slip is minimum, is 5.4%, when capacity is 8MW, network load peak-valley difference slip is up to 15.1%, during remaining capacity, then fall between.But this positive correlation is not linear relationship, but is started to increase comparatively fast, after Face increase is slower, increases when being specially 4MW~6MW than very fast, and the amplitude of growth is larger, and 6MW~8MW increases are slower, growth Amplitude is smaller.This may be primarily due to that integrated power station energy storage system capacity is bigger, and it is stronger to participate in the ability that power grid is adjusted, Battery discharge capacity increases so that its cost depletions increases, and optimization method is its cost depletions of reduction, it has to take the side of compromise Method has slowed down the increasing degree of peak load shifting ability.
Fig. 6 optimization methods of the present invention and do not count and the optimization method of battery loss under energy-storage battery cost depletions and energy storage electricity The comparison of tankage.It can be seen that under optimization method of the present invention, integrated power station energy-storage battery capacity is 4MWh, 5MWh, When 6MWh, 7MWh, 8MWh, battery loss cost is respectively 1053 yuan, 1184 yuan, 1464 yuan, 2012 yuan, 5150 yuan.And not Under meter and battery loss Cost Optimization Approach, battery loss cost is respectively 1489 yuan, 1681 yuan, 1976 yuan, 2768 yuan, 7004 Member.Battery loss cost increases as integrated power station energy-storage battery capacity increases.This is primarily due to integrated electricity It stands the increase of energy-storage battery capacity, required battery necessarily increases, then in the case where single battery cost depletions are certain, always Battery loss cost can also increase.In addition, the battery loss cost under optimization method of the present invention is significantly lower than and takes no account of battery Cost depletions optimization method, using optimization method proposed by the present invention, can stabilize as far as possible load fluctuation, peak load shifting it is same When, moreover it is possible to integrated power station battery loss cost is effectively reduced, significantly improves and fills the integrated power station performance driving economy of storage, when not Carry out the popularization with electric vehicle, when filling the quantity in the integrated power station of storage and capacity substantial increase, reduce battery loss cost It will be considerable to economic benefit caused by integrated power station.
It can be seen that the optimization that the integrated power station operation of storage is filled using a kind of electric vehicle of the present invention from result above Control method can significantly reduce network load peak-valley difference, and the assistant services such as peak load shifting are provided for power grid.Integrated power station participates in The ability of power grid assistant service is positively correlated relation with power station energy storage system capacity, i.e. capacity is bigger, and integrated power station participates in electricity The ability of net assistant service is stronger, and peak load shifting effect is more notable.With do not count and the optimization method of battery loss cost compared with, Optimization method of the present invention can also further reduce the battery damage for filling the integrated power station of storage in the case where reducing network load peak-valley difference Cost is consumed, is a kind of economic, reliable optimal control method.
Finally illustrate, the above embodiments are merely illustrative of the technical solutions of the present invention and it is unrestricted, although with reference to compared with The present invention is described in detail in good embodiment, it will be understood by those of ordinary skill in the art that, it can be to the skill of the present invention Art scheme is modified or replaced equivalently, and without departing from the objective and scope of the technical program, should all be covered in the present invention Right among.

Claims (5)

1. for optimizing the method that electric vehicle fills the integrated power station charge-discharge electric power of storage, which is characterized in that specific steps are such as Under:
1) object function of the integrated power station using power grid peak-valley difference and battery loss cost minimization as optimization aim is determined;
2) constraints of the charge-discharge electric power in the integrated power station of structure, battery capacity and spare capacity;
3) object function described in step 1) and the constraints described in step 2) are combined, builds mathematical model of optimization, and The mathematical model of optimization is sought using particle cluster algorithm, obtains the optimal charge and discharge in each period integration power station and power grid interaction Power;
Using power grid peak-valley difference and battery loss cost minimization as the computational methods of the object function of optimization aim described in step 1) For:
Plx(t)=Ply(t)+Plc(t)+P(t)
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>C</mi> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>24</mn> </munderover> <msub> <mi>r</mi> <mi>d</mi> </msub> <mi>P</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>P</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>&amp;le;</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mfenced>
F=min [α (maxPlx(t)-minPlx(t))+βC]
In formula, Ply(t) it is the daily load of regional power grid, Plx(t) load for power grid after integrated power station is adjusted, C are integrated Electrochemical cell cost depletions, rdFor the battery loss rate converted by unit discharge power, 0.4 is taken, α, β are respectively load curve peak The weight of paddy difference and battery loss cost shared by optimization aim, and alpha+beta=1, P (t) being integrated power station and power grid are interactive Charge-discharge electric power, Plc(t) the day charging and conversion electric load of electric vehicle in region is represented.
2. it is as described in claim 1 for optimizing the method that electric vehicle fills the integrated power station charge-discharge electric power of storage, it is special Sign is that the constraints described in step 2) is:
2-1) integrated power station and the constraints of the charge-discharge electric power P (t) of power grid interaction are:
-Pmax≤P(t)≤Pmax
In formula, PmaxRepresent the maximum power that power grid charges to integrated power station ,-PmaxRepresent what integrated power station was discharged to power grid Maximum power;
2-2) the battery capacity constraints in integrated power station is:
kQmax≤Q(t)≤Qmax
In formula, QmaxThe maximum stored energy capacitance in being integrated power station, k are spare capacity coefficient;
2-3) constraints of spare capacity is:
Qb=kQmax
In formula, QbFor spare capacity, QmaxThe maximum stored energy capacitance in being integrated power station, k are spare capacity coefficient;
2-4) integrated power station with the charge-discharge electric power P (t) of power grid interaction and in integrated power station battery capacity Q (t) satisfactions with Lower formula:
Δ Q=P (t) × t
Q (t+1)=Q (t)+Δ Q-Plc(t)
In formula, Plc(t) the day charging and conversion electric load of electric vehicle in region is represented.
3. it is as claimed in claim 2 for optimizing the method that electric vehicle fills the integrated power station charge-discharge electric power of storage, it is special Sign is:Spare capacity coefficient k value is 20%.
4. it is as claimed in claim 2 for optimizing the method that electric vehicle fills the integrated power station charge-discharge electric power of storage, it is special Sign is that the specific method for seeking mathematical model of optimization using particle cluster algorithm described in step 3) is:
Known conditions and algorithm basic parameter 3-1) are inputted, initializes position and the speed of particle;Known conditions is included in region The charging and conversion electric load of power distribution network daily load and electric vehicle;
Particle position 3-2) is changed according to constraints;
The fitness of population, i.e. object function 3-3) are calculated, records particle individual desired positions and group's desired positions;
3-4) according to the particle rapidity of particle cluster algorithm and location update formula update particle rapidity and position;
3-5) check whether particle position is more than limit value, is then return to step 3-2), on the contrary then be transferred to step 3-6);
The fitness of population 3-6) is calculated, updates and records particle optimal location and group most optimal location;
3-7) judge whether to reach default termination condition, be to stop calculating, and export particle position at this time, i.e., integrated power station With the charge-discharge electric power P (t), on the contrary then return to step 3-4 of power grid interaction).
5. it is as claimed in claim 4 for optimizing the method that electric vehicle fills the integrated power station charge-discharge electric power of storage, it is special Sign is, step 3-4) described in particle rapidity and location update formula be specially:
<mrow> <msubsup> <mi>v</mi> <mrow> <mi>I</mi> <mi>d</mi> </mrow> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>&amp;omega;v</mi> <mrow> <mi>I</mi> <mi>d</mi> </mrow> <mi>k</mi> </msubsup> <mo>+</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> <msubsup> <mi>rand</mi> <mn>1</mn> <mi>k</mi> </msubsup> <mrow> <mo>(</mo> <msubsup> <mi>pbest</mi> <mrow> <mi>I</mi> <mi>d</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msubsup> <mi>x</mi> <mrow> <mi>I</mi> <mi>d</mi> </mrow> <mi>k</mi> </msubsup> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>c</mi> <mn>2</mn> </msub> <msubsup> <mi>rand</mi> <mn>2</mn> <mi>k</mi> </msubsup> <mrow> <mo>(</mo> <msubsup> <mi>gbest</mi> <mrow> <mi>I</mi> <mi>d</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msubsup> <mi>x</mi> <mrow> <mi>I</mi> <mi>d</mi> </mrow> <mi>k</mi> </msubsup> <mo>)</mo> </mrow> </mrow>
<mrow> <msubsup> <mi>x</mi> <mrow> <mi>I</mi> <mi>d</mi> </mrow> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>x</mi> <mrow> <mi>I</mi> <mi>d</mi> </mrow> <mi>k</mi> </msubsup> <mo>+</mo> <msubsup> <mi>v</mi> <mrow> <mi>I</mi> <mi>d</mi> </mrow> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> </mrow>
In formula, vId kIt is that v is the particle I speed that d is tieed up in kth time iteration;ω is inertia weight;c1、c2It is Studying factors, presses C is often taken according to experience1=c2=2;rand1 k,rand2 kIt is the random number between [0,1];xId kIt is particle I d in kth time iteration The position of dimension;pbestId kIt is the coordinate that particle I individuals extreme point is tieed up in d;gbestId kIt is that entire group's global extremum point exists The coordinate of d dimensions.
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