CN106169109A - A kind of Optimized Scheduling of Hydroelectric Power method based on chaos difference particle cluster algorithm - Google Patents
A kind of Optimized Scheduling of Hydroelectric Power method based on chaos difference particle cluster algorithm Download PDFInfo
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Abstract
The invention discloses a kind of Optimized Scheduling of Hydroelectric Power method based on chaos difference particle cluster algorithm; it is characterized in that first choosing target power station; corresponding constraints etc. is set; the startup-shutdown compound mode in power station is represented again with binary-coded form; and given initial population size and iterations; then give the fitness function with penalty function and calculate the fitness of each particle; present speed and the position of each particle is updated according to chaos differential sampling parameter; and obtain new globally optimal solution by comparing, finally judge whether to meet stopping iterated conditional.The present invention improves the ability of other new positions, particle traversal search space, increases population diversity, can be prevented effectively from population Premature Convergence, be absorbed in local optimum, and the present invention can be used for the Optimized Operation field in power station.
Description
Technical field
A kind of method that the present invention relates to Optimized Scheduling of Hydroelectric Power, belongs to economical operation of hydropower plants field.
Background technology
Economical operation of hydropower plants be research power station factory under prescribed conditions in work unit optimum number of units, combination and
The determination of start and stop order, the relevant issues that between unit, in the optimum allocation of load, i.e. factory, optimal operation mode is formulated and realized, real
Also it is to study it in a few days by period and the problem of instantaneous economical operation on border.Sum up exactly: seek at study period (general
It is one day) and wherein day part, make used Optimality Criteria reach the power station work unit of extreme value under known conditions
Optimum number of units K (t), combination z (t) and burden with power P (t) of system distribution and load or burden without work p (f) optimum between work unit
Distribution.Recent years particle cluster algorithm Optimized Scheduling of Hydroelectric Power apply in research gradually demonstrate its wide application before
Scape, starts concern and the research interest of the person that constantly causes hydropower industry.Particle cluster algorithm has that principle is simple, is easily achieved, depends on
Rely parameter is few and fast convergence rate, but there is also the shortcoming that search precision is the highest and is absorbed in local optimum.
Summary of the invention
Present invention aim at solving the deficiency of traditional PSO Algorithm Optimized Scheduling of Hydroelectric Power problem, propose one
Plant Optimized Scheduling of Hydroelectric Power method based on chaos difference particle cluster algorithm, improve other new positions, particle traversal search space
Ability, increases population diversity, is prevented effectively from population Premature Convergence, is absorbed in local optimum.
The present invention proposes a kind of Optimized Scheduling of Hydroelectric Power method based on chaos difference particle cluster algorithm, and described method includes
Following steps:
Step (1) selects target power station to be calculated, and arranges the corresponding constraints in power station: plant load balances about
Bundle, the constraint of power station upper pond level, the constraint of each unit output, each unit generation traffic constraints, power station operating head polishing retrains, rotates standby
By capacity-constrained, unit cavitation erosion vibrating area constraint, unit minimum startup-shutdown time-constrain;
Step (2) determines individual UVR exposure mode, uses binary number to represent unit startup-shutdown state, and wherein 0 represents machine
Group is in stopped status, and 1 represents that unit is in open state;
Step (3) arranges population size size M, maximum iteration time Tmax;Wherein with the startup-shutdown combination of 96 in a day
Scheme is as a particle, and stochastic generation scale is the population of M;
Step (4) calculates each particle fitness, and in-plant economical operation optimizes process with the minimum target of water consumption, in conjunction with
Constraints, can arrange fitness function as follows:
Wherein:
In formula, W is power station total water consumption (m3);It is H for i-th unit of period t at working headt, load
For Pi tTime generating flow (m3/s);Δ T represents period duration;Represent the unit i state at period t, during shutdown
During operationQup,i, Qdn,iRepresent the water consumption of start and stopping process respectively, sent out during startup-shutdown including unit
The water yield that raw mechanical wear etc. is converted into;N is Hydropower Plant number of units;Hop count when T is schedule periods;M destroys number for constraint;
Km、|ΔXm| it is respectively destruction penalty coefficient and the destructiveness of constraint m;
The speed of step (5) more new particle and position, in the speed more new formula of original particle cluster algorithm, exist one
Locally optimal solution pbest, the optimal solution that i.e. each particle finds itself to current iteration number of times is for updating each particle
Speed and position thus generate the next generation, existing will replace about one of pbest, will replace by cognitive process, take and generation
Be to use there is the mechanism of chaos of ergodic property in current particle group, choose two different particles by weights
Position vector poor, this vector difference operator is as the speed of new cognitive Xiang Laigeng new particle and position;
Step (6) updates globally optimal solution, and after being calculated the fitness value of each individuality of current algebraically, picking individual is fitted
Answer angle value maximum, compare with global optimum fitness value, if more than global optimum's fitness value, then replicate this individuality and replace entirely
Office's optimum individual, does not operates;
Step (7) loop iteration, it may be judged whether meet end condition, end condition is maximum iteration time;If meeting, then
Stop iteration, and export globally optimal solution;If being unsatisfactory for, then return step (4) and recalculate the fitness solving particle.
Preferably, constraints described in step (1) particularly as follows:
1. plant load Constraints of Equilibrium meets following formula:
In formula, E is the gross generation in power station, NiT () is the load that i-th unit undertakes under t period internal loading requirement;
2. the following formula of power station upper pond level constraint satisfaction:
Zmin≤Z≤Zmax
In formula, Z is the operating head polishing in power station, Zmin、ZmaxIt is the power station upper pond level bound in each period respectively;
The most each following formula of unit output constraint satisfaction:
Pmin≤Pi(t)≤Pmax
In formula, Pmin, PmaxIt it is the unit power output upper and lower limit of i-th unit;
The most each unit generation traffic constraints meets following formula:
Qmin≤Qi(t)≤Qmax
In formula, Qmin, QmaxIt is the minimum of i-th unit, maximum generation flow;
5. the following formula of power station operating head polishing constraint satisfaction:
Hmin≤H≤Hmax
In formula, H is the operating head polishing in power station, HminIt is power station minimum stable operation head, HmaxIt is power station maximum stable fortune
Row head;
6. the following formula of spinning reserve capacity constraint satisfaction:
In formula,It is unit installed capacity summation,It is unit output summation, NminIt it is the spinning reserve in power station
Lower bound of capacity;
7. the unit cavitation erosion following formula of vibrating area constraint satisfaction:
Pi(t)≤P Qsi Or
In formula,P Qsi It is the cavitation erosion district lower limit of i-th unit,It it is the cavitation erosion district upper limit of i-th unit;
8. unit minimum startup-shutdown time-constrain meets following formula:
XKi≥T Ki Or XGi≥T Gi
In formula, XKiIt is the available machine time of i-th unit,T Ki It is the available machine time lower limit of i-th unit, XGiI-th unit
Downtime,T Gi It it is lower limit downtime of i-th unit.
Preferably, described step (5) specifically includes:
(5.1) mechanism of chaos is used to choose two different particles
Here most commonly seen in selection chaos algorithm one-dimensional nonlinear mapping model:
zi+1=μ zi(1-zi)
In formula, μ is controling parameter, when μ=4,0≤z0When≤1, this mapping is completely in chaos state, utilizes chaos to transport
Dynamic characteristic can be optimized search, first produces one group and the same number of Chaos Variable of optimized variable, takes two in this example
Individual different Chaos Variable, calculates two different values j, k respectively according to chaos algorithm model the most in an iterative process, takes advantage of respectively
With population scale M, then can obtain two random particle j and particle k;
(5.2) for substituting the difference operator of locally optimal solution pbest
According to two random particles j being derived above and particle k, calculating the vector difference of its position, formula is:
Δ=xj-xk
In formula, Δ is that position vector is poor, xjFor the position of particle j, xkPosition for particle k;
So the r element of the velocity of i-th particle can update by below equation:
Location updating formula: xi(t+1)=xi(t)+vi(t+1)
In formula, β is the scale factor in [0,1], ΔrPoor for position vector;c2It is Studying factors, is usually taken to be 2;r2It is 0
~the random number between 1;gbestrFor the value of r element corresponding in globally optimal solution, xirFor i-th example r
The location status that element is current;CRIt is crossover probability, works as CRWhen≤1, some elements in velocity vector retain old value;W is weight
The factor, for accelerating convergence rate, its value should carrying out and reduce with algorithm iteration, be commonly defined as:
In formula, wminAnd wmaxIt is respectively maximum, the minimal weight factor, is usually taken to be 0.4,0.9;T is current iteration number of times;
TmaxFor total iterations.
Compared with traditional particle swarm optimization algorithm, the present invention has beneficial effect highlighted below: at traditional particle
During group's algorithm finds optimal solution by self cognition, by the replacement to locally optimal solution, add and there is randomness, time
The property gone through and regular chaos algorithm and have the differential sampling parameter of variable effects and enter as new cognitive approach, can be effective
Improve the ability of other new positions, particle traversal search space, increase population diversity, it is to avoid population Premature Convergence, be absorbed in office
Portion is optimum.
Accompanying drawing explanation
Fig. 1 is chaos difference particle cluster algorithm flow chart of the present invention.
Detailed description of the invention
In order to make the purpose of the present invention, technical scheme and advantage clearer, below in conjunction with drawings and Examples, right
The present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, and
It is not used in the restriction present invention.If additionally, technical characteristic involved in each embodiment of invention described below
The conflict of not constituting each other just can be mutually combined.
A kind of based on chaos difference particle cluster algorithm the Optimized Scheduling of Hydroelectric Power method that the present invention proposes, step is as follows:
(1) select target power station to be calculated, and the corresponding constraints in power station be set: plant load Constraints of Equilibrium,
Power station upper pond level constraint, the constraint of each unit output, each unit generation traffic constraints, power station operating head polishing retrains, spinning reserve
Capacity-constrained, unit cavitation erosion vibrating area constraint, unit minimum startup-shutdown time-constrain.Retrain as follows:
1. plant load Constraints of Equilibrium:
In formula, E is the gross generation in power station, NiT () is the load that i-th unit undertakes under t period internal loading requirement.
2. power station upper pond level constraint:
Zmin≤Z≤Zmax
In formula, Z is the operating head polishing in power station, Zmin、ZmaxIt is the power station upper pond level bound in each period respectively.
The most each unit output retrains:
Pmin≤Pi(t)≤Pmax
In formula, Pmin, PmaxIt it is the unit power output upper and lower limit of i-th unit.
The most each unit generation traffic constraints:
Qmin≤Qi(t)≤Qmax
In formula, Qmin, QmaxIt is the minimum of i-th unit, maximum generation flow.
5. power station operating head polishing constraint:
Hmin≤H≤Hmax
In formula, H is the operating head polishing in power station, HminIt is power station minimum stable operation head, HmaxIt is power station maximum stable fortune
Row head.
6. spinning reserve capacity constraint:
In formula,It is unit installed capacity summation,It is unit output summation, NminIt it is the spinning reserve in power station
Lower bound of capacity.
7. unit cavitation erosion vibrating area constraint:
Pi(t)≤P Qsi Or
In formula,P Qsi It is the cavitation erosion district lower limit of i-th unit,It it is the cavitation erosion district upper limit of i-th unit.
8. unit minimum startup-shutdown time-constrain:
XKi≥T Ki Or XGi≥T Gi
In formula, XKiIt is the available machine time of i-th unit,T Ki It is the available machine time lower limit of i-th unit, XGiI-th unit
Downtime,T Gi It it is lower limit downtime of i-th unit.
(2) determining individual UVR exposure mode, use binary number to represent unit startup-shutdown state, wherein 0 represents at unit
In stopped status, 1 represents that unit is in open state;
(3) population size size M, maximum iteration time T are setmax;Wherein with the startup-shutdown assembled scheme of 96 in a day
As a particle, stochastic generation scale is the population of M;
(4) each particle fitness is calculated
In-plant economical operation optimization process, with the minimum target of water consumption, in conjunction with constraints, can arrange fitness letter
Number is as follows:
Wherein:
In formula, W is power station total water consumption (m3);It is H for i-th unit of period t at working headt, load
For Pi tTime generating flow (m3/s);Δ T represents period duration;Represent the unit i state at period t, during shutdown
During operationQup,i, Qdn,iRepresent the water consumption of start and stopping process respectively, sent out during startup-shutdown including unit
The water yield that raw mechanical wear etc. is converted into;N is Hydropower Plant number of units;Hop count when T is schedule periods;M destroys number for constraint;
Km、|ΔXm| it is respectively destruction penalty coefficient and the destructiveness of constraint m.
(5) speed of more new particle and position
In the speed more new formula of original particle cluster algorithm, there is a locally optimal solution pbest, i.e. arrive current iteration
The optimal solution that till number of times, each particle finds itself generates the next generation for updating the speed of each particle and position.?
Here we will replace about one of pbest, and i.e. we replace by described cognitive process, the substitute is at current grain
Using in subgroup and have the mechanism of chaos of ergodic property, the position vector choosing two different particles by weights is poor,
This vector difference operator is as the speed of new cognitive Xiang Laigeng new particle and position.Concrete operations are as follows:
(5.1) mechanism of chaos is used to choose two different particles
Here most commonly seen in selection chaos algorithm one-dimensional nonlinear mapping model:
zi+1=μ zi(1-zi)
In formula, μ is controling parameter, when μ=4,0≤z0When≤1, this mapping is completely in chaos state.Chaos is utilized to transport
Dynamic characteristic can be optimized search, first produces one group and the same number of Chaos Variable of optimized variable, takes two in this example
Individual different Chaos Variable, calculates two different values j, k respectively according to chaos algorithm model the most in an iterative process, takes advantage of respectively
With population scale M, then can obtain two random particle j and particle k.
(5.2) for substituting the difference operator of locally optimal solution pbest
According to two random particles j being derived above and particle k, calculating the vector difference of its position, formula is:
Δ=xj-xk
In formula, Δ is that position vector is poor, xjFor the position of particle j, xkPosition for particle k.
So the r element of the velocity of i-th particle can update by below equation:
Location updating formula: xi(t+1)=xi(t)+vi(t+1)
In formula, β is the scale factor in [0,1], ΔrPoor for position vector;c2It is Studying factors, is usually taken to be 2;r2It is 0
~the random number between 1;gbestrFor the value of r element corresponding in globally optimal solution, xirFor i-th example r
The location status that element is current;CRIt is crossover probability, works as CRWhen≤1, some elements in velocity vector retain old value;W is weight
The factor, for accelerating convergence rate, its value should carrying out and reduce with algorithm iteration, be commonly defined as:
In formula, wminAnd wmaxIt is respectively maximum, the minimal weight factor, is usually taken to be 0.4,0.9;T is current iteration number of times;
TmaxFor total iterations.
(6) globally optimal solution is updated
After being calculated the fitness value of each individuality of current algebraically, picking individual fitness value is maximum, with the overall situation
Excellent fitness value compares, if more than global optimum's fitness value, then replicates this individuality and replaces global optimum's individuality, do not carry out
Operation;
(7) loop iteration, it may be judged whether meet end condition, end condition is maximum iteration time;If meeting, then stop
Iteration, and export globally optimal solution;If being unsatisfactory for, then return step (4) and recalculate the fitness solving particle.
Although the preferred embodiments of the present invention being described above in conjunction with accompanying drawing, but the invention is not limited in
The detailed description of the invention stated, above-mentioned detailed description of the invention is only schematically, is not restrictive, this area common
Technical staff, under the enlightenment of the present invention, in the case of without departing from present inventive concept and scope of the claimed protection, also may be used
To make a lot of form.
Claims (3)
1. an Optimized Scheduling of Hydroelectric Power method based on chaos difference particle cluster algorithm, it is characterised in that described method includes
Following steps:
Step (1) selects target power station to be calculated, and arranges the corresponding constraints in power station: plant load Constraints of Equilibrium,
Power station upper pond level constraint, the constraint of each unit output, each unit generation traffic constraints, power station operating head polishing retrains, spinning reserve
Capacity-constrained, unit cavitation erosion vibrating area constraint, unit minimum startup-shutdown time-constrain;
Step (2) determines individual UVR exposure mode, uses binary number to represent unit startup-shutdown state, and wherein 0 represents at unit
In stopped status, 1 represents that unit is in open state;
Step (3) arranges population size size M, maximum iteration time Tmax;Wherein with the startup-shutdown assembled scheme of 96 in a day
As a particle, stochastic generation scale is the population of M;
Step (4) calculates each particle fitness, and in-plant economical operation optimization process is with the minimum target of water consumption, in conjunction with constraint
Condition, can arrange fitness function as follows:
Wherein:
In formula, W is power station total water consumption (m3);It is H for i-th unit of period t at working headt, load is
Time generating flow (m3/s);Δ T represents period duration;Represent the unit i state at period t, during shutdownDuring operationQup,i, Qdn,iRepresent the water consumption of start and stopping process, the machine occurred during startup-shutdown including unit respectively
The water yield that tool abrasion etc. is converted into;N is Hydropower Plant number of units;Hop count when T is schedule periods;M destroys number for constraint;Km、|Δ
Xm| it is respectively destruction penalty coefficient and the destructiveness of constraint m;
, in the speed more new formula of original particle cluster algorithm, there is a local in the speed of step (5) more new particle and position
Optimal solution pbest, the optimal solution that i.e. each particle finds itself to current iteration number of times is for updating the speed of each particle
Degree is with position thus generates the next generation, now will replace about one of pbest, will replace, instead by cognitive process
It is to use there is the mechanism of chaos of ergodic property in current particle group, chooses the position of two different particles by weights
Putting vector difference, this vector difference operator is as the speed of new cognitive Xiang Laigeng new particle and position;
Step (6) updates globally optimal solution, after being calculated the fitness value of each individuality of current algebraically, picking individual fitness
Value is maximum, compares with global optimum fitness value, if more than global optimum's fitness value, then replicates this individuality replacement overall situation
Excellent individuality, does not operates;
Step (7) loop iteration, it may be judged whether meet end condition, end condition is maximum iteration time;If meeting, then stop
Iteration, and export globally optimal solution;If being unsatisfactory for, then return step (4) and recalculate the fitness solving particle.
Optimized Scheduling of Hydroelectric Power method based on chaos difference particle cluster algorithm the most according to claim 1, its feature exists
In, constraints described in step (1) particularly as follows:
1. plant load Constraints of Equilibrium meets following formula:
In formula, E is the gross generation in power station, NiT () is the load that i-th unit undertakes under t period internal loading requirement;
2. the following formula of power station upper pond level constraint satisfaction:
Zmin≤Z≤Zmax
In formula, Z is the operating head polishing in power station, Zmin、ZmaxIt is the power station upper pond level bound in each period respectively;
The most each following formula of unit output constraint satisfaction:
Pmin≤Pi(t)≤Pmax
In formula, Pmin, PmaxIt it is the unit power output upper and lower limit of i-th unit;
The most each unit generation traffic constraints meets following formula:
Qmin≤Qi(t)≤Qmax
In formula, Qmin, QmaxIt is the minimum of i-th unit, maximum generation flow;
5. the following formula of power station operating head polishing constraint satisfaction:
Hmin≤H≤Hmax
In formula, H is the operating head polishing in power station, HminIt is power station minimum stable operation head, HmaxIt is that power station maximum stable runs water
Head;
6. the following formula of spinning reserve capacity constraint satisfaction:
In formula,It is unit installed capacity summation,It is unit output summation, NminIt it is the spinning reserve capacity in power station
Lower limit;
7. the unit cavitation erosion following formula of vibrating area constraint satisfaction:
Pi(t)≤P Qsi Or
In formula,P Qsi It is the cavitation erosion district lower limit of i-th unit,It it is the cavitation erosion district upper limit of i-th unit;
8. unit minimum startup-shutdown time-constrain meets following formula:
XKi≥T Ki Or XGi≥T Gi
In formula, XKiIt is the available machine time of i-th unit,T Ki It is the available machine time lower limit of i-th unit, XGiStopping of i-th unit
The machine time,T Gi It it is lower limit downtime of i-th unit.
Optimized Scheduling of Hydroelectric Power method based on chaos difference particle cluster algorithm the most according to claim 1, its feature exists
In, described step (5) specifically includes:
(5.1) mechanism of chaos is used to choose two different particles
Here most commonly seen in selection chaos algorithm one-dimensional nonlinear mapping model:
zi+1=μ zi(1-zi)
In formula, μ is controling parameter, when μ=4,0≤z0When≤1, this mapping is completely in chaos state, utilizes chaotic motion characteristic
Search can be optimized, first produce one group and the same number of Chaos Variable of optimized variable, this example takes two differences
Chaos Variable, calculates two different values j, k respectively according to chaos algorithm model the most in an iterative process, is multiplied by population respectively
Scale M, then can obtain two random particle j and particle k;
(5.2) for substituting the difference operator of locally optimal solution pbest
According to two random particles j being derived above and particle k, calculating the vector difference of its position, formula is:
Δ=xj-xk
In formula, Δ is that position vector is poor, xjFor the position of particle j, xkPosition for particle k;
So the r element of the velocity of i-th particle can update by below equation:
Location updating formula: xi(t+1)=xi(t)+vi(t+1)
In formula, β is the scale factor in [0,1], ΔrPoor for position vector;c2It is Studying factors, is taken as 2;r2It is between 0~1
Random number;gbestrFor the value of r element corresponding in globally optimal solution, xirCurrent for the r element of i-th example
Location status;CRIt is crossover probability, works as CRWhen≤1, some elements in velocity vector retain old value;W is weight factor, for
Accelerate convergence rate, its value should carrying out and reduce with algorithm iteration, be commonly defined as:
In formula, wminAnd wmaxIt is respectively maximum, the minimal weight factor, is taken as 0.4,0.9;T is current iteration number of times;TmaxFor always
Iterations.
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