CN111404204A - Optimized scheduling method for power system including wind power plant by using improved wolf pack algorithm - Google Patents
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Abstract
A method for optimizing and scheduling a power system including a wind power plant by using an improved wolf pack algorithm comprises the following steps of 1: establishing a wind power generation cost model and a thermal power generation cost model; step 2: establishing an optimal scheduling model of the power system including the wind power plant, which comprises an objective function and constraint conditions; and step 3: and solving the optimal scheduling model of the power system including the wind power plant by using an improved wolf pack algorithm. By adopting the method disclosed by the invention to carry out optimal scheduling on the power system comprising the wind power plant, the total power generation cost can be reduced, and the economy of the power system is improved.
Description
Technical Field
The invention relates to the technical field of electric scheduling of an electric power system including a wind power plant, in particular to an optimized scheduling method of the electric power system including the wind power plant by utilizing an improved wolf pack algorithm.
Background
The power system scheduling refers to the fact that in the process of power load distribution, according to certain specific constraints, generally the starting or stopping of a generator and certain specific constraints of a system, the output and the running state of a generator set in the whole system are adjusted to achieve the purpose of reasonable distribution of system loads, the traditional scheduling method generally aims at economy such as the lowest system power generation cost, but with the rise of new energy industries, more and more clean energy sources such as wind energy, solar energy and the like are connected in a grid mode, the probability of occurrence of random and fluctuating components in a traditional power grid is increased, and therefore the traditional power scheduling model is not applicable any more, and therefore the influence of random variables is considered when the power optimization scheduling model is established.
In the last 90 th century, Vemuri S and the like consider the environmental protection of wind power generation for the first time, model the environmental cost as a target function, take corresponding constraints into consideration, and establish an electric power economic dispatching model considering the environmental constraints of wind power integration, the influence of wind power random volatility is obtained by Ummels B.C and the like by adopting a scene probability function, the influence of the emission of thermal power generation pollution gas on the total cost is considered, a low-carbon-targeted electric power economic dispatching model is established, Papageorgiou L, G and the like set strict constraint conditions, and establish a secondary planning model of hybrid generator set economic dispatching according to the constraint conditions.
The domestic research on the electric power economic dispatching is later than that of the foreign countries, but with the national emphasis on clean energy, a great deal of research results are obtained. The millet Guiyu defines environmental assessment indexes aiming at the problem that the current environmental protection scheduling model can not meet the emission indexes of atmospheric pollutants, and estimates the emission risks of the pollutants by combining the assessment indexes, thereby establishing a multi-objective scheduling model based on the economic principle. In order to solve the optimal scheduling problem of a power system comprising a wind power plant, Niringhua and the like calculate the power generation cost considering the environmental benefit of new energy, introduce the strategies of distribution density and ambiguity, approach the optimal target, and finally verify the practicability of the method through simulation analysis. According to the influence of wind power climbing events on power scheduling, the combined problem of wind turbine generators is researched by aikamao of science and technology university in Huazhong, probability calculation of power flow is carried out according to wind power sample data, and an economic scheduling model of a power system with wind power access is established. When the objective function of economic dispatching is optimized, the Sunyuan chapter and the like introduce the environmental cost caused by wind power network access into the objective function, provide a modeling method of the wind power environmental cost, and establish a power dispatching model considering the environmental protection advantages of wind power.
The method mainly comprises a dynamic programming method, a priority method, an L margin relaxation method, a genetic algorithm, an ant colony algorithm, a particle swarm algorithm and the like, wherein when the dynamic programming method relates to the power change rate of a thermal generator set, the step conversion is difficult to complete, dimension disasters are easily caused along with the increase of the number of thermal generator sets, the priority method is difficult to process the combination problem of the generator sets in different time periods, the calculation of the starting and stopping cost of the generator set is not accurate enough, when the L margin relaxation method is used for solving a non-convex target function, the duality is difficult to guarantee, the algorithm is oscillated with a certain probability during iteration, the genetic algorithm is easy to fall into a local optimal solution during the evolution optimization searching process and can be converged too early, the ant colony algorithm adopts indirect communication among individuals, the iteration time is long, the convergence speed is slow due to a large amount of calculation, and the particle swarm algorithm is difficult to master global information during the calculation process, so that the algorithm is easy to fall into a local optimal solution.
Disclosure of Invention
In order to solve the technical problems, the invention improves the Wolf walking position detection and Wolf rushing step length detection on the basis of the traditional Wolf Pack Algorithm (WPA), and provides an optimized dispatching method for a power system including a wind power plant by utilizing an Improved Wolf Pack Algorithm (IWPA). By adopting the method disclosed by the invention to carry out optimal scheduling on the power system comprising the wind power plant, the total power generation cost can be reduced, and the economy of the power system is improved.
The technical scheme adopted by the invention is as follows:
a method for optimizing and scheduling an electric power system including a wind power plant by utilizing an improved wolf pack algorithm comprises the steps of firstly, establishing a wind power generation cost model and a thermal power generation cost model, wherein the wind power generation cost is the sum of an expected cost, an overestimated cost generated when the wind speed is small and an underestimated cost generated when the wind speed is large; the thermal power generation cost takes the valve point effect of the thermal power generating unit into consideration; then, establishing an optimized dispatching model of the power system including the wind power plant, wherein the optimized dispatching model comprises an objective function and constraint conditions, the objective function is the minimum value of the sum of the wind power generation cost and the thermal power generation cost, and the constraint conditions comprise a power balance constraint, an output power constraint and a climbing rate constraint; and finally, solving the optimal scheduling model of the power system including the wind power plant by using an improved wolf pack algorithm to realize the optimal scheduling of the power system including the wind power plant.
A method for optimizing and scheduling a power system including a wind power plant by utilizing an improved wolf pack algorithm comprises the following steps:
step 1: establishing a wind power generation cost model and a thermal power generation cost model;
step 2: establishing an optimal scheduling model of the power system including the wind power plant, which comprises an objective function and constraint conditions;
and step 3: and solving the optimal scheduling model of the power system including the wind power plant by using an improved wolf pack algorithm.
The invention discloses an optimized scheduling method for a power system including a wind power plant by utilizing an improved wolf pack algorithm, which has the following beneficial effects:
1: the influence of small or large wind speed on the wind power generation cost is considered, and the wind power overestimation cost and the wind power underestimation cost are respectively established and are consistent with the actual operation of the wind turbine generator.
2: the valve point effect of the thermal power generating unit is considered, and a thermal power generation cost model is established and is consistent with the actual operation of the thermal power generating unit.
3: the improved wolf colony algorithm has high convergence speed and high search precision and is superior to a common algorithm under the same condition.
4: the invention enhances the searching capability of the algorithm by improving the wolf-detection walking position and the wolf-detection and rushing step length in the wolf group algorithm. 1 wind power plant and 6 thermal power generating units are introduced into an IEEE-30 system, an improved wolf pack algorithm is applied to an optimized scheduling model of the power system with the wind power plant, the scheduling method can reduce the total power generation cost, and the economy of the power system is improved.
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FIG. 1 is a flow chart of the present invention.
Figure 2 is an iteration diagram of the WPA algorithm and the improved WPA algorithm of the present invention.
Detailed Description
A method for optimizing and scheduling an electric power system including a wind power plant by utilizing an improved wolf pack algorithm comprises the steps of firstly, establishing a wind power generation cost model and a thermal power generation cost model, wherein the wind power generation cost is the sum of an expected cost, an overestimated cost generated when the wind speed is small and an underestimated cost generated when the wind speed is large; the thermal power generation cost takes the valve point effect of the thermal power generating unit into consideration; then, establishing an optimized dispatching model of the power system including the wind power plant, wherein the optimized dispatching model comprises an objective function and constraint conditions, the objective function is the minimum value of the sum of the wind power generation cost and the thermal power generation cost, and the constraint conditions comprise a power balance constraint, an output power constraint and a climbing rate constraint; and finally, solving the optimal scheduling model of the power system including the wind power plant by using an improved wolf pack algorithm to realize the optimal scheduling of the power system including the wind power plant.
A method for optimizing and scheduling a power system including a wind power plant by utilizing an improved wolf pack algorithm comprises the following steps:
step 1: establishing a wind power generation cost model and a thermal power generation cost model;
in the step 1, when a wind power generation cost model is established, the characteristics of wind energy intermittency and randomness and errors of wind power prediction are considered, and expected cost, overestimated cost and underestimated cost are introduced;
the wind power expected cost refers to the basic operation and maintenance cost of the wind power plant in the production process, and the calculation formula of the expected cost is as follows:
wherein, FWcostFor the expected cost of wind power, T represents a set time, T represents a time, j represents a wind motor, PWj,tIs the actual value of the output power of the jth typhoon generator at the moment t, NWThe number of fans connected into the power system; cWA cost factor is expected for the wind turbine.
The wind power overestimated cost refers to the cost generated by supplementing the power difference of the wind power system by using the spare capacity of the power system when the wind speed is smaller or the actual output power of the wind power is smaller than the predicted power due to other external factors, and a calculation formula of the overestimated cost is as follows:
wherein, FW+For wind power overestimation cost, PSj,tIs the output power predicted value, P, of the jth typhoon machine at the moment tWj,tIs the actual value of the output power of the jth typhoon generator at the moment t, CW+And overestimating the cost coefficient for the wind turbine generator.
The wind power underestimation cost means that when the actual output power of the wind turbine is larger than the predicted power due to high wind speed, the output of the thermal power generating unit is properly reduced in consideration of environmental protection requirements, so that part of cost is consumed, and the calculation formula of the underestimation cost is as follows:
wherein, FW-For the expected cost of wind power, CW-And underestimating the cost coefficient for the wind turbine.
The total cost of the wind turbine is the sum of the expected cost, the overestimated cost and the underestimated cost, and is as follows:
FW＝FWcost+FW++FW-。
in the step 1, the thermal power generation cost includes the cost of coal, when a steam turbine valve is opened in the power generation process of the thermal power generating unit, a valve point appears on the consumption characteristic curve of the thermal power generating unit to form a valve point effect, and considering the part of cost, the power generation cost of the thermal power generating unit is as follows:
wherein T represents a set time, T represents a time, NGFor the number of thermal power generating units, i denotes the thermal power generating unit, FGIn order to reduce the power generation cost of the thermal power generating unit,
is the lower limit of the output power of the ith thermal power generating unit, fiIs the cost coefficient of the thermal power generating unit, ai，bi，ciAre all the cost coefficients of the i-th thermal power engine, eiIn order to consider the cost coefficient, P, of the ith thermal power generating unit corresponding to the valve point effecti,jAnd the output power of the ith thermal power generating unit at the moment t.
Step 2: establishing an optimal scheduling model of the power system including the wind power plant, which comprises an objective function and constraint conditions;
in step 2, the objective function is:
minFtotal＝min(FW+FG)；
the constraint conditions are as follows:
(1) and power balance constraint:
wherein N isGNumber of thermal power generating units, NWThe number of the fans connected into the power system is represented by i, j, t and PloadIs the total load of the power system.
(2) Output power constraint:
the output power constraint of the thermal power generating unit is as follows:
wherein,
and
respectively is the upper limit and the lower limit of the output power of the ith thermal power generating unit.
The output power constraint of the wind turbine generator is as follows:
wherein,
and the upper limit of the output power of the ith wind turbine generator set.
(3) And (3) slope climbing rate constraint:
in the operation process of the thermal power generating unit, the switching of the unit is required to be completed in a short time, so that the ramp rate of the thermal power generating unit is required, namely the start and the stop of the unit are completed at a certain time, and the constraint conditions are as follows:
Pi,t-Pi,t-1≤riu×T60
Pi,t-1-Pi,t≤rid×T60
wherein, Pi,tAnd Pi,t-1The output power r of the ith thermal power generating unit at the t moment and the t-1 moment respectivelyiuThe rising ramp rate r of the ith thermal power generating unitidIs the falling rate, T, of the ith thermal power generating unit60A scheduling period of 60 min.
And step 3: the objective function is optimized by adopting an improved wolf colony algorithm, wherein the improvement of the wolf colony algorithm comprises the improvement of exploring the wolf wandering position and the improvement of exploring wolf and rushing step length. And solving the optimal scheduling model of the power system including the wind power plant by using an improved wolf pack algorithm.
The step 3 comprises the following steps:
step 3.1: carrying out initialization setting, wherein the set parameters comprise N artificial wolfs and X initial positioniMaximum number of walks TmaxAnd number of iterations kmaxStep factor S, distance decision factor ω, sounding wolf, update scale factors α and β.
Step 3.2, the walking position of the detected wolf is updated, so that the N detected wolfs share M detected wolfs, and the value of M is defined by [ N/(α +1), N/α]Determining that α is a scaling factor of the total number of the wolf pack, the wolf wanders in h directions, and the initial position of the wolf is xidThe step length of the walking of the wolf is
The initial fitness of the wolf detection is YiIf the probe wolf moves one step in p (p ═ 1,2, …, h) directions based on the current position, the position of the probe wolf in d-dimension is updated as follows:
when h is 4, the directions of the sounding wolf search are respectively: when p is equal to 1, the compound is,
when p is 2, the compound is a compound,
when p is 3, the compound is a compound,
when p is equal to 4, the compound is,
when h is 4, the direction of the exploring wolf search is: when p is equal to 1, the compound is,
when p is 3, the compound is a compound,
when p is 2 or 4,
in fact, only two directions exist, so that the wandering of the sounding wolf is reduced, and the calculation amount is increased. Therefore, the improved method can ensure that the sounding wolf has three directions to wander at least, and the optimizing capability is enhanced.
At this time, a new fitness value Y is calculatedipIf it is more adaptive than the previous fitness YiReplace it if it is better, and update the position of the exploring wolf to XiThen, the new fitness of the exploring wolf is compared with the fitness of the head wolf, if the new fitness of the exploring wolf is better than the fitness of the head wolf, the exploring wolf is used for replacing the head wolf, and the head wolf is called to come to the current position, otherwise, the optimizing is continued until the maximum iteration time Tmax。
Step 3.3: the wolf of terrible assy rushes to the position to update, the wolf of terrible assy means to remove the rest of the other two wolfs, the number of the wolf of terrible assy is N-M, the wolf of terrible assy will be rushed to the wolf immediately after receiving the calling of the wolf of terrible, the position of the wolf of terrible at the k-th iteration in the dimension d is
The step length of the wolf of terrible speedy is
The position of the wolf of terry at the k +1 th iteration in the d dimension is:
wherein,
is the position of the wolf head at the kth iteration, kmaxAnd k is the current iteration number. In the wolf pack algorithm, the step size
No change, but step size with increasing number of iterations and decreasing range of prey
Should be adaptive to decrease, the step size is adaptive to change
And (5) carrying out improvement.
The fitness of the wolf of terrible wolf after being attacked is YiIf Y isiIs superior to YleadThe wolf of terrible changes into the wolf of terrible and calls other wolfs of terrible, otherwise the wolf of terrible continues to rush towards the wolf of terrible until the position of the wolf of terrible is less than dnearWhen the prey is attacked, dnearThe calculation formula of (2) is as follows:
where D is the number of pre-optimization variables, ω is the distance decision factor, D is the optimization variable, maxdAnd mindAre respectively a variabledMaximum and minimum values of.
Step 3.4: when the wolf is hit, the wolf will attack the hunting object together with the wolf, and the position of the hunting object can be regarded as the position of the wolf due to the wolf being close to the hunting object
The initial position of the wolf group is
The step length of the wolf colony attacking the prey is
The position of the wolf group is updated as follows:
wherein k ismaxAnd k is the current iteration number. In the wolf pack algorithm, the step size
No change, but step size with increasing number of iterations and decreasing range of prey
Should be made adaptive smaller. The step size is adaptively changed to match the step size
The improvement is carried out, and the method comprises the following steps of,
when the prey is attacked, the adaptability of the wolf pack position is superior to the original adaptability, and the wolf pack position is replaced and updated, otherwise, the wolf pack position is unchanged.
And 3.5, updating the wolf group, eliminating the R wolf with the worst fitness in the process of searching the prey, randomly generating the R wolf for supplement, wherein R is determined by [ N/2 ×β, N/β ], wherein β is an updating scale factor, and S is a step size factor.
Step 3.6: and (4) judging that the maximum iteration number or the allowable error is reached, if so, outputting an optimization result, and otherwise, returning to the step 3.2.
Figure 1 shows a flow chart of the present invention. A standard IEEE-30 node test system is adopted to carry out simulation analysis on optimized scheduling of a power system comprising a wind power plant, the test period is 24 hours, the specific method is that 1 wind power plant and 6 thermal power generating units are added into the test system, the access position of the wind power plant is 9 nodes of the IEEE-30 node test system, and the access positions of the 6 thermal power generating units are respectively 1 node, 2 node, 5 node, 8 node, 11 node and 13 node of the IEEE-30 node test system.
The method considers the influence of the wind power prediction error on the optimal scheduling of the power system to form the final objective function of minFtotal＝min(FG+FWcost+FW++FW-) Wind turbine predicted cost coefficient CWTaking 200 yuan/MW, wind turbine generator overestimated cost coefficient CW+Taking 300 yuan/MW, wind turbine generator underestimation cost coefficient CW-Taking 250 yuan/MW, adopting WPA algorithm and IPWA algorithm, carrying out simulation analysis in Matlab environment, and iterating two optimization algorithmsThe results are shown in FIG. 2.
As can be seen from FIG. 2, the WPA algorithm obtains the minimum power generation cost of 3.049 × 10 after being iterated for 123 times6Yuan, and the improved WPA algorithm only needs 88 iterations to obtain the minimum power generation cost, which is 3.023 × 106Compared with the WPA algorithm, the power generation total cost of the improved WPA algorithm is reduced by 2.6 ten thousand yuan, the iteration times are reduced by 35 times, the convergence rate is obviously accelerated, and the optimization performance is better.
Claims (6)
1. A wind power plant-containing power system optimal scheduling method utilizing an improved wolf pack algorithm is characterized by comprising the following steps: firstly, establishing a wind power generation cost model and a thermal power generation cost model, wherein the wind power generation cost is the sum of an expected cost, an overestimated cost generated when the wind speed is small and an underestimated cost generated when the wind speed is large; the thermal power generation cost takes the valve point effect of the thermal power generating unit into consideration; then, establishing an optimized dispatching model of the power system including the wind power plant, wherein the optimized dispatching model comprises an objective function and constraint conditions, the objective function is the minimum value of the sum of the wind power generation cost and the thermal power generation cost, and the constraint conditions comprise a power balance constraint, an output power constraint and a climbing rate constraint; and finally, solving the optimal scheduling model of the power system including the wind power plant by using an improved wolf pack algorithm to realize the optimal scheduling of the power system including the wind power plant.
2. A wind power plant-containing power system optimal scheduling method utilizing an improved wolf pack algorithm is characterized by comprising the following steps:
step 1: establishing a wind power generation cost model and a thermal power generation cost model;
step 2: establishing an optimal scheduling model of the power system including the wind power plant, which comprises an objective function and constraint conditions;
and step 3: and solving the optimal scheduling model of the power system including the wind power plant by using an improved wolf pack algorithm.
3. The optimal scheduling method for the power system of the wind power plant by using the improved wolf pack algorithm as claimed in claim 2, wherein: in the step 1, when a wind power generation cost model is established, the characteristics of wind energy intermittency and randomness and errors of wind power prediction are considered, and expected cost, overestimated cost and underestimated cost are introduced;
the wind power expected cost refers to the basic operation and maintenance cost of the wind power plant in the production process, and the calculation formula of the expected cost is as follows:
wherein, FWcostFor the expected cost of wind power, T represents a set time, T represents a time, j represents a wind motor, PWj,tIs the actual value of the output power of the jth typhoon generator at the moment t, NWThe number of fans connected into the power system; cWA cost factor is expected for the wind turbine;
the wind power overestimated cost refers to the cost generated by supplementing the power difference of the wind power system by using the spare capacity of the power system when the wind speed is smaller or the actual output power of the wind power is smaller than the predicted power due to other external factors, and a calculation formula of the overestimated cost is as follows:
wherein, FW+For wind power overestimation cost, PSj,tIs the output power predicted value, P, of the jth typhoon machine at the moment tWj,tIs the actual value of the output power of the jth typhoon generator at the moment t, CW+Overestimating the cost coefficient for the wind turbine;
the wind power underestimation cost means that when the actual output power of the wind turbine is larger than the predicted power due to high wind speed, the output of the thermal power generating unit is properly reduced in consideration of environmental protection requirements, so that part of cost is consumed, and the calculation formula of the underestimation cost is as follows:
wherein, FW-For wind power anticipationCost, CW-Underestimating a cost coefficient for the wind turbine;
the total cost of the wind turbine is the sum of the expected cost, the overestimated cost and the underestimated cost, and is as follows:
FW＝FWcost+FW++FW-。
4. the optimal scheduling method for the power system of the wind power plant by using the improved wolf pack algorithm as claimed in claim 2, wherein: in the step 1, the thermal power generation cost includes the cost of coal, when a steam turbine valve is opened in the power generation process of the thermal power generating unit, a valve point appears on the consumption characteristic curve of the thermal power generating unit to form a valve point effect, and considering the part of cost, the power generation cost of the thermal power generating unit is as follows:
wherein T represents a set time,trepresents time, NGFor the number of thermal power generating units, i denotes the thermal power generating unit, FGIn order to reduce the power generation cost of the thermal power generating unit,
is the lower limit of the output power of the ith thermal power generating unit, fiIs the cost coefficient of the thermal power generating unit, ai，bi，ciAre all the cost coefficients of the i-th thermal power engine, eiIn order to consider the cost coefficient, P, of the ith thermal power generating unit corresponding to the valve point effecti,jAnd the output power of the ith thermal power generating unit at the moment t.
5. The optimal scheduling method for the power system of the wind power plant by using the improved wolf pack algorithm as claimed in claim 2, wherein: in step 2, the objective function is:
minFtotal＝min(FW+FG)；
the constraint conditions are as follows:
(1) and power balance constraint:
wherein N isGNumber of thermal power generating units, NWThe number of the fans connected into the power system is represented by i, j, t and PloadIs the total load of the power system;
(2) output power constraint:
the output power constraint of the thermal power generating unit is as follows:
wherein,
and
respectively setting the upper limit and the lower limit of the output power of the ith thermal power generating unit;
the output power of the wind turbine is constrained to
Wherein,
the upper limit of the output power of the ith wind turbine generator set is set;
(3) and (3) slope climbing rate constraint:
in the operation process of the thermal power generating unit, the switching of the unit is required to be completed in a short time, so that the ramp rate of the thermal power generating unit is required, namely the start and the stop of the unit are completed at a certain time, and the constraint conditions are as follows:
Pi,t-Pi,t-1≤riu×T60
Pi,t-1-Pi,t≤rid×T60；
wherein, Pi,tAnd Pi,t-1The output power r of the ith thermal power generating unit at the t moment and the t-1 moment respectivelyiuThe rising ramp rate r of the ith thermal power generating unitidIs the falling rate, T, of the ith thermal power generating unit60A scheduling period of 60 min.
6. The optimal scheduling method for the power system of the wind power plant by using the improved wolf pack algorithm as claimed in claim 2, wherein: the step 3 comprises the following steps:
step 3.1: carrying out initialization setting, wherein the set parameters comprise N artificial wolfs and X initial positioniMaximum number of walks TmaxAnd number of iterations kmaxStep size factor S, distance decision factor ω, wolf detection, update scale factors α and β;
step 3.2, the walking position of the detected wolf is updated, so that the N detected wolfs share M detected wolfs, and the value of M is defined by [ N/(α +1), N/α]Determining that α is a scaling factor of the total number of the wolf pack, the wolf wanders in h directions, and the initial position of the wolf is xidThe step length of the walking of the wolf is
The initial fitness of the wolf detection is YiIf the probe wolf moves one step in p (p ═ 1,2, …, h) directions based on the current position, the position of the probe wolf in d-dimension is updated as follows:
when h is 4, the directions of the sounding wolf search are respectively: when p is equal to 1, the compound is,
when p is 2, the compound is a compound,
when p is 3, the compound is a compound,
when p is equal to 4, the compound is,
when h is 4, the direction of the exploring wolf search is: when p is equal to 1, the compound is,
when p is 3, the compound is a compound,
when p is 2 or 4,
actually, only two directions exist, so that the wandering of the sounding wolf is reduced, and the calculated amount is increased; therefore, the improved method can ensure that the sounding wolf has three directions to wander at least, and the optimizing capability is enhanced;
at this time, a new fitness value Y is calculatedipIf it is more adaptive than the previous fitness YiReplace it if it is better, and update the position of the exploring wolf to XiThen, the new fitness of the exploring wolf is compared with the fitness of the head wolf, if the new fitness of the exploring wolf is better than the fitness of the head wolf, the exploring wolf is used for replacing the head wolf, and the head wolf is called to come to the current position, otherwise, the optimizing is continued until the maximum iteration time Tmax；
Step 3.3: the wolf of terrible assy rushes to the position to update, the wolf of terrible assy means to remove the rest of the other two wolfs, the number of the wolf of terrible assy is N-M, the wolf of terrible assy will be rushed to the wolf immediately after receiving the calling of the wolf of terrible, the position of the wolf of terrible at the k-th iteration in the dimension d is
The step length of the wolf of terrible speedy is
The position of the wolf of terry at the k +1 th iteration in the d dimension is:
wherein,
is the position of the wolf head at the kth iteration, kmaxK is the current iteration number; in the wolf pack algorithm, the step size
No change, but step size with increasing number of iterations and decreasing range of prey
Should be adaptive to decrease, the step size is adaptive to change
Carrying out improvement;
the fitness of the wolf of terrible wolf after being attacked is YiIf Y isiIs superior to YleadThe wolf of terrible changes into the wolf of terrible and calls other wolfs of terrible, otherwise the wolf of terrible continues to rush towards the wolf of terrible until the position of the wolf of terrible is less than dnearWhen the prey is attacked, dnearThe calculation formula of (2) is as follows:
where D is the number of pre-optimization variables, ω is the distance decision factor, D is the optimization variable, maxdAnd mindAre respectively a variabledMaximum and minimum values of;
step 3.4: when the wolf is hit, the wolf will attack the hunting object together with the wolf, and the position of the hunting object can be regarded as the position of the wolf due to the wolf being close to the hunting object
The initial position of the wolf group is
The step length of the wolf colony attacking the prey is
The position of the wolf group is updated as follows:
wherein k ismaxK is the current iteration number; in the wolf pack algorithm, the step size
No change, but step size with increasing number of iterations and decreasing range of prey
Should be adaptive smaller; the step size is adaptively changed to match the step size
The improvement is carried out, and the method comprises the following steps of,
when the wolf pack position fitness is better than the original fitness during prey, replacing and updating, otherwise, keeping unchanged;
step 3.5, updating wolf clusters, wherein in the process of searching for prey, R wolf with the worst fitness is eliminated, and R wolf is randomly generated for supplement, wherein R is determined by [ N/2 ×β, N/β ], wherein β is an updating scale factor, and S is a step size factor;
step 3.6: and (4) judging that the maximum iteration number or the allowable error is reached, if so, outputting an optimization result, and otherwise, returning to the step 3.2.
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