CN114997630A - Multi-region environment economic scheduling method based on competitive learning constraint multi-target particle swarm algorithm - Google Patents
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Abstract
The invention discloses a multi-region environmental economic dispatching method based on competitive learning constraint multi-target particle swarm optimization. The method comprises the following steps: the elite population is determined through rapid non-dominated sorting and crowded distance sorting, then a competitive particle based on space angle information is selected to guide particle updating, inequality and equality constraints in the system are respectively repaired by adopting boundary processing and a cyclic repair method, and economic and environmental target values are calculated. The method reduces the influence of the globally optimal particles on the population, increases the diversity of particle learning, better avoids the algorithm from falling into local optimization due to premature convergence, and improves the accuracy of the algorithm. The winning particles are selected from the current population, and the individual historical optimal positions are recorded without additional files, so that the structure of the multi-target particle swarm algorithm is simplified, and the calculation efficiency is improved. Different repairing methods are adopted for different constraint conditions, and the feasibility of understanding is improved.
Description
Technical Field
The invention relates to the technical field of power system scheduling, in particular to a multi-region environment economic scheduling method based on competitive learning constraint multi-target particle swarm optimization.
Background
The multi-region economic dispatching of the power system is to meet various operation constraint conditions of the system and solve a dispatching scheme which enables fuel cost to be lowest on the premise of ensuring the safety and stability of the power system. In the case of a thermal power generating unit, a large amount of pollution gases such as nitrogen oxides and sulfides are emitted during operation. In recent years, with the development of green economy, the concern of pollution emission in power system dispatching is increased, and how to balance economic and environmental benefits becomes an urgent problem to be solved. If pollutant emission is considered in the determination of the scheduling scheme, the original single-target economic scheduling is changed into multi-target environment scheduling. The determination of the scheduling scheme becomes very difficult due to the inherent contradiction between fuel cost objectives and pollutant emission objectives, and the inclusion of various constraints.
The solution of the multi-region environmental economic scheduling problem can be mainly divided into a mathematical programming technology and an intelligent optimization algorithm. The core idea of mathematical programming is to convert a plurality of optimization targets into a single-target optimization problem through a constraint method and a weight coefficient method. For the environmental economic scheduling problem, namely, a pollution emission target and an economic target are converted into a single-target optimization problem, a pareto solution set is obtained through multiple times of solution, the method is poor in expansion compatibility and low in calculation efficiency, and the traditional mathematical method is difficult to solve due to the fact that multi-region environmental economic scheduling is a high-dimensional nonlinear complex optimization problem containing multiple constraint conditions.
Besides the traditional method, the multi-target optimization algorithm is suitable for solving a high-dimensional nonlinear problem due to high solving efficiency, the pareto frontier can be obtained by single solving, and the multi-target particle swarm optimization algorithm is used for solving the environmental economic scheduling problem in recent years. However, due to the fact that the multi-target particle swarm algorithm updates individuals in a swarm by using global optimization and individual historical optimization in the updating process, learning diversity of particles is reduced, and the particles are prone to falling into local optimization. And an additional external archive is needed to store the historical optimal solution set of the individual, which increases the complexity of the algorithm and reduces the solving efficiency of the algorithm.
By combining the above analysis, the traditional mathematical method cannot solve the complex multi-target environment economic scheduling problem, and the existing intelligent optimization algorithm has complex constraint processing when solving the problem, is low in efficiency and easy to fall into local optimization, and cannot obtain the pareto solution front edge which is uniformly and widely distributed and high in convergence.
Disclosure of Invention
Aiming at the problems, the invention aims to provide a multi-region environment economic scheduling method based on competitive learning constraint multi-target particle swarm optimization, overcomes the defects that the existing method is complex in constraint processing when solving the scheduling problem and difficult to obtain a pareto solution set with optimal convergence and distribution uniformity, and makes a reasonable decision to determine an optimal scheduling scheme.
In order to solve the technical problem, the invention adopts the technical scheme that: a multi-region environment economic dispatching method based on competitive learning constraint multi-target particle swarm optimization comprises the following steps:
step 1: establishing a multi-region environmental economic dispatching model of the power dispatching system by taking fuel cost and pollution emission as objective functions;
step 2: acquiring parameters of a generator set and constraint conditions of a system, and setting the parameters of the generator set;
and step 3: optimizing and solving the mathematical model established in the step 1 and the step 2 by adopting a competitive learning constraint multi-target particle swarm algorithm and combining a constraint processing mechanism to obtain a pareto solution set
N is the number of solution concentration scheduling schemes, and solution concentration X i Indicating the ith scheduling scheme;
and 4, step 4: and outputting the pareto frontier obtained by optimization and the optimal compromise solution in the system, and determining the actual power output of a generator set in the system according to the scheduling scheme of the optimal compromise solution.
Further, the step 3 comprises the following specific steps:
wherein X i,t Step 3.1: initializing parameters: the population size ps, the maximum calculation times maxFES and the current calculation times FES are 0, and the iteration counting initial value t is 1; initializing population, and effectively solving position information X of a multi-region environment economic dispatching system consisting of M regions i,t Can be encoded as: indicating the position information of the ith particle in the population of the t generation,
is the Nth in the k region k Output power of individual generator sets, T ik Is the transmission power between zone i and zone k;
step 3.2: the particles in the population may not meet the constraint conditions of the system, and the particles violating the constraint are constrained and repaired, and for the constraint of the power generation capacity, the repairing method comprises the following steps:
wherein P is ij The actual output power of the jth generator set in the ith zone,
and
the minimum output power and the maximum output power of the corresponding unit are respectively, and for the transmission capacity constraint, the repairing method comprises the following steps:
wherein T is ik For the transmission power from the i-th zone to the k-th zone,
and
respectively corresponding to the minimum and maximum transmission capacities between the areas, and repairing the actual power balance constraint of the areas by using a power balance repairing operator;
step 3.3: calculating each particle X i,t Fuel cost FC i,t And pollutant emissions E i,t And let FES be FES + ps, FES is the current number of calculations, ps is the population size;
step 3.4: performing rapid non-dominated sorting and crowded distance sorting on the particles according to the target values, determining an elite population L, and solving X in multi-objective optimization 1 And X 2 The following relationship is satisfied:
i.e. for any object f i Can all make X 1 Target value f of i (X 1 ) Not more than X 2 Target value f of i (X 2 ) And at least one object f is present j So that X 1 Target value f of j (X 1 ) Less than X 2 Target value f of j (X 2 ) Is called X 1 Dominating X 2 . The fast non-dominated sorting is to find out all non-dominated solution sets in the population, the crowding distance is to calculate the sparseness degree of each particle in the population, the particles in the non-dominated solution sets are sorted from large to small according to the crowding distance, the particles with large crowding distance are sorted in the front, and the top 20% of the particles are taken to form an elite population L;
step 3.5: using a competitive learning strategy for each particle X in the population i,t Updating is carried out;
step 3.6: by using X W Guiding the current particle X i,t The update equation is as follows:
V i,t+1 ＝R 1 ·V i,t +R 2 (X W -X i,t )
X i,t+1 ＝X i,t +V i,t+1
wherein X W For winner particle, V i,t+1 For updating the velocity information of the particles, X i,t+1 For updated position information of the particles, R 1 And R 2 Is [0,1 ]]In the random number set, the updated particle X is processed by step 3.4 i,t+1 Repairing constraint violation;
step 3.7: then calculating the objective function values of all repaired particles in the population, and making FES (field emission spectroscopy) equal to FES + ps and t equal to t + 1;
step 3.8: judging whether a termination condition is met, namely whether the maximum evaluation frequency is reached, if not, repeating the step 3.4-the step 3.8, and if so, turning to the step 3.9;
step 3.9: outputting pareto frontier
Further, in step 3.2, the power repair of the ith area is as follows:
(1) calculating violation dif of power balance constraint of ith area i When the constraint violation degree is greater than zero, the total power of the current area is smaller than the actual required power, and the power output of the unit needs to be increased; when the constraint violation degree is less than zero, the total power of the current area is larger than the actual required power, the power output of the generator set needs to be reduced, the numbers of all the generator sets in the current area are counted into a set I, dif i The calculation method is as follows:
wherein
For the total power generation of region i, PD i For the load demand of zone i, PL i Network loss for region i, T ik Is the transmission power between zone i and zone k;
(2) when power balance constraint violation dif i When the power output is larger than 0, randomly selecting a generating set j in the area I, namely randomly selecting the jth generating set from the set I, and increasing the power output of the jth generating set to be the power output
(3) When power balance constraint violation dif i When the power output is less than 0, randomly selecting a generator set j in the area I, namely randomly selecting the jth generator set from the set I, and reducing the power output of the jth generator set to be the power output
(4) Recalculating the violation dif of the power balance constraint for the ith region i When dif i Is zero or dif i If the sign of the number j is changed, stopping repairing, otherwise deleting the selected unit with the number j in the set I, and repeating the steps (2) and (3).
Further, in step 3.5, the competition learning strategy is:
after the elite population L is created, two particles in the population L are randomly selected to compete, a winner guides the updating of the current particle, and the particle X to be updated in the population is selected i,t Randomly selecting two particles a and b from elite population, and respectively calculating a, b and X i,t The small-angle elite particle is the winner and is assigned as X W Particles X i,t Will learn to the winner.
Further, the step 4 comprises the following specific steps:
step 4.1: finding points Q of fuel cost optimal solutions in pareto solution sets, respectively 1 And location Q of pollution emission optimal solution 2 Respectively make a point Q 1 And Q 2 The intersection point P is an ideal solution to the vertical line on the target axis, and the economic target and the environmental target are expressed to be optimal simultaneously;
step 4.2: calculating pareto frontier
And taking the point with the minimum distance as the optimal compromise solution, namely the comprehensive optimal scheduling scheme.
Compared with the prior art, the invention has the following beneficial effects:
1. the method is simple to implement, high in operation speed and strong in robustness, the inequality constraint of the system is repaired by adopting an easily-implemented boundary constraint processing method, and the regional power balance of the system is repaired by adopting a circulating repair method.
2. The competitive learning strategy is added into the multi-target particle swarm algorithm, the influence of the global most influence and the individual most influence is eliminated, the particle learning diversity in the swarm is improved, the particles can search the whole space more widely, additional sets are not required to be distributed, historical data are reserved, the structure of the algorithm is simplified, and the efficiency of the algorithm is improved. The rapid non-dominated sorting and the crowded distance sorting are adopted to determine the elite population, so that the algorithm can have higher exploration performance, and the improvement can help to obtain a pareto frontier which is more widely distributed and closer to global optimum, so as to provide an optimal candidate scheme for subsequent decision-making;
3. on the basis of obtaining the optimal pareto front-edge solution set, a comprehensive optimal scheduling method is provided for decision makers by using the distance index, the effect of comprehensively optimizing fuel cost and pollutant discharge is achieved, and the method has high practicability.
Drawings
FIG. 1 is a schematic diagram of a 4-zone 16 unit model.
FIG. 2 is a flow chart of competitive learning constrained multi-objective particle swarm optimization for solving multi-area environmental economic dispatch.
Fig. 3 is a diagram illustrating a competitive learning strategy.
FIG. 4 is a schematic diagram of an optimal tradeoff solution based on distance metrics.
FIG. 5 is a diagram illustrating a competitive learning constraint multi-objective particle swarm algorithm for solving an optimal pareto frontier of multi-region environmental economic dispatch.
Detailed Description
The invention is further described in detail with reference to the drawings and the specific implementation steps but is not to be construed as being limited thereto.
The improved multi-target particle swarm optimization is used for solving a multi-region environment scheduling problem containing various constraint conditions, provides a constraint repairing method, improves the feasibility of understanding, can optimize to obtain an optimal scheduling scheme, distributes optimal output power and transmission power among regions for each unit, and achieves comprehensive optimization of economic and environmental benefits.
A multi-region environmental economic dispatching method based on competitive learning constraint multi-target particle swarm optimization firstly establishes a multi-region environmental economic dispatching mathematical model of 4 regions and 16 units as shown in figure 1, and the total power load requirement of the system is 1250 MW. Region 1 includes the first 4 generator sets, with a demand load of 32% of the total load, region 2 includes the second 4 generator sets, with a demand load of 16% of the total load, region 3 consists of the third 4 generators, with a demand load of 28% of the total load, and region 4 includes the last 4 generator sets, with a demand load of 24% of the total load. The power transmission between the different zones is limited to 100 MW. Acquiring the operation parameters of a specific thermal generator set, and giving the operation parameters in a table I; then, solving the model by using a competitive learning constraint multi-target particle swarm algorithm to obtain a pareto frontier solution set; and calculating the satisfaction degree of each candidate solution on the leading edge on the basis of the calculation, and selecting the scheduling scheme with the maximum satisfaction degree as the scheme for the operation of the final system.
TABLE 14 genset characteristics for zone 16 unit
| Unit | P min | P max | a i | b i | c i | α i | β i | γ i | η i | δ i |
| G 1，1 | 50 | 150 | 0.01 | 4 | 0 | 80 | -3.08 | 0.085 | 1.31 | 0.0569 |
| G 1，2 | 25 | 100 | 0.03 | 2 | 0 | 100 | -1.98 | 0.095 | 1.42 | 0.0677 |
| G 1，3 | 25 | 100 | 0.05 | 3 | 0 | 60 | -2.22 | 0.048 | 1.28 | 0.0561 |
| G 1，4 | 25 | 100 | 0.04 | 1 | 0 | 50 | -1.89 | 0.082 | 0.99 | 0.0406 |
| G 2，1 | 50 | 150 | 0.05 | 4 | 0 | 121 | -2.67 | 0.06 | 1.23 | 0.0552 |
| G 2，2 | 25 | 100 | 0.04 | 2 | 0 | 97 | -2.13 | 0.072 | 1.38 | 0.0467 |
| G 2，3 | 25 | 100 | 0.08 | 3 | 0 | 65 | -2.29 | 0.043 | 1.24 | 0.0489 |
| G 2，4 | 25 | 100 | 0.06 | 1 | 0 | 45 | -1.72 | 0.065 | 1.12 | 0.0456 |
| G 3，1 | 50 | 150 | 0.10 | 4 | 0 | 75 | -2.58 | 0.046 | 1.25 | 0.0502 |
| G 3，2 | 25 | 100 | 0.12 | 2 | 0 | 98 | -2.25 | 0.069 | 1.52 | 0.0622 |
| G 3，3 | 25 | 100 | 0.10 | 3 | 0 | 70 | -2.59 | 0.028 | 1.38 | 0.0511 |
| G 3，4 | 25 | 100 | 0.13 | 1 | 0 | 80 | -1.63 | 0.059 | 0.87 | 0.0423 |
| G 4，1 | 50 | 150 | 0.01 | 4 | 0 | 63 | -1.98 | 0.066 | 1.39 | 0.0431 |
| G 4，2 | 25 | 100 | 0.03 | 2 | 0 | 70 | -2.35 | 0.088 | 1.46 | 0.0631 |
| G 4，3 | 25 | 100 | 0.05 | 3 | 0 | 100 | -2.78 | 0.055 | 1.51 | 0.0588 |
| G 4，4 | 25 | 100 | 0.04 | 1 | 0 | 40 | -2.43 | 0.081 | 1.27 | 0.0378 |
The flow chart of the invention is shown in fig. 2, and the specific implementation steps are as follows:
step 1: establishing a multi-region environmental economic dispatching model of the power dispatching system by taking the optimal fuel cost and the optimal pollution emission as objective functions;
the specific form of the objective function with minimum fuel cost is as follows:
wherein FC ij (P ij ) Is the power generation cost of the jth genset in region i, a ij ，b ij And c ij Is the fuel cost coefficient of the jth genset in region i, e j And f j Is the valve effect coefficient for the jth genset in region i,
is the minimum power generation limit (MW) of the corresponding unit.
The specific form of the objective function with the minimum pollutant emission is as follows:
wherein E ij (P ij ) Is the pollution emission of the jth genset in zone i, α ij ，β ij ，γ ij ，η ij And delta ij Respectively the pollution emission coefficients of the jth generator set in the ith area;
step 2: the constraints of the system are determined. Inequality constraints in the system comprise power generation capacity constraints and transmission capacity constraints among regions, and equality constraints are actual power balance constraints; the unit generating capacity constraint is described by:
wherein
And
respectively representing the maximum output power and the minimum output power of a jth unit in an ith area; the transmission of electric energy between the areas is realized through the connecting lines, and the transmission power between the areas cannot exceed the transmission capability of the connecting lines. The mathematical expression is as follows:
wherein T is ik Is the transmission power from zone i to zone k,
and
respectively the minimum and maximum capacity of the tie for transmitting power from zone i to zone k. The generated power of the genset needs to meet the total load demand during system operation, and the power balance constraint for region i can be expressed as:
wherein
For the total power generation of region i, PD i Load demand for zone i;
and step 3: optimizing and solving the mathematical model established in the step 1 and the step 2 by adopting a competitive learning constraint multi-target particle swarm algorithm to obtain a pareto solution set
N is the number of solution centralized scheduling schemes, and solution centralized X i Representing the ith scheduling scheme;
step 3.1: initializing parameters: the population size ps is 100, the maximum calculation time maxFES is 100000, the current calculation time FES is 0, and the iteration count initial value t is 1; initializing population, and effectively solving position information X of a multi-region environment economic dispatching system consisting of M regions i,t Can be encoded as:
step 3.2: and (4) the particles in the population may not meet the constraint conditions of the system, and constraint repair is carried out on the particles which violate the constraint. For the power generation capacity constraint, the repairing method is as follows:
wherein P is ij The actual output power of the jth generator set in the ith zone,
and
respectively the minimum and maximum output power of the corresponding unit. For the transmission capacity constraint, the repair method is as follows:
wherein T is ik For the transmission power from the i-th zone to the k-th zone,
and
respectively the minimum and maximum transmission capacity between corresponding areas. And for the actual power balance constraint of the region, repairing the region by using a power balance repairing operator, wherein the power repairing of the ith region is as follows:
(1) calculating violation dif of power balance constraint of ith area i . When the constraint violation degree is greater than zero, the total power of the current area is smaller than the actual required power, and the power output of the unit needs to be increased; when the constraint violation degree is less than zero, the total power of the current area is larger than the actual required power, and the power output of the unit needs to be reduced. And counting the numbers of all generator sets in the current area into a set I. dif i The calculation method is as follows:
(2) when power balance constraint violation dif i When the power output is larger than 0, randomly selecting a generating set j in the area I, namely randomly selecting the jth generating set from the set I, and increasing the power output of the jth generating set to be the power output
(3) When power balance constraint violation dif i When the power output is less than 0, randomly selecting a generator set j in the area I, namely randomly selecting the jth generator set from the set I, and reducing the power output of the jth generator set to be the power output
(4) Recalculating the violation dif of the power balance constraint for the ith region i When dif i Is zero or dif i If the symbol of the set I is changed, stopping repairing, otherwise deleting the selected set with the number of j in the set I, and repeating the steps (2) and (3);
step 3.3: calculating for each particle X i,t Fuel cost FC i,t And pollutant emissions E i,t And let FES be FES + ps;
step 3.4: and performing rapid non-dominated sorting and crowded distance sorting on the particles according to the target values to determine the elite population L. The method comprises the following steps:
(1) fast non-dominated sorting gives first two parameters n to each particle i i And S i ，n i To determine the number of particles in the population, S i A set of solutions governed by particle i. Finding n in the population i The 0 particles, i.e. the particles in the population that are not dominated by any other particles, are stored in a set F 1 Will F 1 As a first level non-dominated set, the particles in the set are assigned an identical sequence i rank . For the current set F 1 For each particle j in (1), find the set S dominated by the particle j j And will be aggregated S j N of each particle k in k Subtracting 1, i.e. the number of solutions governing the particle k minus 1, which have been stored in the set F 1 It is used. If n is k -1-0, the particles k are stored in another set F 2 . Then to the set F 2 The above steps are repeated until all particles are classified.
(2) The crowding distance is the perimeter i of a cuboid formed by the particle and the two closest particles d 。i d The larger the particle size, the more sparse the particle size, and the better the diversity. The particles at both ends of the pareto front can be seen as crowding at infinite distance. After fast non-dominant ordering and crowded distance computation, all particles in the population have a non-dominant sequence i rank And congestion distance i d These two attributes. Two different particles i and j are compared according to the non-dominant sequence and the crowding distance: if the level of particle i dominates the level of particle j, i.e. i rank ＜j rank Then particle i can be considered to be better than particle j; if particle i and particle j are at the same level, i rank ＝j rank And the crowding distance of particle i is greater than that of particle j, i.e. i d ＞j d Then particle i can be considered to be better than particle j. According to the results of the rapid non-dominated sorting and the crowded distance sorting, taking 20% of particles in the population which are sorted at the top to form an elite population L;
step 3.5: using a competitive learning strategy for each particle X in the population i,t And (6) updating. The competitive learning strategy is described as:
after creating elite population L, two particles in population L are randomly chosen to compete, and the winner will lead to the update of the current particle. For the particle X to be updated in the population i,t Two particles a and b were randomly selected from the elite population. Calculate a, b and X separately i,t The small elite particles are winners and assigned as X W Particles X i,t Will learn to the winner. An example of contention is shown in figure 3. Wherein a and b are two competitors randomly selected from the Elite population, X i,t Is the particle to be renewed, theta 1 Is a and X i,t Angle between them, theta 2 Is b and X i,t The included angle therebetween. Due to theta 1 ＜θ 2 If a is a winner, it is marked as X W Will be used to guide X i,t Updating of (1);
step 3.6: by using X W Guiding the current particle X i,t The update equation is as follows:
V i,t+1 ＝R 1 ·V i,t +R 2 (X W -X i,t )
X i,t+1 ＝X i,t +V i,t+1
wherein X W For winner particles, R 1 And R 2 Is [0,1 ]]In the step 3.4, the updated particle X is selected from the randomly distributed random number set i,t+1 Repairing constraint violation;
step 3.7: the objective function values for all repaired particles in the population are then calculated and FES + ps, t +1 are given.
Step 3.8: judging whether a termination condition is met, namely whether the maximum evaluation frequency is reached, if not, repeating the step 3.4-the step 3.8, and if so, turning to the step 3.9;
step 3.9: outputting pareto frontier
And 4, step 4: and determining an optimal compromise solution according to the distance evaluation index on the basis of the pareto frontier obtained in the step 3.
Step 4.1: as shown in FIG. 4, points Q are found for the optimal solution for fuel spending in the pareto solution set, respectively 1 And position Q of pollution emission optimal solution 2 Separately, make a point Q 1 And Q 2 And (4) making the intersection point P be an ideal solution to the vertical line on the target axis, and representing that the economic target and the environmental target simultaneously reach the optimum.
And 4.2: calculating pareto frontier
And taking the point with the minimum distance as the optimal compromise solution, namely the comprehensive optimal scheduling scheme.
And 5: and outputting the pareto frontier and the optimal compromise solution.
The output pareto front is shown in fig. 5, the fuel cost of the integrated optimal scheduling scheme is 7764.5291$/h, the pollutant emission is 8025.3658t/h, and the output power of each unit of the integrated optimal scheduling scheme and the transmission power between the regions are listed in table 2.
In order to embody that the method provided by the invention can provide a better scheduling scheme, the optimal scheduling scheme provided by the method of the invention is compared with the optimal scheduling schemes solved by other advanced optimization algorithms. The results are listed in table 3, and it can be seen from table 3 that the fuel cost and the pollutant emission of the scheduling scheme determined by the method provided by the invention are both optimal, which indicates that the method can effectively solve the multi-region environmental economic scheduling problem.
Table 2 optimal scheduling scheme for the method of the present invention
TABLE 3 Integrated optimal scheduling results for the comparison Algorithm
| Method | Fuel cost ($/h) | Pollution emission (t/h) |
| MODE-RMO | 7789.8710 | 8088.8917 |
| MOPSO | 7801.0070 | 8070.4858 |
| BB-MOPSO | 7791.9104 | 8210.5820 |
| TV-MOPSO | 7803.8273 | 8207.4660 |
| Method for producing a composite material | 7764.5291 | 8025.3658 |
Claims (6)
1. A multi-region environment economic dispatching method based on competitive learning constraint multi-target particle swarm optimization is characterized by comprising the following steps:
step 1: establishing a multi-region environmental economic dispatching model of the power dispatching system by taking fuel cost and pollution emission as target functions;
step 2: acquiring parameters of a generator set and constraint conditions of a system, and setting the parameters of the generator set;
and step 3: optimizing and solving the mathematical model established in the step 1 and the step 2 by adopting a competitive learning constraint multi-target particle swarm algorithm and combining a constraint processing mechanism to obtain a pareto solution set
N is the number of solution concentration scheduling schemes, and solution concentration X i Representing the ith scheduling scheme;
and 4, step 4: and outputting the pareto frontier obtained by optimization and the optimal compromise solution in the system, and determining the actual power output of a generator set in the system according to the scheduling scheme of the optimal compromise solution.
2. The multi-region environmental economic dispatching method based on competitive learning constraint multi-target particle swarm algorithm according to claim 1, characterized in that: the step 3 comprises the following specific steps:
step 3.1: initializing parameters: the population size ps, the maximum calculation times maxFES and the current calculation times FES are 0, and the iteration counting initial value t is 1; initializing population, and effectively solving the position information X of a multi-region environment economic dispatching system consisting of M regions i,t Can be encoded as:
wherein X i,t Indicating the position information of the ith particle in the population of the t generation,
is the Nth in the kth region k Output power of individual generator sets, T ik Is the transmission power between zone i and zone k;
step 3.2: the particles in the population may not meet the constraint conditions of the system, and the particles violating the constraint are constrained and repaired, and for the constraint of the power generation capacity, the repairing method comprises the following steps:
wherein P is ij The actual output power of the jth generator set in the ith zone,
and
the minimum output power and the maximum output power of the corresponding unit are respectively, and for the transmission capacity constraint, the repairing method comprises the following steps:
wherein T is ik For the transmission power from the i-th zone to the k-th zone,
and
respectively corresponding to the minimum and maximum transmission capacities between the areas, and repairing the actual power balance constraint of the areas by using a power balance repairing operator;
step 3.3: calculating each particle X i,t Fuel cost FC i,t And pollutant emissions E i,t And let FES be FES + ps, FES is the current number of calculations, ps is the population size;
step 3.4: performing rapid non-dominated sorting and crowded distance sorting on the particles according to the target values, determining an elite population L, and solving X in multi-objective optimization 1 And X 2 The following relationship is satisfied:
i.e. for any object f i Can all make X 1 Target value f of i (X 1 ) Not more than X 2 Target value f of i (X 2 ) And at least one object f is present j So that X 1 Target value f of j (X 1 ) Less than X 2 Target value f of j (X 2 ) Is called X 1 Dominating X 2 The fast non-dominated sorting is to find out all non-dominated solution sets in the population, the crowding distance is to calculate the sparseness degree of each particle in the population, the particles in the non-dominated solution sets are sorted from large to small according to the crowding distance, the particles with large crowding distance are sorted in the front, and the top 20% of the particles are taken to form an elite population L;
step 3.5: using a competitive learning strategy for each particle X in the population i,t Updating is carried out;
step 3.6: by using X W Guiding the current particle X i,t The update equation is as follows:
V i,t+1 ＝R 1 ·V i,t +R 2 (X W -X i,t )
X i,t+1 ＝X i,t +V i,t+1
wherein X W For winner particle, V i,t+1 For updating the velocity information of the particles, X i,t+1 For updated position information of the particles, R 1 And R 2 Is [0,1 ]]In the random number set, the updated particle X is processed by step 3.4 i,t+1 Carrying out constraint violation repair;
step 3.7: then calculating the objective function values of all repaired particles in the population, and making FES (field emission spectroscopy) equal to FES + ps and t equal to t + 1;
step 3.8: judging whether a termination condition is met, namely whether the maximum evaluation frequency is reached, if not, repeating the step 3.4-the step 3.8, and if so, turning to the step 3.9;
step 3.9: outputting pareto frontier
3. The multi-region environmental economic dispatching method based on competitive learning constraint multi-target particle swarm algorithm according to claim 2, characterized in that: in step 3.2, the power restoration of the ith area is as follows:
(1) calculating violation dif of power balance constraint of ith area i When the constraint violation degree is greater than zero, the total power of the current area is smaller than the actual required power, and the power output of the unit needs to be increased; when the constraint violation degree is less than zero, the total power of the current region is larger than the actual required power, the power output of the set needs to be reduced, the numbers of all the generator sets in the current region are counted into a set I, and dif i The calculation method is as follows:
wherein
For the total power generation of region i, PD i For the load demand of zone i, PL i Network loss, T, for region i ik Is the transmission power between zone i and zone k;
(2) when power balance constraint violation dif i When the power output is larger than 0, randomly selecting a generating set j in the area I, namely randomly selecting the jth generating set from the set I, and increasing the power output of the jth generating set to be the power output
(3) When power balance constraint violation dif i When the power output is less than 0, randomly selecting a generator set j in the area I, namely randomly selecting the jth generator set from the set I, and reducing the power output of the jth generator set to be the power output
(4) Recalculating the violation dif of the power balance constraint for the ith region i When dif i Is zero or dif i If the sign of the set I is changed, the repair is stopped, otherwise, the selected unit with the number of j in the set I is deleted, and the steps (2) and (3) are repeated.
4. The multi-region environmental economic dispatching method based on competitive learning constraint multi-target particle swarm algorithm according to claim 2, characterized in that: in step 3.5, the competition learning strategy is:
after the elite population L is created, two particles in the population L are randomly selected to compete, a winner guides the updating of the current particle, and the particle X to be updated in the population is selected i,t Randomly selecting two particles a and b from elite population, and respectively calculating a, b and X i,t The small-angle elite particle is the winner and is assigned as X W Particles X i,t Will learn to the winner.
5. The multi-region environmental economic dispatching method based on competitive learning constraint multi-target particle swarm algorithm according to claim 2, characterized in that: the step 4 comprises the following specific steps:
step 4.1: finding points Q of fuel cost optimal solutions in pareto solution sets, respectively 1 And position Q of pollution emission optimal solution 2 Respectively make a point Q 1 And Q 2 The intersection point P is an ideal solution to the vertical line on the target axis, and the economic target and the environmental target are expressed to be optimal simultaneously;
step 4.2: calculating pareto frontier
And taking the point with the minimum distance as the optimal compromise solution, namely the comprehensive optimal scheduling scheme.
6. The multi-region environmental economic dispatching method based on competitive learning constraint multi-target particle swarm algorithm according to claim 2, characterized in that: step 3.1: initializing parameters: the population size ps is 100, and the maximum number of calculations maxFES is 100000.
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| CN117474297B (en) * | 2023-12-27 | 2024-04-16 | 南京信息工程大学 | Optimization method for ship berth and quay crane distribution for automatic wharf |
| CN117933105A (en) * | 2024-03-25 | 2024-04-26 | 南京信息工程大学 | Optimization method and system for heliostat field layout |
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