CN114066282A - Power economic emission scheduling method based on hybrid nuclear search and slime bacteria optimization - Google Patents

Power economic emission scheduling method based on hybrid nuclear search and slime bacteria optimization Download PDF

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CN114066282A
CN114066282A CN202111389397.4A CN202111389397A CN114066282A CN 114066282 A CN114066282 A CN 114066282A CN 202111389397 A CN202111389397 A CN 202111389397A CN 114066282 A CN114066282 A CN 114066282A
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董如意
马龙
邢雪
石聪
刘亚男
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Abstract

The invention relates to a power economic emission scheduling method based on mixed nuclear search and slime mold algorithm optimization, which comprises the following steps: s1, converting fuel cost and pollution emission into a single objective function by adopting a weight summation method, and establishing an electric power economic emission scheduling model; s2, randomly initializing an active power output scheduling matrix of the generator set; s3, solving the active power output of the last group of generators by a power flow equation according to a Newton iteration method; s4, calculating a penalty function value of the final group of generators with the active power output exceeding the constraint; s5, calculating the sum of fuel cost and pollution emission of the generator set in the scheduling scheme, and normalizing the sum and a penalty function value together; s6, performing a mixed kernel search and slime bacteria optimization algorithm to update the active output of the generator set; s7, outputting the output of the optimal generator set if the maximum iteration times is reached; otherwise go to S3.

Description

Power economic emission scheduling method based on hybrid nuclear search and slime bacteria optimization
Technical Field
The invention relates to the field of economic emission scheduling of a power system, in particular to a hybrid nuclear search and slime mold algorithm optimized power economic emission scheduling method.
Background
Under the background of the vigorous development of global low-carbon economy, China is in line with the trend of the times, and the ambitious goal of realizing 'carbon neutralization' in 2060 years is provided. As a main industry of carbon emission, the annual carbon dioxide emission of the power industry accounts for 40 percent of the total national emission, and plays a role in energy conservation and emission reduction. The problem of economic emission scheduling becomes one of the most realistic tasks in the management of power systems. The economic emission scheduling problem needs to reasonably arrange and schedule the active power output of each power plant, so that the fuel cost and the pollution emission are minimized on the basis of meeting the user load requirements and the power plant output limit. The method is essentially a multi-objective optimization problem with two contradictory targets, and has extremely important significance for stable and economic operation of the power system and reduction of environmental pollution.
Many studies propose the use of group intelligence optimization methods to solve the economic emissions scheduling problem. However, for the multi-objective economic emission scheduling problem, firstly, the problem needs to be converted into a single-objective optimization problem through a weight summation method, and then the problem is solved by using a group intelligent optimization algorithm. Common group intelligence algorithms such as genetic algorithm, particle swarm optimization algorithm, pollen pollination algorithm, differential evolution algorithm and the like. However, these algorithms need to carefully adjust a large number of hyper-parameters, and are prone to fall into local optimality, and the scheduling schemes obtained by searching are not necessarily optimal.
Therefore, developing a power economic emission scheduling method which does not need to set any hyper-parameter and has more comprehensive global and local search capability is a difficult point of power scheduling research.
Disclosure of Invention
The invention aims to provide an electric power economic emission scheduling method which can simultaneously optimize fuel cost and pollution emission and has better overall convergence and optimization capability.
In order to achieve the above object, an embodiment of the present invention provides a power economic emission scheduling method based on a hybrid nuclear search and slime mold algorithm, including the following steps:
s1, converting two objective functions of fuel cost and pollution emission into a single objective optimization function by adopting a weight summation method, and establishing an economic emission scheduling model of the power system by combining power flow equation constraint of the power system and active power output constraint of a generator set;
s2, setting N groups of generator set active power output to be scheduled, randomly initializing M scheduling schemes, and calculating N-1 groups of active power output P according to a formula (1)iI =1,2, … N-1, together forming a generator set active power output scheme matrix a;
Figure 556043DEST_PATH_IMAGE001
,
Figure 685673DEST_PATH_IMAGE002
（1）
wherein P isiminAnd PimaxRespectively the upper and lower limits of the active power output of the ith group of generator set, and rand is [0, 1%]The random number of (2);
s3, solving the active power output P of the Nth group A of generators by the constraint of the power flow equation according to a Newton iteration methodN；
S4, calculating the active power output P of the Nth group of generatorsNPenalty function values outside the generator set constraint range;
s5, calculating the sum of fuel cost and pollution emission of N groups of generator sets in the scheduling scheme A, and forming a fitness function value y together with the penalty function valueiThen normalized to [0,1]]；
S6, performing mixed kernel search and slime bacteria optimization algorithm to update active output P of the generator seti；
S7, if the maximum iteration times are reached, outputting the output P of the optimal generator setgbest(ii) a Otherwise go to S3.
The method according to claim 1, wherein the step S6 specifically includes:
step S6.1: will adapt yiSequencing from small to large to form a new fitness sequence y, wherein the minimum fitness value is ybest, and the maximum fitness value is yworst;
step S6.2: calculating location update speed
Figure 968887DEST_PATH_IMAGE003
As shown in formula (2);
Figure 791349DEST_PATH_IMAGE004
(2)
wherein t is the current iteration frequency, and M is the total iteration frequency;
step S6.3: calculating weights for slime optimization algorithms
Figure 792803DEST_PATH_IMAGE005
As shown in formula (3);
Figure 460545DEST_PATH_IMAGE006
(3)
wherein rand represents random number of [0,1], and mean (y) represents median of fitness y;
step S6.4: calculating the active output of N-1 groups
Figure 598265DEST_PATH_IMAGE007
As shown in equation (4);
Figure 591629DEST_PATH_IMAGE008
(4)
wherein the content of the first and second substances,
Figure 814800DEST_PATH_IMAGE009
in order to optimize the active power output of the generator set,
Figure 551812DEST_PATH_IMAGE010
and
Figure 809618DEST_PATH_IMAGE011
two randomly selected individuals;
step S6.5: sequentially converting active power output P 'of generator set'iReplacing the corresponding active power output P of the generator set of each scheduling scheme in the step AiForming new M × N-1 scheduling scheme matrixes A' as shown in a formula (5);
Figure 708304DEST_PATH_IMAGE012
(5)
step S6.6: according to a Newton iteration method, solving active power output P ' of the Nth group of generators of A ' by current equation constraint 'N；
Step S6.7: calculating active power output P 'of the N group of generators'NPenalty function values outside the generator set constraint range;
step S6.8: calculating the sum of fuel cost and pollution emission of N groups of generator sets in the scheduling scheme A ' and forming a fitness function value y ' together with the penalty function value 'i；
Step S6.9: calculating a kernel vector a, wherein a specific formula is shown in (6);
Figure 418771DEST_PATH_IMAGE013
（6）
step S6.10: computing a near-optimal scheduling plan PbestThe concrete formula is shown as (7);
Figure 693894DEST_PATH_IMAGE014
（7）
step S6.11: calculating new active power output P of generator setnewThe concrete formula is shown as (8);
Figure 806207DEST_PATH_IMAGE015
（8）
wherein rand is a random number of [0,1 ].
Compared with the prior art, the invention has the beneficial effects that:
according to the invention, the original nuclear search optimization algorithm is improved by using the mixed nuclear search and slime bacteria optimization algorithm, so that the situation that the original nuclear search optimization algorithm is trapped in a local optimal solution is avoided, and a more economic and less-pollution power economic dispatching scheme can be solved.
Description of the drawings:
FIG. 1 is a schematic flow diagram of a method framework;
the specific implementation mode is as follows:
in order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
As shown in fig. 1, in an embodiment of the present invention, a power economic emission scheduling method based on a hybrid nuclear search and slime optimization algorithm is provided, which includes the steps of:
s1, converting two objective functions of fuel cost and pollution emission into a single objective optimization function by adopting a weight summation method, and establishing an economic emission scheduling model of the power system by combining power flow equation constraint and generator set active power output constraint, wherein the specific form is as follows:
the specific form of fuel cost is:
Figure 141373DEST_PATH_IMAGE016
wherein N is the number of generator sets in the system; piThe active output of the ith group of generating sets; a isi，biAnd ciIs the fuel cost coefficient of the ith group of generator setsiAnd fiIs the valve point effect coefficient.
The specific form of pollutant emission is as follows:
Figure 339136DEST_PATH_IMAGE017
wherein
Figure 152372DEST_PATH_IMAGE018
，
Figure 384770DEST_PATH_IMAGE019
，
Figure 625258DEST_PATH_IMAGE020
，
Figure 575897DEST_PATH_IMAGE021
And
Figure 192823DEST_PATH_IMAGE022
is a pollution discharge coefficient.
The fuel cost and the pollution emission are converted into a single objective function of
Figure 11219DEST_PATH_IMAGE023
Where w is the additive weight factor,gis a scale factor.
The power system flow equation is constrained to
Figure 422608DEST_PATH_IMAGE024
，
Figure 594964DEST_PATH_IMAGE025
Wherein, PDFor the user load demand, PLFor transmission network loss, BijIs the loss factor.
The active output constraint of the generator set is as follows:
Figure 15581DEST_PATH_IMAGE026
wherein
Figure 956992DEST_PATH_IMAGE027
And
Figure 539283DEST_PATH_IMAGE028
the upper limit and the lower limit of the active output of the ith generating set are shown.
S2, setting N groups of generator set active power output to be scheduled, randomly initializing M scheduling schemes, and initializing and calculating N-1 groups of active power output P according to a formula (1)iI =1,2, … N-1, together forming a generator set active power output scheme matrix a;
Figure 198935DEST_PATH_IMAGE029
，
Figure 157663DEST_PATH_IMAGE002
（1）
wherein P isiminAnd PimaxRespectively the upper and lower limits of the active power output of the ith group of generator set, and rand is [0, 1%]The random number of (2);
s3, solving the active power output P of the Nth group A of generators by the constraint of the power flow equation according to a Newton iteration methodN. The iterative solution step is as follows:
s3.1 generating set active output P according to N-1iAnd calculating the initial active output of the Nth generator set:
Figure 219160DEST_PATH_IMAGE030
wherein
Figure 237932DEST_PATH_IMAGE031
The initial active output of the Nth generating set.
S3.2 according to the active power output P of the N generator setsiAnd calculating the active loss of the system:
Figure 119300DEST_PATH_IMAGE032
wherein
Figure 881720DEST_PATH_IMAGE033
S3.3 according to user load PDN-1 generator set active power output PiActive loss of the system
Figure 797723DEST_PATH_IMAGE034
Calculating the new active output of the Nth generator set
Figure 721817DEST_PATH_IMAGE036
S3.4 calculation error
Figure 356061DEST_PATH_IMAGE038
If epsilon>If the error is allowed, returning to the step S4.2; otherwise, save
Figure 656592DEST_PATH_IMAGE040
And exit.
S4, calculating the active power output P of the Nth group of generatorsNAnd the penalty function value is beyond the constraint range of the generator set. The concrete form of the penalty function is as follows:
Figure 161523DEST_PATH_IMAGE041
where λ is a penalty factor.
S5, calculating the sum of fuel cost and pollution emission of N groups of generator sets in the scheduling scheme A, and forming a fitness function value y together with the penalty function valueiThen normalized to [0,1]]；
The specific process is
Figure 522097DEST_PATH_IMAGE042
，
Figure 378057DEST_PATH_IMAGE043
S6, performing mixed kernel search and slime bacteria optimization algorithm to update active output of the generator set
Figure 482280DEST_PATH_IMAGE044
S6.1, sequencing the fitness yi from small to large to form a new fitness sequence y, wherein the minimum fitness value is ybest and the maximum fitness value is yworst;
step S6.2: calculating location update speed
Figure 107296DEST_PATH_IMAGE003
As shown in equation (2);
Figure 638771DEST_PATH_IMAGE045
(2)
wherein t is the current iteration frequency, and M is the total iteration frequency;
step S6.3: calculating weights for slime optimization algorithms
Figure 716449DEST_PATH_IMAGE005
As shown in formula (3);
Figure 358783DEST_PATH_IMAGE006
(3)
wherein
Figure 838306DEST_PATH_IMAGE046
For the best fitness value, mean (y) represents the median of fitness y;
step S6.4: calculating the active output of N-1 groups
Figure 272174DEST_PATH_IMAGE007
As shown in equation (4);
Figure 102726DEST_PATH_IMAGE047
(4)
Figure 283172DEST_PATH_IMAGE048
for the currently found location of the individual with the highest fitness value,
Figure 148360DEST_PATH_IMAGE010
and
Figure 21638DEST_PATH_IMAGE011
for two randomly selected bodies
S6.5, the N-1 groups have active power output
Figure 808328DEST_PATH_IMAGE007
To obtain a new scheduling scheme matrix
Figure 58044DEST_PATH_IMAGE049
As shown in formula (5);
Figure 512159DEST_PATH_IMAGE050
（5）
s6.6, according to a Newton iteration method, the active power output P of the Nth group of generators A' is obtained through the constraint of a power flow equationN. The iterative solution step is as follows:
s6.7 generating set active output according to N-1
Figure 556338DEST_PATH_IMAGE007
And calculating the initial active output of the Nth generator set:
Figure 830325DEST_PATH_IMAGE051
wherein
Figure 618152DEST_PATH_IMAGE031
The initial active output of the Nth generating set.
S6.8 according to the active output of N generator sets
Figure 192353DEST_PATH_IMAGE007
And calculating the active loss of the system:
Figure 141855DEST_PATH_IMAGE052
wherein
Figure 434296DEST_PATH_IMAGE033
S6.9 according to user load PDActive output of N-1 generator sets
Figure 494656DEST_PATH_IMAGE007
Active loss of the system
Figure 188942DEST_PATH_IMAGE034
Calculating the new active output of the Nth generator set
Figure 574924DEST_PATH_IMAGE053
S6.10 calculation error
Figure 823503DEST_PATH_IMAGE038
If epsilon>If the error is allowed, returning to the step S4.2; otherwise, save
Figure 953133DEST_PATH_IMAGE054
And exit.
S6.11 calculating the active power output P of the Nth group of generatorsNAnd the penalty function value is beyond the constraint range of the generator set. The concrete form of the penalty function is as follows:
Figure 236347DEST_PATH_IMAGE041
where λ is a penalty factor.
S6.12, calculating the sum of fuel cost and pollution emission of N groups of generator sets in the scheduling schemes A and A', and forming a fitness function value y together with the penalty function valueiAnd y'iThen normalized to [0,1]]；
The specific process is
Figure 527651DEST_PATH_IMAGE042
，
Figure 529105DEST_PATH_IMAGE043
Step S6.13: calculating a kernel vector a, wherein a specific formula is shown in (6);
Figure 205636DEST_PATH_IMAGE055
（6）
s6.14, calculating an approximate optimal scheduling scheme Pbest, wherein a specific formula is shown as (7);
Figure 608935DEST_PATH_IMAGE056
（7）
step S6.15: calculating the new active power output Pnew of the generator set, wherein the specific formula is shown as (8);
Figure 71140DEST_PATH_IMAGE015
（8）
s7, if the maximum iteration times are reached, outputting the output P of the optimal generator setgbest(ii) a Otherwise, turning to S3;
wherein rand is a random number of [0,1 ].
Optimal generator set output PgbestNamely the optimal power economy discharge scheduling scheme.
It should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.

Claims (2)

1. A power economic emission scheduling method based on mixed kernel search and slime mold optimization is characterized by comprising the following steps:
s1, converting two objective functions of fuel cost and pollution emission into a single objective optimization function by adopting a weight summation method, and establishing an economic emission scheduling model of the power system by combining power flow equation constraint of the power system and active power output constraint of a generator set;
s2. is provided withNActive output of group generator set needs scheduling and random initializationMA scheduling scheme calculated according to equation (1)N-1 group active power outputP i ，i=1,2,…N-1, forming a generator set active power output scheme matrixA；
Figure DEST_PATH_IMAGE001
，
Figure 20813DEST_PATH_IMAGE002
（1）
WhereinP min AndP max respectively the upper and lower limits of the active power output of the ith group of generator set, and rand is [0, 1%]The random number of (2);
s3, solving by the constraint of a power flow equation according to a Newton iteration methodATo middleNActive power output of group generatorP N ；
S4, calculatingNActive power output of group generatorP N Penalty function values outside the generator set constraint range;
s5, calculating a scheduling schemeAInNThe sum of the fuel cost and the pollution emission of the group generator set and the penalty function value form a fitness function value togethery i Then normalized to [0,1]]；
S6, performing mixed kernel search and slime bacteria optimization method to update active output of the generator setP i ；
S7, if the maximum iteration times are reached, outputting the output of the optimal generator setP gbest (ii) a Otherwise go to S3.
2. The method according to claim 1, wherein the step S6 specifically includes:
step S6.1: will adapt toy i Sequencing from small to large to form a new fitness sequenceyWith a minimum fitness value ofybestMaximum fitness value ofyworst；
Step S6.2: calculating location update speed
Figure DEST_PATH_IMAGE003
As shown in formula (2);
Figure 226666DEST_PATH_IMAGE004
(2)
wherein the content of the first and second substances,tfor the current number of iterations,Mthe total number of iterations;
step S6.3: calculating weights for slime optimization algorithms
Figure DEST_PATH_IMAGE005
As shown in formula (3);
Figure 218893DEST_PATH_IMAGE006
(3)
wherein rand represents random number of [0,1], and mean (y) represents median of fitness y;
step S6.4: calculating the active output of N-1 groups
Figure DEST_PATH_IMAGE007
As shown in equation (4);
Figure 849070DEST_PATH_IMAGE008
(4)
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE009
in order to optimize the active power output of the generator set,
Figure 293958DEST_PATH_IMAGE010
and
Figure 569081DEST_PATH_IMAGE011
two randomly selected individuals;
step S6.5: sequentially transmitting the active power output of the generator setP’ i Replacement ofAEach tone inActive output of generator set corresponding to degree schemeP i Form a newM*（N-1) scheduling scheme matricesA’As shown in equation (5);
Figure 681394DEST_PATH_IMAGE012
(5)
step S6.6: according to Newton iteration method, the power flow equality constraint is used for solvingA’First, theNActive power output of group generatorP’ N ；
Step S6.7: calculate the firstNActive power output of group generatorP’ N Penalty function values outside the generator set constraint range;
step S6.8: computing scheduling schemeA’InNThe sum of the fuel cost and the pollution emission of the group generator set and the penalty function value form a fitness function value togethery’ i ；
Step S6.9: computing kernel vectorsaThe concrete formula is shown as (6);
Figure 16560DEST_PATH_IMAGE013
（6）
step S6.10: computing a near-optimal scheduling schemeP best The concrete formula is shown as (7);
Figure 214323DEST_PATH_IMAGE014
（7）
step S6.11: calculating new active power output P of generator setnewThe concrete formula is shown as (8);
Figure 293138DEST_PATH_IMAGE015
（8）
wherein rand is a random number of [0,1 ].
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