CN111861137A - Parallel multi-target scheduling method for cascade reservoir groups - Google Patents

Parallel multi-target scheduling method for cascade reservoir groups Download PDF

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CN111861137A
CN111861137A CN202010595689.2A CN202010595689A CN111861137A CN 111861137 A CN111861137 A CN 111861137A CN 202010595689 A CN202010595689 A CN 202010595689A CN 111861137 A CN111861137 A CN 111861137A
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卢鹏
韩兵
周鹏程
彭程
盛玉明
张国来
杨百银
杨子俊
马良
彭才德
杨开斌
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PowerChina Resources Ltd
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Abstract

A parallel multi-target scheduling method for cascade reservoir groups belongs to a hydropower station management technology, and particularly relates to a hydropower energy optimization operation management method for cascade reservoir groups. And solving a multi-target dispatching model of the cascade reservoir group by adopting a multi-target bee colony algorithm based on Fork/Join parallel computation, and processing coupling constraints among various periods in the reservoir group dispatching process by using a heuristic constraint repairing strategy. The method can quickly generate a group of widely and uniformly distributed multi-target non-inferior scheduling scheme sets, and provides powerful theoretical and technical support for multi-target scheduling decisions of the cascade reservoir group. The method combines efficient solving modes such as multi-target random parallel optimization, multiple complex constraint heuristic correction and the like, a non-inferior scheduling scheme set which is widely and uniformly distributed in a multi-dimensional target domain space can be obtained through one-time solving, and powerful support is provided for joint scheduling operation of the cascade reservoir group in the drainage basin.

Description

Parallel multi-target scheduling method for cascade reservoir groups
Technical Field
The invention belongs to a hydropower station management technology, and particularly relates to a hydropower energy optimization operation management method for a cascade reservoir group.
Background
The cascade reservoir group combined optimization scheduling needs to comprehensively consider the mutually competing and impartial scheduling targets of flood control, power generation, water supply, shipping, ecological water demand, power grid safety and the like, and is a multi-factor, multi-level and multi-stage complex multi-target optimization problem. At present, a classical mathematical modeling method based on traditional operational research generally converts a multi-target problem into a single-target problem for solving by introducing a target weight coefficient or a target constraint form, and the method is usually limited to obtaining a single or a small number of non-inferior scheduling solution sets, so that the competition and constraint relation among scheduling targets is difficult to be fully reflected, and particularly when the scheduling problem with non-convex and non-continuous multi-target leading edge characteristics is processed, the non-inferior scheduling scheme set obtained by model calculation cannot well reflect the actual non-inferior leading edge characteristics. And influenced by many factors such as hydrological weather, runoff process, power station scheduling mode, unit dynamic characteristics and the like, the combined optimization scheduling problem of the stepped reservoir group presents typical large-scale, strong coupling, multi-constraint, dynamic and discrete complex nonlinear characteristics, the classical mathematical modeling method based on the traditional operational research is very difficult to solve the problem, and is influenced by the complexity of solving the problem, and the algorithm execution efficiency is not high.
Disclosure of Invention
Aiming at the problem that a classical mathematical modeling method based on traditional operational research is difficult to meet the multi-target scheduling problem solving requirement of a watershed cascade reservoir group under a complex constraint condition, the cascade reservoir group parallel multi-target scheduling solving method is provided, and by combining efficient solving modes such as multi-target random parallel optimization, multiple complex constraint heuristic correction and the like, a non-inferior scheduling scheme set which is widely and uniformly distributed in a multi-dimensional target domain space can be obtained through one-time solving, so that powerful support is provided for the combined scheduling operation of the watershed cascade reservoir group.
The parallel multi-target scheduling method for the cascade reservoir group comprises the following specific steps:
s1, setting hydropower station group characteristic parameters and initializing algorithm control parameters, including Eliteset capacity NQ, group size NP and algorithm maximum evolution algebra GmaxAnd number of scout bee starts Limitabandon(ii) a Setting the current evolution generation g of the algorithm to be 1;
s2, constructing and initializing NP population individuals, wherein the expression is as follows:
Figure RE-GDA0002620762550000011
in the formula, xrIs the r individual;
Figure BDA00025578785700000211
encoding the individual; n is the number of step reservoirs; t is the number of time segments;
s3, reservoir dispatching constraint processing, namely judging whether the individual meets the constraint by adopting the following formulas (2) to (7), and correcting the hydropower station group time-segment water level in the individual one by using the formulas (8) and (9) for the population individual which does not meet the constraint;
Step hydraulic connection formula (2):
Figure BDA00025578785700000212
in the formula Ii,tThe flow rate of the reservoir is i; tau isi-1Is the water flow time lag between the reservoir i-1 and the reservoir i;
Figure BDA00025578785700000213
reservoir at t-tau for i-1i-1Water abandon flow in time intervals; ri,tInflow between the reservoir i-1 and the reservoir i;
reservoir water balance constraint (3): vi,t＝Vi,t-1+(Ii,t-Qi,t-Si,t)·Δt；
In the formula, Vi,tThe storage capacity at the end of time t of the reservoir i;
water level/flow/output constraint formula (4):
Figure BDA0002557878570000021
in the formula, Pi,tOutputting force for the reservoir at the time t;
Figure BDA0002557878570000022
and i,tZ、
Figure BDA0002557878570000023
and i,tQ、
Figure BDA0002557878570000024
and i,tPthe water level, the ex-warehouse and the output boundary of the reservoir at the time interval t are respectively shown;
fourthly, the water level/flow/output amplitude constraint formula (5):
Figure BDA0002557878570000025
in the formula,. DELTA.Zi、ΔQi、ΔPiI reservoir water level, flow and output amplitude limit respectively;
reservoir operation water head constraint formula (6):
Figure BDA0002557878570000026
in the formula, Hi,tFor the water head of the reservoir at the time t,
Figure BDA0002557878570000027
Hi,trespectively the upper limit and the lower limit of a stable operation water head of the reservoir;
sixthly, controlling the water level at the beginning and end of the reservoir stage according to a restraint formula (7):
Figure BDA0002557878570000028
in the formula, Zi,0、Zi,T、
Figure BDA0002557878570000029
And
Figure BDA00025578785700000210
dispatching initial stage water level, final stage water level and control values of the water level for the reservoir;
seventhly, a water level constraint corridor generation method is represented by the formula (8):
Figure BDA0002557878570000031
the method for generating the water level constraint corridor is characterized by the following formula (9):
Figure BDA0002557878570000032
in the formula (I), the compound is shown in the specification,
Figure BDA0002557878570000033
and
Figure BDA0002557878570000034
calculating functions of the end storage capacity and the initial storage capacity in the t time period respectively;
Figure BDA0002557878570000035
and
Figure BDA0002557878570000036
the characteristic values of the lower leakage flow and the output are set as the upper and lower boundary values of the flow and the output;
s4, calculating target fitness values of different population individuals, carrying out target fitness value normalization processing, and carrying out non-dominated sorting on the population individuals based on the individual target fitness values; adding all non-dominant individuals at a first level in the population into the Eliteset;
The individual fitness takes the maximum total generated energy of the cascade reservoir group and the minimum total ecological water shortage of each cascade downstream river as a regulation target, and the objective function is respectively described as an expression (10) and an expression (11):
formula (10):
Figure BDA0002557878570000037
Figure BDA0002557878570000038
formula (11):
Figure BDA0002557878570000039
in the formula, E is the total generating capacity of the cascade reservoir group; pi,t、Qi,t、Hi,tGenerating output, discharging flow and average water head for the i reservoir at the t time period respectively; n is the number of step reservoirs; t and delta T are the number of time segments and the length of time segments respectively; w is the step ecological water shortage;
Figure BDA00025578785700000310
is suitable for the discharge flow of the reservoir at t time interval and the downstream river channel thereofDifference of ecological demand flow is suitable;
Figure BDA00025578785700000311
the suitable ecological flow of the downstream river of the power station i in the period t;
the target functions of the formula (10) and the formula (11) have different dimensions, and are normalized to form a dimensionless function value; the scheduling objective normalization is calculated as equation (12):
formula (12):
Figure BDA0002557878570000041
Figure BDA0002557878570000042
in the formula, x r Is the r individual in the evolved population; er, WrThe annual energy production and the water shortage of the No. r individual are respectively determined; emaxAnd Emin、
Figure BDA0002557878570000043
And
Figure BDA0002557878570000044
respectively representing the maximum value and the minimum value of annual power generation and water shortage of all individuals in the population;
s5, population evolution, including the evolution of a bee hiring stage, a bee observing stage and a bee reconnaissance stage;
hiring bee stage: in the stage of employing bees, new honey sources are searched through the formulas (13) to (16) of a search mechanism, and newly generated individuals are subjected to constraint processing by utilizing the formulas (8) and (9); comparing the advantages and disadvantages of the newly generated individuals and the original individuals, and selecting the excellent individuals to the next generation of population by adopting a greedy strategy; updating and maintaining the EliteSet, and adding the EliteSet candidate individuals into the EliteSet;
Formula (13):
Figure BDA0002557878570000045
in the formula, eq,dThe l-th component of elite individual q randomly selected from the elite archive set EliteSet (elite individuals in EliteSet are gradually updated with the population evolution process);
Figure BDA0002557878570000046
the l component of the r variant individual; r1, r2, r3 and r4 are [0, NP]Random integers with different contents, NP is the number of the population; gc is an algorithm evolution algebra; frE (0,1) is a variation factor;
formula (14):
Figure BDA0002557878570000047
in the formula (I), the compound is shown in the specification,
Figure BDA0002557878570000048
is a mean value of 0 and a standard deviation of sigmar(ii) a gaussian random variable; [ e ] aq]distanceFor the crowding distance of elite individual q in the EliteSet,maxmaximum crowding distance for an individual in EliteSet;
formula (15):
Figure BDA0002557878570000049
formula (16):
Figure BDA00025578785700000410
in the formulae (15) and (16),
Figure BDA0002557878570000051
is the l component of the r original individual; rnd (r) is [0,1]The random number of (2); rndr (l) is a randomly generated integer within {0, 1.., NP }; CR is a cross factor of the CR epsilon (0,1)iniThe value is 0.15;
the formulas (15) and (16) are used for improving the diversity of the population, avoiding the algorithm from falling into the local optimum, and performing cross operation on the individuals after mutation and before mutation to generate new individuals;
after the variation and the cross operation are finished, greedy strategy selection is adopted
Figure BDA0002557878570000052
And
Figure BDA0002557878570000053
the better individual in the group enters the next generation of population, and updates and maintains Eliteset;
In the bee observation stage, calculating the probability value of the selected honey source corresponding to the employed bee by using the formula (17), determining a following target by using a wheel disc selection method, and performing neighborhood search by using the same method as the employed bee; in the process of updating and maintaining the Eliteset, decomposing and merging the main tasks of individual constraint processing, fitness calculation and elite individual updating by adopting a Fork/Join parallel calculation mode;
formula (17):
Figure BDA0002557878570000054
in the formula, prProbability of being selected for the r-th hiring bee in the population; voilingjDepth of constraint destruction for hiring bees # j; a feasible margin for judging the constraint damage depth; nv is the number of impossible solutions (when the constraint damage depth of the individual adopting bee is greater than that, the individual is judged as an impossible solution); nd is the number of feasible solutions;
③ detecting bees: if a certain employed bee is in LimitabandonIf the hiring bee is not updated, the hiring bee is changed into a scout bee, and a new solution is searched by random search.
S6: if G < GmaxLet g be g +1, go to S5; otherwise, the solution is completed, and the Eliteset is used as the Pareto optimal leading edge of the multi-target scheduling problem to be output.
In the method, when the multi-target bee colony algorithm is applied to solve the multi-target scheduling model of the cascade reservoir group in the drainage basin, the water level in front of the reservoir dam is selected as a decision variable to carry out individual coding, individual particles are the time-interval water level process of each reservoir, and NP individuals are initialized randomly in the feasible region. And in the model solving process, performing 'water-to-electricity-fixing' simulation calculation according to the water level process, and determining the water level and the downward drainage flow process of the hydropower station at each time period. The factors such as natural water supply conditions, upstream ex-warehouse conditions, self running modes, power system requirements and the like need to be comprehensively considered in the process of controlling the time interval output and the water level storage and discharge of the reservoir, and the time interval is complicated and restricted to be interwoven with the time interval, so that the treatment is very difficult. In order to solve the problem, a heuristic strategy based on a constraint corridor is used for processing coupling constraints among various periods in the reservoir group scheduling process, the reservoir discharge quantity constraint and the output constraint are converted into limits on water levels through a water quantity balance equation, and intersection is taken with the characteristic water level of the reservoir scheduling period to form a water level constraint corridor. In the optimizing process, when the decision variables of the population individuals exceed the boundary of the water level corridor, the decision variables are directly corrected to the boundary value, so that the feasibility of the population individuals is ensured, and the optimizing efficiency of the algorithm is effectively improved.
In will
Figure BDA0002557878570000061
And
Figure BDA0002557878570000062
when the upper and lower boundary values of the flow and the output are taken to carry out forward and backward push calculation by time intervals, the water level boundary of the reservoir under different operating conditions can be obtained
Figure BDA0002557878570000063
And
Figure BDA0002557878570000064
will be time-interval by time interval
Figure BDA0002557878570000065
And
Figure BDA0002557878570000066
obtaining intersection, the decision variable constraint corridor can be generated
Figure BDA0002557878570000067
Figure BDA0002557878570000068
In addition, in the process of solving the model, in order to avoid the algorithm from falling into local optimum, when the water level constraint galleries of different populations of individuals are calculated, the method can ensure that
Figure BDA0002557878570000069
Wherein a and b belong to (0,1), so that the scheduling scheme reflected by the population individuals can cover the whole solution space to improve the diversity of the population.
In the technical scheme, the multi-target optimized scheduling modeling problem of the cascade reservoir group is solved by using a multi-target bee colony algorithm, and strategies such as elite archive sets (Eliteset) and adaptive dynamic parameter control are introduced into the algorithm optimizing process, so that new individuals absorb more information from elite individuals and other individuals, the population diversity is effectively improved, and the algorithm global search capability is enhanced. In the calculation process, the employed bees search honey sources in the neighborhood, and mutation operation is realized by introducing random disturbance on the basis of elite individuals. In general, FrThe value of (A) will influence the convergence rate of the algorithm, and in order to improve the convergence capacity of the algorithm, a Gaussian random variable pair F can be adopted rAnd carrying out self-adaptive dynamic control. Meanwhile, in order to improve the diversity of the population and avoid the algorithm from falling into local optimum, new individuals are generated by performing cross operation on the individuals after mutation and before mutation. In the multi-target bee colony algorithm employing bee stage and observation bee stage, the constraint processing and fitness calculation of a single individual in the colony can be regarded as independent calculation processes, the partial main tasks can be decomposed by a Fork/Join multi-thread parallel calculation mode, and the decomposed sub-colony constraint processing and fitness operation are added into a thread pool as threads to be processed in parallel. In the multi-target scheduling problem solving process of the cascade reservoir group, a thread pool with M threads (the number of the threads is preferably equal to the number of the logical threads of a computer) can be generated, and a memory space is opened up in each thread to store NP/M (NP is the number of the multi-target bee colony algorithm groups) individuals and intermediate calculation results thereof.
Compared with the prior art, the invention has the following advantages and beneficial effects:
1. the cascade reservoir group multi-target scheduling model solving mode is improved through the multi-target bee colony algorithm based on the Fork/Join parallel framework, and the algorithm execution efficiency is effectively improved by adopting a multi-thread parallel computing mode; aiming at the space-time coupling correlation characteristics and multiple complex constraint conditions of multi-target scheduling of the cascade reservoir group, a self-adaptive optimization mechanism and a corresponding heuristic constraint repairing strategy are designed to improve the searching performance and robustness of the algorithm, the quality of the optimized result is practically ensured, and the algorithm has good practicability and engineering operability.
2. The parallel multi-target scheduling solving method provided by the invention has the advantages of high calculating speed and high calculating efficiency, a non-inferior scheduling scheme set which is uniformly and widely distributed in a solution space can be obtained by one-time solving, and the running time and the resolving quality in the same running environment are far superior to those of the traditional modeling method based on the operational research.
Drawings
FIG. 1 is a flow chart of a multi-target scheduling model solution for a cascade reservoir group.
FIG. 2 is a diagram of a multi-objective scheduling non-inferior solution front edge of embodiment 1.
Detailed Description
Example 1: and taking the Laos south Europe river basin cascade power station as an example to perform multi-target power generation-ecological scheduling simulation.
Selecting incoming water with the frequency of 98%, namely extra-low incoming water, as model input listed in table 1, solving the multi-target optimized dispatching model for the reservoir group power generation by adopting the provided MOBCO algorithm, wherein algorithm parameters are set as follows, and calculating to obtain a non-inferior dispatching scheme set of the cascade power station;
the population size NP is 100;
the capacity NQ of the elite file set is 30;
maximum evolution algebra Gmax＝600；
Honey source abandon timing Limitabandon＝10；
LS maximum number of iterations kmax＝20；
TABLE 1 table of 98% frequency water supply situation of each power station of south Europe river basin cascade
Power station 1 month 2 month 3 month 4 month Month 5 6 month 7 month 8 month 9 month 10 month 11 month 12 month
Stage 7 22.2 18.0 15.3 13.6 14.1 23.0 70.2 97.9 81.9 50.6 35.6 27.5
Grade 6 11.8 9.5 8.1 7.2 7.4 12.2 37.1 51.8 43.3 26.8 18.8 14.5
Grade 5 24.4 19.8 16.8 14.9 15.4 25.2 77.0 107.3 89.8 55.5 39.0 30.1
The appropriate ecological flow of the river channel is determined by adopting a hydrological method, the annual maximum ecological runoff process and the annual minimum ecological runoff process are formed by sequencing annual maximum runoff series and annual minimum runoff series of the step power station dam site of the south European river flow field from large to small according to the natural flow data of years at the power station dam site, and selecting the secondary maximum value and the secondary minimum value from the sequence, and the sequences are listed as the basis of multi-target ecological water shortage assessment in table 2. In the embodiment, the lower limit of the suitable ecological flow interval is used as the minimum control value of the ecological flow in each month;
TABLE 2 calculation of suitable ecological flow intervals of south Europe and river steps in combination with hydrology
Figure BDA0002557878570000071
Figure BDA0002557878570000081
The embodiment calculates to obtain a non-inferior scheduling scheme set of the cascade, and carries out comparative analysis on the scheduling result, and the specific steps are as follows:
the method comprises the following steps: setting characteristic parameters of a hydropower station group, initializing algorithm control parameters: eliteset capacity NQ of 30, population size NP of 100, and maximum evolution generation G of algorithmmax600 and number of scout bee starts LimitabandonIs 10; and setting the current evolution algebra g of the algorithm to be 1.
Step two: constructing and initializing NP population individuals by using a formula (1); and (2) judging whether the individual meets the constraint by adopting reservoir scheduling constraints related to the formulas (2) to (7), and correcting the hydropower station group time-period water level in the individual one by applying the hydropower station constraint processing strategies based on the constraint corridor to the individual population which does not meet the constraint by adopting the formulas (8) and (9).
Step three: calculating target fitness values of different population individuals and total generated energy f by using the formula (10) and the formula (11)1And ecological water shortage f2Carrying out target fitness value normalization processing through a formula (12), and carrying out non-dominated sorting on population individuals based on individual target fitness values; all non-domination of the first level in the populationIndividuals were added to EliteSet.
Step four: population evolution, including the evolution of the hiring bee phase, the observation bee phase and the reconnaissance bee phase;
hiring bee stage: in the stage of employing bees, new honey sources are searched through the formulas (13) to (16) of a search mechanism, and newly generated individuals are subjected to constraint processing by utilizing the formulas (8) and (9); comparing the advantages and disadvantages of the newly generated individuals and the original individuals, and selecting the excellent individuals to the next generation of population by adopting a greedy strategy; updating and maintaining the EliteSet, and adding the EliteSet candidate individuals into the EliteSet; calculating the probability of employing the bee to correspond to the honey source being selected by using the formula (17); in the calculation process, a Fork/Join parallel calculation mode is adopted to decompose and merge individual constraint processing, fitness calculation and elite individual updating main tasks so as to improve the execution efficiency of the algorithm.
Observation bee stage: the observation bees determine the following target by adopting a wheel disc selection method according to the honey source selection probability, and the neighborhood search is carried out by adopting the method same as that of the employed bees; updating and maintaining the Eliteset; in the calculation process, a Fork/Join parallel calculation mode is applied to decompose and merge individual constraint processing, fitness calculation and elite individual updating main tasks so as to improve the execution efficiency of the algorithm;
③ detecting bees: if a certain employed bee is in LimitabandonIf the update is not obtained within 10, the hiring bee is changed into a scout bee, and a new solution is searched by random search.
Step five: if G < GmaxChanging g to g +1, and turning to the fourth step; otherwise, the solution is completed, and the Eliteset is used as the Pareto optimal front edge of the multi-objective scheduling problem to be output.
Through the calculation of the steps, the obtained non-inferior scheduling scheme set space distribution results of the power generation quantity and the ecological water shortage quantity of the south-European river basin cascade reservoir group are shown in figure 2, and the specific scheduling index results are shown in table 3.
As can be seen from FIG. 2, the provided MOBCO algorithm has an obvious application effect when solving the multi-objective power generation-ecological scheduling problem, obtains better non-inferior solution front edge distribution, and generates a non-inferior solution front edge with better convergence and a non-inferior solution front edge with continuous and smooth whole. Further analysis is carried out by combining non-inferior solution front edge characteristics, and the restriction and conflict relationship between the generating capacity of the cascade hydropower station and the ecological benefit is very obvious when the south Europe river cascade hydropower station carries out combined dispatching, and the ecological water shortage (water shortage degree) is increased along with the increase of the generating capacity. The difference between the schemes is mainly reflected in the dry season, and the influence of the dry season on the ecology is mainly reflected in the water shortage. According to the scheme with the greatest ecological benefit, the drainage is increased in the dry period to quickly eliminate the water level, and ecological water shortage in the dry period is reduced, so that the ecological benefit is increased, but the whole dry period of the hydropower station is operated at a lower water level, and the power generation benefit is reduced.
Table 3 lists the south europe river step power generation-ecological multi-target scheduling scheme set under 98% frequency incoming water, and 30 schemes in the elite scheme set NQ in the table are all feasible scheduling schemes.
TABLE 398% frequency water supply condition south European river step power generation-ecological multi-target scheduling scheme set
Figure BDA0002557878570000091
Figure BDA0002557878570000101

Claims (1)

1. The parallel multi-target scheduling method of the cascade reservoir group is characterized by comprising the following specific steps:
s1, setting characteristic parameters of hydropower station group and control parameters of initialization algorithm, including Eliteset capacity NQ, group size NP, algorithm maximum evolution algebra GmaxAnd number of scout bee starts Limitabandon(ii) a Setting the current evolution algebra g of the algorithm as 1;
s2, constructing and initializing NP population individuals, wherein the expression is as follows:
Figure RE-FDA0002620762540000011
in the formula, xrIs the r-th oneA body;
Figure RE-FDA0002620762540000012
encoding the individual; n is the number of step reservoirs; t is the number of time segments;
s3, reservoir dispatching constraint processing, namely judging whether the individual meets the constraint by adopting the following formulas (2) to (7), and correcting the hydropower station group time-segment water level in the individual one by using the formulas (8) and (9) for the population individual which does not meet the constraint;
step hydraulic connection formula (2):
Figure RE-FDA0002620762540000013
in the formula Ii,tThe flow rate of the reservoir is i; tau isi-1Is the water flow time lag between the reservoir i-1 and the reservoir i;
Figure RE-FDA0002620762540000014
reservoir at t-tau for i-1 i-1Water abandon flow in time intervals; ri,tInflow between the reservoir i-1 and the reservoir i;
reservoir water balance constraint (3): vi,t＝Vi,t-1+(Ii,t-Qi,t-Si,t)·Δt；
In the formula, Vi,tThe storage capacity at the end of time t of the reservoir i;
water level/flow/output constraint formula (4):
Figure RE-FDA0002620762540000015
in the formula, Pi,tOutputting force for the reservoir at the time t;
Figure RE-FDA0002620762540000016
and i,tZ、
Figure RE-FDA0002620762540000017
and i,tQ、
Figure RE-FDA0002620762540000018
and i,tPthe water level, the ex-warehouse and the output boundary of the reservoir at the time interval t are respectively shown;
fourthly, the water level/flow/output amplitude constraint formula (5):
Figure RE-FDA0002620762540000021
in the formula,. DELTA.Zi、ΔQi、ΔPiI reservoir water level, flow and output amplitude limit respectively;
reservoir operation water head constraint formula (6):
Figure RE-FDA0002620762540000022
in the formula, Hi,tFor the water head of the reservoir at the time t,
Figure RE-FDA0002620762540000023
i,tHrespectively the upper limit and the lower limit of a stable operation water head of the reservoir;
sixthly, controlling the water level at the beginning and end of the reservoir stage according to a restraint formula (7):
Figure RE-FDA0002620762540000024
in the formula, Zi,0、Zi,T、
Figure RE-FDA0002620762540000025
And
Figure RE-FDA0002620762540000026
dispatching initial stage water level, final stage water level and control values of the water level for the reservoir;
seventhly, a water level constraint corridor generation method is represented by the formula (8):
Figure RE-FDA0002620762540000027
the method for generating the water level constraint corridor is characterized by the following formula (9):
Figure RE-FDA0002620762540000028
wherein f (V'i,t-1,Ii,t,Pi BRep) And g (V'i,t,Ii,t,Pi BRep) Calculating functions of the end storage capacity and the initial storage capacity in the t time period respectively;
Figure RE-FDA0002620762540000029
and Pi BRepThe characteristic values of the lower leakage flow and the output are set as the upper and lower boundary values of the flow and the output;
s4, calculating target fitness values of different population individuals, carrying out target fitness value normalization processing, and carrying out non-dominated sorting on the population individuals based on the individual target fitness values; adding all non-dominant individuals at a first level in the population into the Eliteset;
The individual fitness takes the maximum total power generation of the cascade reservoir group and the minimum total ecological water shortage of each cascade downstream river as a scheduling target, and the objective functions are respectively described as an expression (10) and an expression (11):
formula (10):
Figure RE-FDA00026207625400000210
Figure RE-FDA00026207625400000211
formula (11):
Figure RE-FDA0002620762540000031
in the formula, E is the total generating capacity of the cascade reservoir group; pi,t、Qi,t、Hi,tGenerating output, discharging flow and average water head for the i reservoir at the t time period respectively; n is the number of step reservoirs; t and Delta T are respectively equal toThe number of segments and the time period are long; w is the step ecological water shortage;
Figure RE-FDA0002620762540000032
the difference value of the discharge flow of the reservoir at the time t and the suitable ecological demand flow of the downstream river channel is shown as the I;
Figure RE-FDA0002620762540000033
the suitable ecological flow of the downstream river of the power station i in the period t;
the target functions of the formula (10) and the formula (11) have different dimensions, and are normalized to form a dimensionless function value; the scheduling objective normalization is calculated as equation (12):
formula (12):
Figure RE-FDA0002620762540000034
Figure RE-FDA0002620762540000035
in the formula, x r Is the r individual in the evolved population; er, WrThe annual energy production and the water shortage of the No. r individual are respectively determined; emaxAnd Emin、
Figure RE-FDA0002620762540000036
And
Figure RE-FDA0002620762540000037
respectively representing the maximum value and the minimum value of annual power generation and water shortage of all individuals in the population;
s5, population evolution, including the evolution of a bee hiring stage, a bee observing stage and a bee reconnaissance stage;
hiring bee stage: in the stage of employing bees, new honey sources are searched through the formulas (13) to (16) of a search mechanism, and newly generated individuals are subjected to constraint processing by utilizing the formulas (8) and (9); comparing the advantages and disadvantages of the newly generated individuals and the original individuals, and selecting the excellent individuals to the next generation of population by adopting a greedy strategy; updating and maintaining the EliteSet, and adding the EliteSet candidate individuals into the EliteSet;
Formula (13):
Figure RE-FDA0002620762540000038
in the formula, eq,dThe l-th component of elite individual q randomly selected from the elite archive set EliteSet (elite individuals in EliteSet are gradually updated with population evolution);
Figure RE-FDA0002620762540000039
the l component of the r variant individual; r1, r2, r3 and r4 are [0, NP]Random integers with different contents, NP is the number of the population; gc is an algorithm evolution algebra; frE (0,1) is a variation factor;
formula (14):
Figure RE-FDA0002620762540000041
in the formula (I), the compound is shown in the specification,
Figure RE-FDA0002620762540000042
is a mean value of 0 and a standard deviation of sigmar(ii) a gaussian random variable; [ e ] aq]distanceFor the crowding distance of elite individual q in the EliteSet,maxmaximum crowding distance for an individual in EliteSet;
formula (15):
Figure RE-FDA0002620762540000043
formula (16):
Figure RE-FDA0002620762540000044
in the formulae (15) and (16),
Figure RE-FDA0002620762540000045
is the l component of the r original individual; rnd (r) is [0,1]The random number of (2); rndr (l) is a randomly generated integer within {0, 1.., NP }; CR is a cross factor of the CR epsilon (0,1)iniThe value is 0.15;
the formulas (15) and (16) are used for improving the diversity of the population, avoiding the algorithm from falling into local optimum, and performing cross operation on the individuals after mutation and before mutation to generate new individuals;
after the variation and the cross operation are finished, greedy strategy selection is adopted
Figure RE-FDA0002620762540000046
And
Figure RE-FDA0002620762540000047
the better individual in the group enters the next generation of population, and updates and maintains Eliteset;
in the bee observation stage, calculating the probability value of the selected honey source corresponding to the employed bee by using the formula (17), determining a following target by using a wheel disc selection method, and performing neighborhood search by using the same method as the employed bee; in the process of updating and maintaining the Eliteset, decomposing and merging the main tasks of individual constraint processing, fitness calculation and elite individual updating by adopting a Fork/Join parallel calculation mode;
Formula (17):
Figure RE-FDA0002620762540000048
in the formula, prProbability of being selected for the r-th hiring bee in the population; voilingjDepth of constraint damage for hired bees # j; a feasible margin for judging the constraint damage depth; nv is the number of impossible solutions (when the breaking depth of the individual constraint of the employed bee is greater than, the individual is judged as an impossible solution); nd is the number of feasible solutions;
③ detecting bees: if a certain employed bee is in LimitabandonIf the hiring bee is not updated, the hiring bee is changed into a scout beeNew solutions are sought by random search.
S6: if G < GmaxLet g be g +1, go to S5; otherwise, the solution is completed, and the Eliteset is used as the Pareto optimal front edge of the multi-objective scheduling problem to be output.
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