CN105956714B - Novel group search method for optimal scheduling of cascade reservoir group - Google Patents

Novel group search method for optimal scheduling of cascade reservoir group Download PDF

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CN105956714B
CN105956714B CN201610340489.6A CN201610340489A CN105956714B CN 105956714 B CN105956714 B CN 105956714B CN 201610340489 A CN201610340489 A CN 201610340489A CN 105956714 B CN105956714 B CN 105956714B
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吴英
程春田
李江
周毅
冯仲恺
申建建
牛文静
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Huaneng Lancang River Hydropower Co Ltd
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Abstract

The invention relates to the field of power generation dispatching of hydroelectric systems, and discloses a novel group search method for optimal dispatching of cascade reservoir groups. The technical scheme is as follows: taking the water level of the hydropower station as a state variable, taking the maximum comprehensive generated energy of the cascade reservoir group in a dispatching period as an optimization target, and after initializing a certain number of spider individuals, carrying out the internal cooperation behavior of the spider group, the mating behavior of the opposite individuals, the dynamic updating of the elite individuals and the neighborhood variation search strategy generation by generation to gradually approach the optimal dispatching strategy of the cascade reservoir group. The Elite individual dynamic updating strategy can ensure that the Elite spider group guides the population to effectively evolve, and the searching capability and the exploration capability of the method are balanced; the excellent individual neighborhood variation strategy can maintain population diversity, improve the calculation efficiency and the convergence rate of the method, and the method has good popularization value and application prospect.

Description

Novel group search method for optimal scheduling of cascade reservoir group
Technical Field
The invention relates to the field of hydropower system power generation dispatching, in particular to a novel group search method for optimal dispatching of a cascade reservoir group.
Technical Field
With the steady and orderly propulsion of hydroelectric development, China gradually forms a new pattern of giant step reservoir groups. The cooperative unified scheduling of the cascade reservoir group is beneficial to the reasonable and efficient utilization of water energy resources and the safe and stable operation of an electric power system, and can generate remarkable economic, social and ecological comprehensive benefits, so that the optimized scheduling of the cascade reservoir group is an important theoretical and practical subject of the current and even future hydroelectric energy systems. However, complicated hydraulic and electric power connections coexist between the cascade reservoirs, and various complicated space-time constraints such as water level, warehouse-out, output and the like need to be comprehensively considered, so that the cascade reservoir group optimization scheduling problem also becomes a typical multi-stage multi-constraint nonlinear optimal control problem. Existing solutions are broadly divided into two categories: traditional optimization methods represented by linear programming, dynamic programming, large system decomposition and coordination, and the like; an artificial intelligence method represented by a cuckoo algorithm, a frog leap algorithm, a particle swarm algorithm and the like. Although the method has achieved abundant research results, the method is still limited in different degrees in practical engineering application, such as the problem of dimension disaster of dynamic planning, premature convergence of particle swarm optimization, and the like. Therefore, a new method is urgently needed to be researched in the field of optimal scheduling of the cascade reservoir group so as to realize faster and better optimal scheduling.
Inspired by the cooperative mechanism of spider communities in the nature, a novel efficient intelligent optimization method, namely a spider community optimization method, is proposed by scholars, shows more excellent search capability in a plurality of standard test functions, and gradually shows strong vitality in the fields of numerical optimization, network design and the like. However, when the method is applied to solving the optimal scheduling problem of the cascade reservoir group, the problems of premature convergence and the like still exist. Therefore, the achievement of the invention relies on the national science foundation significant international cooperation (51210014) and the national twelve-five science and technology support plan project (2013BAB06B04), takes the problem of optimized dispatching of the Yangjiang cascade reservoir group as the background and takes the downstream 'two-reservoir five-level' cascade reservoir group as the main object, and the invention provides the novel group search method for optimized dispatching of the cascade reservoir group with high efficiency and practicability.
Disclosure of Invention
The invention aims to solve the technical problem of providing a novel group search method for optimal scheduling of a cascade reservoir group, which combines an elite set dynamic update strategy and a neighborhood variation search mechanism to balance global search and local exploration of the method and take the diversity of the group and the convergence speed of the method into consideration.
The technical scheme of the invention is as follows: the invention discloses a novel group search method for optimal dispatching of cascade reservoir groups, which completes the coordination optimization process of the cascade reservoir groups according to the following steps (1) to (7):
(1) setting the individual number of the spider group as Np, the maximum iteration number K, the individual number omega of the elite set and other calculation parameters;
(2) recording the iteration number k as 1, calculating the number of individuals of male and female sex character spider groups by using a formula (I), and then randomly generating a female initial spider group F and a male initial spider group M by using a formula (II) to realize the initialization of all individuals of the spider groups;
Figure BDA0000996198760000021
Figure BDA0000996198760000022
in the formula, Nf、NmThe number of female and male subarachnoid individuals respectively; r is1Is [0,1 ]]Random numbers uniformly distributed in intervals; []Representing a rounding function; j denotes a dimension number, j ═ 1,2, …, D;
Figure BDA0000996198760000023
represents the j dimension of the ith female spider in the k iteration, i is 1,2, …, Nf；
Figure BDA0000996198760000024
Denotes the j-th dimension of the l male spider in the k-th iteration, i.e. 1,2, …, Nm；r2,r3Is [0,1 ]]Random numbers uniformly distributed in intervals;
Figure BDA0000996198760000025
X jrespectively taking the upper limit and the lower limit of the j dimension variable;
at this time, spider-web SkFrom NpA spider comprising NfGroup F of female spiderskAnd NmGroup M of individual male spiderskIt is written as:
Figure BDA0000996198760000026
(3) correcting each spider individual to a feasible region, evaluating and calculating the fitness of each spider individual, and obtaining the corresponding weight of each individual by using a formula III;
Figure BDA0000996198760000027
in the formula, J (S)i)、wiRespectively represent the ith spider SiFitness and weight thereof;
(4) dynamically updating the elite set by adopting an elite set dynamic updating strategy
Figure BDA0000996198760000028
The specific operation is as follows:
setting up
Figure BDA0000996198760000029
The number of elite individuals is taken as omega, the elite set
Figure BDA00009961987600000210
The dynamic updating specific scheme is as follows: copying the individuals with the first omega names in the fitness in the current population into the intermediate set v, if the individuals with the first omega names in the fitness in the current population are copied into the intermediate set v, copying the individuals with the first omega names in the fitness to the intermediate set v
Figure BDA00009961987600000211
Then order
Figure BDA00009961987600000212
Otherwise get
Figure BDA00009961987600000213
Form a new elite set with half of the individuals with excellent V
Figure BDA00009961987600000214
Meanwhile, the evolution formulas of the female spider and the male spider are respectively as follows:
the evolution formula of the female spider is as follows:
Figure BDA00009961987600000215
in the formula, SαRepresents from
Figure BDA00009961987600000216
Selecting the alpha-th elite individual, alpha ═ r12ω]；r11,r12Is [0,1 ]]Random numbers are evenly distributed in intervals.
Fifthly, the male spider evolution formula is as follows:
Figure BDA00009961987600000217
in the formula (I); sβRepresents from
Figure BDA00009961987600000218
Selecting the beta-th elite individual, beta ═ r14ω]；r13,r14Is [0,1 ]]Random numbers are evenly distributed in intervals.
(5) Carrying out a population neighborhood variation search strategy by utilizing the formulas (sixthly) and (seventhly) to enhance the exploration capability of the method;
Figure BDA0000996198760000031
⑦Xi＝argmax{F(Xi'),F(Xi)}
in the formula, r15Is [0,1 ]]Random numbers uniformly distributed in intervals; gamma is a random number following a normal distribution of N (0, 1);
(6) generating new female and male subarachnoid groups by adopting formulas (IV) and (V) respectively to realize the internal cooperative behavior of the subarachnoid groups;
(7) carrying out mating behavior on dominant individuals in the male subarachnoid group by adopting a formula of (eight) - (three) to improve the diversity of the group;
Figure BDA0000996198760000032
Figure BDA0000996198760000033
Figure BDA0000996198760000034
wherein R is a mating radius;
Figure BDA0000996198760000035
the first male spider individual in the kth iteration; t isMIs all at
Figure BDA0000996198760000036
Female individuals within the mating radius R make up a subarachnoid group; psIs TMThe distribution probability of all individuals is weighted;
(8) making K equal to K +1, and if K is less than or equal to K, returning to the step (3); otherwise, stopping calculation and outputting the optimal individual.
Compared with the prior art, the invention has the following beneficial effects: the invention relates to a novel group search method for optimal scheduling of cascade reservoir groups, which is characterized in that the water level of a hydropower station is used as a state variable, the maximum comprehensive generated energy of the cascade reservoir groups in a scheduling period is used as an optimal target, and after a certain number of spider individuals are initialized, the internal cooperation behavior of the spider groups, the mating behavior of heterosexual individuals, the dynamic updating of elite individuals and a neighborhood variation search strategy are carried out generation by generation, and the optimal scheduling strategy of the cascade reservoir groups is gradually approached. Compared with the prior art, the Elite individual dynamic updating strategy can ensure that the Elite spider group guides the population to effectively evolve, and balance the searching capability and the exploration capability of the method; the excellent individual neighborhood variation strategy can maintain the population diversity and improve the calculation efficiency and the convergence rate of the method; the method can effectively improve the search performance of the spider swarm optimization method, and has good popularization value and application prospect in practical engineering.
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FIG. 1 is a schematic diagram of the basic principle of the process of the present invention;
FIG. 2(a) is a calculation of optimal scheduling for a bay plant;
FIG. 2(b) is the optimized scheduling calculation result of the bay power station;
FIG. 2(c) is a result of an optimized scheduling calculation for a Dachaoshan power station;
fig. 2(d) is the result of the optimized scheduling calculation of the glutinous ferry power station;
fig. 2(e) is the result of the optimized scheduling calculation of the scenic flood power station.
Detailed Description
The invention is further described below with reference to the figures and examples.
The cooperative unified scheduling of the cascade reservoir groups is beneficial to the reasonable and efficient utilization of water energy resources and the safe and stable operation of an electric power system, and can generate remarkable comprehensive benefits of economy, society, ecology and the like, but the complex hydraulic and electric power connection between the cascade reservoirs coexist, and various complex space-time constraints such as water level, ex-warehouse, output and the like need to be comprehensively considered, so that the cascade reservoir group optimization scheduling faces serious problems such as 'dimension disaster', 'premature convergence' and the like, and particularly, the problem of large-scale cascade reservoir group optimization scheduling is very difficult to solve. The invention discloses a novel group search method for optimal scheduling of a cascade reservoir group, which is characterized in that the water level of a hydropower station is used as a state variable, the maximum comprehensive generated energy of the cascade reservoir group in a scheduling period is used as an optimization target, and after a certain number of spider individuals are initialized, the internal cooperation behavior of the spider group, the mating behavior of the opposite individuals, the dynamic updating of the elite individuals and the neighborhood variation search strategy are carried out generation by generation, and the optimal scheduling strategy of the cascade reservoir group is gradually approached. The Elite individual dynamic updating strategy can ensure that the Elite spider group guides the population to effectively evolve, and the searching capability and the exploration capability of the method are balanced; the excellent individual neighborhood variation strategy can maintain population diversity, improve the calculation efficiency and the convergence rate of the method, and the method has good popularization value and application prospect.
The invention relates to a novel group search method for cascade reservoir group optimization scheduling, which is developed by using a common maximum model of generated energy in cascade reservoir group optimization scheduling, wherein an objective function is shown as the following formula:
Figure BDA0000996198760000041
in the formula, E is the total power generation amount in a scheduling period, kW.h; n is the number of power stations; i is a power station serial number, i is 1,2, …, N; t is a scheduling period; t is the time period number, T is 1,2, …, T; pi,tThe output of the reservoir i in the time period t is kW; a. theiThe output coefficient of the reservoir i is; qi,tIs the generating flow of the reservoir i in the time period t, m3/s；Hi,tIs the head of the reservoir i at time t, m; deltatThe number of hours of time period t, h.
In order to ensure the feasibility and the availability of the optimization result, the objective function needs to consider various operation constraints to be met in the solving process of the cascade reservoir group optimization scheduling problem, which will be described in the following.
(1) And (3) restraining the water level from beginning to end:
Figure BDA0000996198760000042
in the formula (I), the compound is shown in the specification,
Figure BDA0000996198760000043
is the initial water level of reservoir i, m;
Figure BDA0000996198760000044
is the final water level, m, of reservoir i.
(2) And (3) water balance constraint:
Figure BDA0000996198760000045
in the formula, Vi,tIs the storage capacity, m, of reservoir i in time period t3；ΩiUpstream set of reservoirs, of the leading reservoir, representing reservoir i
Figure BDA0000996198760000046
qi,t、Oi,t、di,tThe interval flow, the delivery flow and the abandon flow of the reservoir i in the time period t, m3/s。
(3) Water level restraint:
Figure BDA0000996198760000047
in the formula, Zi,tIs the water level of the reservoir i in time period t, m;Z i,t、
Figure BDA0000996198760000048
the upper and lower limits of the water level of the reservoir i in the time period t.
(4) And (3) power generation flow restriction:
Figure BDA0000996198760000051
in the formula (I), the compound is shown in the specification,
Figure BDA0000996198760000052
Q i，tthe upper limit and the lower limit of the generating flow of the reservoir i in the time period t are set.
(5) And (4) ex-warehouse flow constraint:
Figure BDA0000996198760000053
in the formula (I), the compound is shown in the specification,
Figure BDA0000996198760000054
O i，tfor the delivery flow of reservoir i in time tUpper and lower limits.
(6) Force restraint:
Figure BDA0000996198760000055
in the formula (I), the compound is shown in the specification,
Figure BDA0000996198760000056
P i,tthe upper limit and the lower limit of the output of the reservoir i in the time period t.
(7) And (3) restriction of hydropower bandwidth:
Figure BDA0000996198760000057
in the formula (I), the compound is shown in the specification,
Figure BDA0000996198760000058
h tthe upper limit and the lower limit of the bandwidth of the hydropower system in the time period t, kW, respectively.
According to the idea, a complete optimization scheduling process is realized according to the following steps (1) to (8):
(1) setting the individual number of the spider group as Np, the maximum iteration number K, the individual number omega of the elite set and other calculation parameters;
(2) recording the iteration number k as 1, calculating the number of individuals of male and female sex character spider groups by using a formula (I), and then randomly generating a female initial spider group F and a male initial spider group M by using a formula (II) to realize the initialization of all individuals of the spider groups;
(3) correcting each spider individual to a feasible region, evaluating and calculating the fitness of each spider individual, and obtaining the corresponding weight of each individual by using a formula III;
(4) dynamically updating the elite set by adopting an elite set dynamic updating strategy
Figure BDA0000996198760000059
(5) Carrying out a population neighborhood variation search strategy by utilizing the formulas (sixthly) and (seventhly) to enhance the exploration capability of the method;
(6) generating new female and male subarachnoid groups by adopting formulas (IV) and (V) respectively to realize the internal cooperative behavior of the subarachnoid groups;
(7) carrying out mating behavior on dominant individuals in the male subarachnoid group by adopting a formula of (eight) - (three) to improve the diversity of the group;
(8) making K equal to K +1, and if K is less than or equal to K, returning to the step (3); otherwise, stopping calculation and outputting the optimal individual.
The method is adopted to manufacture the cascade reservoir group optimized dispatching scheme by taking the cascade reservoir group in the middle and lower reaches of the cang river as a research object. The Langancang river basin is one of 13 major hydropower bases in China, 14-level hydropower stations are designed in a main flow plan, the total installed scale is about 25750MW, and only part of the hydropower stations are put into production and run at the present stage. The study object comprises 5 power stations which are already put into operation, namely, a bay, a diffuse bay, a large mountains, a glutinous rice ferry and a scenic flood, and the topological diagram of the drainage basin and the characteristic parameters of the power stations are respectively shown in the table 1. The optimized scheduling results of each power station are shown in fig. 2(a) - (e), the optimized scheduling result pairs of different methods are shown in table 2, and different schemes represent different operation times respectively. As can be seen from the analysis of fig. 2(a) - (e), in the calculation result of the method of the present invention, the bay, as the leading reservoir, rapidly raises the water level in the water storage period, and gradually falls to the set water level in the dry period, thereby fully playing the step compensation effect; the rest reservoirs rapidly reduce the water level to meet the large flow of incoming water in the flood season, and the rest periods maintain high water head operation as far as possible to reduce water consumption and increase power generation quantity; the optimization results of all reservoirs meet all the constraint conditions of water level, output and the like. The method provided by the invention has the advantages that the scheduling process is reasonable and feasible, and the optimal scheduling practical operation of the cascade reservoir group can be served. As can be seen from table 2, from the viewpoint of the amount of electric power generated, the method of the present invention can obtain more electric power generation than the particle population and the spider population optimization method, and in case of 10, 14.63, 23.82, 19.06, 15.61, 27.67, 12.08, 17.43, 16.71, 9.67, 17.41 billion kWh in the particle population method, respectively, and 6.19, 2.69, 4.57, 7.91, 15.35, 4.13, 4.81, 1.94, 3.33, 2.43 billion kWh in the spider population optimization method, respectively; from the standard deviation of the generated energy, the standard deviation of different schemes of the method is far smaller than that of other two types of comparison methods, which shows that the search mechanism of the method is superior to that of a particle swarm optimization method, and the provided strategy can effectively improve the search mechanism of the spider swarm optimization method and improve the stability and robustness of the optimization result; from the aspect of time consumption of calculation, the method is superior to particle swarm and is similar to a spider swarm optimization method, and the method can effectively improve the optimization scheduling solving efficiency of the cascade hydropower station swarm.
TABLE 1
Figure BDA0000996198760000061
TABLE 2
Figure BDA0000996198760000062

Claims (1)

1. A novel group search method for optimal scheduling of a cascade reservoir group is characterized by comprising the following two parts:
the first part is the solving step of the reservoir group optimization scheduling model, which comprises the following steps:
(1) setting the individual number of the spider group as Np, the maximum iteration number K, the individual number omega of the elite set and other calculation parameters;
(2) recording the iteration number k as 1, calculating the number of individuals of male and female sex character spider groups by using a formula (I), and then randomly generating a female initial spider group F and a male initial spider group M by using a formula (II) to realize the initialization of all individuals of the spider groups;
①
Figure FDF0000011575010000011
②
Figure FDF0000011575010000012
in the formula, Nf、NmThe number of female and male subarachnoid individuals respectively; r is1Is [0,1 ]]Random numbers uniformly distributed in intervals; []Representing a rounding function; j denotes a dimension number, j ═ 1,2, …, D;
Figure FDF0000011575010000013
represents the j dimension of the ith female spider in the k iteration, i is 1,2, …, Nf；
Figure FDF0000011575010000014
Denotes the j-th dimension of the l male spider in the k-th iteration, i.e. 1,2, …, Nm；r2,r3Is [0,1 ]]Random numbers uniformly distributed in intervals;
Figure FDF0000011575010000015
X jrespectively taking the upper limit and the lower limit of the j dimension variable;
at this time, spider-web SkFrom NpA spider comprising NfGroup F of female spiderskAnd NmGroup M of individual male spiderskIt is written as:
Figure FDF0000011575010000016
(3) correcting each spider individual to a feasible region, evaluating and calculating the fitness of each spider individual, and obtaining the corresponding weight of each individual by using a formula III;
③
Figure FDF0000011575010000017
in the formula, J (S)i)、wiRespectively represent the ith spider SiFitness and weight thereof;
(4) dynamically updating the elite set by adopting an elite set dynamic updating strategy
Figure FDF0000011575010000018
The specific operation is as follows:
setting up
Figure FDF0000011575010000019
The number of elite individuals is taken as omega, the elite set
Figure FDF00000115750100000110
The dynamic updating specific scheme is as follows: copying the individuals with the first omega names in the fitness in the current population into the intermediate set v, if the individuals with the first omega names in the fitness in the current population are copied into the intermediate set v, copying the individuals with the first omega names in the fitness to the intermediate set v
Figure FDF00000115750100000111
Then order
Figure FDF00000115750100000112
Otherwise get
Figure FDF00000115750100000113
Form a new elite set with half of the individuals with excellent V
Figure FDF00000115750100000110
(ii) a Meanwhile, the evolution formulas of the female spider and the male spider are respectively as follows:
the evolution formula of the female spider is as follows:
Figure FDF00000115750100000115
in the formula, SαRepresents from
Figure FDF00000115750100000116
Selecting the alpha-th elite individual, alpha ═ r12ω]；r11,r12Is [0,1 ]]Random numbers uniformly distributed in intervals;
fifthly, the male spider evolution formula is as follows:
Figure FDF00000115750100000117
in the formula (I); sβRepresents from
Figure FDF00000115750100000118
Selected byBeta-elite individual, beta ═ r14ω]；r13,r14Is [0,1 ]]Random numbers uniformly distributed in intervals;
(5) carrying out a population neighborhood variation search strategy by utilizing the formulas (sixthly) and (seventhly) to enhance the exploration capability of the method;
⑥
Figure FDF0000011575010000021
⑦Xi＝argmax{F(Xi'),F(Xi)}
in the formula, r15Is [0,1 ]]Random numbers uniformly distributed in intervals; gamma is a random number following a normal distribution of N (0, 1);
(6) generating new female and male subarachnoid groups by adopting formulas (IV) and (V) respectively to realize the internal cooperative behavior of the subarachnoid groups;
(7) carrying out mating behavior on dominant individuals in the male subarachnoid group by adopting a formula of (eight) - (three) to improve the diversity of the group;
⑧
Figure FDF0000011575010000022
⑨
Figure FDF0000011575010000023
⑩
Figure FDF0000011575010000024
wherein R is a mating radius;
Figure FDF0000011575010000025
the first male spider individual in the kth iteration; t isMIs all at
Figure FDF0000011575010000026
Female individuals within the mating radius R make up a subarachnoid group; psIs TMThe distribution probability of all individuals is weighted;
(8) making K equal to K +1, and if K is less than or equal to K, returning to the step (3); otherwise, stopping calculation and outputting the optimal individual;
the second part is a cascade reservoir group optimal scheduling model, which comprises the following specific steps:
the fitness in the model solving method is mainly calculated by the maximum objective function of the generated energy in the optimized dispatching of the cascade reservoir group, and can be expressed as follows:
Figure FDF0000011575010000027
in the formula, E is the total power generation amount in a scheduling period, kW.h; n is the number of power stations; i is a power station serial number, i is 1,2, …, N; t is a scheduling period; t is the time period number, T is 1,2, …, T; pi,tThe output of the reservoir i in the time period t is kW; a. theiThe output coefficient of the reservoir i is; qi,tIs the generating flow of the reservoir i in the time period t, m3/s；Hi,tIs the head of the reservoir i at time t, m; deltatHours of time period t, h;
on the other hand, the objective function needs to meet the following reservoir dispatching operation constraints and conditions:
(1) and (3) restraining the water level from beginning to end:
Figure FDF0000011575010000028
in the formula (I), the compound is shown in the specification,
Figure FDF0000011575010000029
is the initial water level of reservoir i, m;
Figure FDF00000115750100000210
is the final water level, m, of reservoir i;
(2) and (3) water balance constraint:
Figure FDF00000115750100000211
in the formula, Vi,tIs the storage capacity, m, of reservoir i in time period t3；ΩiUpstream set of reservoirs, of the leading reservoir, representing reservoir i
Figure FDF00000115750100000212
qi,t、Oi,t、di,tThe interval flow, the delivery flow and the abandon flow of the reservoir i in the time period t, m3/s；
(3) Water level restraint:
Figure FDF0000011575010000031
in the formula, Zi,tIs the water level of the reservoir i in time period t, m;Z i,t、
Figure FDF0000011575010000032
the upper limit and the lower limit of the water level of the reservoir i in the time period t;
(4) and (3) power generation flow restriction:
Figure FDF0000011575010000033
in the formula (I), the compound is shown in the specification,
Figure FDF0000011575010000034
Q i,tthe upper limit and the lower limit of the generating flow of the reservoir i in the time period t are set;
(5) and (4) ex-warehouse flow constraint:
Figure FDF0000011575010000035
in the formula (I), the compound is shown in the specification,
Figure FDF0000011575010000036
O i,tthe upper limit and the lower limit of the outlet flow of the reservoir i in the time period t are set;
(6) force restraint:
Figure FDF0000011575010000037
in the formula (I), the compound is shown in the specification,
Figure FDF0000011575010000038
P i,tthe upper limit and the lower limit of the output of the reservoir i in the time period t;
(7) and (3) restriction of hydropower bandwidth:
Figure FDF0000011575010000039
in the formula (I), the compound is shown in the specification,
Figure FDF00000115750100000310
h tthe upper limit and the lower limit of the bandwidth of the hydropower system in the time period t, kW, respectively.
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