CN111461478B - Large-scale water-light energy complementary scheduling method and system - Google Patents

Large-scale water-light energy complementary scheduling method and system Download PDF

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CN111461478B
CN111461478B CN202010053998.7A CN202010053998A CN111461478B CN 111461478 B CN111461478 B CN 111461478B CN 202010053998 A CN202010053998 A CN 202010053998A CN 111461478 B CN111461478 B CN 111461478B
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冯仲恺
牛文静
刘帅
蒋志强
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Abstract

The invention discloses a large-scale water-light energy complementary scheduling method and system, and belongs to the field of water-light complementary scheduling. Firstly, randomly generating an initial population in a search space, updating the optimal positions of individuals and the optimal positions of the whole situation in the current population according to the fitness value of each individual, and then updating the positions of all the individuals in the population; and improving the convergence speed of the population by using a local search strategy, screening the population by using a self-adaptive variation strategy, updating by iteratively calculating the positions of all individuals in the population, and obtaining the global optimal position of the population as the optimal scheme of the water-light energy complementary scheduling after the maximum iteration times are reached. The invention solves the technical problems of difficult getting rid of local optimization, weak development capability and the like of the existing GSA algorithm, has the advantage of strong optimization capability, can reasonably process the balance between exploration and development aiming at the problem of water-light cooperative scheduling, and has good engineering practicability.

Description

Large-scale water-light energy complementary scheduling method and system
Technical Field
The invention belongs to the field of water-light complementary scheduling, and particularly relates to a large-scale water-light energy complementary scheduling method and system.
Background
China is rich in energy reserves, fossil energy is mainly coal, coal reserves are in the third world, and hydraulic resource theories are in the first world. The new energy resources such as wind energy, solar energy and the like are rich. However, China has a large population, the energy occupation is low, and the distribution is extremely unbalanced. With the improvement of the technical level, the direction of researchers is gradually expanded to a new technical field of solar energy. In the operation of a power grid, various power loads usually participate, for the cooperative scheduling of a cascade reservoir group and a photovoltaic power station, the variance of the load participated by the power grid is usually taken as the final target of optimization, and the specific formula is as follows:
Figure BDA0002372172230000011
wherein f is the objective function value; rhosThe generation output probability of the s photovoltaic power station is obtained; ps,m,tThe output of the mth photovoltaic power station in t time periods after the generation of the s probability. L istThe load demand of the power system for the t-th period. Pn,tThe output of the nth power station in the t period is obtained; m is the number of photovoltaic power stations; n is the total number of hydropower stations; t is the total number of time periods.
The constraints that need to be satisfied are as follows:
(1) and (3) water balance constraint:
Figure BDA0002372172230000021
wherein, NUnThe number of upstream power plants directly connected to the nth hydroelectric power plant; vn,tThe storage capacity of the nth hydropower station in the t period; q. q.sn,tThe interval flow of the nth hydropower station in the t period is obtained; i isn,tThe total warehousing flow of the nth hydropower station in the tth time period is obtained; o isn,tThe total ex-warehouse flow of the nth hydropower station in the t time period is obtained; qn,tThe generated flow rate of the nth hydropower station in the t period is obtained.
(2) Water head restraint: hn,t＝0.5(Zn,t+Zn,t-1)-dn,t. Wherein Z isn,tThe water level of the nth hydropower station in front of the dam in the tth time period; hn,tHead for nth hydropower station at t time period; dn,tDownstream of the nth hydropower station in the t-th period.
(3) And (3) water level restriction before dam:
Figure BDA0002372172230000022
wherein,
Figure BDA0002372172230000023
the minimum value of the dam front water level of the nth hydropower station in the tth time period is obtained;
Figure BDA0002372172230000024
the maximum value of the dam front water level of the nth hydropower station in the tth time period is obtained;
(4) and (3) power generation flow restriction:
Figure BDA0002372172230000025
wherein,
Figure BDA0002372172230000026
generating flow upper limit for the nth hydropower station in the t period;
Figure BDA0002372172230000027
the lower limit of the generating flow of the nth hydropower station in the t period;
(5) reservoir delivery flow restraint:
Figure BDA0002372172230000028
wherein,
Figure BDA0002372172230000029
the upper limit of the ex-warehouse flow of the nth hydropower station in the t period is set;
Figure BDA00023721722300000210
the lower limit of the ex-warehouse flow of the nth hydropower station in the t period is set;
(6) and (3) power station output restraint:
Figure BDA00023721722300000211
wherein,
Figure BDA00023721722300000212
the hydropower station is the hydropower station with the upper limit of hydropower output in the t time period;
Figure BDA00023721722300000213
the hydropower station is the hydropower station with the lower limit of hydropower output in the t time period;
(7) photovoltaic power station output restraint:
Figure BDA00023721722300000214
wherein，
Figure BDA00023721722300000215
The lower limit of luminous energy output of the nth hydropower station in the t period,
Figure BDA0002372172230000031
and the output upper limit of the luminous energy of the nth hydropower station in the tth period is defined.
Generally, the optimization objective in a power system with cascaded hydropower station clusters is generally to determine an optimal scheduling scheme in order to maximize the overall power system benefit while satisfying a set of physical constraints (e.g., water balance constraints, generation flow constraints). With the large-scale injection of solar photovoltaic power generation, the influence of the external environment on the prediction uncertainty becomes prominent, and the formulation of a scientific decision scheme becomes more difficult. To effectively address this challenge, it is important to develop an appropriate optimization model in consideration of the uncertainty of solar power generation. The Gravity Search Algorithm (GSA) is a novel population-based evolutionary algorithm, inspired by newton's laws of gravity and motion. In GSA, each potential solution is considered as a planet in the universe, whose quality can be measured by a fitness value related to the target problem. However, because these factors tend to have individuals of the same quality later in evolution, GSA is difficult to get rid of problems of local optimality and weak easy-to-develop ability.
Disclosure of Invention
Aiming at the defects or improvement requirements of the prior art, the invention provides a large-scale water-light energy complementary scheduling method and system, so that the technical problems that the existing GSA algorithm is difficult to get rid of local optimization, the development capability is weak and the like are solved.
To achieve the above object, according to one aspect of the present invention, there is provided a large-scale complementary scheduling method for water and light energy, including the following steps:
(1) determining constraint conditions among power stations, wherein the power stations comprise hydropower stations and photovoltaic power stations, the ex-warehouse flow of each hydropower station at different moments is used as a decision variable and is coded, then an initial population is randomly generated in a search space according to the decision variable, the initial population is used as a current population, and any individual in the population represents a water-light energy complementary scheduling scheme;
(2) acquiring the fitness of all individuals in the current population, updating the optimal positions of the individuals and the global optimal position in the current population according to the fitness value of each individual, and then updating the positions of all the individuals in the population;
in the first iteration of the population, the optimal position of the individual refers to the position of the individual in the first iteration of the population, and in the second iteration and the previous iterations, the optimal position of the individual refers to the better position of the individual in the current iteration of the population and the position of the individual in the previous iteration; the global optimal position refers to the position of an optimal individual in the current iteration of the population;
(3) based on the population obtained after updating the positions of all individuals of the population, local search is carried out on the population by adopting a local search strategy so as to improve the convergence speed of the population;
(4) screening populations by adopting a self-adaptive variation strategy to improve the diversity of the populations;
(5) returning individuals exceeding the boundary to the boundary range to form a next generation population based on the population obtained after mutation by adopting a mutation strategy;
(6) and (3) judging whether the algebra of the current population reaches the preset maximum iteration times, if not, taking the next generation population as the current population, returning to the step (2), if so, stopping calculation, and outputting the optimal individual corresponding to the global optimal position as the optimal scheme of the water-light energy complementary scheduling.
Preferably, X is for any individual in the population of the kth generationi(k) Can be expressed as
Figure BDA0002372172230000041
Wherein N represents the number of power stations; t represents the number of periods;
Figure BDA0002372172230000042
Figure BDA0002372172230000043
is Xi(k) The flow out of the nth hydropower station in the t period,
Figure BDA0002372172230000044
for the lower limit of the generating flow of the nth hydropower station in the t-th time period, rand (0,1) is [0,1 ]]Random numbers with uniformly distributed intervals, k represents the number of iterations, Xi(k) With N x T dimensions.
Preferably, the ith individual X of the kth generationi(k) Fitness F [ X ] ofi(k)]Comprises the following steps:
Figure BDA0002372172230000051
where ρ issThe occurrence probability of the s photovoltaic power station is shown; s is the total number of probabilities,
Figure BDA0002372172230000052
Ltload demand for the power system at the tth time period; ps,m,tIs at a probability ρsThe output of the next mth photovoltaic power station in the t period; pn,tThe output of the nth hydropower station in the t period is obtained; m is the total number of photovoltaic power plants; n is the total number of hydropower stations; t is the total number of time periods; ga[Xi(k)]And caA constraint violation value and a penalty coefficient which are respectively an a-th inequality constraint; e.g. of the typeb[Xi(k)]And cbConstraint violation values and penalty coefficients for the b-th equation, respectively; a and B are the number of inequality constraints and equality constraints, respectively.
Preferably, is prepared from
Figure BDA0002372172230000053
Updating the global optimal position in the current population
Figure BDA0002372172230000054
Updating the optimal position of the individual in the current population; wherein gBest (k) is the global optimal position of the kth iteration of the population, and gBest (k) { gBest }d(k),d＝1,2...,D}，gBestd(k) The global optimum position of the kth iteration of the population in the d dimension, the global optimum position of the kth-1 iteration of the gBest (k-1) population,
Figure BDA0002372172230000055
Figure BDA0002372172230000056
the optimal position of the ith individual in the D dimension for the kth iteration, D is the maximum dimension of the ith individual, pBesti(k) For the individual optimal position, pBest, of the ith individual of the kth iteration of the populationi(k-1) is the individual optimal position of the ith individual in the k-1 iteration of the population.
Preferably, is prepared from
Figure BDA0002372172230000061
Updating the positions of all individuals in the population, wherein,
Figure BDA0002372172230000062
Figure BDA0002372172230000063
Figure BDA0002372172230000064
Rij(k)＝||xi(k)-xj(k)||
Figure BDA0002372172230000065
wherein,
Figure BDA0002372172230000066
and
Figure BDA0002372172230000067
the ith individuals of the kth generation population and the (k + 1) th generation population are respectively positioned in the d-dimension,
Figure BDA0002372172230000068
the position of the ith individual in the jth dimension of the kth generation population; position of ith individual in kth iteration of population
Figure BDA0002372172230000069
Position of ith individual in population k +1 iteration
Figure BDA00023721722300000610
Figure BDA00023721722300000611
And
Figure BDA00023721722300000612
the speed of the ith individual in the d-dimension for the kth iteration and the (k + 1) th iteration respectively,
Figure BDA00023721722300000613
acceleration in d-dimension, rand, for the ith individual of the kth iterationjAnd randiIs [0,1 ]]Random numbers uniformly distributed among them; kbest is the first K individuals with better fitness;
Figure BDA00023721722300000614
the worst fitness of all individuals in the kth iteration population;
Figure BDA00023721722300000615
the optimal fitness of all individuals in the kth iteration population is obtained;
Figure BDA00023721722300000616
the force of the ith individual on the jth individual in the d-dimension; mpi(k) Is the passive mass of the ith individual, Maj(k) Is the active mass of the jth individual, Rij(k) For the ith individual and the jth individualEuclidean distance of (G)0Is the initial value of the universal gravitation constant, G (k) is the value of the universal gravitation constant of the kth iteration, alpha is the attenuation coefficient, and epsilon is a constant value.
Preferably, the population is searched locally using the following formula:
Figure BDA0002372172230000071
Figure BDA0002372172230000072
Figure BDA0002372172230000073
Figure BDA0002372172230000074
c2＝1-c1
in the formula,
Figure BDA0002372172230000075
local search position of ith individual in d dimension for k iteration; r is3And r4Is [0,1 ]]Random numbers uniformly distributed in intervals; deltadIs the median value of the d-th dimension in the search space;
Figure BDA0002372172230000076
an opponent factor in the d dimension for the ith individual of the kth iteration; c. C1And c2Is a learning factor;
Figure BDA0002372172230000077
the dimension d is the upper limit value of the search space;x dis the d-dimension lower limit value of the search space;
Figure BDA0002372172230000078
for a preset maximum iterationThe number of times.
Preferably, step (4) comprises:
the positions of individuals in the current population are sorted according to fitness value, wherein the first a (a) is<m) individuals directly enter the population for the next iteration, and the rest m-a individuals adopt the self-adaptive variation operation to generate the variation individuals and the former a (a) individuals<m) individuals are used as the population of the next iteration; the self-adaptive variation mode is as follows:
Figure BDA0002372172230000079
the variation position of the ith individual in the d dimension for the k iteration, alpha is an individual subscript randomly selected from the population,
Figure BDA0002372172230000081
representing the position of the d-dimension of the alpha individual for the k-th iteration; phi is [ -0.5,0.5 [ ]]Random numbers uniformly distributed in intervals; elite is the set of the first three optimal individual positions obtained from the current population,
Figure BDA0002372172230000082
for the individual position in the d-dimension of the β -th individual for the kth iteration, β is a randomly selected individual subscript in the Elite.
Preferably, is prepared from
Figure BDA0002372172230000083
Returning individuals that are outside the boundary to within the boundary, wherein,
Figure BDA0002372172230000084
r1is [0,1 ]]Random numbers are evenly distributed in intervals.
According to another aspect of the present invention, there is provided a large-scale complementary scheduling system for water and light energy, comprising:
the initial population generation module is used for determining constraint conditions among power stations, wherein the power stations comprise hydropower stations and photovoltaic power stations, the ex-warehouse flow of each hydropower station at different moments is used as a decision variable and is coded, then an initial population is randomly generated in a search space according to the decision variable and is used as a current population, and any individual in the population represents a water-light energy complementary scheduling scheme;
the position updating module is used for acquiring the fitness of all individuals in the current population, updating the optimal positions of the individuals and the global optimal position in the current population according to the fitness value of each individual, and then updating the positions of all the individuals in the population; in the first iteration of the population, the optimal position of the individual refers to the position of the individual in the first iteration of the population, and in the second iteration and the previous iterations, the optimal position of the individual refers to the better position of the individual in the current iteration of the population and the position of the individual in the previous iteration; the global optimal position refers to the position of an optimal individual in the current iteration of the population;
the local search module is used for carrying out local search on the population by adopting a local search strategy based on the population obtained after updating all individual positions of the population so as to improve the convergence speed of the population;
the self-adaptive variation module is used for screening the population by adopting a self-adaptive variation strategy so as to improve the diversity of the population;
the next generation population generation module is used for returning individuals exceeding the boundary to the boundary range to form a next generation population based on the population obtained after the variation by adopting the variation strategy;
the scheduling scheme determining module is used for judging whether the algebra of the current population reaches the preset maximum iteration times, if not, taking the next generation population as the current population, and repeatedly executing the operation from the position updating module to the next generation population generating module; and if so, stopping calculation, and outputting the optimal individual corresponding to the global optimal position as an optimal scheme of the water-light energy complementary scheduling.
In general, compared with the prior art, the above technical solution contemplated by the present invention can achieve the following beneficial effects:
the method solves the problem of the combined system of the cascade hydropower station group and the photovoltaic power station, has simple principle, enhances the global search capability and effectively avoids the problem that the existing GSA algorithm is difficult to get rid of local optimum; a local search strategy is adopted to improve the population convergence precision so as to enhance the algorithm development capability; and the population diversity is improved by adopting self-adaptive variation operation. In conclusion, the method has the advantages of strong optimizing capability, difficulty in premature convergence, easiness in implementation and the like, and can obtain a satisfactory result in the cooperative scheduling of the cascade hydropower station and the photovoltaic power station system.
Drawings
Fig. 1 is a schematic flow chart of a large-scale water-light energy complementary scheduling method according to an embodiment of the present invention;
FIG. 2(a) is a box-type diagram of the cooperative scheduling result of the lower-grade power station and the photovoltaic power station in case 1-1 of the embodiment of the present invention;
FIG. 2(b) is a box-type diagram of the cooperative scheduling result of the lower-grade power station and the photovoltaic power station in case 1-2 of the embodiment of the present invention;
FIG. 2(c) is a box-type diagram of the cooperative dispatching result of the lower-grade power station and the photovoltaic power station in the embodiment 1-3 of the invention;
FIG. 2(d) is a box-type diagram of the cooperative scheduling result of the lower-stage power station and the photovoltaic power station in case 2-1 of the embodiment of the present invention;
FIG. 2(e) is a box-type diagram of the cooperative scheduling result of the lower-grade power station and the photovoltaic power station in case 2-2 of the embodiment of the present invention;
FIG. 2(f) is a box-type diagram of the cooperative scheduling result of the lower-grade power station and the photovoltaic power station in case 2-3 of the embodiment of the present invention;
FIG. 3(a) is a schematic diagram of the cascade power station and photovoltaic power station scheduling process of the method of the present invention in case 1-1;
FIG. 3(b) is a schematic diagram of the cascade power station and photovoltaic power station scheduling process of the method of the present invention in case 1-2;
fig. 3(c) is a diagram of the cascade power station and photovoltaic power station scheduling process of the method of the present invention under cases 1-3.
Detailed Description
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. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
In order to overcome the defects that a standard GSA method is difficult to get rid of local optimum and has weak easy development capability, the invention provides a large-scale water-light energy complementary scheduling method and a system. On the basis of a standard GSA method, a local search strategy is adopted to improve the population convergence speed; and the population diversity is improved by adopting self-adaptive variation operation. Has engineering practicability and feasibility.
Fig. 1 is a schematic flow chart of a large-scale water-light energy complementary scheduling method provided by an embodiment of the present invention, the method relates to cooperative optimal scheduling of a cascade reservoir group and a photovoltaic power station, and the specific steps include:
(1) constraints between power stations are determined, the power stations including hydropower stations and photovoltaic power stations. And selecting parameters required by calculation, taking the flow of each hydropower station discharged from the reservoir at different time intervals as decision variables, and coding. Let the number of iterations k be 1 and initialize all individuals in the population in the search space.
For any individual in the kth generation population
Figure BDA0002372172230000111
Can be expressed as
Figure BDA0002372172230000112
Wherein N represents the number of power stations; t represents the number of periods;
wherein the ith individual of the kth iteration
Figure BDA0002372172230000113
The initialization mode of the ex-warehouse flow of the nth hydropower station in the tth time period is as follows:
Figure BDA0002372172230000114
wherein,
Figure BDA0002372172230000115
is composed of
Figure BDA0002372172230000116
In the nth hydroelectric stationThe flow rate of the warehouse-out in the time period,
Figure BDA0002372172230000117
for the lower limit of the generating flow of the nth hydropower station in the t-th time period, rand (0,1) is [0,1 ]]Random numbers evenly distributed over the interval, k representing the number of iterations,
Figure BDA0002372172230000118
with N x T dimensions.
(2) Calculating the fitness of all individuals of the current population
Ith individual X of the k generationi(k) Fitness F [ X ] ofi(k)]Comprises the following steps:
Figure BDA0002372172230000121
where ρ issThe occurrence probability of the s photovoltaic power station is shown; s is the total number of probabilities,
Figure BDA0002372172230000122
Ltload demand for the power system at the tth time period; ps,m,tIs at a probability ρsThe output of the next mth photovoltaic power station in the t period; pn,tThe output of the nth hydropower station in the t period is obtained; m is the total number of photovoltaic power plants; n is the total number of hydropower stations; t is the total number of time periods; ga[Xi(k)]And caA constraint violation value and a penalty coefficient which are respectively an a-th inequality constraint; e.g. of the typeb[Xi(k)]And cbConstraint violation values and penalty coefficients for the b-th equation, respectively; a and B are the number of inequality constraints and equality constraints, respectively.
(3) And updating the global optimal position and the individual optimal position of the population according to the fitness.
In the first iteration of the population, the optimal position of the individual refers to the position of the individual in the first iteration of the population, and in the second iteration and the previous iterations, the optimal position of the individual refers to the better position of the individual in the current iteration of the population and the position of the individual in the previous iteration; the global optimal position refers to the position of the optimal individual in the current iteration of the population.
Specifically, from
Figure BDA0002372172230000123
Updating the global optimal position in the current population
Figure BDA0002372172230000124
Updating the optimal position of the individual in the current population; wherein gBest (k) is the global optimal position of the kth iteration of the population, and gBest (k) { gBest }d(k),d＝1,2...,D}，gBestd(k) The global optimum position of the kth iteration of the population in the d dimension, the global optimum position of the kth-1 iteration of the gBest (k-1) population,
Figure BDA0002372172230000131
Figure BDA0002372172230000132
the optimal position of the ith individual in the D dimension for the kth iteration, D is the maximum dimension of the ith individual, pBesti(k) For the individual optimal position, pBest, of the ith individual of the kth iteration of the populationi(k-1) is the individual optimal position of the ith individual in the k-1 iteration of the population.
(4)
By
Figure BDA0002372172230000133
Updating the positions of all individuals in the population, wherein,
Figure BDA0002372172230000134
Figure BDA0002372172230000135
Figure BDA0002372172230000136
Rij(k)＝||xi(k)-xj(k)||
Figure BDA0002372172230000137
wherein,
Figure BDA0002372172230000138
and
Figure BDA0002372172230000139
the ith individuals of the kth generation population and the (k + 1) th generation population are respectively positioned in the d-dimension,
Figure BDA00023721722300001310
the position of the ith individual in the jth dimension of the kth generation population; position of ith individual in kth iteration of population
Figure BDA00023721722300001311
Position of ith individual in population k +1 iteration
Figure BDA00023721722300001312
Figure BDA00023721722300001313
And
Figure BDA00023721722300001314
the speed of the ith individual in the d-dimension for the kth iteration and the (k + 1) th iteration respectively,
Figure BDA00023721722300001315
acceleration in d-dimension, rand, for the ith individual of the kth iterationjAnd randiIs [0,1 ]]Random numbers uniformly distributed among them; kbest is the first K individuals with better fitness;
Figure BDA0002372172230000141
is as followsThe worst fitness of all individuals in the iterative population for k times;
Figure BDA0002372172230000142
the optimal fitness of all individuals in the kth iteration population is obtained;
Figure BDA0002372172230000143
the force of the ith individual on the jth individual in the d-dimension; mpi(k) Is the passive mass of the ith individual, Maj(k) Is the active mass of the jth individual, Rij(k) Is the Euclidean distance, G, of the ith and jth individuals0Is the initial value of the universal gravitation constant, G (k) is the value of the universal gravitation constant for the kth iteration, alpha is the attenuation coefficient, and epsilon is a very small constant value.
(5) And (3) improving the population convergence rate by using a local search strategy, wherein the expression is as follows:
Figure BDA0002372172230000144
Figure BDA0002372172230000145
Figure BDA0002372172230000146
Figure BDA0002372172230000147
c2＝1-c1
in the formula: r is3And r4Is [0,1 ]]Random numbers are evenly distributed in intervals.
Figure BDA0002372172230000148
The local search position in the d-dimension for the ith individual for the kth iteration. DeltadIs the median value of the d-th dimension in the search space.
Figure BDA0002372172230000149
An opponent factor in the d dimension for the ith individual; c. C1And c2Is a learning factor;
Figure BDA00023721722300001410
the dimension d is the upper limit value of the search space;x dis the d-dimension lower limit value of the search space;
Figure BDA00023721722300001411
is a preset maximum number of iterations.
(5) Using a self-adaptive variation strategy to improve the diversity of the population, and sequencing the positions of individuals in the current population according to the fitness value, namely a (a)<m) individuals directly enter the population for the next iteration, and the rest m-a individuals adopt the self-adaptive variation operation to generate the variation individuals and the former a (a) individuals<m) individuals are used as the population of the next iteration; the self-adaptive variation mode is as follows:
Figure BDA0002372172230000151
Figure BDA0002372172230000152
the variation position of the ith individual in the d dimension for the k iteration, alpha is an individual subscript randomly selected from the population,
Figure BDA0002372172230000153
representing the position of the d-dimension of the alpha individual for the k-th iteration; phi is [ -0.5,0.5 [ ]]Random numbers uniformly distributed in intervals; elite is the set of the first three optimal individual positions obtained from the current population,
Figure BDA0002372172230000154
an individual position in the d-dimension for the β -th individual for the kth iteration, β being an individual subscript randomly selected from Elite;
(6) returning individuals beyond the boundary to be within the boundary range; the corresponding formula is:
Figure BDA0002372172230000155
Figure BDA0002372172230000156
in the formula: r is1Is [0,1 ]]Random numbers are evenly distributed in intervals. If the modified individuals remain outside the boundary, then the search space of the excess dimensions is generated randomly.
(7) Let k be k + 1. If it is
Figure BDA0002372172230000157
And (3) returning to the step (2), otherwise, stopping calculation, and taking the individual output corresponding to the global optimal position as an optimal scheme for cooperative scheduling of the cascade reservoir group and the photovoltaic power station system.
Figure BDA0002372172230000158
Is a preset maximum number of iterations.
The invention is further described below with reference to the figures and examples.
The invention takes five power stations of flood home crossing, east wind, gufengying, wujiang crossing and paper beach construction and five photovoltaic power stations on the Wujiang river main stream as implementation objects, and the corresponding parameters are set as follows: the population size is 30%,
Figure BDA0002372172230000159
Each constraint damage penalty coefficient is set to 1e 3. To verify the utility of the present invention, the present invention was compared with Particle Swarm Optimization (PSO), Differential Evolution (DE), Sine and Cosine Algorithm (SCA), Gray Wolf Optimization (GWO), and Gravity Search Algorithm (GSA).
Three optical energy inputs of four power grid load requirements are selected as implementation working conditions, table 1 shows statistical results of random operation for 10 times under six cases, and statistical results of maximum values, average values, worst values, standard deviations and range deviations are listed.
As can be seen from Table 1, the performance of the process of the invention is superior to the other processes for all the values listed. For example, the process of the present invention can be improved by about 99.5% and 99.3% over the target range, respectively, as compared to DE and PSO. Thus, the method of the present invention allows a good trade-off between development of the population and the exploratory power.
TABLE 1
Figure BDA0002372172230000161
Fig. 2(a) to 2(f) show the optimal solution distribution diagrams of the method of the invention and five other methods for six different cases, and it can be seen from the diagrams that the method of the invention has a smaller proportional distribution for the best solution so far and achieves the best performance among five statistical measures (maximum, mean, second or third quartile, median and minimum). Thus, in this case, the robustness of the inventive method is fully demonstrated.
Fig. 3(a) to 3(c) show the scheduling process diagrams of the cascaded power station and the photovoltaic power station of the method of the invention under three cases. It can be seen from the figure that the method of the present invention can obtain a relatively smooth residual load distribution curve. Thus, the solution presented by the method of the invention is illustrated as being superior to existing solutions.
In another embodiment of the present invention, there is also provided a large-scale complementary scheduling system for water and light energy, including:
the initial population generation module is used for determining constraint conditions among power stations, wherein the power stations comprise hydropower stations and photovoltaic power stations, the ex-warehouse flow of each hydropower station at different moments is used as a decision variable and is coded, then an initial population is randomly generated in a search space according to the decision variable and is used as a current population, and any individual in the population represents a water-light energy complementary scheduling scheme;
the position updating module is used for acquiring the fitness of all individuals in the current population, updating the optimal positions of the individuals and the global optimal position in the current population according to the fitness value of each individual, and then updating the positions of all the individuals in the population; in the first iteration of the population, the optimal position of the individual refers to the position of the individual in the first iteration of the population, and in the second iteration and the previous iterations, the optimal position of the individual refers to the better position of the individual in the current iteration of the population and the position of the individual in the previous iteration; the global optimal position refers to the position of an optimal individual in the current iteration of the population;
the local search module is used for carrying out local search on the population by adopting a local search strategy based on the population obtained after updating all individual positions of the population so as to improve the convergence speed of the population;
the self-adaptive variation module is used for screening the population by adopting a self-adaptive variation strategy so as to improve the diversity of the population;
the next generation population generation module is used for returning individuals exceeding the boundary to the boundary range to form a next generation population based on the population obtained after the variation by adopting the variation strategy;
the scheduling scheme determining module is used for judging whether the algebra of the current population reaches the preset maximum iteration times, if not, taking the next generation population as the current population, and repeatedly executing the operation from the position updating module to the next generation population generating module; and if so, stopping calculation, and outputting the optimal individual corresponding to the global optimal position as an optimal scheme of the water-light energy complementary scheduling.
The specific implementation of each module may refer to the description in the method embodiment, and the embodiment of the present invention will not be repeated.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (5)

1. A large-scale water-light energy complementary scheduling method is characterized by comprising the following steps:
(1) determining constraint conditions among power stations, wherein the power stations comprise hydropower stations and photovoltaic power stations, the ex-warehouse flow of each hydropower station at different moments is used as a decision variable and is coded, then an initial population is randomly generated in a search space according to the decision variable, the initial population is used as a current population, and any individual in the population represents a water-light energy complementary scheduling scheme;
(2) acquiring the fitness of all individuals in the current population, updating the optimal positions of the individuals and the global optimal position in the current population according to the fitness value of each individual, and then updating the positions of all the individuals in the population;
in the first iteration of the population, the optimal position of the individual refers to the position of the individual in the first iteration of the population, and in the second iteration and the previous iterations, the optimal position of the individual refers to the better position of the individual in the current iteration of the population and the position of the individual in the previous iteration; the global optimal position refers to the position of an optimal individual in the current iteration of the population;
(3) based on the population obtained after updating the positions of all individuals of the population, local search is carried out on the population by adopting a local search strategy so as to improve the convergence speed of the population;
(4) screening populations by adopting a self-adaptive variation strategy to improve the diversity of the populations;
(5) returning individuals exceeding the boundary to the boundary range to form a next generation population based on the population obtained after mutation by adopting a mutation strategy;
(6) judging whether the algebra of the current population reaches a preset maximum iteration number, if not, taking the next generation population as the current population, returning to the step (2), if so, stopping calculation, and outputting the optimal individual corresponding to the global optimal position as an optimal scheme of water-light energy complementary scheduling;
for any individual X in the kth generation populationi(k) Can be expressed as
Figure FDA0003521794370000011
Wherein N represents the number of power stations; t represents the number of periods;
Figure FDA0003521794370000012
Figure FDA0003521794370000013
is Xi(k) The flow out of the nth hydropower station in the t period,
Figure FDA0003521794370000021
for the lower limit of the generating flow of the nth hydropower station in the t-th time period, rand (0,1) is [0,1 ]]Random numbers with uniformly distributed intervals, k represents the number of iterations, Xi(k) Having N x T dimensions;
ith individual X of the k generationi(k) Fitness F [ X ] ofi(k)]Comprises the following steps:
Figure FDA0003521794370000022
where ρ issThe occurrence probability of the s photovoltaic power station is shown; s is the total number of probabilities,
Figure FDA0003521794370000023
Ltload demand for the power system at the tth time period; ps,m,tIs at a probability ρsThe output of the next mth photovoltaic power station in the t period; pn,tThe output of the nth hydropower station in the t period is obtained; m is the total number of photovoltaic power plants; n is the total number of hydropower stations; t is the total number of time periods; ga[Xi(k)]And caA constraint violation value and a penalty coefficient which are respectively an a-th inequality constraint; e.g. of the typeb[Xi(k)]And cbConstraint violation values and penalty coefficients for the b-th equation, respectively; a and B are the number of inequality constraints and equality constraints respectively;
by
Figure FDA0003521794370000024
Updating the global optimal position in the current population
Figure FDA0003521794370000025
Updating the optimal position of the individual in the current population; wherein gBest (k) is the global optimal position of the kth iteration of the population, and gBest (k) { gBest }d(k),d＝1,2...,D}，gBestd(k) The global optimum position of the kth iteration of the population in the d dimension, the global optimum position of the kth-1 iteration of the gBest (k-1) population,
Figure FDA0003521794370000026
Figure FDA0003521794370000027
the optimal position of the ith individual in the D dimension for the kth iteration, D is the maximum dimension of the ith individual, pBesti(k) For the individual optimal position, pBest, of the ith individual of the kth iteration of the populationi(k-1) the optimal position of the individual of the ith individual in the kth-1 iteration of the population;
by
Figure FDA0003521794370000031
Updating the positions of all individuals in the population, wherein,
Figure FDA0003521794370000032
Figure FDA0003521794370000033
Figure FDA0003521794370000034
Rij(k)＝||xi(k)-xj(k)||
Figure FDA0003521794370000035
wherein,
Figure FDA0003521794370000036
and
Figure FDA0003521794370000037
the ith individuals of the kth generation population and the (k + 1) th generation population are respectively positioned in the d-dimension,
Figure FDA0003521794370000038
the position of the ith individual in the jth dimension of the kth generation population; position of ith individual in kth iteration of population
Figure FDA0003521794370000039
Position of ith individual in population k +1 iteration
Figure FDA00035217943700000310
Figure FDA00035217943700000311
And
Figure FDA00035217943700000312
the speed of the ith individual in the d-dimension for the kth iteration and the (k + 1) th iteration respectively,
Figure FDA00035217943700000313
acceleration in d-dimension, rand, for the ith individual of the kth iterationjAnd randiIs [0,1 ]]Random numbers uniformly distributed among them; kbest is the first K individuals with better fitness;
Figure FDA00035217943700000314
the worst fitness of all individuals in the kth iteration population;
Figure FDA00035217943700000315
for the kth iteration populationThe optimal fitness of all individuals in the population;
Figure FDA00035217943700000316
the force of the ith individual on the jth individual in the d-dimension; mpi(k) Is the passive mass of the ith individual, Maj(k) Is the active mass of the jth individual, Rij(k) Is the Euclidean distance, G, of the ith and jth individuals0Is the initial value of the universal gravitation constant, G (k) is the value of the universal gravitation constant of the kth iteration, alpha is the attenuation coefficient, and epsilon is a constant value.
2. The method of claim 1, wherein the population is searched locally using the formula:
Figure FDA0003521794370000041
Figure FDA0003521794370000042
Figure FDA0003521794370000043
Figure FDA0003521794370000044
c2＝1-c1
in the formula,
Figure FDA0003521794370000045
local search position of ith individual in d dimension for k iteration; r is3And r4Is [0,1 ]]Random numbers uniformly distributed in intervals; deltadIs the median value of the d-th dimension in the search space;
Figure FDA0003521794370000046
an opponent factor in the d dimension for the ith individual of the kth iteration; c. C1And c2Is a learning factor;
Figure FDA0003521794370000047
the dimension d is the upper limit value of the search space;x dis the d-dimension lower limit value of the search space;
Figure FDA0003521794370000048
is a preset maximum number of iterations.
3. The method of claim 2, wherein step (4) comprises:
the positions of individuals in the current population are sorted according to fitness value, wherein the first a (a) is<m) individuals directly enter the population for the next iteration, and the rest m-a individuals adopt the self-adaptive variation operation to generate the variation individuals and the former a (a) individuals<m) individuals are used as the population of the next iteration; the self-adaptive variation mode is as follows:
Figure FDA0003521794370000049
Figure FDA00035217943700000410
the variation position of the ith individual in the d dimension for the k iteration, alpha is an individual subscript randomly selected from the population,
Figure FDA00035217943700000411
representing the position of the d-dimension of the alpha individual for the k-th iteration; phi is [ -0.5,0.5 [ ]]Random numbers uniformly distributed in intervals; elite is the set of the first three optimal individual positions obtained from the current population,
Figure FDA00035217943700000412
for the individual position in the d-dimension of the β -th individual for the kth iteration, β is a randomly selected individual subscript in the Elite.
4. The method of claim 3, wherein the method is performed by
Figure FDA00035217943700000413
Returning individuals that are outside the boundary to within the boundary, wherein,
Figure FDA0003521794370000051
r1is [0,1 ]]Random numbers are evenly distributed in intervals.
5. A large-scale water-light energy complementary scheduling system is characterized by comprising:
the initial population generation module is used for determining constraint conditions among power stations, wherein the power stations comprise hydropower stations and photovoltaic power stations, the ex-warehouse flow of each hydropower station at different moments is used as a decision variable and is coded, then an initial population is randomly generated in a search space according to the decision variable and is used as a current population, and any individual in the population represents a water-light energy complementary scheduling scheme;
the position updating module is used for acquiring the fitness of all individuals in the current population, updating the optimal positions of the individuals and the global optimal position in the current population according to the fitness value of each individual, and then updating the positions of all the individuals in the population; in the first iteration of the population, the optimal position of the individual refers to the position of the individual in the first iteration of the population, and in the second iteration and the previous iterations, the optimal position of the individual refers to the better position of the individual in the current iteration of the population and the position of the individual in the previous iteration; the global optimal position refers to the position of an optimal individual in the current iteration of the population;
the local search module is used for carrying out local search on the population by adopting a local search strategy based on the population obtained after updating all individual positions of the population so as to improve the convergence speed of the population;
the self-adaptive variation module is used for screening the population by adopting a self-adaptive variation strategy so as to improve the diversity of the population;
the next generation population generation module is used for returning individuals exceeding the boundary to the boundary range to form a next generation population based on the population obtained after the variation by adopting the variation strategy;
the scheduling scheme determining module is used for judging whether the algebra of the current population reaches the preset maximum iteration times, if not, taking the next generation population as the current population, and repeatedly executing the operation from the position updating module to the next generation population generating module; if so, stopping calculation, and outputting the optimal individual corresponding to the global optimal position as an optimal scheme of the water-light energy complementary scheduling;
for any individual X in the kth generation populationi(k) Can be expressed as
Figure FDA0003521794370000061
Wherein N represents the number of power stations; t represents the number of periods;
Figure FDA0003521794370000062
Figure FDA0003521794370000063
is Xi(k) The flow out of the nth hydropower station in the t period,
Figure FDA0003521794370000064
for the lower limit of the generated flow of the nth hydropower station in the t-th period,
Figure FDA0003521794370000065
for the upper limit of the generating flow of the nth hydropower station in the t-th time period, rand (0,1) is [0,1 ]]Random numbers with uniformly distributed intervals, k represents the number of iterations, Xi(k) Having N x T dimensions
Ith individual X of the k generationi(k) Fitness F [ X ] ofi(k)]Comprises the following steps:
Figure FDA0003521794370000066
where ρ issThe occurrence probability of the s photovoltaic power station is shown; s is the total number of probabilities,
Figure FDA0003521794370000067
Ltload demand for the power system at the tth time period; ps,m,tIs at a probability ρsThe output of the next mth photovoltaic power station in the t period; pn,tThe output of the nth hydropower station in the t period is obtained; m is the total number of photovoltaic power plants; n is the total number of hydropower stations; t is the total number of time periods; ga[Xi(k)]And caA constraint violation value and a penalty coefficient which are respectively an a-th inequality constraint; e.g. of the typeb[Xi(k)]And cbConstraint violation values and penalty coefficients for the b-th equation, respectively; a and B are the number of inequality constraints and equality constraints respectively;
by
Figure FDA0003521794370000068
Updating the global optimal position in the current population
Figure FDA0003521794370000069
Updating the optimal position of the individual in the current population; wherein gBest (k) is the global optimal position of the kth iteration of the population, and gBest (k) { gBest }d(k),d＝1,2...,D}，gBestd(k) The global optimum position of the kth iteration of the population in the d dimension, the global optimum position of the kth-1 iteration of the gBest (k-1) population,
Figure FDA0003521794370000071
Figure FDA0003521794370000072
the optimal position of the ith individual in the D dimension for the kth iteration, D is the maximum dimension of the ith individual, pBesti(k) For the individual optimal position, pBest, of the ith individual of the kth iteration of the populationi(k-1) isThe optimal position of the individual of the ith individual in the kth-1 iteration of the population;
by
Figure FDA0003521794370000073
Updating the positions of all individuals in the population, wherein,
Figure FDA0003521794370000074
Figure FDA0003521794370000075
Figure FDA0003521794370000076
Rij(k)＝||xi(k)-xj(k)||
Figure FDA0003521794370000077
wherein,
Figure FDA0003521794370000078
and
Figure FDA0003521794370000079
the ith individuals of the kth generation population and the (k + 1) th generation population are respectively positioned in the d-dimension,
Figure FDA00035217943700000710
the position of the ith individual in the jth dimension of the kth generation population; position of ith individual in kth iteration of population
Figure FDA00035217943700000711
Position of ith individual in population k +1 iteration
Figure FDA00035217943700000712
Figure FDA00035217943700000713
And
Figure FDA00035217943700000714
the speed of the ith individual in the d-dimension for the kth iteration and the (k + 1) th iteration respectively,
Figure FDA00035217943700000715
acceleration in d-dimension, rand, for the ith individual of the kth iterationjAnd randiIs [0,1 ]]Random numbers uniformly distributed among them; kbest is the first K individuals with better fitness;
Figure FDA00035217943700000716
the worst fitness of all individuals in the kth iteration population;
Figure FDA00035217943700000717
the optimal fitness of all individuals in the kth iteration population is obtained;
Figure FDA00035217943700000718
the force of the ith individual on the jth individual in the d-dimension; mpi(k) Is the passive mass of the ith individual, Maj(k) Is the active mass of the jth individual, Rij(k) Is the Euclidean distance, G, of the ith and jth individuals0Is the initial value of the universal gravitation constant, G (k) is the value of the universal gravitation constant of the kth iteration, alpha is the attenuation coefficient, and epsilon is a constant value.
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