CN117610828A - Step-size dense-by-dense multi-target cascade hydropower station group optimal scheduling method - Google Patents
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Abstract
The invention discloses a step-by-step dense multi-target step hydropower station group optimal scheduling method, which comprises the following steps: s1, constructing a long-term multi-objective optimal scheduling model in a huge cascade reservoir group; s2, optimizing the model by adopting a step-size secret-by-secret strategy; according to the method, the step-by-step secret-by-secret strategy is introduced, so that the optimal scheduling solution of the large-scale cascade hydropower station group is realized, the solution efficiency and the solution precision of the medium-long-term scheduling problem of the giant cascade reservoir group are effectively improved, and an efficient solution scheme is provided for the long-term multi-objective optimal scheduling problem of the giant cascade hydropower station group.
Description
Technical Field
The invention relates to the technical field of medium-and-long-term optimal scheduling of cascade hydropower stations, in particular to a step-size dense-by-step multi-target cascade hydropower station optimal scheduling method.
Background
The water and electricity in China are mainly concentrated in large-scale areas in southwest areas, the large-scale cascade reservoir groups planned or built in the areas usually bear the tasks of large-scale, long-distance and cross-area power transmission in multi-province cities, the important tasks of electric power and electric quantity balance of a plurality of electric networks, peak regulation, frequency modulation and the like are needed to be borne, the influence on safe and stable operation of the electric networks is remarkable, meanwhile, the cascade reservoir operation is also related to a plurality of important problems of flood control, water supply, shipping, ecology, environment and the like on two sides of a river, and the comprehensive utilization requirement of the cascade hydropower station group is needed to be considered. Therefore, the dispatching management relationship of the giant cascade reservoir is very complex, and the requirement on the dispatching refinement degree is extremely high. And secondly, the hydrodynamics of the river basin under the condition of the production of a new power station also changes, the regulation performance of the steps, the guarantee output and the existing medium-long running index can be obviously changed, so that the long-term optimal scheduling in the reservoir group is more difficult, and the running water level feasible region of the step reservoir group under the complex and refined scheduling requirement needs to be re-excavated. Therefore, the research on the high-efficiency operation technology of the huge cascade reservoir group is an urgent need for developing new situations of hydropower in China.
The problem faced by long-term optimization scheduling in a huge cascade reservoir group with an oversized river basin is mainly the problem that the solution is difficult due to complex multi-objective problem modeling and complex constraint conditions. The main expression is as follows: (1) the comprehensive utilization requirement is very complex, and the problems are difficult to model due to the fact that the comprehensive utilization requirement relates to various aspects of power generation, navigation, flood control, ecology, environment and the like; (2) the restriction is very complex, besides the hydraulic restriction among the cascade power stations, various comprehensive utilization restrictions and special operation requirements of a certain or certain power stations are also provided, in addition, the characteristic of large-scale power transmission of the cascade hydropower station group also needs to consider the power transmission restriction of each subarea output restriction, the safety and stability restriction of the power grid and the power transmission restriction of cross-regional power transmission, thereby exacerbating the problem solving difficulty. (3) The number of the cascade power stations is huge, the precision requirement of a scheduling period is high, and a large number of complex constraints of high dimension, strong coupling and nonlinearity lead to difficult problem solving. Along with the comprehensive production of numerous huge cascade reservoir groups in China, the method provides a problem to be solved for each link of the huge cascade reservoir group optimal scheduling, wherein the improvement of the huge cascade hydropower station group optimal scheduling solving efficiency under the complex constraint condition is one of the problems to be solved by the river basin power generation group.
Disclosure of Invention
The invention aims to overcome the defects and provide a step-by-step dense multi-target step hydropower station group optimal scheduling method, so as to solve the problems in the background technology.
The invention aims to solve the technical problems, and adopts the technical scheme that: a step-size dense-by-dense multi-target cascade hydropower station group optimization scheduling method comprises the following steps:
s1, constructing a long-term multi-objective optimal scheduling model in a huge cascade reservoir group;
s2, optimizing the model by adopting a step-size secret-by-secret strategy.
Further, the step S1 specifically includes:
s1.1, taking two targets of maximum generated energy and minimum water discarding amount as objective functions to ensure the economic benefit of the step system and reduce the water discarding risk of the system:
wherein T represents the number of scheduling periods; m represents the number of step power stations; a is that m，t The output coefficient of the power station m in the period t is represented; q (Q) m，t Represents the power generation flow of the power station m in the period t, m 3 /s；H m，t Represents the water purification head of the power station m in the period t, m; qs m，t Represents the reject flow of the power station m in the period t, m 3 S; Δt represents the period length, s;
s1.2, setting corresponding hydraulic and electric constraints according to the characteristics of reservoirs and hydropower stations.
Further, the hydraulic and electric constraints are as follows:
(1) Water level constraint:
wherein Z is m，t 、 Z m，t Respectively representing the water level and the upper and lower limits of the power station m in the t period, and m;
(2) Power station output constraint:
wherein P is m，t 、 P m，t Respectively representing the output of the power station m in the t period and the upper limit and the lower limit thereof, MW;
(3) And (3) constraint of storage capacity:
wherein V is m，t 、V m，t 、Respectively represent the storage capacity of the power station m in the t period and the upper limit and the lower limit thereof, m 3 ；
(4) Generating flow constraint:
in which Q m，t 、Q m，t 、Respectively representing the power generation flow and the upper and lower limits thereof of the power station m in the t period, m 3 /s；
(5) Water balance constraint:
V m，t+1 ＝V m，t +(R m，t -Q m，t -Qs m，t )·Δt (7)
wherein V is m，t 、V m，t+1 Respectively represents the initial and final storage capacity of the power station m in the t period, m 3 ；R m，t 、Qs m，t Respectively representing the warehouse-in flow and the reject flow of the power station m in the t period, m 3 /s；
(6) Leakage flow constraint:
S m，t ＝Q m，t +Qs m，t (9)
wherein S is m，t 、 S m，t Respectively represent the lower leakage flow and the upper and lower limits thereof of the power station m in the t period, and m 3 S; the discharging flow consists of two parts, namely power generation flow and waste water flow;
(7) Start-end water level control constraint:
in the method, in the process of the invention,respectively represent the initial water level control value and period of the reservoir mThe telescope water level, m;
(8) Water level fluctuation constraint:
in the method, in the process of the invention,representing the maximum water level fluctuation limit of a power station m in a single period, and m; the constraint limits the water level amplitude of the power station between adjacent time periods, and the water level amplitude is determined by the power station according to navigation and comprehensive operation requirements;
(9) Delivery flow fluctuation constraint:
in the method, in the process of the invention,representing the maximum delivery flow fluctuation limit of a power station m single period, m 3 S; the constraint limits the delivery flow amplitude of the power station between adjacent time periods, and the delivery flow amplitude is determined by the power station according to navigation and comprehensive operation requirements;
(10) Force climbing constraint:
in the method, in the process of the invention,representing the maximum output lifting limit and MW of the power station m in a single period;
(11) Hydropower station output fluctuation limit:
(P m，t-Δ+1 -P m，t-Δ )(P m，t -P m，t-1 )≥0 (15)
wherein Δ=1, 2, …, t min ，t min Representing the minimum interval period number of the m output rise and fall of the power station; the constraint ensures the operation safety of the power grid and the unit by limiting the frequent fluctuation of the output of the power station between adjacent time periodsAll of them.
Further, the step S2 specifically includes the following steps:
s2.1: setting the step length of a model scheduling period to be solved as n times of a target step length, namely, changing the length to nDeltat, shortening the number of scheduling periods to be 1/n of the original number, synchronously reducing the variable dimension of the model, and reducing T to 1, n+1,2n+1, T, wherein the single solving efficiency can be greatly improved;
s2.2: solving the model by adopting an NSGA-III algorithm, and enabling the model to quickly converge in a smaller dimension to obtain a local optimal solution of the model under the condition of a larger step length;
s2.3: linearly expanding the result of the large step length into an initial solution calculated by the small step length according to the principle of equal flow or uniform water level lifting, namely uniformly lifting a variable corresponding to the small step length in the large step length;
s2.4: substituting the generated initial solution into a model, and solving by adopting an NSGA-III algorithm, wherein the better initial solution can guide the evolution direction and improve the evolution effect;
s2.5: and repeating the step S2.3 and the step S2.4 until the step length meets the requirement.
Further, the NSGA-III algorithm solving process is specifically as follows:
(1) Initialization of
Setting NSGA-III algorithm and calculation parameters including population scale, maximum evolution algebra and genetic probability;
(2) Determining an initial population of large steps
Dividing calculation time periods by larger step length, and generating a series of individuals meeting water level constraint in a water level operation range;
(3) Initial solution correction
Because of a plurality of time coupling constraints in the model, the change of decision variables in any period can cause the damage of constraint conditions in adjacent periods, and genetic operations such as population selection, crossing, variation and the like are performed among infeasible solutions in solving, so that population diversity is easily lost quickly; therefore, the constraint adjustment strategy is adopted to process complex time coupling constraints, and the method is operated as follows:
and (5) regulating the force climbing limit:
when the limit constraint of the output climbing is destroyed, the output of the associated time period needs to be regulated, the basic principle of regulation is to keep the total electric quantity of all the regulating time periods unchanged, the initial search is initiated by the t=1 time period, and whether the limit constraint of climbing is destroyed is judged from time period to time period at the end of the dispatching period; if it isThen the continuous climbing period interval [ j+1, t+1 ] is reversely searched out]Length is defined as L; the output difference value of adjacent time periods is equal to the climbing upper limit as an adjustment target, and the output increment of the continuous climbing time period is determined to beAnd adjusting the output of each period of continuous climbing according to a formula (16); then, continuing the backward search until the end;
force fluctuation limit adjustment:
the constraint damage of the output fluctuation control is generalized into two forms, namely a convex form and a concave form, which are respectively expressed as inconsistent output change trend in the adjacent time period within a specified duration; correcting the output of the related period in an equal proportion mode, and ensuring that the output lifting change meets the minimum duration requirement; output P for 3 periods of time m,t 、P m,t+1 、P m,t+2 The corresponding correction amounts are:
thereby realizing uniform fluctuation of the corrected output;
correcting part of non-feasible individuals through the operation, and improving the number of feasible solutions;
(4) Fitness ranking
Calculating individual fitness according to the generating capacity target and the water discarding target respectively, judging individual dominance relation and carrying out hierarchical sequencing; considering the complexity of the problem, the dominant relationship of the two bodies is determined by adopting the following method: (1) if both are feasible solutions; determining a dominance relation according to the individual fitness; (2) if the feasible solution and the infeasible solution are included at the same time, the feasible solution is dominant; (3) if the constraint damage degree is equal to the constraint damage degree, determining a dominant relationship at random;
(5) Genetic manipulation
Sequentially selecting, crossing and mutating to obtain a new generation sub population;
(6) Offspring individual correction
The individuals with the offspring having constraint damage are corrected by adopting the method in the step (3);
(7) Generating the next generation
Combining the parent population and the child population, respectively carrying out non-dominant hierarchical sorting and crowding distance calculation, and selecting the individuals in front according to the set population scale to form a new population;
(8) Loop computation
Iterating the steps (5) - (7) circularly until reaching the termination condition;
(9) Determining initial population of small step size
Expanding the solution line shape of the large step length obtained by the calculation into an initial solution of the small step length calculation;
(10) Loop computation
Similar to the calculation process of the large step size, the operations of steps (3) to (8) are carried out on the population with the small step size;
(11) Outputting Pareto solution sets
And solving the model according to the steps.
The invention has the beneficial effects that:
1. according to the method, the step-by-step secret-by-secret strategy is introduced, so that the optimal scheduling solution of the large-scale cascade hydropower station group is realized, the solution efficiency and the solution precision of the medium-long-term scheduling problem of the giant cascade reservoir group are effectively improved, and an efficient solution scheme is provided for the long-term multi-objective optimal scheduling problem of the giant cascade hydropower station group.
2. The invention solves the problems of complex constraint processing, multi-objective construction, quick model solving and the like in the long-term optimal scheduling of the giant cascade hydropower station group, constructs a long-term multi-objective optimal scheduling model of the giant cascade reservoir group according to the scheduling operation characteristics of the cascade hydropower station group and the complex requirements of comprehensive utilization of water resources, optimizes the model by adopting a non-dominant ordered genetic algorithm (NSGA-III) based on a reference point and a solution time step secret-by-secret strategy, improves the calculation precision and the solution efficiency of the model based on a solution time step secret strategy, and finally outputs a Pareto solution set meeting the requirements, thereby providing reasonable and reliable decision support for actual scheduling operation.
3. According to the invention, two targets of maximum long-term power generation capacity and minimum water discarding capacity in the giant cascade reservoir group are constructed as objective functions, so that the economic benefit of a cascade system is ensured, and the water discarding risk of the system is reduced; secondly, solving the model by adopting a non-dominant ordered genetic algorithm (NSGA-III) which has the best calculation effect at present and is most widely applied and is based on reference points; finally, aiming at the situation that the calculation result is possibly infeasible or falls into local optimum when the solution time period of the method is more, based on a step-by-step secret-by-secret strategy, the local optimum solution is found by optimizing in a smaller optimizing space with a larger step; then encrypting the step length, substituting the solution as an initial solution into a smaller step length model to improve the precision, so that the step length is encrypted step by step, and optimizing for multiple times to improve the calculation efficiency; the method can realize the optimal scheduling solution of the large-scale cascade hydropower station group, and effectively improve the solution efficiency and the solution precision of the medium-long term scheduling problem of the giant cascade reservoir group.
4. The solving method is improved from two aspects of an evolutionary algorithm and a multi-objective mechanism, has the capability of obtaining a non-inferior scheduling scheme set with better convergence and distribution, and plays a vital role in realizing the maximization of the comprehensive benefit of the whole cascade reservoir group.
Drawings
FIG. 1 is a flow chart of optimal scheduling of a multi-target cascade hydropower station group based on time interval density by time interval density;
FIG. 2 is a graph comparing computation time and Pareto front results at different evolutionary algebra;
FIG. 3 is a diagram of the end water level process of each reservoir period for a single-step growth 2000 Pareto solution set;
FIG. 4 is a graph of single step growth 2000 Pareto front calculation results;
FIG. 5 is a graph comparing the power generation of each plant;
FIG. 6 is a comparison graph of the water reject from each plant;
fig. 7 is a Pareto solution set contrast graph for each scenario.
Detailed Description
The invention is described in further detail below with reference to the drawings and the specific examples.
As shown in FIG. 1, the step-by-step dense multi-target step hydropower station group optimal scheduling method comprises the following steps:
s1, constructing a long-term multi-objective optimal scheduling model in a huge cascade reservoir group;
s2, optimizing the model by adopting a step-size secret-by-secret strategy.
Further, the step S1 specifically includes:
s1.1, taking two targets of maximum generated energy and minimum water discarding amount as objective functions to ensure the economic benefit of the step system and reduce the water discarding risk of the system:
wherein T represents the number of scheduling periods; m represents the number of step power stations; a is that m，t The output coefficient of the power station m in the period t is represented; q (Q) m，t Represents the power generation flow of the power station m in the period t, m 3 /s；H m，t Represents the water purification head of the power station m in the period t, m; qs m，t Represents the reject flow of the power station m in the period t, m 3 S; Δt represents the period length, s;
s1.2, setting corresponding hydraulic and electric constraints according to the characteristics of reservoirs and hydropower stations.
Further, the hydraulic and electric constraints are as follows:
(1) Water level constraint:
wherein Z is m，t 、 Z m，t Respectively representing the water level and the upper and lower limits of the power station m in the t period, and m;
(2) Power station output constraint:
wherein P is m，t 、 P m，t Respectively representing the output of the power station m in the t period and the upper limit and the lower limit thereof, MW;
(3) And (3) constraint of storage capacity:
wherein V is m，t 、V m，t 、Respectively represent the storage capacity of the power station m in the t period and the upper limit and the lower limit thereof, m 3 ；
(4) Generating flow constraint:
in which Q m，t 、Q m，t 、Separate tableShows the power generation flow of the power station m in the t period and the upper limit and the lower limit thereof, m 3 /s；
(5) Water balance constraint:
V m，t+1 ＝V m，t +(R m，t -Q m，t -Qs m，t )·Δt (7)
wherein V is m，t 、V m，t+1 Respectively represents the initial and final storage capacity of the power station m in the t period, m 3 ；R m，t 、Qs m，t Respectively representing the warehouse-in flow and the reject flow of the power station m in the t period, m 3 /s；
(6) Leakage flow constraint:
S m，t ＝Q m，t +Qs m，t (9)
wherein S is m，t 、 S m，t Respectively represent the lower leakage flow and the upper and lower limits thereof of the power station m in the t period, and m 3 S; the discharging flow consists of two parts, namely power generation flow and waste water flow;
(7) Start-end water level control constraint:
in the method, in the process of the invention,respectively representing an initial water level control value and an expected final water level of the reservoir m;
(8) Water level fluctuation constraint:
in the method, in the process of the invention,representing the maximum water level fluctuation limit of a power station m in a single period, and m; the constraint limits the water level amplitude of the power station between adjacent time periods, and the water level amplitude is determined by the power station according to navigation and comprehensive operation requirements;
(9) Delivery flow fluctuation constraint:
in the method, in the process of the invention,representing the maximum delivery flow fluctuation limit of a power station m single period, m 3 S; the constraint limits the delivery flow amplitude of the power station between adjacent time periods, and the delivery flow amplitude is determined by the power station according to navigation and comprehensive operation requirements;
(10) Force climbing constraint:
in the method, in the process of the invention,representing the maximum output lifting limit and MW of the power station m in a single period;
(11) Hydropower station output fluctuation limit:
(P m，t-Δ+1 -P m，t-Δ )(P m，t -P m，t-1 )≥0 (15)
wherein Δ=1, 2, …, t min ，t min Representing the minimum interval period number of the m output rise and fall of the power station; the constraint ensures the operation safety of the power grid and the unit by limiting the frequent fluctuation of the output of the power station between adjacent time intervals.
Further, the step S2 specifically includes the following steps:
s2.1: setting the step length of a model scheduling period to be solved as n times of a target step length, namely, changing the length to nDeltat, shortening the number of scheduling periods to be 1/n of the original number, synchronously reducing the variable dimension of the model, and reducing T to 1, n+1,2n+1, T, wherein the single solving efficiency can be greatly improved;
s2.2: solving the model by adopting an NSGA-III algorithm, and enabling the model to quickly converge in a smaller dimension to obtain a local optimal solution of the model under the condition of a larger step length;
s2.3: linearly expanding the result of the large step length into an initial solution calculated by the small step length according to the principle of equal flow or uniform water level lifting, namely uniformly lifting a variable corresponding to the small step length in the large step length;
s2.4: substituting the generated initial solution into a model, and solving by adopting an NSGA-III algorithm, wherein the better initial solution can guide the evolution direction and improve the evolution effect;
s2.5: and repeating the step S2.3 and the step S2.4 until the step length meets the requirement.
Further, the NSGA-III algorithm solving process is specifically as follows:
(1) Initialization of
Setting NSGA-III algorithm and calculation parameters including population scale, maximum evolution algebra and genetic probability;
(2) Determining an initial population of large steps
Dividing calculation time periods by larger step length, and generating a series of individuals meeting water level constraint in a water level operation range;
(3) Initial solution correction
Because of a plurality of time coupling constraints in the model, the change of decision variables in any period can cause the damage of constraint conditions in adjacent periods, and genetic operations such as population selection, crossing, variation and the like are performed among infeasible solutions in solving, so that population diversity is easily lost quickly; therefore, the constraint adjustment strategy is adopted to process complex time coupling constraints, and the method is operated as follows:
and (5) regulating the force climbing limit:
when the limit constraint of the output climbing is destroyed, the output of the associated period is required to be adjustedThe whole basic principle is to keep the total electric quantity of all adjustment periods unchanged, initiate initial search by t=1 period, and judge whether climbing constraint is broken or not from period to period at the end of a scheduling period; if it isThen the continuous climbing period interval [ j+1, t+1 ] is reversely searched out]Length is defined as L; the output difference value of adjacent time periods is equal to the climbing upper limit as an adjustment target, and the output increment of the continuous climbing time period is determined to beAnd adjusting the output of each period of continuous climbing according to a formula (16); then, continuing the backward search until the end;
force fluctuation limit adjustment:
the constraint damage of the output fluctuation control is generalized into two forms, namely a convex form and a concave form, which are respectively expressed as inconsistent output change trend in the adjacent time period within a specified duration; correcting the output of the related period in an equal proportion mode, and ensuring that the output lifting change meets the minimum duration requirement; output P for 3 periods of time m，t 、P m，t+1 、P m，t+2 The corresponding correction amounts are:
thereby realizing uniform fluctuation of the corrected output;
correcting part of non-feasible individuals through the operation, and improving the number of feasible solutions;
(4) Fitness ranking
Calculating individual fitness according to the generating capacity target and the water discarding target respectively, judging individual dominance relation and carrying out hierarchical sequencing; considering the complexity of the problem, the dominant relationship of the two bodies is determined by adopting the following method: (1) if both are feasible solutions; determining a dominance relation according to the individual fitness; (2) if the feasible solution and the infeasible solution are included at the same time, the feasible solution is dominant; (3) if the constraint damage degree is equal to the constraint damage degree, determining a dominant relationship at random;
(5) Genetic manipulation
Sequentially selecting, crossing and mutating to obtain a new generation sub population;
(6) Offspring individual correction
The individuals with the offspring having constraint damage are corrected by adopting the method in the step (3);
(7) Generating the next generation
Combining the parent population and the child population, respectively carrying out non-dominant hierarchical sorting and crowding distance calculation, and selecting the individuals in front according to the set population scale to form a new population;
(8) Loop computation
Iterating the steps (5) - (7) circularly until reaching the termination condition;
(9) Determining initial population of small step size
Expanding the solution line shape of the large step length obtained by the calculation into an initial solution of the small step length calculation;
(10) Loop computation
Similar to the calculation process of the large step size, the operations of steps (3) to (8) are carried out on the population with the small step size;
(11) Outputting Pareto solution sets
And solving the model according to the steps.
The specific application of the method of the invention is as follows:
(1) Engineering background and parameter selection
In the embodiment, the reservoir group from the gold lower part to the three gorges step in the Yangtze river basin of China is selected as a research object. The final unit of the white crane beach in 2022 is formally put into production to generate electricity, which marks that a six-reservoir giant step reservoir taking three gorges as the core is fully built. As a global installed scale and a cascade reservoir group with generated energy at the first place in the world, the method plays an important role in optimizing an energy structure, maintaining safe and stable operation of a power grid, and preventing flood and navigation. Therefore, the method has important significance in researching the characteristics of the reservoir group scheduling in the subgold-three gorges cascade, taking the comprehensive utilization target into consideration, establishing a reasonable long-term multi-target power generation optimal scheduling model in the reservoir group, and seeking an efficient solving method.
In the embodiment, ten days are taken as a calculation period, the year is taken as a calculation period, the population scale is set to be 500, the under-the-gold-three gorges step scheduling process is calculated, the test environment is a Windows 10 operating system, and the CPU: intel i7-11700f 8 core 16 threads, memory: 32GB; the test was performed in a Python 3.8 environment.
(2) Analysis of the results of the calculation
(2.1) algebraic evolution determination
In order to determine reasonable evolution algebra, the evolution algebra is respectively set to be 500, 1000, 1500, 2000 and 3000 generations for evolution, a Pareto solution set under each evolution algebra and a solution set obtained by adopting the traditional POA method for calculation are shown in a figure 2, wherein 'X' in the figure represents the POA method calculation result, and 'term' represents the Pareto solution set of the model provided by the invention. From the graph, as the evolution algebra increases from 500 generations to 1500 generations, the total power generation amount of the system is rapidly increased, and the water discarding amount is greatly reduced. When the evolution algebra is more than or equal to 1500 generations, the calculation result tends to be stable, the average power generation amount of the Pareto solution set obtained at the moment is equal to the POA calculation result, and the water discarding amount is obviously less than the POA calculation result; when evolving to 2000 generations, the average power generation of the Pareto solution set is improved by about 20 hundred million kWh compared with that of 1500 generations, and the improvement ratio is about 0.6%. From generation 2000 to generation 3000, the calculation time is increased to 823s, and the average power generation amount and the water discarding amount of the pareto solution set are not obviously changed. From the calculation efficiency and the requirement of the result, the evolution reaches 2000 generations to obtain better results.
(2.2) Single step Long Serial computing
Fig. 3 shows the Pareto solution set for each reservoir last water level process obtained by the 2000 generation of ten-day step evolution (starting from the last ten days of 1 month). According to the graph, power stations such as Wu Dongde, white crane beaches, stream ferry and Sanxia are compensated in the dead period, the output requirement of a system is met, the water level is gradually reduced before the flood season, the storage capacity is vacated, the flood control requirement in the flood season is met, the water level of the water storage is controlled to be at the flood limit water level in the flood season, the water head is gradually raised at the tail of the flood season, and the water is gradually stored to the normal high water level.
The Pareto front obtained by the step evolution of 2000 generations in ten days is shown in fig. 4, and the generated energy and the discarded water quantity of each power station are shown in fig. 5 and 6 (the 'X' in fig. 3, 4 and 5 represents the calculation result of the traditional POA method, and the 'term' represents the solution in the Pareto solution set obtained by the model provided by the invention). According to the example calculation result, compared with the result of the traditional optimal scheduling system, the Wu Dongde and white crane beach electric quantity obtained by the traditional POA optimal scheduling system is higher, but the electric quantity of the Xilong and Sanxia is lower than the calculation result of the model provided by the invention, because the result obtained by the algorithm provided by the invention can increase the down flow of Wu Dongde at the initial period of the period of time, and the water levels of Wu Dongde and white crane beaches are reduced, so that the water levels of the Xilong and Sanxia are improved, and the overall benefit is improved. As can be seen from the Pareto front calculation result in FIG. 2, the electric quantity obtained by the conventional optimized scheduling calculation is about 3246 hundred million kWh, and the water reject quantity is about 555 hundred million m 3 The electric quantity corresponding to the Pareto front obtained by the method is 3260-3275 hundred million kWh, and is improved by 10-20 hundred million kWh compared with the traditional optimized scheduling electric quantity; the corresponding water discarding amount is 150-200 hundred million m 3 Compared with the traditional optimized scheduling, the water discarding amount is 350-400 hundred million m less 3 . Detailed analysis of the reject volume is shown in fig. 6, it can be seen that the reject volume of each power station in the method provided by the invention is smaller than the reject volume of the conventional optimized scheduling, and particularly the reject volume of Ge Zhouba is greatly reduced. The rationality of the model calculations presented herein is demonstrated by the comparative analysis described above.
(2.3) step-by-step secret-by-secret policy calculation
In order to illustrate the effectiveness of the step-size encryption policy, 6 calculation schemes are set, wherein schemes 1 to 4 are fixed step-size schemes, and schemes 5 to 6 are step-size encryption schemes, and the steps are as follows in detail:
scheme 1: and calculating 1500 generations according to the step length of the step length determining method.
Scheme 2: and calculating 2000 generations according to the step length of the step length determining method.
Scheme 3: and calculating 2000 generations according to the step length by a step length determining method.
Scheme 4: and calculating 2000 generations according to the step length of 2 months by a step length determining method.
Scheme 5: the step size encryption method is that step sizes are set to be 1 month (3 delta t) and 1 ten days (delta t) and respectively evolved for 1000 generations and 1000 generations (which is equivalent to 2000 generations of total evolution algebra).
Scheme 6: the step-by-step secret-by-secret method is characterized in that the step length is set to be 2 months (6Deltat), 1 month (3Deltat) and 1 ten days (Deltat), and the evolution algebra of various step lengths is respectively as follows: 500 generations, 1000 generations (corresponding to total evolution generation 2000 generations).
The detailed calculation results are shown in table 1, and Pareto fronts obtained by each scheme are shown in fig. 7.
Table 1 main index of each calculation scheme
From the above calculation results, it can be seen that in terms of calculation time consumption, the time consumption of the scheme 4, i.e. the scheme with the fixed step length of 2 months, is minimum, and only 266.3s; secondly, scheme 3 with a fixed step length of 1 month takes 341.2s; the longest time is scheme 2 with a fixed step length of 1 ten days and evolution algebra=2000, and the time is 543.9s; the calculation time of the step-size encryption scheme 5 and the calculation time of the scheme 6 are centered, and the calculation time of the scheme 6 adopting the multi-step encryption is far less than that of the scheme 2 of the fixed-step evolution 2000 generation, and is also less than that of the scheme 5 of the single-step encryption and the scheme 1 of the fixed-step evolution 1500 generation. In the calculation result scheme, as shown in table 1 and fig. 7, since step sizes of scheme 3 and scheme 4 are larger, after the direct calculation result is interpolated into a ten-day step size result, the generated energy is significantly smaller than the result obtained by the ten-day step size calculation, and the average water discarding amount is larger. The average power generation amount and the water discarding amount of the Pareto result obtained by adopting the step-by-step dense scheme in the scheme 5 are better than those of schemes 1 to 4, and the time consumption is less than that of scheme 2, because the step-by-step dense strategy is adopted to calculate by adopting a larger step in the initial stage, the calculation scale is reduced, the local optimal solution can be found in a shorter time, and a better initial solution is provided for the next step of small step calculation, so that the calculation efficiency is improved. The scheme 6 adopts a 2-step encryption strategy, the average power generation amount obtained by the calculation result is maximum and reaches 3290 hundred million kWh, 1.9 hundred million kWh is more than the scheme 5 which is ranked second, 42.9 hundred million kWh and 20.1 hundred million kWh are more than the scheme 1 and the scheme 2 which are calculated by fixed step, meanwhile, the water discarding amount is not obviously different from the scheme 1 and the scheme 2, the time consumption is only 392s, and the time consumption is only longer than that of the scheme 3 and the scheme 4 which directly adopt month and double month step sizes. In general, schemes 5 and 6, which employ step-wise dense computation, can find a better solution set in a shorter time than a fixed step, and scheme 6, which uses multiple steps to dense, takes less time and yields better results.
In summary, the method provided by the invention realizes the optimized scheduling solution of the large-scale cascade hydropower station group by introducing a step dense-by-dense strategy, and effectively improves the solution efficiency and the solution precision of the medium-long-term scheduling problem of the huge cascade reservoir group.
The foregoing embodiments are merely preferred embodiments of the present invention, and should not be construed as limiting the present invention, and the embodiments and features of the embodiments in the present application may be arbitrarily combined with each other without collision. The protection scope of the present invention is defined by the claims, and the protection scope includes equivalent alternatives to the technical features of the claims. I.e., equivalent replacement modifications within the scope of this invention are also within the scope of the invention.
Claims (5)
1. A step-size dense-by-dense multi-target cascade hydropower station group optimization scheduling method is characterized by comprising the following steps of: it comprises the following steps:
s1, constructing a long-term multi-objective optimal scheduling model in a huge cascade reservoir group;
s2, optimizing the model by adopting a step-size secret-by-secret strategy.
2. The optimal scheduling method for the step-by-step dense multi-target step hydropower station group according to claim 1, wherein the method comprises the following steps: the step S1 specifically comprises the following steps:
s1.1, taking two targets of maximum generated energy and minimum water discarding amount as objective functions to ensure the economic benefit of the step system and reduce the water discarding risk of the system:
wherein T represents the number of scheduling periods; m represents the number of step power stations; a is that m,t The output coefficient of the power station m in the period t is represented; q (Q) m,t Represents the power generation flow of the power station m in the period t, m 3 /s；H m,t Represents the water purification head of the power station m in the period t, m; qs m,t Represents the reject flow of the power station m in the period t, m 3 S; Δt represents the period length, s;
s1.2, setting corresponding hydraulic and electric constraints according to the characteristics of reservoirs and hydropower stations.
3. The optimal scheduling method for the step-by-step dense multi-target step hydropower station group according to claim 2, which is characterized by comprising the following steps: the hydraulic and electric constraints are specifically as follows:
(1) Water level constraint:
wherein Z is m,t 、 Z m,t Respectively representing the water level and the upper and lower limits of the power station m in the t period, and m;
(2) Power station output constraint:
wherein P is m,t 、 P m,t Respectively representing the output of the power station m in the t period and the upper limit and the lower limit thereof, MW;
(3) And (3) constraint of storage capacity:
wherein V is m,t 、V m,t 、Respectively represent the storage capacity of the power station m in the t period and the upper limit and the lower limit thereof, m 3 ；
(4) Generating flow constraint:
in which Q m，t 、Q m，t 、Respectively representing the power generation flow and the upper and lower limits thereof of the power station m in the t period, m 3 /s；
(5) Water balance constraint:
V m，t+1 ＝V m，t +(R m，t -Q m，t -Qs m，t )·Δt (7)
wherein V is m，t 、V m，t+1 Respectively represents the initial and final storage capacity of the power station m in the t period, m 3 ；R m，t 、Qs m，t Respectively representing the warehouse-in flow and the reject flow of the power station m in the t period, m 3 /s；
(6) Leakage flow constraint:
S m，t ＝Q m，t +Qs m，t (9)
wherein S is m，t 、 S m，t Respectively represent the lower leakage flow and the upper and lower limits thereof of the power station m in the t period, and m 3 S; the discharging flow consists of two parts, namely power generation flow and waste water flow;
(7) Start-end water level control constraint:
in the method, in the process of the invention,respectively representing an initial water level control value and an expected final water level of the reservoir m;
(8) Water level fluctuation constraint:
in the method, in the process of the invention,representing the maximum water level fluctuation limit of a power station m in a single period, and m; the constraint limits the water level amplitude of the power station between adjacent time periods, and the water level amplitude is determined by the power station according to navigation and comprehensive operation requirements;
(9) Delivery flow fluctuation constraint:
in the method, in the process of the invention,representing the maximum delivery flow fluctuation limit of a power station m single period, m 3 S; the constraint limits the delivery flow amplitude of the power station between adjacent time periods, and the delivery flow amplitude is determined by the power station according to navigation and comprehensive operation requirements;
(10) Force climbing constraint:
in the method, in the process of the invention,representing the maximum output lifting limit and MW of the power station m in a single period;
(11) Hydropower station output fluctuation limit:
(P m，t-Δ+1 -P m，t-Δ )(P m，t -P m，t-1 )≥0 (15)
wherein Δ=1, 2, …, t min ，t min Representing the minimum interval period number of the m output rise and fall of the power station; the constraint ensures the operation safety of the power grid and the unit by limiting the frequent fluctuation of the output of the power station between adjacent time intervals.
4. The optimal scheduling method for the step-by-step dense multi-target step hydropower station group according to claim 1, wherein the method comprises the following steps: the step S2 specifically includes the following steps:
s2.1: setting the step length of a model scheduling period to be solved as n times of a target step length, namely, changing the length to nDeltat, shortening the number of scheduling periods to be 1/n of the original number, synchronously reducing the variable dimension of the model, and reducing the variable dimension of the model to be [1, n+1,2n+1, …, T ], wherein the single solving efficiency can be greatly improved;
s2.2: solving the model by adopting an NSGA-III algorithm, and enabling the model to quickly converge in a smaller dimension to obtain a local optimal solution of the model under the condition of a larger step length;
s2.3: linearly expanding the result of the large step length into an initial solution calculated by the small step length according to the principle of equal flow or uniform water level lifting, namely uniformly lifting a variable corresponding to the small step length in the large step length;
s2.4: substituting the generated initial solution into a model, and solving by adopting an NSGA-III algorithm, wherein the better initial solution can guide the evolution direction and improve the evolution effect;
s2.5: and repeating the step S2.3 and the step S2.4 until the step length meets the requirement.
5. The optimal scheduling method for the step-by-step dense multi-target step hydropower station group is characterized by comprising the following steps of: the NSGA-III algorithm solving process specifically comprises the following steps:
(1) Initialization of
Setting NSGA-III algorithm and calculation parameters including population scale, maximum evolution algebra and genetic probability;
(2) Determining an initial population of large steps
Dividing calculation time periods by larger step length, and generating a series of individuals meeting water level constraint in a water level operation range;
(3) Initial solution correction
Because of a plurality of time coupling constraints in the model, the change of decision variables in any period can cause the damage of constraint conditions in adjacent periods, and genetic operations such as population selection, crossing, variation and the like are performed among infeasible solutions in solving, so that population diversity is easily lost quickly; therefore, the constraint adjustment strategy is adopted to process complex time coupling constraints, and the method is operated as follows:
and (5) regulating the force climbing limit:
when the limit constraint of the output climbing is destroyed, the output of the associated time period needs to be regulated, the basic principle of regulation is to keep the total electric quantity of all the regulating time periods unchanged, the initial search is initiated by the t=1 time period, and whether the limit constraint of climbing is destroyed is judged from time period to time period at the end of the dispatching period; if it isThen reverse search for continuous climbingTime interval [ j+1, t+1 ]]Length is defined as L; the output difference value of adjacent time periods is equal to the climbing upper limit as an adjustment target, and the output increment of the continuous climbing time period is determined to beAnd adjusting the output of each period of continuous climbing according to a formula (16); then, continuing the backward search until the end;
force fluctuation limit adjustment:
the constraint damage of the output fluctuation control is generalized into two forms, namely a convex form and a concave form, which are respectively expressed as inconsistent output change trend in the adjacent time period within a specified duration; correcting the output of the related period in an equal proportion mode, and ensuring that the output lifting change meets the minimum duration requirement; output P for 3 periods of time m,t 、P m,t+1 、P m,t+2 The corresponding correction amounts are:
thereby realizing uniform fluctuation of the corrected output;
correcting part of non-feasible individuals through the operation, and improving the number of feasible solutions;
(4) Fitness ranking
Calculating individual fitness according to the generating capacity target and the water discarding target respectively, judging individual dominance relation and carrying out hierarchical sequencing; considering the complexity of the problem, the dominant relationship of the two bodies is determined by adopting the following method: (1) if both are feasible solutions; determining a dominance relation according to the individual fitness; (2) if the feasible solution and the infeasible solution are included at the same time, the feasible solution is dominant; (3) if the constraint damage degree is equal to the constraint damage degree, determining a dominant relationship at random;
(5) Genetic manipulation
Sequentially selecting, crossing and mutating to obtain a new generation sub population;
(6) Offspring individual correction
The individuals with the offspring having constraint damage are corrected by adopting the method in the step (3);
(7) Generating the next generation
Combining the parent population and the child population, respectively carrying out non-dominant hierarchical sorting and crowding distance calculation, and selecting the individuals in front according to the set population scale to form a new population;
(8) Loop computation
Iterating the steps (5) - (7) circularly until reaching the termination condition;
(9) Determining initial population of small step size
Expanding the solution line shape of the large step length obtained by the calculation into an initial solution of the small step length calculation;
(10) Loop computation
Similar to the calculation process of the large step size, the operations of steps (3) to (8) are carried out on the population with the small step size;
(11) Outputting Pareto solution sets
And solving the model according to the steps.
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