CN106127348B - Reservoir group joint optimization scheduling feasible decision space identification method - Google Patents
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Abstract
The invention belongs to the field of hydroelectric power generation dispatching of an electric power system, and discloses a feasible decision space identification method for reservoir group joint optimization dispatching, which reduces the calculated amount and the storage amount of the traditional method, realizes a considerable dimensionality reduction effect, and has a good application prospect in the field of reservoir group joint dispatching. The technical scheme is as follows: firstly, defining requirements, constructing a reservoir group optimization scheduling model, and determining a target function and constraint conditions; secondly, dynamically identifying feasible regions of each reservoir in a single stage, two stages and multiple stages by adopting a specific knowledge rule, and effectively reducing a search space; and finally, solving by adopting the existing reservoir group optimal scheduling method, such as dynamic planning, particle swarm optimization and the like. The invention can automatically realize constraint condition pretreatment, scientifically identify the feasible decision space of the reservoir group scheduling problem, reduce the calculated amount and the storage amount of the traditional method, greatly relieve the problem of dimension disaster and provide a reasonable and feasible method for the efficient solution of the reservoir group joint optimization scheduling problem.
Description
Technical Field
The invention relates to the field of hydroelectric power generation dispatching of an electric power system, in particular to a feasible decision space identification method for reservoir group joint optimization dispatching.
Background
The reservoir group joint optimization scheduling is a complex nonlinear optimization problem under the action of multiple complex constraint strong coupling, and is mainly reflected in that: on one hand, as a water resource utilization carrier with multiple social attributes, besides meeting self safe and stable operation constraints, the reservoir often has comprehensive utilization requirements of water conservancy, electric power, environmental protection and other departments, and generally needs to bring related benefit requirements of each unit into a scheduling model in the form of constraint conditions, so that a reservoir group needs to process constraint condition sets with numerous numbers and different forms when carrying out joint optimization scheduling; on the other hand, complex interweaving, coupling and other comprehensive effects exist among various constraints, so that the feasible search space is greatly narrowed, and complex space-time correlation characteristics are presented, the change of the running state of a single reservoir at any time interval is likely to cause the damage of the constraint conditions of the power station or a downstream power station at the relevant time interval, the overall benefit of the reservoir group system and the reduction of the water energy utilization efficiency are caused, and the optimization difficulty of the traditional method is directly increased; in addition, the reservoir group system expanded year by year enables more complex hydraulic and electric power connection to exist between power stations and between the upstream and the downstream of the cascade, the search space is expanded while the number of constraint conditions is increased, the complexity of the problem is increased nonlinearly along with the power stations and the number of constraint conditions, and the difficulty in modeling and solving is aggravated. Therefore, how to efficiently process the complex constraint set in the reservoir group scheduling problem to realize the simplification and combination of constraint conditions with different types becomes a key for improving the performance of the algorithm, which is one of the core problems of reservoir group scheduling.
Scholars at home and abroad conduct certain research on reservoir group scheduling constraint processing methods, and the existing methods can be roughly divided into four types: first, the penalty function method: incorporating constraint destruction terms into an objective function in the form of a penalty function to form an adaptive value function, and guiding the algorithm to gradually turn to a reasonable region; secondly, a repair solution method: adjusting the non-feasible solution by using a specific repair operator, and mapping the non-feasible solution to the boundary or the interior of a feasible domain to keep the feasibility of the solution; and thirdly, a multi-target method: converting the original problem into a multi-objective optimization problem, namely, regarding the degree of violation of constraint conditions of individuals as a target item equivalent to an original target function, processing the converted problem by using a multi-objective optimization technology, and gradually approaching the problem to the optimal solution direction; fourthly, feasible domain identification method: the search space is reduced according to a certain method, so that the algorithm is optimized in a relatively small range, and the performance of the algorithm is improved. However, each of the four aforementioned methods has advantages and disadvantages: the penalty function method is simple in form and strong in operability, but the penalty factor is difficult to select and generally needs to be obtained by trial calculation according to actual problems; the solution repair method needs to develop personalized design according to specific problems, the method is poor in universality, and the complexity of an algorithm is increased to a certain extent by a repair operator; the multi-target method can utilize the feasible degree of Pareto dominance mechanism effective area decomposition, but is relatively difficult to realize and difficult to ensure the feasibility of the final solution; the feasible region identification method does not need to change an optimization algorithm optimizing mechanism and effectively guarantees the feasibility of the solution, but the static identification mechanism is mostly adopted in the prior literature reports, and the constraint integration level is poor. Therefore, the research and development of a reasonable, feasible, novel and efficient constraint processing mechanism for improving the efficiency and the precision of the traditional method for solving the reservoir group combined optimization scheduling still have very important significance
The invention relies on the important plan key support project (91547201) of the national science foundation and the important international cooperation (51210014) of the national science foundation, uses the problem of dimension disaster commonly faced by the cascade reservoir group joint optimization scheduling as the background, and uses the data mining technology and the set operation theory as the means, and invents a reservoir group joint optimization scheduling decision space identification method with strong practicability and wide popularization value.
Disclosure of Invention
The invention aims to solve the technical problem of providing a feasible decision space identification method for reservoir group joint optimization scheduling, which comprises the steps of firstly determining requirements, constructing a reservoir group optimization scheduling model, and determining a target function and constraint conditions; secondly, dynamically identifying feasible regions of each reservoir in single stage, two stages and multiple stages by adopting a set operation theory and knowledge rule method, and effectively reducing feasible decision space; and finally, solving by adopting the existing reservoir group optimal scheduling method, such as dynamic planning, particle swarm optimization and the like.
The technical scheme of the invention is as follows: the invention discloses a feasible decision space identification method for reservoir group joint optimization scheduling, which completes the dimension reduction solving process of the reservoir group optimization scheduling problem according to the following steps (1) to (4):
(1) according to the characteristics of the watershed and the actual production demand, a reservoir group optimization scheduling model is constructed, and an objective function and constraint conditions are determined, wherein the objective function and the constraint conditions can be generally described as the following model, and the formula is expressed as follows:
wherein E (x) represents an optimization objective; x represents the variable to be optimized, x ═ x1,x2,…,xn]T(ii) a n is the dimension of the variable x; h isl(x) 0 denotes the ith term equality constraint; gl(x) 0 or less represents the inequality constraint of the first term(ii) a p represents the number of equality constraints; m represents the number of inequality constraints;
according to the theory of mathematical optimization, the feasible domain F is a set of points satisfying all constraints, and the mathematical formula is
F＝{x|hl(x)＝0,l＝1,2,…,p；gl(x)≤0,l＝p+1,p+2,…,p+m}。
It can be seen that the feasible region F is only affected by the comprehensive action of the constraint condition set, and has no direct relation with the form, content, and the like of the objective function to be optimized. Therefore, how to fully utilize the constraint condition set to identify the feasible domain is the problem to be solved by the invention.
(2) The water level, the generating flow, the discharging flow and the output of the reservoir in each time period all need to operate in a safe range, and respectively form a water level limit set SZGenerating flow restriction set SQDelivery flow restriction set SOOutput limit set SPThe water balance equation constraint set can be recorded as SBThe corresponding mathematical expression is:
wherein, i is reservoir serial number, i is 1,2, …, N; n represents the number of power stations; j is the time period number, j is 1,2, …, T; t represents the number of periods; zi,jRepresents the water level, m, of reservoir i at time period j;
the upper limit and the lower limit of the water level of the reservoir i in the time interval j, m, respectively; qi,jRepresents the generated flow m of the reservoir i in the time period j3/s；
The upper limit and the lower limit of the generating flow of the reservoir i in the time interval j are respectively set;
respectively representing the upper limit and the lower limit of the outlet flow of the reservoir i in the time interval j; pi,jRepresenting the output, kW, of the plant i during time period j;
respectively representing the upper limit and the lower limit of the output of the reservoir i in the time interval j; vi,jIs the storage capacity, m, of reservoir i in time period j3；Ii,j、Oi,j、qi,j、Di,jRespectively the warehousing flow, the ex-warehouse flow, the interval flow and the abandon flow of the reservoir i in the time interval j, m3/s；
The optimal scheduling of the hydroelectric system needs to reasonably regulate and control the water storage and discharge process of each reservoir on the premise of comprehensively considering various complex constraints such as water level, output, flow and the like, so that the optimal overall benefit of the system is obtained. From the optimization perspective, the problem belongs to the constraint optimization problem shown in (1), which necessarily requires that feasible regions simultaneously satisfy inequality constraints such as water level limits, output limits, and flow limits of all hydropower stations in different time periods, and equality constraints including a water quantity balance equation and a flow balance equation. Therefore, in order to satisfy all the constraint conditions at the same time, the feasible search space of the reservoir group joint scheduling problem must only be the intersection of all the limited operation condition sets, namely
F＝SZ∩SQ∩SO∩SP∩SB
In the process of making a scheduling scheme of a hydro-electric system, if only the water level limit is considered, the feasible region is as shown in fig. 1(a), and only the water level is required to be operated at the original fixed water levelOptimizing in a line space, and the search space is the most huge; if only water level and flow constraints are considered, as shown in fig. 1(b), the intersection of the two is a feasible space, and now, compared with fig. 1(a), it is obvious that the feasible region can be reduced to some extent; if the constraints of water level, flow rate and output are considered, the search interval can be divided into 7 parts according to fig. 1 (c). It can be seen that FIG. 1(c) can subtract S compared to FIG. 1(a)2And S6FIG. 1(c) can subtract S compared to FIG. 1(b)6The maximum reduction of the feasible domain is realized. Therefore, the feasible search space is identified in advance by adopting the method, the search calculation and the additional storage of the invalid state are greatly reduced, the memory occupation and the calculation time consumption of the method are reduced, and the synchronous improvement of the scheduling solving efficiency and the calculation scale of the hydropower station group is realized.
(3) The water level and the delivery flow of each reservoir in each stage are respectively set as corresponding state values and decision values, the feasible regions of each reservoir in a single stage, two stages and multiple stages are dynamically identified by adopting the following method, so that the effective reduction of the search space is realized, wherein:
① identifying the single-stage feasible region uses a single-stage feasible region identification method, comprising the steps of:
a) by the flow of electricity generated SQAnd the outbound traffic set SOObtaining a flow set
The calculation method is as follows:
wherein
In the formula (I), the compound is shown in the specification,
for the corrected discharge flow, m, of reservoir i in time period j3/s；
Is composed of
Corresponding upper and lower limits.
b) By using SBWill SZConversion into corresponding outbound flow restriction sets
The calculation method is as follows:
wherein
In the formula (I), the compound is shown in the specification,
the possible outlet flow, m, corresponding to the water level limit constraint of the reservoir i in the time interval j3/s；
Is composed of
The corresponding upper and lower limits; f. ofiA characteristic curve showing the storage capacity-water level of the reservoir i;
c) get
And
obtaining a revised outbound traffic limit set
The calculation method is as follows:
wherein
In the formula (I), the compound is shown in the specification,
for reservoir i in time period j,
And
taking the corresponding ex-warehouse flow m after intersection3/s；
Are respectively as
The corresponding upper and lower limits;
d) will SPConversion into corresponding outbound flow restriction sets
The specific operation is as follows:
1) firstly, judging the form of each reservoir between the output of each time period and the delivery flow: setting a small delivery flow increment QΔ，
If it is
If yes, the model is monotone increasing;
if it is
If yes, the model is of a monotone decreasing type;
otherwise, the model is in a quasi-parabolic shape;
in the formula, Pi,jDenotes at a given flowCalculating the output of the plant, wherein · represents a given flow;
2) then the S isPConversion to corresponding outbound traffic restriction set
For the type of the monotonically increasing type,
in the formula, Wi(. represents given water)
The delivery of force, the delivery flow, m, calculated by electricity for water determination3/s。
In the case of the monotone decreasing type,
for the quasi-parabolic type, due to symmetry, there are two outbound flow intervals,
in the formula (I), the compound is shown in the specification,
respectively represent
Two subintervals of (a);
respectively representing sub-intervals
And
corresponding delivery flow, m3/s；
Is composed of
The corresponding upper and lower limits;
are respectively as
The corresponding upper and lower limits.
e) Get
And
the intersection of (A) obtains the final outbound traffic restriction set
The specific operation is as follows:
1) for the type of the monotonically increasing type,
wherein
In the formula (I), the compound is shown in the specification,
for reservoir i in time period j,
And
taking the corresponding possible warehouse-out flow m after intersection3/s；
Is composed of
The corresponding upper and lower limits;
2) in the case of the monotone decreasing type,
wherein
3) For the quasi-parabolic type of the curve,
wherein
In the formula (I), the compound is shown in the specification,
respectively represent
Two subintervals of (a);
for reservoir i in time period j,
And
taking the corresponding possible warehouse-out flow m after intersection3/s；
For reservoir i in time period j,
And
taking the corresponding possible warehouse-out flow m after intersection3/s；
Respectively represent
The corresponding upper and lower limits;
respectively represent
The corresponding upper and lower limits;
② the method for identifying two-stage feasible region includes such steps as sequentially searching (j-1 → j) from time interval j-1 to time interval j, and calling the identification method to obtain decision set
Then, according to the time interval j +1 state reverse order search (j +1 → j), calling a single-stage feasible domain identification method to obtain a decision set
Finally, get
And
the intersection of the two can obtain the feasible range of the decision variables. Fig. 3 is a comparison diagram of single-stage and two-stage feasible domain identification, and it can be seen that various constraints can be organically integrated by using the method of the present invention, so as to realize dynamic reduction of search space and avoid blind calculation in an infeasible search space.
③ identifying the multi-stage feasible region using the multi-stage feasible region identification method, the operation steps are that setting the stage to be optimized as j, if only the initial water level of the dispatching period is given, only the period sequence recursion from the beginning of the dispatching period to the period j is needed, calling the single-stage feasible region identification method to obtain the feasible search space, if the end state of the dispatching period is given, respectively obtaining the feasible regions corresponding to the period j from the initial sequence recursion of the dispatching period (1 → j) and the reverse sequence recursion of the end of the dispatching period (T → j), then calling the two-stage feasible region identification method to take the intersection of the two, so as to further eliminate the infeasible search space;
(4) after the steps are completed, a greatly reduced feasible decision space can be obtained; then, the existing reservoir group optimal scheduling method, such as dynamic planning and particle swarm optimization, is adopted to solve in the space, and then a high-quality scheduling result can be quickly obtained.
Compared with the prior art, the invention has the following beneficial effects: the invention relates to a feasible decision space identification method for reservoir group joint optimization scheduling, which comprises the steps of firstly determining requirements, constructing a reservoir group optimization scheduling model, and determining a target function and constraint conditions; secondly, dynamically identifying feasible regions of each reservoir in single stage, two stages and multiple stages by adopting specific knowledge rules and a set operation theory, and effectively reducing the search space; and finally, solving by adopting the existing reservoir group optimal scheduling method, such as dynamic planning, particle swarm optimization and the like.
Compared with the prior art, the method can effectively identify the feasible decision space of the reservoir group, reduce or even avoid the search of the traditional method in the infeasible decision space, intelligently realize the pretreatment of complex constraint conditions, realize the effective compression of the feasible region on the global scale, and greatly reduce the redundant calculation of the infeasible solution; meanwhile, the problem of dimension disaster can be greatly relieved, the actual dispatching condition of the reservoir group can be quickly and scientifically responded, the calculated amount and the storage amount of the traditional method are effectively reduced, the calculation efficiency and the result quality of the reservoir group joint optimization dispatching are practically guaranteed, and a reasonable and feasible method is provided for the dimension reduction of the reservoir group joint optimization dispatching problem.
Drawings
FIG. 1(a) is a diagram of a feasible region considering only a set of water level limits;
FIG. 1(b) is a diagram of feasible regions considering a set of water level restrictions and a set of flow restrictions;
FIG. 1(c) is a diagram of feasible regions considering a set of water level limits, a set of flow limits, and a set of output limits;
FIG. 2(a) is a monotonically increasing pattern between output and output flow;
FIG. 2(b) is a monotonically decreasing pattern between output and output flow;
FIG. 2(c) is a quasi-parabolic graph of the behavior between output and flow out of the reservoir;
FIG. 3(a) is a schematic diagram of single-phase feasible domain identification;
FIG. 3(b) is a schematic diagram of two-stage feasible region identification;
FIG. 4(a) is a diagram of the effect of reducing the feasible region of the Longtan reservoir in the red river basin in the rich water year;
FIG. 4(b) is a diagram of the feasible region reduction effect of the Longtan reservoir in the red river basin in the open water year;
FIG. 4(c) is a diagram showing the effect of reducing the operable area of the Longtan reservoir in the red river basin in the dry year;
FIG. 5(a) is a decision variable distribution diagram obtained by the method of the present invention when the dynamic programming is adopted for solving under the combined scheduling of 3 water reservoirs in the red river basin;
fig. 5(b) is a decision variable distribution diagram obtained by using the method of the present invention when the dynamic programming is adopted for solving under the combined scheduling of 3 water reservoirs in the red river basin.
Detailed Description
The invention is further described below with reference to the figures and examples.
Along with the rapid development of hydropower in China, the calculation scale and the solving difficulty of the reservoir group joint optimization scheduling problem are increased day by day, wherein the problem of dimension disaster caused by various complex constraint conditions is a great challenge faced by the existing method. The lack of an optimization method for simply and efficiently processing complex constraint conditions directly results in the expansion of the search space of the algorithm and the increase of invalid calculation amount. How to realize reasonable and effective reduction of feasible regions is one of the main difficulties of reservoir group combined optimization scheduling. The invention discloses a feasible decision space identification method for reservoir group joint optimization scheduling, which comprises the steps of firstly determining requirements, constructing a reservoir group optimization scheduling model, and determining a target function and constraint conditions; secondly, dynamically identifying feasible regions of each reservoir in single stage, two stages and multiple stages by adopting specific knowledge rules and a set operation theory, and effectively reducing the search space; and finally, solving by adopting the existing reservoir group optimal scheduling method, such as dynamic planning, particle swarm optimization and the like.
According to the introduction, the primary complete reservoir group combined optimization scheduling process is realized according to the following steps (1) to (4):
(1) constructing a reservoir group optimal scheduling model according to the characteristics of the watershed and the actual production demand, and determining a target function and constraint conditions, wherein the model is expressed as follows:
wherein E (x) represents an optimization objective; x represents the variable to be optimized, x ═ x1,x2,…,xn]T(ii) a n is the dimension of the variable x; h isl(x) 0 denotes the ith term equality constraint; gl(x) 0 or less represents the inequality constraint of the ith term; p represents the number of equality constraints; m represents the number of inequality constraints;
(2) let feasible region be F, i.e. the set of points that satisfy all constraints, denoted as F ═ x | hi(x)＝0,i＝1,2,…,p；gi(x) Equal to or less than 0, j is equal to 1,2, …, m, and simultaneously, the water level, the generating flow, the ex-warehouse flow and the output of each period of the reservoir all need to operate in a safe range, and respectively form a water level limit set SZGenerating flow restriction set SQDelivery flow restriction set SQOutput limit set SPThe water balance equation constraint set can be recorded as SBThe corresponding mathematical expression is:
in the formula, Zi,jRepresents the water level, m, of reservoir i at time period j;
the upper limit and the lower limit of the water level of the reservoir i in the time interval j, m, respectively; qi,jRepresents the generated flow m of the reservoir i in the time period j3/s；
The upper limit and the lower limit of the generating flow of the reservoir i in the time interval j are respectively set;
respectively representing the upper limit and the lower limit of the outlet flow of the reservoir i in the time interval j; pi,jRepresenting the output, kW, of the plant i during time period j;
respectively representing the upper limit and the lower limit of the output of the reservoir i in the time interval j; vi,jIs the storage capacity, m, of reservoir i in time period j3；Ii,j、Oi,j、qi,j、Di,jRespectively the warehousing flow, the ex-warehouse flow, the interval flow and the abandon flow of the reservoir i in the time interval j, m3/s；
(3) The water level and the delivery flow of each reservoir in each stage are respectively set as corresponding state values and decision values, the feasible regions of each reservoir in single stage, two stages and multiple stages are dynamically identified by adopting knowledge rules and set operation theory, and the effective reduction of decision space is realized, wherein:
① identifying the single-stage feasible region uses a single-stage feasible region identification method, comprising the steps of:
a) by the flow of electricity generated SQAnd the outbound traffic set SOObtaining a flow set
The calculation method is as follows:
wherein
In the formula (I), the compound is shown in the specification,
for the corrected discharge flow, m, of reservoir i in time period j3/s；
Is composed of
Corresponding upper and lower limits;
b) by using SBWill SZConversion into corresponding outbound flow restriction sets
The calculation method is as follows:
wherein
In the formula (I), the compound is shown in the specification,
the possible outlet flow, m, corresponding to the water level limit constraint of the reservoir i in the time interval j3/s；
Is composed of
The corresponding upper and lower limits; f. ofi,1A characteristic curve showing the storage capacity-water level of the reservoir i;
c) get
And
obtaining a revised outbound traffic limit set
The calculation method is as follows:
wherein
In the formula (I), the compound is shown in the specification,
for reservoir i in time period j,
And
taking the corresponding possible warehouse-out flow m after intersection3/s；
Is composed of
The corresponding upper and lower limits;
d) will SPConversion into corresponding outbound flow restriction sets
The specific operation is as follows:
1) firstly, judging the form of each reservoir between the output of each time period and the delivery flow: setting a small delivery flow increment QΔ，
If it is
If yes, the model is monotone increasing;
if it is
If yes, the model is of a monotone decreasing type;
otherwise, the model is in a quasi-parabolic shape;
in the formula, Pi,j(. cndot.) represents the calculated output at a given flow, where · represents the given flow;
2) then the S isPConversion to corresponding outbound traffic restriction set
For the type of the monotonically increasing type,
in the formula, Wi(. represents given water)
The delivery of force, the delivery flow, m, calculated by electricity for water determination3/s。
In the case of the monotone decreasing type,
for the quasi-parabolic type, due to symmetry, there are two outbound flow intervals,
in the formula (I), the compound is shown in the specification,
respectively represent
Two subintervals of (a);
e) get
And
the intersection of (A) obtains the final outbound traffic restriction set
The specific operation is as follows:
1) for the type of the monotonically increasing type,
wherein
In the formula (I), the compound is shown in the specification,
for reservoir i in time period j,
And
taking the corresponding possible warehouse-out flow m after intersection3/s；
Is composed of
The corresponding upper and lower limits;
2) in the case of the monotone decreasing type,
wherein
3) For the quasi-parabolic type of the curve,
wherein
In the formula (I), the compound is shown in the specification,
respectively represent
Two subintervals of (a);
for reservoir i in time period j,
And
taking the corresponding possible warehouse-out flow m after intersection3/s；
For reservoir i in time period j,
And
taking the corresponding possible warehouse-out flow m after intersection3/s；
Respectively represent
The corresponding upper and lower limits;
respectively represent
The corresponding upper and lower limits;
② the method for identifying two-stage feasible region includes such steps as sequentially searching (j-1 → j) from time interval j-1 to time interval j, and calling the identification method to obtain decision set
Then, according to the time interval j +1 state reverse order search (j +1 → j), a decision set is obtained
Finally, get
And
the intersection of the two can obtain the feasible range of the decision variable;
③ identifying the multi-stage feasible region using the multi-stage feasible region identification method, the operation steps are that setting the stage to be optimized as j, if only the initial water level of the dispatching period is given, only the period sequence recursion from the beginning of the dispatching period to the period j is needed, calling the single-stage feasible region identification method to obtain the feasible search space, if the end state of the dispatching period is given, respectively obtaining the feasible regions corresponding to the period j from the initial sequence recursion of the dispatching period (1 → j) and the reverse sequence recursion of the end of the dispatching period (T → j), then calling the two-stage feasible region identification method to take the intersection of the two, so as to further eliminate the infeasible search space;
(4) after the feasible region reduction is completed, the existing reservoir group optimization scheduling method, such as dynamic planning and particle swarm optimization, is adopted for solving.
The method is adopted to realize effective reduction and dimension reduction of the feasible region of the joint optimization scheduling by taking the red river basin Longtan-Yangtze beach-large step hydropower station group as a research object. The basic data of each plant are shown in Table 1. Setting the scheduling period to be 1 year, selecting the calculation step length to be 1 month, and setting the total scheduling time interval number to be 12.
Firstly, taking a Longtan reservoir as a research object, and respectively selecting three scenes of a rich water year, an open water year and a dry water year as input water in each time period; and setting all the constraints at the same level to meet the comparability condition, and further comparing and analyzing feasible spaces under different incoming water conditions. Meanwhile, for the convenience of clear comparison, the corresponding flow decision space is converted into a water level state space. The feasible domain reduction effect in three scenarios is shown in fig. 4(a) - (c). As can be seen from the graph analysis, the forms of the feasible decision space have different performances under different water supply conditions, such as plump water year and approximate obesity type; convergence in the horizontal year just like thin and long type; in dry water, the water content is reduced again, and the strip-shaped narrow type is presented. In general, when a worker makes a scheduling plan, the water level is usually limited between a normal high water level and a dead water level for operation, obviously, the optimization range is relatively large, and compared with the method, the feasible region obtained by the method is obviously reduced, the constraint condition processing dimensionality is effectively reduced, and the dimensionality reduction is realized. In addition, in order to verify the effectiveness of the method, the optimization scheduling is carried out by combining a Particle Swarm Optimization (PSO), and the calculation result is shown in Table 2. Compared with the calculation result of reusing the PSO algorithm under the condition of reducing the feasible domain by using the method of the invention, the calculation time consumption of the two methods is similar on the premise of controlling the same search times, but the calculation result obtained by the method of the invention is obviously superior to the PSO algorithm, which shows that on the premise of calculating the same search times, the method of the invention can search more feasible solutions, thereby obtaining a better scheduling result.
And then, taking the 3 water reservoirs in the cascade basin as research objects to carry out reservoir group combined optimization scheduling. The dynamic planning is used as an optimization method, the calculation is completed by respectively adopting two modes of independent use of the dynamic planning and combination of the dynamic planning after the feasible region is reduced by the method, the runoff of an actual measurement interval in a certain year is selected as the system input, and the state vectors of the initial water level and the final water level of the system in the dispatching period are set as the same vector; the period is taken as 2 months, the step size is 1 month, namely the total calculation time period is 2. The decision variables of the two methods at corresponding discrete steps are compared and shown in FIGS. 5(a) and (b). It can be seen from the figure that after the method is adopted, a dynamic programming method is utilized to solve the joint optimization scheduling problem, a large number of invalid state combinations can be eliminated, the distribution of the selected decision variables in the space is relatively sparse, and the distribution map obtained by singly using the dynamic programming method is very dense. The calculation results shown in table 3 indicate that, under the condition of obtaining the same power generation amount of 18.23 hundred million kW · h, after the method is adopted, the number of decision variables and the calculation time consumption are less than 20% of those of the dynamic programming method used alone when the dynamic programming method is used for solving.
TABLE 1
TABLE 2
TABLE 3
Therefore, the method can reduce the calculated amount and the storage amount of the traditional method, realize considerable dimensionality reduction effect, effectively improve the performance of the method, and has good application prospect in the field of reservoir group joint scheduling.
Claims (1)
1. A feasible decision space identification method for reservoir group combined optimization scheduling is characterized by comprising the following steps:
(1) the water level, the generating flow, the discharging flow and the output of the reservoir in each time period all need to operate in a safe range, and respectively form a water level limit set SZGenerating flow restriction set SQDelivery flow restriction set SOOutput limit set SPThe water balance equation constraint set can be recorded as SBThe corresponding mathematical expression is:
wherein, i is reservoir serial number, i is 1,2, …, N; n represents the number of power stations; j is the time period number, j is 1,2, …, T; t represents the number of periods; zi,jRepresents the water level, m, of reservoir i at time period j;
the upper limit and the lower limit of the water level of the reservoir i in the time interval j, m, respectively; qi,jRepresents the generated flow m of the reservoir i in the time period j3/s；
The upper limit and the lower limit of the generating flow of the reservoir i in the time interval j are respectively set;
respectively representing the upper limit and the lower limit of the outlet flow of the reservoir i in the time interval j; pi,jRepresenting the output, kW, of the plant i during time period j;
respectively representing the upper limit and the lower limit of the output of the reservoir i in the time interval j; vi,jIs the storage capacity, m, of reservoir i in time period j3；Ii,j、Oi,j、qi,j、Di,jRespectively the warehousing flow, the ex-warehouse flow, the interval flow and the abandon flow of the reservoir i in the time interval j, m3/s；
(2) Setting the water level and the delivery flow of each reservoir in each stage as corresponding state values and decision values respectively, and dynamically identifying feasible decision spaces of each reservoir in single stage, two stages and multiple stages by adopting the following method, thereby realizing effective reduction of search space, wherein:
① identifying the single-stage feasible region uses a single-stage feasible region identification method, comprising the steps of:
a) by the flow of electricity generated SQAnd the outbound traffic set SOObtaining a flow set
The calculation method is as follows:
wherein
In the formula (I), the compound is shown in the specification,
for the corrected discharge flow, m, of reservoir i in time period j3/s；
Is composed of
Corresponding upper and lower limits;
b) by using SBWill SZConversion into corresponding outbound flow restriction sets
The calculation method is as follows:
wherein
In the formula (I), the compound is shown in the specification,
the possible outlet flow, m, corresponding to the water level limit constraint of the reservoir i in the time interval j3/s；
Is composed of
The corresponding upper and lower limits; f. ofiA characteristic curve representing the storage capacity-water level of the reservoir i;
c) get
And
obtaining a revised outbound traffic limit set
The calculation method is as follows:
wherein
In the formula (I), the compound is shown in the specification,
for reservoir i in time period j,
And
taking the corresponding ex-warehouse flow m after intersection3/s；
Are respectively as
The corresponding upper and lower limits;
d) will SPConversion into corresponding outbound flow restriction sets
The specific operation is as follows:
1) firstly, judging the form of each reservoir between the output of each time period and the delivery flow: setting a small delivery flow increment QΔ，
If it is
If yes, the model is monotone increasing;
if it is
If yes, the model is of a monotone decreasing type;
otherwise, the model is in a quasi-parabolic shape;
in the formula, Pi,j(. represents the plant calculated output at a given flow, where represents the given flow;
2) then the S isPConversion to corresponding outbound traffic restriction set
For the type of the monotonically increasing type,
in the formula, Wi(. is) the output flow of the reservoir calculated by electricity water determination after the output of the reservoir is given, m3/s；
In the case of the monotone decreasing type,
for the quasi-parabolic type, due to symmetry, there are two outbound flow intervals,
in the formula (I), the compound is shown in the specification,
respectively represent
Two subintervals of (a);
respectively representing sub-intervals
And
corresponding delivery flow, m3/s；
Is composed of
The corresponding upper and lower limits;
are respectively as
The corresponding upper and lower limits;
e) get
And
the intersection of (A) obtains the final outbound traffic restriction set
The specific operation is as follows:
1) for the type of the monotonically increasing type,
wherein
In the formula (I), the compound is shown in the specification,
for reservoir i in time period j,
And
taking the corresponding possible warehouse-out flow m after intersection3/s；
Is composed of
The corresponding upper and lower limits;
2) in the case of the monotone decreasing type,
wherein
3) For the quasi-parabolic type of the curve,
wherein
In the formula (I), the compound is shown in the specification,
respectively represent
Two subintervals of (a);
for reservoir i in time period j,
And
taking the corresponding possible warehouse-out flow m after intersection3/s；
For reservoir i in time period j,
And
taking the corresponding possible warehouse-out flow m after intersection3/s；
Respectively represent
The corresponding upper and lower limits;
respectively represent
The corresponding upper and lower limits;
② the method for identifying two-stage feasible region includes such steps as sequentially searching (j-1 → j) from time interval j-1 to time interval j, and calling the identification method to obtain decision set
Then, according to the time interval j +1 state reverse order search (j +1 → j), calling a single-stage feasible domain identification method to obtain a decision set
Finally, get
And
the intersection of the two can obtain the feasible range of the decision variable;
③ identifying the multi-stage feasible region using the multi-stage feasible region identification method, the operation steps are that setting the stage to be optimized as j, if only the initial water level of the dispatching period is given, only the period sequence recursion from the beginning of the dispatching period to the period j is needed, calling the single-stage feasible region identification method to obtain the feasible search space, if the end state of the dispatching period is given, respectively obtaining the feasible regions corresponding to the period j from the initial sequence recursion of the dispatching period (1 → j) and the reverse sequence recursion of the end of the dispatching period (T → j), then calling the two-stage feasible region identification method to take the intersection of the two, so as to further eliminate the infeasible search space;
(3) after the steps are completed, a greatly reduced feasible decision space can be obtained; and then, solving in the space by adopting dynamic programming or particle swarm optimization to obtain a scheduling result.
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