CN115409234A - Cascade hydropower station optimal scheduling model solving method based on hybrid algorithm - Google Patents
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Abstract
The invention discloses a hybrid algorithm-based gradient hydropower station optimal scheduling model solving method, which comprises the following steps of: establishing an optimal scheduling model of the cascade hydropower station; obtaining an initial scheduling process of the cascade hydropower station meeting the relevant constraint conditions of water level, flow and storage capacity by adopting nonlinear programming; on the basis of an initial scheduling process, a step-by-step optimization algorithm is adopted to convert a multi-stage optimization problem into a plurality of two-stage optimization subproblems, in the two-stage optimization subproblems, random numbers are extracted from the state variable of each power station within the value range of the state variable to form a combination set, the combination with the optimal target function value replaces the original state variable value, all subproblems are traversed in sequence, one iteration is completed, iterative computation is repeated until the iteration termination condition is met, and the final cascade hydropower station optimization scheduling process is obtained; the method can be used for solving the problem of optimal scheduling of the cascade hydropower station, which is difficult to obtain initial feasible solution due to narrow constraint range or mismatch of upstream and downstream power station constraints and the like.
Description
Technical Field
The invention belongs to the technical field of reservoir group scheduling, and particularly relates to a hybrid algorithm-based gradient hydropower station optimal scheduling model solving method.
Background
The cascade hydropower station joint optimization scheduling refers to the purpose of uniformly scheduling a plurality of hydropower stations as a whole from the aspects of flood control, benefit and the like so as to achieve the optimal total benefit. The problem of the cascade hydropower station joint optimization scheduling can be summarized as finding a solution which enables an objective function to be optimal under the condition of meeting a series of constraint conditions, wherein the constraint conditions are generally water level range constraint, flow range constraint and output range constraint, the feasible domain space formed by all the constraint conditions is wider, the feasible solution is easier to search, the situation in practical application is often more complicated, on one hand, the constraint is numerous, and special constraints can exist besides conventional constraints, such as different water level amplitude variation control requirements of different power stations in different time periods, reserved flood control reservoir capacity requirements in flood seasons, water abandonment requirements and the like; on the other hand, due to the complex constraint, a feasible solution is not easy to find, iteration is needed for realizing for many times, and if an improper solution method is adopted, the feasible solution cannot be finally obtained.
The existing cascade hydropower station combined optimization scheduling model solving method is most widely applied to dynamic planning and an improved algorithm thereof, and a step-by-step optimization algorithm is one of the algorithms. The gradual optimization algorithm needs to firstly give an initial scheduling process and then further optimize on the basis of the initial scheduling process. Under the condition of complex constraint, the condition that the number of violations of the constraint is more probably exists in the initial scheduling process determined by depending on single-base dynamic planning or a scheduling graph, and the difficulty of finding the optimal solution by a stepwise optimization algorithm is further increased; and the traditional gradual optimization algorithm only considers the objective function values of the current two stages when the two-stage optimization subproblem is optimized, and the method is not suitable under the condition of flow amplitude variation constraint, because the flow amplitude variation constraint not only influences the current two stages, but also is related to the stages before and after the two stages.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a hybrid algorithm-based cascade hydropower station optimal scheduling model solving method, aiming at solving the problem of cascade hydropower station optimal scheduling that initial feasible solution is difficult to obtain under complex constraint conditions.
In order to achieve the purpose, the invention provides the following technical scheme:
a method for solving a cascade hydropower station optimal scheduling model based on a hybrid algorithm comprises the following steps:
s1, establishing a cascade hydropower station optimization scheduling model, including a scheduling target and constraint conditions;
s2, obtaining an initial scheduling process of the cascade hydropower station meeting the relevant constraint conditions of water level, flow and storage capacity by adopting nonlinear programming;
and S3, on the basis of the initial scheduling process, converting the multi-stage optimization problem into a plurality of two-stage optimization subproblems by adopting a stepwise optimization algorithm, in the two-stage optimization subproblems, extracting random numbers from the state variable of each power station within the value range to form a combination set, replacing the original state variable value with the combination with the optimal objective function value, continuing to solve the next two-stage optimization subproblem, sequentially traversing all subproblems, completing one iteration, and repeating iterative computation until the iteration termination condition is met to obtain the final cascade hydropower station optimization scheduling process.
Preferably, in the step S1, the scheduling target is the maximum cascade power generation, and the constraint condition further includes a water level amplitude constraint, a flow amplitude constraint, a cascade power station reserved storage capacity constraint and a water abandon constraint in addition to the water level range constraint, the flow range constraint and the output range constraint in the field of optimal scheduling of water power stations.
Preferably, in the step S2, when the initial scheduling process of the cascade hydropower station is solved by using the nonlinear programming, the water level range constraint needs to be converted into the reservoir capacity range constraint according to the water level-reservoir capacity relation curve; if the water level amplitude variation constraint exists, calculating the water level according to a reservoir capacity-water level function relational expression, wherein the reservoir capacity-water level function relational expression is a polynomial function; the output of the power station is calculated by adopting the flow water consumption rate of the power station.
Preferably, the objective function of the nonlinear programming in step S2 is:
wherein E is the objective function value; p i,j 、
γ i,j Respectively the output, the power generation flow and the flow water consumption rate of the power station i in the time period j; Δ t j An hour interval of period j; n is the number of power stations; t is the time interval length;
the violation degree of the minimum output constraint at the time period j for the power station i; lambda [ alpha ] i,4 A penalty coefficient for power station i violating the minimum output constraint;
the constraint conditions include:
and (3) flow range constraint:
flow amplitude variation constraint: | Q i,j -Q i,j-1 |≤ΔQ i,j
The water level range constraint is converted into a reservoir capacity range constraint:
water level amplitude variation restraint: l f i (S i,j )-f i (S i,j-1 )|≤ΔZ i,j
And (3) water balance constraint:
reserving storage capacity constraint:
force restraint:
in the formula, Q i,j 、
ΔQ i,j 、
S i,j 、
ΔZ i,j 、I i,j 、
ΔP i,j Respectively representing the ex-warehouse flow, the minimum ex-warehouse flow, the maximum ex-warehouse flow, the ex-warehouse flow variation, the minimum out-force, the maximum output force, the warehouse capacity, the minimum warehouse capacity, the maximum warehouse capacity, the water level variation, the warehouse entry flow, the power generation flow, the water discharge flow and the difference value between the output force and the minimum output force of the power station i in the time interval j;
the sum of the corresponding storage capacities of the normal water storage levels of the power station with the reserved storage capacity constraint for the time interval j; a. The j Reserving a storage capacity constraint for the time interval j; omega j A set formed by power stations with reserved storage capacity constraint exists for the time interval j; omega T A set formed by time intervals with reserved storage capacity constraints; f. of i () is a storage capacity-water level function relation of the power station i;
the initial solution obtained according to the nonlinear programming is not necessarily a feasible solution, but certainly meets the requirements of water level constraint and flow constraint, and the penalty term applied to the minimum output constraint is to prevent the problem of nonlinear programming from having no solution caused by too narrow output constraint range.
Preferably, the objective function of the two-stage optimization sub-problem in step S3 is
Wherein E' is the objective function value of the subproblem; lambda i,1 、λ i,2 、λ i,3 、λ i,4 、λ i,5 Respectively determining a penalty coefficient of the power station i for violating the minimum ex-warehouse constraint, a penalty coefficient for violating the maximum ex-warehouse constraint, a penalty coefficient for violating the ex-warehouse variable amplitude constraint, a penalty coefficient for violating the minimum output constraint and a penalty coefficient for violating the no-water-abandoning constraint; omega s The method is a set formed by a power station and a time interval with the constraint of not abandoning water, if the constraint of not abandoning water exists, then omega s Is an empty set; i denotes an indicative function.
Preferably, in the step S3, the two-stage optimization sub-problem takes the water level of each power station as a state variable, and if there is no cascade power station reserved reservoir capacity constraint, the generation manner of the water level combination extracts n different random numbers for each power station within the water level range of the power station, and generates the water level combination set of the cascade power station according to cartesian products; if the cascade power station reserved storage capacity constraint exists, the water level combination set is composed of combinations meeting the following constraints:
the specific implementation mode is as follows:
(1) will omega j The power stations in (1) are sorted from upstream to downstream by i 1 ,i 2 ,...,i K Wherein K = | Ω j I is the number of power stations in the set;
(2) to power station i 1 Extracting n in the following storage capacity range K Individual random numbers:
(3) to power station i 1 Each value of storage capacity of
Station i 2 Extracting 1 random number and
correspondingly:
(4) by analogy, until the K power station, n is formed K A seed storage capacity combination is converted into a water level combination according to a storage capacity-water level functional relation;
(5) and (4) for N-K power stations without reserved storage capacity constraint, extracting N different random numbers in the water level range of the power stations respectively, and generating a water level combination set of the cascade power station with the water level combination set in the step (4) according to the Cartesian product.
The invention achieves the following beneficial effects:
(1) For the problem that the initial feasible solution is difficult to obtain due to the fact that the constraint range is narrow or the constraints of the upstream power station and the downstream power station are not matched, the initial solution meeting all water level constraints and flow constraints is quickly generated through nonlinear programming, then the initial solution is further optimized through a step-by-step optimization algorithm, and the globally optimal solution is more efficiently approached while the constraint damage is reduced as much as possible.
(2) The invention improves the traditional stepwise optimization algorithm, combines with nonlinear programming, and realizes the optimal scheduling model solution under the condition of complex constraints (water level amplitude variation constraint, flow amplitude variation constraint, cascade power station reserved storage capacity constraint and water abandonment constraint).
Drawings
Fig. 1 is a schematic flow chart of a hybrid algorithm-based solution method for a cascade hydropower station optimized scheduling model provided by the invention;
FIG. 2 is a comparison graph of the calculation results of the method and the single-library dynamic programming-stepwise optimization hybrid algorithm of the present invention for the A power station in example 1;
FIG. 3 is a comparison graph of the calculation results of the method and the single-library dynamic programming-stepwise optimization hybrid algorithm of the present invention for the B power station in example 1;
FIG. 4 is a comparison graph of the calculation results of the method and the single-library dynamic programming-stepwise optimization hybrid algorithm of the present invention for the power station C in example 1;
FIG. 5 is a comparison graph of the calculation results of the single-base dynamic programming-stepwise optimization hybrid algorithm of the present invention for the D power station in example 1;
FIG. 6 is a comparison graph of the calculation results of the method and the single-library dynamic programming-stepwise optimization hybrid algorithm of the present invention for the E power station in example 1;
FIG. 7 is a comparison graph of the calculation results of the method and the single-library dynamic programming-stepwise optimization hybrid algorithm of the present invention for the F power station in example 1;
FIG. 8 is a diagram showing the calculation results of the method of the present invention for the station A in example 2;
FIG. 9 is a diagram showing the calculation results of the method of the present invention for the station B in example 2;
FIG. 10 is a graph of the calculation results of the method of the present invention for the C plant in example 2;
FIG. 11 is a graph of the calculation results of the method of the present invention for the D power station in example 2;
FIG. 12 is a graph showing the calculation results of the E power station in example 2 according to the method of the present invention;
FIG. 13 is a graph of the calculation results of the method of the present invention for the F power plant in example 2.
Detailed Description
The technical solution of the present invention is further described with reference to the accompanying drawings and specific embodiments.
As shown in fig. 1, the hybrid algorithm-based solution method for the optimal scheduling model of the cascade hydropower station of the invention comprises the following steps:
s1, establishing a cascade hydropower station optimized dispatching model which comprises a dispatching target and a constraint condition. The constraint conditions can also comprise water level amplitude variation constraint, flow amplitude variation constraint, cascade power station reserved storage capacity constraint and water abandon constraint besides water level range constraint, flow range constraint and output range constraint which are common in the field of optimal scheduling of water power stations.
And S2, obtaining an initial scheduling process of the cascade hydropower station meeting the relevant constraint conditions of water level, flow and storage capacity by adopting nonlinear programming.
Further, when the initial scheduling process of the cascade hydropower station is solved by adopting nonlinear programming, the water level range constraint needs to be converted into a reservoir capacity range constraint according to a water level-reservoir capacity relation curve; if the water level amplitude variation constraint exists, calculating the water level according to a reservoir capacity-water level functional relation, wherein the reservoir capacity-water level functional relation is a polynomial function; the output of the power station is calculated by adopting the flow water consumption rate of the power station.
Further, the objective function of the nonlinear programming is:
in the formula, E is an objective function value; p i,j 、
γ i,j Respectively representing the output, the power generation flow and the flow water consumption rate of the power station i in the time period j; Δ t j An hour interval of period j; n is the number of power stations; t is the time interval length;
the violation degree of the minimum output constraint at the time period j for the power station i; lambda i,4 Penalty factor for station i violating the minimum output constraint.
The constraint conditions include:
and (3) flow range constraint:
flow amplitude variation constraint: | Q i,j -Q i,j-1 |≤ΔQ i,j
The water level range constraint is converted into a storage capacity range constraint:
water level amplitude variation restraint: l f i (S i,j )-f i (S i,j-1 )|≤ΔZ i,j
And (3) water balance constraint:
and (4) reserving storage capacity constraint:
force restraint:
in the formula, Q i,j 、
ΔQ i,j 、
S i,j 、
ΔZ i,j 、I i,j 、
ΔP i,j Respectively representing the ex-warehouse flow, the minimum ex-warehouse flow, the maximum ex-warehouse flow, the ex-warehouse flow variation, the minimum out-force, the maximum output force, the warehouse capacity, the minimum warehouse capacity, the maximum warehouse capacity, the water level variation, the warehouse entry flow, the power generation flow, the water discharge flow and the difference value between the output force and the minimum output force of the power station i in the time interval j;
the sum of the corresponding storage capacities of the normal water storage levels of the power station with the reserved storage capacity constraint for the time interval j; a. The j Reserving a storage capacity constraint for time period j; omega j With reserve capacity constraint for time period jA collection of power stations; omega T A set formed by time intervals with reserved storage capacity constraints; f. of i The (DEG) is a storage capacity-water level function relation of the power station i.
The initial solution obtained by the nonlinear programming is not necessarily a feasible solution, but must meet all the water level and flow constraint requirements.
And S3, on the basis of the initial scheduling process, converting the multi-stage optimization problem into a plurality of two-stage optimization subproblems by adopting a stepwise optimization algorithm, in the two-stage optimization subproblems, extracting random numbers from the state variable of each power station within the value range to form a combination set, replacing the original state variable value with the combination with the optimal objective function value, continuing to solve the next two-stage optimization subproblem, sequentially traversing all subproblems, completing one iteration, and repeating iterative computation until the iteration termination condition is met to obtain the final cascade hydropower station optimization scheduling process.
Further, the objective function of the two-stage optimization sub-problem is
Wherein E' is the objective function value of the subproblem; lambda [ alpha ] i,1 、λ i,2 、λ i,3 、λ i,4 、λ i,5 Respectively determining a penalty coefficient of the power station i for violating the minimum ex-warehouse constraint, a penalty coefficient for violating the maximum ex-warehouse constraint, a penalty coefficient for violating the ex-warehouse variable amplitude constraint, a penalty coefficient for violating the minimum output constraint and a penalty coefficient for violating the no-water-abandoning constraint; omega s The method is a set formed by power stations and time periods with water abandoning prevention constraints, and if the water abandoning prevention constraints do not exist, the omega is s Is an empty set; i denotes an indicative function.
Further, the two-stage optimization subproblem takes the water level of each power station as a state variable, if no cascade power station reserved storage capacity constraint exists, the generation mode of the water level combination is that n different random numbers are extracted from the water level range of each power station, and a water level combination set of the cascade power station is generated according to the Cartesian product; if the cascade power station reserved storage capacity constraint exists, the water level combination set is composed of combinations meeting the following constraints:
the specific implementation mode is as follows:
(1) will omega j The power stations in (1) are sorted from upstream to downstream by i 1 ,i 2 ,...,i K Wherein K = | Ω j I is the number of power stations in the set;
(2) to power station i 1 Extracting n in the following storage capacity range K Individual random numbers:
(3) to power station i 1 Each value of storage capacity of
Station i 2 Extracting 1 random number and
correspondingly:
(4) by analogy, until the K power station, n is formed K A seed storage capacity combination, which is converted into a water level combination according to a storage capacity-water level function relation;
(5) and (4) for N-K power stations without reserved storage capacity constraint, extracting N different random numbers in the water level range of the power stations respectively, and generating a water level combination set of the cascade power station with the water level combination set in the step (4) according to the Cartesian product.
The invention is further illustrated in the following example 1 with reference to a cascade power station consisting of six hydropower stations a, B, C, D, E and FA synthetic algorithm solution method for a cascade hydropower station optimization scheduling model. The six power stations are sequentially an A power station, a B power station, a C power station, a D power station, an E power station and an F power station from upstream to downstream, wherein the A, B, C, D and E are all power stations adjusted in seasons or more, and the F is a daily adjustment power station. The minimum ecological flow of the A power station in 3-7 months is 1160m 3 S, 900m in other months 3 S; the minimum ecological flow of the B power station in 3-7 months is 1260m 3 S, other months 1160m 3 S; the minimum delivery flow of the C power station is 1200m 3 S; the minimum delivery flow of the D power station is 1700m 3 S; e power station 9-10 months of the ten-day period of the middle of the month, the flow rate of the discharged power station is not less than 8000m 3 And/s, the flow rate of the discharged materials in other time periods is not less than 6000m 3 S; the minimum ex-warehouse flow of the F power station is 5500m 3 And s. The daily rise and daily fall of the power stations A, B, C, D and E are set to be 2m/D. Taking water in a certain typical year as an example, taking ten days as a calculation scale, calculating a 36-ten-day six-bank optimized scheduling scheme, wherein 3 ten days of water in the water sequence do not meet the requirement of the minimum outbound flow of the D power station, 7 ten days of water in the water sequence do not meet the constraint of the minimum outbound flow of the E power station, the phenomena that the requirement of the incoming water and the outbound flow are not matched, the upstream minimum outbound flow plus the interval flow and the requirement of the minimum outbound flow of the downstream power station are not matched exist, and the problem of optimized water allocation of the six power stations is more prominent. Table 1 shows the comparison of the calculation results of the method of the present invention and the single-base dynamic programming-stepwise optimization hybrid algorithm (i.e., the initial solution is calculated by the single-base dynamic programming method and then further optimized by the stepwise optimization algorithm) which is widely used, and fig. 2 to 7 show the comparison of the ex-warehouse flow of each power station calculated by the two methods. In the calculation process of the method, the penalty coefficient lambda is calculated i,1 、λ i,2 、λ i,3 、λ i,5 Are all set to 10000, lambda i,4 100000, and the number of generated random numbers per station in the two-stage optimization sub-problem is set to 8. As can be seen from the table 1, the calculation result of the invention has larger power generation, smaller water abandon and better comprehensive benefit of the cascade power station; as can be seen from FIGS. 2-7, in the results obtained by the single-base dynamic planning-gradual optimization hybrid algorithm, 7 ten days of the D hydropower station violate the ex-warehouse traffic of not less than 1700m 3 Constraint of/s, E station violates ex-warehouse traffic in 4 ten daysLess than 6000m 3 The constraint of/s, the F power station violates the warehouse-out flow not less than 5500m in 2 ten days 3 The constraints of/s are marked by triangle marks respectively, but the method provided by the invention does not violate any constraint, thereby ensuring the reasonability of the calculation result. The result shows that the method provided by the invention can realize reasonable distribution of water quantity among cascade power stations through nonlinear programming under the conditions that constraint conditions are complex and initial feasible solutions are not easy to obtain, ensures that the generated initial solutions meet all water level constraints and flow constraints, and then further optimizes through a stepwise optimization algorithm, thereby reducing constraint damage as much as possible and simultaneously approaching a global optimal solution more efficiently.
TABLE 1 comparison of the method of the present invention with the Single-Bank dynamic programming-stepwise optimization hybrid Algorithm
The following further explains the application of the method provided by the invention under the constraint condition of the reserved storage capacity of the stepped hydropower station by combining the scheduling of the six hydropower stations A, B, C, D, E and F in 8, 21, 9, 20 and 8 days in a certain annual flood season. In the embodiment, besides the conventional water level range constraint, flow range constraint and output range constraint, a water level amplitude variation constraint is provided, namely the daily amplitude of the station A is required to be not more than 3m/D, the daily amplitude of the station B is required to be not more than 2m/D, the daily amplitude of the station C is required to be not more than 3m/D, the daily amplitude of the station D is required to be not more than 2m/D, the daily amplitude of the station E is required to be not more than 3m/D, and the daily amplitude of the station E is required to be not more than 2m/D; and requires a reservation of 96.3 hundred million m for four power stations A, B, C and D at 31 days 8 months 3 And (4) flood control storage capacity. Tables 2 and 3 show the scheduling scheme results obtained by the present invention and the reservation of 96.3 hundred million m for four power stations A, B, C and D at 31 days in 8 months 3 As a result of distribution of flood control storage capacity, 11.27 hundred million m is reserved in the A power station 3 And B power station reserves 58.77 hundred million meters 3 C power station reservation of 21.57 hundred million m 3 D power station reservation of 4.69 hundred million m 3 (ii) a Fig. 8-13 are specific scheduling processes, each plant not violating the corresponding scheduling constraints.
TABLE 2 optimal scheduling calculation results
| Power station | A power station | B power station | C power station | D power station | E power station | F power station | Step ladder |
| Generated energy/(hundred million kW. H) | 74.12 | 92.46 | 82.18 | 39.69 | 161.56 | 20.07 | 470.08 |
| Water reject volume/(hundred million) 3 ) | 25.95 | 0.00 | 22.28 | 28.65 | 57.39 | 213.33 | 347.60 |
TABLE 3 Reserve storage capacity Allocation for monthly 31-day cascaded power stations
| Index (es) | A power station | B power station | C power station | D power station | Step ladder |
| Water level/m | 965.44 | 794.77 | 582.90 | 374.95 | - |
| Reserved storage capacity/(hundred million m) 3 ) | 11.27 | 58.77 | 21.57 | 4.69 | 96.30 |
The above-described embodiments are intended to illustrate rather than limit the invention, and any equivalent variations of the invention are within the scope of the claims and fall within the scope of the invention.
Claims (6)
1. A solving method for a cascade hydropower station optimal scheduling model based on a hybrid algorithm is characterized by comprising the following steps of: it comprises the following steps:
s1, establishing a cascade hydropower station optimized dispatching model, including a dispatching target and a constraint condition;
s2, obtaining an initial scheduling process of the cascade hydropower station meeting relevant constraint conditions of water level, flow and storage capacity by adopting nonlinear programming;
and S3, on the basis of the initial scheduling process, converting the multi-stage optimization problem into a plurality of two-stage optimization subproblems by adopting a stepwise optimization algorithm, in the two-stage optimization subproblems, extracting random numbers from the state variable of each power station within the value range to form a combination set, replacing the original state variable value with the combination with the optimal objective function value, continuing to solve the next two-stage optimization subproblem, sequentially traversing all subproblems, completing one iteration, and repeating iterative computation until the iteration termination condition is met to obtain the final cascade hydropower station optimization scheduling process.
2. The hybrid algorithm-based cascaded hydropower station optimal scheduling model solution method of claim 1, wherein: in the step S1, the scheduling objective is that the cascade power generation amount is maximum, and the constraint condition includes a water level amplitude constraint, a flow rate amplitude constraint, a cascade power station reserved storage capacity constraint, and a non-water-abandoning constraint in addition to a water level range constraint, a flow rate range constraint, and an output range constraint in the field of optimal scheduling of water power stations.
3. The hybrid algorithm-based cascaded hydropower station optimal scheduling model solution method of claim 1, wherein the method comprises the following steps: in the step S2, when the initial scheduling process of the cascade hydropower station is solved by adopting the nonlinear programming, the water level range constraint needs to be converted into the reservoir capacity range constraint according to a water level-reservoir capacity relation curve; if the water level amplitude variation constraint exists, calculating the water level according to a reservoir capacity-water level function relational expression, wherein the reservoir capacity-water level function relational expression is a polynomial function; the output of the power station is calculated by adopting the flow water consumption rate of the power station.
4. The hybrid algorithm-based cascaded hydropower station optimized scheduling model solution method according to claim 1 or 3, characterized in that: the nonlinear programming objective function in step S2 is:
wherein E is the objective function value; p is i,j 、
γ i,j Respectively representing the output, the power generation flow and the flow water consumption rate of the power station i in the time period j; Δ t j An hour interval for time period j; n is the number of power stations; t is the time interval length;
the violation degree of the power station i to the minimum output constraint in the time period j is determined; lambda [ alpha ] i,4 A penalty coefficient for power station i violating the minimum output constraint;
the constraint conditions include:
and (3) flow range constraint:
flow amplitude variation constraint: | Q i,j -Q i,j-1 |≤ΔQ i,j
The water level range constraint is converted into a storage capacity range constraint:
water level amplitude variation restraint: l f i (S i,j )-f i (S i,j-1 )|≤ΔZ i,j
And (3) water balance constraint:
and (4) reserving storage capacity constraint:
force restraint:
in the formula, Q i,j 、
ΔQ i,j 、
S i,j 、
ΔZ i,j 、I i,j 、
ΔP i,j Respectively representing the ex-warehouse flow, the minimum ex-warehouse flow, the maximum ex-warehouse flow, the ex-warehouse flow variation, the minimum out-force, the maximum output force, the warehouse capacity, the minimum warehouse capacity, the maximum warehouse capacity, the water level variation, the warehouse entry flow, the power generation flow, the water discharge flow and the difference value between the output force and the minimum output force of the power station i in the time interval j;
the sum of the corresponding storage capacities of the normal water storage positions of the power stations with reserved storage capacity constraints exists in the time interval j; a. The j Reserving a storage capacity constraint for time period j; omega j A set formed by power stations with reserved storage capacity constraint exists for the time interval j; omega T Reserving a repository for the presenceA set of constrained time periods; f. of i () is a storage capacity-water level function relation of the power station i; the initial solution obtained according to the nonlinear programming is not necessarily a feasible solution, but the requirements of water level constraint and flow constraint are met, and the penalty term applied to the minimum output constraint is to prevent the problem of nonlinear programming from having no solution caused by too narrow output constraint range.
5. The hybrid algorithm-based cascaded hydropower station optimal scheduling model solution method of claim 1, wherein the method comprises the following steps: the objective function of the two-stage optimization sub-problem in the step S3 is
Wherein E' is the objective function value of the subproblem; lambda [ alpha ] i,1 、λ i,2 、λ i,3 、λ i,4 、λ i,5 Respectively determining a penalty coefficient of the power station i for violating the minimum ex-warehouse constraint, a penalty coefficient for violating the maximum ex-warehouse constraint, a penalty coefficient for violating the ex-warehouse variable amplitude constraint, a penalty coefficient for violating the minimum output constraint and a penalty coefficient for violating the no-water-abandoning constraint; omega s The method is a set formed by a power station and a time interval with the constraint of not abandoning water, if the constraint of not abandoning water exists, then omega s Is an empty set; i denotes an indicative function.
6. The hybrid algorithm-based cascaded hydropower station optimal scheduling model solution method of claim 1, wherein the method comprises the following steps: in the step S3, the two-stage optimization subproblem takes the water level of each power station as a state variable, and if there is no cascade power station reserved reservoir capacity constraint, the generation mode of the water level combination extracts n different random numbers for each power station within the water level range of each power station, and generates a water level combination set of the cascade power station according to the cartesian product; if the cascade power station reserved storage capacity constraint exists, the water level combination set is composed of combinations meeting the following constraints:
the specific implementation mode is as follows:
(1) will be omega j The power stations in the system are sorted from upstream to downstream by i 1 ,i 2 ,...,i K Where K = | Ω j I is the number of power stations in the set;
(2) to power station i 1 Extracting n in the following storage capacity range K Individual random numbers:
(3) to power station i 1 Each value of storage capacity of
Station i 2 Extracting 1 random number and
correspondingly:
(4) by analogy, until the K power station, n is formed K A seed storage capacity combination is converted into a water level combination according to a storage capacity-water level functional relation;
(5) and (4) for N-K power stations without reserved storage capacity constraint, extracting N different random numbers in the water level range of the power stations respectively, and generating a water level combination set of the cascade power station with the water level combination set in the step (4) according to the Cartesian product.
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