A multi-objective game scheduling model for reservoir groups based on spatiotemporal collaborative dimensionality reduction and its solution method

Abstract

The present invention discloses a multi-objective game scheduling model for a reservoir group based on spatiotemporal collaborative dimensionality reduction and its solution method. The model includes the following steps: using the water level of each reservoir as a decision variable, calculating the various stakeholders and constraints of the reservoir scheduling system for the reservoir group, and constructing a multi-objective game scheduling model for the reservoir group; constructing a long-, medium-, and short-term hierarchical nesting mechanism to obtain the monthly, daily, and hourly target water levels of the reservoir group based on the multi-objective game scheduling model to generate dynamic constraint intervals at the monthly, daily, and hourly scales; iteratively optimizing the model at the hourly scale based on a deviation feedback mechanism returning to the daily scale; and using key reservoir indicators as the basis for judging the importance of reservoirs, retaining high-importance reservoirs and clustering low-importance reservoirs into equivalent virtual reservoirs. The advantages of this model are: solving the "curse of dimensionality" problem caused by the dual-dimensional coupling of time and space in the traditional scheduling model for large-scale multi-objective scheduling of reservoir groups, and reducing computational complexity while ensuring scheduling accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of reservoir group scheduling, and in particular to a reservoir group multi-objective game scheduling model based on spatiotemporal collaborative dimensionality reduction and a solution method thereof. Background Art

[0002] Reservoir group scheduling plays a key role in multiple tasks such as flood control, water supply, irrigation, and power generation. A scientific and reasonable reservoir group scheduling strategy can not only effectively meet the diversified needs of social and economic development, but also achieve efficient resource utilization on the basis of ensuring ecological security, achieve a dynamic balance among multiple objectives, and maximize comprehensive benefits.

[0003] However, existing reservoir group scheduling methods still have some shortcomings. First, current reservoir group scheduling models mostly use a single time scale and are based on traditional mathematical optimization methods such as linear programming and integer programming. When faced with complex game scenarios involving multiple decision-makers, diverse decision variables, and complex constraints, these methods face the problem of exponential growth in decision variables and computational complexity exceeding the scope of conventional computing power as the scheduling cycle lengthens and the number of reservoirs increases. This is the "curse of dimensionality" problem. Secondly, insufficient consideration of cross-time scale coordination mechanisms has led to a lack of dynamic connection between long-term goals (such as annual power generation plans) and short-term responses (such as real-time flood scheduling), making it difficult to effectively respond to complex environmental changes. At the same time, models at different time scales operate independently, resulting in the accumulation of errors in key parameters such as water level and flow during the transmission process, further exacerbating the problem of model decoupling distortion.

[0004] In summary, existing methods cannot achieve global optimization of multi-scale, multi-objective and multi-constraints while ensuring computational efficiency. Summary of the Invention

[0005] The purpose of the present invention is to provide a multi-objective game scheduling model for a reservoir group based on spatiotemporal collaborative dimensionality reduction and a solution method thereof, thereby solving the aforementioned problems existing in the prior art.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] A multi-objective game scheduling model for a reservoir group based on spatiotemporal collaborative dimensionality reduction and its solution method include the following steps:

[0008] S1. Construction of game scheduling model: Identify the stakeholders of the reservoir scheduling system, use the water level of each reservoir as the decision variable, calculate the stakeholders and constraints of the reservoir group scheduling, and build a multi-objective game scheduling model for the reservoir group;

[0009] S2. Time scale decomposition and nesting: A hierarchical nesting mechanism is constructed for the long-, medium-, and short-term periods. Based on the multi-objective game scheduling model for a reservoir group, the target water levels of the reservoir group at the monthly, daily, and hourly scales are obtained to generate dynamic constraint intervals at the monthly, daily, and hourly scales, respectively. The model is then iteratively optimized at the hourly scale based on a deviation feedback mechanism that returns to the daily scale.

[0010] S3. Spatial scale clustering: The key indicators of reservoirs are used as the basis for judging the importance of reservoirs. Reservoirs of high importance are retained, and reservoirs of low importance are clustered into equivalent virtual reservoirs.

[0011] Preferably, step S2 specifically includes the following contents:

[0012] S21. Using the monthly water level as the decision variable, the reservoir group multi-objective game scheduling model is used to calculate the monthly target water level of the reservoir group, achieve target decomposition, and generate a monthly dynamic constraint interval.

[0013] S22. Using the daily water level as the decision variable and the monthly reservoir group target water level as the constraint, the reservoir group multi-objective game scheduling model is used to calculate the daily reservoir group target water level, achieve target decomposition, and generate a daily dynamic constraint interval.

[0014] S23. Taking the hourly water level as the decision variable and the daily reservoir group target water level as the constraint, the multi-objective game scheduling model of the reservoir group is called to calculate the hourly reservoir group target water level; based on the deviation feedback mechanism, the deviation between the hourly water level and the daily reservoir group target water level is calculated. When the deviation is greater than the preset threshold, it returns to the daily scale level for iterative optimization to achieve intra-day fine-grained adjustment.

[0015] Preferably, the iterative optimization at the daily scale in step S23 is specifically to solve the multi-objective game equilibrium of the multi-objective game scheduling model, and take the minimum deviation between the daily average water level and the monthly reservoir group target water level as the goal, obtain the optimal solution set on the daily scale according to the Pato front, and realize intra-day fine adjustment.

[0016] Preferably, a real-time penalty mechanism is introduced at the hourly scale level, the multi-objective game scheduling model is optimized in real time every 24 hours, and intra-day fine-tuning is achieved based on the daily scale level.

[0017] Preferably, the calculation formula for the monthly scale dynamic constraint interval is:

[0018]

[0019] in, is the target water level of the reservoir group on a monthly scale; is the monthly water level constraint interval; ΔZ m is the monthly relaxation threshold; ΔZ baseis the basic relaxation amount; are the standard deviation and mean of the forecast error of the inflow flow in that month respectively;

[0020] The calculation formula of the daily scale dynamic constraint interval is:

[0021]

[0022] in, is the daily target water level; is the daily water level constraint interval; ΔZ d is the daily relaxation threshold; ΔZ base is the basic relaxation amount; are the standard deviation and mean of the forecast error of the inflow flow on that day;

[0023] The calculation formula of hourly scale dynamic constraint interval is:

[0024]

[0025] in, is the hourly target water level; is the hourly water level constraint interval; ΔZ t is the daily relaxation threshold; ΔZ base is the basic relaxation amount; are the standard deviation and mean of the inflow flow prediction error for the current hour, respectively.

[0026] Preferably, step S3 specifically includes the following contents:

[0027] S31. Set corresponding thresholds for the two key reservoir indicators, the regulating capacity index or the ecological sensitivity;

[0028] S32. Calculate the regulation capacity index or ecological sensitivity of each reservoir, and determine whether the regulation capacity index or ecological sensitivity of each reservoir is greater than or equal to a corresponding threshold. If so, determine the reservoir as a high-importance reservoir; otherwise, determine the reservoir as a low-importance reservoir;

[0029] S33. Use spectral clustering or K-means algorithm to construct a spatial feature matrix for each low-importance reservoir based on reservoir location, storage capacity, maximum discharge flow, and design function, and cluster the spatial feature matrix to cluster the low-importance reservoirs into equivalent virtual reservoirs.

[0030] Preferably, the calculation formula for the reservoir's regulating capacity index and ecological sensitivity is:

[0031]

[0032] E s =∑w k ×fk (ΔQ)

[0033] Among them, I r is the reservoir regulation capacity index; V eff To effectively regulate storage capacity; Q avg is the average runoff of the reservoir during the dispatching period; E s is the ecological sensitivity of the reservoir; w k is the kth ecological goal weight; f k (ΔQ) is the ecological response function that quantifies the negative impact of flow change ΔQ on the kth ecological target.

[0034] Preferably, the constructed spatial feature matrix is,

[0035]

[0036] Among them, F i is the spatial characteristic matrix of the i-th reservoir; Lat and Lon are the longitude and latitude coordinates respectively; is the maximum storage capacity of the i-th reservoir; is the maximum discharge of the i-th reservoir; w ik is the dispatch target weight, which represents the weight of the i-th reservoir on the k-th functional target;

[0037] Clustering the spatial feature matrix is

[0038]

[0039] Among them, W ij is the similarity between reservoirs i and j; F j is the spatial feature matrix of the jth reservoir; σ takes the median of the feature interval.

[0040] Preferably, step S3 further includes:

[0041] S34. Establish an equivalent storage capacity curve for the equivalent virtual reservoir.

[0042]

[0043] Among them, V agg (h) is the equivalent storage capacity of the equivalent virtual reservoir when the water level is h; V i (h) is the original storage capacity of the i-th reservoir when the water level is h; a i is the storage capacity weight of the i-th reservoir allocated according to the regulation capacity; b is the standard deviation correction coefficient used to compensate for the clustering error; is the average storage capacity of the reservoir; C is the total number of reservoirs.

[0044] Preferably, in step S1, the reservoir scheduling system includes five stakeholders, namely flood control goals, power generation goals, shipping goals, water supply goals and ecological goals;

[0045] The constraints include water balance constraints, water level upper and lower limit constraints, reservoir discharge capacity constraints, outflow flow constraints, hourly water balance constraints, and flow mutation constraints.

[0046] The beneficial effects of the present invention are as follows: 1. The present invention proposes a scale-based dimensionality reduction method that significantly reduces the computational complexity of complex game systems. 2. The present invention dynamically couples rolling time-domain optimization and hierarchical dimensionality reduction methods to achieve cross-scale multi-objective collaboration, providing theoretical support and practical guidance for the efficient allocation of water resources. 3. The present invention clusters reservoirs to reduce the dimensionality of scheduling calculations, thereby improving the computational efficiency of the entire scheduling process. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 is a flow chart of a method in an embodiment of the present invention. DETAILED DESCRIPTION

[0048] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0049] Example 1

[0050] In this embodiment, addressing the shortcomings of existing models, such as low computational efficiency when faced with complex game scenarios, the present invention addresses multi-objective demands such as flood control, power generation, shipping, water supply, and ecological protection. This method proposes a three-level temporal nested optimization method at monthly, daily, and hourly scales, as well as a spatial clustering method based on "equivalent virtual reservoirs." This method proposes a multi-objective game scheduling model and solution method for reservoir clusters based on spatiotemporal dimensionality reduction, which helps achieve cross-scale multi-objective coordination and efficient resource allocation for reservoir clusters. This method introduces a rolling optimization mechanism on the temporal scale. Through hierarchical modeling and cross-scale parameter transfer, it decomposes long-term problems into short-term ones, implementing a step-by-step rolling optimization process. This improves the accuracy and real-time performance of system optimization and achieves the coordinated optimization of long-term strategic goals and short-term dynamic responses. In the spatial dimension, multiple reservoirs are classified based on factors such as their function, geographic location, and scheduling requirements, and reservoirs belonging to the same category are merged into a single "equivalent virtual reservoir." This spatiotemporal dimensionality reduction method addresses the "curse of dimensionality" problem caused by the dual coupling of time and space in traditional scheduling models for multi-objective scheduling of large-scale reservoir clusters, reducing computational complexity by two orders of magnitude while ensuring scheduling accuracy. The method specifically includes the following parts:

[0051] 1. Construction of Game Scheduling Model

[0052] Identify the stakeholders of the reservoir operation system, use the water level of each reservoir as the decision variable, calculate the stakeholders and constraints of the reservoir group operation, and build a multi-objective game operation model for the reservoir group. Specifically:

[0053] 1.1. Definition of game players: The reservoir operation system includes five stakeholders, namely flood control goals, power generation goals, shipping goals, water supply goals, and ecological goals.

[0054] 1.2. Calculation of game objectives and constraints: Taking the water level of each reservoir as the decision variable, the flood control objectives, power generation objectives, shipping objectives, water supply objectives, ecological objectives and their constraints of the reservoir group operation are calculated according to the following formula, and a multi-objective game operation model for the reservoir group is constructed.

[0055] The calculation formula for each target is as follows:

[0056] ① Power generation target, expressed as the maximum total power generation of the cascade reservoirs during the calculation period,

[0057]

[0058] N i (t) = K i Q i (t)H i (t)

[0059] Where T is the total number of calculation periods; n is the number of reservoirs in the cascade group; N i (t) is the output of the i-th reservoir in the t-th period; K i is the output coefficient of the i-th reservoir; Q i (t) is the power generation flow of the i-th reservoir in the t-th period; H i (t) is the average power generation head of the i-th reservoir in the t-th period; Δt is the calculation period step.

[0060] ② Water supply target: expressed as the minimum water shortage,

[0061]

[0062] Among them, Q out,i (t) is the outflow of the i-th reservoir in the t-th period; Q eco,i (t) is the target water flow required for navigation of the i-th reservoir in the t-th period; n is the number of cascade reservoirs; Δt is the step length of the calculation period.

[0063] ③ Shipping target: expressed as the maximum navigation guarantee rate,

[0064]

[0065] Among them, Qout,i (t) is the outflow of the i-th reservoir in the t-th period; Q ship,i (t) is the minimum navigable flow of the i-th reservoir in the t-th period; #() is an indicator function, which is 1 if the conditions in the brackets are met, otherwise it is 0.

[0066] ④Flood control target: expressed as the maximum flood control safety guarantee rate,

[0067]

[0068] Among them, Q out,i (t) is the outflow of the i-th reservoir in the t-th period; Q saf,i (t) is the safe flood discharge of the i-th reservoir in the t-th period; #() is an indicator function, which is 1 if the conditions in the brackets are met, and 0 otherwise.

[0069] ⑤ Ecological goal: to minimize ecological water shortage,

[0070]

[0071] Among them, Q out,i (t) is the outflow of the i-th reservoir in the t-th period; Q eco,i is the minimum ecological flow of the i-th reservoir.

[0072] The calculation formulas for each constraint condition are as follows:

[0073] ① Water balance constraints:

[0074]

[0075] in, and are the storage capacity, inflow and outflow of the i-th reservoir in the t-th period during the scheduling period.

[0076] ② Upper and lower limit constraints of water level (reservoir capacity):

[0077]

[0078] in, is the water level in front of the dam of the i-th reservoir at the t-th period; is the water level constraint range of the reservoir.

[0079] ③Reservoir discharge capacity constraints:

[0080]

[0081] in, is the water level in front of the dam of the i-th reservoir at the t-th period The maximum discharge capacity under the

[0082] ④Outbound flow constraints:

[0083]

[0084] Where, is the lower limit of the discharge flow of the i-th reservoir; is the discharge flow of the i-th reservoir in the t-1 period during the scheduling period; ΔQ i is the upper limit of the daily outflow fluctuation of the i-th reservoir.

[0085] ⑤Hourly water balance constraints:

[0086]

[0087] Among them, V h+1 and V h are the storage capacity of the reservoir at hour h and hour h-1 respectively; and are the inflow and outflow of the reservoir at hour h respectively.

[0088] ⑥ Traffic mutation restriction:

[0089]

[0090] in, and are the discharge of the reservoir at hour h and hour h-1, ΔQ max It is the upper limit of the flow rate change rate between adjacent hours.

[0091] 2. Time Scale Decomposition and Nesting

[0092] A hierarchical nested mechanism of long (monthly)-medium (daily)-short (hourly) periods is established, and the target water levels of the reservoir group at the monthly, daily and hourly scales are obtained based on the multi-objective game scheduling model of the reservoir group to generate dynamic constraint intervals at the monthly, daily and hourly scales respectively; and the model is iteratively optimized at the hourly scale level based on the deviation feedback mechanism returning to the daily scale level.

[0093] 2.1. Monthly scale: Taking the monthly water level as the decision variable, the multi-objective game scheduling model of the reservoir group is called to calculate the monthly target water level of the reservoir group, realize the target decomposition and generate the monthly dynamic constraint interval. The calculation formula of the monthly dynamic constraint interval is:

[0094]

[0095] in, is the target water level of the reservoir group on a monthly scale; is the monthly water level constraint interval; ΔZ m is the monthly relaxation threshold; ΔZbase is the basic relaxation amount; are the standard deviation and mean of the forecast error of the inflow flow for that month respectively.

[0096] 2.2 Daily scale: Taking the daily scale water level as the decision variable and the monthly scale reservoir group target water level as the constraint, the reservoir group multi-objective game scheduling model is called to calculate the daily scale reservoir group target water level, realize the target decomposition and generate the daily scale dynamic constraint interval. The calculation formula of the daily scale dynamic constraint interval is:

[0097]

[0098] in, is the daily target water level; is the daily water level constraint interval; ΔZ d is the daily relaxation threshold; ΔZ base is the basic relaxation amount; are the standard deviation and mean of the inflow flow forecast error for the day, respectively.

[0099] 2.3. Hourly scale: Taking the hourly scale water level as the decision variable and the daily scale reservoir group target water level as the constraint, the reservoir group multi-objective game scheduling model is used to calculate the hourly scale reservoir group target water level. The calculation formula for the hourly scale dynamic constraint interval is:

[0100]

[0101]

[0102] in, is the hourly target water level; is the hourly water level constraint interval; ΔZ t is the daily relaxation threshold; ΔZ base is the basic relaxation amount; are the standard deviation and mean of the inflow flow prediction error for the current hour, respectively.

[0103] At the hourly scale level, the deviation between the hourly scale water level and the daily scale reservoir group target water level is calculated based on the deviation feedback mechanism. When the deviation is greater than the preset threshold, it returns to the daily scale level for iterative optimization to achieve fine-grained adjustment within the day.

[0104] The specific process is: to solve the multi-objective game equilibrium of the multi-objective game scheduling model (the objective function includes flood control objectives, power generation objectives, shipping objectives, water supply objectives, and ecological objectives), and to minimize the deviation between the daily average water level and the monthly reservoir group target water level. According to the Patou front, the optimal solution set on the daily scale is obtained to achieve fine-grained adjustment within the day.

[0105] The formula for minimizing the deviation between the daily average water level and the monthly reservoir group target water level is as follows:

[0106]

[0107] in, is the water level of the reservoir group on the tth day on a daily scale, It is the target water level of the reservoir group on a monthly scale.

[0108] At the hourly level, a real-time penalty mechanism should be introduced to update the real-time optimization model every 24 hours, make fine adjustments within the day based on the medium-term plan, and optimize the model objective function in real time.

[0109] 3. Spatial Scale Clustering

[0110] The key indicators of reservoirs are used as the basis for judging the importance of reservoirs. Reservoirs with high importance are retained, and reservoirs with low importance are clustered into equivalent virtual reservoirs.

[0111] 3.1. Set corresponding thresholds for the two key reservoir indicators: regulating capacity index or ecological sensitivity.

[0112] 3.2. Calculate the regulating capacity index or ecological sensitivity of each reservoir and determine whether the regulating capacity index or ecological sensitivity of each reservoir is greater than or equal to the corresponding threshold. If so, the reservoir is determined to be a high-importance reservoir and retained. Otherwise, the reservoir is determined to be a low-importance reservoir. The calculation formula for the regulating capacity index and ecological sensitivity is:

[0113]

[0114] E s =∑w k ×f k (ΔQ)

[0115] Among them, I r is the reservoir regulation capacity index; V eff To effectively regulate storage capacity; Q avg is the average runoff of the reservoir during the dispatching period; E s is the ecological sensitivity of the reservoir; w k is the kth ecological goal weight; f k (ΔQ) is the ecological response function that quantifies the negative impact of flow change ΔQ on the kth ecological target.

[0116] 3.3. Using spectral clustering or K-means algorithm, a spatial feature matrix is ​​constructed for each low-importance reservoir based on reservoir location, storage capacity, maximum discharge flow, design function, etc., and the spatial feature matrix is ​​clustered to cluster the low-importance reservoirs into equivalent virtual reservoirs.

[0117] The spatial feature matrix is ​​expressed as,

[0118]

[0119] Among them, F i is the spatial characteristic matrix of the i-th reservoir; Lat and Lon are the longitude and latitude coordinates respectively; is the maximum storage capacity of the i-th reservoir; is the maximum discharge of the i-th reservoir; w ik is the scheduling target weight, which represents the weight of the i-th reservoir on the k-th functional target.

[0120] The formula for clustering the spatial feature matrix is:

[0121]

[0122] Among them, W ij is the similarity between reservoirs i and j; F j is the spatial feature matrix of the jth reservoir; σ takes the median of the feature interval.

[0123] 3.4. Establish an equivalent storage capacity curve for the equivalent virtual reservoir; the formula is:

[0124]

[0125] Among them, V agg (h) is the equivalent storage capacity of the equivalent virtual reservoir when the water level is h; V i (h) is the original storage capacity of the i-th reservoir when the water level is h; a i is the storage capacity weight of the i-th reservoir allocated according to the regulation capacity; b is the standard deviation correction coefficient used to compensate for the clustering error; is the average storage capacity of the reservoir; C is the total number of reservoirs.

[0126] Example 2

[0127] A series of comprehensive water conservancy projects with good regulation capabilities and large storage capacity have been planned in the upper reaches of the Yangtze River, including the Jinsha River Middle Reservoir Group, the Jinsha River Lower Reservoir Group, the Yalong River Reservoir Group, the Minjiang River Reservoir Group, the Jialing River Reservoir Group, the Wujiang River Reservoir Group, and the Three Gorges-Gezhouba cascade reservoir group on the main stream, with a regulation storage capacity of 110 billion m 3. This embodiment takes the cascade reservoir group in the upper reaches of the Yangtze River as an example, which includes a cascade system consisting of 12 reservoirs, including Liyuan (R1), Ahai (R2), Jin'anqiao (R3), Longkaikou (R4), Ludila (R5), Guanyinyan (R6), Wudongde (R7), Baihetan (R8), Xiluodu (R9), Xiangjiaba (R10), Tingzikou (R11), and Three Gorges (R12). In this embodiment, the method provided in Example 1 is used to optimize the scheduling strategy of the above-mentioned reservoir group from June to August 2023, which specifically includes the following contents,

[0128] 1. Construction of Game Scheduling Model

[0129] 1.1. Definition of Game Subjects: The scheduling objectives of the cascade reservoir group in the upper reaches of the Yangtze River include five game objectives, namely flood control objectives, power generation objectives, shipping objectives, water supply objectives, and ecological objectives.

[0130] 1.2. Calculation of Game Objectives and Constraints: Using the water levels of the 12 reservoirs as decision variables, the following formulas are used to calculate the flood control, power generation, shipping, water supply, and ecological objectives, as well as their constraints, for the reservoir cluster operation. This constructs the overall framework of the multi-objective game scheduling model for the reservoir cluster. The calculation formulas for the relevant objectives and constraints are described in Example 1.

[0131] 2. Time Scale Decomposition and Nesting

[0132] Target decomposition and constraint generation need to be achieved on the long-term (monthly) scale. The model outputs the monthly target water level and generates dynamic constraint intervals.

[0133] Then, with the long-term output target water level as a constraint, the model outputs the daily target water level and generates a dynamic constraint interval.

[0134] Finally, the medium-term (daily) target water level is used as a constraint, and the model outputs the hourly target water level, generating a dynamic constraint interval.

[0135] At the short-term (hourly) level, a deviation feedback mechanism is introduced to calculate the deviation between the hourly water level and the daily reservoir target water level. When the deviation exceeds a preset threshold, it returns to the daily level for iterative optimization, achieving refined intra-day adjustments. The specific optimization process involves solving a multi-objective game equilibrium (multiple objectives include power generation, water supply, shipping, and flood control), with the goal of minimizing the deviation between the daily average water level and the monthly reservoir target water level. Based on the Pareto front, the optimal solution set at the medium-term scale is obtained.

[0136] A real-time penalty mechanism is introduced in the short-term layer, and the real-time optimization model is updated every 24 hours. Intraday fine-tuning is performed based on the medium-term plan to optimize the objective function of the model in real time.

[0137] 3. Spatial Scale Clustering

[0138] Calculate the reservoir key indicator regulation capacity index or ecological sensitivity, and determine the reservoir with high regulation capacity index or high ecological sensitivity as a high-importance reservoir and retain it. This embodiment takes the regulation capacity judgment as an example, and sets the high regulation capacity (I r >0.8) are high-importance reservoirs and need to be optimized independently, while low-importance reservoirs can be simplified by clustering.

[0139] Taking the Three Gorges Reservoir as an example, its I r The value is 1.05, and the rest of the reservoirs I r The values ​​are 0.78, 0.69, 0.91, 0.86, 0.8, 0.72, 1.23, 1.76, 1.45, 0.92, 0.78, and 1.05, respectively, so there are 8 high-importance reservoirs and 4 low-importance reservoirs.

[0140] Clustering of four low-importance reservoirs. First, construct the spatial feature vector. In the actual calculation, the parameters are standardized. Specifically, the longitude and latitude are normalized to the interval [0,1], and the reservoir capacity is divided by 109m 3 , discharge flow divided by 5000m 3 / s, the standardized vectors are: F1 = [0.1, 0.34, 0.8, 1.2, 0.5], F2 = [0.13, 0.35, 0.6, 0.9, 0.7], F5 = [0.12, 0.34, 0.7, 1.3], and F6 = [0.14, 0.36, 0.6, 1.2]. The clustering results are C1 = {R1, R2, R3} and C2 = {R4, R5, R6}, which are clustered into two equivalent virtual reservoirs. The equivalent storage capacity curve is then established for the equivalent virtual reservoirs.

[0141] In this embodiment, the traditional method and the method of the present invention were used for comparative evaluation. From the perspective of variable dimension, the number of variables required for calculating 12 reservoirs by the traditional method is 12×92×24=26496. After the collaborative dimensionality reduction of time and space by the method of the present invention, the number of variables is (5×30+3×5+4×1)×24=4056, which is a reduction of about 85%. In terms of calculation time, the traditional method takes 147 minutes to run the model once, while the method of the present invention only takes 24 minutes, which improves the efficiency by 84%. In terms of overall benefits, the benefits of each scheduling target of the method of the present invention are on par with those of the traditional method.

[0142] By adopting the above technical solution disclosed in the present invention, the following beneficial effects are obtained:

[0143] This paper provides a multi-objective game scheduling model for a reservoir group based on spatiotemporal collaborative dimensionality reduction and its solution method. The paper proposes a scale-based dimensionality reduction method that significantly reduces the computational complexity of complex game systems. The paper dynamically couples rolling time-domain optimization and hierarchical dimensionality reduction methods to achieve cross-scale multi-objective collaboration, providing theoretical support and practical guidance for the efficient allocation of water resources. By clustering reservoirs, the paper reduces the dimensionality of scheduling calculations, thereby improving the computational efficiency of the entire scheduling process.

[0144] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A multi-objective game scheduling model for a reservoir group based on spatiotemporal collaborative dimensionality reduction and its solution method, characterized by: The following steps are included: S1. Game Scheduling Model Construction: Using the water level of each reservoir as the decision variable, the various stakeholders and constraints of reservoir group scheduling are calculated to construct a multi-objective game scheduling model for the reservoir group. The reservoir scheduling system includes five stakeholders: flood control objectives, power generation objectives, shipping objectives, water supply objectives, and ecological objectives. S2. Time scale decomposition and nesting: A hierarchical nesting mechanism is constructed for the long-, medium-, and short-term periods. Based on the multi-objective game scheduling model for a reservoir group, the target water levels of the reservoir group at the monthly, daily, and hourly scales are obtained to generate dynamic constraint intervals at the monthly, daily, and hourly scales, respectively. The model is then iteratively optimized at the hourly scale based on a deviation feedback mechanism that returns to the daily scale. S3. Spatial scale clustering: Using key reservoir indicators as the basis for judging the importance of reservoirs, high-importance reservoirs are retained, and low-importance reservoirs are clustered into equivalent virtual reservoirs; Step S3 specifically includes the following contents: S31. Set corresponding thresholds for the two key reservoir indicators, the regulating capacity index or the ecological sensitivity; The calculation formula of the reservoir's regulating capacity index and ecological sensitivity is: E s =∑w k ×f k (ΔQ) Among them, I r is the reservoir regulation capacity index; V eff To effectively regulate storage capacity; Q avg is the average runoff of the reservoir during the dispatching period; E s is the ecological sensitivity of the reservoir; w k is the kth ecological goal weight; f k (ΔQ) is the ecological response function that quantifies the degree of negative impact of flow change ΔQ on the kth ecological goal; S32. Calculate the regulation capacity index or ecological sensitivity of each reservoir, and determine whether the regulation capacity index or ecological sensitivity of each reservoir is greater than or equal to a corresponding threshold. If so, determine the reservoir as a high-importance reservoir; otherwise, determine the reservoir as a low-importance reservoir; S33. Using spectral clustering or K-means algorithm, construct a spatial feature matrix for each low-importance reservoir based on reservoir location, storage capacity, maximum discharge flow, and design function, and cluster the spatial feature matrix to cluster the low-importance reservoirs into equivalent virtual reservoirs; The constructed spatial feature matrix is: Among them, F i is the spatial characteristic matrix of the i-th reservoir; Lat and Lon are the longitude and latitude coordinates respectively; is the maximum storage capacity of the i-th reservoir; is the maximum discharge of the i-th reservoir; w ik is the dispatch target weight, which represents the weight of the i-th reservoir on the k-th functional target; Clustering the spatial feature matrix is Among them, W ij is the similarity between reservoirs i and j; F j is the spatial feature matrix of the jth reservoir; σ takes the median of the feature interval.

2. The multi-objective game scheduling model for a reservoir group based on spatiotemporal coordinated dimensionality reduction and its solution method according to claim 1 is characterized by: Step S2 specifically includes the following contents: S21. Using the monthly water level as the decision variable, the reservoir group multi-objective game scheduling model is used to calculate the monthly target water level of the reservoir group, achieve target decomposition, and generate a monthly dynamic constraint interval. S22. Using the daily water level as the decision variable and the monthly reservoir group target water level as the constraint, the reservoir group multi-objective game scheduling model is used to calculate the daily reservoir group target water level, achieve target decomposition, and generate a daily dynamic constraint interval. S23. Taking the hourly water level as the decision variable and the daily reservoir group target water level as the constraint, the multi-objective game scheduling model of the reservoir group is called to calculate the hourly reservoir group target water level; based on the deviation feedback mechanism, the deviation between the hourly water level and the daily reservoir group target water level is calculated. When the deviation is greater than the preset threshold, it returns to the daily scale level for iterative optimization to achieve intra-day fine-grained adjustment.

3. The multi-objective game scheduling model for a group of reservoirs based on spatiotemporal coordinated dimensionality reduction and its solution method according to claim 2 is characterized by: The iterative optimization at the daily scale in step S23 is specifically to solve the multi-objective game equilibrium of the multi-objective game scheduling model, and take the minimum deviation between the daily average water level and the monthly reservoir group target water level as the goal, obtain the optimal solution set on the daily scale according to the Patou front, and realize intra-day fine adjustment.

4. The multi-objective game scheduling model for a group of reservoirs based on spatiotemporal coordinated dimensionality reduction and its solution method according to claim 3 is characterized by: A real-time penalty mechanism is introduced at the hourly scale, and the multi-objective game scheduling model is optimized in real time every 24 hours, achieving intra-day fine-grained adjustments based on the daily scale.

5. The multi-objective game scheduling model for a reservoir group based on spatiotemporal coordinated dimensionality reduction and its solution method according to claim 2 is characterized by: The calculation formula of the monthly scale dynamic constraint interval is: in, is the target water level of the reservoir group on a monthly scale; is the monthly water level constraint interval; ΔZ m is the monthly relaxation threshold; ΔZ base is the basic relaxation amount; are the standard deviation and mean of the forecast error of the inflow flow in that month respectively; The calculation formula of the daily scale dynamic constraint interval is: in, is the daily target water level; is the daily water level constraint interval; ΔZ d is the daily relaxation threshold; ΔZ base is the basic relaxation amount; are the standard deviation and mean of the forecast error of the inflow flow on that day; The calculation formula of hourly scale dynamic constraint interval is: in, is the hourly target water level; is the hourly water level constraint interval; ΔZ t is the daily relaxation threshold; ΔZ base is the basic relaxation amount; are the standard deviation and mean of the inflow flow prediction error for the current hour, respectively.

6. The multi-objective game scheduling model for a reservoir group based on spatiotemporal coordinated dimensionality reduction and its solution method according to claim 1 is characterized by: Step S3 also includes, S34. Establish an equivalent storage capacity curve for the equivalent virtual reservoir. Among them, V agg (h) is the equivalent storage capacity of the equivalent virtual reservoir when the water level is h; V i (h) is the original storage capacity of the i-th reservoir when the water level is h; a i is the storage capacity weight of the i-th reservoir allocated according to the regulation capacity; b is the standard deviation correction coefficient used to compensate for the clustering error; is the average storage capacity of the reservoir; C is the total number of reservoirs.

7. The multi-objective game scheduling model for a group of reservoirs based on spatiotemporal coordinated dimensionality reduction and its solution method according to claim 1 is characterized by: In step S1, the constraints include water balance constraints, water level upper and lower limit constraints, reservoir discharge capacity constraints, outflow flow constraints, hourly water balance constraints, and flow mutation constraints.

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