Cascade reservoir pre-discharge water quantity aggregation decomposition method based on flood control reservoir capacity joint optimization design

Abstract

The invention discloses a cascade reservoir pre-discharge water quantity aggregation decomposition method based on flood control storage capacity joint optimization design. The method comprises the following steps: deducing a flood control storage capacity joint optimization calculation formula of a two-storage and multi-storage aggregation system; the forecast pre-drainage dispatching of the single reservoir is expanded to a cascade reservoir, flood control risk analysis is conducted, and finally the upper limit of the pre-drainage water amount is determined; deducing a pre-discharge water quantity aggregation decomposition calculation formula of the two-reservoir and multi-reservoir aggregation system, deducing a flood season total power generation increment formula of the two-reservoir and multi-reservoir aggregation system, and solving; and calculating the average total power generation capacity of the cascade reservoir for many years by adopting the originally designed flood control storage capacity, comparing the average total power generation capacity with the total power generation capacity after the flood control storage capacity joint optimization design of the cascade reservoir, and analyzing the increment change condition of the flood control storage capacity joint optimization design on the power generation benefit of the cascade reservoir. According to the method, the application of the equivalent flood control storage capacity of the cascade reservoir can be deepened, the limitation of designing the flood control storage capacity of planning design of a single reservoir is overcome, and a decision basis is provided for optimization of flood season scheduling of the cascade reservoir.

Description

Technical Field

[0001] This invention relates to a method for the aggregation and decomposition of pre-discharge volume of cascade reservoirs, specifically a method for the aggregation and decomposition of pre-discharge volume of cascade reservoirs based on the joint optimization design of flood control capacity, belonging to the technical field of flood control safety and operation management design of water conservancy and hydropower projects. Background Technology

[0002] Pre-discharge refers to the reservoir capacity between the operating water level and the flood control limit during the forecasted pre-discharge scheduling. Its purpose is to increase power generation and accommodate water storage after the flood season. Dynamic control of the operating water level during the flood season can safely lower the water level to the flood control limit within the effective forecast period based on forecast information, thus ensuring the flood control safety of the reservoir dam and downstream flood control targets. However, the scheduling and operation of cascade reservoirs within the same basin during the flood season does not consider the complementary relationship of flood control capacity between cascade reservoirs and the impact of upstream reservoir regulation on downstream areas. Therefore, after the completion and commissioning of cascade reservoirs, it is not advisable to implement dynamic control of the operating water level during the flood season based on the design flood control capacity of a single reservoir. Instead, a joint optimization design based on the flood control capacity of the cascade reservoirs should be implemented to improve the utilization efficiency of flood resources.

[0003] In the prior art, 1) a method for real-time dynamic control of flood control water level of cascade reservoirs disclosed in CN103088784A is proposed. This invention establishes a real-time dynamic control model for flood control water level of cascade reservoirs based on the "large system aggregation and decomposition idea" and uses successive optimization method to optimize the real-time dynamic control scheme for flood control water level of cascade reservoirs; 2) a method for dynamic control of flood season operation water level of three-dimensional and above cascade reservoirs disclosed in CN105676890A is proposed. This invention is based on aggregation-decomposition theory and pre-storage and pre-release method, analyzes the relationship between the upper limit of pre-storage water level of three-dimensional and above cascade reservoirs, and establishes a flood control risk rate within the effective forecast period of flood forecast, giving... The non-dominated solution set for dynamic control of operating water level during the flood season is used to select the optimal dynamic control decision scheme for operating water level during the flood season; 3) A dynamic control method for operating water level of cascade reservoirs during the flood season based on time-varying design floods disclosed in CN109558626A is used to deduce time-varying design floods of multiple design frequencies, and combine the date, design frequency and time-varying design flood value to form a time-varying inflow flood identification model to judge the design frequency and shape of the inflow flood; before entering the flood season, the upstream reservoir reduces its own flood season operating water level to impound the inflow flood and reduce the flood control pressure on the downstream reservoir, and the downstream reservoir increases the power generation of the cascade reservoirs by exceeding the flood season limit water level. However, the above-mentioned existing technologies are all based on the flood control capacity of a single reservoir design and do not consider the problem of joint optimization design of flood control capacity of cascade reservoirs. Based on this, this application proposes a method for aggregation and decomposition of pre-discharge volume of cascade reservoirs based on joint optimization design of flood control capacity. Summary of the Invention

[0004] The purpose of this invention is to provide a method for the aggregation and decomposition of pre-discharge water volume of cascade reservoirs based on the joint optimization design of flood control storage capacity in order to solve at least one of the above-mentioned technical problems. The method is simple and quick to calculate, and has clear logic, and can be extended to related fields.

[0005] This invention achieves the above objective through the following technical solution: a method for aggregated decomposition of pre-discharge volume of cascade reservoirs based on joint optimization design of flood control storage capacity, comprising the following steps:

[0006] S1. Collect characteristic parameters of cascade reservoirs, daily flow series during the flood season, and safe flow thresholds at downstream outlet sections of cascade reservoirs. Based on the power generation calculation process and the scheduling characteristics during the flood season, simplify the reservoir capacity constraints, reservoir dam water level fluctuation constraints, and power station output constraints. Conduct joint optimization design of flood control capacity for cascade reservoirs and derive joint optimization calculation formulas for flood control capacity of two-reservoir and multi-reservoir aggregation systems.

[0007] S2. Extend the forecasting and pre-discharge scheduling of a single reservoir to cascade reservoirs, conduct flood risk analysis, and finally determine the upper limit of the pre-discharge volume;

[0008] S3. Based on the joint optimization calculation formula of flood control capacity of two-reservoir and multi-reservoir aggregation system, derive the aggregation decomposition calculation formula of pre-discharge volume of two-reservoir and multi-reservoir aggregation system, derive the formula of total power generation increment of two-reservoir and multi-reservoir aggregation system during flood season and solve it;

[0009] S4. Under the premise that the inflow of the cascade reservoirs remains unchanged, calculate the multi-year average total power generation of the cascade reservoirs using the original design flood control capacity, and compare it with the total power generation after the joint optimization design of the flood control capacity of the cascade reservoirs. Analyze the incremental changes in the power generation benefits of the cascade reservoirs due to the joint optimization design of the flood control capacity.

[0010] As a further aspect of the present invention: In S1, the joint optimization calculation formula for flood control capacity of the two-reservoir and multi-reservoir aggregation system is as follows:

[0011]

[0012] In the formula: t is the time variable, s, t=1,2,...,T, where T is the length of the calculation period; m is the reservoir number from top to bottom in the cascade reservoir series, m=1,2,...,M, where M is the number of reservoirs; n y Indicates the number of years; k m Let be the comprehensive output coefficient of the m-th reservoir; Z u,m (·) represents the function relating the upstream water level to the reservoir capacity of the m-th reservoir, which is fitted using a power function, i.e. (a m >0,b m>0), and because as the reservoir capacity increases, the change in water level above the dam corresponding to a unit change in reservoir capacity decreases sharply, that is... Therefore, 0 < b m <1; V m (t) and V m (t+1) represent the reservoir capacity of the m-th reservoir at times t and t+1, respectively. 3 ;q in,m (t) and q out,m (t) represents the average inflow and outflow of the m-th reservoir at time t, respectively. 3 / s; The total flood control capacity of reservoir M during the flood season is m 3 ;λ and λ * These represent the percentage of the original and optimized flood control capacity of the headwater reservoir relative to the total flood control capacity of the two reservoirs. V nor,m Let m be the reservoir capacity corresponding to the flood control high water level of the m-th reservoir. 3 .

[0013] As a further aspect of the present invention, S2 includes the following sub-steps:

[0014] S21. Give the formula for the pre-release scheduling of M reservoirs during time period t:

[0015] S22. Determine the flood control risks of the multi-reservoir aggregation system;

[0016] S23. Determine the upper limit of the pre-discharge volume of the multi-reservoir aggregation system.

[0017] As a further aspect of the present invention: In S21, the pre-release scheduling of the aggregated reservoir is expressed as follows:

[0018]

[0019] In the formula: T c Forecast period; q in,m (t) and Let m be the average inflow of the m-th reservoir and the combined reservoir at time t. 3 / s;q z,m (t) represents the flow rate between the m-th reservoir and the (m+1)-th reservoir, where m 3 / s;V *low V *up , and These are the minimum aggregated reservoir capacity (aggregated reservoir capacity after pre-release scheduling), the maximum aggregated reservoir capacity (aggregated reservoir capacity before pre-release scheduling), the initial safe reservoir capacity, and the aggregated pre-release volume within the forecast period; among which... V x,m Let m be the reservoir capacity corresponding to the flood control limit water level of the m-th reservoir.

[0020] As a further aspect of the present invention: in S22, the sources of flood risk can be divided into the following two categories:

[0021] The first category is the risk of pre-release scheduling decisions caused by errors in flood inflow forecasts, which can be further divided into four types of random events for discussion:

[0022] Event E1:

[0023] Event E2:

[0024] Event E3:

[0025] Event E4:

[0026] in, This refers to the maximum inflow rate of the Juhe Reservoir predicted during the forecast period.

[0027] The second category is the uncertainty risk of the flood hydrograph, when a flood has a frequency of p, i.e., T p Once a year, T p =1 / p When the design flood occurs at the end of the forecast period, the pre-discharge volume of the cascade reservoirs may not have been fully discharged. At this time, the total storage capacity of the cascade reservoirs is greater than the sum of the storage capacities corresponding to the flood control limits of each reservoir, i.e. If the original flood control standard is not met at this time, it will cause greater flood control risks; the p-frequency design flood is obtained by amplifying the typical flood hydrograph and the design flood results using the same frequency method; if the reservoir water level at the end of the pre-release scheduling and the upcoming p-frequency design flood are independent of each other, then the risk caused by the uncertainty of the flood hydrograph can be estimated using the full probability formula:

[0028]

[0029] In the formula: For reservoir m, from water level When adjusting to a certain frequency for a design flood, the highest flood level exceeds the flood control limit level Z. x,m The probability of a design flood occurring at a specific frequency when the highest flood level of the design flood at frequency p is reached.

[0030] Based on the cascade reservoir capacity aggregation decomposition model based on water volume, assuming that all reservoirs in the aggregation system release water synchronously, the risk caused by the uncertainty of the flood hydrograph in the case of a single reservoir can be extended to the cascade reservoirs; given the design flood frequency p1 and flood control risk p2, the risk R caused by the uncertainty of the flood hydrograph of the aggregation reservoir is... * It can be represented as:

[0031]

[0032] In the formula: For function Z d The inverse function of (·).

[0033] As a further aspect of the present invention: in S23, the upper limit of the pre-discharge volume is determined based on the flood control risk;

[0034] Flood risk generally refers to the probability of an undesirable event occurring under specific conditions and within a specific time period. The flood control standards corresponding to the four types of random events in aggregated reservoirs are important references for flood control scheduling strategies, mainly determined by adjusting the design flood at a certain frequency from the original design flood limit level for each individual reservoir. The pre-release scheduling of both individual and aggregated reservoirs also requires that the original design flood control standards not be lowered; that is, the pre-release scheduling of both individual and aggregated reservoirs must not lower the original design flood control standards.

[0035]

[0036] In the formula: e h h = 1, 2, 3, 4, representing the number of the four types of random events, respectively.

[0037] As a further aspect of the present invention, S3 includes the following sub-steps:

[0038] S31: Derive the expression for the multi-year average total power generation during the flood season after the aggregated decomposition of the pre-discharge volume of the two-reservoir aggregation system based on the joint optimization design of flood control reservoir capacity;

[0039] S32: Derive the expression for the multi-year average total power generation during the flood season after the aggregation and decomposition of the pre-discharge volume of the multi-reservoir aggregation system based on the joint optimization design of flood control reservoir capacity.

[0040] As a further aspect of the present invention: In S31, the multi-year average total power generation ΔE during the flood season after the pre-discharge volume of the two-reservoir aggregation system based on the joint optimization design of flood control reservoir capacity is calculated. * as follows:

[0041]

[0042] In the formula: η is the proportion of the pre-discharge volume of the head reservoir relative to the total pre-discharge volume of the two reservoirs;

[0043] Further deduction:

[0044]

[0045] In the formula: The relationship between η and ΔE and λ * similar, It monotonically decreases within the range and its sign depends on the given variable λ.* and The value is determined;

[0046] In the discussion of where the objective function ΔE reaches its maximum value, let Three-variable function The problem of finding the maximum or minimum value is reduced to two variables ΔE(λ). * Problem ,η); Let the function ΔE(λ) * The partial derivatives (λ0, η0) are continuous in some neighborhood of the point (λ0, η0) and have continuous first and second order partial derivatives. The point (λ0, η0) satisfies the following expression:

[0047]

[0048] From the above formula, we can further derive:

[0049]

[0050] Then the point (λ0, η0) is the function ΔE(λ * The extreme points of ,η); according to the sufficient condition for a multivariate function to take extreme values, the objective function ΔE(λ) is the extreme point of η. * The value of η may or may not have an extremum at the point (λ0,η0), and it is difficult to determine this by taking low-order partial derivatives.

[0051]

[0052] Therefore, numerical simulation is used to discuss the objective function ΔE(λ). * The extreme cases of ,η), if in λ * If there is an extreme point (λ0,η0) within the domain of η, then the maximum value of the objective function is (λ0,η0); otherwise, the maximum value of the objective function is obtained at the boundary of the domain.

[0053] Further deduction:

[0054]

[0055] In the formula, r λ For Lagrange multipliers, b m These are the parameters of the power function curve relating water level and reservoir capacity;

[0056] The above equation is solved numerically using the augmented Lagrange penalty function method.

[0057] As a further aspect of the present invention: In S32, the multi-year average total power generation during the flood season after the pre-discharge volume of the multi-reservoir aggregation system based on the joint optimization design of flood control reservoir capacity is calculated. as follows:

[0058]

[0059] The equations constructed using the Lagrange multiplier method are optimized using the augmented Lagrange multiplier method, and then solved using the gradient descent algorithm.

[0060]

[0061] In the formula: η m This represents the proportion of the pre-discharge volume of reservoir m relative to the total pre-discharge volume of reservoir M.

[0062] A cascade reservoir pre-discharge volume aggregation and decomposition system based on joint optimization design of flood control storage capacity, comprising:

[0063] Joint Optimization Design Module: Responsible for the joint optimization design and calculation formula derivation of flood control capacity, collecting characteristic parameters of cascade reservoirs, daily-scale flow series during the flood season, and downstream safe outlet flow data of cascade reservoirs, simplifying reservoir capacity constraints, reservoir dam water level fluctuation constraints, and power station output constraints based on power generation calculation process and scheduling characteristics during the flood season, performing joint optimization design of flood control capacity for cascade reservoirs, and deriving joint optimization calculation formulas for flood control capacity of two-reservoir and multi-reservoir aggregation systems;

[0064] Pre-discharge risk control module: responsible for extending pre-discharge scheduling to cascade reservoirs, analyzing flood control risks and determining the upper limit of pre-discharge volume, extending the forecast and pre-discharge scheduling of a single reservoir to cascade reservoirs, conducting flood control risk analysis, and finally determining the upper limit of pre-discharge volume;

[0065] Aggregation and Decomposition Calculation Module: Responsible for the aggregation and decomposition calculation of pre-discharge volume and the solution of power generation increment. Based on the joint optimization calculation formula of flood control capacity of two-reservoir and multi-reservoir aggregation system, it derives the aggregation and decomposition calculation formula of pre-discharge volume of two-reservoir and multi-reservoir aggregation system, and derives and solves the formula of total power generation increment of two-reservoir and multi-reservoir aggregation system during the flood season.

[0066] Benefit assessment module: It is responsible for comparing the power generation before and after optimization, evaluating the benefit increment, and calculating the multi-year average total power generation of the cascade reservoirs using the original design flood control capacity, under the premise that the inflow of the cascade reservoirs remains unchanged. It then compares the total power generation after the joint optimization design of the flood control capacity of the cascade reservoirs, and analyzes the incremental changes in the power generation benefits of the cascade reservoirs due to the joint optimization design of the flood control capacity.

[0067] The beneficial effects of this invention are:

[0068] 1) This invention addresses the issue of cascade reservoirs with equivalent flood control capacity from a planning and design perspective. It deepens the application of equivalent flood control capacity in cascade reservoirs, overcomes the limitations of the design flood control capacity of a single reservoir, and provides a decision-making basis for optimizing the flood season scheduling of cascade reservoirs. Under the assumption that the water level fluctuations of cascade reservoirs are not considered during the flood season, this invention, based on the joint optimization design of flood control capacity, aggregates and decomposes the pre-discharge volume of cascade reservoirs according to the forecasting capability and forecast period of cascade reservoirs, thereby improving the total power generation of cascade reservoirs during the flood season.

[0069] 2) The method of this invention is simple and accurate, and can explicitly derive the expression for the aggregation and decomposition of the pre-discharge volume of cascade reservoirs based on the joint optimization design of flood control capacity. This makes it more convenient for practical engineering applications. Based on the power generation calculation formula of the joint optimization design of flood control capacity, this patent uses mathematical formula derivation to derive the aggregation and decomposition formula of the pre-discharge volume of two-reservoir and multi-reservoir aggregation systems, while ensuring that the total flood control capacity remains unchanged and the current forecasting capability is maintained. The augmented Lagrange penalty function method can directly solve for the pre-discharge volume and increased power generation of each reservoir under the optimal aggregation and decomposition, which has important practical significance for flood control and power generation scheduling of cascade reservoirs during the flood season. Attached Figure Description

[0070] Figure 1 This is a flowchart of the method of the present invention;

[0071] Figure 2 This is a schematic diagram of the pre-discharge volume aggregation and decomposition for the M-unit aggregated cascade reservoir system based on the joint optimization design of flood control storage capacity. Detailed Implementation

[0072] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0073] Example 1, as Figures 1 to 2 As shown in the figure, this embodiment provides a method for the aggregation and decomposition of pre-discharge volume of cascade reservoirs based on the joint optimization design of flood control storage capacity. The method for the aggregation and decomposition of pre-discharge volume of cascade reservoirs includes the following steps:

[0074] Step 1: Collect characteristic parameters of cascade reservoirs, daily flow series during the flood season, and safe flow thresholds at downstream outlet sections of cascade reservoirs. Based on the power generation calculation process and the scheduling characteristics during the flood season, simplify the reservoir capacity constraints, reservoir dam water level fluctuation constraints, and power station output constraints. Conduct joint optimization design of flood control capacity for cascade reservoirs and derive the joint optimization calculation formula for flood control capacity of two-reservoir and multi-reservoir aggregation systems.

[0075] Specifically, collecting such as Figure 2 The diagram shows the characteristic parameters of a cascade reservoir in a certain watershed, a long series of daily inflow processes, and the relationship between reservoir A and [other water features]. M Downstream safe flow rate and other data. A1, A2, ..., A in the diagram. M The diagram represents M cascade reservoirs, B represents the downstream flood control point or flood control target, and the arrows indicate the direction of water flow. Analysis of the hydraulic connections between the cascade reservoirs in a certain watershed reveals that A1, A2, ..., A... M Although the reservoirs were planned and designed by different design units, they are relatively close to each other. The catchment areas above the dam sites of reservoirs M are similar, the area between them is small, and they do not have flood control functions. Meanwhile, A1, A2, ..., A... M The reservoirs share the flood control responsibility for the major downstream city B, and the flood control capacity of reservoirs M can be considered approximately equal. Furthermore, since the outflow from upstream reservoirs is not significantly affected by the backwater effect of downstream reservoirs during the flood season, given the reserved flood control capacity, it can be disregarded.

[0076] If a cascade reservoir has the following characteristics: ① similar climate characteristics within its controlled area and no major tributaries flowing into it between the watersheds; ② the cascade reservoirs jointly undertake flood control tasks for the downstream areas, then the flood control capacity of the cascade reservoirs can be aggregated and decomposed. The former ensures the correlation and homogeneity between the inflows of each reservoir, while the latter unifies the effectiveness of the flood control capacity of each reservoir.

[0077] The purpose of flood control capacity aggregation in cascade reservoirs is to determine the total flood control capacity to ensure flood safety. While maintaining a constant total flood control capacity, the original design flood control capacity of each reservoir is aggregated first. The aggregated flood control capacity of the cascade reservoirs is equal to the sum of the optimized flood control capacities of all sub-reservoirs. The purpose of decomposing the aggregated flood control capacity is to increase power generation efficiency. Under the premise of satisfying reservoir series constraints, the aggregated flood control capacity is appropriately decomposed to increase the power generation efficiency of the cascade reservoirs. The hydraulic connection formulas mainly used for the aggregation and decomposition of flood control capacity in cascade reservoirs are as follows:

[0078] The joint optimization design formula for the flood control capacity of the two reservoirs and Reservoir M is as follows:

[0079]

[0080] In the formula: k m Let be the comprehensive output coefficient of the m-th reservoir; t is the time variable, s, t = 1, 2, ..., T, where T is the length of the calculation period; m is the reservoir number from top to bottom in the cascade, m = 1, 2, ..., M, where M is the number of reservoirs; n y Indicates the number of years; Z u,m(·) represents the relationship between the upstream water level and reservoir capacity of the m-th reservoir, which is fitted using a power function. (a m >0,b m >0), and because as the reservoir capacity increases, the change in water level above the dam corresponding to a unit change in reservoir capacity decreases sharply, that is... Therefore, 0 < b m <1; V m (t) and V m (t+1) represent the reservoir capacity of the m-th reservoir at times t and t+1, respectively. 3 ;q in,m (t) and q out,m (t) represents the average inflow and outflow of the m-th reservoir at time t, respectively. 3 / s; The total flood control capacity of reservoir M during the flood season is m 3 ;λ and λ * These represent the percentage of the original and optimized flood control capacity of the headwater reservoir relative to the total flood control capacity of the two reservoirs. V nor,m Let m be the reservoir capacity corresponding to the flood control high water level of the m-th reservoir. 3 ;

[0081] Step 2: Extend the forecasting and pre-discharge scheduling of a single reservoir to cascade reservoirs, conduct flood risk analysis, and finally determine the upper limit of the pre-discharge volume.

[0082] Step 2 includes the following sub-steps:

[0083] Step 2-1: Give the pre-release scheduling expression for the M reservoirs within time period t:

[0084]

[0085] In the formula: T c Forecast period; q in,m (t) and Let m be the average inflow of the m-th reservoir and the combined reservoir at time t. 3 / s;q z,m (t) represents the flow rate between the m-th reservoir and the (m+1)-th reservoir, where m 3 / s. V *low V *up , and These represent the minimum aggregated reservoir capacity (aggregate capacity after pre-release scheduling), the maximum aggregated reservoir capacity (aggregate capacity before pre-release scheduling), the initial safe reservoir capacity, and the aggregated pre-release volume, respectively, within the forecast period. V x,m Let m be the reservoir capacity corresponding to the flood control limit water level of the m-th reservoir.

[0086] Step 2-2: This step is used to analyze the flood control risks associated with dynamic water level control during the flood season. The sources of these risks can be divided into two categories.

[0087] The first category is the risk of pre-release scheduling decisions caused by errors in flood inflow forecasts, which can be further divided into four types of random events for discussion:

[0088] Event E1:

[0089] Event E2:

[0090] Event E3:

[0091] Event E4:

[0092] in, This refers to the maximum inflow rate of the reservoir predicted within the forecast period. Events E1 and E2 can lead to incorrect pre-release scheduling decisions. For example, if event E2 is within the forecast period T... c Forecast maximum inflow during the specified period Less than the safe flow rate q at the downstream flood control section safe However, the actual maximum inbound flow Greater than the safe flow rate q safe Therefore, the reservoir made a decision not to implement pre-release scheduling when it should have started; and due to the forecast period T c Maximum actual inbound flow during the period Greater than the safe flow rate q safe Events E2 and E3 will trigger flood control scheduling.

[0093] The second category is the uncertainty risk of flood hydrographs. When a flood has a frequency of p (equivalent to T) p Once a year, T p =1 / p) When the design flood occurs at the end of the forecast period, the pre-discharge volume of the cascade reservoirs may not have been fully discharged. At this time, the total reservoir capacity of the cascade reservoirs is greater than the sum of the reservoir capacities corresponding to the flood control limits of each reservoir, that is... The failure to meet the original design flood control standard at this time will lead to greater flood control risks. The p-frequency design flood is obtained by amplifying the typical flood hydrograph and the design flood results using the same-frequency method. If the reservoir water level at the end of the pre-release operation and the upcoming p-frequency design flood are independent of each other, then the risk caused by the uncertainty of the flood hydrograph can be estimated using the law of total probability.

[0094]

[0095] In the formula: For reservoir m, from water level When adjusting to a certain frequency for a design flood, the highest flood level exceeds the flood control limit level Z. x,m When the design flood at frequency p is at its highest controlled flood level, the probability of the design flood occurring at that specific frequency is given by the water level Z. x,m The risk of a 100-year design flood is 0.01, i.e., R. m (0.01,Z x,m ) = 0.01; N f For the total flood process during the pre-discharge scheduling phase, we have n f =1,2,...,N f ; For the m-th reservoir to encounter the n-th reservoir within the forecast period f The water level at the end of the pre-discharge schedule after the flood.

[0096] Based on a cascade reservoir capacity aggregation decomposition model using water volume, assuming synchronized discharge from all reservoirs within the aggregation system, the risk caused by the uncertainty of the flood hydrograph in the case of a single reservoir can be extended to the cascade reservoirs. Given the design flood frequency p1 and flood control risk p2, the risk R caused by the uncertainty of the flood hydrograph in the aggregation reservoirs is... * It can be represented as:

[0097]

[0098] In the formula: For function Z d The inverse function of (·).

[0099] Steps 2-3: Determine the upper limit of the pre-discharge volume based on the flood control risk.

[0100] Flood control risk generally refers to the probability of an undesirable event occurring under specific conditions and within a specific time period. In summary, the flood control risks corresponding to the four types of random events in aggregated reservoirs are summarized in Table 1. Flood control standards are an important reference for flood control scheduling strategies, mainly determined by adjusting the design flood at a certain frequency from the original design flood limit level for each individual reservoir. The pre-release scheduling of both individual and aggregated reservoirs also requires that the original design flood control standard not be lowered; that is:

[0101]

[0102] In the formula: e h h = 1, 2, 3, 4, representing the number of the four types of random events, respectively.

[0103] Table 1 shows the flood control risks corresponding to four types of random events.

[0104]

[0105] The above formula serves as a constraint, and the upper limit of the pre-discharge volume of the Juhe Reservoir can be determined using Monte Carlo simulation and trial-and-error methods. The lower limit of the reservoir capacity for dynamic control of the flood season water level is set as follows:

[0106] Step 3: Based on the joint optimization calculation formula of flood control capacity of the two-reservoir and multi-reservoir aggregation system, derive the aggregation and decomposition calculation formula of pre-discharge volume of the two-reservoir and multi-reservoir aggregation system, derive the formula of total power generation increment during the flood season of the two-reservoir and multi-reservoir aggregation system and solve it.

[0107] Step 3 includes the following sub-steps:

[0108] Step 3-1: Derive the expression for the multi-year average total power generation during the flood season after the aggregated decomposition of the pre-discharge volume of the two-reservoir aggregation system based on the joint optimization design of flood control reservoir capacity:

[0109]

[0110] In the formula: η is the proportion of the pre-discharge volume of the head reservoir relative to the total pre-discharge volume of the two reservoirs. It can be seen that... This holds true regardless of the condition, indicating that ΔE varies with... Increase with the increase, at the same time Heng was established. It decreases monotonically.

[0111] Further deduction:

[0112]

[0113] In the formula: The relationship between η and ΔE and λ * similar, It monotonically decreases within the range and its sign depends on the given variable λ. * and The value is determined.

[0114] The above analysis shows that only variables Relationship with the first-order partial derivative of ΔE Independent variable λ * The influence of η, i.e., the change in power generation ΔE of the cascade reservoirs, varies with the pre-discharge volume of the aggregate reservoir. As the value increases, the objective function ΔE increases accordingly. Therefore, in the discussion of where the objective function ΔE reaches its maximum value, we can let... Three-variable function The problem of finding the maximum or minimum value is reduced to two variables ΔE(λ). * Problem ,η). Let the function be ΔE(λ). * The partial derivatives (λ0, η0) are continuous in some neighborhood of the point (λ0, η0) and have continuous first and second order partial derivatives. The point (λ0, η0) satisfies the following expression:

[0115]

[0116] From the above formula, we can further derive:

[0117]

[0118]

[0119] Then the point (λ0, η0) is the function ΔE(λ * The extreme points of ,η), according to the sufficient condition for a multivariate function to take extreme values, the objective function ΔE(λ) * The value of η may or may not have an extremum at the point (λ0,η0), making it difficult to determine by taking low-order partial derivatives.

[0120]

[0121] Therefore, numerical simulation is used to discuss the objective function ΔE(λ). * The extreme cases of ,η), if in λ * If there is an extreme point (λ0,η0) within the domain of η, then the maximum value of the objective function is (λ0,η0); otherwise, the maximum value of the objective function is obtained at the boundary of the domain.

[0122] Further deduction:

[0123]

[0124] r λ For Lagrange multipliers, b m These are the parameters of the power function curve relating water level and reservoir capacity;

[0125] The augmented Lagrange penalty function method is used for numerical solution.

[0126] Step 3-2: Derive the multi-year average total power generation during the flood season after the aggregation and decomposition of the pre-discharge volume of the multi-reservoir aggregation system based on the joint optimization design of flood control reservoir capacity. as follows:

[0127]

[0128] The equations constructed using the Lagrange multiplier method are optimized using the augmented Lagrange multiplier method, and then solved using the gradient descent algorithm.

[0129]

[0130] In the formula: η m This represents the proportion of the pre-discharge volume of reservoir m relative to the total pre-discharge volume of reservoir M.

[0131] Example 2: A cascade reservoir pre-discharge volume aggregation and decomposition system based on joint optimization design of flood control storage capacity. This cascade reservoir pre-discharge volume aggregation and decomposition system is used to execute the cascade reservoir pre-discharge volume aggregation and decomposition method in the example, and the cascade reservoir pre-discharge volume aggregation and decomposition system includes:

[0132] Joint Optimization Design Module: Responsible for the joint optimization design and calculation formula derivation of flood control capacity, collecting characteristic parameters of cascade reservoirs, daily-scale flow series during the flood season, and downstream safe outlet flow data of cascade reservoirs, simplifying reservoir capacity constraints, reservoir dam water level fluctuation constraints, and power station output constraints based on power generation calculation process and scheduling characteristics during the flood season, performing joint optimization design of flood control capacity for cascade reservoirs, and deriving joint optimization calculation formulas for flood control capacity of two-reservoir and multi-reservoir aggregation systems;

[0133] Pre-discharge risk control module: responsible for extending pre-discharge scheduling to cascade reservoirs, analyzing flood control risks and determining the upper limit of pre-discharge volume, extending the forecast and pre-discharge scheduling of a single reservoir to cascade reservoirs, conducting flood control risk analysis, and finally determining the upper limit of pre-discharge volume;

[0134] Aggregation and Decomposition Calculation Module: Responsible for the aggregation and decomposition calculation of pre-discharge volume and the solution of power generation increment. Based on the joint optimization calculation formula of flood control capacity of two-reservoir and multi-reservoir aggregation system, it derives the aggregation and decomposition calculation formula of pre-discharge volume of two-reservoir and multi-reservoir aggregation system, and derives and solves the formula of total power generation increment of two-reservoir and multi-reservoir aggregation system during the flood season.

[0135] Benefit assessment module: It is responsible for comparing the power generation before and after optimization, evaluating the benefit increment, and calculating the multi-year average total power generation of the cascade reservoirs using the original design flood control capacity, under the premise that the inflow of the cascade reservoirs remains unchanged. It then compares the total power generation after the joint optimization design of the flood control capacity of the cascade reservoirs, and analyzes the incremental changes in the power generation benefits of the cascade reservoirs due to the joint optimization design of the flood control capacity.

[0136] Working Principle: Through a collaborative mechanism of aggregation and decomposition, the cascade reservoir group is treated as a virtual, jointly managed whole. First, based on the consistent flood control objectives downstream and the complementary characteristics of the flood control capacities of each reservoir, the originally dispersed reservoir capacities are jointly optimized to form an aggregated flood control capacity pool, and its optimization calculation formula is established. Subsequently, the forecasting and pre-discharge scheduling is extended from individual reservoirs to the aggregated system. By analyzing the flood control risks caused by forecasting errors and uncertainties in the flood hydrograph, the upper limit of the total pre-discharge volume of the system is determined. This total pre-discharge volume is scientifically allocated to each reservoir according to the optimization objectives using mathematical decomposition formulas. This allows for the calculation of the multi-year average total power generation of the cascade reservoirs using the original design flood control capacity, while maintaining a constant inflow to the cascade reservoirs. This is then compared with the total power generation after the joint optimization design of the cascade reservoir flood control capacity, analyzing the incremental changes in the power generation benefits of the cascade reservoirs due to the joint optimization design.

[0137] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0138] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A method for aggregated decomposition of pre-discharge water volume in cascade reservoirs based on joint optimization design of flood control storage capacity, characterized in that, The method for aggregating and decomposing the pre-release water volume of cascade reservoirs includes the following steps: S1. Collect characteristic parameters of cascade reservoirs, daily flow series during the flood season, and safe flow thresholds at downstream outlet sections of cascade reservoirs. Based on the power generation calculation process and scheduling characteristics during the flood season, simplify the reservoir capacity constraints, reservoir dam water level fluctuation constraints, and power station output constraints. Conduct joint optimization design of flood control capacity for cascade reservoirs and derive joint optimization calculation formulas for flood control capacity of two-reservoir and multi-reservoir aggregation systems. S2. Extend the forecasting and pre-discharge scheduling of a single reservoir to cascade reservoirs, conduct flood risk analysis, and finally determine the upper limit of the pre-discharge volume; S3. Based on the joint optimization calculation formula of flood control reservoir capacity of the two-reservoir and multi-reservoir aggregation system, derive the aggregation decomposition calculation formula of pre-discharge volume of the two-reservoir and multi-reservoir aggregation system, derive the formula of total power generation increment of the two-reservoir and multi-reservoir aggregation system during the flood season and solve it; S4. Under the premise that the inflow of the cascade reservoirs remains unchanged, calculate the multi-year average total power generation of the cascade reservoirs using the original design flood control capacity, and compare it with the total power generation after the joint optimization design of the flood control capacity of the cascade reservoirs. Analyze the incremental changes in the power generation benefits of the cascade reservoirs due to the joint optimization design of the flood control capacity.

2. The method for aggregating and decomposing pre-discharge water volume in cascade reservoirs according to claim 1, characterized in that: In S1, the joint optimization calculation formula for flood control capacity of the two-reservoir and multi-reservoir aggregation system is as follows: In the formula: t is the time variable, t = 1, 2, ..., T, where T is the length of the calculation period; m is the reservoir number from top to bottom in the cascade reservoir series, m = 1, 2, ..., M, where M is the number of reservoirs; n y Indicates the number of years; k m Let be the comprehensive output coefficient of the m-th reservoir; kW·h / m 3 Z u,m (·) represents the function relating the upstream water level to the reservoir capacity of the m-th reservoir, which is fitted using a power function, i.e. Furthermore, as the reservoir capacity increases, the change in water level upstream of the dam corresponding to a unit change in reservoir capacity decreases sharply, i.e. Therefore, 0 < b m <1; V m (t) and V m (t+1) represent the reservoir capacity of the m-th reservoir at times t and t+1, respectively. 3 ;q in,m (t) and q out,m (t) represents the average inflow and outflow of the m-th reservoir at time t, respectively. 3 / s; The total flood control capacity of reservoir M during the flood season is m 3 ;λ and λ * These represent the percentage of the original and optimized flood control capacity of the headwater reservoir relative to the total flood control capacity of the two reservoirs. V nor,m Let m be the reservoir capacity corresponding to the flood control high water level of the m-th reservoir. 3 .

3. The method for aggregating and decomposing pre-discharge water volume in cascade reservoirs according to claim 2, characterized in that: S2 includes the following sub-steps: S21. Give the formula for the pre-release scheduling of M reservoirs during time period t: S22. Determine the flood control risks of the multi-reservoir aggregation system; S23. Determine the upper limit of the pre-discharge volume of the multi-reservoir aggregation system.

4. The method for aggregating and decomposing pre-discharge water volume in cascade reservoirs according to claim 3, characterized in that: In S21, the forecast and pre-release scheduling of the aggregated reservoir is expressed as follows: In the formula: T c Forecast period; q in,m (t) and Let m be the average inflow of the m-th reservoir and the combined reservoir at time t. 3 / s;q z,m (t) represents the flow rate between the m-th reservoir and the (m+1)-th reservoir, where m 3 / s;V *low V *up , and These are the minimum aggregated storage capacity, the maximum aggregated storage capacity, the initial safe storage capacity, and the aggregated pre-discharge volume within the forecast period; among which... V x,m Let m be the reservoir capacity corresponding to the flood control limit water level of the m-th reservoir.

5. The method for aggregating and decomposing pre-discharge water volume in cascade reservoirs according to claim 3, characterized in that: In S22, the flood control risks of the multi-reservoir aggregation system include two categories: The first category is the risk of pre-release scheduling decisions caused by errors in the flood inflow forecast, which is discussed in four types of random events: Event E1: Event E2: Event E3: Event E4: in, This refers to the maximum inflow rate of the Juhe Reservoir predicted during the forecast period. The second category is the uncertainty risk of the flood hydrograph, when a flood has a frequency of p, i.e., T p Once a year, T p =1 / p The design flood occurs at the end of the forecast period, and the pre-discharge volume of the cascade reservoirs has not been fully discharged. At this time, the total reservoir capacity of the cascade reservoirs is greater than the sum of the reservoir capacities corresponding to the flood control limits of each reservoir, that is... If the original flood control standard is not met at this time, it will cause greater flood control risks; the p-frequency design flood is obtained by amplifying the typical flood hydrograph and the design flood results using the same frequency method; if the reservoir water level at the end of the pre-release scheduling and the upcoming p-frequency design flood are independent of each other, then the risk caused by the uncertainty of the flood hydrograph is estimated using the full probability formula: In the formula: For reservoir m from water level When adjusting to a certain frequency for a design flood, the highest flood level exceeds the flood control limit level Z. x,m The probability of a design flood occurring at a specific frequency when the highest flood level of the design flood at frequency p is reached. Based on the cascade reservoir capacity aggregation decomposition model based on water volume, assuming that all reservoirs in the aggregation system release water synchronously, the risk caused by the uncertainty of the flood hydrograph in the case of a single reservoir can be extended to the cascade reservoirs; given the design flood frequency p1 and flood control risk p2, the risk R caused by the uncertainty of the flood hydrograph of the aggregation reservoir is... * Represented as: In the formula: For function Z d The inverse function of (·).

6. The method for aggregating and decomposing pre-discharge water volume in cascade reservoirs according to claim 3, characterized in that: In S23, the upper limit of the pre-discharge volume is determined based on the flood control risk. The pre-discharge scheduling of single reservoirs and combined reservoirs does not reduce the original design flood control standard, that is: In the formula: e h h = 1, 2, 3, 4, representing the number of the four types of random events, respectively.

7. The method for aggregating and decomposing pre-discharge water volume in cascade reservoirs according to claim 1, characterized in that: S3 includes the following sub-steps: S31: Derive the expression for the multi-year average total power generation during the flood season after the aggregated decomposition of the pre-discharge volume of the two-reservoir aggregation system based on the joint optimization design of flood control reservoir capacity; S32: Derive the expression for the multi-year average total power generation during the flood season after the aggregation and decomposition of the pre-discharge volume of the multi-reservoir aggregation system based on the joint optimization design of flood control reservoir capacity.

8. The method for aggregating and decomposing pre-release water volume in cascade reservoirs according to claim 7, characterized in that: In S31, the multi-year average total power generation during the flood season ΔE after the aggregation and decomposition of the pre-discharge volume of the two-reservoir aggregation system based on the joint optimization design of flood control reservoir capacity is... * as follows: In the formula: η is the proportion of the pre-discharge volume of the head reservoir relative to the total pre-discharge volume of the two reservoirs; Further deduction: In the formula: The relationship between η and ΔE and λ * similar, It monotonically decreases within the range and its sign depends on the given variable λ. * and The value is determined; In the discussion of where the objective function ΔE reaches its maximum value, let Three-variable function The problem of finding the maximum or minimum value is reduced to two variables ΔE(λ). * Problem ,η); Let the function ΔE(λ) * The partial derivatives (λ0, η0) are continuous in some neighborhood of the point (λ0, η0) and have continuous first and second order partial derivatives. The point (λ0, η0) satisfies the following expression: From the above formula, we can further derive: Then the point (λ0, η0) is the function ΔE(λ * The extreme points of ,η); according to the sufficient condition for a multivariate function to take extreme values, the objective function ΔE(λ) is the extreme point of η. * The value of η may or may not have an extremum at the point (λ0,η0), and it is difficult to determine this by taking low-order partial derivatives. Therefore, numerical simulation is used to discuss the objective function ΔE(λ). * The extreme cases of ,η), if in λ * If there is an extreme point (λ0,η0) within the domain of η, then the maximum value of the objective function is (λ0,η0); otherwise, the maximum value of the objective function is obtained at the boundary of the domain. Further deduction: In the formula: r λ For Lagrange multipliers, b m These are the parameters of the power function curve relating water level and reservoir capacity; The above equation is solved numerically using the augmented Lagrange penalty function method.

9. The method for aggregating and decomposing pre-discharge water volume in cascade reservoirs according to claim 8, characterized in that: In S32, the multi-year average total power generation during the flood season after the aggregation and decomposition of the pre-discharge water volume of the multi-reservoir aggregation system based on the joint optimization design of flood control reservoir capacity is... as follows: The equations constructed using the Lagrange multiplier method are optimized using the augmented Lagrange multiplier method, and then solved using the gradient descent algorithm. In the formula: η m This represents the proportion of the pre-discharge volume of reservoir m relative to the total pre-discharge volume of reservoir M.

10. A cascade reservoir pre-discharge volume aggregation and decomposition system based on joint optimization design of flood control storage capacity, characterized in that, The cascade reservoir pre-discharge volume aggregation and decomposition system is used to execute the cascade reservoir pre-discharge volume aggregation and decomposition method based on the joint optimization design of flood control storage capacity as described in any one of claims 1 to 9; The cascade reservoir pre-discharge water volume aggregation and decomposition system includes: Joint Optimization Design Module: Responsible for the joint optimization design and calculation formula derivation of flood control capacity, collecting characteristic parameters of cascade reservoirs, daily-scale flow series during the flood season, and downstream safe outlet flow data of cascade reservoirs, simplifying reservoir capacity constraints, reservoir dam water level fluctuation constraints, and power station output constraints based on power generation calculation process and scheduling characteristics during the flood season, performing joint optimization design of flood control capacity for cascade reservoirs, and deriving joint optimization calculation formulas for flood control capacity of two-reservoir and multi-reservoir aggregation systems; Pre-discharge risk control module: responsible for extending pre-discharge scheduling to cascade reservoirs, analyzing flood control risks and determining the upper limit of pre-discharge volume, extending the forecast and pre-discharge scheduling of a single reservoir to cascade reservoirs, conducting flood control risk analysis, and finally determining the upper limit of pre-discharge volume; Aggregation and Decomposition Calculation Module: Responsible for the aggregation and decomposition calculation of pre-discharge volume and the solution of power generation increment. Based on the joint optimization calculation formula of flood control capacity of two-reservoir and multi-reservoir aggregation system, it derives the aggregation and decomposition calculation formula of pre-discharge volume of two-reservoir and multi-reservoir aggregation system, and derives and solves the formula of total power generation increment of two-reservoir and multi-reservoir aggregation system during the flood season. Benefit assessment module: It is responsible for comparing the power generation before and after optimization, evaluating the benefit increment, and calculating the multi-year average total power generation of the cascade reservoirs using the original design flood control capacity, under the premise that the inflow of the cascade reservoirs remains unchanged. It then compares the total power generation after the joint optimization design of the flood control capacity of the cascade reservoirs, and analyzes the incremental changes in the power generation benefits of the cascade reservoirs due to the joint optimization design of the flood control capacity.

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