Design and combination method for optimal characteristic water level of Golden-Under-Stair and Three Gorges Reservoir Group

Abstract

The invention discloses an optimal characteristic water level design combination method for a Golden lower cascade reservoir group and a Three Gorges reservoir group, which comprises the following steps: collecting operation water level characteristic parameters and scheduling requirements of key large reservoirs at the upstream of the Yangtze River and hydrological station observation flow data series, and analyzing the hydraulic connection between cascade reservoirs and the production and confluence characteristics of interval drainage basins; simulating and calculating the multi-year average generating capacity of each reservoir, and calculating the sum of the multi-year average generating capacity of the cascade reservoirs; flood control, power generation and full storage rate are selected as objective functions, a cascade reservoir multi-objective combined dispatching model is constructed, a parameterization-simulation-optimization framework and a multi-objective evolutionary algorithm are adopted for solving, and cascade reservoir simulation optimization dispatching is carried out; establishing a cascade reservoir flood control capacity complementary equivalent relationship, and calculating flood control risks of the cascade reservoir group; dynamically controlling the running water level of the cascade reservoir group, and determining an optimal combination and a flexible decision interval of the running water levels of the Golden lower cascade reservoir group and the Three Gorges reservoir group; flood control and benefit-making benefits of the reservoir can be fully exerted.

Description

Technical Field

[0001] The present invention relates to the technical field of water conservancy and hydropower engineering design and operation management, and particularly to an optimal characteristic water level design combination method for the Jinxia cascade and the Three Gorges reservoir group. Background Technique

[0002] In China, the development sequence of water conservancy and hydropower projects often adopts a bottom-up approach. For reservoirs in the same river basin, during their respective preliminary design stages, different design units often use single-station data series to calculate the design flood according to the "Code for Calculation of Design Flood of Water Conservancy and Hydropower Projects: SL44—2006" at different times. The flood control storage capacity of each reservoir is determined according to the river basin flood control plan and task allocation, without considering the impact of upstream reservoir regulation on the downstream, that is, the hydraulic connection of cascade reservoirs and the complementary relationship of flood control storage capacity. The flood control storage capacity refers to the storage capacity between the flood control high water level and the flood limit water level, and its purpose is to ensure the flood control safety of the reservoir dam and downstream flood control targets. Therefore, during the operation period of cascade reservoirs, it is not advisable to continue using the flood control storage capacity designed for a single reservoir. Instead, the flood control storage capacity of cascade reservoirs should be jointly optimized and designed and used in an overall plan to improve the utilization efficiency of flood resources.

[0003] Reservoir operation scheduling belongs to a non-linear, multi-constraint problem, which can be solved by constructing a multi-stage reservoir operation scheduling model, but it can only implicitly express the complementary relationship of the flood control storage capacity of cascade reservoirs. In the upper reaches of the Yangtze River, a pattern of cascade reservoir groups has been formed for the main rivers and tributaries. Due to the hydraulic and hydrological connections between cascade reservoirs, for the same flood control target downstream of cascade reservoirs, the flood control storage capacities of each reservoir have an equivalent effect. During the reservoir planning and design stage, the design flood, flood control storage capacity, and operation water level are often determined based on the dam and flood control safety, without considering the joint operation scheduling problem of the river basin reservoir group, making it difficult to meet the actual needs of current complex reservoir group operation management. Therefore, it is necessary to select the reservoir to store flood and use the flood control storage capacity, study the complementary and equivalent relationship of the flood control storage capacity of cascade reservoirs, seek to determine the optimal operation water level combination and flexible decision-making interval of the reservoir group, and give full play to the flood control and beneficial utilization benefits of the reservoir. Summary of the Invention

[0004] The purpose of the present invention is to overcome the above deficiencies and provide an optimal characteristic water level design combination method for the Jinxia cascade and the Three Gorges reservoir group, seeking to determine the optimal operation water level combination and flexible decision-making interval of the reservoir group, and giving full play to the flood control and beneficial utilization benefits of the reservoir.

[0005] To solve the above technical problems, the technical solution adopted by the present invention is: an optimal characteristic water level design combination method for the Jinxia cascade and the Three Gorges reservoir group, including the following steps:

[0006] Step 1: Collect the characteristic parameters of the operating water levels and the dispatching requirements of key large reservoirs in the upper reaches of the Yangtze River, as well as the series of observed flow data at hydrological stations, and analyze the hydraulic connections between cascade reservoirs and the characteristics of runoff generation and concentration in the intermediate river basins;

[0007] Step 2: According to the design dispatching diagrams and dispatching regulations of each reservoir, simulate and calculate the annual average power generation of each reservoir, and calculate the sum of the annual average power generation of the cascade reservoirs;

[0008] Step 3: Select flood control, power generation, and full storage rate as the objective functions, construct a multi-objective joint dispatching model for cascade reservoirs, solve it using the "parameterization - simulation - optimization" framework and multi-objective evolutionary algorithm, and carry out simulation and optimization dispatching of cascade reservoirs;

[0009] Step 4: Based on the flood regional composition method and the runoff generation and concentration model for the intermediate reaches of cascade reservoirs, establish the complementary equivalent relationship of flood control storage capacities of cascade reservoirs, and calculate the flood control risks of the cascade reservoir group;

[0010] Step 5: Based on the complementary equivalent relationship between the Jinsha downstream cascade and the Three Gorges flood control storage capacity, realize the dynamic control of the operating water levels of the cascade reservoir group, and seek and determine the optimal combination and flexible decision-making interval of the operating water levels of the Jinsha downstream cascade and the Three Gorges reservoir group.

[0011] Preferably, the specific steps of Step 2 include the following sub-steps:

[0012] Step 2-1: The dispatching operation mode of a single reservoir based on the design conventional dispatching diagram of the reservoir is used to simulate the dispatching operation of each reservoir respectively, without considering the hydraulic connection characteristics of each reservoir, and ignoring the backwater effect in the relationship between the reservoir discharge flow and the tail water level;

[0013] Step 2-2: The conventional dispatching diagram of the reservoir stipulates the output and water level control parameters of the operation dispatching diagram of each hydropower station. The dispatching model can perform equal-output regulation calculations according to the specified water levels in each time period;

[0014] Step 2-3: Equal-output regulation calculation of cascade reservoirs.

[0015] More preferably, in Step 2-3, the equal-output regulation calculation formula for cascade reservoirs is as follows:

[0016]

[0017] Q fd,m (t) = N m (t) · K m (h m (t) + h s,m ) (2)

[0018] h m (t) = (Z u,m (V m (t)) + Zu,m (V m (t + 1))) / 2 - Z d,m (Q out,m (t), Z m+1 (t)) - h s,m (3)

[0019] Where: t is the time variable, s; T is the total length of the research period, t = 1, 2, …, T; m is the serial number of the cascade reservoir (the total number is M) from top to bottom, m = 1, 2, …, M; is the conventional scheduling function of the m-th reservoir under Scheme A, where "…" represents the decision factors other than time and reservoir capacity (water level) in the scheduling diagram, such as the inflow; K m (·) is the water consumption rate function of the power generation flow of the m-th reservoir, m 3 / kW; h s,m is the power generation head loss of the m-th reservoir, m; h m (t) is the net head of the m-th reservoir at time t, m; N m (t) is the output of the m-th reservoir at time t, MW; Q fd,m (t) is the power generation flow of the m-th reservoir at time t, m 3 / s; Q out,m (t) is the outflow of the m-th reservoir at time t, m 3 / s; V m (t) and V m (t + 1) are the reservoir capacities of the m-th reservoir at the beginning and end of time t and t + 1 respectively, m 3 ; Z u,m (·) is the water level-reservoir capacity relationship function of the m-th reservoir dam; Z d,m (·) represents the tail water level-outflow relationship function of the m-th reservoir; Z m+1 (t) is the water level of the dam of the (m + 1)-th reservoir.

[0020] More preferably, the constraint conditions corresponding to the equal-output regulation calculation formula of the cascade reservoir include water balance constraint, power station unit output constraint, reservoir capacity and amplitude constraint, outflow and amplitude constraint, initial boundary condition constraint and non-negative constraint:

[0021]

[0022]

[0023] V m (0) = V b,m , V m (T) = V e,m (8)

[0024] Where: Qin,m (t) is the inflow of the m-th reservoir in the t-th period, m 3 / s; are the minimum / maximum output limits of the m-th reservoir in the t-th period, kW; are the minimum / maximum storage capacity limits of the m-th reservoir in the t-th period, m 3 ; and are the minimum / maximum outflow limits of the m-th reservoir in the t-th period, m 3 / s; is the maximum storage capacity variation of the m-th reservoir between adjacent periods, m 3 ; is the outflow variation of the m-th reservoir between adjacent periods, m 3 / s; V b,m and V e,m are the initial and final storage capacities of the m-th reservoir at the beginning of the reservoir operation, m 3 .

[0025] Preferably, step 3 includes the following sub-steps:

[0026] Step 3.1: Under the constraints of the current joint operation plan of cascade reservoirs, establish a multi-objective joint optimization operation model for the 6 cascade reservoirs in the lower reaches of the Jinsha River and the Three Gorges-Gezhouba, with the maximum annual average power generation, minimum flood control risk, and highest full storage rate of the cascade reservoirs as the objective functions respectively;

[0027] Step 3.2: Use Gaussian RBF to fit the optimal operation rules;

[0028] Step 3.3: Use an adaptive multi-objective evolutionary algorithm for solution.

[0029] More preferably, in step 3.1, with the maximum annual average power generation, minimum flood control risk, and highest full storage rate of the cascade reservoirs as the objective functions respectively, specifically as follows:

[0030] (1) Maximum annual average power generation:

[0031]

[0032] In the formula: is the sum of the annual average power generations of the cascade reservoirs, kW·h; is the annual average power generation of the m-th reservoir, kW·h; n y is the number of years of the input series;

[0033] (2) Minimum flood control risk:

[0034]

[0035] Where: FCR * and FCR m are the flood control risks of the cascade reservoir and the m-th reservoir respectively; is the maximum flood regulation storage capacity of the reservoir, m 3 ; is the storage capacity corresponding to the highest safety water level in front of the dam of the m-th reservoir at time period t, m 3 ;

[0036] (3) Highest full storage rate:

[0037]

[0038] Where: IE * and IE m are the average annual full storage rates of the cascade reservoir and the m-th reservoir respectively; V zc,m -V s,m is the storage capacity between the normal storage level and the dead storage level of the m-th reservoir, that is, the regulating storage capacity, m 3 ; θ m is the proportion of the regulating storage capacity of the m-th reservoir in the cascade reservoir.

[0039] More preferably, the specific process of step 3.2 is as follows:

[0040] Use two trigonometric functions sin(2πt / 366 - p1) and cos(2πt / 366 - p2) to characterize time, where p1 and p2 are phase shifts, satisfying p1, p2 ∈ [0, 2π]; Take the time period t, the corresponding cascade reservoir storage capacity value at time period t, the inflow Q in,1 (t) of the Wudongde Reservoir, and the flow Q qj,45 (t) in the Xiangjiaba - Three Gorges section as a total of 9 decision factor vectors x(t), that is:

[0041]

[0042] And perform normalization processing in the interval [0, 1];

[0043] Radial basis function (RBF) is a scalar function symmetric along the radial direction, representing the relationship between the variable space distance and the function value. After superimposing multiple RBFs, a flexible response surface can be obtained; The type of RBF varies with the φ(·) function. When φ(·) is a Gaussian function, the effect of fitting the reservoir operation rule is good. Therefore, use Gaussian RBF combined with the proposed decision factor vector x(t) to construct the reservoir optimal operation rule as follows:

[0044]

[0045] Where: I is the number of Gaussian RBFs adopted by each reservoir; is the scheduling rule constructed by Gaussian RBF for Scheme C; J is the number of variables in the decision factor x(t); ω m,i is the weight corresponding to the i-th Gaussian RBF of the m-th reservoir, satisfying and ∑ω m,i = 1; c j,i , b j,i are the parameters of the i-th Gaussian RBF respectively, When constructing the scheduling rule with Gaussian RBF, the number of required parameters [ω m,i , c j,i , b j,i , p1, p2] is I(M + 2(J - 2)) + 2.

[0046] Preferably, Step 4 specifically includes the following sub-steps:

[0047] Step 4.1: On the premise of ensuring the safety of the flood control section and the unchanged flood regulation high water level of the Three Gorges Reservoir, the flood control storage capacity reserved by the Jinsha River downstream cascade reservoirs is equivalent to the minimum increase in the effective flood control storage capacity of the Three Gorges Reservoir, that is:

[0048] ΔV TGR = αV J + β(18)

[0049] Where: ΔV TGR represents the complementary equivalent flood control storage capacity of the Three Gorges Reservoir,; V J =(V WDD , V BHT , V XLD , V XJB ) T represents the flood control storage capacity reserved by each reservoir in the lower reaches of the Jinsha River, and the reserved storage capacity of each reservoir does not exceed the maximum value of its own flood control storage capacity, that is V i ∈[0, max{V fh,i}], α=(α WDD , α BHT , α XLD , α XJB ) represents the complementary equivalent coefficient of the flood control storage capacity of each reservoir in the lower reaches of the Jinsha River; β is the intercept value;

[0050] Step 4.2: Calculate the flood control risk of the cascade reservoir group: The meaning of the flood control loss equation is a theoretical expression that characterizes the relationship between the total flood control loss of the reservoir group system, the change in the total storage capacity of the reservoir group system, and the proportion coefficient of the storage capacity allocation between reservoirs, and a discriminant of the proportion coefficient that can be used to guide the storage capacity allocation is derived through mathematical analysis.

[0051] More preferably, in step 4.2, the calculation formula for the flood control risk of the cascade reservoir group is as follows:

[0052]

[0053]

[0054] In the formula: R is the flood control risk of the reservoir group, V c,j is the critical storage capacity of the j-th reservoir, V i,j is the storage capacity of the j-th reservoir at the end of the i-th period, g(.) is the joint distribution of storage capacities within the prediction period, is the flood control risk outside the prediction period estimated based on the average storage capacity at the end of the first period. It is assumed that the flood control risks inside and outside the prediction period are independent; the constraints are as follows:

[0055] (V 0,1 - V 1,1 ) = α(V 0,2 - V 1,2 ) (20)

[0056] In the formula: V 0,j is the storage capacity of the j-th reservoir at the beginning of the start time, and α is the replacement coefficient of the change in storage capacity within the prediction period;

[0057] Solve for the storage capacity replacement coefficient α. When deriving the flood control risk of the reservoir group according to the Lagrange multiplier method, the relationship between V 1,1 , V 1,2 and α is obtained, and then the boundary of the storage capacity possibility that minimizes the flood control risk is obtained;

[0058]

[0059] Apply the derived flood control storage capacity allocation rule based on the storage capacity allocation ratio coefficient to the cascade reservoir group system for case studies, and compare with the results of the conventional numerical simulation method to verify the calculation accuracy of representing the flood control loss of the reservoir group system using the flood control loss equation, and the rationality of directly guiding the flood season operation water level allocation strategy based on the ratio coefficient discriminant.

[0060] Preferably, step 5 includes the following sub-steps:

[0061] Step 5.1: On the premise of controllable flood control risk, dynamically control the operation water levels of the cascade reservoir group based on the forecast information and flood control storage capacity compensation;

[0062] Step 5.2: Based on the joint design of the cascade reservoirs and the results of multi-objective optimal dispatching, find the optimal combination of the operation water levels of the Jinxia cascade and the Three Gorges reservoir group;

[0063] Step 5.3: Generate a large number of input samples through runoff simulation. Adopt a multi-objective evolutionary algorithm based on the Pareto optimal theory to robustly optimize the cumulative objective, extreme value objective, and threshold objective, and determine the flexible decision interval of the operating water levels of cascade reservoirs to guide reservoir operation scheduling, where the cumulative objective is the average annual power generation, the extreme value objective is the minimum output, and the threshold objective is the output guarantee rate.

[0064] Advantages of the present invention:

[0065] 1. If the original single reservoir's flood control storage capacity designed by multiple different units at different times is still used during the operation period of cascade reservoirs, it will lead to the problem of low power generation benefit during the flood season. The present invention fully considers the complementary and equivalent relationship of the flood control storage capacity of cascade reservoirs, conducts aggregation decomposition and optimal design with the same flood control objective, and improves the total power generation of cascade reservoirs during the flood season; the present invention seeks to determine the optimal combination of operating water levels and the flexible decision interval of reservoir groups, and gives full play to the flood control and beneficial utilization benefits of reservoirs.

[0066] 2. The method of the present invention is concise and accurate, and is more convenient for engineering practical application; on the premise of ensuring that the total reserved flood control storage capacity remains unchanged, that is, the flood control risk is controllable, the present invention determines the optimal combination and flexible decision interval of the operating water levels of the Jinxia cascade and the Three Gorges reservoir group to guide reservoir operation scheduling.

[0067] 3. The present invention overcomes the limitations of single reservoir design, fully considers the complementary and equivalent relationship of the flood control storage capacity of cascade reservoirs, and provides a theoretical basis and technical support for the joint design and optimal scheduling of 6 cascade reservoirs. Description of the Drawings

[0068] Figure 1 is the flowchart of the method of the present invention;

[0069] Figure 2 is the conventional operation chart of the Wudongde Reservoir Power Station;

[0070] Figure 3 is the generalized diagram of the unregulated interval basin of the Jinxia cascade and the Three Gorges Reservoir;

[0071] Figure 4 is the research process of the complementary and equivalent relationship of the flood control storage capacity of the Jinxia cascade and the Three Gorges Reservoir;

[0072] Figure 5 is the schematic diagram of the principle of the dynamic control method of the operating water levels of cascade reservoirs during the flood season;

[0073] Figure 6 is the schematic diagram of the flexible decision interval of the operating water levels of the Jinxia cascade reservoir. Detailed Embodiment

[0074] The present invention will be further described in detail below with reference to the drawings and specific embodiments.

[0075] Embodiment 1: A combined method for designing the optimal characteristic water levels of the Jinxia cascade and the Three Gorges Reservoir group, comprising the following steps:

[0076] Step 1: Collect the characteristic parameters of the operating water levels and the scheduling requirements of key large reservoirs in the upper reaches of the Yangtze River, and the series of observed flow data of hydrological stations. Analyze the hydraulic connections between cascade reservoirs and the characteristics of runoff generation and concentration in the intermediate catchments.

[0077] Step 2: According to the design operation charts and scheduling regulations of each reservoir, simulate and calculate the annual average power generation of each reservoir, and calculate the sum of the annual average power generations of the cascade reservoirs;

[0078] Furthermore, Step 2 includes the following sub-steps:

[0079] Step 2-1: The operation mode of a single reservoir based on the conventional reservoir design operation chart. Respectively simulate the operation of each reservoir, without considering the hydraulic connection characteristics of each reservoir, and neglect the backwater effect in the relationship between the reservoir discharge flow and the tail water level;

[0080] Step 2-2: The conventional reservoir operation chart stipulates the output and water level control parameters of the operation charts of each hydropower station. The scheduling model can perform equal-output regulation calculations according to the water levels specified in each time period;

[0081] Step 2-3: The equal-output regulation calculation formula for cascade reservoirs is as follows:

[0082]

[0083] Q fd,m (t) = N m (t)·K m (h m (t) + h s,m ) (2)

[0084] h m (t) = (Z u,m (V m (t)) + Z u,m (V m (t + 1))) / 2 - Z d,m (Q out,m (t), Z m+1 (t)) - h s,m (3)

[0085] In the formula: t is the time variable, s; T is the total length of the research period, t = 1, 2,..., T; m is the serial number of the cascade reservoirs (the total number is M) from top to bottom, m = 1, 2,..., M; is the conventional scheduling function of the m-th reservoir under Scheme A, where "..." represents the decision factors other than time and storage capacity (water level) in the operation chart, such as the inflow; Km (·) is the power generation flow water consumption rate function of the m-th reservoir, m 3 / kW; h s,m is the power generation head loss of the m-th reservoir, m; h m (t) is the net head of the m-th reservoir at time t, m; N m (t) is the output of the m-th reservoir at time t, MW; Q fd,m (t) is the power generation flow of the m-th reservoir at time t, m 3 / s; Q out,m (t) is the outflow of the m-th reservoir at time t, m 3 / s; V m (t) and V m (t + 1) are the reservoir storage capacities of the m-th reservoir at the beginning and end of time t and t + 1 respectively, m 3 ; Z u,m (·) is the reservoir water level - storage capacity relationship function of the m-th reservoir; Z d,m (·) represents the tail water level - outflow relationship function of the m-th reservoir; Z m+1 (t) is the water level above the dam of the (m + 1)-th reservoir.

[0086] The main constraint conditions include water balance constraint, power station unit output constraint, reservoir storage capacity and amplitude constraint, outflow and amplitude constraint, initial boundary condition constraint and non - negative constraint, etc.:

[0087] V m (t + 1) = V m (t)+(Q in,m (t)-Q out,m (t))·Δt (4)

[0088]

[0089] V m (0) = V b,m ,V m (T) = V e,m (8)

[0090] In the formula: Q in,m (t) is the inflow of the m-th reservoir at time t, m 3 / s; are the minimum / maximum output limits of the m-th reservoir at time t, kW; are the minimum / maximum reservoir storage capacity limits of the m-th reservoir at time t, m 3 ; and are the minimum / maximum outflow limits of the m-th reservoir at time t, m 3 / s; is the maximum storage capacity variation of the m-th reservoir in adjacent periods, m 3 ; is the variation of the discharge flow of the m-th reservoir in adjacent periods, m 3 / s; V b,m and V e,m are the initial and final storage capacities of the m-th reservoir at the beginning of the reservoir operation, m 3 .

[0091] Step 3: Select flood control, power generation, and full storage rate as the objective functions, construct a multi-objective joint operation model for cascade reservoirs, solve it using the "parameterization - simulation - optimization" framework and multi-objective evolutionary algorithm, and conduct simulation and optimization operation of cascade reservoirs.

[0092] Furthermore, Step 3 includes the following sub-steps:

[0093] Step 3.1: Under the constraints of the current joint operation plan of cascade reservoirs, establish a multi-objective joint optimization operation model for the 6 cascade reservoirs in the lower reaches of the Jinsha River and the Three Gorges - Gezhouba, with the maximum annual average power generation, minimum flood control risk, and highest full storage rate of cascade reservoirs as the objective functions respectively.

[0094] (1) Maximum annual average power generation:

[0095]

[0096] In the formula: is the sum of the annual average power generations of cascade reservoirs, kW·h; is the annual average power generation of the m-th reservoir, kW·h; n y is the number of years of the input series.

[0097] (2) Minimum flood control risk:

[0098]

[0099] In the formula: FCR * and FCR m are the flood control risks of the cascade reservoirs and the m-th reservoir respectively; is the maximum flood regulation storage capacity of the reservoir, m 3 ; is the storage capacity corresponding to the highest safety water level (flood limit water level, normal storage water level in the non-flood season) in front of the dam of the m-th reservoir at time t, m 3 .

[0100] (3) Highest full storage rate:

[0101]

[0102] In the formula: IE * and IE mare the multi-year average full storage rates of the cascade reservoir and the m-th reservoir, respectively; V zc,m -V s,m is the storage capacity between the normal storage level and the dead storage level of the m-th reservoir, i.e., the regulating storage capacity, m 3 ; θ m is the proportion of the regulating storage capacity of the m-th reservoir in the cascade reservoir. The main constraint conditions are the same as those of the operation chart model scheme.

[0103] Step 3.2: Optimize the operation rule by using Gaussian RBF fitting

[0104] Reservoir operation generally takes the current time period, the state of the reservoir (storage capacity or water level) at the current time period, and the inflow discharge information as decision factors, and the outflow discharge of the reservoir at each time period as decision variables. Considering that the unregulated basin area from Xiangjiaba to the Three Gorges Dam site is relatively large, the inflow discharge in the decision factors of the cascade reservoir includes the inflow discharge of the Wudongde Reservoir at the current time period and the discharge of the unregulated basin area from Xiangjiaba to the Three Gorges Dam site. In order to improve the continuity and flexibility of the time period information in the operation rule, two trigonometric functions, sin(2πt / 366 - p1) and cos(2πt / 366 - p2), are used to represent time, where p1 and p2 are phase shifts, satisfying p1, p2 ∈ [0, 2π]. Therefore, the time period t, the storage capacity value of the corresponding cascade reservoir (except Gezhouba) at time period t, the inflow discharge Q in,1 (t) of the Wudongde Reservoir, and the discharge Q qj,45 (t) in the Xiangjiaba - Three Gorges section, a total of 9 variables are used as the decision factor vector x(t), that is:

[0105]

[0106] And perform normalization processing in the interval [0, 1].

[0107] Radial basis function (RBF) is a scalar function symmetric along the radius, representing the relationship between the variable space distance and the function value. After superimposing multiple RBFs, a flexible response surface can be obtained. The type of RBF varies with the φ(·) function. Research shows that when φ(·) is a Gaussian function (i.e., Gaussian RBF), the effect of fitting the reservoir operation rule is better. Therefore, Gaussian RBF is used in combination with the formulated decision factor vector x(t) to construct the reservoir optimal operation rule as follows:

[0108]

[0109] In the formula: I is the number of Gaussian RBFs used for each reservoir; is the operation rule constructed by Gaussian RBF for Scheme C; J is the number of variables in the decision factor x(t); ωm,i is the weight corresponding to the i-th Gaussian RBF of the m-th reservoir, satisfying and ∑ω m,i = 1; c j,i , b j,i are the parameters of the i-th Gaussian RBF respectively. When constructing the scheduling rule with Gaussian RBF, the number of required parameters [ω m,i , c j,i , b j,i , p1, p2] is I(M + 2(J - 2)) + 2.

[0110] Step 3.3: Solve using the adaptive multi-objective evolutionary algorithm. The advantages of this method in terms of optimization efficiency and the reliability of the Pareto solution set compared to the classical evolutionary algorithm have been widely applied to the joint optimal operation of cascade reservoirs. Set the initial population size to 200. After normalizing the 3 objective functions, uniformly set the ε value to 0.001, and set the maximum number of optimization steps to 200,000, which is equivalent to calculating the objective functions approximately 5.6 million times.

[0111] Step 4: Based on the flood area composition method and the cascade reservoir reach runoff yield and concentration model, establish the complementary equivalent relationship of the flood control storage capacity of cascade reservoirs and calculate the flood control risk of the cascade reservoir group.

[0112] Furthermore, Step 4 includes the following sub-steps:

[0113] Step 4.1: On the premise of ensuring the safety of the flood control control section and the unchanged flood regulation high water level of the Three Gorges Reservoir, the flood control storage capacity reserved by the Jinsha River downstream cascade reservoirs is equivalent to the minimum increase in the effective flood control storage capacity of the Three Gorges Reservoir, that is:

[0114] ΔV TGR = αV J + β(18)

[0115] In the formula: ΔV TGR represents the complementary equivalent flood control storage capacity of the Three Gorges Reservoir,; V J =(V WDD , V BHT , V XLD , V XJB ) T represents the flood control storage capacity reserved by each reservoir in the lower reaches of the Jinsha River, and the reserved storage capacity of each reservoir does not exceed the maximum value of its own flood control storage capacity, that is V i ∈[0, max{V fh,i}], α=(α WDD , α BHT , α XLD , α XJB) represents the complementary equivalent coefficient of the flood control storage capacities of the reservoirs in the lower reaches of the Jinsha River; β is the intercept value.

[0116] Step 4.2: Calculate the flood control risk of the cascade reservoir group. The meaning of the flood control loss equation is a theoretical expression that characterizes the relationship between the total flood control loss of the reservoir group system, the change in the total storage capacity of the reservoir group system, and the proportion coefficient of the storage capacity allocation among the reservoirs. Combining with mathematical analysis, a discriminant formula for the proportion coefficient that can be used to guide the storage capacity allocation is derived. The calculation formula for the flood control risk of the cascade reservoir group is:

[0117]

[0118] In the formula: R is the flood control risk of the reservoir group, V c,j is the critical storage capacity of the j-th reservoir, V i,j is the storage capacity of the j-th reservoir at the end of the i-th period, g(.) is the joint distribution of the storage capacities during the prediction period (current period), is the flood control risk outside the prediction period estimated based on the average storage capacity at the end of the first period. It is assumed that the flood control risks inside and outside the prediction period are independent. The constraints are as follows:

[0119] (V 0,1 -V 1,1 ) = α(V 0,2 -V 1,2 ) (20)

[0120] In the formula: V 0,j is the storage capacity of the j-th reservoir at the beginning of the start time, and α is the replacement coefficient of the change in the storage capacity during the prediction period.

[0121] Solve for the storage capacity replacement coefficient α. When deriving the flood control risk of the reservoir group according to the Lagrange multiplier method, the relationship between V 1,1 , V 1,2 and α is obtained, and then the boundary of the storage capacity possibility that minimizes the flood control risk is obtained.

[0122]

[0123] Apply the derived flood control storage capacity allocation rule based on the proportion coefficient of the storage capacity allocation to the cascade reservoir group system to conduct a case study, and compare it with the results of the conventional numerical simulation method to verify the calculation accuracy of characterizing the flood control loss of the reservoir group system using the flood control loss equation, and the rationality of directly guiding the flood season operation water level allocation strategy based on the discriminant formula of the proportion coefficient.

[0124] Step 5: Based on the complementary equivalent relationship between the flood control storage capacities of the Jinxia cascade and the Three Gorges, realize the dynamic control of the operation water levels of the cascade reservoir group, and seek and determine the optimal combination and flexible decision-making interval of the operation water levels of the Jinxia cascade and the Three Gorges reservoir group.

[0125] Furthermore, Step 5 includes the following sub-steps:

[0126] Step 5.1: On the premise that flood control risks are controllable, dynamically control the operating water levels of cascade reservoirs based on forecast information and flood control storage compensation.

[0127] Step 5.2: Based on the joint design of cascade reservoirs and the results of multi-objective optimal operation, find the optimal combination of the operating water levels of the Jinsha-Xia cascade and the Three Gorges reservoir group.

[0128] Step 5.3: Generate a large number of input samples through runoff simulation, and use a multi-objective evolutionary algorithm based on the Pareto optimal theory to robustly optimize the cumulative objective (average annual power generation), extreme value objective (minimum output), and threshold objective (output guarantee rate), and determine the flexible decision-making interval of the operating water levels of cascade reservoirs to guide reservoir operation scheduling.

[0129] Example 2: As Figure 1 shown, the method of this example includes the following steps:

[0130] Step 1: Collect data such as the characteristic parameters of cascade reservoirs in the upper reaches of the Yangtze River Basin, the long-term daily-scale inflow process, and the safe flow downstream of the reservoirs. Among them, the Jinsha River Huatan (Qiaojia) Station, Pingshan (Xiangjiaba) Station, and Yichang Station have daily-scale historical measured flow data from 1959 to 2023 (a total of 65 years) after restoration.

[0131] There are a total of 6 cascade reservoirs in the Jinsha-Xia cascade and the Three Gorges-Gezhouba, all of which are uniformly operated and managed by China Three Gorges Corporation, making them the largest cascade reservoir group in the world. Table 1 lists the design characteristic parameter values of the 6 cascade reservoirs of Yangtze Power. The total flood control storage capacity of the cascade reservoirs is 37.644 billion m 3 , the total installed capacity is 70,035 MW, and the designed annual power generation is 290.55 billion kWh. According to the water level-flow relationship at the tailwater outlet section of each reservoir, when the water levels of the Baihetan, Xiluodu, Xiangjiaba, and Gezhouba reservoirs exceed 800 m, 560 m, 367 m, and 63 m respectively, the tailwater-outflow relationship of the Wudongde, Baihetan, Xiluodu, and Three Gorges reservoirs needs to consider the backwater effect of the downstream reservoirs.

[0132] The Jinsha-Xia cascade and the Three Gorges cascade reservoirs were planned and designed by different design units and jointly undertake the flood control tasks in the middle and lower reaches of the Yangtze River. Due to the uneven temporal and spatial distribution of rainfall and runoff in the Yangtze River Basin, the flood control storage capacities of these reservoirs are complementary and equivalent. Therefore, carrying out the joint design of the flood control storage capacities of cascade reservoirs and the joint optimal operation of water projects can significantly improve the comprehensive utilization benefits of the reservoir group.

[0133] Table 1 Characteristic parameters of 6 cascade reservoirs of Yangtze Power

[0134]

[0135] Step 2: Construct a scheme based on the reservoir's normal operation chart and operation rule model

[0136] The operation plan for a single reservoir is guided by the reservoir's normal operation chart. The reservoir's normal operation chart provides water storage and release strategies for the long-term control and runoff regulation of the reservoir. With time (month, dekad) as the abscissa and the reservoir water level or water storage as the ordinate, it is divided into different output areas (or water supply areas) by some indicator lines that control the power generation output (or water storage and water supply) of the reservoir power station. Figure 2 The normal operation chart of the Wudongde Reservoir Power Station is given. The advantage of the reservoir operation chart is that it is simple, intuitive, easy to apply, and can effectively display the continuity of the operation rules over time.

[0137] Step 2.1 The operation chart stipulates the output and water level control parameters of each hydropower station. The equal-output regulation calculation of cascade reservoirs can be carried out according to the water levels specified in each period:

[0138]

[0139] Q fd,m (t) = N m (t)·K m (h m (t) + h s,m )(2)

[0140] h m (t) = (Z u,m (V m (t)) + Z u,m (V m (t + 1))) / 2 - Z d,m (Q out,m (t), Z m+1 (t)) - h s,m (3)

[0141] In the formula: t is the time variable, s; T is the total length of the research period, t = 1, 2,..., T; m is the serial number of the cascade reservoir (the total number is M) from top to bottom, m = 1, 2,..., M; is the normal operation function of the m-th reservoir under Plan A, where "..." represents the decision factors other than time and reservoir capacity (water level) in the operation chart, such as the inflow; K m (·) is the power generation flow water consumption rate function of the m-th reservoir, m 3 / kW; h s,m is the power generation head loss of the m-th reservoir, m; h m (t) is the net head of the m-th reservoir in the t-th period, m; N m (t) is the output of the m-th reservoir in the t-th period, MW; Q fd,m (t) is the power generation flow of the m-th reservoir in the t-th period, m3 / s; Q out,m Q(t) is the discharge from the m-th reservoir at time t, m 3 / s; V m V(t) and V m V(t + 1) are the reservoir storage volumes of the m-th reservoir at the beginning and end of time t and t + 1 respectively, m 3 ; Z u,m Z(·) is the water level - storage relationship function of the m-th reservoir; Z d,m Z(·) represents the tail water level - discharge relationship function of the m-th reservoir; Z m+1 Z(t) is the water level above the dam of the (m + 1)-th reservoir.

[0142] Step 2.1 The main constraints include water balance constraint, power generation unit output constraint, reservoir storage volume and variation range constraint, discharge and variation range constraint, initial boundary condition constraint, and non - negative constraint, etc.:

[0143] V m V(t + 1) = V m (t)+(Q in,m (t)-Q out,m (t))·Δt (4)

[0144]

[0145] V m V(0) = V b,m ,V m V(T) = V e,m (8)

[0146] In the formula: Q in,m Q(t) is the inflow to the m-th reservoir at time t, m 3 / s; Pmin(t) and Pmax(t) are the minimum / maximum output limits of the m-th reservoir at time t, kW; Vmin(t) and Vmax(t) are the minimum / maximum reservoir storage volume limits of the m-th reservoir at time t, m 3 ; Qmin(t) and Qmax(t) are the minimum / maximum discharge limits of the m-th reservoir at time t, m 3 / s; ΔV is the maximum variation range of the reservoir storage volume of the m-th reservoir between adjacent time periods, m 3 ; ΔQ is the variation range of the discharge of the m-th reservoir between adjacent time periods, m 3 / s; V b,m V0 and V e,m VT are the reservoir storage volumes at the beginning and end of the dispatching period of the m-th reservoir respectively, m 3 .

[0147] Step 3: Construct a multi-objective joint optimal operation model for cascade reservoirs

[0148] Under the constraints of the current cascade reservoir operation plan, a multi-objective joint optimal operation model for six cascade reservoirs in the lower reaches of the Jinsha River and the Three Gorges-Gezhouba is established, and simulation optimization operation is carried out by combining the "parameterization-simulation-optimization" framework and the multi-objective evolutionary algorithm.

[0149] Step 3.1 Considering the requirements of flood control and water utilization, etc., the optimization objective functions are respectively the maximum annual average power generation of the cascade reservoirs, the minimum flood control risk, and the highest full storage rate:

[0150] (1) Maximum annual average power generation:

[0151]

[0152] Where: is the sum of the annual average power generation of the cascade reservoirs, kW·h.

[0153] (2) Minimum flood control risk:

[0154]

[0155] Where: FCR * and FCR m are the flood control risks of the cascade reservoirs and the mth reservoir respectively; is the maximum flood regulation storage capacity of the reservoir, m 3 ; is the storage capacity corresponding to the highest safety water level (flood limit water level, normal storage water level in the non-flood season) in front of the mth reservoir at time t, m 3 .

[0156] (3) Highest full storage rate:

[0157]

[0158] Where: IE * and IE m are the annual average full storage rates of the cascade reservoirs and the mth reservoir respectively; V zc,m -V s,m is the storage capacity between the normal storage water level and the dead water level of the mth reservoir, that is, the regulating storage capacity, m 3 ; θ m is the proportion of the regulating storage capacity of the mth reservoir in the cascade reservoirs. The constraint conditions are the same as those of the operation chart model plan.

[0159] Step 3.2 In general, reservoir operation takes the current time period, the state of the reservoir at the current time period (reservoir storage or water level), and the inflow information as decision factors, and the outflow of the reservoir in each time period as decision variables. Considering the large uncontrolled section from Xiangjiaba to the Three Gorges Dam site, the inflow in the decision factors of cascade reservoirs includes the inflow of Wudongde Reservoir in the current time period and the flow in the uncontrolled section from Xiangjiaba to the Three Gorges Dam site. To improve the continuity and flexibility of the time period information in the operation rules throughout the year, two trigonometric functions, sin(2πt / 366 - p1) and cos(2πt / 366 - p2), are used to represent time, where p1 and p2 are phase shifts, and p1, p2 ∈ [0, 2π]. Therefore, the time period t, the corresponding reservoir storage values of the cascade reservoirs (except Gezhouba) at time period t, the inflow of Wudongde Reservoir Q in,1 (t), and the flow Q qj,45 (t) in the Xiangjiaba - Three Gorges section, a total of 9 variables are used as the decision factor vector x(t), that is:

[0160]

[0161] And they are normalized in the interval [0, 1].

[0162] Radial basis function (RBF) is a scalar function symmetric along the radial direction, representing the relationship between the variable space distance and the function value. By superimposing multiple RBFs, a flexible and variable response surface can be obtained. The type of RBF varies with the φ(·) function. Research shows that when φ(·) is a Gaussian function (i.e., Gaussian RBF), the effect of fitting the reservoir operation rules is better. Therefore, Gaussian RBF is combined with the proposed decision factor vector x(t) to construct the reservoir optimal operation rules as follows:

[0163]

[0164] In the formula: I is the number of Gaussian RBFs used for each reservoir; is the operation rule constructed by Gaussian RBF for Scheme C; J is the number of variables in the decision factor x(t); ω m,i is the weight corresponding to the i-th Gaussian RBF of the m-th reservoir, satisfying and ∑ω m,i = 1; c j,i , b j,i are the parameters of the i-th Gaussian RBF respectively, When constructing the operation rule with Gaussian RBF, the required parameters [ω m,i , c j,i , b j,i, the number of [p1, p2] is I(M + 2(J - 2)) + 2.

[0165] In this study, J = 9 and M = 5. To avoid the underfitting or high operating cost caused by a relatively small or large number of Gaussian RBFs, 5 Gaussian RBFs (I = 5) are used for each reservoir to describe the scheduling rules. Then, there are a total of 97 parameters for the cascade reservoir scheduling rules. Each corresponds to a function response mode, and different modes are linearly added with different weights ω m to obtain the final out - flow discharge Q out,m (t) of the m - reservoir at time t based on Gaussian RBF.

[0166] Step 3.3 uses the Adaptive Borg Multi - Objective Evolutionary Algorithm (Borg MOEA) to optimize the optimal scheduling scheme. Related research has proven the advantages of Borg MOEA over classical evolutionary algorithms in terms of optimization efficiency and the reliability of the Pareto solution set. Currently, it has been widely applied to the joint optimal scheduling of cascade reservoirs. Set the initial population size to 200, normalize the 3 objectives and uniformly set the ε value to 0.001, and set the maximum number of optimization steps of Borg MOEA to 200,000, which is equivalent to calculating the objective function approximately 5.6 million times.

[0167] Step 4: Based on the flood area composition method and the cascade reservoir reach - scale runoff generation and concentration model, establish the complementary equivalent relationship of the flood control storage capacity of cascade reservoirs and calculate the flood control risk of the cascade reservoir group.

[0168] The current research on the joint flood control scheduling of cascade reservoirs focuses on the scheduling theoretical models, algorithms, and the application of scheduling results, without considering the randomness and uncertainty of flood area composition. Figure 3 Give the generalized map of the reach between the downstream cascade of the Jinsha River and the Three Gorges Reservoir. Figure 4 This is the research process for the complementary equivalent relationship of the flood control storage capacity of the downstream Jinsha River and the Three Gorges cascade reservoirs. First, use the most likely area composition method based on the Copula function to calculate the flood process at the Xiangjiaba - Pingshan Station, the control section at the exit of the Jinsha River. Then, establish a runoff generation and concentration model for the uncontrolled reach between Xiangjiaba and the Three Gorges Dam site. The input of the multiple - input single - output (MISO) system model is the flow data of the Xiangjiaba, Gaochang, Fushun, Beibei, and Wulong control stations and the rainfall data of 3 uncontrolled sub - reaches, and the output is the flow process at the Three Gorges Reservoir Dam site. Finally, calculate the complementary equivalent relationship of the flood control storage capacity of the downstream Jinsha River cascade and the Three Gorges Reservoir.

[0169] This paper defines the complementary equivalent coefficient of flood control storage capacity as follows: for the flood control effect of the Jingjiang River or Chenglingji, on the premise of ensuring the safety of flood control control stations and the unchanged highest flood regulation water level of the Three Gorges Reservoir, the flood control storage capacity reserved by each reservoir in the lower reaches of the Jinsha River is equivalent to the minimum effective flood control storage capacity that needs to be increased in the Three Gorges Reservoir, that is:

[0170] ΔV TGR =αV J +β (18)

[0171] In the formula: ΔV TGR represents the complementary equivalent flood control storage capacity of the Three Gorges Reservoir, ΔV TGR ∈[0,221.5]; V J =(V WDD ,V BHT ,V XLD ,V XJB ) T represents the flood control storage capacity reserved by each reservoir in the lower reaches of the Jinsha River, and the reserved capacity of each reservoir does not exceed the maximum value of its own flood control storage capacity, that is V i ∈[0,max{V fh,i}], (i = WDD, BHT, XLD, XJB); α = (α WDD ,α BHT ,α XLD ,α XJB ) represents the complementary equivalent coefficient of flood control storage capacity of each reservoir in the lower reaches of the Jinsha River; β is the intercept value; WDD, BHT, XLD, XJB are the names of each reservoir.

[0172] Step 4.2 First, derive the flood control risk loss equation of the cascade reservoir group system. The meaning of the flood control loss equation is a theoretical expression that characterizes the relationship between the total flood control loss of the reservoir group system, the change in the total storage capacity of the reservoir group system, and the proportion coefficient of the storage capacity distribution among the reservoirs, and a discriminant formula for the proportion coefficient that can be used to guide the storage capacity distribution is derived through mathematical analysis. The flood control risk calculation formula for the cascade reservoir group is as follows:

[0173]

[0174] In the formula: R is the flood control risk of the reservoir group, V c,j is the critical storage capacity of the jth reservoir, V i,j is the storage capacity of the jth reservoir at the end of the i-th time period, g(.) is the joint distribution of storage capacities within the prediction period (current time period), is the flood control risk outside the prediction period estimated based on the average storage capacity at the end of the first time period, assuming that the flood control risks inside and outside the prediction period are independent. The constraints are as follows:

[0175] (V 0,1 -V 1,1 )=α(V 0,2 -V 1,2) (20)

[0176] Where: V 0,j is the storage capacity of the j-th reservoir at the initial moment of the start time, and α is the replacement coefficient of the change in storage capacity during the forecast period.

[0177] Solve for the storage capacity replacement coefficient α, and derive the relationship between V 1,1 , V 1,2 and α when calculating the flood control risk of the reservoir group according to the Lagrange multiplier method, and then obtain the possible boundary of the storage capacity that minimizes the flood control risk.

[0178]

[0179] Apply the derived flood control storage capacity allocation rule based on the storage capacity allocation ratio coefficient to the reservoir group system on the Yangtze River for case studies, and compare with the results of conventional numerical simulation methods to verify the calculation accuracy of representing the flood control loss of the reservoir group system using the flood control loss equation, and the rationality of directly guiding the flood season operation water level allocation strategy based on the ratio coefficient discriminant.

[0180] Step 5: Based on the complementary equivalent relationship between the Jinxia cascade and the Three Gorges flood control storage capacity, realize the dynamic control of the operation water levels of the cascade reservoir group, and determine the optimal combination and flexible decision-making interval of the operation water levels of the Jinxia cascade and the Three Gorges reservoir group.

[0181] Step 5.1 In conventional optimal dispatching, the number of decision variables of the cascade reservoir group increases linearly with the increase in the number of reservoirs, and the number of calculations of the multi-objective function value increases exponentially accordingly. For a reservoir group system with more than 10 reservoirs, it is very easy to cause the curse of dimensionality. For this kind of multi-objective dimensionality disaster problem, a feasible solution idea is to introduce the large system aggregation - decomposition method. It is commonly used in the joint flood control and power generation dispatching of large system reservoir groups. Its core idea is to aggregate multiple reservoirs into a virtual aggregated reservoir in terms of water volume, determine the state of the aggregated reservoir at time t, and then decompose its total output to each independent reservoir. Figure 5 Give the schematic diagram of the real-time dynamic control method for the flood season operation water levels of the cascade reservoir group.

[0182] Flood control risks and beneficial utilization benefits are mutually contradictory. How to improve the comprehensive utilization benefits of reservoirs on the premise of controllable flood control risks? The main model methods adopted include: ① The dynamic control scheduling model of the operating water level based on flood control risk analysis; ② The dynamic control method of the operating water level based on forecasting and storage capacity compensation. On the premise of not reducing the flood control standard, an acceptable risk rate is estimated, and the real-time flood control risk is evaluated and controlled to make it reach within the acceptable level; according to the hydrological asynchrony or the difference in its storage capacity, compensation scheduling or peak staggering scheduling is carried out according to the requirements of downstream flood control control points to realize the control of the reservoir's operating water level during the flood season. When dealing with the transition problem between adjacent flood season periods, in order to make full use of water resources, the power generation flow is usually gradually increased and the water level is lowered before the start of the main flood season, and water is stored appropriately in advance before the end of the main flood season to store flood water resources as much as possible.

[0183] Step 5.2 For the joint optimization regulation and benefit evaluation of the characteristic water levels and dispatching operations of the reservoir group, a double-layer nested optimization dispatching model is mainly constructed to obtain the deterministic optimal dispatching trajectory to derive the dispatching rules, and thus an optimization dispatching diagram suitable for the reservoir group is constructed. Taking the dispatching nodes as decision variables, intelligent algorithms are used for solution. During the solution process, multiple objectives are considered: in terms of flood control and disaster reduction, the criterion is to minimize the maximum downstream discharge; in terms of water utilization, the water utilization rate is used as the index; in terms of water supply, combined with the joint dispatching plan of the cascade reservoir group and the power generation operation mode, the average low-flow rate at the Yichang section is used as the evaluation index; for power generation benefits, the degree of increase in power generation is analyzed. Based on the above-mentioned cascade reservoir joint design and multi-objective simulation and optimization dispatching results, the optimal combination of the operating water levels of the Jinxia cascade and the Three Gorges reservoir group is determined.

[0184] Step 5.3 Most reservoir dispatching problems can be formulated as standard Markov decision processes. The "different tracks, same effect" phenomenon can be used to study the reservoir optimization dispatching decision interval. By improving the traditional dynamic programming method, the unique optimal solution is converted into a sufficiently large decision space, and then the optimized water level and output interval are obtained, and the dispatching decision interval within the 10% - 90% quantiles is determined to improve the operability of the optimization dispatching. However, the joint dispatching of cascade reservoir groups often faces challenges such as runoff uncertainty and multi-objective requirements. Affected by the "curse of dimensionality", it is difficult to expand the runoff input sequence and the target dimension is limited. To solve the above problems, a direct strategy search algorithm represented by "parameter - simulation - optimization" can be combined with a multi-objective evolutionary algorithm based on Pareto optimal theory. A large number of input samples are generated through runoff simulation, and a series of non-dominated solution sets are provided to show the trade-off relationship between multiple objectives. A cascade reservoir power generation joint dispatching model is constructed and combined with the "parameterization - simulation - optimization" framework to perform robustness optimization on the cumulative objective (annual average power generation), extreme value objective (minimum output), and threshold objective (output guarantee rate). Figure 6The schematic diagram of the flexible decision-making interval of the operating water levels of the cascade reservoirs in the lower reaches of the Jinsha River is given to guide the operation of the cascade reservoir dispatching.

[0185] The above embodiments are only the preferred technical solutions of the present invention and should not be regarded as limitations on the present invention. The protection scope of the present invention should be the technical solutions recorded in the claims, including the equivalent replacement solutions of the technical features in the technical solutions recorded in the claims. That is, the equivalent replacement improvements within this scope are also within the protection scope of the present invention.

Claims

1. A combined method for optimal characteristic water level design of the Jinxia cascade and the Three Gorges reservoir group, characterized by: The following steps are involved: Step 1: Collect the operating water level characteristic parameters and dispatching requirements of the key large reservoirs in the upper reaches of the Yangtze River, and the flow data series of hydrological stations, and analyze the hydraulic connection between cascade reservoirs and the flow generation and convergence characteristics of the interval basins; Step 2: According to the design dispatch diagram and dispatch regulations of each reservoir, simulate and calculate the multi-year average power generation of each reservoir, and calculate the sum of the multi-year average power generation of the cascade reservoirs; Step 3: Select flood control, power generation, and storage rate as the objective functions, build a multi-objective joint dispatching model for cascade reservoirs, adopt the "parameterization-simulation-optimization" framework and multi-objective evolutionary algorithm to solve, and carry out simulation optimization dispatching of cascade reservoirs; Step 4: Based on the flood area composition method and the runoff generation and confluence model of cascade reservoirs, establish the complementary equivalent relationship of flood control storage capacity of cascade reservoirs and calculate the flood control risk of the cascade reservoir group; Step 5: Based on the complementary and equivalent relationship between the Jinxia cascade and the Three Gorges flood control storage capacity, realize dynamic control of the operating water level of the cascade reservoir group, and seek and determine the optimal combination and flexible decision-making range of the operating water level of the Jinxia cascade and the Three Gorges reservoir group.

2. The method for designing the optimal characteristic water level of the Jinxia cascade and the Three Gorges reservoir group according to claim 1 is characterized by: The step 2 specifically includes the following sub-steps: Step 2-1: Based on the conventional dispatching diagram of the reservoir design, the dispatching operation of each reservoir is simulated separately, without considering the hydraulic connection characteristics of each reservoir and ignoring the top-up effect in the relationship between the reservoir outflow and tailwater level; Step 2-2: The conventional dispatching diagram of the reservoir specifies the output and water level control parameters of each hydropower station operation dispatching diagram. The dispatching model can perform equal output regulation calculations according to the water level specified in each time period; Step 2-3: Calculation of output regulation of cascade reservoirs.

3. The method for designing the optimal characteristic water level of the Jinxia cascade and the Three Gorges Reservoir Group according to claim 2 is characterized by: In step 2-3, the calculation formula for the equal output regulation of cascade reservoirs is as follows: Q fd,m (t)=N m (t)·K m (h m (t)+h s,m ) (2) h m (t)=(Z u,m (V m (t))+Z u,m (V m (t+1))) / 2-Z d,m (Q out,m (t),Z m+1 (t))-h s,m (3) Where: t is the time variable, s; T is the total length of the study period, t = 1, 2, ..., T; m is the sequence number of the cascade reservoirs (the total number is M) from top to bottom, m = 1, 2, ..., M; is the conventional dispatching function of the mth reservoir under scheme A, where "..." represents the decision factors other than time and reservoir capacity (water level) in the dispatching diagram, such as inflow; K m (·) is the water consumption rate function of the power generation flow of the mth reservoir, m 3 / kW;h s,m is the power generation head loss of the mth reservoir, m; h m (t) is the net water head of the mth reservoir in period t, m; N m (t) is the output of the mth reservoir in period t, MW; Q fd,m (t) is the power generation flow of the mth reservoir in period t, m 3 / s;Q out,m (t) is the outflow of the mth reservoir in period t, m 3 / s; V m (t) and V m (t+1) are the storage capacities of the mth reservoir at the beginning and end of the periods t and t+1, respectively. 3 ; Z u,m (·) is the relationship function between water level and storage capacity on the mth reservoir dam; Z d,m (·) represents the relationship function between the tailwater level and outflow flow of the mth reservoir; Z m+1 (t) is the water level above the dam of the m+1th reservoir.

4. The method for designing the optimal characteristic water level of the Jinxia cascade and the Three Gorges reservoir group according to claim 3 is characterized by: The constraints corresponding to the output regulation calculation formula of cascade reservoirs include water balance constraints, power station unit output constraints, reservoir capacity and amplitude constraints, outflow and amplitude constraints, initial boundary condition constraints and non-negative constraints: V m (t+1)=V m (t)+(Q in,m (t)-Q out,m (t))·Δt (4) V m (0)=V b,m ,V m (T)=V e,m (8) Where: Q in,m (t) is the inflow of the mth reservoir in period t, m 3 / s; are the minimum / maximum output limits of the mth reservoir in period t, kW; are the minimum / maximum storage capacity limits of the mth reservoir in period t, m 3 ; and are the minimum / maximum outflow limits of the mth reservoir in period t, m 3 / s; is the maximum storage capacity variation of the mth reservoir in adjacent periods, m 3 ; is the outflow variation of the mth reservoir in adjacent periods, m 3 / s; V b,m and V e,m are the initial and final storage capacities of the mth reservoir during the dispatch period, m 3 .

5. The method for designing the optimal characteristic water level of the Jinxia cascade and the Three Gorges reservoir group according to claim 1 is characterized by: The step 3 includes the following sub-steps: Step 3.1: Under the constraints of the current joint dispatching scheme of cascade reservoirs, a multi-objective joint optimization dispatching model for the lower reaches of the Jinsha River and the six cascade reservoirs from the Three Gorges to the Gezhouba Dam is established, with the maximum average power generation of the cascade reservoirs over many years, the minimum flood control risk and the maximum storage rate as the objective functions; Step 3.2: Use Gaussian RBF fitting to optimize the scheduling rules; Step 3.3: Use adaptive multi-objective evolutionary algorithm to solve.

6. A method for designing the optimal characteristic water level of the Jinxia cascade and the Three Gorges Reservoir Group according to claim 5, characterized in that: In step 3.1, the objective functions are respectively to maximize the average power generation of the cascade reservoirs over many years, minimize the flood control risk, and maximize the storage rate, as follows: (1) Maximum average power generation over many years: Where: is the sum of the average power generation of the cascade reservoirs over many years, kW·h; is the average power generation of the m-th reservoir over many years, kW·h; n y is the number of years in the input series; (2) Minimum flood risk: Where: FCR * and FCR m are the flood control risks of the cascade reservoirs and the mth reservoir respectively; is the maximum flood control storage capacity of the reservoir, m 3 ; is the storage capacity corresponding to the highest safe water level in front of the dam of the mth reservoir at time period t, m 3 ; (3) Highest accumulation rate: In the formula: IE * and IE m are the multi-year average storage rates of the cascade reservoirs and the mth reservoir respectively; V zc,m -V s,m is the storage capacity between the normal water level and the dead water level of the mth reservoir, i.e., the regulating storage capacity, m 3 θ m is the proportion of the regulating storage capacity of the mth reservoir in the cascade reservoirs.

7. The method for designing the optimal characteristic water level of the Jinxia cascade and the Three Gorges reservoir group according to claim 5 is characterized by: The specific process of step 3.2 is as follows: Two trigonometric functions, sin(2πt / 366-p1) and cos(2πt / 366-p2), are used to represent time, where p1 and p2 are phase shifts, satisfying p1,p2∈[0,2π]. The time period t, the storage capacity of the cascade reservoirs corresponding to the time period t, and the inflow flow Q of the Wudongde Reservoir are calculated. in,1 (t), flow rate Q between Xiangjiaba and Three Gorges qj,45 (t) A total of 9 variables are used as decision factor vector x(t), namely: And normalize it in the interval [0,1]; Radial Basis Function (RBF) It is a radially symmetric scalar function that represents the relationship between the variable space distance and the function value. By superimposing multiple RBFs, a flexible response surface can be obtained. The type of RBF varies depending on the φ(·) function. When φ(·) is a Gaussian function, the effect of fitting the reservoir operation rule is good. Therefore, Gaussian RBF is used in combination with the proposed decision factor vector x(t) to construct the reservoir optimization operation rule as follows: Where: I is the number of Gaussian RBFs used in each reservoir; is the dispatch rule constructed by Gaussian RBF for scheme C; J is the number of variables in the decision factor x(t); ω m,i is the weight corresponding to the ith Gaussian RBF of the mth reservoir, satisfying ω m,i ∈[0,1], And ∑ω m,i =1;c j,i , b j,i are the parameters of the i-th Gaussian RBF, c j,i ∈[-1,1],b i,j ∈(0,1], When using Gaussian RBF to construct scheduling rules, the required parameters [ω m,i ,c j,i ,b j,i ,p1,p2] is I(M+2(J-2))+2.

8. The method for designing the optimal characteristic water level of the Jinxia cascade and the Three Gorges reservoir group according to claim 1 is characterized by: The step 4 specifically includes the following sub-steps: Step 4.1: Under the premise of ensuring the safety of the flood control section and the unchanged high water level of the Three Gorges Reservoir, the reserved flood control storage capacity of the Jinxia cascade reservoir is equivalent to the minimum increase in the effective flood control storage capacity of the Three Gorges Reservoir, that is: ΔV TGR =αV J +b (18) Where: ΔV TGR represents the complementary equivalent flood control storage capacity of the Three Gorges Reservoir; V J =(V WDD ,V BHT ,V XLD ,V XJB ) T represents the flood control storage capacity reserved by each reservoir in the lower reaches of the Jinsha River, and the reserved storage capacity of each reservoir does not exceed the maximum value of its own flood control storage capacity, that is, V i ∈[0,max{V fh,i }], α=(α WDD ,α BHT ,α XLD ,α XJB ) represents the complementary equivalent coefficient of flood control storage capacity of each reservoir in the lower reaches of Jinsha River; β is the intercept value; Step 4.2: Calculate the flood risk of cascade reservoirs: The flood loss equation is a theoretical expression that characterizes the relationship between the total flood loss of the reservoir system, the change in the total storage capacity of the reservoir system, and the storage capacity allocation ratio coefficient between reservoirs. Combined with mathematical analysis, the discriminant of the proportional coefficient that can be used to guide storage capacity allocation is derived.

9. A method for designing the optimal characteristic water level of the Jinxia cascade and the Three Gorges reservoir group according to claim 8, characterized in that: In step 4.2, the calculation formula for the flood control risk of the cascade reservoir group is: Where: R is the flood control risk of the reservoir group, V c,j is the critical storage capacity of the jth reservoir, V i,j is the storage capacity of the jth reservoir at the end of period i, g(.) is the joint distribution of storage capacity during the forecast period, The flood control risk outside the forecast period is estimated based on the mean reservoir capacity at the end of the first period, assuming that the flood control risks inside and outside the forecast period are independent; the constraints are as follows: (V 0,1 -V 1,1 )=α(V 0,2 -V 1,2 ) (20) Where: V 0,j is the storage capacity of the jth reservoir at the beginning time, α is the replacement coefficient of the storage capacity change during the forecast period; Solve the storage capacity replacement coefficient α and deduce the flood risk time V of the reservoir group according to the Lagrange multiplier method 1,1 , V 1,2 and α, and then obtain the reservoir capacity possibility boundary that minimizes the flood control risk; The derived flood control storage capacity allocation rule based on the storage capacity allocation proportional coefficient was applied to a cascade reservoir system to carry out a case study and compared with the results of conventional numerical simulation methods to verify the calculation accuracy of the flood control loss equation used to characterize the flood control losses of the reservoir system, as well as the rationality of directly guiding the flood season operating water level allocation strategy based on the proportional coefficient discriminant.

10. The method for designing the optimal characteristic water level of the Jinxia cascade and the Three Gorges reservoir group according to claim 1, characterized in that: The step 5 comprises the following sub-steps: Step 5.1: Under the premise that flood control risks are controllable, dynamic control of the operating water level of the cascade reservoir group is achieved based on forecast information and flood control storage capacity compensation; Step 5.2: Based on the joint design of cascade reservoirs and the results of multi-objective optimization scheduling, find the optimal combination of operating water levels of the Jinxia cascade and the Three Gorges Reservoir Group; Step 5.3: Generate a large number of input samples through runoff simulation, and use a multi-objective evolutionary algorithm based on Pareto optimal theory to robustly optimize the cumulative target, maximum target and threshold target, and determine the flexible decision interval of the operating water level of the cascade reservoirs to guide the reservoir scheduling and operation. The cumulative target is the average power generation over many years, the maximum target is the minimum output, and the threshold target is the output guarantee rate.

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