Transpose step-by-step optimization method for load distribution among cascade hydropower stations

Abstract

The application discloses a kind of transposed step-by-step optimization methods of cascade hydropower station interplant load distribution, comprising: obtaining basic hydrological engineering data and power grid load demand, generating the initial cumulative output sequence of each hydropower station;With cumulative output as state variable, in the order of first time period and then library, optimization is carried out using transposed step-by-step optimization algorithm;In the optimization process, the dynamic feasible region of the cumulative output of the current hydropower station is constructed, and the physical operation constraints of each reservoir are strictly checked;The optimal cumulative output point is selected by calculating the consumed energy storage objective function value;Based on the optimization result after global iteration convergence, the water head and load filling scheduling instructions are output.The application directly converts load balance into boundary constraint of iterative feasible region, reduces the calculation overhead of exploring infeasible solution, and improves the optimization efficiency of algorithm and cascade water utilization rate.

Description

Technical Field

[0001] This invention relates to the field of cascade hydropower optimization scheduling technology, and in particular to a method for progressive optimization of load distribution between cascade hydropower plants. Background Technology

[0002] Cascade reservoir systems play a fundamental role in peak shaving and load following in new power systems. Optimizing load allocation among hydropower plants allows for the deep exploration and maximization of the water potential energy across the entire basin. While meeting comprehensive hydrological constraints such as flood control, navigation, and ecology, improving the tracking accuracy and response speed of the entire cascade system's total output to the grid's target load is of significant technical importance for ensuring real-time power balance in large-scale interconnected power grids and improving water resource conversion efficiency.

[0003] Current conventional methods for optimizing the joint scheduling of cascade reservoir groups typically employ dynamic programming and its derivative algorithms. These methods mostly select basic hydraulic parameters such as reservoir water level, real-time reservoir capacity, or outflow as the dominant state variables, and use empirical hydraulic formulas to forward deduce and chain-calculate the output process of each hydropower station. However, in inter-station load sharing scenarios, the total system output must strictly track the strongly coupled dynamic load curve issued by the power grid. Existing optimization paths relying on physical variables such as water level cannot directly embed load balance constraints into the iterative exploration space; they are usually only used as external verification conditions or transformed into soft penalty function terms after the objective function for ex-post compensation. This processing mechanism leads to the algorithm exploring and generating a large number of invalid physical states that violate the overall load requirements of the power grid during the spatial discrete solution process.

[0004] In summary, existing methods face technical bottlenecks when dealing with the cross-coupling of strong equality constraints in the power grid and complex inequality physical boundaries in reservoirs, including large redundancy in the optimization space, low solution convergence efficiency, and poor overall load tracking quality. Therefore, there is an urgent need to study an inter-plant load allocation and scheduling method that can reconstruct the search space constraint mechanism from the bottom layer, in order to improve the optimization calculation efficiency and allocation accuracy of large-scale cascade hydropower systems under complex dynamic commands. Summary of the Invention

[0005] The purpose of this invention is to provide a method for progressively optimizing the load distribution between cascade hydropower plants, in order to solve the aforementioned problems existing in the prior art.

[0006] Technical solution: A stepwise optimization method for load distribution between cascade hydropower plants, comprising:

[0007] Acquire basic hydrological engineering data and power grid load demand during the scheduling period;

[0008] Generate the initial cumulative power output sequence for each hydropower station;

[0009] Using cumulative output as the state variable, the transpose stepwise optimization algorithm is used to find the optimal solution in the order of time period first and then storage unit by storage unit.

[0010] In the optimization process, the dynamic feasible domain of the current hydropower station's cumulative output is constructed, and the physical operation constraints of the reservoir are verified.

[0011] Calculate the objective function value of energy storage consumption and select the optimal cumulative output point;

[0012] Based on the optimization results after global iteration convergence, output the water head conservation scheduling command and the load filling scheduling command.

[0013] Optionally, generate the initial cumulative power output sequence for each hydropower station, including:

[0014] Based on the reference head and comprehensive output coefficient in the basic hydrological engineering data, the initial allocation weights of each hydropower station are constructed.

[0015] The initial power output of each hydropower station is obtained by weighting the grid load demand for the current period using the initial allocation weights.

[0016] When the initial output value of any hydropower station exceeds the operating boundary, it is cut off and the remaining hydropower stations are normalized and allocated until the sum of the initial output values ​​of all hydropower stations matches the grid load demand.

[0017] The initial cumulative output sequence of each hydropower station is generated based on the allocated initial output values.

[0018] Optionally, a transpose-based successive optimization algorithm can be used for optimization, including:

[0019] Set preset state boundary conditions. The preset state boundary conditions are that the initial cumulative output of each time period is zero and the final cumulative output of each time period is equal to the grid load demand of the current time period.

[0020] In the order of time periods, the cumulative output discretization search is performed sequentially for each hydropower station in the current time period;

[0021] When searching for the optimal solution for the current hydropower station, the cumulative power output status of other hydropower stations within the current time period is fixed.

[0022] Optionally, construct the dynamic feasible region of the current hydropower station's cumulative output, including:

[0023] Based on the cumulative output status of the previous hydropower station, the current hydropower station's own output constraints, and the accessibility constraints of the remaining downstream hydropower stations to the remaining grid load demand, determine the left boundary and right boundary of the cumulative output.

[0024] Extract the intersection of the left and right boundaries of the cumulative output to generate the dynamic feasible region of the cumulative output. Optionally, the optimization process also includes using the candidate cumulative output set to map and solve for the corresponding flow rate and average head. The mapping solution includes:

[0025] Convert the candidate cumulative output points in the candidate cumulative output set into the corresponding candidate output values;

[0026] Using the flow rate through the machine as the variable to be determined, a residual function containing candidate output values ​​is constructed.

[0027] Within the flow search interval, the monotonic root-finding algorithm is used to solve for the flow rate that makes the residual function converge;

[0028] The final reservoir capacity and average head are calculated based on the obtained flow rate.

[0029] Optionally, after calculating the corresponding final reservoir capacity and average head based on the obtained flow rate, the following steps are also included:

[0030] Using the flow rate, final reservoir capacity, and average head, the current candidate cumulative output point is verified against the final water level constraint, outflow constraint, and unit output change rate constraint during the verification period.

[0031] Eliminate candidate cumulative output points that fail any of the above constraint checks;

[0032] After completing the optimization of all hydropower stations in the current period and determining the optimal solution, the final reservoir capacity of the corresponding hydropower station's optimal solution is used as the initial reservoir capacity for the next period and passed forward.

[0033] Optionally, during the global iteration convergence determination process, the global iteration is terminated when the convergence condition is met, resulting in the optimal inter-plant power output allocation sequence. The convergence condition includes:

[0034] Calculate the difference in the energy consumption objective function value corresponding to the optimal solution obtained in two consecutive global iterations;

[0035] Calculate the maximum relative deviation between the total output of the cascade reservoir group and the power grid load demand under the current global iteration;

[0036] When the difference between the energy storage objective function values ​​is less than a preset difference threshold and the maximum relative deviation is less than a preset load deviation threshold, the first convergence condition is deemed to be met.

[0037] Optionally, a residual function containing candidate output values ​​is constructed, including:

[0038] The flow rate and average head are input into the pre-configured turbine unit output characteristic function to calculate the corresponding theoretical output value of the unit.

[0039] The difference between the theoretical output value and the candidate output value of the computer group;

[0040] The difference is used as the objective function value to construct the residual function.

[0041] A progressive optimization system for load distribution between cascade hydropower plants includes:

[0042] At least one processor; and,

[0043] A memory communicatively connected to at least one of the processors; wherein,

[0044] The memory stores instructions that can be executed by the processor to implement the stepwise optimization method for load distribution between cascade hydropower plants as described above.

[0045] A computer-readable storage medium includes a stored executable program, wherein, when the executable program is executed, it controls the device where the computer-readable storage medium is located to perform a progressive optimization method for load distribution between cascade hydropower plants as described above.

[0046] Beneficial effects: This invention directly transforms load balancing into boundary constraints of the iterative feasible region, reducing the computational overhead of exploring infeasible solutions and improving the algorithm's optimization efficiency and the utilization rate of cascade hydropower. Attached Figure Description

[0047] Figure 1 This is a schematic diagram of a stepwise optimization method for load distribution between cascade hydropower plants provided in an embodiment of this application.

[0048] Figure 2 This is a schematic diagram of the transpose stepwise optimization algorithm provided in the embodiments of this application.

[0049] Figure 3 This is the cumulative output diagram of the discrete i-th power station provided in the embodiments of this application.

[0050] Figure 4 This is a schematic diagram of the process for generating the initial cumulative output sequence of each hydropower station provided in the embodiments of this application.

[0051] Figure 5 This is a schematic diagram of the process for constructing a residual function containing candidate output values, provided in an embodiment of this application. Detailed Implementation

[0052] In this invention, both hydropower station and reservoir refer to nodes in a cascade water conservancy project that include power plants. The two terms can be used interchangeably in contexts that do not involve specific physical attribute distinctions.

[0053] Example 1: A method for progressively optimizing load distribution between cascade hydropower plants is provided, such as... Figure 1 As shown, the method includes the following steps:

[0054] Step 101: Obtain basic hydrological engineering data and power grid load demand during the scheduling period.

[0055] In the daily operation and scheduling management of cascade hydropower stations, various hydrological data and engineering parameters are the physical basis for building optimization models, and the load indicators issued by the power grid are the boundary targets that drive the cascade system to allocate power output.

[0056] The basic hydrological engineering data includes, but is not limited to, the hydraulic topology of the upstream and downstream of the cascade, the inflow process of each time period, the installed capacity, upper and lower limits of output, output change rate, and comprehensive output coefficient of each hydropower station, as well as the water level and reservoir capacity relationship curves, tailwater level and discharge relationship curves, and head loss relationship curves that reflect the physical characteristics of the reservoir.

[0057] Power grid load demand refers to the total system load process that the power grid dispatch center requires the entire cascade hydropower station group to jointly respond to and bear within a set dispatch period (e.g., a day is divided into 96 time periods, each time period is 15 minutes).

[0058] In the data acquisition phase, the system collects real-time monitoring data from the SCADA system and the hydrological monitoring system, and combines this data with pre-stored static engineering parameters in the database to initialize the basic physical operating environment.

[0059] Step 102: Generate the initial cumulative power output sequence for each hydropower station.

[0060] To enable the successive optimization algorithm to conduct a global search from a high-quality starting point, this step requires pre-assigning an initial output state for each hydropower station. Unlike randomly generating initial values, generating a reasonable initial cumulative output sequence reduces the number of optimization rounds in the early stages of iteration, thus accelerating model convergence.

[0061] Specifically, based on the hydrological characteristics and unit parameters of the current time period, the system initially decomposes the total grid load demand into individual hydropower stations, forming preliminary allocated output values. These allocated output values ​​are then accumulated level by level according to the topological order of the cascade from upstream to downstream, constructing a cumulative state sequence reflecting the total output level undertaken by the hydropower station from the head of the cascade to the current station. This process not only provides an iterative starting point for the algorithm but also ensures the basic feasibility of the initial state.

[0062] Step 103: Using the cumulative output as the state variable, the transpose stepwise optimization algorithm is used to find the optimal solution in the order of time period first and then storage.

[0063] Transpose refers to changing the state variable setting in traditional successive optimization algorithms, which uses water level or reservoir capacity as the state variable, to one that uses cumulative output as the state variable. A transposed successive optimization algorithm is as follows: Figure 2 As shown in the figure, P t,i ∑ represents the output value of the i-th hydropower station in time period t. k=1 i P t,i This represents the total cumulative power output from the first reservoir to the ith reservoir during time period t.

[0064] Traditional successive optimization algorithms (POA) typically use reservoir water level or storage capacity as state variables. When dealing with strongly coupled power grid load demands, they often have to treat load balancing as a penalty function of the objective function for ex-post penalties, resulting in a large amount of computational resources being consumed in an invalid search space that does not meet load balancing constraints.

[0065] To address this issue, this solution introduces a transposed architecture. The state variables are transposed, meaning the water level variable is discarded, and the cumulative output of the hydropower station is used directly as the state node in the dynamic programming. Cumulative output is defined as the prefix sum of output from the first hydropower station in the cascade to the current hydropower station. When the search reaches the last hydropower station in the cascade, its cumulative output value is exactly equal to the total output of the entire cascade. Therefore, by fixing the cumulative output of the last hydropower station to the grid load demand value, the structure ensures that the feasible solution obtained through the search naturally satisfies the load balance equation constraint, eliminating the possibility of invalid solutions that violate load demand entering the search space.

[0066] Through this mechanism, the total load demand issued by the power grid at a certain time period is naturally transformed into the cumulative output boundary constraint of the hydropower stations at the end of the cascade. The strategy of embedding the load constraint within the feasible region search dimension eliminates the generation of infeasible solutions and improves the solution efficiency for power grid dispatch command responses.

[0067] The optimization process of the transpose successive optimization algorithm described above is executed in a global iterative manner. In each round of global iteration, the system traverses from the first time period to the Tth time period (i.e., the Tth time period at the end of the scheduling period) according to the time period index; within each time period, it traverses from the first upstream hydropower station to the nth downstream hydropower station according to the reservoir topology. For the currently optimized hydropower station, the feasible region construction, candidate point evaluation, and optimal selection operations described in steps 104 to 105 are performed, and after completion, the system moves on to the next hydropower station. When a round of global iteration ends, the system checks the convergence condition: if it is met, the system terminates; otherwise, it proceeds to the next round of global iteration.

[0068] Step 104: During the optimization process, construct the dynamic feasible domain of the current hydropower station's cumulative output and verify the physical operation constraints of the reservoir.

[0069] After determining the iterative architecture following the transpose, the system explores the state discretization of the target hydropower station within the current time period. To avoid blind discretization, the system does not search within an infinite domain or static boundary, but instead constructs a bidirectionally tightening dynamic feasible region in real time. This dynamic feasible region is constrained by both the physical output limit of the current hydropower station itself and the ability of the downstream remaining hydropower station group to fill the unallocated grid load.

[0070] The candidate cumulative power output states generated within this dynamic range are further back-mapped to physical hydrological parameters, such as flow rate, water level, and final reservoir capacity. The system verifies whether the water level at the end of the time period exceeds limits, whether the outflow meets ecological or navigation requirements, and whether the unit power output fluctuations exceed the ramp rate constraints based on the retrieved hydrological parameters. Through rigorous physical verification, it is ensured that each retained candidate power output allocation scheme is physically feasible in a real engineering environment.

[0071] According to one aspect of this application, a candidate cumulative output set is generated within the dynamic feasible domain of cumulative output, and the corresponding flow rate and average head are solved by mapping the candidate cumulative output set.

[0072] Within the dynamic feasible region determined in the aforementioned steps, the system performs equidistant sampling according to a preset discrete step length to generate a set of candidate cumulative power output points. For each candidate point, it is converted into a candidate power output value for the current hydropower station. By constructing a power output residual function with the flow rate as the independent variable, the system uses a monotonic root-finding algorithm to solve for the flow rate that satisfies the power output balance. Then, the corresponding final reservoir capacity and average head are calculated inversely, realizing an implicit mapping from the transposed state variable space to the physical hydrological parameter space.

[0073] Step 105: Calculate the target function value of energy storage consumption and select the optimal cumulative output point.

[0074] For candidate cumulative output schemes that pass all hydrological and unit operation constraints physical verification, the system will enter the quantitative evaluation stage of economic efficiency and hydropower utilization efficiency. In this step, the system calculates the water consumption index of the entire cascade under the premise of meeting load demand, based on the head status of each reservoir, the flow consumption through the generator, or the change in reservoir energy storage.

[0075] The objective function is designed to measure the degree of energy consumption of the entire cascade reservoir group by different allocation schemes. By comparing the objective function values ​​calculated from all feasible candidate points, the scheme that minimizes the energy consumption of the entire cascade, i.e., the scheme with the highest water energy conversion and utilization efficiency, is selected as the optimal cumulative output decision node of the current hydropower station in the current time period, and drives the algorithm to enter the next stage of optimization.

[0076] Step 106: Based on the optimization results after global iterative convergence, output the water head conservation scheduling command and the load filling scheduling command.

[0077] The optimization process terminates when the algorithm identifies that the global state tends to stabilize and meets the set multiple convergence conditions. The system then reverse-engineers and extracts the specific inter-power plant output allocation sequence, which is applied to each powerhouse and even each generating unit, from the final fixed optimal cumulative output network. Based on the load sharing pattern among power plants presented by this sequence, and combined with the regulation performance characteristics of each reservoir, the abstract mathematical optimal solution is transformed into specific dispatching operation instructions.

[0078] For example, for large-capacity, high-head reservoirs, the system outputs commands to control the flow rate and maintain high water level. For control reservoirs that perform peak shaving tasks, load tracking commands are issued to respond to grid demand shortfalls. These commands are ultimately sent to dispatching terminals at all levels, forming a closed-loop control system.

[0079] According to one aspect of this application, a method for progressively optimizing load distribution between cascade hydropower plants may further include the following steps:

[0080] Acquire basic hydrological engineering data and power grid load demand during the scheduling period;

[0081] Based on basic hydrological engineering data and power grid load demand, an initial cumulative power output sequence for each hydropower station is generated.

[0082] Using cumulative output as the state variable, the transpose stepwise optimization algorithm is used for iterative optimization in the order of first time period and then each reservoir.

[0083] In the optimization process, the dynamic feasible region of the current hydropower station's cumulative output is constructed, and a candidate cumulative output set is generated within the dynamic feasible region. The candidate cumulative output set is mapped to solve the corresponding flow rate, final reservoir capacity and average head, and the physical operation constraints of the reservoir are verified. Candidate cumulative output points that fail the verification are eliminated.

[0084] Based on the candidate cumulative output points that have passed the verification, the objective function value of energy storage consumption is calculated and the optimal cumulative output point is selected.

[0085] The global iteration is terminated when the convergence condition is met, and the optimal inter-plant power output sequence is obtained.

[0086] Based on the optimal inter-plant power output sequence, output water head maintenance scheduling instructions and load filling scheduling instructions.

[0087] For example, the overall execution process of this method is illustrated using a hydropower system comprising three cascade hydropower stations (upstream station A, midstream station B, and downstream station C). Assume the scheduling period consists of four time periods. First, the system acquires hydrological data for each station and the grid load demand curves for the four time periods. Initial allocation weights are constructed based on the reference head and output coefficient of each station, and after truncation and normalization, an initial cumulative output sequence is generated.

[0088] The first iteration of the transpose-based progressive optimization is as follows: In the first time period, the system constructs a dynamic feasible region for the cumulative output of station A. The left boundary is determined by the lower limit of station A's own output and the remaining achievable capacity of stations B and C, while the right boundary is determined by the upper limit of station A's own output and the minimum load of stations B and C. Within the feasible region, candidate points are generated at hierarchical step sizes. For each candidate point, the flow rate through the generator and the final reservoir capacity of station A are calculated. After verifying the water level constraint, feasible points are retained, and the corresponding energy storage consumption value is calculated. The optimal point is selected to fix the cumulative output of station A. The above process is repeated for station B. The dynamic feasible region of station B is simultaneously constrained by the fixed state of station A and the remaining capacity of station C. Station C, as the terminal power station, has a cumulative output equal to the grid load demand. After completing the optimization of all three stations in the first time period, the optimal final reservoir capacity of each station is transferred to the second time period as the initial reservoir capacity. After traversing all four time periods, a global iteration is completed, and the dual convergence condition is checked. If it is not satisfied, the next iteration begins.

[0089] According to another aspect of this application, a progressive optimization system for load distribution between cascade hydropower plants is provided, comprising:

[0090] At least one processor; and a memory communicatively connected to at least one of the processors; wherein the memory stores instructions executable by the processor to implement a stepwise optimization method for load allocation between cascade hydropower plants proposed in this invention.

[0091] According to another aspect of this application, a computer-readable storage medium is provided, the computer-readable storage medium including a stored executable program, wherein, when the executable program is executed, it controls the device where the computer-readable storage medium is located to execute a progressive optimization method for load distribution between cascade hydropower plants proposed in this invention.

[0092] Example 2: Based on Example 1 above, the generation of the initial cumulative power output sequence for each hydropower station is further described in detail. In one possible implementation, such as... Figure 4 As shown, it includes the following steps:

[0093] Step 201: Based on the reference head and comprehensive output coefficient in the basic hydrological engineering data, construct the initial allocation weights for each hydropower station.

[0094] In the joint operation of cascade hydropower stations, the load-bearing capacity of each station is directly related to its current hydraulic potential energy and unit power generation efficiency. This step quantifies these two core indicators to provide a benchmark for subsequent load allocation.

[0095] Specifically, the reference head is a baseline head calculated based on the pre-stored mapping relationship between the initial water level and the downstream tailwater level during the scheduling period, reflecting the magnitude of the water flow potential energy of the turbine unit. The comprehensive output coefficient is a physical parameter characterizing the water energy conversion efficiency of the turbine-generator unit; its value is usually derived from the turbine characteristic curve near the optimal operating point, considering constants such as efficiency and gravitational acceleration. After extracting the above two parameters, the system calculates the weights using the following formula:

[0096] w t,i =K i *H t,i ref ;

[0097] Among them, w t,i K represents the initial weight allocation for the i-th hydropower station in time period t. i H represents the overall power output coefficient of the i-th hydropower station. t,i ref This represents the reference head of the i-th hydropower station during time period t.

[0098] By multiplying the comprehensive output coefficient, which reflects conversion efficiency, by the reference head, which reflects potential energy, the initial allocation weights constructed by the system can accurately characterize the relative water consumption cost of each hydropower station generating a unit of electricity within a given time period. Hydropower stations with higher heads and higher unit efficiency have greater allocation weights and will prioritize undertaking more grid load demands in subsequent allocations.

[0099] Furthermore, in some optional implementations, if some hydropower stations are under maintenance of some units, a unit availability correction operator can be introduced into the above calculation logic to multiply the calculated initial allocation weight by the proportion of units available for use during that period, so as to further improve the physical fit of the weight.

[0100] Step 202: Use the initial allocation weights to weighted allocate the power grid load demand for the current period to obtain the initial output value of each hydropower station.

[0101] After obtaining the initial allocation weights for all hydropower stations in the entire cascade, the system decomposes the total grid load demand to individual physical nodes according to the proportional allocation logic. This step utilizes a normalization mapping mechanism to ensure that the total output of the entire cascade is numerically equal to the target value issued by the grid during the initial allocation stage. The specific weighted allocation logic is as follows:

[0102] P t,i (0) =Dt *w t,i / ∑(w t,k );

[0103] Among them, P t,i (0) D represents the initial output value of the i-th hydropower station in time period t, obtained after the initial weighted allocation calculation. t w represents the total grid load demand in time period t. t,i The initial weights for the current target hydropower station are ∑(w t,k ) represents the sum of the initial weights of all hydropower stations from the 1st to the nth in the cascade reservoir group, where k is the index.

[0104] Step 203: When the initial output value of any hydropower station exceeds the operating boundary, it is truncated and the remaining hydropower stations are normalized and allocated until the sum of the initial output values ​​of all hydropower stations matches the grid load demand. The operating boundary is the upper and lower limits of output in the basic hydrological engineering data.

[0105] The weighted allocation in the aforementioned steps only considers unit efficiency and potential energy, without taking into account physical capacity limitations. Some hydropower stations with high heads may be allocated output targets exceeding their installed capacity or difficult to achieve due to flood control restrictions. Therefore, a truncation correction based on boundary conditions must be performed. Specifically, the system compares the initial output value of each hydropower station with its pre-configured upper and lower limits. If the initial output value of a hydropower station is greater than its upper limit, the system performs a truncation operation, forcibly updating the initial output value of the hydropower station to its upper limit; similarly, if it is less than the lower limit, it is forcibly updated to the lower limit.

[0106] After a single cutoff, the total output of all hydropower stations will deviate from the grid load demand due to the reduction or supplementation of some values. At this point, the system extracts the resulting output deviation and, after excluding the hydropower stations whose output has been fixed by the cutoff, re-normalizes and redistributes this deviation proportionally according to the initial allocation weights of the remaining hydropower stations. After each redistribution, the values ​​of the remaining hydropower stations are re-verified to ensure they do not exceed the limits.

[0107] This process forms a closed-loop iterative feedback mechanism. The system continuously executes truncation determination and residual deviation redistribution operations until no hydropower station in the cascade exceeds its own operating boundary, and the sum of the initial output values ​​of all cascades is strictly equal to the current grid load demand. This ensures that the generated initial solution satisfies both the physical feasibility at the node level and the load tracking equation constraint at the system level.

[0108] Step 204: Generate the initial cumulative output sequence of each hydropower station based on the allocated initial output values.

[0109] After obtaining the compliant initial output values ​​of each hydropower station after truncation and normalization correction, the system converts them into the standard state variable form required by the subsequent transpose stepwise optimization algorithm. Following the water flow topology of the cascade reservoir group, and according to the hierarchical structure from upstream to downstream, a prefix accumulation operation is performed on the values ​​of each hydropower station. The calculation logic is as follows:

[0110] S t,i (0) =∑(P t,k (0) );

[0111] Among them, S t,i (0) Let ∑(P) represent the initial cumulative output state variables of the i-th hydropower station in time period t. t,k (0) ) represents the sum of the initial output values ​​of all nodes from the first hydropower station in the cascade topology to the i-th hydropower station.

[0112] By using prefix accumulation, the originally discrete power output values ​​distributed across various reservoirs are transformed into a continuous, cumulative state ladder sequence. The final value of this sequence naturally equals the total power output of the entire ladder. Using this structure as the input baseline sequence for transpose-based optimization allows subsequent algorithms to directly perform neighborhood searches within the cumulative structure that satisfies load balance constraints, thus supporting the implementation of the algorithm's dimensional transpose from the underlying design of the data structure.

[0113] In some optional implementations, if there is a complex topology where the cascade has tributaries merging, the system will first complete the accumulation within the tributaries according to the pre-configured topological adjacency matrix when performing the accumulation operation. At the merging node, the accumulated value of the main stream is summed with the accumulated values ​​at the end of each tributary, and the process continues to be pushed downstream to ensure that the accumulation mechanism can adapt to complex real watershed engineering networks.

[0114] Example 3: Building upon Example 1, this example further details the iterative processes, dynamic feasible region construction, and boundary correction mechanisms of the transpose successive optimization algorithm during the optimization process. This example aims to improve computational efficiency and ensure global consistency of solutions by physically tightening the optimization space.

[0115] In one possible implementation, a transpose-based successive optimization algorithm is used for optimization, including the following steps:

[0116] Preset state boundary conditions are set, where the initial cumulative output of each time period is zero and the final cumulative output of each time period equals the grid load demand of the current time period. The cumulative output of each hydropower station within the current time period is discretized and searched sequentially according to the time period order, updating the cumulative output state of each hydropower station. When searching for the optimal solution for the current hydropower station, the cumulative output states of other hydropower stations within the current time period are fixed. The cumulative output of the discretized i-th hydropower station is as follows: Figure 3 As shown.

[0117] In the iterative architecture of the transpose successive optimization algorithm, by setting the cumulative output sequence of each hydropower station in each time period as a state variable, the system establishes a direct mapping from grid-level constraints to station-level states. To ensure that each round of iterative search always lies within the solution space that satisfies load balance, a strict boundary structure is set for each time period: at the beginning of the time period, i.e., the 0th hydropower station, the initial value of cumulative output is set to 0; at the end of the time period, i.e., the nth hydropower station, the cumulative output value must be strictly equal to the grid load demand value of that time period.

[0118] The optimization process employs a traversal order that proceeds first time-by-time and then per hydropower station. When performing a discretized search for a specific hydropower station within a particular time period, the system decomposes the complex multivariate optimization problem across all cascades into a series of one-dimensional state optimization tasks by fixing the current cumulative output state of all non-target hydropower stations within that time period. This dimensionality reduction approach lowers computational complexity and, through the state transfer mechanism between time periods, achieves cross-time-period coordination of hydropower utilization throughout the entire scheduling period.

[0119] In one possible implementation, constructing the dynamic feasible region of the current hydropower station's cumulative output includes:

[0120] Obtain the current hydropower station's own output constraints and the accessibility constraints of the remaining downstream hydropower stations to the remaining grid load demand; determine the left boundary of cumulative output based on the own output constraints; determine the right boundary of cumulative output based on the accessibility constraints; extract the intersection of the left boundary and the right boundary of cumulative output to generate the dynamic feasible region of cumulative output.

[0121] Furthermore, the process involves obtaining the cumulative output status of the upstream hydropower station, the current hydropower station's own output constraints, and the accessibility constraints of the remaining downstream hydropower stations to the remaining grid load demand; determining the left boundary of the cumulative output based on the cumulative output status of the upstream hydropower station, its own output constraints, and accessibility constraints; determining the right boundary of the cumulative output based on the cumulative output status of the upstream hydropower station, its own output constraints, and accessibility constraints; and extracting the intersection of the left and right boundaries of the cumulative output to generate the dynamic feasible region of the cumulative output.

[0122] Before discretizing the state of the target hydropower station, the system constructs a bidirectional shrinking dynamic feasible region by spatially projecting the physical constraints. Unlike conventional search methods that only consider the constraints of the current node, this embodiment introduces the reachability constraints of the remaining downstream hydropower stations to ensure that the decisions of the current node do not lead to a global deadlock situation in which the downstream cascades cannot make up for the load gap.

[0123] Self-output constraints refer to the minimum and maximum output ranges determined by the current hydropower station based on real-time head, unit maintenance status, and vibration avoidance zones. Reachability constraints are the minimum and maximum total output capabilities that all remaining cascade nodes, starting from the first node after the current hydropower station and extending to the final hydropower station, can provide under their respective output extreme value limits. By calculating the physical intersection of these two-way constraints, the system can filter out a large number of locally feasible but globally infeasible state nodes, achieving rapid pruning of the invalid space in the early stages of the search.

[0124] Specifically, the intersection of the left and right boundaries of the cumulative output is extracted to generate the dynamic feasible region of the cumulative output, including:

[0125] The maximum value of the sum of the cumulative output status of the previous-level hydropower station and the current hydropower station's lower output limit, and the difference between the grid load demand and the sum of the remaining downstream hydropower station's upper output limit, is determined as the left boundary of cumulative output. The minimum value of the difference between the sum of the cumulative output status of the previous-level hydropower station and the current hydropower station's upper output limit, and the difference between the grid load demand and the remaining downstream hydropower station's lower output limit, is determined as the right boundary of cumulative output. When the left boundary of cumulative output is greater than the right boundary, the current cascade status is deemed infeasible, the grid load demand for the corresponding time period is adjusted to within the reachable output range of the entire cascade, and an alarm message is output. The reachable output range of the entire cascade is determined based on its own output constraints and reachability constraints.

[0126] In the specific calculation process, the derivation of the left and right boundaries of the cumulative output follows a strict physical extreme value matching principle. The specific calculation logic is as follows:

[0127] L t,i (J) =max(S t,i-1 (J) +P t,i min D t -∑(P t,k max ));

[0128] U t,i (J) =min(S t,i-1 (J) +P t,i max Dt -∑(P t,k min ));

[0129] Among them, L t,i (J) with U t,i (J) S represents the left and right boundaries of the cumulative output of the i-th hydropower station in the t-th time period during the J-th global iteration; t,i-1 (J) This indicates the fixed cumulative output state of the upstream hydropower station; P t,i min With P t,i max These are the minimum and maximum output limits for the current hydropower station, respectively; D t This represents the grid load demand during that period; ∑(P t,k max ) and ∑(P t,k min ) represent the sum of the upper and lower limits of the output of all remaining downstream hydropower stations from the (i+1)th to the nth station, respectively.

[0130] A concrete example of normalization is as follows: Assume the grid load demand is 1.0 at a certain time period, and the cumulative output of the upstream hydropower station is 0.4. The current output range of the hydropower station is 0.1 to 0.3. The sum of the maximum outputs of all remaining downstream hydropower stations is 0.5, and the sum of the minimum outputs is 0.2. Calculations show that the left boundary is the maximum value among 0.4 + 0.1 and 1.0 - 0.5, i.e., 0.5. The right boundary is the minimum value among 0.4 + 0.3 and 1.0 - 0.2, i.e., 0.7. Therefore, the determined dynamic feasible region is 0.5 to 0.7.

[0131] If an anomaly occurs during the calculation where the left boundary is greater than the right boundary, it indicates that under the current physical boundaries, even if the downstream cascade operates at full capacity, it will be difficult to meet the predetermined load target. In this case, the system will trigger infeasibility determination logic, correct the grid load demand for that period to the current physical achievable output limit range of all cascades, simultaneously record the load deviation, and output alarm information to the dispatch terminal.

[0132] The aforementioned closed-loop correction mechanism prevents algorithm crashes caused by a disconnect between load demand and physical constraints, thereby enhancing the system's operational resilience under extreme hydrological conditions.

[0133] In some alternative implementations, the system can also automatically trigger short-term adjustment suggestions for the operating water level of the controlled hydropower station based on the magnitude of the deviation while outputting alarms, thereby expanding the output accessibility in subsequent periods by changing the water head.

[0134] Example 4: Based on Example 3 above, this example further details the process of using candidate cumulative output sets to map and solve for the corresponding flow rate and average head, and then performing physical constraint verification. This scheme transposes the state variables into cumulative output, thus losing the natural variable of water level or water volume that is directly related to the physical model. Therefore, an implicit mapping inversion mechanism needs to be constructed.

[0135] In one possible implementation, the optimization process further includes using a candidate cumulative output set to map and solve for the corresponding flow rate and average head. The mapping solution includes the following steps:

[0136] Step 401: Convert the candidate cumulative output points in the candidate cumulative output set into the corresponding candidate output values.

[0137] Furthermore, the difference between the candidate cumulative output points in the candidate cumulative output set and the fixed cumulative output state of the previous level hydropower station is calculated to convert them into the corresponding candidate output values.

[0138] Specifically, after discrete sampling is performed within the dynamic feasible region of the current hydropower station's cumulative output, a series of candidate cumulative output points are obtained. To restore the system-level cumulative state to the independent output target of the current physical node, the system extracts the currently traversed candidate cumulative output points and subtracts the fixed cumulative output state of the previous-level hydropower station from them, calculating the difference between the two. This difference represents the candidate output value that the current hydropower station needs to undertake under this candidate state. This achieves dimensionality reduction and decoupling from system-level scheduling targets to single-station-level physical parameters.

[0139] Step 402: Using the flow rate through the machine as the variable to be determined, construct a residual function containing candidate output values, such as... Figure 5 As shown, it specifically includes:

[0140] Step 4021: Input the flow rate and average head into the pre-configured turbine output characteristic function to calculate the corresponding theoretical output value of the unit.

[0141] In establishing the physical inversion mapping closed loop, the mean head is influenced by both the final reservoir capacity and the tailrace level. Furthermore, the final reservoir capacity is highly coupled with the turbine flow rate, making it difficult to directly analyze the turbine flow rate using explicit algebraic equations. Against this backdrop, the system extracts turbine characteristic curve data from pre-entered equipment logs and establishes a nonlinear parameter mapping relationship between the turbine flow rate and the mean head. By inputting the turbine flow rate and mean head data in the exploratory phase, the theoretical unit output level under the current hydrological and hydraulic boundary is calculated.

[0142] The power output characteristic function of the turbine unit is constructed based on the product form P=K×Q×H, where K is the comprehensive power output coefficient, Q is the flow rate through the unit, and H is the average head.

[0143] Step 4022: The difference between the theoretical output value and the candidate output value of the computer group.

[0144] The system extracts the theoretical power output value of the generating unit obtained through feature mapping, and the candidate power output value obtained in step 401 through cumulative power output sequence difference. A subtraction operation is performed on these two physical quantities to obtain the final deviation. This difference quantifies the degree of deviation between the actual theoretical power generation capacity of the hydropower station and the target power output expected to be allocated by the grid dispatch model.

[0145] Step 4023: Use the difference as the objective function value, that is, use the difference as the residual value to construct the residual function.

[0146] The system uses the flow rate through the machine as the independent variable and the output deviation extracted above as the control target to construct a residual mapping mechanism.

[0147] G(q t,i )=N i (q t,i H t,i (q t,i ))-P t,i c ;

[0148] Wherein G(q) t,i ) represents the residual function with the flow rate through the machine as the independent variable, q t,i H represents the flow rate of the i-th hydropower station during the current time period. t,i (q t,i N represents the average head function constrained by the flow rate. i (q t,i H t,i (q t,i P represents the theoretical power output of the unit derived from the mapping between the flow rate and the average head. t,i c This represents the candidate output value of the current hydropower station obtained from the previous process.

[0149] By establishing the above equation structure, the originally complex hydrological and hydraulic chain deduction is transformed into a single-variable numerical root-finding task.

[0150] Step 403: Within the preset flow search interval in the basic hydrological engineering data, use the monotonic root-finding algorithm to solve for the flow rate that makes the residual function converge.

[0151] Based on the established residual function, the system initiates a numerical root-finding operation within the pre-calibrated search interval consisting of the minimum and maximum flow rates. Within a given operating head range, the output power and flow rate of the hydro-generator unit exhibit a strict monotonically increasing physical correlation. Introducing a monotonically increasing root-finding algorithm can avoid multiple solutions and maintain the algorithm's convergence stability.

[0152] In this embodiment, the system uses a binary search method for implicit iteration, compressing the search interval of the machine flow by halving it time and time again until the absolute value of the residual function is less than the preset convergence tolerance.

[0153] Furthermore, in some alternative implementations, the secant method or Newton's iteration method can be used as alternative monotonic root-finding algorithms, which use the slope of the local first derivative of the residual function to guide the iteration direction and shorten the time consumption to approach the target zero.

[0154] Step 404: Based on the obtained flow rate, and combined with the water balance parameters and water level-reservoir capacity relationship in the basic hydrological engineering data, the corresponding final reservoir capacity and average head are calculated by inversion.

[0155] After acquiring the flow rate data that meets the convergence criteria, the system performs a routine water balance state deduction. Specifically, based on the initial reservoir capacity state of the current hydropower station, the acquired inflow rate within the interval, the outflow rate transmitted from the previous hydropower station, and the just-obtained flow rate, the system calculates and updates the final reservoir capacity data for the current time period. The system derives the current reservoir water level according to the pre-stored water level-capacity mapping relationship and calculates the tailrace water level by combining it with the tailrace water level-discharge mapping relationship. After calculating the difference between the two and subtracting the head loss data along the flow path, the system obtains the average head parameter corresponding to the current hydraulic state.

[0156] The mapping relationship between water level and reservoir capacity, as well as the mapping relationship between tailwater level and discharge, are configured in the system database in the form of pre-stored piecewise linear interpolation data tables. The system obtains the corresponding physical quantities through linear interpolation.

[0157] In one possible implementation, after calculating the corresponding final reservoir capacity and average head based on the obtained flow rate, the following is also included:

[0158] Step 405: Using the flow rate through the generator, the final reservoir capacity, and the average head, verify the end-of-period water level constraint, outflow constraint, and generator output change rate constraint for the current candidate cumulative output point.

[0159] After reconstructing and extracting the complete set of hydrological state parameters, the system performs boundary safety defense. The calculated final reservoir capacity data is converted into the water level at the end of the time period to determine whether it is within the allowable range formed by the flood control limit water level and the dead water level; the outflow is obtained by summing the flow rate through the generator and the discharge flow rate, and it is determined whether its value covers the safety indicators of downstream ecological base flow and navigation discharge; the current candidate output value is extracted and differentially calculated with the actual output value of the previous time period to assess whether the fluctuation meets the physical limit conditions of the ramp rate specified in the unit hardware operation manual.

[0160] Step 406: Eliminate candidate cumulative output points that fail any of the above constraint checks.

[0161] After performing the aforementioned multi-dimensional constraint verification, if it is detected that the current candidate cumulative output point causes any hydrological or hardware operation physical boundary to exceed the limit, the status flag of the candidate cumulative output point will be immediately changed. The system will determine it as an infeasible solution and permanently remove it from the candidate solution data set, retaining only the candidate points that have passed the full constraint verification for subsequent energy storage evaluation and analysis of the cascade system.

[0162] Step 407: After completing the optimization of all hydropower stations in the current time period and determining the optimal solution, the last reservoir capacity of the corresponding hydropower station's optimal solution is used as the initial reservoir capacity for the next time period and passed forward.

[0163] Given the continuous dynamic decision-making characteristics of optimal load scheduling in a cascade hydropower station group, the system achieves coherent transmission of hydraulic constraints across different time periods through reservoir capacity data. Once the optimal allocation scheme for all hydropower stations from the first to the last cascade in the current time period is calculated, the actual hydrological state of the entire cascade at that time segment is solidified. The corresponding final reservoir capacity data from the optimal cumulative output solution of each hydropower station is extracted and directly assigned to overwrite the initial reservoir capacity variables of each hydropower station in the next scheduling period. This mechanism achieves the coupling and concatenation of time-series data, ensuring a global closed loop for water and energy transfer calculations throughout the entire long-cycle scheduling period.

[0164] Based on this, by introducing the accessibility of downstream remaining load to construct a two-way dynamic feasible domain, the scheduling dead zone of local feasibility but global deadlock is effectively cut off, and the physical coordination of the allocation between plants across the entire cascade is improved; the implicit inversion mechanism constructed simultaneously clears the blind spot of hydrological parameter verification in the transposed state, ensuring the engineering executability of the output scheme.

[0165] Example 5 further describes the process of generating a candidate cumulative output set within the dynamic feasible region of cumulative output. This example proposes a continuous mapping variable step size strategy based on the tiered comprehensive input ratio to solve the problem that a fixed search step size is difficult to balance optimization efficiency and allocation accuracy.

[0166] In one possible implementation, the optimization process further includes generating a candidate cumulative output set within the dynamic feasible region of the cumulative output. Generating the candidate cumulative output set includes the following steps:

[0167] Step 501: Extract the inflow data of the cascade reservoir group and the pre-stored average inflow data for the same period over many years based on the basic hydrological engineering data.

[0168] In discrete state-space optimization, the choice of step size determines the computational scale and the refinement of the results. This step is used to obtain basic data reflecting the current hydrological abundance and scarcity characteristics of the system, providing data support for dynamically adjusting the step size.

[0169] Specifically, the system extracts inflow data for the cascade reservoirs at various time periods within the scheduling period from externally input hydrological forecast sequences. This data reflects the current real-time hydrological boundary conditions. Simultaneously, it retrieves pre-stored multi-year average inflow data from a historical hydrological database. This pre-stored data characterizes the normalized hydrological inflow level of the basin during the current calendar period and is a benchmark reference value obtained by statistically averaging hydrological sequences from the same historical period over the past few decades.

[0170] Step 502: Calculate the comprehensive inflow ratio of the cascade reservoirs based on the inflow data of the cascade reservoir group and the average inflow of the same period over many years.

[0171] After obtaining the two sets of sequence data mentioned above, a dimensionless ratio index is constructed to quantify the current relative abundance or scarcity. Since the cascade reservoir group includes multiple spatially distributed power station nodes, a macroscopic parameter reflecting the overall hydrological characteristics of the entire basin needs to be calculated. The specific calculation is as follows:

[0172] R t =(1 / n)*∑(I i,t / I i,t avg );

[0173] Among them, R t I represents the overall inflow ratio of the cascade reservoirs in time period t, n represents the total number of hydropower stations included in the cascade reservoir group, and I i,t I represents the inflow data of the i-th hydropower station in time period t. i,t avg Let ∑(I) represent the average inflow rate of the i-th hydropower station during the same period over many years. i,t / I i,t avg This indicates that the individual inflow ratios of all hydropower stations are summed.

[0174] Through the above formula, the system eliminates the magnitude differences between hydropower stations with different basin areas and different runoff scales, and obtains a unified comprehensive evaluation index that can intuitively reflect the abundance or scarcity of water inflow across the entire cascade during the current period.

[0175] Step 503: Determine the graded adjustment coefficient based on the continuous mapping relationship between the cascade comprehensive inflow ratio and the preset hydrological abundance and scarcity threshold. When the hydrology is in the abundant water stage, the deviation length is amplified by the graded adjustment coefficient greater than one, and when the hydrology is in the dry water stage, the deviation length is reduced by the graded adjustment coefficient less than one.

[0176] After obtaining the cascade integrated inflow ratio, the system substitutes it into a pre-constructed three-segment continuous mapping function, outputting a scaling factor to control the discrete accuracy. This mapping relationship is constructed considering that during the high-water season, the reservoir's regulation capacity is limited, increasing the pressure on flood control and water wastage prevention. The system allows for a moderate deviation in output allocation; in this case, increasing the search step size can effectively reduce the number of state nodes and improve global optimization efficiency. Conversely, during the low-water season, hydropower resources are scarce, and the system is more sensitive to the value of electricity and water consumption rate. Therefore, it is necessary to reduce the search step size to obtain a high-precision micro-optimal allocation scheme. The specific continuous mapping relationship is as follows:

[0177] When the overall inflow ratio of the tiered system is less than or equal to the preset low water threshold, the system determines that it is currently in a low water stage and directly assigns the tiered adjustment coefficient to the preset minimum adjustment coefficient, which is a constant less than 1.

[0178] When the tiered comprehensive inflow ratio is greater than or equal to the preset high water threshold, it is determined that the current stage is high water, and the tiered adjustment coefficient is directly assigned to the preset maximum adjustment coefficient, which is a constant greater than 1.

[0179] When the overall inflow ratio of the cascade reservoirs falls between the low-water threshold and the high-water threshold, linear interpolation is used to determine the adjustment coefficient.

[0180] α t =α min +(α max -α min )*(R t -R low ) / (R high -R low );

[0181] Where, α t α is the calculated graded adjustment coefficient. max With α min R corresponds to the preset maximum and minimum adjustment coefficients, respectively. t R represents the tiered comprehensive warehousing ratio. high With R lowThese correspond to preset high-water and low-water thresholds, respectively. By introducing this continuous mapping equation, the system avoids abrupt changes in step size and jumps in the optimization state caused by direct rigid phase division.

[0182] In this embodiment, the low water threshold is set to 0.5, the high water threshold is set to 1.2, the maximum adjustment coefficient is set to 1.5, and the minimum adjustment coefficient is set to 0.5.

[0183] Step 504: Calculate the graded step size based on the current optimized reservoir scheduling accuracy requirements and graded adjustment coefficients.

[0184] The system extracts the pre-configured scheduling accuracy requirements for the current target hydropower station. These values ​​are typically set by dispatchers based on unit capacity and grid performance standards, serving as the foundational discrete interval for the algorithm. A multiplication operation is then performed to calculate the final step size.

[0185] Δ t =α t *Δ0;

[0186] Where, Δ t α represents the step size of the calculated output. t This represents the hierarchical adjustment coefficient extracted in the preceding steps, and Δ0 represents the preset baseline scheduling accuracy requirement.

[0187] A simplified normalized example is given, assuming a preset low-water threshold of 0.5, a high-water threshold of 1.2, a maximum adjustment coefficient of 1.5, and a minimum adjustment coefficient of 0.5. When the comprehensive inflow ratio at each tier is assessed to be 1.2 for a certain period, it falls within the high-water range. Substituting this into the mapping relationship, the tiered adjustment coefficient is amplified to 1.5. If the system's baseline scheduling accuracy requirement is 0.02, then the actual tiered step size will adaptively amplify to 1.5 * 0.02 = 0.03. Conversely, if the inflow ratio drops to 0.5, the adjustment coefficient is limited to 0.5, and the actual tiered step size will adaptively shrink to 0.5 * 0.02 = 0.01.

[0188] Step 505: Generate a candidate cumulative output set according to the hierarchical step size within the dynamic feasible region of cumulative output.

[0189] After obtaining the graded step size adapted to the current hydrological conditions, the system uses the derived left and right boundaries of the cumulative output as the extreme value intervals and the graded step size as the discrete intervals to perform equidistant sampling within the dynamic feasible region of the cumulative output. All generated discrete coordinate nodes are retained and combined to construct a candidate cumulative output set for the current hydropower station. This set serves as the basic input sequence for physical mapping inversion, ensuring not only the reachability of the search space but also achieving a dynamic balance between physical boundaries and computational overhead.

[0190] Furthermore, in some optional implementations, for the edge of the vibration zone with highly nonlinear characteristics, the system can also add additional locally denser sampling points near the boundary of the vibration zone on the basis of uniform sampling, so as to enhance the algorithm's ability to avoid the no-go zone of the equipment operation.

[0191] In response to seasonal hydrological variations, the scheme utilizes the cascade integrated inflow level to continuously adjust the discrete search step size. During the wet season, it effectively expands the search field to quickly avoid the risk of water wastage, while during the dry season, it automatically tightens the step size to obtain a more refined hydropower utilization scheme.

[0192] Example 6: Based on the above examples, the global iterative convergence condition and the anti-spurious convergence oscillation mechanism are further described in detail. When performing dynamic programming optimization in discrete state space, conventional single objective function determination is prone to getting stuck in a dead loop in the later stages of iteration, where the micro-state keeps changing but the macro-objective no longer decreases. Therefore, this example constructs a dual convergence determination and alternating oscillation identification mechanism.

[0193] In one possible implementation, during the global iteration convergence determination process, the global iteration is terminated when the convergence condition is met, resulting in the optimal inter-plant power output allocation sequence. Meeting the convergence condition includes the following steps:

[0194] Step 601: Calculate the difference in the energy consumption objective function value corresponding to the optimal solution obtained in two adjacent global iterations.

[0195] During the global optimization process, each complete traversal iteration produces a target function result across all levels. The system extracts the absolute value of the target function calculated in the current round and performs a subtraction operation with the absolute value of the target function saved in the previous round to obtain the absolute value of the deviation between the two.

[0196] Δ F =|F (J) -F (J-1) |;

[0197] Where, Δ F F represents the difference in the objective function generated by two consecutive global iterations. (J) F represents the energy consumption and storage objective function value obtained in the J-th global iteration. (J-1) This represents the energy consumption and storage objective function value obtained in the (J-1)th global iteration. This difference is used to quantify the degree of convergence progress of the algorithm at the macroeconomic benefit level.

[0198] Step 602: Calculate the maximum relative deviation between the total output of the cascade reservoir group and the power grid load demand under the current global iteration.

[0199] In addition to monitoring economic indicators, the system also needs to conduct a comprehensive check on the physical equation constraints of the power grid load response. The output values ​​of all hydropower stations across all time periods are summed to obtain the actual total output sequence. This sequence is then compared with the load demand sequence issued by the power grid, time-by-time. The absolute value of the deviation is calculated and divided by the corresponding load demand target to obtain the relative error for each time period. The maximum value is extracted from all time periods as the maximum relative deviation parameter for that round. This step ensures that the optimization results strictly meet the hard tracking requirements of the power grid commands across all time segments.

[0200] Step 603: When the difference between the energy storage objective function values ​​is less than a preset difference threshold and the maximum relative deviation is less than a preset load deviation threshold, the first convergence condition is determined to be met.

[0201] The system is pre-configured with two independent tolerance boundaries, corresponding to the two macroscopic test parameters mentioned above. When Δ is detected... F When the maximum relative deviation is less than ε1 and the maximum relative deviation is less than ε2, the flag indicating that the first convergence condition is met is activated. Here, ε1 is a preset difference threshold, typically set as a very small constant, used to determine whether economic benefits have reached a plateau; ε2 is a preset load deviation threshold, typically set as a strict lower limit for grid performance assessment. This step establishes the convergence benchmark for the cascade system at the level of macroscopic objectives and external physical constraints.

[0202] In one optional implementation, the preset difference threshold is set to 10. -4 The preset load deviation threshold is set to 10. -3 It should be understood that the preset difference threshold can be determined through experiments based on the magnitude of the total installed capacity of the cascade and the requirements for iterative accuracy, while the preset load deviation threshold can be determined based on the requirements for allowable load tracking deviation in the power grid dispatch assessment procedures.

[0203] One possible implementation, which terminates the global iteration when the convergence condition is met, also includes:

[0204] Step 1: During the global iteration process, track the discrete output update state corresponding to the optimal solution of all reservoirs in all time periods.

[0205] Because the transpose successive optimization algorithm uses a discrete grid for spatial search, when the grid step size is reduced to an extremely small value, the fine-tuning of the states between different nodes may cause minimal changes in the macroscopic objective function, thus prematurely triggering the aforementioned first convergence condition. To prevent the system from remaining in an unstable internal state, a two-dimensional state update matrix is ​​constructed. In each round of dual traversal of the time period and the reservoir, the cumulative output solution updated at the current node is numerically compared with the solution from the previous round to track the solidification status of the internal micro-nodes.

[0206] Step 2: When the discrete power output update state of any reservoir changes in any time period between two adjacent iterations, count and statistically analyze the changes in power output of the entire cascade.

[0207] For the update status tracked above, the system defines a binary indicator variable. When a substantial change in the value of a node is detected, the corresponding indicator variable is assigned a value of 1; when the value remains consistent, it is assigned a value of 0. A global accumulation operation is performed on all indicator variables across the entire scheduling period and the entire tiered topology.

[0208] C (J) =∑(δ t,i );

[0209] Among them, C (J) δ represents the frequency of output change across all stages obtained in the J-th global iteration. t,i Let ∑(δ) represent the state indicator variable of the i-th hydropower station in time period t. t,i This indicates the summation of indicator variables over all time periods and all hydropower stations. This frequency parameter accurately quantifies the instability and activity level of the current cascade system's internal state.

[0210] Step 3: When the frequency of output change across all stages is less than the preset stability threshold, the second convergence condition is determined to be met.

[0211] The system extracts a preset stability threshold parameter. This parameter limits the number of micro-jump nodes the system can tolerate. When determining C... (J) When ε < 3, the system activates the flag indicating that the second convergence condition is met. ε3 is a preset stability threshold. In scheduling scenarios requiring absolute stability, ε3 can be strictly set to 0, meaning that no hydropower station within the cascade should experience state drift at any given time.

[0212] By setting this condition, the false convergence state—where the objective function enters a flat region but the solution space is still undergoing intense searching—can be effectively isolated. The preset stability threshold can be determined based on the scale of the cascade reservoir group and the actual scheduling accuracy requirements. In this embodiment, the preset stability threshold is set to 0.

[0213] Step 4: When both the first and second convergence conditions are met, determine that the convergence condition is met and terminate the global iteration.

[0214] The system constructs a logic AND gate decision structure. Only when the system reads that both the first and second convergence condition flags are active is the entire transpose stepwise optimization algorithm considered to have reached complete convergence. At this point, the system issues an interrupt command, stopping subsequent rounds of state transpose and spatial discretization exploration, and outputs the currently captured cumulative output variable set as the final optimal solution.

[0215] The process of tracking the discrete output update state corresponding to the optimal solution of all reservoirs at all time periods also includes:

[0216] (1) When the optimal solution state under the current global iteration is consistent with the optimal solution state under the previous global iteration, but not equal to the optimal solution state under the previous global iteration, it is determined that the corresponding reservoir is in an alternating oscillation state.

[0217] Under certain hydrological boundaries, discrete dynamic programming algorithms are prone to endless back-and-forth jumps between two nearby discrete points, i.e., alternating AB oscillations. The system performs pattern recognition by extracting three rounds of continuous historical slice data.

[0218] For the sake of simplicity, S will be used as the term below. (J) The optimal cumulative output state S of node (t,i) in the Jth iteration. t,i (J) .

[0219] S (J) =S (J-2) And S (J) ≠S (J-1) ;

[0220] Among them, S (J) S represents the optimal cumulative output state of the current node in the J-th global iteration. (J-1) With S (J-2) These represent the optimal states in the previous round and the round before that, respectively. When the above mathematical logic is detected to be true, the system determines that the physical node has fallen into an unproductive alternating oscillation trap.

[0221] (2) The number of reservoirs that satisfy the alternating oscillation state is statistically obtained within the scope of the cascade reservoir group.

[0222] The system traverses the two-dimensional state update matrix, performing filtering and cumulative counting on all hydropower station nodes marked as alternating oscillation states. The total parameters obtained in this step characterize the severity and spread of the local optimum oscillation trap within the current cascade system.

[0223] (3) When the proportion of alternating oscillation states exceeds the preset threshold, it is determined that the current global iteration has spurious convergence and forced to continue iterative optimization.

[0224] The system divides the statistically obtained number of oscillating reservoirs by the total number of reservoirs in the system to calculate the oscillation ratio parameter. This parameter is then compared with a pre-configured ratio threshold. When the oscillation ratio is determined to be greater than the threshold, the system identifies that the algorithm has fallen into a pseudo-convergence deadlock state. At this point, even if the macroscopic first convergence condition has been met, the system will intercept and terminate the program's execution, forcibly triggering the next round of iterative calculation.

[0225] Furthermore, in an alternative implementation, when the system is forced to continue iterating, a preset random perturbation operator can be injected synchronously into the nodes that are trapped in alternating oscillations, or the discrete step size of the corresponding time period can be temporarily changed. By destroying the original symmetrical discrete grid structure, the algorithm is forced to jump out of the current repetitive loop trap, thereby restoring the normal convergence descent channel.

[0226] In one optional implementation, the preset proportion threshold is set to 10% of the total number of reservoirs in the entire cascade system. Those skilled in the art can adjust this proportion according to the actual scale of the cascade system and the requirements for convergence stability.

[0227] Furthermore, to address the numerical instability in the later stages of discrete state optimization, a logic for tracking micro-state changes and identifying alternating jumps was constructed to suppress pseudo-convergence and ensure the reliability of the algorithm's output allocation sequence under complex boundaries.

[0228] Example 7 further describes the process of calculating the energy storage depletion objective function value. Because the physical operating boundaries of a cascade reservoir group differ significantly under different hydrological seasons, a single objective function framework is prone to evaluation bias under extreme conditions. Therefore, this example provides an adaptive switching and defense mechanism for the objective function.

[0229] In one possible implementation, calculating the target function value of energy storage consumption and selecting the optimal cumulative output point includes the following steps:

[0230] Step 701: If no significant water wastage occurs during the scheduling period of the cascade reservoir group, calculate the energy storage objective function value using the end-of-period storage capacity change and average head of each reservoir.

[0231] When the amount of water discharged during the scheduling period of the cascade reservoir group does not exceed the preset water discharge threshold, the energy storage objective function value is calculated using the time-varying amount of the final storage capacity of each reservoir and the average head.

[0232] In conventional scheduling scenarios, the majority of water released from the reservoir is converted into power generation by turbine units. In this case, the system aims to minimize potential energy consumption while ensuring the entire cascade meets grid load demands. Differential calculations are performed on the final reservoir capacity data from adjacent time periods to obtain the actual net water consumption of the reservoir. Combining the average head and overall output coefficient of the downstream cascade, the equivalent energy storage consumption of the entire cascade is calculated.

[0233] F=∑ t (∑ i (((V i,t-1 -V i,t ) / Δt)*∑ m (H m,t *K m )));

[0234] Where F represents the objective function value of energy storage consumption, ∑ t This represents the summation of the total number of scheduling periods, ∑ i V represents the summation of the total number of cascade hydropower stations. i,t-1 V represents the reservoir capacity of the i-th hydropower station at the end of the (t-1)-th time period. i,t This represents the reservoir capacity of the i-th hydropower station at the end of time period t, where Δt is the duration of a single scheduling period, (V i,t-1 -V i,t ) / Δt represents the equivalent average flow corresponding to the net decrease in reservoir capacity of reservoir i during time period t, ∑ m H represents a nested summation from the current i-th reservoir to the last reservoir. m,t K represents the average head of the corresponding reservoir during the corresponding time period. m This represents the overall output coefficient of the corresponding reservoir.

[0235] Through the aforementioned mathematical structure, the absolute reduction in reservoir capacity is given an energy dimension. Since the water released by the upstream reservoir can be utilized by downstream cascades in subsequent time series, the nested summation operation integrates the potential energy contribution of the current reservoir release to all downstream cascades across the entire watershed. Using this objective function value as the core evaluation index, the candidate cumulative output point that minimizes it is selected as the optimal solution.

[0236] Step 702: When significant water wastage occurs during the scheduling period, the change in the final reservoir capacity in the calculated energy storage target function value is replaced with the flow rate of the corresponding time period, or a preset water wastage penalty correction term is superimposed on the energy storage target function value.

[0237] When the amount of water discharged during the scheduling period exceeds the preset water discharge threshold, the change in the final reservoir capacity in the calculated energy storage target function value will be replaced with the flow rate of the corresponding time period, or a preset water discharge penalty correction term will be superimposed on the energy storage target function value.

[0238] Among all the candidate cumulative output points that pass the verification, the candidate cumulative output point that minimizes the energy storage objective function value is selected as the optimal cumulative output point.

[0239] The system is pre-configured with water abandonment status monitoring logic. By extracting the inflow, available reservoir capacity, and maximum physical limit of turbine flow for the current period, it extrapolates the theoretical water abandonment volume. When the theoretical water abandonment volume exceeds the preset tolerance threshold, or when the flood discharge channel is forcibly opened due to flood control dispatch instructions, the system determines that a significant water abandonment state has occurred. In a significant water abandonment state, the reduction in reservoir capacity includes a large amount of water that has not flowed through the turbine units to perform work. If the basic objective function based on the reservoir capacity difference is continued to be used, the system will incorrectly equate this ineffective water loss to power generation and energy storage consumption, causing the optimization model to overestimate during the optimization evaluation, and thus tending to suppress the total power generation output in discrete decision-making.

[0240] To avoid distortion of this physical metric, the system provides two parallel adaptive defense calculation paths.

[0241] In a first optional implementation, a target item replacement mechanism is triggered. The actual flow rate data obtained through implicit inversion in the preceding steps is extracted, the flow component of the flood discharge channel is removed, and the reservoir capacity change term in the basic objective function is replaced with the flow rate product term for the corresponding time period. The calculation after the switch is as follows:

[0242] F alt1 =∑ t (∑ i (q t,i *∑ m (H m,t *K m )));

[0243] Among them, F alt1 q represents the corrected objective function value output under the first replacement strategy. t,i This represents the flow rate through the turbine of the i-th hydropower station during time period t.

[0244] The aforementioned replaced objective function physically approximates the equivalent energy utilization level of the cascade turbine flow. Since the upstream inflow contribution is not deducted from the turbine flow term, this approximation shows high consistency with the original objective function ranking in scenarios where reservoir capacity changes between cascades are relatively small. In practical scheduling applications, those skilled in the art can select either the first replacement strategy or the second water discharge penalty strategy based on the degree of hydraulic coupling between cascades.

[0245] This alternative approach, by eliminating the interference of water wastage, allows the objective function to be precisely anchored to the water body that actually performs physical work, thus restoring the rationality of the indicator's evaluation of water energy utilization efficiency.

[0246] In the second optional implementation, the system retains the original reservoir capacity difference calculation structure, but adds an additional penalty operator matrix to the basic objective function. The calculated interval water discharge values ​​are extracted to construct a positive water discharge penalty correction term.

[0247] F alt2 =F+∑ t (∑ i (W t,i *λ i ));

[0248] Among them, F alt2 W represents the corrected objective function value output under the second strategy, F represents the uncorrected basic energy consumption storage objective function value, and W represents the corrected objective function value output under the second strategy. t,i λ represents the water discharge rate extracted from the i-th hydropower station during time period t. i This represents the pre-configured water discharge penalty weighting coefficient for the corresponding hydropower station. This weighting coefficient is usually set to a large penalty scalar value.

[0249] By superimposing this penalty term, the system forces the transpose stepwise optimization algorithm to spontaneously eliminate power allocation schemes that would lead to large-scale water wastage during neighborhood search. Within the framework of satisfying the physical constraints of grid load tracking, this introduces convergence guidance to reduce water resource waste. Dispatchers can adjust the value of this penalty weight coefficient in real time according to the safety level of the basin's flood control plan.

[0250] The introduced adaptive switching system for extreme hydrological targets eliminates the distortion interference of flood discharge flow on the evaluation of energy storage consumption, ensuring the objectivity of water resource conversion efficiency assessment over the entire calendar period.

[0251] Example 8 further details the process of generating scheduling control commands based on the optimal inter-plant power output sequence and mapping them to physical execution terminals. The purely software-based transpose stepwise optimization algorithm is extended to the industrial control execution layer, constructing a complete closed loop from model optimization to equipment control.

[0252] In one possible implementation, generating head control and load replenishment instructions for controlling the operation of each cascade hydropower station based on the optimal inter-station power output sequence includes the following steps:

[0253] Step 801: Based on the multi-year regulating reservoir capacity parameters, real-time water level parameters, and pre-configured marginal hydropower value in the basic hydrological engineering data, identify the leading reservoir and control reservoir in the cascade reservoir group.

[0254] After obtaining the optimal power output allocation results for the entire cascade, the system needs to define the roles of each reservoir based on its physical properties and hydropower endowment in order to formulate targeted control strategies. The system extracts the basic hydrological engineering data and reads the multi-year regulating capacity parameters and real-time water level parameters of each reservoir. The multi-year regulating capacity parameters reflect the reservoir's long-term physical storage capacity for runoff; the pre-configured marginal hydropower value refers to the expected total electrical energy revenue that a unit volume of water can convert into electricity by flowing through itself and all downstream cascade turbine units under the current head condition.

[0255] The marginal value of hydropower is calculated as follows:

[0256] E i =∑ m=i n K m ·H m,t E i Let K be the marginal hydropower value of the i-th reservoir. m Let H be the overall output coefficient of the m-th reservoir. m,t Let be the average head of the m-th reservoir during time period t. This indicator reflects the total power generation that can be converted into power across the entire downstream cascade when a unit volume of water is released from the i-th reservoir.

[0257] The system performs a ranking and comparison logic on all reservoirs within the cascade topology. Reservoirs with multi-year regulating capacity parameters greater than a preset capacity threshold and ranking high in marginal hydropower value within the cascade are identified as leading reservoirs; reservoirs with available regulating capacity and unit ramp-up response times less than a preset response period are identified as control reservoirs. Through this identification operation, the functional partitioning of the cascade reservoir group at the scheduling execution level is completed.

[0258] Among them, the reservoirs with marginal hydropower value ranking at the top of the cascade are identified as the leading reservoirs, for example, reservoirs with marginal hydropower value greater than the average marginal hydropower value of all reservoirs in the cascade are identified as leading reservoirs, or reservoirs with marginal hydropower value ranking in the top N of the cascade reservoir group.

[0259] Step 802: When the real-time water level of the headwater reservoir is higher than the preset control water level and the marginal hydropower value is greater than that of the downstream reservoir, a water conservation head scheduling instruction is generated to maintain the high water level operation.

[0260] Specifically, when the real-time water level of the headwater reservoir is higher than the preset control water level and the marginal hydropower value of the headwater reservoir is greater than the marginal hydropower value of its downstream reservoir, a water conservation head scheduling instruction to maintain high water level operation is generated.

[0261] For physical nodes identified as "leading reservoirs," the system maintains their high potential energy state. The head effect of the leading reservoir directly amplifies its own power generation efficiency and that of all downstream cascades along its route. The system continuously extracts real-time water level parameters from the leading reservoirs and compares them with the control water levels required by pre-set flood control and dispatching procedures. When the real-time water level is determined to be higher than the preset control water level, and the marginal hydropower value of the current leading reservoir is determined to be greater than that of its adjacent downstream reservoir, the system determines that the conditions for energy storage and water conservation are met.

[0262] At this point, the system extracts the output segment belonging to the head reservoir from the optimal inter-plant allocation output sequence output by the previous optimization and encapsulates it into a head-maintaining scheduling instruction. This instruction logically limits the flow rate growth rate of the head reservoir, requiring it to prioritize maintaining the head height by suppressing downstream flow while meeting the basic allocation output, thereby minimizing the energy consumption of the entire cascade.

[0263] Step 803: When there is a local load deficit in the target period and the controlled reservoir has available regulation capacity, a load filling scheduling instruction to increase the output level of the controlled reservoir is generated based on the optimal inter-plant allocation output sequence.

[0264] Specifically, it can also be that when the total output of the cascade corresponding to the optimal inter-plant power allocation sequence during the target period is lower than the grid load demand, resulting in a local load deficit, and when the controlled reservoir has available adjustment capabilities based on the current water level and output limit in the basic hydrological engineering data, a load filling dispatch instruction to improve the output level of the controlled reservoir is generated according to the optimal inter-plant power allocation sequence.

[0265] In actual industrial operation environments, due to forecasting errors in grid load demand, or the output limitation of some baseload hydropower stations due to unforeseen circumstances, local power gaps may occur between the total cascade output and the system target during certain periods. The system monitors the deviation between the total cascade output and the grid load demand in real time. When a load deficit greater than the preset dead zone value is detected within the target period, the system retrieves the online controlled reservoirs and assesses their current available regulation capacity, i.e., calculates the available water volume between the current real-time water level and the dead water level, and the available power margin between the generating units and the upper limit of output. Specifically, it calculates the available water volume corresponding to the difference between the reservoir capacity corresponding to the current real-time water level and the dead reservoir capacity, and the available power margin corresponding to the difference between the upper limit of output of the controlled reservoir and the currently allocated output.

[0266] After confirming the availability of regulation capacity, the load shortfall is used as the incremental compensation value and added to the base output allocation value of the controlled reservoir in the optimal inter-plant output allocation sequence. Based on this, a load filling dispatch instruction is generated. This instruction requires the controlled reservoir to rapidly increase its active power output by utilizing its superior unit response characteristics to smooth out system power fluctuations.

[0267] In one possible implementation, after generating the head-protection scheduling instructions and load-filling scheduling instructions for controlling the operation of each cascade hydropower station based on the optimal inter-plant power output allocation sequence, the following is also included:

[0268] Step 804: Perform protocol parsing and format conversion on the water head retention scheduling command and the load filling scheduling command.

[0269] The scheduling instructions generated by the aforementioned logic are represented in system memory as a two-dimensional data array composed of floating-point numbers and timestamps, which cannot be directly recognized by the underlying industrial control hardware. The system extracts the array data of the aforementioned head-saving scheduling instructions and load-filling scheduling instructions and imports them into a pre-set industrial communication protocol stack. According to the network protocol type used by the distributed control system of the cascade hydropower station, the aforementioned floating-point instruction data is parsed and repackaged. It is then converted into a remote adjustment and control data message format that conforms to relevant industrial standards, and each message is labeled with the corresponding device address code and checksum to ensure the integrity and identifiability of the data in the transmission channel.

[0270] Industrial communication protocols can adopt commonly used power system remote communication standards such as IEC 60870-5-104, IEC 61850, or DNP3.0. Those skilled in the art can select the appropriate protocol type based on the existing communication infrastructure of each cascade hydropower station.

[0271] Step 805: The format-converted dispatching command is sent to the automatic generation control terminal of the corresponding cascade hydropower station to drive the guide vane opening of the turbine generator unit to perform real-time following adjustment.

[0272] The system establishes secure data connections with the field networks of each cascade hydropower station, and uses a remote control gateway to distribute the format-converted dispatch instruction data packets to the automatic generation control terminals of each hydropower station in a timely manner. The automatic generation control terminals receive and unpack the packets to obtain the target output setpoint, which is then input into the local proportional-integral-derivative (PID) control loop. The local control loop compares the setpoint with the current actual active power feedback value of the turbine generator unit, calculates the control deviation, and converts it into a corresponding mechanical displacement signal. This signal ultimately drives the electro-hydraulic governor of the turbine generator unit, physically changing the guide vane opening, thereby regulating the actual water flow into the turbine casing. Through this mechanical action, the actual speed and output power of the unit undergo physical changes, strictly following the optimal allocation trajectory issued by the system, realizing a global closed loop for load allocation between cascade hydropower stations from algorithm optimization to physical execution.

[0273] Furthermore, in some optional implementations, the terminal will simultaneously collect real-time status data from vibration zone sensors during the guide vane opening adjustment process. If the currently calculated target guide vane opening value is detected to fall into the unit's vibration exclusion zone, the automatic power generation control terminal will activate over-limit protection logic. This will prevent the unit from suffering mechanical fatigue damage due to resonance by accelerating its passage through the exclusion zone on the time axis or locking the opening at a safe value at the boundary of the exclusion zone.

[0274] According to one aspect of this application, a stepwise optimization method for load distribution between cascade hydropower plants is also provided, comprising the following steps:

[0275] Obtain hydrological data, engineering data, and power grid load demand during the scheduling period for the cascade reservoir group;

[0276] An optimization model is constructed with the objective of minimizing the energy storage consumption of the entire cascade under the condition of meeting the power grid load demand, and satisfying the constraints of load balance, water balance, water level, output, and outflow.

[0277] During each time period of the scheduling period, the initial cumulative power output sequence corresponding to each reservoir is generated, and the boundary condition for time period t is set as: S t,0 (0) =0, S t,n (0) =D t ,

[0278] Where D t Let S be the grid load demand in time period t. t,i (0) Let be the initial cumulative power output of the i-th reservoir in time period t, and n be the total number of cascade hydropower stations.

[0279] The transpose stepwise optimization algorithm is used to iteratively optimize the initial cumulative output sequence. During the iteration process, the dynamic feasible region of cumulative output is constructed for the current optimized reservoir in the order of first time period and then reservoir. A candidate cumulative output set is generated based on the adaptive variable step size discretization strategy.

[0280] The candidate points in the candidate cumulative output set are converted into the output values ​​of each reservoir, and the corresponding flow rate, average head and final reservoir capacity are solved by implicit iterative mapping of output-hydrological variables to verify water level constraints, flow constraints and output constraints.

[0281] Calculate the objective function value corresponding to the candidate point that satisfies all constraints, select the candidate cumulative output value that minimizes the objective function value as the optimal solution for the current reservoir in the current time period, and after completing the optimization of all reservoirs in the current time period, forward the optimal final capacity of each reservoir to the next time period.

[0282] The global iteration is performed based on the dual convergence criteria of objective function stability test and discrete output change frequency statistics until the convergence condition is met, so as to obtain the optimal cumulative output sequence and the optimal inter-plant allocated output sequence.

[0283] Based on the optimal power output sequence among power plants, water head control instructions and load replenishment instructions are generated and issued to each cascade hydropower station.

[0284] Furthermore, a transpose-based successive optimization algorithm is used to iteratively optimize the initial output sequence, including:

[0285] In the J-th iteration, the i-th power station has its previous state S fixed. t,i-1 (J) and the next level state S t,i+1 (J) constant;

[0286] Discretize the cumulative output of the i-th reservoir and re-search for the S of the current node. t,i (J) Generate a candidate set of m candidate discrete points within its feasible region:

[0287] ;

[0288] The cumulative output values ​​in the candidate set are converted into the output values ​​of each reservoir, and then converted into corresponding hydrological variable verification constraints.

[0289] Calculate the objective function value corresponding to the candidate discrete cumulative output values ​​that satisfy all constraints, and select the discrete cumulative output value that minimizes the objective function value as the optimal solution S for the current time period. t,i * ;

[0290] By sequentially traversing all reservoirs in upstream and downstream topological order, the candidate cumulative output set for this iteration is obtained:

[0291] .

[0292] The current dynamic feasible domain for the cumulative output of the optimized reservoir structure includes:

[0293] In the J-th global iteration and at the t-th time interval, when optimizing to the i-th reservoir, let the upper and lower limits of the current reservoir output be P. t,i min and P t,i max Then, the left boundary L is obtained from the cumulative output status of the previous level hydropower station, the current hydropower station's own output constraint, and the accessibility constraint of the remaining downstream hydropower stations to the remaining grid load demand. t,i (J) and right boundary U t,i (J) :

[0294] ;

[0295] ;

[0296] The intersection of the left and right boundaries is defined as the current dynamic feasible region of the reservoir's cumulative output:

[0297] ;

[0298] When L t,i (J) >U t,i (J) If the current time period is deemed infeasible under the current water level, the load demand for that time period is adjusted to the range of the total achievable output of the cascade, and the load deviation is recorded and alarm information is output.

[0299] The corresponding flow rate, average head, and final reservoir capacity are solved through an implicit iterative mapping of power output and hydrological variables, including:

[0300] Cumulative output point S of candidates t,i c Calculate the corresponding candidate output P t,i c =S t,i c -S t,i-1 (J) ;

[0301] With machine flow rate q t,i For the variable to be determined, construct the residual function G(q). t,i ):

[0302] ;

[0303] Among them, the final storage capacity satisfies:

[0304] ;

[0305] The average head satisfies:

[0306] ;

[0307] Among them, V i,t V i,t-1 Let be the reservoir capacity of the i-th reservoir at the end of time period t and at the end of time period t-1, respectively. To sum the values ​​of all directly upstream reservoirs u of the i-th reservoir, For the upstream reservoir u at t-τ u,i Outflow rate during the time period (considering the water flow confluence time τ) u,i ), r i,t Let be the discharge flow of the i-th reservoir in time period t. Let be the average net head of the i-th reservoir in time period t. , Let Z(V) be the upstream water level of the i-th reservoir at the beginning and end of the time period, respectively, obtained by looking up the water level-storage capacity curve Z(V) using the reservoir capacity V. This is the downstream tailwater level. This is due to head loss.

[0308] In the traffic search interval [q t,i min q t,i max The internal solution uses a binary iterative method to solve for |G(q) t,i The flow rate q is less than the preset residual threshold. t,i min q t,i max These represent the lower and upper limits of the flow rate under physical conditions or operational constraints, respectively.

[0309] After obtaining the flow rate through the generator, the corresponding average head, final reservoir capacity, and outflow rate are calculated, and the constraints of the change rate of water level, outflow rate, and unit output at the end of the period are verified. Candidate points that pass the verification are entered into the objective function evaluation, and candidate points that fail the verification are removed.

[0310] After all reservoirs have been optimized in time period t, the final reservoir capacity V corresponding to the optimal solution for each reservoir is calculated. i,t * The initial storage capacity V for time period t+1 i,t ini .

[0311] During the scheduling period, the initial cumulative power output sequence for each reservoir is generated, including:

[0312] According to the reference head H of the i-th reservoir in time period t t,i ref With the overall output coefficient K i Construct the initial weight allocation w t,i =K i *H t,i ref ;

[0313] The grid load demand D in time period t is determined according to the initial allocation weights. t We perform a weighted allocation to obtain the initial output:

[0314] ;

[0315] When the initial output of any reservoir exceeds its upper or lower limit, the initial output of that reservoir is truncated to the corresponding boundary value, and the remaining reservoirs are re-normalized proportionally until all reservoirs simultaneously meet the output constraints and the sum of the initial outputs of all reservoirs equals D. t ;

[0316] according to Generate the initial cumulative power output sequence of each reservoir for each time period.

[0317] Adaptive variable step size discretization strategies include:

[0318] Calculate the tiered comprehensive inbound ratio for time period t. ,in Let be the average inflow of the i-th reservoir during the same period over many years;

[0319] The graded adjustment coefficient α is determined based on the tiered comprehensive inbound ratio. t The tiered adjustment coefficients satisfy:

[0320] When R t <=R low At that time, α t =α min ;

[0321] When R t >=R high At that time, α t =α max ;

[0322] When R low <R t <R high At that time, α t =α min +(α max -α min )*(R t -Rlow ) / (R high -R low );

[0323] Calculate the graded step size Δ based on the current optimized reservoir scheduling accuracy requirement Δ0. t =α t *Δ0, and in the dynamic feasible region Ω t,i (J) Candidate discrete points are generated according to hierarchical step sizes;

[0324] Where, α max >1、α min <1, which allows the distance step size to be increased during the wet season to improve global search efficiency, and the distance step size to be decreased during the dry season to improve local optimization accuracy.

[0325] The stability test of the objective function includes:

[0326] Calculate the objective function difference ΔF corresponding to the optimal inter-plant power output sequence obtained from two consecutive global iterations. (J) =|F (J) -F (J-1) |;

[0327] Calculate the maximum relative deviation η between the current total output of the entire cascade and the given load demand of the power grid. (J) ;

[0328] When ΔF (J) Less than the preset iteration difference threshold ε1, and η (J) When the load deviation is less than the preset load deviation threshold ε2, the objective function stability test is deemed to have met the convergence requirement.

[0329] Discrete output variation frequency statistics include:

[0330] During the global iteration process, the discrete output update status of all reservoirs is tracked at all time periods;

[0331] When the discrete output of a reservoir changes between two adjacent iterations during a certain period, the corresponding indicator function is recorded as 1; otherwise, it is recorded as 0.

[0332] The frequency C of the total output variation of all reservoirs is obtained by summing the indicator functions of all reservoirs over all time periods. (J) ;

[0333] When C (J) When the value is less than the preset stability threshold ε3, the discrete output change frequency statistics are determined to meet the convergence requirements.

[0334] Furthermore, when S is satisfied (J) =S (J-2) And S (J) ≠S (J-1)When the number of state pairs exceeds a preset ratio, it is determined that there is alternating AB oscillation, and the algorithm continues to iterate without terminating.

[0335] The algorithm terminates and outputs the optimal inter-plant power allocation sequence only when the stability test of the objective function and the statistics of discrete power output change frequency both meet the convergence requirements.

[0336] The objective function is:

[0337] ;

[0338] In the formula, F is the objective function value, T is the total number of scheduling periods, n is the total number of cascade hydropower stations, and V i,t-1 With V i,t Let H be the reservoir capacity at the end of time period t-1 and time period t, respectively, where Δt is the duration of a single scheduling period. m,t Let K be the average head of the m-th reservoir during time period t. m Let be the overall output coefficient of the m-th reservoir;

[0339] When there is significant water wastage during the scheduling period, the reservoir capacity change term in the objective function is replaced with the flow rate through the turbines for the corresponding time period, or a water wastage correction term is added to avoid overestimating the energy consumption.

[0340] This invention transforms the power grid load equality constraint into the absolute boundary of the underlying search feasible region by transposing the state variables into cumulative output and changing the iteration order of the physical space. This eliminates the huge invalid exploration space that violates load balance and improves the solution response speed. It solves the scheduling problem of cascade reservoir groups under complex power grid commands.

[0341] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all fall within the protection scope of the present invention.

Claims

1. A method for progressively optimizing load distribution among cascade hydropower plants, characterized in that, include: Acquire basic hydrological engineering data and power grid load demand during the scheduling period; Generate the initial cumulative power output sequence for each hydropower station; Using cumulative output as the state variable, the transpose stepwise optimization algorithm is used to find the optimal solution in the order of time period first and then storage unit by storage unit. In the optimization process, the dynamic feasible domain of the current hydropower station's cumulative output is constructed, and the physical operation constraints of the reservoir are verified. Calculate the objective function value of energy storage consumption and select the optimal cumulative output point; Based on the optimization results after global iteration convergence, output the water head conservation scheduling command and the load filling scheduling command.

2. The method according to claim 1, characterized in that, Generate the initial cumulative power output sequence for each hydropower station, including: Based on the reference head and comprehensive output coefficient in the basic hydrological engineering data, the initial allocation weights of each hydropower station are constructed. The initial power output of each hydropower station is obtained by weighting the grid load demand for the current period using the initial allocation weights. When the initial output value of any hydropower station exceeds the operating boundary, it is cut off and the remaining hydropower stations are normalized and allocated until the sum of the initial output values ​​of all hydropower stations matches the grid load demand. The initial cumulative output sequence of each hydropower station is generated based on the allocated initial output values.

3. The method according to claim 1, characterized in that, The optimization is performed using a transpose-based successive optimization algorithm, including: Set preset state boundary conditions. The preset state boundary conditions are that the initial cumulative output of each time period is zero and the final cumulative output of each time period is equal to the grid load demand of the current time period. In the order of time periods, the cumulative output discretization search is performed sequentially for each hydropower station in the current time period; When searching for the optimal solution for the current hydropower station, the cumulative power output status of other hydropower stations within the current time period is fixed.

4. The method according to claim 1, characterized in that, Construct the dynamic feasible region of the current hydropower station's cumulative output, including: Based on the cumulative output status of the previous hydropower station, the current hydropower station's own output constraints, and the accessibility constraints of the remaining downstream hydropower stations to the remaining grid load demand, determine the left boundary and right boundary of the cumulative output. Extract the intersection of the left boundary and the right boundary of the cumulative output to generate the dynamic feasible region of the cumulative output.

5. The method according to claim 1, characterized in that, The optimization process also includes using the candidate cumulative output set to map and solve for the corresponding flow rate and average head. The mapping solution includes: Convert the candidate cumulative output points in the candidate cumulative output set into the corresponding candidate output values; Using the flow rate through the machine as the variable to be determined, a residual function containing candidate output values ​​is constructed. Within the flow search interval, the monotonic root-finding algorithm is used to solve for the flow rate that makes the residual function converge; The final reservoir capacity and average head are calculated based on the obtained flow rate.

6. The method according to claim 5, characterized in that, After calculating the corresponding final reservoir capacity and average head based on the obtained flow rate, the process also includes: Using the flow rate, final reservoir capacity, and average head, the current candidate cumulative output point is verified against the final water level constraint, outflow constraint, and unit output change rate constraint during the verification period. Eliminate candidate cumulative output points that fail any of the above constraint checks; After completing the optimization of all hydropower stations in the current period and determining the optimal solution, the final reservoir capacity of the corresponding hydropower station's optimal solution is used as the initial reservoir capacity for the next period and passed forward.

7. The method according to claim 1, characterized in that, In the process of determining the convergence of the global iteration, the global iteration is terminated when the convergence condition is met, resulting in the optimal inter-plant power output allocation sequence. The convergence condition includes: Calculate the difference in the energy consumption objective function value corresponding to the optimal solution obtained in two consecutive global iterations; Calculate the maximum relative deviation between the total output of the cascade reservoir group and the power grid load demand under the current global iteration; When the difference between the energy storage objective function values ​​is less than a preset difference threshold and the maximum relative deviation is less than a preset load deviation threshold, the first convergence condition is deemed to be met.

8. The method according to claim 5, characterized in that, Construct a residual function containing candidate output values, including: The flow rate and average head are input into the pre-configured turbine unit output characteristic function to calculate the corresponding theoretical output value of the unit. The difference between the theoretical output value and the candidate output value of the computer group; The difference is used as the objective function value to construct the residual function.

9. A progressive optimization system for load distribution between cascade hydropower plants, characterized in that, include: At least one processor; as well as, A memory communicatively connected to at least one of the processors; wherein, The memory stores instructions that can be executed by the processor to implement the stepwise optimization method for load distribution between cascade hydropower plants as described in any one of claims 1 to 8.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored executable program, wherein, when the executable program is executed, it controls the device where the computer-readable storage medium is located to perform a progressive optimization method for load distribution between cascade hydropower plants as described in any one of claims 1 to 8.

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