A step-type hydropower station power generation output prediction method and system

Abstract

The application discloses a kind of stepped hydropower station power generation output prediction method and system, it is related to hydropower station power generation output prediction technical field, comprising: obtaining original operation data, constructs joint state vector;Based on joint state vector and preset time window, determine the dynamic feasible power generation output interval of hydropower unit at current time;Based on dynamic feasible power generation output interval and unit parameter, candidate unit combination satisfying operation constraint condition is screened;Output model is constructed, and probability prediction model is trained using historical data, to predict the selected probability of each candidate unit combination under given state;Coupling decision is carried out to output model and selected probability, determine target unit combination and its corresponding preliminary output prediction value;Preliminary output prediction value is smoothed, and final power generation output prediction value is obtained;The application solves the problem that the output prediction error of unit combination switching critical interval is relatively large caused by the continuous modeling of discrete start-stop process of hydropower unit.

Description

Technical Field

[0001] This invention relates to the field of hydropower generation output prediction technology, and more specifically, to a method and system for predicting the power generation output of a cascade hydropower station. Background Technology

[0002] In the short-term power generation scheduling and output prediction process of cascade hydropower stations, the power generation output is not only affected by hydrological conditions such as inflow, water level, and head, but also closely related to various factors such as unit start-up and shutdown combinations and grid dispatching requirements, exhibiting obvious nonlinear and multi-constraint coupling characteristics.

[0003] In existing technologies, power generation prediction methods mostly employ continuous function-based modeling approaches, such as regression models or neural network models, to fit historical operating data in order to predict future output. However, these methods typically simplify the unit operation process as a continuously changing process, failing to fully consider the discrete characteristics resulting from the start-up and shutdown of hydropower units by the number of units.

[0004] In actual operation, hydropower units exhibit distinct characteristics of combined operation: unit start-up and shutdown are performed on a unit-by-unit basis and are constrained by the minimum output of a single unit. When switching between different unit combinations, the total power output of the power station exhibits a discontinuous "step-like jump" change characteristic. Especially near the critical range of unit combination switching, the output change has significant discontinuity.

[0005] Because existing prediction methods fail to effectively characterize the aforementioned discrete transition characteristics, their output results are too smooth, often resulting in large prediction errors near the critical point of unit combination switching. This manifests as a systematic deviation between predicted output and actual output, thereby affecting the accuracy and reliability of dispatching decisions. Summary of the Invention

[0006] In order to overcome the above-mentioned defects of the prior art, the embodiments of the present invention provide a method and system for predicting the power output of a stepped hydropower station, which solves the problem that the prediction error of the power output in the critical interval of unit combination switching is large due to the continuous modeling of the discrete start-up and shutdown process of hydropower units.

[0007] To achieve the above objectives, the present invention provides the following technical solution: Firstly, this application provides a method for predicting the power output of a cascade hydropower station. The method includes: acquiring the original operating data of the cascade hydropower station during the prediction period and constructing a joint state vector; determining the dynamically feasible power output range of the hydropower units at the current moment through forward simulation and iterative calculation based on the joint state vector and a preset time window; screening candidate unit combinations that meet the operating constraints based on the dynamically feasible power output range and unit parameters; constructing a power output model to describe the segmented mapping relationship between flow and output, and training a probabilistic prediction model using historical data to predict the selection probability of each candidate unit combination under a given state; coupling the power output model with the selection probability to determine the target unit combination and its corresponding preliminary power output prediction value; and smoothing the preliminary power output prediction value to eliminate discontinuous power output fluctuations caused by unit combination switching, thereby obtaining the final power output prediction value.

[0008] In one embodiment, constructing a joint state vector includes: preprocessing the original operating data to obtain a continuous and valid data sequence at a unified time scale; extracting multidimensional state variables from the data sequence that characterize the current hydrological conditions, unit operating status, and grid dispatching requirements; and fusing the multidimensional state variables to construct a joint state vector containing continuous and discrete variables.

[0009] In one embodiment, based on the joint state vector and a preset time window, the dynamic feasible power generation output range of the hydropower unit at the current moment is determined through forward simulation and iterative calculation. This includes: establishing dynamic constraint equations based on the reservoir water level at the current moment and the predicted inflow process, combined with a preset constraint set; within a preset flow range, performing constraint verification on candidate power generation flow rates through forward rolling simulation to select a set of feasible power generation flow rates; for each flow rate value in the set of feasible power generation flow rates, iteratively calculating the upstream water level and the tailwater level until the head value converges to obtain a self-consistent flow-head combination; calculating the corresponding power generation output based on the self-consistent flow-head combination, and summarizing them to form a dynamic feasible power generation output range.

[0010] In one embodiment, for each flow value in the feasible power generation flow set, the upstream water level and the tailwater level are iteratively calculated until the head value converges to obtain a self-consistent flow-head combination. This includes: obtaining the initial value of the upstream water level at the current moment based on the current feasible power generation flow; calculating the tailwater level and determining the initial head according to the tailwater level-outflow relationship; updating the reservoir capacity status according to the power generation flow and recalculating the upstream water level based on the updated capacity; recalculating the head based on the updated upstream water level and tailwater level and comparing it with the result of the previous iteration; repeating the iteration until the head difference between two adjacent calculations meets a preset convergence threshold, and outputting the final self-consistent head value.

[0011] In one embodiment, screening candidate unit combinations that meet operational constraints includes: generating all possible start-up combination states based on the number of units and the capacity of a single unit; matching the theoretical output range of each combination with the dynamically feasible power generation output range, and filtering out combinations that do not meet hydraulic feasibility; and for the remaining combinations, sequentially performing unit output characteristic verification and operational continuity verification to obtain the final set of candidate unit combinations.

[0012] In one embodiment, a power output model is constructed to describe the segmented mapping relationship between flow rate and output, including: for each candidate unit combination, determining its corresponding feasible flow rate subset and reconstructing it into a continuous feasible flow rate interval; establishing a mapping relationship between the flow rate interval and the unit combination, and identifying the critical flow rate point where the unit combination switches; dividing the overall flow rate interval into multiple continuous sub-intervals using the critical flow rate point as the dividing boundary; independently defining the output function in each sub-interval, and not applying continuity constraints at the critical points of adjacent intervals, forming a segmented output model with discontinuous transition characteristics.

[0013] In one embodiment, constructing the output model further includes model training, specifically: acquiring historical operating data and constructing a standardized historical feature sample set, the sample set containing a joint state vector and corresponding historical unit combination labels; constructing a multi-class probabilistic prediction model, using the joint state vector as input and the probability distribution of each candidate unit combination as output; using a cross-entropy loss function and the historical unit combination labels as supervision signals to train the model; and using the trained probabilistic prediction model to infer the current joint state vector and output the corresponding unit combination probability distribution.

[0014] In one embodiment, the output model is coupled with the selection probability to determine the target unit combination and its corresponding preliminary output prediction value. This includes: determining the corresponding unit combination and its output function based on the flow range of the target flow in the segmented output model at the current moment; selecting the unit combination with the highest probability as the optimal candidate combination according to the probability distribution of each unit combination output by the probability prediction model, and determining whether the combination matches the current flow range; if it matches, the optimal combination is determined as the target unit combination; if it does not match, the target unit combination is re-selected from the candidate combination set that meets the flow feasibility; and substituting the output function of the target unit combination and the current flow value into the calculation to obtain the preliminary power generation prediction value under the combination.

[0015] In one embodiment, the preliminary power output prediction value is smoothed to eliminate discontinuous power output fluctuations caused by unit combination switching, and the final power generation prediction value is obtained. This includes: presetting a switching critical interval based on the critical flow point in the segmented power output model; determining whether the flow corresponding to the current target power output demand falls within the switching critical interval; if so, activating the switching penalty mechanism to perform weighted fusion of the power output candidate values ​​of adjacent unit combinations to suppress power output jumps; if not, directly using the power output function value corresponding to the current combination to calculate the value; and outputting the final power generation prediction value after smoothing correction.

[0016] Secondly, this application provides a cascade hydropower station power output prediction system, which includes: a data processing module for acquiring the original operating data of the cascade hydropower stations during the prediction period and constructing a joint state vector; an interval construction module for determining the dynamic feasible power output interval of the hydropower units at the current moment through forward simulation and iterative calculation based on the joint state vector and a preset time window; a screening module for screening candidate unit combinations that meet the operating constraints based on the dynamic feasible power output interval and unit parameters; a model construction module for constructing a power output model to describe the segmented mapping relationship between flow and output, and training a probabilistic prediction model using historical data to predict the selection probability of each candidate unit combination under a given state; a prediction module for coupling the power output model with the selection probability to determine the target unit combination and its corresponding preliminary power output prediction value; and a correction module for smoothing the preliminary power output prediction value to eliminate the discontinuous fluctuations in power output caused by the switching of unit combinations and obtain the final power output prediction value.

[0017] As can be seen from the above technical solutions, the embodiments of this application have the following advantages: This paper integrates the modeling and collaborative optimization of the "continuous hydraulic process" and "discrete unit combination decision" of cascade hydropower stations. A joint state vector is used to uniformly represent hydrological, unit, and scheduling information. A rolling time window is combined to construct a dynamically feasible power output range under cross-time constraints, extending power generation capacity assessment from a static single-moment process to a dynamic process with future feasibility. Based on this, a candidate flow discretization and forward rolling simulation screening mechanism is introduced to effectively characterize the discrete characteristics of unit operation and improve the accuracy of feasible region identification. Simultaneously, implicit coupling iterative solution of head and flow ensures the self-consistency and physical consistency of hydraulic calculations. Furthermore, a unit combination set is constructed through layer-by-layer constraint screening, and switching costs and probabilistic learning models are introduced to achieve a fusion decision from physical constraints to data-driven decision-making, ensuring that unit combination selection satisfies both engineering feasibility and historical operating patterns. Finally, through a segmented output model and critical flow range identification, unit switching behavior is explicitly transformed into a discontinuous structure of the output function. A switching penalty function is used to smooth sensitive intervals, effectively suppressing output fluctuations caused by frequent switching in critical areas. Compared to conventional techniques: First, a unified modeling framework of "rolling hydraulic constraints + discrete unit combination" is proposed to achieve deep coupling between continuous physical processes and discrete control decisions; second, an interpretable unit combination switching boundary is constructed through a segmented mapping mechanism driven by critical flow points; third, a hybrid decision-making approach that integrates probabilistic prediction models and physical screening mechanisms is introduced to improve the robustness and generalization ability of combination selection; and fourth, the suppression of discontinuous jumps is achieved through switching penalties and interval correction mechanisms, so that the final prediction results achieve unified optimization in terms of physical consistency, engineering feasibility, and time stability. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a schematic diagram of a method for predicting the power output of a cascade hydropower station, provided in an embodiment of this application.

[0020] Figure 2 This is a schematic diagram of a cascade hydropower station power output prediction system provided in an embodiment of this application.

[0021] Figure 3 This is a scatter plot of the combined flow probability of the generating units provided in the embodiments of this application.

[0022] Figure 4This is a schematic diagram of the head iteration convergence curve provided in an embodiment of this application. Detailed Implementation

[0023] To enable those skilled in the art to better understand the technical solutions in this application, the technical solutions in the embodiments of this application will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0024] It should be noted that, in this document, terms such as “comprising,” “including,” or any other variations thereof are intended to cover non-exclusive inclusion, such that an article or device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such an article or device. Without further limitation, an element defined by the phrase “comprising one…” does not exclude the presence of other identical elements in the article or device that includes the aforementioned element.

[0025] Reference Figure 1 As shown in the diagram, a flowchart of a method for predicting the power output of a cascade hydropower station provided by the present invention includes the following steps: S1. Obtain the original operating data of the target cascade hydropower station during the predicted period, and construct a joint state vector containing hydrological state variables and unit operating state variables based on the original operating data.

[0026] Within a preset forecast period, raw operational data is collected from the hydrological monitoring system, the power plant monitoring system, and the power grid dispatching system. This raw operational data includes: inflow rate, reservoir water level, operating status data of each generating unit, rated capacity parameters of the generating units, minimum technical output parameters of the generating units, and power grid dispatching command data. In this embodiment, a joint state vector containing hydrological state variables and unit operating state variables is constructed based on the original operating data, including: The raw operating data is preprocessed, which includes unifying the time scale of data from different sources and with different sampling frequencies, mapping all types of data to the same time resolution, and correcting missing data through interpolation to obtain a continuous and effective data sequence. Based on the data sequence, hydrological state variables characterizing the hydrological process are extracted, including inflow and reservoir water level; Based on the unit operation status data, the operation status of each unit at each moment is discretized and encoded. Binary variables are used to represent the start-up and shutdown status of a single unit. The operation status is recorded as "1" and the shutdown status is recorded as "0". The units are combined in the order of their unit numbers to form the unit start-up and shutdown status vector. The power grid dispatching instructions are parsed and feature extracted, and the dispatching instructions are converted into quantifiable variables, including load demand level, peak shaving instruction intensity or output constraint information, thereby forming dispatching state variables; Hydrological state variables, unit start-up and shutdown state vectors, and scheduling state variables are spliced ​​and merged to construct a joint state vector containing continuous and discrete variables, which is used to characterize the comprehensive operating status of the cascade hydropower stations at the current moment.

[0027] S2, based on the joint state vector, introduce a preset time window to construct a dynamically feasible power generation output range considering future constraints, including: Based on the current reservoir water level and the predicted inflow process, a water balance equation across time steps is constructed, and combined with a set of constraints, including upper and lower limits of water level, flood control constraints, outflow constraints, and water level change rate constraints, to form a dynamic constraint equation covering the time rolling window. The specific calculation formula for the water balance equation is as follows:

[0028] In the formula, Let k be the reservoir capacity at time k. For the next moment's reservoir capacity, The incoming water flow rate For outbound flow, For time step.

[0029] The upper and lower limits of the water level are specifically as follows:

[0030] The specific flood control constraints are as follows:

[0031] The outbound flow constraint is as follows:

[0032] The water level change rate constraint is as follows:

[0033] In the formula, Let k be the reservoir water level. This is the minimum operating water level. The maximum permissible water level, The flood control limit level indicates the maximum safe water level reserved for flood prevention. To maximize the allowable outbound flow rate, This represents the maximum water level fluctuation per unit time. This represents the reservoir water level at the previous moment.

[0034] At the current moment, multiple candidate power generation flow sets are generated within the preset power generation flow range, and the candidate power generation flow is input into the dynamic constraint equation as a decision variable. Through forward rolling simulation, a feasible power generation flow set that meets the constraint conditions throughout the entire time window is selected. The specific calculation formula for the candidate power generation flow rate is as follows:

[0035] In the formula, For candidate power generation flow, To minimize the power generation flow, The traffic distance distance is the interval between candidate traffic streams. It is a discrete index.

[0036] The method of forward rolling simulation is used to filter out a set of feasible power generation flows that meet the constraints throughout the entire time window, including: The candidate power generation flow set includes each candidate power generation flow, which is initialized, and the outflow flow at the current time is set. Set initial storage capacity ; Based on the initialization results, a time-period simulation is performed for each candidate flow rate. For any subsequent time k, the outflow flow rate is calculated in chronological order. The reservoir capacity is updated according to the water balance equation, and the reservoir water level is calculated based on the relationship function between the reservoir capacity and the water level. The storage capacity and water level The relational function, specifically: The reservoir capacity-water level relationship function is used to characterize the correspondence between reservoir capacity and water level. This relationship is determined based on characteristic curves or historical data obtained during the reservoir design phase. In one embodiment, the function... This is achieved through a pre-stored reservoir capacity-water level comparison table, which consists of discrete reservoir capacity values ​​and corresponding water level values. During the calculation process, a linear interpolation method is used to obtain the water level value corresponding to any reservoir capacity. Specifically, when the reservoir capacity... Located at a known storage capacity data point and At that time, the corresponding water level is calculated as follows: In the formula, and These are the corresponding known water level data points.

[0037] During the simulation, at each time k, it is determined whether the set of constraints is satisfied, and the candidate power generation flow that satisfies the set of constraints is determined as the feasible power generation flow.

[0038] For each feasible power generation flow, an implicit coupling relationship between head and flow is constructed. By combining the relationship between upstream water level and reservoir capacity with the relationship between tailwater level and flow, an iterative solution is used to obtain a head value consistent with the feasible power generation flow, thereby obtaining a self-consistent flow and head combination that satisfies the hydraulic balance condition. Based on the combination of flow rate and head, combined with the unit efficiency characteristics, the corresponding power generation output is calculated and summarized to form the dynamic feasible power generation output range at the current moment. The specific formula for calculating the power generation output is as follows:

[0039] In the formula, To generate electricity, To determine unit efficiency, table lookup or interpolation methods are used to obtain the values. For the density of water, It is the acceleration due to gravity. For water head.

[0040] The dynamic feasible power generation output range and the corresponding feasible power generation flow set are output as constraints to step S3 for subsequent screening and matching of discrete unit combinations.

[0041] Furthermore, for each feasible power generation flow, an implicit coupling relationship between head and flow is constructed. By combining the upstream water level and reservoir capacity relationship with the tailrace water level and flow relationship, an iterative solution is used to obtain a head value consistent with the feasible power generation flow, thereby obtaining a self-consistent flow and head combination that satisfies the hydraulic balance condition, including: Based on the feasible power generation flow set, the initial value of the water level in front of the dam at the current moment is obtained. The initial value of the water level in front of the dam includes the reservoir capacity in front of the dam and the initial value of the water level in front of the dam. Based on historical data, a tailwater level function is constructed to establish the relationship between tailwater level and flow rate. The specific calculation formula for the tailwater level function is as follows:

[0042] In the formula, Tailwater level, indicating the water level height at the tailwater outlet of the hydroelectric power station. The total outflow represents the total outflow through the turbines and spillway facilities. , , These are the preset fitting coefficients.

[0043] Based on the initial water level in front of the dam and the tailwater level function, the initial head is calculated and used as the initial input for iterative solution. The initial head is calculated using the following formula:

[0044] In the formula, Let be the initial head, representing the estimated head value corresponding to the i-th feasible power generation flow rate at the 0th iteration. This represents the initial water level in front of the dam. In order to have traffic The corresponding downstream water level at that time.

[0045] Based on the feasible power generation flow, the impact of the reservoir outflow on the reservoir capacity is reversed, the reservoir capacity status is updated, and the water level in front of the dam is recalculated according to the updated reservoir capacity status through the relationship function between reservoir capacity and water level. The updated reservoir capacity status The specific calculation formula is as follows:

[0046] Based on the updated upstream and downstream water level functions, the head is recalculated, and the head difference between two adjacent iterations is calculated. The specific formula for calculating the water head is as follows:

[0047] The specific formula for calculating the head difference is as follows:

[0048] In the formula, The water head at the (n+1)th iteration. Let be the water level in front of the dam at the (n+1)th iteration. This is the head difference. Let be the water head at the nth iteration.

[0049] Compare the head difference with the preset convergence threshold If a comparison is made, ,like Figure 4 As shown, determine if the iteration has converged and output the current head value. ,like The current result is used as the input for the next iteration.

[0050] It should be noted that by introducing a time-rolling window, the traditional static analysis based solely on the current state is extended to dynamic modeling that considers future hydrological changes and scheduling constraints. This ensures that the constructed feasible power generation range not only meets the physical conditions at the current moment but also maintains sustainability throughout the entire prediction period. Simultaneously, by discretizing candidate power generation flows and combining this with forward-rolling simulation screening, the limitation of continuous models in failing to characterize the discrete characteristics of unit operation is effectively avoided, improving the accuracy of feasible region identification. Furthermore, by introducing an implicit coupling relationship between head and flow, and achieving self-consistent solution of the hydraulic state through iterative methods, the nonlinear relationship between water level, flow, and head is realistically reflected, significantly improving the physical consistency and accuracy of power generation calculation. Finally, using the dynamic feasible power generation range and feasible flow set as constraint inputs in the subsequent unit combination optimization process not only enhances the reliability of the prediction results but also provides a more engineering-feasible decision boundary for short-term scheduling decisions.

[0051] S3, based on the number of generating units and their individual capacity, enumerates all possible unit start-up and shutdown combinations and matches them with feasible power generation ranges to filter out a set of candidate unit combinations that meet hydraulic and operational constraints, including: Obtain basic parameter information of hydropower station units, including the number of units N, rated capacity of each unit, minimum technical output, and unit numbering order; based on the number of units, construct a binary state vector space of length N to represent all possible unit start-up and shutdown combinations.

[0052] Based on a binary state vector space, all possible unit start-stop combinations are enumerated to generate a complete set of unit combinations. Each combination state is represented by a binary vector of length N, where a value of 1 in the i-th bit indicates that the i-th unit is in operation, and a value of 0 indicates that it is in shutdown. This yields a complete set of unit combinations. The initial set of combinations of states; Based on the initial combination set, the number of units in operation in each unit combination is counted, and combined with the rated capacity parameters of the corresponding units, the maximum and minimum power generation output of each unit combination is obtained, and the theoretical output range corresponding to each combination is constructed. Based on the theoretical output range of each unit combination, a matching and screening process is performed with the dynamically feasible power generation output range. Specifically, it is determined whether the theoretical output range of each unit combination intersects with the dynamically feasible power generation range. If there is an intersection, the unit combination is retained; otherwise, it is discarded, thereby obtaining the first candidate unit combination set that meets the hydraulic constraints. Based on the first candidate unit combination, unit operation constraints are further introduced for screening. The operation constraints include minimum number of units in operation constraints, maximum number of units in operation constraints, and upper and lower limits of unit output constraints. For any unit combination, it is determined whether the number of operating units and output allocation of its corresponding units meet the operation constraints. If they do, the unit combination is retained; otherwise, it is eliminated, thus obtaining a second candidate unit combination set that meets the basic operation constraints. Based on the second candidate unit combination set and combined with the feasible power generation flow set, the consistency of each unit combination is checked. Specifically, for any unit combination, it is determined whether it can achieve reasonable power output distribution under the corresponding feasible power generation flow conditions and ensure that the output of each operating unit is between its minimum technical output and rated capacity. If the conditions are met, the combination is retained; otherwise, it is eliminated, thus obtaining the third candidate unit combination set that satisfies the hydraulic constraints and unit output distribution constraints. Based on the third candidate unit combination set, the unit start-up and shutdown switching constraints are further considered. The unit operating state vector at the current moment is compared, the switching cost between each candidate combination and the current combination is calculated, and the unit combination with the switching cost exceeding the preset threshold is eliminated, thereby obtaining the candidate unit combination set that satisfies the operation continuity constraint.

[0053] The specific calculation formula for the switching cost between each candidate combination and the current combination is as follows:

[0054] In the formula, Let m be the total switching cost of the m-th candidate unit combination relative to the current combination. Let be the operating state variable of the i-th unit at the current moment, and let be a binary variable. =1 indicates that the unit is in operation. =0 indicates that the unit is in a stopped state. Let be the operating state variable of the i-th unit in the m-th candidate unit combination. Let be the startup cost coefficient for the i-th generating unit, used to characterize the cost incurred in switching the unit from a shutdown state to an operating state. This cost includes, but is not limited to, startup energy consumption, equipment wear and tear, and scheduling adjustment costs. Let be the downtime cost coefficient for the i-th generating unit, used to characterize the cost or impact of switching the unit from an operating state to a downtime state. Let be the start-up behavior indicator function for the i-th unit. The value is 1 when the unit changes from shutdown (0) to operation (1), and 0 otherwise. The function is the shutdown behavior indicator function for the i-th unit. It takes the value 1 when the unit changes from running (1) to shutting down (0), and 0 otherwise.

[0055] It should be noted that, starting from the complete set of unit combinations, hydraulic constraints, operational constraints, flow consistency constraints, and start-stop switching constraints are introduced layer by layer to progressively screen unit combinations. This not only effectively eliminates physically infeasible or operationally unreasonable combinations, significantly reducing the search space and improving the efficiency of subsequent optimization calculations, but also ensures that the final candidate unit combinations meet hydraulic constraints such as water balance, water level control, and output boundaries throughout the entire prediction period. At the same time, it takes into account the minimum technical output of the units, the number of units, and the rationality of output allocation. Furthermore, by introducing switching cost constraints, it avoids equipment losses and operational instability caused by frequent start-stops, thereby achieving effective coupling between discrete unit combinations and continuous hydraulic processes, and improving the physical consistency, engineering feasibility, and operational stability of power generation output prediction results.

[0056] S4. For each candidate unit combination, construct an output model to describe the segmented mapping relationship between flow and output. Each segment corresponds to a specific unit combination state, and there is a discontinuous transition relationship between the segments. Use historical data to train a probability prediction model to predict the probability of each candidate unit combination being selected under a given hydrological state and scheduling requirements. The input of the model is the joint state vector in step S1, and the output is the probability distribution of each unit combination.

[0057] In this embodiment, for each candidate unit combination, an output model is constructed to describe the segmented mapping relationship between flow rate and output, including: Obtain the set of feasible power generation flow and the corresponding power generation output mapping relationship output in step S2, as well as the set of candidate unit combinations obtained in step S3, and extract the unit operation status vector at the current moment. Based on the feasible power generation flow set, the continuous flow interval is divided into several flow sampling points according to a preset discrete precision to form a discrete flow sequence, and the power generation output value corresponding to each flow sampling point is obtained. For each candidate unit combination, based on the minimum technical output constraint and rated capacity constraint of the units, the output feasibility judgment conditions of the unit combination at each flow sampling point are constructed, specifically including: Determine whether, under a discrete flow sequence, there exists a set of unit output allocation schemes such that:

[0058] And it satisfies:

[0059] In the formula, Let m be the set of operating units corresponding to the m-th candidate unit combination, that is, the set of unit numbers that are in the "operational state". Let i be the actual allocated output value of the i-th generating unit under the current flow rate. This refers to the power generation output value calculated using the power generation output formula at the given flow sampling point. For the minimum technical output of the i-th unit, This represents the maximum allowable output of the i-th generating unit.

[0060] Based on the discrimination results, for each candidate unit combination, a subset of flow rates that meet the output feasibility requirements is selected from the discrete flow rate sequence, thereby constructing a set of feasible flow rate intervals corresponding to the unit combination. The feasible flow interval set is reconstructed into a continuous feasible flow interval set, which specifically includes: sorting the flow intervals in ascending order according to the flow size; and merging the flow subsets with adjacent intervals less than a preset threshold. Based on a continuous feasible flow range, a unique mapping function is constructed from flow to unit combination; The specific calculation formula for the unique mapping function is as follows:

[0061]

[0062] In the formula, This is the only mapping function from flow rate to unit combination. Let be the evaluation function for each combination. For a set of continuous feasible flow intervals, Number of operating units For the allocatable output under this combination, Calculate the power output for hydroelectric power generation (from S2). As a cost of switching, , , These are the weighting coefficients.

[0063] Based on a unique mapping function, the critical flow point for changes in unit combination is identified, specifically defined as:

[0064] In the formula, The critical flow point, It is a preset minimum positive number.

[0065] Based on the set of critical flow points, the overall flow range is divided into several sub-ranges, and an output function is defined in each sub-range. The specific calculation formula for the output function is as follows: ,

[0066] In the formula, For the output function, For the j-th interval, the corresponding unit combination, Let J be the power generation output of the unit combination corresponding to the j-th interval. Let J be the starting flow rate of the j-th segment interval. The termination flow of the j-th segment interval, For target traffic.

[0067] At the critical flow points in adjacent intervals, no continuity constraints are applied, such that: in, To approach the critical point from the left, To approach the critical point from the right, This is the left-hand limit output value. The right limit output value is used to form the discontinuous output transition characteristic caused by the unit combination switching, thus obtaining the segmented output model.

[0068] It should be noted that, based on the continuous hydraulic feasible output mapping obtained in step S2, discrete operational constraints such as minimum technical output, rated capacity, and switching costs of the units are introduced to perform a structured division of the continuous flow space based on "realizability discrimination." This not only accurately identifies the applicable range of different unit combinations in each flow interval, avoiding the defect of traditional continuous models ignoring the discrete characteristics of units, but also effectively solves the selection uncertainty problem under multiple overlapping intervals by constructing a unique mapping function, making the model deterministic and computable. Furthermore, through critical flow point identification and segmented modeling, the unit combination switching process is explicitly characterized as a structural discontinuous transition of the output function, thereby truly reflecting the coupling characteristics of "continuous hydraulic process + discrete unit switching" in hydropower station operation, significantly improving the physical consistency, engineering feasibility, and ability to characterize the dispatch decision boundary of the power generation prediction results.

[0069] Furthermore, a probabilistic prediction model is trained using historical data to output the probability distribution of the selection of each candidate unit combination under given hydrological conditions and scheduling requirements, including: Historical operational data is acquired, including hydrological monitoring data, unit operating status data, and power grid dispatch command data, and constructed into a historical joint status sample set. The historical joint state sample set is standardized, including continuous variable normalization and discrete variable one-hot encoding, to obtain a standardized historical feature sample set, which includes joint state vectors and corresponding historical unit combination labels. Based on a standardized historical feature sample set, the data is divided into training and validation sets, and a probabilistic prediction model is constructed. This model is a pre-defined multi-class probabilistic prediction model, whose input is a joint state vector and output is the probability distribution vector of each candidate unit combination, wherein: ,

[0070] In the formula, Let be the probability distribution vector. The number of candidate unit combinations. Let m be the probability that the m-th unit combination is selected under the state of standardized feature samples.

[0071] For the probabilistic prediction model, parameter training is performed, specifically including: using the unit combination labels in historical samples as supervision signals, and optimizing using the cross-entropy loss function, which is defined as:

[0072] In the formula, For loss function, This is a unit combination label. Among them, This is an indicator function that takes the value 1 when the condition is true and 0 otherwise.

[0073] During training, gradient descent is used to iteratively update the model parameters, and the model performance is evaluated on the validation set. The model hyperparameters are adjusted to improve prediction accuracy and generalization ability until the preset convergence condition is met. Based on the trained probabilistic prediction model, the joint state vector at any given moment is input, and the corresponding unit combination probability distribution is output.

[0074] It should be noted that training the probabilistic prediction model using historical data maps multi-source information such as hydrological conditions, unit operating conditions, and grid dispatching requirements into a unified probability distribution output. This not only automatically learns the selection patterns of unit combinations under different operating conditions from the data, avoiding the subjectivity and limitations of traditional reliance on manual experience or rule setting, but also characterizes the relative optimality of each candidate unit combination through multi-class probabilistic modeling, enabling the model to reflect the uncertainty and multiple solutions of combination selection. Furthermore, by combining feature standardization and supervised learning training mechanisms, the model's ability to fit complex nonlinear relationships and its generalization performance are improved. Thus, given real-time operating conditions, it can quickly and stably output a reasonable probability distribution of unit combinations, providing a reliable basis for the subsequent fusion of segmented power output models, and ultimately improving the accuracy and engineering applicability of overall power generation output prediction.

[0075] S5 integrates the output model with the probability distribution of unit combinations, calculates the output value corresponding to the maximum probability, thereby realizing the coupled prediction of discrete unit state and continuous hydraulic process, identifies the critical interval of unit combination switching, and introduces a switching penalty function in this interval to smooth and correct the prediction results, so as to obtain the final power generation output prediction result and avoid unstable prediction caused by frequent switching.

[0076] In this embodiment, the output model is fused with the probability distribution of unit combinations to calculate the preliminary output prediction value corresponding to the highest probability, including: Based on the segmented output model, the flow interval corresponding to the target flow at the current moment is determined. And obtain the unit combination and its output function corresponding to the interval; Based on the unit combination, the probability value of the corresponding unit combination is extracted from the probability distribution vector, and the probabilities of all candidate unit combinations are sorted to determine the unit combination corresponding to the highest probability, thus obtaining the optimal unit combination. The optimal unit combination is matched with its corresponding flow range in the segmented output model, and it is determined whether the current target flow falls within the range. If it does, the combination is directly adopted as the target unit combination. Figure 3 As shown; If the current flow does not belong to the interval corresponding to the optimal unit combination, the target unit combination is re-selected from the candidate combination set that satisfies the flow feasibility. By substituting the output function of the target unit combination with the current flow value into the calculation, the preliminary power output prediction value under this combination is obtained.

[0077] It should be noted that, given the multiple solutions and uncertainties in the selection of unit combinations, the combination most likely to conform to historical operating patterns and current operating conditions is prioritized based on probability distribution results, thereby improving the stability and rationality of the decision. At the same time, by introducing a flow feasibility verification mechanism, it is ensured that the selected optimal combination must meet hydraulic conditions and unit operating constraints, avoiding physical impossibilities caused by relying solely on the maximum probability. Finally, precise calculations are performed using piecewise output functions, so that the power generation prediction results possess both data-driven optimality and executability under hydraulic mechanism constraints, thereby significantly improving the robustness and engineering applicability of the model in complex scheduling environments.

[0078] Furthermore, the critical interval for unit combination switching is identified, and a switching penalty function is introduced within this interval to smooth the prediction results, thereby avoiding unstable predictions caused by frequent switching. This includes: Obtain the segmented output model and the corresponding unit combination segmented structure, and extract the set of critical flow points corresponding to adjacent unit combinations, wherein the critical flow points are the flow boundary points where the unit combination switches. Based on the set of critical flow points, the flow intervals between adjacent critical points are expanded to construct the switching critical intervals for unit combination switching. Specifically, an interval is constructed with each critical flow point as the center, according to a preset flow disturbance width. In the formula, To switch the set of critical intervals, Preset flow disturbance width; Based on the aforementioned set of critical switching intervals, the current target traffic is interval-based. If the target traffic Q is satisfied... If the condition is met, the system is determined to be in a sensitive area for unit combination switching; otherwise, it is determined to be in a stable operating area. If the current location is in a switching sensitive area, extract the combination of two adjacent units and their corresponding output functions to construct a candidate output set based on the switching state; For the candidate output set of the switching state, a switching penalty function is introduced to constrain and correct the switching behavior of different unit combinations; The switching penalty function The specific calculation formula is as follows:

[0079] In the formula, and It is a combination of two adjacent units. For the combined switching weight coefficients, This is the weighting coefficient for output variation. This represents the difference in output between adjacent combinations.

[0080] Based on the switching penalty function, the candidate output is weighted and evaluated to obtain the corrected output value; The specific calculation formula for the corrected output value is as follows:

[0081] In the formula, This is the corrected output value. Let m be the power output function of unit combination m at flow rate Q. This represents the unit configuration status at the previous moment. This is the penalty function for unit combination switching.

[0082] If it is determined that the current unit is not in a switching sensitive area, the output value is directly calculated using the segmented output function corresponding to the current unit combination, without the need to introduce a switching penalty function for correction. The output is smoothed to predict the final power generation output, thereby suppressing the output jump caused by frequent unit combination switching and achieving the continuity and stability of the prediction results.

[0083] It should be noted that, based on the segmented output model, a switching-sensitive interval formed by the expansion of the critical flow point is introduced. This ensures that unit combination changes are only constrained within the area where switching may occur in a physically meaningful sense, thereby avoiding unnecessary combination fluctuations within the stable operating range. Simultaneously, by constructing a switching penalty function related to the state at the previous moment, the cost of unit combination switching and the output fluctuation amplitude are uniformly incorporated into the evaluation system, achieving weighted correction of candidate outputs. This allows the model to prioritize maintaining operational continuity while ensuring hydraulic feasibility and meeting unit constraints. Ultimately, this effectively suppresses the problem of frequent unit switching caused by small flow fluctuations near the critical point, making the power generation prediction results smoother and more stable in the time dimension, significantly improving the model's engineering usability and the reliability of scheduling decisions.

[0084] Reference Figure 2 As shown in the diagram, the present invention provides a structural schematic of a cascade hydropower station power output prediction system, which includes a data processing module, an interval construction module, a filtering module, a model construction module, a prediction module, and a correction module. The modules are interconnected. The data processing module is used to acquire the raw operating data of the cascade hydropower stations during the forecast period and construct a joint state vector. The interval construction module is used to determine the dynamic feasible power generation range of the hydropower unit at the current moment through forward simulation and iterative calculation based on the joint state vector and preset time window. The screening module is used to screen candidate unit combinations that meet the operating constraints based on the dynamic feasible power output range and unit parameters. The model building module is used to build an output model that describes the segmented mapping relationship between flow and output, and to train a probabilistic prediction model using historical data to predict the probability of each candidate unit combination being selected under a given state. The prediction module is used to couple the power output model with the selected probability to determine the target unit combination and its corresponding preliminary power output prediction value. The correction module is used to smooth the initial power output forecast, eliminate discontinuous power output fluctuations caused by unit combination switching, and obtain the final power generation output forecast.

[0085] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0086] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, in the form of a computer program product.

[0087] Those skilled in the art will recognize that the modules and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0088] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0089] In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting the power output of a cascade hydropower station, characterized in that, include: Obtain the raw operating data of the cascade hydropower stations during the forecast period and construct a joint state vector; Based on the joint state vector and the preset time window, the dynamic feasible power generation range of the hydropower unit at the current moment is determined through forward simulation and iterative calculation. Based on the dynamic feasible power output range and unit parameters, candidate unit combinations that meet the operating constraints are selected. A power output model is constructed to describe the segmented mapping relationship between flow and output, and a probabilistic prediction model is trained using historical data to predict the probability of each candidate unit combination being selected under a given state. The construction of the output model for describing the segmented mapping relationship between flow rate and output includes: For each candidate unit combination, determine its corresponding feasible traffic subset and reconstruct it into a continuous feasible traffic range; Establish a mapping relationship between flow ranges and unit combinations, and identify the critical flow points at which unit combinations switch. The overall flow range is divided into multiple continuous sub-ranges using the critical flow point as the dividing boundary; The output function is defined independently in each sub-interval, and no continuity constraint is applied at the critical point of adjacent intervals, forming a piecewise output model with discontinuous transition characteristics; The output model is coupled with the selection probability to determine the target unit combination and its corresponding preliminary output prediction value. The initial power output forecast is smoothed to eliminate discontinuous power output fluctuations caused by unit combination switching, thus obtaining the final power generation output forecast.

2. The method for predicting the power output of a cascade hydropower station according to claim 1, characterized in that, The construction of the joint state vector includes: Preprocess the raw operational data to obtain a continuous and valid data sequence at a unified time scale; Extract multidimensional state variables representing the current hydrological conditions, unit operating status, and power grid dispatching requirements from the data sequence; Multidimensional state variables are fused to construct a joint state vector containing continuous and discrete variables.

3. The method for predicting the power output of a cascade hydropower station according to claim 1, characterized in that, The process of determining the dynamically feasible power output range of the hydropower unit at the current moment through forward simulation and iterative calculation, based on the joint state vector and a preset time window, includes: Based on the current reservoir water level and the predicted inflow process, and combined with a pre-set set of constraints, dynamic constraint equations are established. Within a preset flow range, candidate power generation flow rates are constrained and verified by forward rolling simulation to select a set of feasible power generation flow rates. For each flow value in the set of feasible power generation flows, the upstream water level and the tailwater level are calculated iteratively until the head value converges, thus obtaining a self-consistent flow-head combination. The corresponding power generation output is calculated based on the self-consistent flow-head combination, and the results are summarized to form a dynamic feasible power generation output range.

4. The method for predicting the power output of a cascade hydropower station according to claim 3, characterized in that, For each flow value in the feasible power generation flow set, the upstream water level and tailwater level are iteratively calculated until the head value converges, obtaining a self-consistent flow-head combination, including: Based on the current feasible power generation flow, obtain the initial value of the water level in front of the dam at the current moment; Calculate the tailwater level and determine the initial head based on the tailwater level-outflow relationship; The reservoir capacity is updated based on the power generation flow, and the upstream water level is recalculated based on the updated capacity. The head is recalculated based on the updated upstream water level and tailwater level, and compared with the results of the previous iteration. The iteration is repeated until the head difference between two adjacent calculations meets the preset convergence threshold, and the final self-consistent head value is output.

5. The method for predicting the power output of a cascade hydropower station according to claim 1, characterized in that, The screening of candidate unit combinations that meet the operational constraints includes: Based on the number of units and the capacity of each unit, generate all possible startup combinations; The theoretical output range of each combination is matched with the dynamically feasible power generation output range, and combinations that do not meet the hydraulic feasibility requirements are eliminated. For the remaining combinations, the unit output characteristics and operational continuity are verified sequentially to obtain the final set of candidate unit combinations.

6. The method for predicting the power output of a cascade hydropower station according to claim 1, characterized in that, Constructing the output model also includes model training, specifically: Acquire historical operational data and construct a standardized historical feature sample set, which includes a joint state vector and corresponding historical unit combination labels; A multi-class probabilistic prediction model is constructed, with the joint state vector as input and the probability distribution of each candidate unit combination as output; The model is trained using the cross-entropy loss function and the historical unit combination labels as supervision signals. Using the trained probability prediction model, reason about the current joint state vector and output the corresponding unit combination probability distribution.

7. The method for predicting the power output of a cascade hydropower station according to claim 1, wherein the step of coupling the power output model with the selected probability to determine the target unit combination and its corresponding preliminary power output prediction value includes: Based on the current target flow rate within the flow range of the segmented output model, determine the corresponding unit combination and its output function; Based on the probability distribution of each unit combination output by the probability prediction model, the unit combination with the highest probability is selected as the optimal candidate combination, and it is determined whether the combination matches the current flow range. If a match is found, the combination is identified as the target unit combination; if no match is found, the target unit combination is re-selected from the set of candidate combinations that meet the flow feasibility requirements. By substituting the output function of the target unit combination with the current flow value into the calculation, the preliminary power output prediction value under this combination is obtained.

8. The method for predicting the power output of a cascade hydropower station according to claim 1, characterized in that, The smoothing process for the preliminary power output forecast, which eliminates discontinuous power output fluctuations caused by unit combination switching, to obtain the final power generation output forecast includes: Based on the critical flow point in the segmented output model, a preset switching critical interval is established; Determine whether the flow rate corresponding to the current target output demand falls within the switching critical range; If so, the switching penalty mechanism is activated to weight and merge the output candidate values ​​of adjacent unit combinations in order to suppress output jumps; If not, the output function value corresponding to the current combination will be used directly for calculation. The output is the final predicted power generation value after smoothing correction.

9. A system using the power output prediction method for a cascade hydropower station as described in any one of claims 1-8, characterized in that, include: The data processing module is used to acquire the raw operating data of the cascade hydropower stations during the forecast period and construct a joint state vector. The interval construction module is used to determine the dynamic feasible power generation range of the hydropower unit at the current moment through forward simulation and iterative calculation based on the joint state vector and preset time window. The screening module is used to screen candidate unit combinations that meet the operating constraints based on the dynamic feasible power output range and unit parameters. The model building module is used to build an output model that describes the segmented mapping relationship between flow and output, and to train a probabilistic prediction model using historical data to predict the probability of each candidate unit combination being selected under a given state. The prediction module is used to couple the power output model with the selected probability to determine the target unit combination and its corresponding preliminary power output prediction value. The correction module is used to smooth the initial power output forecast, eliminate the discontinuous fluctuations in power output caused by unit combination switching, and obtain the final power generation output forecast.

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