Reservoir dispatching controllability evaluation method based on forward and reverse calculation and dispatching requirements

Abstract

The invention discloses a reservoir scheduling controllability evaluation method based on forward and reverse calculation and scheduling demands, and the method comprises the steps: building a calibration reservoir-river channel numerical model based on the watershed terrain and hydrological basic data; the target scene inflow process and the initial scheduling scheme are input to carry out forward hydraulic simulation, a downstream control section prediction flow process is generated, and a linearized space-time response kernel is constructed; according to preset flood control scheduling constraints and scheduling requirements, a reverse optimization objective function is constructed, and an optimal ex-warehouse adjustment sequence meeting reservoir water level and discharge physical constraints is solved; and correcting the initial scheduling scheme based on the optimal ex-warehouse adjustment sequence, and generating a controllability evaluation result by calibrating forward verification of the reservoir-river channel numerical model. According to the method, the flood wave diffusion mechanism is accurately described through the response kernel, the inversion problem under complex constraints is solved through reverse optimization, and quantitative evaluation and boundary recognition of reservoir dispatching controllability are achieved.

Description

Technical Field

[0001] This invention belongs to the field of water conservancy project scheduling, and in particular, it is a method for assessing the controllability of reservoir scheduling based on forward and reverse calculations and scheduling requirements. Background Technology

[0002] With the increasing frequency of extreme hydrological events due to global climate change, how to reduce downstream flood peaks through precise pre-release of water to lower reservoir levels while ensuring the safety of dam structures and reservoir inundation has become a major challenge for flood control decision-making. Accurately assessing the controllability of reservoir scheduling systems under specific inflow scenarios—that is, determining whether a scheduling scheme that satisfies all physical constraints—is of significant engineering importance for developing scientific flood control emergency response plans.

[0003] Currently, reservoir operation plans are mainly formulated based on human experience or forward simulation techniques based on physical models. Operators typically employ a trial-and-error approach: assuming an outflow plan, observing the flood's evolution, and then verifying the downstream consequences. Alternatively, they may use a simple concept of water propagation time lag to roughly estimate upstream and downstream flows. While this approach is applicable to routine small and medium-sized flood operations, it often proves insufficient to quickly find a feasible solution that balances multiple constraints when facing complex flood events with high peak volumes and large volumes.

[0004] However, existing technologies have the following deep-seated problems when dealing with complex extreme floods: simple time-delay models ignore the flattening, deformation, and diffusion effects that inevitably occur during the evolution of flood waves in the river channel, and cannot accurately describe the dynamic response process of upstream outflow changes to downstream sections, resulting in distorted flow superposition calculations; in addition, traditional forward trial-and-error methods are difficult to accurately solve for the optimal scheduling timing and magnitude under the dual constraints of nonlinear reservoir water level constraints and downstream flood control safety constraints, leading to decisions that are often conservative or risky due to neglecting one aspect for another; furthermore, point assessments based on a single scenario cannot reveal the critical boundary when the system shifts from controllable to uncontrollable, and it is difficult to quantify the ultimate carrying capacity of the scheduling system under different inflow intensities. Summary of the Invention

[0005] The purpose of this invention is to provide a method for assessing the controllability of reservoir scheduling based on forward and reverse calculations and scheduling requirements, so as to solve the above-mentioned problems existing in the prior art.

[0006] The technical solution, based on forward and reverse calculations and a method for assessing the controllability of reservoir scheduling based on scheduling requirements, includes:

[0007] Acquire and construct and calibrate a calibrated reservoir-river numerical model that describes the physical mechanism of reservoir storage and discharge and river flood evolution based on watershed topographic and hydrological data;

[0008] The pre-stored target scenario inflow process and initial scheduling scheme are input into the calibrated reservoir-river numerical model for forward hydraulic simulation, generating the predicted flow process at the downstream control section. Based on the pre-stored outflow micro-disturbance response under the baseline operating state, a linearized spatiotemporal response kernel characterizing the spatiotemporal coupling effect of upstream outflow changes on downstream control section flow changes is constructed.

[0009] Based on the downstream control section predicted flow process, according to the preset flood control scheduling constraints and scheduling requirements, an inverse optimization objective function containing a downstream flow tracking error term and an outflow adjustment penalty term is constructed. The linearized spatiotemporal response kernel is used as the constraint transfer operator to solve the optimal outflow adjustment sequence that satisfies the physical constraints of reservoir water level and discharge.

[0010] The initial scheduling scheme is corrected based on the optimal outflow adjustment sequence, and a controllability assessment result is generated to characterize whether the current scenario meets the scheduling requirements through positive verification of the calibrated reservoir-river numerical model.

[0011] Beneficial effects: This invention accurately characterizes the flood wave diffusion mechanism by using response kernels, solves the inversion problem under complex constraints by using inverse optimization, and realizes the quantitative assessment and boundary identification of the controllability of reservoir scheduling. Attached Figure Description

[0012] Figure 1 A flowchart illustrating the steps of a reservoir scheduling controllability assessment method based on forward and reverse calculations and scheduling requirements, provided in this application embodiment.

[0013] Figure 2 A flowchart illustrating the steps for constructing a reverse optimization objective function as provided in this application embodiment.

[0014] Figure 3 A flowchart illustrating the steps for solving the optimal outbound adjustment sequence provided in this application embodiment.

[0015] Figure 4 A flowchart illustrating the steps for constructing a linearized spatiotemporal response kernel provided in this application embodiment. Detailed Implementation

[0016] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0017] It should be noted that the terms include and have, and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units is not necessarily limited to those steps or units that are explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to such process, method, product, or device.

[0018] like Figure 1 As shown, a method for assessing the controllability of reservoir scheduling based on forward and reverse calculations and scheduling requirements includes the following steps:

[0019] Based on the watershed topographic and hydrological data, a calibration reservoir-river numerical model describing the physical mechanisms of reservoir storage and discharge and river flood evolution was constructed and calibrated.

[0020] In this embodiment, the basic watershed topographic and hydrological data mainly include watershed digital elevation model data, river network topology data, reservoir engineering characteristic data, and historical hydrological and meteorological observation data. Specifically, the reservoir engineering characteristic data includes the reservoir's water level-storage capacity curve V=f(Z) and water level-discharge capacity curve Q=g(Z, Opening), where f is a function describing the relationship between water level and storage capacity, Z is the reservoir's water level, g is a function describing the relationship between water level and discharge capacity, and Opening is the opening or closing status parameter of the discharge facility. The calibrated reservoir-river channel numerical model consists of two core modules: one is a lumped water balance equation set used to calculate reservoir water volume changes, and the other is the Saint-Venant equation set or its simplified Muskingen model used to calculate river flood evolution. During the construction process, the original basic data needs to be preprocessed, including unifying the coordinate system, unifying the calculation time step, and interpolating and filling in missing data. The calibration process utilizes historical measured flood data and adjusts the Manning roughness coefficient and river cross-sectional geometric parameters of the model to ensure that the error between the simulated flow process and the measured flow process meets the preset accuracy requirements, such as the Nash efficiency coefficient (NSE) being greater than 0.9, thus obtaining a calibrated reservoir-river numerical model that can truly reflect the hydraulic characteristics of the basin.

[0021] The pre-stored target scenario inflow process and initial scheduling scheme are input into the calibrated reservoir-river numerical model for forward hydraulic simulation, generating the predicted flow process at the downstream control section, and obtaining the outflow micro-disturbance response under the baseline operating state. A linearized spatiotemporal response kernel is constructed to characterize the spatiotemporal coupling effect of upstream outflow changes on downstream control section flow changes.

[0022] In this embodiment, the target scenario consists of the inflow process I(t) and the initially set outflow scheduling scheme Q. base (t) Definition. Downstream control section predictive flow process Q predThe output of the model under baseline conditions is represented by a one-dimensional column vector of length T in the data structure. The linearized spatiotemporal response kernel S is a two-dimensional matrix of length T, used to locally linearize the complex nonlinear hydraulic response relationship near the baseline trajectory. Specifically, this response kernel is constructed using a micro-perturbation analysis method. Based on the baseline outflow scheme, a small pulse perturbation is applied to the outflow, and the resulting response changes downstream are observed, thereby capturing the diffusion, flattening, and hysteresis characteristics of flood waves propagating in the river channel. By constructing this response kernel, the change in downstream flow Δ... Q_down Approximately expressed as the response kernel S and the upstream outbound adjustment Δ q The matrix product provides a mathematical foundation for subsequent inverse optimization.

[0023] Based on the downstream control section predicted flow process, according to the preset flood control scheduling constraints and scheduling requirements, an inverse optimization objective function is constructed, which includes a downstream flow tracking error term and an outflow adjustment penalty term. The linearized spatiotemporal response kernel is used as the constraint transfer operator to solve for the optimal outflow adjustment sequence that satisfies the physical constraints of reservoir water level and discharge.

[0024] Specifically, flood control scheduling constraints include the warning water level Z at the downstream control section. warn , ensure water level and maximum allowable discharge Q max These are hard indicators; scheduling requirements reflect the manager's scheduling intentions, such as whether pre-emptive release of water from the reservoir is necessary. The inverse optimization objective function is a mathematical function that minimizes system deviation, typically consisting of two parts: the first is the downstream flow tracking error term, used to measure the difference between the actual downstream flow and the target flow, characterizing the accuracy of scheduling; the second is the outflow adjustment penalty term, used to limit the magnitude and rate of outflow adjustment, characterizing the stability and feasibility of scheduling. The constraint transitivity operator refers to using a constructed linearized spatiotemporal response kernel S to transform the control requirements for downstream flow into constraints on upstream outflow. For example, in the solution process, the nonlinear reservoir level constraint and the physical constraint of the discharge are transformed into constraints on the outflow adjustment amount Δ. q By applying a set of linear inequalities, the complex nonlinear optimization problem is transformed into a standard quadratic programming (QP) problem or other convex optimization problems for solution, ultimately yielding the optimal outbound adjustment sequence Δ under the current scenario. q_star .

[0025] The initial scheduling scheme is corrected based on the optimal outflow adjustment sequence, and a controllability assessment result is generated to characterize whether the current scenario meets the scheduling requirements through positive verification of the calibrated reservoir-river numerical model.

[0026] In this embodiment, the optimal outbound adjustment sequence Δ obtained by solving the problem is... q_star Superimposed on the initial scheduling scheme Qbase Above, generate the revised outbound scheduling scheme Q. final Given that the above solution process is based on the linearization assumption, in order to ensure the engineering safety of the solution, the outbound scheduling scheme Q needs to be modified. final The data is re-input into a nonlinear calibrated reservoir-river numerical model for forward validation. By running the model again, it is checked whether the corrected reservoir water level process and downstream flow process truly meet all flood control scheduling constraints. If they are met, the current scenario is determined to be controllable, and corresponding scheduling suggestions are output; if they are not met, for example, if the corrected water level still exceeds the limit, or the optimization algorithm reports no solution, the current scenario is determined to be uncontrollable, and higher-level emergency measures are required. Through this forward and reverse closed-loop validation mechanism, scheduling risks caused by linearization errors are effectively avoided.

[0027] This embodiment addresses the technical challenge of quantitatively assessing system controllability under extreme scenarios by relying solely on forward trial and error in traditional reservoir scheduling. It achieves scientific evaluation and optimization of reservoir scheduling schemes by constructing a deep coupling mechanism between physical hydrological models and mathematical optimization algorithms. This embodiment can be executed using a computer system. The system input includes watershed topography, hydrological and meteorological data, and scheduling rules, and the output is a controllability assessment conclusion for a specific scenario. In this embodiment, the time-series data is typically represented in the computer as a one-dimensional vector arranged by time steps, and the response relationships are represented as a two-dimensional matrix.

[0028] like Figure 4 As shown, in one possible implementation, a linearized spatiotemporal response kernel is constructed, including:

[0029] During the forecast period of the initial scheduling scheme, unit pulse disturbances are applied step by step at discrete time steps to generate a predetermined group of disturbance outbound scheduling schemes corresponding to different disturbance times.

[0030] In this embodiment, to obtain gradient information of the nonlinear hydrological system, sensitivity testing of the system is required. Specifically, a flow disturbance amplitude Δ is determined that is physically small enough to satisfy the linearity assumption, but numerically large enough to overcome the truncation error. q_pulse For example, take 1% of the design flow rate or 10 to 50 cubic meters per second. For each time step i (i from 1 to T) within the forecast period, construct a disturbance outbound scheduling scheme. Specifically: maintain the initial scheduling scheme Q base The flow rate remains unchanged at all times except for the i-th time step, and the disturbance amplitude Δ is added only to the flow rate at the i-th time step. q_pulse T different disturbance outbound scheduling schemes were generated, each scheme representing a scenario where a single pulse input is applied at a specific time.

[0031] Each group of disturbance outflow scheduling schemes is input into the calibrated reservoir-river numerical model to perform forward calculations, thereby obtaining the downstream control section flow process corresponding to each disturbance time.

[0032] Specifically, the constructed and calibrated physical model is used as a black-box computational engine. T sets of disturbance outflow scheduling schemes are input into the model one by one or in parallel for forward hydraulic simulation. For the i-th set of inputs, the model will output the corresponding downstream control section flow process Q. down_i Because the model incorporates physical mechanisms describing unsteady flow in open channels, such as the Saint-Venant equations, the output Q... down_i This naturally includes the nonlinear deformation characteristics of flood waves during their propagation in the river channel. It should be noted that for the baseline scenario without perturbation, the model also needs to be run once to obtain the predicted flow process Q at the baseline downstream control section. pred .

[0033] Calculate the flow response increment sequence of the downstream control section flow process relative to the predicted flow process of the downstream control section, and extract the sensitivity coefficient column vector based on the flow response increment sequence.

[0034] In this embodiment, for each disturbance time i, the response difference output by the model is calculated. Specifically, the flow process Q at the downstream control section of the i-th disturbance is... down_i Subtract the predicted flow rate Q at the downstream control section of the baseline pred This yields the incremental sequence of downstream flow response caused by the outflow disturbance at time i. This incremental sequence is then divided by the disturbance amplitude Δ. q_pulse After normalization, the i-th sensitivity coefficient column vector s is obtained. i Mathematically, this column vector s i The j-th element s in ji This approximates how many units of flow increase the downstream section flow at time j will result from an increase of 1 unit of flow in the upstream outflow at time i.

[0035] Assemble all sensitivity coefficient column vectors in chronological order to generate a linearized spatiotemporal response kernel.

[0036] Specifically, the T sensitivity coefficient column vectors s1, s2, ..., s T Arranged sequentially as column vectors, these vectors are assembled into a T x T square matrix, which is the linearized spatiotemporal response kernel S. This matrix fully records the linearized influence of input changes at any time during the forecast period on output changes at any time.

[0037] In a further possible embodiment, the linearized spatiotemporal response kernel is a matrix with a lower triangular or quasi-lower triangular structure. The distribution of non-zero elements in the sensitivity coefficient column vector represents the diffusion and attenuation pattern of flood waves generated by upstream outflow disturbance at a single moment during the evolution along the river channel. By multiplying the linearized spatiotemporal response kernel with the preset outflow adjustment vector, the hydraulic response relationship described by the nonlinear partial differential equations in the calibration reservoir-river channel numerical model is equivalent to a discrete convolution operation near the baseline state.

[0038] In this embodiment, since water flow is causal, meaning future disturbances cannot affect past states, matrix S exhibits a lower triangular or quasi-lower triangular structure. Specifically, when row index j is less than column index i, element s... ji The value is zero. Observing a column of the matrix, representing the disturbance response at a certain moment, the non-zero values ​​along the time axis (in the direction of increasing row index) exhibit a distribution pattern of first increasing, reaching a peak, and then decreasing with a tail. This characterizes the flattening (peak value reduction), hysteresis (peak time postponement), and diffusion (waveform elongation) phenomena that occur during the propagation of a single flood wave downstream along the river channel. Compared with the traditional simple pure hysteresis model, i.e., only performing time shifting, the response kernel matrix constructed in this embodiment can be operated through matrix-vector multiplication, i.e., S multiplied by Δ. q By implementing convolution operations in the discrete time domain, the local dynamic characteristics of a system of nonlinear partial differential equations near a reference trajectory can be mathematically approximated with high precision.

[0039] In some preferred embodiments, to ensure the effectiveness of the linearization approximation, a verification step can be added after constructing the response kernel. Specifically, a set of test outflow adjustment sequences is randomly generated, and linear prediction calculations are performed using the constructed matrix S, while nonlinear simulation calculations are performed using the physical model. The results of the two are compared. If the error exceeds a preset threshold, such as 5%, it indicates that the current disturbance amplitude Δ q_pulse If an inappropriate perturbation amplitude or an excessively large time step is selected, the system will automatically reduce the perturbation amplitude or refine the time step, and re-execute the above construction process until the accuracy meets the requirements. This improves the adaptability and robustness of the method under complex river conditions.

[0040] like Figure 2 As shown, in an exemplary embodiment, constructing the inverse optimization objective function includes:

[0041] Based on flood control scheduling constraints and scheduling requirements, the predicted flow process of downstream control sections is re-engineered in time series to generate the target flow process of downstream control sections that includes peak shaving and peak shifting characteristics.

[0042] In this embodiment, the system reads the flood control safety threshold of the downstream control section, such as the warning flow rate Q. warn and guarantee traffic Qsecure Setting the target directly to these fixed thresholds might lead to overly passive scheduling. Therefore, a preferred compensation scheduling strategy is adopted to reshape the target curve. In a preferred implementation, generating the downstream control section target flow process includes: comparing the predicted flow process of the downstream control section with the allowable flow upper limit in the flood control scheduling constraints to generate a basic restricted flow curve with amplitude truncation; based on the compensation scheduling strategy in the scheduling requirements, shifting the basic restricted flow curve forward in the time dimension or increasing the flow setpoint within the time window before the flood peak arrives to construct a downstream control section target flow process with pre-release characteristics, so as to guide the optimal outflow adjustment sequence to generate scheduling behavior of pre-emptying reservoir capacity in the inverse optimization objective function. Specifically, the baseline predicted flow process Q output by the model is... pred The target flow is compared hourly with the upper limit of the allowable flow. For periods when the predicted flow exceeds the upper limit, the target flow is set at the upper limit of the allowable flow. For periods when the predicted flow does not exceed the upper limit, the target flow is not simply followed, but adjusted according to the strategy of pre-release and reservoir emptying. For example, in the lead-up to the arrival of the flood, the target flow is artificially raised to near the warning flow Q. warn The level of the flow restriction curve can be adjusted, or the flow restriction curve can be shifted forward several time steps on the time axis, for example, shifted by 3 to 6 hours. Through this time series reshaping, the target flow process Q at the downstream control section can be constructed. target Having the characteristic of early release, in subsequent reverse optimization calculations, the algorithm will be guided to automatically find the upstream outflow adjustment sequence that can produce this early release effect, thereby physically emptying the reservoir capacity to cope with subsequent flood peaks.

[0043] The difference between the target flow process and the predicted flow process at the downstream control section is calculated at each time step to obtain the downstream flow error sequence.

[0044] Specifically, the downstream control section target flow process Q target Predicted flow process Q at the downstream control section of the benchmark pred Performing vector subtraction, we obtain the downstream flow error sequence e. That is, for each time step i, the error e... i equals Q target_i Subtract Q pred_i The error sequence e clearly quantifies the gap between the current baseline scheduling scheme and the ideal scheduling objective. If e i A positive value means the algorithm needs to increase the leakage at that moment; if e i A negative value means that the discharge needs to be reduced.

[0045] Construct an inverse optimization objective function, where the downstream flow tracking error term represents the Euclidean distance between the downstream flow error sequence and the optimal outbound adjustment sequence under the linearized spatiotemporal response kernel mapping, and the outbound adjustment penalty term represents the cumulative magnitude of the optimal outbound adjustment sequence and the rate of change of adjacent time steps.

[0046] In this embodiment, a mathematical model to be solved is established. Let the outbound adjustment sequence to be solved be a vector Δ. q Based on the linearized spatiotemporal response kernel matrix S, the downstream response resulting from upstream adjustment is approximately S multiplied by Δ. q To make the downstream response approximate the error sequence e as closely as possible, the downstream flow tracking error term is defined as a vector (S·Δ). q -e) is the square of the L2 norm. Meanwhile, to prevent drastic fluctuations in outflow from damaging hydraulic structures or causing downstream river scouring, a penalty mechanism needs to be introduced. The outflow adjustment penalty term is defined as consisting of two parts: first, a regularization term for the adjustment magnitude, i.e., Δ... q The first is the squared norm of the second law; the second is the smoothness constraint term, i.e., Δ. q The square of the second norm of the first-order difference vector, i.e., D·Δ q The squared 2-norm of , where D is the difference matrix. In summary, the inverse optimization objective function J can be expressed as:

[0047] min J = || S *Δ q - e || 2 +λ1 * ||Δ q || 2 +λ2 * ||D *Δ q || 2 ;

[0048] λ1 and λ2 are preset weighting coefficients used to balance the weights between tracking accuracy and operational stability.

[0049] In some alternative implementations, a time weight matrix W can be introduced to more finely control the optimization preferences at different time periods. In this case, the error term can be rewritten in weighted L2 form (S*Δ). q - e) T * W*(S*Δ q - e), where T This is a transpose. For example, the weight is increased during critical periods when the flood peak is approaching, forcing the algorithm to more strictly meet the target requirements during those periods, while the weight is decreased during the dry season.

[0050] like Figure 3 As shown, according to one aspect of this application, solving for the optimal outbound adjustment sequence includes:

[0051] Based on the water balance principle followed by the calibrated reservoir-river numerical model, the nonlinear reservoir water level boundary constraint defined in the flood control scheduling constraint is transformed into a linear cumulative constraint on the optimal outflow adjustment sequence.

[0052] In this embodiment, the problem of physical constraint embedding is addressed. The original water level constraint is about the absolute water level Z. t Nonlinear inequalities: Z min ≤Z t ≤Z max Z min Z is the minimum water level value. max This is the maximum water level value. To include it in Δ... q The quadratic programming model with variables needs to be linearized. The specific process is as follows: According to the principle of water balance, the change in reservoir capacity Δ at a certain time t is... V_t It equals the cumulative sum of outbound adjustments for all periods prior to this moment multiplied by the time step Δ. t The negative value of Δ (assuming the inflow rate remains constant). That is, Δ V_t = - ∑(Δ q_k *Δ t ), where k ranges from 1 to t. Using the reservoir capacity curve V=f(Z) at the reference water level Z... base_t The slope of the tangent at a point converts the change in reservoir capacity into a change in water level: Δ Z_t ≈Δ V_t / A t ;where A t Let be the surface area of ​​the reservoir. Based on the above relationships, the water level constraint at time t can be transformed into a constraint on Δ. q Linear inequalities of vectors: Z min - Z base_t ≤( -Δ t / A t )* ∑(Δ q_k )≤Z max - Z base_t For the entire forecast period T, this set of constraints can be written in matrix form: A level *Δ q ≤B level ;where A level It is a cumulative summation coefficient matrix with a lower triangular structure, reflecting the cumulative impact of the current outflow adjustment on the water level at all future times; B level Constrained by water level boundary (Z) min Z max ) and the benchmark water level Z base_t The constraint constant vector formed by the difference is used to limit the outbound adjustment sequence Δ. q Within the feasible range at each time step. The originally complex nonlinear hydraulic constraints were successfully reduced to standard linear inequality constraints.

[0053] By combining the inverse optimization objective function with linear cumulative constraints and preset instantaneous amplitude constraints of outflow, a constrained quadratic programming model is constructed. Solving the quadratic programming model yields the optimal outflow adjustment sequence that minimizes the inverse optimization objective function while satisfying the reservoir capacity safety and river flow capacity.

[0054] Specifically, the objective function is combined with the linear cumulative constraint and the upper and lower bound constraints of the outbound flow rate itself to form a standard quadratic programming (QP) model; where the upper and lower bound constraints of the outbound flow rate itself, i.e., Q... min ≤Q base +Δ q ≤Q max Q min Q is the minimum allowable leakage. max Q represents the maximum allowable leakage. base This is the initial scheduling scheme. The quadratic programming model is solved using a numerical optimization solver, such as an interior-point method or an effective set method solver. The solver will search for the vector Δ within the feasible region. q_star This minimizes the value of the objective function J. This vector represents the optimal outflow adjustment sequence that satisfies both the reservoir's capacity safety and the river's flow capacity constraints. If the solver reports no feasible solution, it directly outputs the uncontrollable signal for that scenario.

[0055] In one possible embodiment, since the above optimization is based on the assumption of local linearization, nonlinear errors may cause the actual water level to deviate slightly from the linear prediction when the flow rate is adjusted significantly. Therefore, closed-loop verification is required to ensure the safety of the project. Further, controllability assessment results are generated, including:

[0056] The optimal outbound adjustment sequence is superimposed on the initial scheduling scheme to generate a modified outbound scheduling scheme.

[0057] In this embodiment, a vector addition operation is performed. The increment vector Δ is... q_star Superimposed on the reference vector Q base The final revised outbound scheduling scheme Q was obtained. final At this point, it is necessary to modify the outbound scheduling scheme Q. final Perform a physical validity check, such as checking for negative flow rates; if present, force the flow rate to zero.

[0058] The modified outflow scheduling scheme is input into the calibration reservoir-river numerical model to perform a forward hydraulic simulation, which yields the modified reservoir water level process and the modified downstream control section flow process.

[0059] Specifically, the reservoir-river numerical model is invoked again for calibration. This time, the model input is no longer the initial scheme, but the revised outflow scheduling scheme Q. final The model is run, and the actual system response is calculated using the complete set of nonlinear equations, including the corrected reservoir water level process Z. final and the process of correcting the downstream control section flow rate Q down_final By employing a delinearization process, complex hydraulic phenomena that linear models fail to capture are revealed.

[0060] The system verifies whether the process of adjusting the reservoir water level and the process of adjusting the downstream control section flow simultaneously meet the flood control scheduling constraints. If they do, a controllability assessment result representing the current scenario as controllable is generated. If they do not meet the constraints, a controllability assessment result representing the current scenario as uncontrollable is generated.

[0061] In this embodiment, the Z-axis output by the model is... final and Q down_final A point-by-point comparison is performed with the hard indicators in the flood control scheduling constraints. The judgment logic not only includes whether the limit is exceeded, but also introduces a safety buffer in some preferred embodiments. Specifically, if the reservoir water level is adjusted during the Z-process... final If the maximum allowable water level is exceeded at any time, or if the flow rate at the downstream control section is adjusted, the process Q... down_final If the discharge exceeds the design discharge capacity of the downstream dike, it is directly deemed uncontrollable. If, although the limit is not exceeded, the process of adjusting the reservoir water level (Z) is considered uncontrollable... final If the water level remains within a range extremely close to the highest water level for an extended period, such as less than 0.05 meters, it is considered critically controllable or weakly controllable, indicating a significant risk to decision-makers. Only when all indicators are within safe limits and the flow process conforms to the expected peak-shaving pattern is a controllable conclusion reached. This stringent determination based on nonlinear closed-loop principles is crucial for ensuring the safety of water conservancy projects.

[0062] In one embodiment of this application, the method further includes constructing a multi-scenario parameter combination set and performing batch evaluation, specifically:

[0063] Based on the pre-stored historical flood statistics and scheduling management requirements, the parameter dimensions are determined, and a multi-scenario parameter combination set covering the preset parameter space is generated.

[0064] Alternatively, based on the pre-stored historical flood statistics and scheduling management requirements, the parameter dimensions, including the peak inflow amplification factor, the maximum allowable flow at the downstream control section, and the maximum allowable reservoir water level, are determined, and a multi-scenario parameter combination set covering the preset parameter space is generated.

[0065] In this embodiment, key parameter dimensions affecting controllability are defined, including: the peak inflow amplification factor k, for example, ranging from 1.0 to 2.0, representing different flood return periods; and the maximum allowable flow rate Q at the downstream control section. limit This characterizes the downstream flood control standard; and the starting water level Z. start For these parameter dimensions, the system generates a multi-scenario parameter combination set. For example, a full-factor grid method (Cartesian product) can be used for scanning. In a preferred embodiment, to improve computational efficiency in high-dimensional space, Latin hypercube sampling (LHS) or an adaptive sampling strategy based on boundary approximation is employed. For example, sparse sampling is performed, automatically refining sampling points in regions where transitions between controllable and uncontrollable states are detected, accurately depicting the boundaries of state transitions with minimal computation.

[0066] For each parameter combination in the multi-scenario parameter combination set, the aforementioned methods are invoked to perform forward prediction, backward optimization, and forward verification, respectively.

[0067] In other words, for each parameter combination in the multi-scenario parameter combination set, a corresponding scenario-level water inflow process and scenario-level scheduling constraints are constructed. Based on the scenario-level water inflow process and scenario-level scheduling constraints, the calibrated reservoir-river numerical model, linearized spatiotemporal response kernel, and inverse optimization objective function are called to perform forward prediction, inverse optimization, and forward verification for each parameter combination, generating single-scenario controllability assessment results corresponding to each parameter combination.

[0068] Specifically, the system iterates through every sample point in the parameter combination set. For each point, it scales the baseline flood process using the peak inflow amplification factor k to generate scenario-level inflow, and uses the maximum allowable flow Q at the downstream control section. limit Set scenario-level constraints. Record the final calculation state of each sample point. In a preferred implementation, the construction and execution process for each parameter combination is implemented internally by parameter mapping and loop calling logic. Specifically, assume the currently traversed parameter combination is composed of the peak flow amplification factor k and the maximum allowable flow rate Q at the downstream control section. limit and the upper limit threshold parameter Z of the water level limit The system executes a scenario-level data construction subroutine: for the water inflow process, it reads the baseline water inflow vector I. base Multiply each element by a coefficient k to generate a new column vector, which is the scenario-level water inflow process I. scene As the current inbound boundary condition, the system needs to update the boundary vectors in the quadratic programming model for scheduling constraints. Specifically, the outbound flow upper limit constraint vector Q is updated. ub Each element value in the array is reset to the current parameter Q. limitSimultaneously, the linear cumulative constraint matrix inequality A derived from the water balance equation... level *Δ q ≤B level Recalculate the right-hand term vector B. level Vector B level The t-th element in the table is specifically the upper limit threshold parameter Z of the water level. limit Subtract the benchmark water level Z base_t This is then multiplied by the area coefficient of the reservoir capacity curve at this moment. This transforms the abstract parameter combination into an optimization solver that can directly identify the mathematical constraint boundaries. After completing the above construction, the system enters the forward and reverse execution subroutines. It calls the API interface of the reservoir-river numerical model and passes in the scenario-level inflow process I. scene The system first sets the initial scheduling scheme and constraints, then performs positive prediction and extracts the linearized spatiotemporal response kernel matrix S. Next, it instantiates a quadratic programming solver object, loads the objective function constructed based on the S matrix, and the updated constraint vector Q. ub and B level The optimization calculation is performed. The solver returns two key results: the optimal outbound adjustment sequence Δ. q_star And solve for the status code ExitFlag. Adjust the optimal outbound sequence Δ q_star The initial scheme is superimposed, and the numerical model API is called again for forward verification simulation, outputting the corrected water level and flow rates. The system associates this entire set of input parameters with the output status code and verification results and stores them in a temporary database, then automatically enters the loop for the next parameter combination.

[0069] In one possible embodiment, generating a controllability assessment result further includes constructing a controllability boundary surface, specifically:

[0070] Using the convergence of the inverse optimization objective function as a binary classification criterion, parameter combinations that successfully obtain the optimal outbound adjustment sequence that satisfies the physical constraints and pass the positive verification are marked as controllable points; otherwise, they are marked as uncontrollable points.

[0071] Alternatively, by using the convergence of the inverse optimization objective function as a binary classification criterion, parameter combinations that successfully obtain the optimal outbound adjustment sequence that satisfies physical constraints and pass positive verification in the multi-scenario parameter combination set are marked as controllable points, forming the controllable domain in the parameter space; parameter combinations that cannot obtain a feasible solution by the inverse optimization objective function or whose modified outbound scheduling scheme fails to pass positive verification are marked as uncontrollable points, forming the uncontrollable domain in the parameter space.

[0072] In this embodiment, a leap from quantitative calculation to qualitative classification is achieved. The system assigns a binary label to the calculation results of each scenario. Specifically, if the QP solver finds a feasible solution and the solution passes nonlinearity verification, the parameter combination (point) is marked as a controllable point; conversely, if the QP solver reports no solution, indicating that the objective cannot be achieved under physical constraints, or if verification fails, it is marked as an uncontrollable point. Thus, the parameter space is divided into a controllable domain Ω by a discrete lattice. C and uncontrollable domain Ω N In a preferred implementation, the controllability determination stage utilizes the convergence of the inverse optimization objective function as a binary classification criterion, which can be implemented using a logical judgment algorithm. This algorithm comprises two levels of judgment criteria. The first level is mathematical feasibility determination: the system checks the ExitFlag status code returned by the optimization solver. The first level is determined to be true only if ExitFlag equals a specific value indicating convergence to the global optimum. If ExitFlag equals a value indicating no feasible solution or iterative divergence, it is directly determined to be false. The second level is physical safety determination: triggered only when the first level is true. The system scans the corrected water level process and corrected flow rate process from the forward verification output. The system calculates the maximum value in the corrected water level process and the current upper limit threshold parameter Z. limit The difference, and the maximum value during the corrected flow process, and the maximum allowable flow Q at the current downstream control section. limit The difference between the two levels is used. If both differences are less than or equal to zero, or less than a very small allowable error tolerance, the second level is considered true; otherwise, it is considered false. Based on the above two-level logic, the system labels each point in the parameter space. The system sets the label of the current parameter combination to logic 1, i.e., marks it as a controllable point, only when both the first and second level judgments are true; otherwise, the label is set to logic 0, i.e., marked as an uncontrollable point, in any other case, including mathematical unsolvability or physical exceedance. Cluster analysis is performed on these discrete labeled points in the multidimensional parameter space. The set of all points labeled 1 is defined as the controllable region, and the set of all points labeled 0 is defined as the uncontrollable region.

[0073] Extract the critical interface separating the controllable and uncontrollable domains in the parameter space to generate a controllability boundary surface describing the reservoir scheduling system under different combinations of inflow intensity and scheduling criteria.

[0074] Specifically, classification algorithms, such as Support Vector Machines (SVM) or isosurface extraction algorithms, are used to process the labeled point matrix and fit a hypersurface separating controllable and uncontrollable points. This hypersurface is the controllability boundary surface. This surface visually demonstrates the system's limiting capabilities. For example, on a two-dimensional plane of inflow amplification factor and downstream flow restriction, this boundary is a curve. The lower left of the curve represents the safe zone, and the upper right represents the risk zone. By observing this boundary curve, dispatchers can clearly determine: when the inflow intensity reaches a certain level, how much the downstream flow restriction standard needs to be relaxed to ensure the reservoir does not overflow; or, under the current downstream standard, how many years of flood return the reservoir can withstand at most. Visualized boundary information has extremely high reference value for developing emergency plans for floods exceeding standard levels. In other words, during visualization output, the system uses isosurface extraction algorithms or SVM classification boundary fitting algorithms to construct a smooth surface between the controllable and uncontrollable domains; this surface is the controllability boundary surface output to the user.

[0075] In another possible embodiment, generating the controllability assessment result can also be:

[0076] Based on historical representative flood processes and parameterized factors, scenario-level inflow process data are constructed.

[0077] In this embodiment, to ensure that the evaluation scenario is both statistically significant and consistent with the hydrological characteristics of the watershed, the flood wave is not generated simply using mathematical functions, but rather using a historical flood scaling method. Specifically, the system selects one or more representative typical floods from the historical database as the baseline waveform Q. hist The peak inflow amplification factor k and the peak arrival time offset Δ are used in a multi-scenario parameter combination set. T Transform the reference waveform. Scenario-level inflow process I scene (t) is calculated as: I scene (t)=k·Q hist (t -Δ T The generated inflow process retains the unique fluctuation rate and peak shape characteristics of the watershed, and simulates floods with different return periods through parameter k. Furthermore, in some implementations, the inflow process for the target scenario can be calculated using a watershed runoff generation and confluence model, combined with areal precipitation fields generated by numerical weather prediction.

[0078] Extract scheduling strategy features from typical scenarios and analyze the disaster-causing factors of critical uncontrollable scenarios.

[0079] Specifically, the system performs in-depth data mining on the massive amounts of data generated from batch calculations. It not only outputs controllability boundaries but also automatically filters out critical scenarios near these boundaries. For these critical scenarios—those on the edge of controllability and uncontrollability—the system extracts key features for revising the reservoir discharge schedule, such as the maximum pre-discharge lead time, the duration of full-load discharge, and the timing of the highest reservoir water level. By comparing and analyzing the differences between controllable and uncontrollable scenarios, the system can identify the main sources of constraint conflicts leading to uncontrollability. For example, the system might automatically diagnose and report that in a scenario with an inflow amplification factor of 1.3, the main disaster-causing factor is the downstream dike's flow capacity limitation; while in a scenario with a factor of 1.5, the disaster-causing factor becomes insufficient reservoir capacity. This attribution analysis provides qualitative references for dispatchers to develop targeted engineering measures.

[0080] Generate chart-based and text-based reservoir scheduling controllability assessment reports.

[0081] In this embodiment, complex data is transformed into visualized decision support information. The controllability assessment results generated by the system include, but are not limited to, the following forms: First, a parameter space controllability distribution map, which fills areas with different colors and plots clear boundary curves on a two-dimensional plane with the inflow peak amplification factor as the horizontal axis and the downstream maximum allowable flow rate as the vertical axis; second, a typical scenario tripartite diagram, which displays the inflow and outflow process diagram, the reservoir water level change process diagram, and the downstream cross-sectional flow process diagram on the same time axis for a specific parameter point selected by the user, highlighting the warning water level line and the flow restriction line to intuitively show when and what constraints the dispatching scheme touched; and third, a tabular assessment report, which summarizes and statistically analyzes the system controllability probability under different inflow frequencies. Through these multi-dimensional charts, dispatchers can clearly grasp the safety margin of the current dispatching system at a glance.

[0082] In one possible implementation, constructing a linearized spatiotemporal response kernel can be achieved by: reading a scenario parameter set from a scheduling decision system or a predefined configuration file. This scenario parameter set should include at least fields such as the inflow peak amplification factor, peak arrival time offset, previous reservoir water level, forecast period length, and initial outflow strategy type. The scenario parameter set is then subjected to integrity checks and value rationality verification to obtain a valid scenario parameter set that meets the evaluation requirements. Based on the valid scenario parameter set and historical representative flood processes, the flow values ​​and time axes of the historical representative flood processes are scaled and shifted according to the inflow peak amplification factor and peak arrival time offset. Alternatively, based on the areal precipitation field generated from numerical weather prediction results, the inflow process data for the target scenario is calculated using a watershed runoff generation and confluence model. In this inflow process data, the inflow flow value is given at each time step, ensuring that the time step size is consistent with the time discretization of the calibrated reservoir-channel model. Based on the initial outflow strategy type and previous reservoir water level values ​​specified in the valid scenario parameter set, combined with flood control scheduling constraints, initial outflow scheduling scheme data is constructed. The construction rules include: when the reservoir water level is below the flood control limit, the outflow is set according to the power generation priority strategy or the minimum ecological discharge strategy; when the inflow process data shows that the future flood peak will cause the reservoir water level to approach or exceed the preset high water level, the outflow is increased according to the principles of phased flow restriction and time-phased pre-discharge. The initial outflow scheduling plan data provides the preset outflow value at each time step, which, together with the inflow process data, constitutes the input for subsequent positive prediction.

[0083] Using inflow process data, initial outflow scheduling data, and the reservoir capacity-water level-outflow relationship as inputs, the water balance equation and outflow constraint calculations are performed at each time step to obtain the corresponding reservoir capacity and water level values, forming the predicted reservoir water level process. During the storage and release calculation, based on the flood control scheduling constraint data, if the reservoir water level at a certain time step is expected to exceed the maximum allowable water level, the outflow in the initial outflow scheduling data is truncated to ensure that the predicted reservoir water level process does not violate hard safety constraints, and this truncation behavior is recorded for subsequent sensitivity analysis. Using inflow process data and the downstream flow process jointly determined by the predicted reservoir water level process and the initial outflow scheduling data as upper boundary conditions and source terms, the river flood evolution module in the calibrated reservoir-river model is called. Using pre-calibrated hydraulic parameters and numerical formats, the evolution of the flood along the river is calculated to obtain the flow values ​​at the downstream control section at each time step, forming the predicted flow process at the downstream control section. The physical rationality of the predicted reservoir water level process and the predicted flow process at the downstream control section is verified to check for any abrupt changes, abnormal oscillations, or discontinuities that do not conform to engineering and hydrological common sense. If anomalies are found, the time step is adjusted or a more stable calculation option is adopted for the local numerical format, and the reservoir storage and release calculation and river flood evolution calculation are re-performed until a physically reasonable predicted reservoir water level process and predicted flow process at the downstream control section are obtained.

[0084] Based on the forecast period length and calculation time step, the entire assessment period is divided into several discrete time steps, and some or all of these time steps are selected as the disturbance time step set. According to the system's allowable regulation accuracy and the applicability range of the reservoir-channel model's linearization, a disturbance outflow amplitude that is physically small enough and numerically sufficient to produce a detectable response is determined. This disturbance outflow amplitude remains unchanged in all subsequent disturbance trials to ensure the comparability of sensitivity coefficients. Using the initial outflow scheduling scheme data and the predicted reservoir water level process as a benchmark, for each specific time step in the disturbance time step set, the disturbance outflow amplitude is added to the benchmark value for the corresponding outflow at that time step, while keeping the outflow at other time steps unchanged, forming the disturbance outflow scheduling scheme data. For each set of disturbance outflow scheduling scheme data, reservoir storage and release calculations and river flood evolution calculations are repeatedly performed to obtain the corresponding disturbed reservoir water level process and disturbed downstream control section flow process. For time steps not included in the disturbance time step set, the upstream outflow is consistent with the baseline outflow scheme. Therefore, the difference between the disturbance downstream control section flow process and the predicted downstream control section flow process should be close to zero in these time steps. The difference between the disturbance downstream control section flow process obtained from each disturbance trial calculation and the predicted downstream control section flow process is calculated to obtain the sequence of downstream control section flow increments caused by the upstream outflow disturbance in all future time steps under the corresponding disturbance time step. This sequence of downstream control section flow increments is divided by the disturbance outflow amplitude to obtain a sensitivity coefficient matrix column vector with the disturbed time step as the column index and the response time step as the row index. This process is repeated for all time steps in the disturbance time step set, and all the obtained column vectors are arranged in chronological order to form a complete linearized spatiotemporal response kernel matrix. Each element in the linearized spatiotemporal response kernel matrix represents the linear increment of the downstream control section flow at any specific response time step resulting from a unit increase in outflow at a specific outflow disturbance time step. A linearized spatiotemporal response kernel matrix is ​​used to perform linear superposition prediction on a set of randomly generated outflow adjustment sequences to obtain the corresponding linear predicted downstream flow process. This linear predicted downstream flow process is then compared with the actual simulated downstream flow process obtained by calibrating a reservoir-channel model under the same outflow adjustment conditions. The applicability of the linearized spatiotemporal response kernel matrix to the current baseline operating state is determined based on whether the error between the two is within a preset threshold. If the error is too large, the amplitude of the disturbance outflow can be appropriately reduced or the applicable linearization time window can be shortened. The forward calculation and response kernel matrix construction can then be re-executed until a linearized spatiotemporal response kernel matrix that meets the accuracy requirements is obtained.

[0085] According to one aspect of this application, solving for the optimal outflow adjustment sequence can also involve: reading the downstream control section's warning water level, guaranteed water level, and corresponding warning and design flows from the flood control scheduling constraint data; combining the warning and design flows with the safety margin parameters given in the scheduling demand description data; calculating the allowable flow upper limit for the downstream control section at each time step; and forming an allowable flow upper limit sequence. The allowable flow upper limit sequence can be constant or change over time to reflect factors such as the superposition of inflows from tributaries and the reinforcement status of dikes. The predicted flow at the downstream control section is compared hourly with the allowable flow upper limit sequence. For time steps where the predicted flow is lower than the allowable upper limit, the target flow is set to the predicted flow to avoid unnecessary control intervention; for time steps where the predicted flow exceeds the allowable upper limit, the target flow is set to a value slightly lower than the allowable flow upper limit, reserving a certain flow margin. This constructs a basic downstream target flow curve without compensation scheduling characteristics. If the scheduling demand description data specifies the use of a compensatory scheduling strategy, then based on the basic downstream target flow curve, the target curve is reshaped by shifting forward a portion of the high-flow segment, appropriately increasing the early flow, and correspondingly decreasing the later flow. This ensures that the downstream control section approaches but does not exceed the warning flow before the flood peak arrives, thus reserving more storage capacity for the reservoir area. This yields the final target flow process at the downstream control section. If no compensatory scheduling strategy is used, the basic downstream target flow curve is directly taken as the target flow process at the downstream control section.

[0086] A one-to-one subtraction operation is performed on the target flow process and the predicted flow process at the downstream control section. At each time step, the target flow is subtracted from the predicted flow, resulting in a downstream flow error sequence. Positive values ​​in the downstream flow error sequence indicate a target requirement to increase the flow at that moment, while negative values ​​indicate a target requirement to decrease the flow at that moment. Based on the time range where the downstream flow error sequence is non-zero or its absolute value exceeds a preset threshold, the time period requiring intervention by adjusting upstream outflow is determined, generating an outflow adjustment time window. Within the outflow adjustment time window, each time step corresponds to a desired outflow adjustment amount. These outflow adjustment amounts are arranged chronologically to form the outflow adjustment decision variable vector in the inverse optimization problem, with its dimension equal to the number of time steps within the outflow adjustment time window. Using a linearized spatiotemporal response kernel matrix, the outflow adjustment decision variable vector is mapped to a linear predicted downstream flow change at each time step via matrix multiplication. This is then subtracted from the downstream flow error sequence, and an error term measuring the difference between the two is defined in the form of the squared L2 norm, resulting in the main objective function term aimed at reducing the downstream flow error. To avoid overly drastic outbound adjustments in scheduling practice, a penalty term is defined to characterize the magnitude of each component of the outbound adjustment decision variable vector and the magnitude of the difference between adjacent time steps. For example, the squared L2 norm of the outbound adjustment decision variable vector is used to represent the overall adjustment cost, and the squared L2 norm of the difference in outbound adjustment amounts between adjacent time steps is used to represent the adjustment smoothness cost. These two cost terms are weighted according to the weight parameters set by the scheduling management to obtain the outbound adjustment penalty term. The main objective function term and the outbound adjustment penalty term are linearly combined to obtain the complete comprehensive inverse optimization objective function. Mathematically, the comprehensive inverse optimization objective function can be expressed as a weighted sum of the error minimization term and the outbound adjustment constraint term, where the error minimization term ensures that the downstream control section flow is as close as possible to the target flow process, and the outbound adjustment penalty term limits the upstream outbound adjustment to an engineeringly acceptable range.

[0087] Based on the maximum allowable discharge flow, minimum ecological discharge flow, and generator capacity given in the flood control scheduling constraint data, the outflow flow at each time step within the outflow adjustment time window is limited. Specifically, using the outflow flow in the initial outflow scheduling plan data as a benchmark, and adding the desired outflow adjustment amount, candidate outflow flow sequences for each time step are obtained. These candidate outflow flow sequences are required to satisfy a linear inequality constraint that the outflow flow is not less than the minimum allowable discharge flow and not greater than the maximum allowable discharge flow hourly. Using the predicted reservoir water level process as a reference, and combining the candidate outflow flow sequences with inflow process data, the impact of outflow adjustments on future reservoir water level increases and decreases at each time step is estimated using the water balance relationship. Based on this, a reservoir water level safety constraint is constructed to ensure that the reservoir water level does not exceed the maximum allowable reservoir water level and is not lower than the minimum operating reservoir water level. This constraint can be transformed into a linear or piecewise linear inequality constraint on the outflow adjustment decision variable vector using a pre-calculated reservoir capacity-water level-outflow relationship table and a linear approximation method. To avoid safety risks to hydraulic structures due to excessively rapid outflow adjustments, a maximum permissible range of outflow flow variation between adjacent time steps is set based on the initial outflow scheduling data. The difference between adjacent time steps in the outflow adjustment decision variable vector is compared with this maximum permissible range to construct an outflow change rate constraint, limiting the time change rate of the outflow adjustment decision variable vector in the form of linear inequalities. The comprehensive inverse optimization objective function is combined with the outflow flow constraint, reservoir water level safety constraint, and outflow change rate constraint to construct a constrained optimization problem model with the outflow adjustment decision variable vector as the independent variable. The objective function of this constrained optimization problem model is the comprehensive inverse optimization objective function, and the constraint set consists of the aforementioned linear or piecewise linear inequalities. A numerical algorithm suitable for solving quadratic programming or convex optimization problems is used to solve the constrained optimization problem model, obtaining the optimal outflow adjustment sequence that satisfies multiple constraints under the current scenario. If the optimization algorithm reports no feasible solution, this scenario is recorded as temporarily uncontrollable under the current iteration and will be further evaluated in subsequent iterations.

[0088] The optimal outflow adjustment sequence is added to the outflow flow at the corresponding time step of the initial outflow scheduling plan data to obtain the adjusted outflow flow value within the outflow adjustment time window. At other time steps, the initial outflow scheduling plan data remains unchanged, forming a complete modified outflow scheduling plan. The modified outflow scheduling plan reflects the specific outflow time sequence required by the upstream reservoir to meet downstream scheduling needs and reservoir safety constraints under the current scenario. Using the inflow process data and the modified outflow scheduling plan as input, the calibrated reservoir-river model is invoked, and reservoir storage and release calculations and river flood evolution calculations are repeatedly performed to obtain the modified reservoir water level process and the modified downstream control section flow process. The modified downstream control section flow process is compared with the downstream control section target flow process by time step, and the flow deviation at each time step is calculated. The maximum value and root mean square value of the flow deviation are statistically analyzed to determine whether they are within the allowable deviation range specified in the scheduling demand description data. Simultaneously, the modified reservoir water level process is compared with the highest and lowest allowable reservoir water levels given in the flood control scheduling constraint data to check for any periods exceeding limits or excessively approaching the limits. If the deviation of the downstream control section flow process meets the requirements throughout the forecast period, and the reservoir water level process does not violate the reservoir area safety constraints, then the current scenario is marked as a controllable scenario; if either condition is not met, then the current scenario is marked as an uncontrollable scenario or a boundary scenario requiring human intervention, and the relevant indicators are recorded as the basis data for subsequent multi-scenario controllability assessment.

[0089] In one embodiment of this application, generating controllability assessment results may further involve: reading flood control scheduling constraint data, historical flood statistics, and scheduling demand description data, and selecting several parameters that significantly affect scheduling controllability as dimensions for multi-scenario analysis. These parameters include at least the peak inflow amplification factor, the inflow process duration scaling factor, the previous reservoir water level, the maximum allowable flow at the downstream control section, and the highest allowable reservoir water level. For each parameter, based on historical data, engineering design standards, and management requirements, its minimum value, maximum value, and suggested step size are determined, generating multi-scenario parameter dimension definition data. Based on the multi-scenario parameter dimension definition data, a discrete value sequence is generated for each parameter, and a full-space grid of all parameter combinations is constructed using the Cartesian product method to obtain an initial parameter combination candidate set. If the number of parameter dimensions or the value step size is too small, resulting in an excessively large candidate set, Latin hypercube sampling, stratified sampling, or adaptive sampling methods based on historical flood weights can be used to select a representative subset from the parameter combination candidate set, forming a draft of a multi-scenario parameter combination set with controllable size but strong representativeness. Based on engineering operation procedures and physical constraints, parameter combinations in the initial draft of the multi-scenario parameter combination set that exhibit obvious conflicts or are physically impossible are filtered out. For example, the initial reservoir water level cannot be significantly higher than the normal storage level, the maximum allowable reservoir water level cannot be lower than the flood control limit level, and the maximum allowable downstream flow cannot be lower than the normal discharge during historical routine scheduling. For some parameter combinations that are slightly unreasonable but can be adjusted to make them reasonable, the relevant parameter values ​​are appropriately modified, and the modified combinations are retained in the set. The final result is the multi-scenario parameter combination set used for formal evaluation, where each parameter combination can be mapped to an inflow scenario and a set of constraints.

[0090] For each specific parameter combination in the multi-scenario parameter combination set, it is decomposed into parameter components such as the peak inflow amplification factor, the inflow process duration scaling factor, the previous reservoir water level value, the maximum allowable flow at the downstream control section, and the highest allowable reservoir water level. Based on these parameter components, the basic inflow curve is scaled and translated to generate scenario-level inflow process data corresponding to that parameter combination. Simultaneously, based on parameter components such as the maximum allowable flow at the downstream control section and the highest allowable reservoir water level, scenario-level scheduling constraint data for that scenario is generated, including the downstream flow restriction curve and the reservoir high water level restriction curve. The scenario-level inflow process data and scenario-level scheduling constraint data together define the specific scheduling scenario corresponding to the current parameter combination. Using the scenario-level inflow process data, the previous reservoir water level value, and the scenario-level scheduling constraint data as input, scenario-level initial outflow scheduling scheme data for the current scenario is constructed according to a unified initial scheduling strategy rule. This initial scheduling strategy may include: prioritizing power generation or ecological outflow when the inflow is low, and adjusting the outflow flow according to a phased peak shaving and flow restriction strategy when the predicted reservoir water level approaches different constraint curves. This ensures consistency of initial scheduling schemes across multiple scenarios, facilitating subsequent comparisons of the sources of controllability differences under different scenarios. Taking scenario-level inflow process data, scenario-level initial outflow scheduling scheme data, and scenario-level scheduling constraint data as input, it invokes a forward prediction and linearized spatiotemporal response kernel construction process. Specifically, this includes: performing reservoir storage and release calculations to obtain the scenario-level predicted reservoir water level process for this scenario; performing river flood evolution calculations to obtain the scenario-level predicted downstream control section flow process for this scenario; and obtaining the scenario-level linearized spatiotemporal response kernel matrix for this scenario through small-disturbance trial calculations. The output provides the necessary baseline state and mapping relationships for reverse outflow optimization under this scenario. Taking scenario-level downstream control section predicted flow process, scenario-level scheduling constraint data, and scheduling demand description data as input, it invokes a reverse outflow optimization process. Specifically, this includes: generating the scenario-level downstream control section target flow process under the given scenario; calculating the scenario-level downstream flow error sequence and constructing a comprehensive inverse optimization objective function; solving for the scenario-level optimal outflow adjustment sequence under the constraints of the linearized spatiotemporal response kernel matrix and the scenario-level reservoir predicted water level process; and generating a scenario-level modified outflow scheduling scheme based on this. A forward simulation of the scenario-level modified outflow scheduling scheme is performed using a calibrated reservoir-channel model to obtain the scenario-level modified reservoir water level process and the scenario-level modified downstream control section flow process. Based on whether both simultaneously satisfy the scenario-level scheduling constraints and scheduling demand description data, a scenario-level controllability judgment result is given for the scenario corresponding to the current parameter combination. Each parameter combination is associated and stored with its corresponding scenario-level controllability judgment result, forming a multi-scenario evaluation result dataset containing fields such as parameter combination identifier, scenario-level modified outflow scheduling scheme, scenario-level modified reservoir water level process, scenario-level modified downstream control section flow process, and scenario-level controllability judgment result.

[0091] Using a multi-scenario assessment dataset as input, statistics are performed on each parameter dimension to calculate the proportion of parameter combinations judged as controllable scenarios within different value ranges, forming controllability proportion curves for each single parameter dimension. For example, for the peak inflow amplification factor parameter, the proportion of scenarios corresponding to parameter combinations judged as controllable scenarios within each amplification factor range is statistically analyzed, thereby identifying the overall controllability trend of the system under different inflow intensities. Similarly, similar controllability proportion curves are calculated for parameters such as the maximum allowable flow rate at the downstream control section and the highest allowable reservoir water level, facilitating a visual representation of the impact of single-factor changes on controllability. Two or three of the most important parameters are selected from the multi-scenario assessment dataset, such as the peak inflow amplification factor, the maximum allowable flow rate at the downstream control section, and the highest allowable reservoir water level. Coordinate point clouds of these parameters in two-dimensional or three-dimensional space are constructed, and each coordinate point is marked as a controllable or uncontrollable point based on its scenario-level controllability judgment result. Through classification boundary fitting, cluster analysis, or interpolation methods, the controllability boundary curve or boundary surface separating controllable and uncontrollable points in the parameter space is estimated. The shape of the controllability boundary reflects the trade-off between inflow intensity, downstream flow restriction standards, and high reservoir water level constraints. For example, given a certain inflow amplification factor, it represents the minimum downstream allowable maximum flow rate and the maximum allowable reservoir water level combination required to keep the system controllable. Several representative controllable and uncontrollable scenarios are selected from the multi-scenario assessment dataset, such as critical scenarios near the controllability boundary and typical scenarios in clearly controllable or clearly uncontrollable regions. Scenario-level modified outflow scheduling schemes, scenario-level modified reservoir water level processes, and scenario-level modified downstream control section flow processes corresponding to these scenarios are analyzed. This extracts characteristic data of scheduling strategies, such as common outflow regulation modes, reservoir water level utilization levels, and downstream flow control methods under controllable scenarios. Simultaneously, for uncontrollable scenarios, the main sources of constraint conflicts causing uncontrollability are analyzed, providing scheduling personnel with qualitative references on which constraints need to be relaxed or what additional engineering measures need to be taken under extreme scenarios. The controllability proportion curve, controllability boundary curve or boundary surface, and scheduling strategy characteristic data of typical scenarios are integrated to generate reservoir scheduling controllability assessment results output in the form of charts and reports. The charts include curves showing the system's controllability as a function of the upper limit of the reservoir's high water level under different inflow intensities and downstream flow restriction standards; distribution maps of controllable and uncontrollable areas on the planes of peak inflow amplification factor and maximum downstream allowable flow; and triptychs of outflow-reservoir water level-downstream flow for several typical scenarios. The text report summarizes the main conclusions of the controllability assessment, including the system's controllable range under current design standards, the potential decrease in controllability under higher safety standards, and recommended directions for adjusting dispatching strategies. The output of this reservoir dispatching controllability assessment provides quantitative and visual technical support for dispatching decisions.

[0092] According to one aspect of this application, a computer system is provided for performing the reservoir scheduling controllability assessment method based on forward and reverse calculation and scheduling requirements as described in any of the above embodiments, comprising a processor, a memory, an input / output interface, and a communication bus. The memory stores computer program instructions and watershed basic data required for the assessment, such as topographic data, hydrological sequences, and response kernel matrices. The processor is connected to the memory and executes the computer program instructions to perform steps such as constructing a calibration model, calculating a linearized spatiotemporal response kernel, solving the inverse optimization problem, and generating controllability boundaries.

[0093] Specifically, the system is logically divided into a data preprocessing module, a forward simulation engine, a sensitivity analysis module, an optimization solver module, and a visualization interaction module. The forward simulation engine is configured to run the Saint-Venant equations solution program; the sensitivity analysis module is configured to perform small-perturbation trial calculations and assemble matrix S; the optimization solver module has an embedded quadratic programming algorithm library, such as interfaces for Gurobi or Cplex, for solving constrained linear inequalities. Input / output interfaces connect to display devices to show users controllable boundary surfaces and typical scenario process diagrams. Furthermore, the system can connect to a watershed hydrological and rainfall telemetry system via a network interface to acquire real-time hydrological data as the initial state for assessment.

[0094] In summary, the reservoir scheduling controllability assessment method based on forward and reverse computation and scheduling requirements includes: constructing and calibrating a reservoir-river channel numerical model; using micro-perturbation analysis to construct a linearized spatiotemporal response kernel characterizing the spatiotemporal coupling effect of upstream outflow changes on downstream control section flow changes; constructing an inverse optimization objective function based on scheduling requirements, including a downstream flow tracking error term and an outflow adjustment penalty term, transforming the nonlinear reservoir level constraint into a linear cumulative constraint, and solving for the optimal outflow adjustment sequence that satisfies the physical constraints through quadratic programming; substituting the linear optimization solution back into the physical model for forward closed-loop verification, and extracting the system's controllability boundary surface based on multi-scenario parameter scanning.

[0095] This invention addresses the problem that traditional time-delay models cannot describe the waveform flattening, diffusion, and hysteresis deformation that occur when flood waves evolve along the river channel by constructing a linearized spatiotemporal response kernel matrix with a lower triangular structure and utilizing matrix-vector multiplication in equivalent discrete convolution operations near the baseline trajectory. It reduces the complexity of nonlinear hydraulic responses to a high-precision linear mapping, improving the accuracy of describing upstream and downstream flow response relationships. By constructing an inverse optimization model with embedded physical constraints, it transforms nonlinear reservoir water level safety limits into linear cumulative constraints on outflow adjustments. Furthermore, it replaces traditional manual forward trial and error with a quadratic programming algorithm, solving the problem of accurately back-calculating the optimal outflow timing and magnitude under the dual complex constraints of reservoir safety and downstream flood control. This represents a shift from passive verification to active optimization, ensuring the mathematical optimality and engineering feasibility of the scheduling scheme. Finally, it establishes a closed-loop verification mechanism based on forward and inverse coupling and a multi-scenario parameterized evaluation system. Using the convergence of the inverse optimization algorithm as a binary classification criterion, it extracts controllable boundary surfaces in the multidimensional parameter space, solving the problem that single-scenario evaluation cannot quantify system safety limits and identify critical disaster-causing factors. It provides the dispatching department with visualized safety boundary information, clarifying the controllable range of the system under different inflow intensities.

[0096] 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 reservoir scheduling controllability assessment method based on forward and reverse calculation and scheduling requirements, characterized in that, include: Acquire and construct and calibrate a calibrated reservoir-river numerical model that describes the physical mechanism of reservoir storage and discharge and river flood evolution based on watershed topographic and hydrological data; The pre-stored target scenario inflow process and initial scheduling scheme are input into the calibrated reservoir-river numerical model for forward hydraulic simulation, generating the predicted flow process of the downstream control section, and obtaining the outflow micro-disturbance response under the baseline operating state. A linearized spatiotemporal response kernel characterizing the spatiotemporal coupling effect of upstream outflow changes on downstream control section flow changes is constructed. Based on the downstream control section predicted flow process, according to the preset flood control scheduling constraints and scheduling requirements, an inverse optimization objective function containing a downstream flow tracking error term and an outflow adjustment penalty term is constructed. The linearized spatiotemporal response kernel is used as the constraint transfer operator to solve the optimal outflow adjustment sequence that satisfies the physical constraints of reservoir water level and discharge. The initial scheduling scheme is corrected based on the optimal outflow adjustment sequence, and a controllability assessment result is generated to characterize whether the current scenario meets the scheduling requirements through positive verification of the calibrated reservoir-river numerical model.

2. The method according to claim 1, characterized in that, Construct the inverse optimization objective function, including: Based on flood control scheduling constraints and scheduling requirements, the predicted flow process of the downstream control section is re-engineered in time series to generate the target flow process of the downstream control section that includes peak shaving and peak shifting characteristics. The difference between the target flow process and the predicted flow process at the downstream control section is calculated at each time step to obtain the downstream flow error sequence. Construct an inverse optimization objective function, where the downstream flow tracking error term represents the Euclidean distance between the downstream flow error sequence and the optimal outbound adjustment sequence under the linearized spatiotemporal response kernel mapping, and the outbound adjustment penalty term represents the cumulative magnitude of the optimal outbound adjustment sequence and the rate of change of adjacent time steps.

3. The method according to claim 2, characterized in that, Solving for the optimal outbound adjustment sequence includes: Based on the water balance principle followed by the calibrated reservoir-river numerical model, the nonlinear reservoir water level boundary constraint defined in the flood control scheduling constraint is transformed into a linear cumulative constraint on the optimal outflow adjustment sequence. By combining the inverse optimization objective function with linear cumulative constraints and the preset instantaneous amplitude constraints of outbound flow, a constrained quadratic programming model is constructed. Solving the quadratic programming model yields the optimal outflow adjustment sequence that minimizes the inverse optimization objective function while satisfying the reservoir capacity safety and river flow capacity requirements.

4. The method according to claim 1, characterized in that, Constructing a linearized spatiotemporal response kernel includes: During the forecast period of the initial scheduling scheme, unit pulse disturbances are applied step by step at discrete time steps to generate a predetermined group of disturbance outbound scheduling schemes corresponding to different disturbance times. Each group of disturbance outflow scheduling schemes is input into the calibration reservoir-river numerical model to perform forward calculations, and the flow process of the downstream control section corresponding to each disturbance time is obtained. Calculate the flow response increment sequence of the downstream control section flow process relative to the predicted flow process of the downstream control section, and extract the sensitivity coefficient column vector accordingly. Assemble all sensitivity coefficient column vectors in chronological order to generate a linearized spatiotemporal response kernel.

5. The method according to claim 4, characterized in that, The linearized spatiotemporal response kernel is a matrix with a lower triangular or quasi-lower triangular structure. The distribution of non-zero elements in the sensitivity coefficient column vector represents the diffusion and attenuation pattern of flood waves generated by upstream outflow disturbances at a single moment during their evolution along the river channel. By performing matrix multiplication between the linearized spatiotemporal response kernel and the preset outflow adjustment vector, the hydraulic response relationship described by the nonlinear partial differential equations in the calibrated reservoir-channel numerical model is equivalent to a discrete convolution operation near the baseline state.

6. The method according to claim 2, characterized in that, The process of generating the target flow rate at the downstream control section includes: The predicted flow process at the downstream control section is compared with the upper limit of the allowable flow in the flood control scheduling constraints to generate a basic limit flow curve with amplitude truncation. Based on the compensation scheduling strategy in the scheduling requirements, the basic restricted flow curve is forward shifted in the time dimension or the flow setpoint is increased within the time window before the flood peak arrives. This constructs a target flow process for the downstream control section with pre-release characteristics, so as to guide the optimal outflow adjustment sequence to generate scheduling behavior that pre-empties storage capacity in the inverse optimization objective function.

7. The method according to claim 1, characterized in that, Generate controllability assessment results, including: The optimal outbound adjustment sequence is superimposed on the initial scheduling scheme to generate a modified outbound scheduling scheme. The modified outflow scheduling scheme is input into the calibration reservoir-river numerical model to perform a forward hydraulic simulation, which yields the modified reservoir water level process and the modified downstream control section flow process. The system verifies whether the process of adjusting the reservoir water level and the process of adjusting the downstream control section flow simultaneously meet the flood control scheduling constraints. If they do, a controllability assessment result representing the current scenario as controllable is generated. If they do not meet the constraints, a controllability assessment result representing the current scenario as uncontrollable is generated.

8. The method according to claim 7, characterized in that, This also includes constructing a multi-scenario parameter combination set and performing batch evaluation, specifically: Based on the pre-stored historical flood statistics and scheduling management requirements, the parameter dimensions, including the peak inflow amplification factor, the maximum allowable flow at the downstream control section, and the maximum allowable reservoir water level, are determined, and a multi-scenario parameter combination set covering the preset parameter space is generated. For each parameter combination in the multi-scenario parameter combination set, construct the corresponding scenario-level water inflow process and scenario-level scheduling constraints; Based on scenario-level inflow processes and scenario-level scheduling constraints, the calibrated reservoir-river numerical model, linearized spatiotemporal response kernel, and inverse optimization objective function are invoked. For each parameter combination, forward prediction, inverse optimization, and forward verification are performed to generate single-scenario controllability assessment results corresponding to each parameter combination.

9. The method according to claim 8, characterized in that, The controllability assessment results are generated, which further includes constructing the controllability boundary surface, specifically: Using the convergence of the inverse optimization objective function as a binary classification criterion, the parameter combinations that successfully obtain the optimal outbound adjustment sequence that satisfies the physical constraints and pass the positive verification in the multi-scenario parameter combination set are marked as controllable points, forming the controllable domain in the parameter space; The parameter combinations that cannot be solved by reverse optimization of the objective function or that fail to pass the forward verification of the corrected outbound scheduling scheme are marked as uncontrollable points, forming an uncontrollable domain in the parameter space; Extract the critical interface separating the controllable and uncontrollable domains in the parameter space to generate a controllability boundary surface describing the reservoir scheduling system under different combinations of inflow intensity and scheduling criteria.

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