Power station water level prediction control method, system and equipment based on model order reduction and medium

Abstract

The invention discloses a power station water level prediction control method, system and equipment based on model order reduction and a medium, and relates to the technical field of hydropower station engineering automatic regulation and control. The method comprises the following steps: constructing a river channel one-dimensional hydrodynamic model, performing single river channel roughness coefficient calibration, and determining different operation conditions and corresponding constant flow states; when the river channel one-dimensional hydrodynamic model is in a constant flow state, applying a flow sudden change disturbance to perform parameter identification, and establishing an ID model and an IDZ model under different operation conditions; constructing a power station MPC model, and embedding the ID model as a prediction part into the power station MPC model to obtain a power station ID-MPC open-loop control model; and the IDZ model is coupled with the power station ID-MPC open-loop control model, and the output of the power station ID-MPC open-loop control model is transmitted to the IDZ model for water level deviation control. According to the invention, the control precision and real-time performance can be effectively improved.

Description

Technical Field

[0001] This invention relates to the field of automated control technology for hydropower station projects, and in particular to a method, system, equipment, and medium for predicting and controlling hydropower station water levels based on model order reduction. Background Technology

[0002] The upstream water flow of run-of-river hydropower stations is uncertain, and the water flow has a large time lag and many disturbances. The inflow has a strong nonlinear characteristic, which leads to large fluctuations in the water level in front of the dam, which is not conducive to the safe and stable operation of the power station.

[0003] Although various control algorithms are now widely used in water system regulation, such as PID control, fuzzy control, and model predictive control (MPC), they still have certain limitations in practical applications.

[0004] PID control is simple in structure and easy to implement, performing well in steady-state regulation. However, its control effect is limited when dealing with water systems exhibiting time-varying, nonlinear, or hysteresis characteristics. Fuzzy control does not rely on precise mathematical models and is suitable for systems with difficult modeling and complex mechanisms, exhibiting strong robustness and adaptability. However, its control rules depend on expert experience and lack a systematic optimization mechanism, limiting control accuracy and response speed. MPC can consider constraints and achieve rolling optimization, but its performance is highly dependent on the accuracy of the prediction model. Currently used water balance models or single-set ID model parameters have limited prediction accuracy. Furthermore, MPC often uses hydrodynamic models for feedback correction, but the slow model solving speed may cause correction data to fail to be transmitted to the control module in a timely manner, affecting the quality of the control strategy generated in the next moment and reducing the system's real-time response capability and control accuracy. Summary of the Invention

[0005] The purpose of this invention is to provide a power plant water level prediction and control method, system, equipment and medium based on model order reduction, which aims to solve or improve at least one of the above-mentioned technical problems.

[0006] To achieve the above objectives, the present invention provides the following solution:

[0007] A power plant water level prediction and control method based on model order reduction includes:

[0008] A one-dimensional hydrodynamic model of the river channel is constructed, and the roughness coefficient of a single channel is calibrated based on the one-dimensional hydrodynamic model of the river channel to determine different operating conditions and the corresponding steady flow state.

[0009] When the one-dimensional hydrodynamic model of the river channel is in a steady flow state, a sudden flow disturbance is applied to identify parameters and establish ID model and IDZ model under different operating conditions.

[0010] A power plant MPC model is constructed, and the ID model is embedded as a prediction part into the power plant MPC model to obtain the power plant ID-MPC open-loop control model.

[0011] The IDZ model is coupled with the ID-MPC open-loop control model of the power plant, so that the output of the ID-MPC open-loop control model of the power plant is transmitted to the IDZ model for water level deviation control.

[0012] Optionally, a one-dimensional hydrodynamic model of the river channel is constructed, and the roughness coefficient of a single channel is calibrated based on the one-dimensional hydrodynamic model to determine different operating conditions and the corresponding steady flow state, specifically including:

[0013] Constructing a one-dimensional hydrodynamic model of the river channel, the Saint-Venant equations are expressed as follows:

[0014]

[0015] Where B is the cross-sectional width of the water passage, in meters; Z is the water level, in meters; t is the time, in seconds; and Q is the flow rate, in cubic meters per second. 3 / s; x is the longitudinal distance of the channel along the main flow direction, in meters; α is the momentum correction factor; A is the cross-sectional area, in square meters. 2 g is the acceleration due to gravity, in m / s². 2 S f The frictional gradient is given by m; q represents the lateral water flow per unit length of the river channel, with positive values ​​indicating inflow, negative values ​​indicating outflow, and zero values ​​indicating no lateral exchange. 2 / s; z is the water surface elevation, which is the vertical height of the water surface relative to the reference plane, in meters;

[0016] The parameters of the constructed model, such as river roughness, were calibrated. Based on historical monitoring data of flow rate and water level, the range of historical operation was determined. Multi-level test conditions were set to determine different operating conditions and corresponding steady flow states.

[0017] Optionally, when the one-dimensional hydrodynamic model of the river channel is in a steady flow state, a sudden flow disturbance is applied to identify parameters and establish ID models and IDZ models under different operating conditions, specifically including:

[0018] Under steady flow conditions, a sudden flow disturbance is introduced into a one-dimensional hydrodynamic model of the river channel. The water level response process at the downstream section is obtained through model simulation, and the characteristic parameters corresponding to different operating conditions are retrieved based on the simulation results. These parameters include the time delay parameter τ and the high-frequency response coefficient b. d1 b d2 The area A of the return water zone is calculated using the formula. d The time delay parameter τ represents the time difference between the start of the upstream disturbance and the occurrence of the downstream water level response characteristic point; the high-frequency response coefficient bd1 b d2 The parameters were identified using the least squares algorithm to quantify the coupling effect of the flow rate change on the water level gradient.

[0019] The formula for calculating the area of ​​the backwater zone is:

[0020]

[0021] Where ΔH is the change in water level after applying an upstream flow step, in meters; Δt is the duration of the change, in seconds; K is the slope of the water level change, in meters per second; and ΔQ is the flow step, in meters. 3 / s;

[0022] Multivariate fitting methods were used to fit the relevant parameters of the ID model and IDZ model, determine the parametric function relationship, and establish the ID model and IDZ model under different operating conditions.

[0023] Optionally, a power plant MPC model is constructed, and the ID model is embedded as a prediction component into the power plant MPC model to obtain a power plant ID-MPC open-loop control model, specifically including:

[0024] A power plant MPC model is constructed, and the ID model is embedded as a prediction part into the power plant MPC model to obtain the power plant ID-MPC open-loop control model.

[0025] In the ID-MPC open-loop control model of the power plant, the water level difference between adjacent time points is calculated to perform rolling water level prediction, as expressed by the formula:

[0026]

[0027] Where: y(x) is the model output, representing the deviation of the downstream water depth from the steady-state value, in meters; q1 is the change in the upstream inflow relative to the steady-state value, in meters. 3 / s; q2 is the change in downstream outflow relative to the steady-state value, m 3 / s;A d τ is the area of ​​the backwater zone, in m2; τ is the time delay, in s;

[0028] The objective function of the MPC model is defined and solved using the ADMM-based split cone optimization algorithm; wherein the objective function is:

[0029]

[0030] Where J is the cost function, and the optimal control sequence u0, u1, ..., u0 is found to minimize J. N-1 N represents the prediction time domain length, ranging from 0 to N-1 (a total of N terms); x k+1Let m be the predicted water level for the (k+1)th step in the future; x be the predicted water level. target For the target water level, m; u k Let m be the outbound flow rate at step k. 3 / s;u k+1 Let m be the outbound flow rate at step k+1. 3 / s;Q k R represents the penalty weight for state tracking error. k The penalty weight for controlling the magnitude of the quantity; R Δ,k Penalty weights to control the rate of change;

[0031] The objective function is subjected to max-min normalization to avoid excessively large differences in the magnitude of the data between the power station's outflow and water level deviation, which would lead to an imbalance in R. k R Δ,k The weight parameters are too small or ineffective; the normalization function is:

[0032]

[0033] Where: x is the original data value; min(x) is the minimum value in the dataset; max(x) is the maximum value in the dataset; x′ is the normalized value, within the range [0,1];

[0034] Set constraints, including the power station's outflow constraint, the power station's outflow range under a single constraint step, and the power station's operating water level constraint, as shown in the formula: ;

[0035] Control input upper and lower limits: u kd ≤u k ≤u ku ;

[0036] Control amplitude limit: |u k -u k-1 |≤u kb ;

[0037] Water level operation limit: Z min ≤Z≤Z max ;

[0038] Among them, u kd To control the lower limit of outbound flow, m 3 / s;u k Let m be the outbound flow rate at step k. 3 / s;u ku To control the traffic limit, m 3 / s;u k-1 Let m be the outbound flow rate at step k-1. 3 / s;u kb The maximum flow rate deviation between adjacent step sizes, m 3 / s;Z minZ represents the minimum operating water level of the power station, in meters. max Z represents the maximum operating water level of the power station, in meters; Z represents the operating water level range of the power station, in meters.

[0039] Set the prediction time step and perform rolling prediction. By solving the constrained optimization problem in the finite time domain at each sampling time, the optimal control sequence is obtained, and only the first control variable is applied to the system.

[0040] Optionally, the IDZ model is coupled with the power plant ID-MPC open-loop control model, so that the output of the power plant ID-MPC open-loop control model is transmitted to the IDZ model for water level deviation control, specifically including:

[0041] The time-domain expression of the IDZ model is determined, the water level difference between adjacent time points is calculated, and water level rolling prediction is performed. The specific formula is as follows:

[0042]

[0043] Where y(x) is the model output, representing the deviation of the downstream water depth from the steady-state value, in m; q1 is the change in the upstream inflow relative to the steady-state value, in m. 3 / s; q2 is the change in downstream outflow relative to the steady-state value, m 3 / s;A d The area of ​​the backwater zone is in meters. 2 τ is the time delay, in seconds; b d1 and b d2 The coefficients are constants.

[0044] The IDZ model is coupled with the power plant ID-MPC open-loop control model, and the control output of the power plant ID-MPC open-loop control model is transmitted to the IDZ model. The IDZ model is then used to simulate the water level and correct the water level state of the ID-MPC model.

[0045] This invention also provides a power plant water level prediction and control system based on model order reduction, comprising:

[0046] The operating condition determination unit is used to construct a one-dimensional hydrodynamic model of the river channel and calibrate the roughness coefficient of a single channel based on the one-dimensional hydrodynamic model of the river channel to determine different operating conditions and the corresponding steady flow state.

[0047] The parameter identification unit is used to apply a flow change disturbance to identify parameters when the one-dimensional hydrodynamic model of the river channel is in a steady flow state, and to establish the ID model and IDZ model under different operating conditions.

[0048] A power plant water level prediction model construction unit is used to construct a power plant MPC model and embed the ID model as the prediction part into the power plant MPC model to obtain a power plant ID-MPC open-loop control model.

[0049] The water level deviation control unit is used to couple the IDZ model with the power plant ID-MPC open-loop control model, so that the output of the power plant ID-MPC open-loop control model is transmitted to the IDZ model for water level deviation control.

[0050] The present invention also provides an electronic device, including a memory and a processor, wherein the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to perform the power plant water level prediction and control method based on model reduction described above.

[0051] The present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the model-based water level prediction and control method for power plants as described above.

[0052] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0053] This invention discloses a method, system, equipment, and medium for power plant water level prediction and control based on model order reduction. The method includes constructing a one-dimensional hydrodynamic model of the river channel and calibrating the roughness coefficient of the single channel based on the one-dimensional hydrodynamic model to determine different operating conditions and corresponding steady flow states. When the one-dimensional hydrodynamic model of the river channel is in a steady flow state, a sudden flow disturbance is applied to identify parameters and establish ID models and IDZ models under different operating conditions. A power plant MPC model is constructed, and the ID model is embedded into the power plant MPC model as a prediction part to obtain a power plant ID-MPC open-loop control model. The IDZ model is coupled with the power plant ID-MPC open-loop control model, so that the output of the power plant ID-MPC open-loop control model is transmitted to the IDZ model for water level deviation control. This invention reduces the order of the hydrodynamic model to establish a low-order adaptive ID and IDZ model with a linear structure, embeds the adaptive ID model into the MPC framework, and couples the adaptive IDZ model for feedback correction, forming a complete closed-loop control system, effectively improving the control accuracy and real-time performance. Attached Figure Description

[0054] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0055] Figure 1 This is a flowchart illustrating the principle of the model construction method in this embodiment;

[0056] Figure 2 This embodiment presents a closed-loop control system architecture diagram for ID-MPC;

[0057] Figure 3 The simulation results of the ID model and IDZ model in this embodiment are shown in the figure.

[0058] Figure 4 This embodiment shows the water level control process of the closed-loop control system of ID-MPC;

[0059] Figure 5 This embodiment shows the process of measuring and controlling water levels;

[0060] Figure 6 This embodiment presents a comparison chart of actual outbound flow and controlled outbound flow.

[0061] Figure 7 This embodiment presents a diagram of the IDZ model feedback correction ID-MPC water level process. Detailed Implementation

[0062] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0063] The purpose of this invention is to provide a power plant water level prediction and control method, system, equipment and medium based on model order reduction, which aims to solve or improve at least one of the above-mentioned technical problems.

[0064] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0065] Example 1

[0066] like Figure 1As shown in this embodiment, a power station water level prediction and control method based on model order reduction is provided. This method adopts four steps for power station water level prediction and control: construction of a one-dimensional hydrodynamic model of a single channel; adaptive parameter identification of integral time delay model and integral time delay zero model; construction of ID-MPC open-loop control model of hydropower station; and construction of IDZ water level feedback correction model.

[0067] The method proposed in this embodiment includes constructing an adaptive ID-MPC model and coupling it with an adaptive IDZ model for water level deviation correction. This achieves water level prediction and rolling control, providing strong support for the intelligent scheduling and efficient operation of hydropower station systems.

[0068] Specifically, the steps include the following:

[0069] S1. Construct a one-dimensional hydrodynamic model of the river channel, and calibrate the roughness coefficient of a single channel based on the one-dimensional hydrodynamic model of the river channel to determine different operating conditions and the corresponding steady flow state.

[0070] S2. When the one-dimensional hydrodynamic model of the river channel is in a steady flow state, a sudden flow disturbance is applied to identify parameters and establish the ID model and IDZ model under different operating conditions.

[0071] S3. Construct the power plant MPC model and embed the ID model as the prediction part into the power plant MPC model to obtain the power plant ID-MPC open-loop control model.

[0072] S4. Couple the IDZ model with the power plant ID-MPC open-loop control model, and transmit the output of the power plant ID-MPC open-loop control model to the IDZ model for water level deviation control.

[0073] Based on the above steps, it can be seen that the method in this embodiment mainly includes four parts: construction of a one-dimensional hydrodynamic model for a single channel; adaptive parameter identification of the integral time-delay model and the integral time-delay zero model; construction of the ID-MPC open-loop control model for the hydropower station; and construction of the IDZ water level feedback correction model. These four parts will be explained in detail below.

[0074] I. Constructing a one-dimensional hydrodynamic model of a single river channel

[0075] This section corresponds to step S1, specifically:

[0076] A one-dimensional hydrodynamic model of the river channel is constructed, and its Saint-Venant equations are expressed as follows:

[0077]

[0078] Where B is the cross-sectional width of the water passage, in meters; Z is the water level, in meters; t is the time, in seconds; and Q is the flow rate, in cubic meters per second.3 / s; x is the longitudinal distance of the channel along the main flow direction, in meters; α is the momentum correction factor; A is the cross-sectional area, in square meters. 2 g is the acceleration due to gravity, in m / s². 2 S f The frictional gradient is given by m; q represents the lateral water flow per unit length of the river channel, with positive values ​​indicating inflow, negative values ​​indicating outflow, and zero values ​​indicating no lateral exchange. 2 / s.

[0079] The model was calibrated using the river channel roughness parameter to improve its accuracy. Furthermore, based on historical monitoring data of time-series flow and water level, the historical operating range was determined, multi-level experimental conditions were set, and the corresponding steady flow states were obtained.

[0080] II. Parameter Identification of Integral Delay Model and Integral Delay Zero Model

[0081] This section corresponds to step S2, specifically:

[0082] When the one-dimensional hydrodynamic model of the river channel is in a steady flow operation, a sudden flow disturbance is applied to the steady-flow hydrodynamic model to identify parameters, obtaining adaptive parameters for the ID model and IDZ model under different operating conditions. That is, the solution of the high-order Saint-Venant equations, which are generally used for hydraulic simulation, is simplified into two first-order piecewise linearized models (ID model and IDZ model).

[0083] This step specifically includes:

[0084] Under steady flow conditions, a sudden flow disturbance is introduced into a one-dimensional hydrodynamic model. The water level response process at the downstream section is obtained through model simulation, and the characteristic parameters corresponding to different operating conditions are retrieved based on the simulation results. These parameters include the time delay parameter τ and the high-frequency response coefficient b. d1 b d2 The area A of the return water zone is calculated using the formula. d The time delay parameter τ represents the time difference between the onset of the upstream disturbance and the occurrence of the characteristic point of the downstream water level response, while the high-frequency response coefficient b... d1 b d2 The parameters were identified using a least squares algorithm to quantify the coupling effect of flow rate change on water level gradient.

[0085] The formula for calculating the area of ​​the backwater zone is:

[0086]

[0087] Where ΔH is the change in water level after applying an upstream flow step, in meters; Δt is the duration of the change, in seconds; K is the slope of the water level change, in meters per second; and ΔQ is the flow step, in meters. 3 / s.

[0088] Multivariate fitting methods are used to fit the relevant parameters of the ID model and the IDZ model to determine the parametric function relationship, which facilitates interpolation solutions.

[0089] III. Construction of Open-Loop Control Model for Hydropower Station ID-MPC

[0090] This section corresponds to step S3, specifically:

[0091] The time-domain expression of the ID model is introduced and embedded in the MPC model as the model prediction part. It calculates the water level difference between adjacent time points and performs rolling water level prediction. The specific formula is as follows:

[0092]

[0093] Where: y(x) is the model output, representing the deviation of the downstream water depth from the steady-state value, in meters; q1 is the change in the upstream inflow relative to the steady-state value, in meters. 3 / s; q2 is the change in downstream outflow relative to the steady-state value, m 3 / s;A d τ represents the area of ​​the backwater zone, in m2; τ represents the time delay, in s.

[0094] The objective function of the MPC model is defined, and the solution is obtained using a split cone optimization algorithm based on ADMM (Alternating Direction Multiplier Method). This invention does not limit the solution method. The objective function is as follows:

[0095]

[0096] Where J is the cost function, and the optimal control sequence u0, u1, ..., u0 is found to minimize J. N-1 N represents the prediction time domain length, ranging from 0 to N-1 (a total of N terms); x k+1 Let m be the predicted water level for the (k+1)th step in the future; x be the predicted water level. target For the target water level, m; u k Let m be the outbound flow rate at step k. 3 / s;u k+1 Let m be the outbound flow rate at step k+1. 3 / s;;Q k R represents the penalty weight for state tracking error. k To control the penalty weights for the magnitude of the quantity, R k The larger the value, the more it inhibits large control actions; R Δ,k The larger the penalty weight for controlling the rate of change, the smoother the control action.

[0097] The objective function is subjected to max-min normalization to avoid excessively large differences in the magnitude of the data between the power station's outflow and water level deviation, which would lead to an imbalance in R. k RΔ,k The weight parameters are too small or ineffective. The normalization function is as follows:

[0098]

[0099] Where: x is the original data value; min(x) is the minimum value in the dataset; max(x) is the maximum value in the dataset; x′ is the normalized value, which is in the range [0,1].

[0100] The constraints mainly include the power station's outflow constraint, the power station's outflow range under a single constraint step, and the power station's operating water level constraint. The specific formulas are as follows:

[0101] Control input upper and lower limits:

[0102] u kd ≤u k ≤u ku

[0103] Control amplitude limit:

[0104] |u k -u k-1 |≤u kb

[0105] Water level operation restrictions:

[0106] Z min ≤Z≤Z max

[0107] Where: u kd To control the lower limit of outbound flow, m 3 / s;u k Let m be the outbound flow rate at step k. 3 / s;u ku To control the traffic limit, m 3 / s;u k-1 Let m be the outbound flow rate at step k-1. 3 / s;u kb The maximum flow rate deviation between adjacent step sizes, m 3 / s;Z min Z represents the minimum operating water level of the power station, in meters. max Z represents the maximum operating water level of the power station, in meters; Z represents the operating water level range of the power station, in meters.

[0108] Set the prediction time step size. A prediction time step that is too short will result in a model that lacks foresight; a prediction time step that is too long will lead to an excessively large solution dimension, abnormal solutions, and low prediction accuracy.

[0109] Model rolling prediction. By solving the constrained optimization problem in the finite time domain at each sampling time, the optimal control sequence is obtained, and only the first control variable is applied to the system. As the time domain rolls forward, the optimization objective is continuously updated, achieving dynamic rolling optimization control of the system.

[0110] IV. Construction of IDZ Water Level Feedback Correction Model

[0111] This section corresponds to step S4, specifically:

[0112] By introducing the time-domain expression of the IDZ model, the water level difference between adjacent time points is calculated to perform rolling water level prediction. The specific formula is as follows:

[0113]

[0114] Where: y(x) is the model output, representing the deviation of the downstream water depth from the steady-state value, in meters; q1 is the change in the upstream inflow relative to the steady-state value, in meters. 3 / s; q2 is the change in downstream outflow relative to the steady-state value, m 3 / s;A d τ is the area of ​​the backwater zone, m2; τ is the time delay, s; b d1 and b d2 Constant coefficients.

[0115] The IDZ model and the ID-MPC model are coupled together. The control output of the ID-MPC model is transmitted to the IDZ model. The IDZ model simulates the water level to correct the water level state of the ID-MPC model and then performs the next rolling prediction. This avoids errors caused by disturbance factors or the accuracy of the prediction model, which could lead to excessive deviation of the initial state of the rolling correction at the next time step.

[0116] Example 2

[0117] To better illustrate the execution process of the method of the present invention, this example takes the Pubugou-Shenxigou Hydropower Station in the Dadu River Basin as an example, and selects 14000 min (5 min step) data (flow rate and water level) of a certain month in 2023 to construct and display the results of the hydropower station water level prediction model based on model order reduction.

[0118] Based on the Saint-Venant equations, a one-dimensional hydrodynamic model for a single channel is constructed. Under steady flow conditions, the adaptive parameters of ID and IDZ are identified using the calibrated hydrodynamic model. The identified adaptive ID parameters are then embedded into the prediction module of the MPC model, thereby constructing an ID-MPC open-loop control model suitable for hydropower station operation. Simultaneously, the IDZ model is coupled to correct the water level of the control model in real time, forming a closed-loop test system of the control model (ID-MPC) and the simulation model (IDZ).

[0119] To better understand the model building process, a closed-loop control system architecture diagram of ID-MPC is drawn, as shown below. Figure 2 As shown;

[0120] Taking the Shenxigou Hydropower Station as the research object, a one-dimensional hydrodynamic model of the river channel was constructed based on the Saint-Venant equations, and the comprehensive roughness coefficient of the river channel was calibrated using historical hydrological data. A model covering 550-3550m was designed to address the typical hydrological characteristics of 2023. 3 / s (step length 1000m) 3 Under a multi-stage flow rate condition (655-660m / s), combined with the downstream water level control requirement of 655-660m (gradient 1-2m), the target water level is stabilized under different flow rates by adjusting the outflow. Based on this, a 5% abrupt disturbance is applied to the initial upstream flow rate (i.e., adjusted to 577.5, 1627.5, 2782.5, 3832.5m). 3 The system was simulated to transition from steady state to a new equilibrium ( / s). By monitoring the water level-flow response curve and combining it with parameter identification methods, the characteristic values ​​of the IDZ parameters were extracted (see Tables 1 to 4), providing key parameter support for subsequent dynamic characteristic analysis.

[0121] Table 1 Parameter Results (m 2 )

[0122]

[0123] Table 2 τ parameter results (min)

[0124]

[0125] Table 3b d1 Parameter results

[0126]

[0127]

[0128] Table 4b d2 Parameter results

[0129]

[0130] A bivariate fitting (steady water level, initial flow rate) was performed on Tables 1 to 4, and the fitting function relationship is as follows:

[0131] Relation 1:

[0132] A d (x,y)=3257861654.2810-9995338.3353x+2085.3685y

[0133] +7670.1996x2 -3.4832xy+0.0218y 2

[0134] Relation 2:

[0135] τ(x,y)=-20230.8735-62.1985x-0.0040y-0.0477x 2 +0.0000005y 2

[0136] Relationship 3:

[0137] b d1 (x,y)=-0.4776+0.0015x+0.00000164y-0.00000111x 2

[0138] Relation 4:

[0139] b d2 (x,y)=1.8330-0.0057x+0.00000584y+0.00000436x 2

[0140] -0.00000001xy

[0141] Where: x is the downstream stable water level, m; y is the initial flow rate, m. 3 / s.

[0142] For the Pubugou-Shenxigou river channel, an ID-MPC closed-loop control system was constructed. First, the objective function was defined and normalized. The normalized maximum and minimum values ​​were set as follows: the water level operating range was 5m, the maximum water level deviation was 5m, and the minimum was 0m; the flow rate was consistent with the outflow constraint, with a maximum flow rate set at 3550m³. 3 / s, minimum value is 0m 3 / s; the flow rate variation is consistent with the flow rate variation constraint, with a maximum flow rate of 500m³ / s. 3 / s, minimum 0m 3 / s. The water level operating range is constrained to 655~660m, and the outflow variation constraint is set to 0~500m. 3 / s, the upper and lower limits of outbound flow rate are set to 0~3550m³ / s. 3 / s.

[0143] Regarding model parameter assignment, the parameters of the ID and IDZ models are adaptively obtained through a bivariate fitting function; the remaining parameters are manually set based on experience, and corresponding weight coefficients are assigned to the relevant parts. In this case, the weight is assigned 1, the weight is assigned 0.002, and the initial weight is assigned 0.01. The predicted time domain N is assigned 10, the target water level is 659.1, and the initial water level is provided by the feedback correction model.

[0144] The test results are as follows:

[0145] (1) The ID model and IDZ model have high accuracy when performing simulations based on historical time-series data. In particular, the IDZ model has a Nash coefficient of approximately 0.98, which can be used as a high-fidelity simulation model under control scenarios to replace the actual values ​​under control scenarios (the control conditions do not yet exist, so the actual values ​​cannot be used for effective correction; the high-fidelity simulation model can serve as an effective substitute). See details. Figure 3 .

[0146] (2) The target water level was set to 659.1 m. The water level control process of the ID-MPC closed-loop control system was output. The water level control effect was good, and the water level control deviation was significantly less than 0.05 m. See details. Figure 4 .

[0147] (3) Verify the rationality of the control model, and output the historical water level and controlled water level processes, as well as the historical outflow and controlled outflow processes. Verification revealed that under 14000 minutes of control performance, the cumulative flow error was approximately 4800 m³ / min. 3 / s, with a cumulative error of approximately 0.19% and an average flow rate error of approximately 0.34m³. 3 / s, the error is within a reasonable range. See details. Figure 5 and Figure 6 .

[0148] (4) To determine the effectiveness of the IDZ feedback correction, the water level predicted by the ID-MPC is output and compared with the feedback correction effect. The correction effect of the IDZ model at high frequencies is clearly visible. However, due to the small control time step, the flow deviation at a single step size results in a relatively small magnitude of water level deviation. See details... Figure 7 .

[0149] In summary, the power plant water level prediction and control method based on model order reduction of the present invention can effectively control the operating water level of the power plant.

[0150] By adopting the above-disclosed technical solution of this invention, the following beneficial effects are obtained:

[0151] This invention provides a power plant water level prediction and control method based on model order reduction. The method proposes a control architecture based on adaptive ID-MPC, which significantly improves the accuracy of water level prediction and the foresight of the control strategy by integrating adaptive parameters and a rolling optimization mechanism, possessing both rolling prediction and real-time control capabilities. To address the water level fluctuation problem caused by high-frequency control actions, an adaptive IDZ feedback correction module is designed, which effectively compensates for the state deviation of the ID-MPC prediction model under sudden flow changes through a dynamic feedback mechanism. Both the constructed prediction and correction models are based on linearized structures, inheriting the physical characteristics of the hydrodynamic model, achieving high-precision simulation while ensuring computational efficiency, and solving the problem of mismatch between traditional reduced-order models and actual flow characteristics.

[0152] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0153] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A power station water level prediction and control method based on model order reduction, characterized in that, include: A one-dimensional hydrodynamic model of the river channel is constructed, and the roughness coefficient of a single channel is calibrated based on the one-dimensional hydrodynamic model of the river channel to determine different operating conditions and the corresponding steady flow state. When the one-dimensional hydrodynamic model of the river channel is in a steady flow state, a sudden flow disturbance is applied to identify parameters and establish ID model and IDZ model under different operating conditions. A power plant MPC model is constructed, and the ID model is embedded as a prediction part into the power plant MPC model to obtain the power plant ID-MPC open-loop control model. The IDZ model is coupled with the ID-MPC open-loop control model of the power plant, so that the output of the ID-MPC open-loop control model of the power plant is transmitted to the IDZ model for water level deviation control.

2. The power plant water level prediction and control method based on model order reduction according to claim 1, characterized in that, A one-dimensional hydrodynamic model of the river channel is constructed, and the roughness coefficient of a single channel is calibrated based on the one-dimensional hydrodynamic model to determine different operating conditions and the corresponding steady flow state, specifically including: Constructing a one-dimensional hydrodynamic model of the river channel, the Saint-Venant equations are expressed as follows: Where B is the cross-sectional width of the water passage, in meters; Z is the water level, in meters; t is the time, in seconds; and Q is the flow rate, in cubic meters per second. 3 / s; x is the longitudinal distance of the channel along the main flow direction, in meters; α is the momentum correction factor; A is the cross-sectional area, in square meters. 2 g is the acceleration due to gravity, m / s² 2 S f The frictional gradient is given by m; q represents the lateral water flow per unit length of the river channel, with positive values ​​indicating inflow, negative values ​​indicating outflow, and zero values ​​indicating no lateral exchange. 2 / s; z is the water surface elevation, in meters; The parameters of the constructed model, such as river roughness, were calibrated. Based on historical monitoring data of flow rate and water level, the range of historical operation was determined. Multi-level test conditions were set to determine different operating conditions and corresponding steady flow states.

3. The power plant water level prediction and control method based on model order reduction according to claim 1, characterized in that, When the one-dimensional hydrodynamic model of the river channel is in a steady flow state, a sudden flow disturbance is applied to identify parameters, and ID models and IDZ models under different operating conditions are established, specifically including: Under steady flow conditions, a sudden flow disturbance is introduced into a one-dimensional hydrodynamic model of the river channel. The water level response process at the downstream section is obtained through model simulation, and the characteristic parameters corresponding to different operating conditions are retrieved based on the simulation results. These parameters include the time delay parameter τ and the high-frequency response coefficient b. d1 b d2 The area A of the return water zone is calculated using the formula. d The time delay parameter τ represents the time difference between the start of the upstream disturbance and the occurrence of the downstream water level response characteristic point; the high-frequency response coefficient b d1 b d2 The parameters were identified using the least squares algorithm to quantify the coupling effect of the flow rate change on the water level gradient. The formula for calculating the area of ​​the backwater zone is: Where ΔH is the change in water level after applying an upstream flow step, in meters; Δt is the duration of the change, in seconds; K is the slope of the water level change, in meters per second; and ΔQ is the flow step, in meters. 3 / s; Multivariate fitting methods were used to fit the relevant parameters of the ID model and IDZ model, determine the parametric function relationship, and establish the ID model and IDZ model under different operating conditions.

4. The power plant water level prediction and control method based on model order reduction according to claim 1, characterized in that, A power plant MPC model is constructed, and the ID model is embedded as a prediction component into the power plant MPC model to obtain the power plant ID-MPC open-loop control model, which specifically includes: A power plant MPC model is constructed, and the ID model is embedded as a prediction part into the power plant MPC model to obtain the power plant ID-MPC open-loop control model. In the ID-MPC open-loop control model of the power plant, the water level difference between adjacent time points is calculated to perform rolling water level prediction, as expressed by the formula: Where: y(x) is the model output, representing the deviation of the downstream water depth from the steady-state value, in meters; q1 is the change in the upstream inflow relative to the steady-state value, in meters. 3 / s; q2 is the change in downstream outflow relative to the steady-state value, m 3 / s;A d τ is the area of ​​the backwater zone, in m2; τ is the time delay, in s; The objective function of the MPC model is defined and solved using the ADMM-based split cone optimization algorithm; wherein the objective function is: Where J is the cost function, and the optimal control sequence u0, u1, ..., u0 is found to minimize J. N-1 N represents the prediction time domain length, ranging from 0 to N-1 (a total of N terms); x k+1 Let m be the predicted water level for the (k+1)th step in the future; x be the predicted water level. target Target water level, m; u k Let m be the outbound flow rate at step k. 3 / s;u k+1 Let m be the outbound flow rate at step k+1. 3 / s;Q k R represents the penalty weight for state tracking error. k The penalty weight for controlling the magnitude of the quantity; R Δ,k Penalty weights to control the rate of change; The objective function is subjected to max-min normalization to avoid excessively large differences in the magnitude of the data between the power station's outflow and water level deviation, which would lead to an imbalance in R. k R Δ,k The weight parameters are too small or ineffective; the normalization function is: Where: x is the original data value; min(x) is the minimum value in the dataset; max(x) is the maximum value in the dataset; x′ is the normalized value, within the range [0,1]; Set constraints, including the power station's outflow constraint, the power station's outflow range under a single constraint step, and the power station's operating water level constraint, as shown in the formula: ; Control input upper and lower limits: u kd ≤u k ≤u ku ; Control amplitude limit: |u k -u k-1 |≤u kb ; Water level operation limit: Z min ≤Z≤Z max ; Among them, u kd To control the lower limit of outbound flow, m 3 / s;u k Let m be the outbound flow rate at step k. 3 / s;u ku To control the traffic limit, m 3 / s;u k-1 Let m be the outbound flow rate at step k-1. 3 / s;u kb The maximum flow rate deviation between adjacent step sizes, m 3 / s;Z min Z represents the minimum operating water level of the power station, in meters. max Z represents the maximum operating water level of the power station, in meters; Z represents the operating water level range of the power station, in meters. Set the prediction time step and perform rolling prediction. By solving the constrained optimization problem in the finite time domain at each sampling time, the optimal control sequence is obtained, and only the first control variable is applied to the system.

5. The power station water level prediction and control method based on model order reduction according to claim 1, characterized in that, The IDZ model is coupled with the power plant ID-MPC open-loop control model, so that the output of the power plant ID-MPC open-loop control model is transmitted to the IDZ model for water level deviation control. Specifically, this includes: The time-domain expression of the IDZ model is determined, the water level difference between adjacent time points is calculated, and water level rolling prediction is performed. The specific formula is as follows: Where y(x) is the model output, representing the deviation of the downstream water depth from the steady-state value, in m; q1 is the change in the upstream inflow relative to the steady-state value, in m. 3 / s; q2 is the change in downstream outflow relative to the steady-state value, m 3 / s;A d The area of ​​the backwater zone is in meters. 2 τ is the time delay, in seconds; b d1 and b d2 The coefficients are constants. The IDZ model is coupled with the power plant ID-MPC open-loop control model, and the control output of the power plant ID-MPC open-loop control model is transmitted to the IDZ model. The IDZ model is then used to simulate the water level and correct the water level state of the ID-MPC model.

6. A power station water level prediction and control system based on model order reduction, characterized in that, include: The operating condition determination unit is used to construct a one-dimensional hydrodynamic model of the river channel and calibrate the roughness coefficient of a single channel based on the one-dimensional hydrodynamic model of the river channel to determine different operating conditions and the corresponding steady flow state. The parameter identification unit is used to apply a flow change disturbance to identify parameters when the one-dimensional hydrodynamic model of the river channel is in a steady flow state, and to establish the ID model and IDZ model under different operating conditions. A power plant water level prediction model construction unit is used to construct a power plant MPC model and embed the ID model as the prediction part into the power plant MPC model to obtain a power plant ID-MPC open-loop control model. The water level deviation control unit is used to couple the IDZ model with the power plant ID-MPC open-loop control model, so that the output of the power plant ID-MPC open-loop control model is transmitted to the IDZ model for water level deviation control.

7. An electronic device, characterized in that, The device includes a memory and a processor, wherein the memory stores a computer program and the processor runs the computer program to enable the electronic device to perform the power plant water level prediction and control method based on model reduction according to any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, It stores a computer program, which, when executed by a processor, implements the power plant water level prediction and control method based on model reduction as described in any one of claims 1-5.

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