Economic dispatching method for variable frequency hybrid pumped storage station and gate valve based on dynamic optimization of front pool water level

Abstract

This invention discloses a method for coordinated economic scheduling of power frequency and variable frequency hybrid cascade pumping stations and gate valves based on dynamic optimization of forebay water level. The method collects static parameters and real-time operating data of the water diversion project; constructs a pumping station characteristic curve model covering four operating conditions: single pump operation, power frequency parallel operation, variable frequency parallel operation, and power frequency and variable frequency hybrid operation; uses forebay water level as the optimization decision variable, iterates through different forebay water levels and calculates the total system power, determines the optimal speed combination through speed optimization, and constructs a drift law library of water supply flow and optimal forebay water level; establishes an economic scheduling model with the goal of minimizing pump power consumption cost, using forebay water level as a dynamic decision variable and obtaining the safe operating boundary based on the drift law library; monitors water supply deviation at each scheduling moment, and when the deviation exceeds a threshold, re-solves the model using the actual forebay water level and remaining water demand as boundary conditions, generates a scheduling plan for the remaining time period, and issues it for execution.

Description

Technical Field

[0001] This invention relates to the field of water conservancy engineering technology, specifically to an economical scheduling method for a hybrid cascade pumping station and gate valves based on dynamic optimization of the forebay water level. Background Technology

[0002] Long-distance water diversion projects are an important means to address the uneven spatial and temporal distribution of water resources and achieve optimal allocation of regional water resources. With the acceleration of urbanization and economic and social development in my country, inter-basin, long-distance water diversion projects are playing an increasingly crucial role in ensuring urban and rural water supply security and improving the regional ecological environment. As the core power facilities of long-distance water diversion projects, cascade pumping stations undertake the core task of progressively lifting and transporting water from the source to higher water-receiving areas. The energy consumption of these pumping stations directly determines the long-term operating cost of the project and is a core indicator for evaluating the economic efficiency of the dispatching scheme.

[0003] Currently, research on the optimal scheduling technology of cascade pumping stations mainly focuses on the following aspects: First, pump unit combination optimization based on pump characteristic curves, which aims to ensure the pumping station operates within its high-efficiency range by selecting a reasonable number and combination of pump units. Second, operating condition adjustment based on variable frequency speed control technology, which achieves precise matching of flow rate and head by changing the pump speed. Third, operation strategy optimization based on time-of-use electricity pricing, which shifts some water supply tasks during high-energy-consumption periods to low-electricity-price periods to reduce electricity costs. However, most existing research focuses on single-frequency or single-variable-frequency pumping station scenarios, with insufficient research on complex pumping station systems with mixed configurations of frequency and variable-frequency units.

[0004] The following key technical issues exist in the actual operation of the power frequency and variable frequency hybrid pump station:

[0005] First, there are significant differences in characteristics between fixed-frequency and variable-frequency units. Fixed-frequency pumps have a fixed rated speed and a unique operating point; variable-frequency pumps, on the other hand, can continuously adjust their speed, and their performance curves change dynamically with the speed. When the two types of units are connected in parallel, there is a strong nonlinear hydraulic coupling relationship. Traditional simple superposition performance curve modeling methods cannot accurately depict the operating point of multiple units operating together, the matching law between total flow and total power, and the energy consumption calculation has a large deviation.

[0006] Secondly, the forebay water level directly determines the system's static head, and its changes have a two-way effect on pump station energy consumption: raising the forebay water level can reduce the static water level difference that the pumps need to overcome, but it will force the unit's operating point to shift towards the high flow range, which can easily cause a significant decrease in pump operating efficiency and an increase in actual shaft power instead of a decrease. Existing scheduling methods generally set the forebay water level as a fixed boundary parameter, without including it in the optimization variables, and thus cannot explore the energy consumption reduction potential brought about by water level regulation.

[0007] Third, there is a complex hydraulic coupling relationship between the cascade pumping stations and the gate valve system. The pumping volume of each pumping station, the opening degree of the gate valve and the head loss of the pipeline affect each other. In addition, multiple factors such as time-of-use electricity price fluctuations and reservoir water level changes make the overall economic dispatch problem exhibit highly nonlinear, multi-constraint and strongly coupled characteristics.

[0008] In practical engineering, existing scheduling schemes largely rely on manual experience or offline optimization, lacking the ability to compensate for water demand deviations and execution errors in real time. When actual operating conditions deviate from the plan, static scheduling schemes cannot adaptively adjust, leading to a significant decrease in operational economy. Furthermore, the start-up and shutdown of power frequency units are subject to complex timing constraints such as minimum continuous operating time and maximum number of start-ups and shutdowns, further increasing the difficulty of generating scheduling schemes.

[0009] In summary, the existing technology lacks a comprehensive optimization scheduling method that can simultaneously take into account accurate modeling of variable frequency hybrid pumping stations, dynamic optimization of forebay water level, coordinated economic scheduling of gate valves in cascade pumping stations, and adaptive rolling updates. Summary of the Invention

[0010] The purpose of this application is to provide an economical scheduling method for a hybrid cascade pumping station and gate valve based on dynamic optimization of the forebay water level.

[0011] To achieve the above objectives, this invention provides a method for the coordinated and economical scheduling of a hybrid cascade pumping station and gate valves based on dynamic optimization of the forebay water level, comprising the following steps:

[0012] Collect static parameters and real-time operational data of the water diversion project; the real-time operational data includes at least the forebay water level, reservoir water level, pipeline flow rate, and time-of-use electricity price of the power grid;

[0013] A pump station characteristic curve model is constructed for parallel operation of power frequency pump sets under multiple operating conditions. The multiple operating conditions include single pump operation, parallel operation of power frequency pump sets, parallel operation of variable frequency pump sets, and mixed operation of power frequency and variable frequency pump sets. Among them, each pump set operating in parallel has the same head at the same node, and the total flow of the system is equal to the sum of the flow of each pump set in parallel.

[0014] Based on the pump station characteristic curve model, the total system flow rate is obtained. The forebay water level is used as the optimization decision variable. Within the water level safety constraint range, different forebay water levels are traversed and the corresponding total power of the pump station system is calculated. The optimal speed combination corresponding to each forebay water level is determined by speed optimization, thereby obtaining the optimal forebay water level under different water supply flow rates and constructing a drift law library between water supply flow rate and optimal forebay water level.

[0015] A coordinated economic scheduling model for gate valves of cascade pumping stations is established with the goal of minimizing the power consumption cost of water pumps within the scheduling cycle. The water level of the forebay is incorporated as a dynamic decision variable into the coordinated economic scheduling model for gate valves of cascade pumping stations, and the safe operating boundary of the water level of the forebay is obtained from the drift law library based on the current water supply flow.

[0016] At each scheduling moment within the scheduling cycle, the deviation between the actual water supply and the planned water supply is compared with a preset threshold. When the deviation exceeds the preset threshold, the actual forebay water level and the remaining water demand are used as the initial boundary conditions. The corrected forebay water level setting trajectory is extracted from the drift law library, and the cascade pump station and gate valve coordinated economic scheduling model is re-solved to generate a pump station and gate valve coordinated scheduling scheme for the remaining time period of the day and issue it for execution.

[0017] Preferably, the static parameters of the project include: pump station unit fitting coefficient, pipeline length, pipeline diameter, pipeline friction coefficient, forebay surface area, reservoir characteristic water level, and valve flow coefficient; the real-time operating data include: forebay water level, high-level water tank water level, reservoir water level, pipeline flow rate, unit operating status, and grid time-of-use electricity price.

[0018] Preferably, the construction of the pump station characteristic curve model for the variable frequency pump set under multiple operating conditions in parallel includes:

[0019] Generate single-pump characteristic curves for the power frequency pump set: Collect multiple sets of measured data on flow rate, head, power, and efficiency of a single power frequency pump at its rated speed, and establish flow rate-head characteristic curves, flow rate-power characteristic curves, and flow rate-efficiency characteristic curves using quadratic polynomials to obtain the single-pump characteristic curves of the power frequency pump set; the speed of the power frequency pump is fixed, and the fitted single-pump characteristic curves of the power frequency pump set are used for single-pump operating condition calculations.

[0020] Variable frequency pump reference curve fitting and speed conversion: The reference characteristic curve is obtained by second fitting of the rated operating condition data of the variable frequency pump. The speed ratio is defined as the ratio of the actual speed to the rated speed. Based on the pump similarity law, the real-time characteristic curve of the variable frequency pump under different operating speeds is calculated.

[0021] Based on the constraints of equal pump head and total system flow equal to the sum of flow rates of all parallel pump sets, characteristic curve models of the pump station are constructed for single-pump operation, parallel operation of power frequency pump sets, parallel operation of variable frequency pump sets, and mixed operation of power frequency and variable frequency pump sets.

[0022] For single-pump operation, the single-pump characteristic curve of the power frequency pump set or the real-time characteristic curve of the variable frequency pump is directly used as the characteristic curve model of the pump station.

[0023] For parallel operation of power frequency pump sets, the individual pump characteristic curves of each power frequency pump participating in the parallel operation are used as input. Under a given head condition, the flow rate of each pump is calculated using the flow-head characteristic curves of each power frequency pump set, and the total system flow rate is obtained by summing them. The data point set of head-to-flow rate is obtained by traversing different head values, and the head-flow rate joint characteristic curve of the power frequency pump set is obtained by fitting. The power-flow rate joint characteristic curve and the efficiency-flow rate joint characteristic curve of the power frequency pump set are obtained according to the same principle. The head-flow rate joint characteristic curve, the power-flow rate joint characteristic curve, and the efficiency-flow rate joint characteristic curve of the power frequency pump set constitute the pump station characteristic curve model.

[0024] For parallel operation of variable frequency pump sets, the real-time characteristic curves of each variable frequency pump set at its respective operating speed are used as input. Based on parallel constraints, the flow rates of each pump are calculated and accumulated to obtain the total system flow rate under given head and actual speed ratio conditions. Different combinations of head and actual speed ratio are traversed to obtain data point sets and fit them to obtain the head-flow rate joint characteristic curve of the variable frequency pump set. The power-flow rate joint characteristic curve and the efficiency-flow rate joint characteristic curve of the variable frequency pump set are obtained according to the same principle. The head-flow rate joint characteristic curve, the power-flow rate joint characteristic curve, and the efficiency-flow rate joint characteristic curve of the variable frequency pump set constitute the pump station characteristic curve model.

[0025] For the mixed operation of power frequency and variable frequency pump sets, the single pump characteristic curve of the power frequency pump set and the real-time characteristic curve of the variable frequency pump set are used as inputs. Based on parallel constraints, the total flow rate of the power frequency part and the variable frequency part are calculated separately and then added together to obtain the total system flow rate. Under the condition of setting the head calculation range and the speed ratio range, different head and speed ratio combinations are traversed to obtain the data point set, and a fully connected neural network model is used to fit the head-flow characteristic curve of the power frequency and variable frequency pump set pump station. Based on the same principle, the power-flow joint characteristic curve and the efficiency-flow joint characteristic curve of the power frequency and variable frequency pump set are obtained. The head-flow joint characteristic curve, the power-flow joint characteristic curve, and the efficiency-flow joint characteristic curve of the power frequency and variable frequency pump set constitute the pump station characteristic curve model.

[0026] Preferably, the acquired data point set is fitted using a fully connected neural network model to obtain the head-flow characteristic curve of the power frequency variable frequency pump unit, and the power-flow joint characteristic curve and the efficiency-flow joint characteristic curve of the power frequency variable frequency pump unit are obtained according to the same principle, including:

[0027] The flow rates of each pump in the power frequency pump group and the variable frequency pump group at the same head are superimposed to obtain the total system flow rate corresponding to that head. All combinations within the set head calculation range and speed ratio range are traversed to form a set of joint characteristic data points with head and speed ratio of each variable frequency pump as input and total system flow rate as output.

[0028] The joint characteristic data point set is trained and fitted using a fully connected neural network model to obtain the joint characteristic curve of the power frequency variable frequency pump set, that is, the function relationship between the total system flow and the head and the speed ratio of each variable frequency pump.

[0029] Based on the combined head-flow characteristic curve of the power frequency variable frequency pump set, the corresponding total system flow is calculated under a given head and speed ratio combination. Then, the total system flow is substituted into the power-flow characteristic curve of each pump set, and the total system power is obtained by summing them up. In this way, the correspondence between the total system power and the total system flow is established, and the combined power-flow characteristic curve of the power frequency variable frequency pump set is obtained by fitting.

[0030] Based on the combined head-flow characteristic curve of the power frequency variable frequency pump set, the corresponding total system flow rate is calculated under a given head and speed ratio combination. Then, the total system flow rate is substituted into the efficiency-flow characteristic curve of each pump set, and the overall system efficiency is calculated by weighting by flow rate. Finally, the correspondence between the overall system efficiency and the total system flow rate is established, and the combined efficiency-flow characteristic curve of the power frequency variable frequency pump set is obtained by fitting.

[0031] Preferably, the process involves obtaining the total system flow rate based on the pump station characteristic curve model, using the forebay water level as the optimization decision variable, traversing different forebay water levels within the water level safety constraint range, and calculating the corresponding total power of the pump station system; determining the optimal speed combination corresponding to each forebay water level through speed optimization, thereby obtaining the optimal forebay water level under different water supply flow rates, and constructing a drift law library between water supply flow rate and optimal forebay water level, including:

[0032] The range of water levels in the forebay is defined, and the upper and lower limits of the range are determined by the design maximum and design minimum water levels in the forebay.

[0033] Within the traversal range, values ​​are discretely selected according to a preset step size to obtain multiple candidate forebay water levels;

[0034] For each candidate forebay water level, based on the current water supply flow demand and the pump station characteristic curve model, and under the condition of satisfying the speed ratio constraints of each variable frequency pump, with the goal of minimizing the total power of the pump station system, the optimal speed ratio combination of each variable frequency pump is calculated using an optimization algorithm, so that the pump station system outputs the target flow with the minimum total power at the forebay water level.

[0035] Record the minimum total power of the pumping station system corresponding to each candidate forebay water level and its corresponding optimal speed ratio combination;

[0036] Multiple typical water supply flow values ​​are set, which cover the range from the minimum to the maximum water supply flow of the water diversion project;

[0037] For each typical water supply flow, the forebay water level is traversed and the minimum total power of the pumping station system corresponding to each candidate water level is calculated. The forebay water level corresponding to the minimum total power is selected as the optimal forebay water level under that water supply flow.

[0038] Each typical water supply flow rate is associated with and stored in conjunction with its corresponding optimal forebay water level, minimum total system power, and corresponding optimal speed ratio, forming a mapping relationship between water supply flow rate and optimal forebay water level, thereby constructing the drift law library.

[0039] Preferably, the step of calculating the optimal speed ratio combination for each variable frequency pump using an optimization algorithm includes:

[0040] The head-flow combined characteristic curve and the power-flow combined characteristic curve in the pump station characteristic curve model are used as inputs for constraints and cost functions;

[0041] An optimization problem is established with the goal of minimizing the total power of the pumping station system. The decision variables of the optimization problem are the speed ratio of each variable frequency pump and the flow distribution of each pump group. The constraints include the total system flow being equal to the target water supply flow, the system head being equal to the current system head corresponding to the forebay water level, the speed ratio of each variable frequency pump being within the allowable range, and the flow of each pump group being within the allowable operating range.

[0042] The optimization problem is solved using an optimization algorithm to obtain the optimal speed ratio combination of each variable frequency pump and the optimal flow distribution scheme of each pump group;

[0043] The construction of the drift pattern library also includes:

[0044] When the current water supply flow does not fall within the typical water supply flow value, the corresponding optimal forebay water level is obtained by interpolation from the mapping relationship using an interpolation method.

[0045] Based on the time-of-use electricity price information of the power grid, the optimal forebay water level corresponding to different electricity price periods under each typical water supply flow is associated and stored in the drift pattern database, forming a time-of-use drift pattern sub-database.

[0046] Preferably, the step of establishing a coordinated economic scheduling model for cascade pumping station gate valves with the objective of minimizing the power consumption cost of water pumps within a scheduling cycle includes incorporating the forebay water level as a dynamic decision variable into the coordinated economic scheduling model for cascade pumping station gate valves, and obtaining the safe operating boundary of the forebay water level from the drift law database based on the current water supply flow, including:

[0047] An objective function is constructed with the goal of minimizing the sum of the power consumption costs of water pumps in each time period within the scheduling cycle. The power consumption costs of water pumps are determined based on the shaft power of each pump group participating in operation in each time period, the time-of-use electricity price of the corresponding time period, and the duration of the time period.

[0048] The forebay water level at each time period is incorporated as a dynamic decision variable into the cascade pump station gate valve coordinated economic scheduling model. The forebay water level at each time period is continuously measured within the dynamic safe operation range of the corresponding time period.

[0049] The dynamic safe operation range is obtained from the drift law database based on the current water supply flow: the smaller value between the highest designed water level of the forebay and the optimal water level of the forebay corresponding to the current water supply flow is used as the upper limit of the forebay water level, and the larger value between the lowest designed water level of the forebay and the optimal water level of the forebay corresponding to the current water supply flow is used as the lower limit of the forebay water level. The dynamic safe operation range is composed of the upper limit of the forebay water level and the lower limit of the forebay water level.

[0050] The cascade pump station gate valve coordinated economic scheduling model also includes the following constraints:

[0051] Hydraulic balance and dynamic constraints on forebay water level: the forebay water level changes dynamically with the difference between inflow and outflow rates, and the safe operating boundary is adaptively adjusted according to the current water supply flow rate.

[0052] Hydraulic coupling constraints mean that the pump station head must overcome static head, pipeline friction resistance, and local resistance of gate valves.

[0053] Due to the physical characteristics of the unit, the power of the fixed frequency pump is determined by the start-stop state and the working head, while the speed of the variable frequency pump is limited to a safe range and the power follows a similarity law.

[0054] Complex timing logic and regulation rate constraints, including minimum continuous operating time constraints, start-stop interval constraints, and maximum number of start-stops limits.

[0055] Preferably, at each scheduling moment within the scheduling cycle, the deviation between the actual water supply and the planned water supply is compared with a preset threshold. When the deviation exceeds the preset threshold, using the current actual forebay water level and remaining water demand as initial boundary conditions, the corrected forebay water level setting trajectory is extracted from the drift pattern database, the cascade pump station and gate valve coordinated economic scheduling model is re-solved, and a pump station and gate valve coordinated scheduling scheme for the remaining time period of the day is generated and issued for execution, including:

[0056] At each scheduling moment, the deviation between the actual water supply and the planned water supply is monitored in real time;

[0057] When the absolute value of the deviation between the actual water supply and the planned water supply exceeds a preset threshold, a rolling correction mechanism is triggered.

[0058] Set the current actual water level in the forebay as the initial value of the optimization model, replacing the original planned value;

[0059] The remaining water demand flow is reallocated, and a hard constraint on accumulated deficit is added to force the recovery of deviations; the accumulated deficit is the difference between the planned cumulative water supply and the actual cumulative water supply up to the current moment.

[0060] Based on the redistributed remaining water demand flow rate, the forebay water level setting trajectory for each remaining time period is extracted from the drift pattern library to form the corrected forebay water level setting trajectory.

[0061] Using the modified forebay water level setting trajectory as a reference trajectory, the actual forebay water level at the current moment as the initial condition, and the actual pump group operating state at the current moment as the initial operating state, the cascade pump station gate valve coordinated economic scheduling model is re-solved to obtain the start-stop scheme, speed ratio setting value, flow distribution scheme and gate valve opening command for each pump group during the remaining time of the day.

[0062] The re-solved collaborative scheduling scheme is then sent to the pump station control system and the gate valve control system for execution.

[0063] Preferably, it also includes the steps of generating and rolling revision of the day-ahead scheduling plan:

[0064] Before the start of the scheduling cycle, based on the planned water supply for the day and the time-of-use electricity price information of the power grid, the optimal forebay water level setting value for each time period is queried from the drift pattern database to generate the forebay water level daily setting trajectory.

[0065] The daily set trajectory of the forebay water level is used as the input of the coordinated economic scheduling model of the gate valves of the cascade pumping station. With the goal of minimizing the power consumption cost of the pumps within the scheduling cycle, the daily scheduling scheme for each time period is solved and issued for execution.

[0066] If rolling correction is not triggered during intraday scheduling, the day-ahead scheduling scheme will continue to be executed, and the day-ahead water level trajectory of the forebay will be tracked and corrected based on the actual forebay water level at the current moment.

[0067] If a rolling correction is triggered, the scheduling instructions for the remaining time period in the daytime scheduling scheme are replaced with the re-solved collaborative scheduling scheme, and the setting value for the remaining time period in the daytime setting trajectory of the forebay water level is replaced with the corrected forebay water level setting trajectory.

[0068] Preferably, the pump station characteristic curve model is dynamically updated during the scheduling process:

[0069] Each time a rolling correction is triggered, the actual operating flow rate, head, power, and efficiency data of each pump group at the current moment are recorded.

[0070] When the accumulated actual operating data reaches a preset threshold, the actual operating data is used to correct the characteristic curve parameters of the corresponding pump group in the pump station characteristic curve model online.

[0071] The corrected pump set characteristic curve parameters are updated to the pump station characteristic curve model for subsequent speed optimization and economic scheduling model solving.

[0072] Compared with the prior art, the beneficial effects of the present invention are:

[0073] 1. This invention classifies pump stations into four operating conditions (single pump operation, parallel operation of power frequency pumps, parallel operation of variable frequency pumps, and mixed operation of power frequency pumps and variable frequency pumps). It builds a refined mathematical model by combining the similarity law of water pumps and the hydraulic balance equation. By fitting the characteristic curve of a single pump with a quadratic polynomial and converting the characteristic curve of the variable frequency pump at different speeds using the similarity law, it uses a fully connected neural network model to fit the nonlinear mapping relationship between the head and speed ratio to the total flow of the system under the mixed operation condition. This accurately describes the variation law of the pump station's flow, head, and energy consumption under different operating conditions, solving the problem of accurate modeling of the characteristics of mixed power frequency pump stations. It is superior to the traditional single equivalent curve modeling method and ensures that the scheduling scheme fits the actual engineering situation.

[0074] 2. This invention uses the forebay water level as an optimization decision variable. Within the water level safety constraint range, it traverses candidate forebay water levels and accurately calculates the total system power by combining the characteristic curves of each pump group. It reveals a U-shaped relationship between the forebay water level and pump station energy consumption, showing a decrease followed by an increase. This breaks through the traditional misconception that the forebay water level is a fixed parameter and that higher water levels mean greater energy savings. Without altering the reservoir operation strategy or adding new engineering equipment, it reduces the actual pump station head by dynamically controlling the forebay water level, achieving low-cost, no-modification energy saving, and demonstrating strong engineering applicability.

[0075] 3. This invention constructs a drift law database of water supply flow rate and optimal forebay water level, transforming complex nonlinear hydraulic coupling relationships into benchmark mapping relationships, and establishing a rapid query mechanism for optimal forebay water level under different reservoir water levels and different water supply flow rates. This law database not only provides accurate water level setting basis for the scheduling model under different time periods and operating conditions, but also significantly reduces the complexity of online optimization calculations, laying a data foundation for the rapid solution of the cascade pumping station-gate valve coordinated economic scheduling model.

[0076] 4. This invention establishes a coordinated economic scheduling model for gate valves in cascade pumping stations with the goal of minimizing the power consumption cost of water pumps. The model incorporates the forebay water level as a dynamic decision variable and considers complex time-of-use constraints such as time-of-use electricity price fluctuations, hydraulic coupling constraints between pumps, valves, and pipe networks, as well as the minimum continuous operating time and maximum number of start-stop cycles of power frequency units. This achieves globally optimal coordinated scheduling of pumps, gates, and valves under cross-time period coupling constraints, solving the problem of significant economic decline in static scheduling plans under dynamic deviations.

[0077] 5. This invention introduces a rolling rescheduling mechanism based on model predictive control and establishes a deviation monitoring and adaptive triggering system. When the actual water supply deviates from the planned amount by a preset threshold, the system uses the current actual forebay water level and remaining water demand as initial boundary conditions. It extracts the corrected forebay water level setting trajectory from the drift pattern database and automatically triggers the rescheduling procedure. This regenerates the pump, gate, and valve linkage scheduling scheme with the lowest economic cost for the remaining time period of the day, realizing real-time compensation and correction of water supply prediction deviations and execution errors, significantly improving the practicality and robustness of the scheduling scheme.

[0078] 6. This invention designs a layered iterative solution architecture of "discrete layer-continuous layer". The upper layer uses a genetic algorithm or heuristic rules to preferentially determine the start-stop combination matrix of the power frequency pump, relaxing the complex mixed integer nonlinear programming problem into a nonlinear programming problem under a given discrete state. The lower layer uses the alternating direction multiplier method for distributed parallel solution, transforming the global hydraulic coupling constraint into a local penalty term, so that the optimization problems of a single pump and a single valve are independent and calculated in parallel, effectively avoiding the combinatorial explosion problem caused by the traditional branch and bound method, greatly improving the solution efficiency and meeting the real-time scheduling requirements of engineering.

[0079] 7. This invention establishes an online dynamic update mechanism for the pump station characteristic curve model. It records the actual operating data of each pump group each time a rolling correction is triggered. When the accumulated data reaches a preset threshold, the recursive least squares method is used to correct the pump group characteristic curve parameters online. This allows the model to track the slow changes in pump group performance (such as performance degradation caused by impeller wear, pipeline aging, etc.), forming a positive cycle of "data accumulation → model update → optimized scheduling," ensuring the accuracy and reliability of the scheduling optimization results during long-term operation. Attached Figure Description

[0080] Figure 1 This is a schematic diagram of the topology of the water diversion project in Embodiment 1 of this case.

[0081] Figure 2 This is a flowchart of the multi-condition characteristic curve modeling of the cascade pumping station in Embodiment 1 of this case.

[0082] Figure 3This is a schematic diagram showing the relationship between the forebay water level and power in Embodiment 1 of this case.

[0083] Figure 4 This is a flowchart of the coordinated economic scheduling and MPC rolling update process of the cascade pumping station and gate valve in Implementation Example 1 of this case.

[0084] Figure 5 This is a schematic diagram of the structure of a control system according to Embodiment 2 of this case.

[0085] in, Figure 2 First, basic engineering data (pump set fitting coefficients, pipeline parameters, forebay area, etc.) are collected. Then, quadratic polynomial fittings are performed on the flow-head, flow-power, and flow-efficiency of individual units. Next, the speed conversion of the variable frequency unit is completed using the pump similarity law. Based on this, joint characteristic curves are constructed for four operating conditions: single pump operation, fixed frequency pump set combination, fixed frequency / variable frequency pump set combination, and variable frequency pump set parallel operation. Finally, a fully connected neural network model is used to fit the combined head-flow characteristic curve of the fixed frequency / variable frequency pump set, providing a precise data foundation for optimized scheduling. Figure 3 The figure in the middle is a schematic diagram of the relationship between the forebay water level and power, which shows the relationship between the forebay water level and the pump station energy consumption. It presents a U-shaped feature of first decreasing and then increasing, indicating that there is an optimal forebay water level that minimizes the energy consumption per unit of water delivery. Detailed Implementation

[0086] The technical solutions of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. The components of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely represents selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application. It should be noted that similar reference numerals and letters in the following drawings indicate similar items; therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings. Furthermore, in the description of this application, the terms "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0087] Example 1

[0088] This embodiment uses a long-distance water diversion project as an example. Please refer to [link / reference]. Figure 1The water transmission chain of the project is as follows: natural water source intake → inlet control gate valve → primary pumping station forebay → primary cascade pumping station → primary high-level water tank → secondary pumping station forebay → secondary cascade pumping station → secondary high-level water tank → diversion pipeline → receiving reservoir.

[0089] The water diversion project has the following characteristics: an inlet gate valve is installed between the water intake and the forebay of the first-stage pumping station; each receiving reservoir is equipped with an inlet gate and a flow regulating valve at the inlet front end; the inlet gate is controlled by binary control (fully open / fully closed); the flow regulating valve supports stepless opening adjustment from 0 to 1; at least one of the two-stage pumping stations is equipped with multiple power frequency units and variable frequency units; the water intake to the forebay, the high-level pool to the downstream forebay, and the high-level pool to the reservoir adopt gravity flow mode; the water is transported across elevations by pressurized pumping from the pumping station; there are head losses along the flow path and local head losses during the water transport process.

[0090] This embodiment uses a primary pumping station as an example for detailed explanation. This pumping station is equipped with two identical industrial frequency centrifugal pumps (rated speed n0 = 1450 rpm, rated flow rate of each pump). =5.0m³ / s, rated head H0=65m) and 2 identical variable frequency centrifugal pumps (rated speed) =1450rpm, rated flow rate of single pump =4.5m³ / s, rated head H0=60m, speed range 0.6~1.0 times rated speed). Pipeline comprehensive resistance coefficient s=0.002s² / m 5 The cross-sectional area of ​​the forebay of the first-stage pumping station is A=5000m², and the design water level of the reservoir is H_reservoir=85.0m.

[0091] like Figure 1 As shown, this invention provides an economical scheduling method for a hybrid cascade pumping station and gate valves based on dynamic optimization of the forebay water level, comprising the following steps:

[0092] Step S1: Collect the static parameters and real-time operation data of the water diversion project.

[0093] 1. Acquisition of static parameters for the project

[0094] The static parameters of the project include fixed parameters such as the fitting coefficient of the pump station unit, pipeline length, pipeline diameter, pipeline friction coefficient, forebay surface area, reservoir characteristic water level, and valve flow coefficient.

[0095] 2. Real-time data acquisition

[0096] Real-time operational data is collected in real time by monitoring equipment, including dynamic data such as the water level in the forebay, the water level in the high-level pool, the water level in the reservoir, the pipeline flow rate, the unit operating status, and the time-of-use electricity price of the power grid.

[0097] In practice, the fitting coefficients of the pump set include the quadratic polynomial coefficients of the head flow rate, power flow rate, and efficiency flow rate.

[0098] Step S2: Construct a pump station characteristic curve model for the variable frequency pump set under multiple operating conditions in parallel.

[0099] In this invention, multiple operating conditions are specifically divided into four categories: single-pump operation, parallel operation of power frequency pump sets, parallel operation of variable frequency pump sets, and mixed operation of power frequency and variable frequency pump sets. Mathematical models are established for four levels: single unit, power frequency combination, power frequency / variable frequency combination, and variable frequency combination. Pump station characteristic curves are constructed for each of these three operating conditions. Parallel operation of pump sets follows the principle that each pump set in parallel has the same head at the same node, and the total system flow is equal to the sum of the flow rates of each parallel pump set. The performance parameters of the variable frequency pump change with rotational speed according to a similarity law. Specifically, the head represents the difference in water level the pump needs to lift = outlet water level - forebay water level. Taking a primary pump station with three power frequency pumps (#1, #2, #3) and two variable frequency pumps (#4, #5) as an example, the single-pump characteristic curves of each pump are constructed, and then the combined characteristic curves of each operating condition are synthesized according to parallel constraints. The flow rates of each pump in the power frequency pump set and the variable frequency pump set at the same head are superimposed to obtain the total system flow rate corresponding to that head. All combinations within the set head calculation range (e.g., 30m to 80m) and speed ratio range (e.g., 0.6 to 1.0) are traversed, and the combined head-flow rate characteristic curve, power-flow rate characteristic curve, and efficiency-flow rate characteristic curve of the power frequency and variable frequency pump set are obtained by fitting with a fully connected neural network model.

[0100] Furthermore, given a fixed outlet water level and supply flow rate, while raising the forebay water level can reduce the system's static head and theoretically decrease the work done by the pump against gravitational potential energy, it also causes the pump's actual operating point to shift drastically along the performance curve towards higher flow rates. This forces the unit to deviate significantly from its high-efficiency operating range, leading not only to a sharp drop in pump efficiency but also to negative effects such as high-flow-rate overload and a surge in pipeline resistance. Ultimately, this results in an increase in actual shaft power instead of a decrease. Therefore, there exists an optimal forebay water level. Thus, the following step S3 is set.

[0101] Step S3: Calculation method for optimal forebay water level in the scenario of a hybrid pump station based on industrial and variable frequency pumps.

[0102] The total system flow rate is obtained based on the pump station characteristic curve model. The forebay water level is used as the optimization decision variable. Within the water level safety constraint range, different forebay water levels are traversed and the corresponding total power of the pump station system is calculated. The optimal speed combination corresponding to each forebay water level is determined by speed optimization, thereby obtaining the optimal forebay water level under different water supply flow rates, and constructing a drift law library between water supply flow rate and optimal forebay water level. Specifically, the forebay water level traversal range is set to [47m, 52m], with a step size of 0.1m. For each candidate forebay water level, under the condition of satisfying the speed ratio constraints of each variable frequency pump (0.6~1.0), with the goal of minimizing the total power of the pump station system, the optimal speed ratio combination of each variable frequency pump is solved by an optimization algorithm. Multiple typical water supply flow rates (such as 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, and 4.0 m³ / s) are set. For each typical water supply flow rate, the forebay water level is traversed, and the forebay water level corresponding to the minimum total power is selected as the optimal forebay water level under that water supply flow rate. This forms a drift pattern database of water supply flow rate and optimal forebay water level, thereby providing a reference for querying the optimal forebay water level under the corresponding flow rate at different time periods.

[0103] Furthermore, the daily scheduling process of water diversion projects is simultaneously affected by multiple factors, including fluctuations in time-of-use electricity prices, the hydraulic matching relationship between gate valve opening and pumping volume, and the constraint of the end-of-day water level recovery in the final-stage reservoir. This results in a highly nonlinear scheduling problem. Meanwhile, the water supply demand continuously changes throughout the day, causing the optimal forebay water level to drift. Traditional, fixed static scheduling plans struggle to adapt to on-site water supply prediction deviations and equipment execution errors, leading to a significant decrease in scheduling efficiency. To address these shortcomings, this invention designs a pump and gate valve rolling optimization and deviation adaptive scheduling mechanism based on model predictive control, with corresponding steps S4 and S5. The overall implementation idea is as follows:

[0104] First, relying on the drift pattern library built offline as described above, the complex hydraulic coupling relationship of pump groups is transformed into a flow-optimal water level benchmark mapping that can be quickly queried, simplifying the difficulty of online solution. Second, a multi-objective collaborative scheduling mathematical model is constructed that takes into account pump power consumption costs, unit start-up and shutdown penalties, and water supply flow deviation penalties, and the forebay water level is set as a continuously adjustable dynamic decision variable. Finally, a water supply deviation-triggered online rescheduling logic is set up. When the deviation between the actual water supply and the planned value exceeds a preset threshold, the current real-time forebay water level and the remaining water delivery task are used as the initial boundary for optimization. A fast solution algorithm combining decomposition coordination and piecewise linearization is adopted to regenerate the optimal scheduling scheme for pump groups and gate valves for the remaining time period of the day, completing real-time compensation for operational deviations.

[0105] Step S4: Construct a coordinated economic scheduling model for cascade pumping stations and gate valves.

[0106] A coordinated economic scheduling model for gate valves of cascade pumping stations was built with the goal of minimizing the total power consumption cost of water pumps within the scheduling cycle. The water level of the forebay was incorporated as a dynamic decision variable into the model solution system. During scheduling modeling, the dynamic safe operating boundary of the forebay water level was determined by combining real-time water supply flow and retrieving the drift law library.

[0107] Step S5: Scheduling Deviation Monitoring and Adaptive Rolling Correction.

[0108] At each scheduling moment within the scheduling cycle, the deviation between the actual water supply and the planned water supply is compared. When the deviation exceeds the preset threshold, the current measured forebay water level and the remaining water delivery task are used as the initial boundary conditions for optimization. The corrected forebay water level setting trajectory is retrieved from the drift law library, and the cascade pump station gate valve collaborative economic scheduling model is resolved. The pump station and gate valve collaborative scheduling scheme for the remaining time period of the day is generated and issued for execution.

[0109] As described above, the method in this case solves the core problems of energy consumption optimization and adaptive compensation for water supply deviation in a hybrid cascade pumping station by combining dynamic optimization of the forebay water level with rolling rescheduling. First, by using the forebay water level as the optimization decision variable, different forebay water levels are traversed within the water level safety constraint range, and the corresponding total power of the pumping station system is calculated. The optimal speed combination corresponding to each forebay water level is determined through speed optimization, thereby obtaining the optimal forebay water level under different water supply flow rates. A drift law library of water supply flow rate and optimal forebay water level is constructed, breaking through the traditional conservative scheduling mode that treats the forebay water level as a fixed parameter, and achieving low-cost energy reduction without modifying the engineering equipment. Finally, a rolling rescheduling mechanism based on model predictive control is introduced. At each scheduling moment within the scheduling cycle, the deviation between the actual water supply and the planned water supply is compared with a preset threshold. When the deviation exceeds the preset threshold, the actual forebay water level and the remaining water demand at the current moment are used as the initial boundary conditions. The corrected forebay water level setting trajectory is extracted from the drift pattern library, and the coordinated economic scheduling model of the cascade pump station and gate valve is resolved. The pump, gate, and valve linkage scheduling scheme for the remaining time period of the day is generated and issued for execution. This enables the scheduling scheme to have the ability to compensate and correct for water supply prediction deviations and execution errors in real time. An adaptive scheduling architecture is formed from offline drift pattern mining to online optimized scheduling and then to real-time deviation monitoring and rolling correction. This realizes the economic, reliable, and adaptive operation of the industrial variable frequency hybrid cascade pump station and gate valve system under dynamic disturbance conditions.

[0110] As a specific implementation method, this embodiment details the specific content and methods for collecting static parameters and real-time operating data of the project.

[0111] The static parameters of the project include: the fitting coefficients of the pump station units, such as the head-flow curve coefficients of each fixed-frequency pump and variable-frequency pump. , , ( ), power-flow curve coefficient ( Efficiency flow curve coefficient ( The performance curves provided by the pump manufacturer were obtained through quadratic polynomial fitting. In practice, the pipe length L = 3500m; the pipe diameter D = 2.8m; and the pipe friction coefficient s = 0.002s² / m. 5 The cross-sectional area of ​​the forebay is A = 5000 m²; the characteristic water levels of the reservoir include the design water level H_reservoir = 85.0 m, the dead water level 75.0 m, and the normal storage water level 88.0 m; the valve flow coefficient is ζ(θ)≈0.05 when the inlet gate valve is fully open and ζ(θ)≈0.82 when it is half open.

[0112] Real-time operating data includes: forebay water level monitored in real time by a water level gauge with an accuracy of ±1cm; high-level water tank water level; reservoir water level; pipeline flow rate monitored in real time by an electromagnetic flow meter with an accuracy of ±0.5%; unit operating status is represented as: the start / stop status variable of the power frequency pump u_i∈{0,1}, and the actual speed range of the variable frequency pump n_j∈[870,1450]rpm; the time-of-use electricity prices are as follows: peak period 9:00-12:00 and 17:00-22:00 electricity price is 0.95 yuan / kWh, normal period is 0.62 yuan / kWh, and valley period 23:00-8:00 the next day electricity price is 0.32 yuan / kWh.

[0113] Taking a real-time moment as an example, the real-time data at 8:00 AM on a certain day is as follows: First-stage forebay water level 48.5m, reservoir water level 82.3m, total outlet flow of the first-stage pumping station 15.0 m³ / s, 2 power frequency pumps operating, 2 variable frequency pumps operating, the current speed of variable frequency pump No. 2 is 1160 rpm (speed ratio k = 1160 / 1450 = 0.80), and the current time period is peak hour with an electricity price of 0.95 yuan / kWh. The application of the above data in the scheduling model is as follows:

[0114] The difference between the forebay water level and the reservoir water level determines the system static head H_static = reservoir water level H_reservoir - forebay water level H_forebay = 82.3 - 48.5 = 33.8 m; the pipeline flow rate combined with the pipeline friction coefficient calculates the dynamic head H_dynamic = s•Q² = 0.002 × 15² = 0.45 m; thus, by clarifying the specific collection content and measurement methods of the static parameters and real-time operation data of the project, accurate and complete input data are provided for subsequent pump station characteristic curve modeling, optimal forebay water level calculation and economic dispatch model construction.

[0115] As a preferred embodiment, this embodiment details the process of constructing the pump station characteristic curve model. The construction of the pump station characteristic curve model under multiple operating conditions and parallel operation of the variable frequency pump set includes the following steps:

[0116] First, generate the single-pump characteristic curve of the power frequency pump set: collect multiple sets of measured data of flow rate, head, power and efficiency of a single power frequency pump at its rated speed, and use quadratic polynomials to establish flow rate-head characteristic curve, flow rate-power characteristic curve and flow rate-efficiency characteristic curve respectively to obtain the single-pump characteristic curve of the power frequency pump set; the speed of the power frequency pump is fixed, and the fitted single-pump characteristic curve of the power frequency pump set is used for single-pump operating condition calculation.

[0117] The flow rate and head characteristic curve of a single industrial frequency pump is fitted using a quadratic polynomial, and the specific expression is as follows:

[0118]

[0119] in, The pump head (m) is the pump unit head. Pump flow rate ( ), The power of the pump shaft (kW) is the power of the mains pump. The efficiency of the power frequency pump is expressed as a percentage (%). The fitting coefficients for the pump station unit are denoted as .

[0120] Taking the No. 1 power frequency pump in this embodiment as an example, the following results were obtained based on the measured data: =72.8, =1.35, =-0.82, that is, H(Q)=72.8+1.35Q-0.82Q². The pump head H at the rated flow rate Q0=5.0m³ / s is H=72.8+1.35×5.0-0.82×25.0=72.8+6.75-20.5≈59.1m, which is within the acceptable range for engineering compared with the factory rated head of 65m.

[0121] The flow-power characteristic curve is fitted using the same quadratic polynomial form, specifically expressed as:

[0122]

[0123] Where N is the shaft power of the power frequency pump (kW), and the result is obtained by taking power frequency pump No. 1 as an example. =185.2, =162.5, =-8.3, that is, N(Q)=185.2+162.5Q-8.3Q², when the rated flow rate Q0=5.0m³ / s, the shaft power is approximately P=185.2+162.5×5.0-8.3×25.0=185.2+812.5-207.5≈790.2kW.

[0124] The flow efficiency characteristic curve is fitted using the same quadratic polynomial form, specifically expressed as:

[0125]

[0126] Where η is the efficiency (%) of the power frequency pump, which is obtained by taking the No. 1 power frequency pump as an example. =18.5, =16.8, =-1.72, that is, η(Q)=18.5+16.8Q-1.72Q². The pump efficiency reaches its maximum value of about 59.5% near Q=4.88m³ / s. The flow rate corresponding to the highest efficiency point is slightly less than the rated flow rate, which is consistent with the general characteristics of a centrifugal pump.

[0127] Secondly, the reference curve fitting and speed conversion of the variable frequency pump are performed: the reference characteristic curve is obtained by second fitting of the rated operating condition data of the variable frequency pump. The speed ratio nᵣ is defined as the ratio of the actual speed n to the rated speed n0. Based on the pump similarity law, the real-time characteristic curve of the variable frequency pump under different operating speeds is calculated.

[0128] The conversion formula for the similarity law is:

[0129]

[0130]

[0131]

[0132]

[0133] in, Rated speed The following parameters are considered: flow rate, head, shaft power, and efficiency. Actual speed The corresponding parameters below, such as This represents the actual flow rate of the water pump at its actual operating speed n. This represents the speed ratio.

[0134] Taking the No. 1 variable frequency pump as an example, the rated speed The reference characteristic curve at 1450 rpm is: In the formula, 68.5, 1.42, and -0.78 are all fixed coefficients obtained from the fitting solution. When the variable frequency pump operates at a speed of n = 1160 rpm (i.e., When =1450 / 1160=0.80), according to the similarity law, the characteristic curve at the actual speed is converted to:

[0135] ;

[0136]

[0137] With speed ratio Taking 0.80 as an example, under the same flow rate, the power is reduced to about 51.2% of the rated value (i.e., 0.80³), which demonstrates the significant energy-saving effect of variable frequency speed regulation.

[0138] Furthermore, efficiency remains unchanged during the similarity law transformation, i.e., η' = ( / ), where η0 is the efficiency-flow characteristic curve at rated speed.

[0139] Then, based on the constraints that the pump heads of each pump are equal and the total system flow is equal to the sum of the flow rates of each parallel pump group, characteristic curve models of the pump station are constructed for single-pump operation, parallel operation of power frequency pump groups, parallel operation of variable frequency pump groups, and mixed operation of power frequency and variable frequency pump groups. The following are the basic constraints for parallel operation:

[0140] When pump sets are operating in parallel, the head of each pump is equal to the head of the system.

[0141]

[0142] For pump sets operating in parallel, the total system flow rate The sum of the flow rates of each pump unit

[0143]

[0144] Pipeline head loss calculate:

[0145]

[0146] in, This is the overall resistance coefficient of the pipeline, i.e., roughness coefficient.

[0147] Based on the constraints of equal pump head and total system flow equal to the sum of flow rates of all parallel pump sets, characteristic curve models of the pump station are constructed for single-pump operation, parallel operation of power frequency pump sets, parallel operation of variable frequency pump sets, and mixed operation of power frequency and variable frequency pump sets.

[0148] (1) For single pump operation, the single pump characteristic curve of the power frequency pump group or the real-time characteristic curve of the variable frequency pump is directly used as the pump station characteristic curve model; for example, when only the No. 1 power frequency pump is put into operation, the pump station characteristic curve is H=72.8+1.35Q-0.82Q².

[0149] (2) For the parallel operation of power frequency pump sets, the single pump characteristic curve of each power frequency pump participating in the parallel operation is used as input. Under a given head condition, the flow rate of each pump is calculated by using the flow rate and head characteristic curve of each power frequency pump set and the total flow rate of the system is accumulated. The head and total flow rate data point set is obtained by traversing different head values, and the head and flow rate joint characteristic curve of the power frequency pump set is obtained by fitting. The power and flow rate joint characteristic curve and the efficiency and flow rate joint characteristic curve of the power frequency pump set are obtained according to the same principle. The head and flow rate joint characteristic curve, the power and flow rate joint characteristic curve and the efficiency and flow rate joint characteristic curve of the power frequency pump set constitute the pump station characteristic curve model.

[0150] First, for the power frequency pump set, the combined characteristic curves of the head-flow rate, power-flow rate, and efficiency-flow rate of the power frequency pump set k are as follows:

[0151]

[0152]

[0153]

[0154] in, For power frequency pump sets The rise, For power frequency pump sets power, For power frequency pump sets efficiency, For pump set flow rate, For power frequency pump sets The coefficients of the head-flow characteristic curve.

[0155] When multiple industrial frequency pump sets are combined, a joint characteristic curve is constructed based on the head constraint and flow relationship when the pump sets are connected in parallel. Taking two industrial frequency pumps of the same model (No. 1 and No. 2, with identical parameters) connected in parallel as an example, given a head H = 50m, the specific calculation process is as follows:

[0156] Step 1: Flow rate calculation for each power frequency pump unit

[0157] The pump station characteristic curves for each power frequency pump set have been determined above. Based on the fact that the head of each pump set is the same under parallel operation, at a given head... Based on the characteristic curves of each power frequency pump set, the flow rate of each pump is calculated using a quadratic polynomial solution method.

[0158] Specifically, the flow-head characteristic curve of a single industrial frequency pump is H = 72.8 + 1.35Q - 0.82Q². Since the two pumps are of the same model, the flow rate of each pump is the same under the same head H, denoted as q. The quadratic polynomial is rewritten as a quadratic equation with H as the independent variable: -0.82q² + 1.35q + (72.8 - H) = 0, which gives q = 1.55 m³ / s.

[0159] Step 2: Total Flow Calculation

[0160]

[0161] This refers to the total flow rate of the parallel operation of the power frequency pump sets. The number of parallel power frequency pump sets, For pump units at a given head The flow rate. Then the total system flow rate is calculated. =2×1.55=3.10m³ / s.

[0162] Step 3: Combined characteristic curve of the power frequency pump set

[0163] By changing different head in the water supply scenario The value is then used in conjunction with step 2 to calculate the corresponding value. To obtain the corresponding operating conditions under different head conditions and By using the corresponding relationship data, the head-flow joint characteristic curve of the frequency pump group operating in parallel can be obtained, and then the corresponding power-flow joint characteristic curve and efficiency-flow joint characteristic curve of the frequency pump group can be calculated.

[0164] Specifically, within a preset head range, several head operating points are discretized with a fixed step size. For any operating condition Hᵢ, it is substituted into the single-pump characteristic curve equation of the power frequency pump set to solve for the single-pump flow rate q(Hᵢ). The total system flow rate at that head is obtained by superimposing the results with the number of parallel pumps. Taking two identical industrial frequency pumps as an example, the total system flow rate... =2 Summary of all ( , The data sample was fitted using a quadratic polynomial to obtain the joint head-flow characteristic curve of the parallel operation of the power frequency pump sets. In specific implementation, with a step size of ΔH=2m, the system iterates through the head range H∈[30,70]m to obtain 21 head values: H=30, 32, 34, ..., 70m. For each head value Hᵢ, the flow rate of each pump is calculated using the above formula. When H=40m, we get q=2.65m³ / s, Q_total=5.30m³ / s; when H=55m, we get q=1.20m³ / s. =2.40 m³ / s; when H=65 m, we get q=0.42 m³ / s. =0.84 m³ / s. A total of 21 ( , Data points, with head H as the vertical axis and total system flow rate as the horizontal axis. Using a quadratic polynomial as the x-axis, a combined head-flow characteristic curve of the parallel operation of the power frequency pump units was obtained. .

[0165] Then, the corresponding power-flow characteristic curve and efficiency-flow characteristic curve are obtained: for each head The single pump flow rate obtained below Substituting the values ​​into the single-pump power-flow characteristic curve N(q) and the single-pump efficiency-flow characteristic curve η(q), we obtain the single-pump power Ni and the single-pump efficiency ηi. Taking two identical industrial frequency pumps as an example, the total power in parallel is N_total = 2 × Pi. The overall efficiency of the parallel system is calculated using the hydraulic power formula: η_total = Where ρ is the density of water and g is the acceleration due to gravity. (Summarize the following...) The corresponding samples of P_total and η_total were also fitted with a quadratic polynomial to obtain the power-flow joint characteristic curve and the efficiency-flow joint characteristic curve of the power frequency pump group, respectively.

[0166] (3) For the parallel operation of variable frequency pump sets, the real-time characteristic curves of each variable frequency pump set at its own operating speed are used as input. Based on the parallel constraints, the flow rate of each pump is calculated and accumulated to the total flow rate of the system under the given head and actual speed ratio. Different combinations of head and actual speed ratio are traversed to obtain the data point set and fit it to obtain the head-flow joint characteristic curve of the variable frequency pump set. The power-flow joint characteristic curve and the efficiency-flow joint characteristic curve of the variable frequency pump set are obtained according to the same principle. The head-flow joint characteristic curve, the power-flow joint characteristic curve and the efficiency-flow joint characteristic curve of the variable frequency pump set constitute the pump station characteristic curve model.

[0167] First, for variable frequency units and variable frequency pump sets Rated speed The characteristic curves are as follows:

[0168]

[0169]

[0170]

[0171] in, For variable frequency pump sets The rise, This refers to the pump unit flow rate. Variable frequency pump set At rated speed The parameters of the head-flow characteristic curve are obtained, and the parameters of the head-flow characteristic curve at each speed are calculated using the "conversion based on the similarity law of variable frequency units" mentioned above. The power-flow characteristic curve and efficiency-flow curve of the variable frequency pump unit are obtained using the same principle.

[0172] Similar to iterative calculations using a combination of power frequency and variable frequency, the head and flow rate data point sets under the given head calculation range and speed range are calculated respectively, thereby obtaining the head and flow rate characteristic curves of parallel variable frequency pump sets.

[0173] Taking two variable frequency pumps of the same model (No. 4 and No. 5) connected in parallel as an example, given a head H = 44m and the speed ratio of each variable frequency pump ( =0.85, Under the condition that (=0.80), the calculation process for the parallel operation of variable frequency pump sets is as follows:

[0174] Step 1: Calculate the flow rate for each pump unit

[0175] For variable frequency pump j, at the speed ratio The real-time head-flow characteristic curve after conversion based on the similarity law is as follows:

[0176]

[0177] When expanded, it appears as follows:

[0178] With No. 4 variable frequency pump ( Taking (=0.85) as an example, the reference characteristic curve at rated speed is: =68.5+1.42 -0.78 After conversion:

[0179] H=0.85²×68.5+0.85×1.42×Q-0.78×Q²=49.49+1.207Q-0.78Q²

[0180] Under the condition of H=44m, solve the equation: 0.78Q²-1.207Q-5.49=0, and obtain the solution. =3.54m³ / s (take the positive root).

[0181] With No. 5 variable frequency pump ( Taking (=0.80) as an example, after conversion:

[0182] H=0.80²×68.5+0.80×1.42×Q-0.78×Q²=43.84+1.136Q-0.78Q²

[0183] Under the condition of H=44m, solve the equation: 0.78Q²-1.136Q-0.16=0, and obtain the solution. =1.30m³ / s (take the positive root).

[0184] Step 2: Calculate the total flow rate of the variable frequency pump sets in parallel.

[0185] ;

[0186] Based on the previous step, we can obtain Q_total = + =3.54 + 1.30 = 4.84 m³ / s

[0187] Step 3: Construction of Joint Characteristic Curves for Variable Frequency Pump Units

[0188] Set the head calculation range H∈[20,70]m (step size 1m) and the speed ratio range. ∈[0.60,1.00] (step size 0.02), for each (H,k4,k5) combination, calculate the flow rate of each variable frequency pump at the corresponding speed using the method described above, and sum them to obtain Q_total(H, , Since the two variable frequency pumps can operate at different speeds, the data point set is in a multi-dimensional form (H, , (Q General).

[0189] The calculation results are presented using several typical working conditions as examples:

[0190] Head H (m) ( , ) (m³ / s) (m³ / s) Q total (m³ / s) 44 (0.85,0.80) 3.54 1.30 4.84 44 (0.90,0.85) 3.82 2.65 6.47 44 (1.00,1.00) 4.42 3.95 8.37 50 (0.90,0.85) 2.95 1.78 4.73 50 (1.00,1.00) 3.85 3.42 7.27

[0191] Summarize all (H, , The data sample (Q_total) was fitted using a quadratic polynomial to obtain the joint head-flow characteristic curve of the variable frequency pump set. For two variable frequency pumps of the same model operating at the same speed ratio (...),... = = In the simplified case of H_parallel(Q_total, ...), the joint characteristic curve can be represented as H_parallel(Q_total, ...) The functional relationship between ).

[0192] Then, the corresponding power-flow combined characteristic curve and efficiency-flow combined characteristic curve of the variable frequency pump set are obtained: for each (H, , The flow rates of each pump, obtained under the combined conditions, are substituted into the power-flow characteristic curve and efficiency-flow characteristic curve of each pump at the corresponding speed to obtain the power and efficiency of each pump; the total power in parallel is the sum of the power of each pump. The overall system efficiency, weighted by flow rate, is calculated as ηtotal = Σ(Qj × ηj) / Qtotal. By summing the corresponding samples of each Qtotal, Ntotal, and ηtotal, and using quadratic polynomial fitting, the combined power-flow characteristic curve and the combined efficiency-flow characteristic curve of the variable frequency pump unit are obtained. These three combined characteristic curves constitute the pump station characteristic curve model under the parallel operation condition of the variable frequency pump units. Following the same principle, the combined power-flow characteristic curve and the combined efficiency-flow characteristic curve of the variable frequency pump unit can be obtained.

[0193] (4) For the mixed operation of power frequency and variable frequency pump sets, the single pump characteristic curve of the power frequency pump set and the real-time characteristic curve of the variable frequency pump set are used as inputs. Based on the parallel constraint, the total flow of the power frequency part and the variable frequency part are calculated separately and then added together to obtain the total flow of the system. Under the condition of setting the head calculation range and the speed ratio range, different head and speed ratio combinations are traversed to obtain the data point set and the fully connected neural network model is used to fit the head and flow characteristic curve of the power frequency and variable frequency pump set pump station. Based on the same principle, the power flow joint characteristic curve and the efficiency flow joint characteristic curve of the power frequency and variable frequency pump set are obtained. The head flow joint characteristic curve, the power flow joint characteristic curve and the efficiency flow joint characteristic curve of the power frequency and variable frequency pump set constitute the pump station characteristic curve model.

[0194] When multiple power frequency and variable frequency pump sets are combined, a joint characteristic curve is constructed based on the head constraint and flow relationship when the pump sets are connected in parallel. Specifically, this is exemplified by two power frequency pumps (No. 1 and No. 2) and two variable frequency pumps (No. 4 and No. 5) all operating in parallel. Given a head H and the speed ratio of each variable frequency pump (…),… , Under the given conditions, the calculation process is as follows:

[0195] Step 1: Flow rate calculation for each power frequency and variable frequency pump set

[0196] The pump station characteristic curves for each power frequency and variable frequency pump set have been determined above. Based on the principle that the head of each pump set is the same under the parallel combination of pump sets, the flow rate corresponding to the power frequency and variable frequency pump sets is calculated separately.

[0197] Total flow rate of the power frequency pump set:

[0198]

[0199] This refers to the total flow rate of the parallel section of the power frequency pump set. The number of parallel power frequency pump sets, For a power frequency pump set at a given head The flow rate is calculated as follows. Specifically, based on the single-pump characteristic curve of the power frequency pump set, H = 72.8 + 1.35Q - 0.82Q², the flow rate of each power frequency pump is calculated and summed under a given head H. Since the two power frequency pumps are of the same model and each pump has the same flow rate, denoted as qi, the total flow rate of the power frequency part is Qi = 2 × qi(H).

[0200] Total flow rate of variable frequency pump set:

[0201]

[0202] This represents the total flow rate of the parallel section of the variable frequency pump set. The number of parallel power frequency pump sets, For variable frequency pump sets at a given head The flow rate. Specifically, based on the real-time characteristic curves of each variable frequency pump at the corresponding speed ratio, the flow rate of each variable frequency pump is calculated and summed at a given head H to obtain the total flow rate of the variable frequency section Qvariable = Q4(H, ... )+Q5(H, ).

[0203] Step 2: Total Flow Calculation

[0204] Total system traffic:

[0205] Specifically, Qtotal = 2 × qlab(H) + Q4(H, )+Q5(H, ).

[0206] Step 3: Iteratively calculate the parallel characteristic curve of the pump set

[0207] Set the head calculation range and speed range: R The head obtained from each set of discrete samples Ratio of speed Calculate the total system flow rate under the corresponding operating conditions. Establish a system consisting of total flow rate and head. The data points were used to fit the pump station's head-flow characteristic curve under the combined operation of power generation and variable frequency drives (VFDs). Following the same calculation principle, a power-related sample dataset was constructed, and the corresponding power-flow characteristic curve was fitted. Specifically, the head calculation range H∈[20,70]m (step size 1m) and the speed ratio range can be set. Under the condition of ∈[0.60,1.00] (step size 0.02), traverse different combinations of head and speed ratio to obtain the data point set.

[0208] The aforementioned multi-condition characteristic curve model of the variable frequency pump set provides a precise mathematical foundation for calculating the optimal forebay water level. Specifically, through quadratic polynomial fitting and similarity law conversion, head-flow rate, power-flow rate, and efficiency-flow rate characteristic curves were established for single-pump and multi-pump parallel operation conditions. These curves are the core input parameters for power calculation, efficiency evaluation, and operating point solution in the forebay water level reduction optimization model. During the forebay water level traversal, the constructed characteristic curves need to be repeatedly called to calculate the flow rate, efficiency, and power of each pump set at different water levels, thereby evaluating the total system energy consumption corresponding to each candidate forebay water level. Therefore, the accuracy of the characteristic curve modeling directly determines the accuracy of the optimal forebay water level solution, and the two constitute a progressive relationship between model construction and optimization solution.

[0209] As described above, the method in this case solves the problem of accurately determining the operating point when power frequency and variable frequency pump units are mixed and connected in parallel by dividing the pump unit into four operating conditions and establishing corresponding refined mathematical models. Compared with the traditional simplified modeling method that uses a single equivalent curve, this method constructs characteristic curves for four scenarios: single pump operation, power frequency combination, power frequency and variable frequency combination, and variable frequency combination. Among them, the power frequency pump unit uses the inverse quadratic polynomial to accurately determine the flow rate of each pump operating point, the variable frequency pump unit uses the similarity law to convert the characteristic curves at different speeds, and the mixed combination uses a fully connected neural network model to capture nonlinear coupling relationships, ensuring that the scheduling model can obtain accurate operating points under any pump unit combination and speed configuration.

[0210] As a preferred implementation, since the total system flow rate under the mixed operation of power frequency and variable frequency pump sets is a nonlinear function of the head H and the speed ratio of each variable frequency pump, traditional quadratic polynomials are difficult to accurately fit the multidimensional nonlinear relationship. Therefore, a fully connected neural network model is used for fitting. The acquisition of data point sets is fitted using a fully connected neural network model to obtain the head-flow characteristic curve of the power frequency and variable frequency pump set pump station. Based on the same principle, the power-flow joint characteristic curve and the efficiency-flow joint characteristic curve of the power frequency and variable frequency pump set are obtained. Specifically, the following steps are included:

[0211] Step 1: Generation of joint feature data point set

[0212] The flow rates of each pump in the fixed-frequency pump set and the variable-frequency pump set at the same head are superimposed to obtain the total system flow rate corresponding to that head. All combinations within the set head calculation range and speed ratio range are iterated through to form a system flow rate based on the head H and the speed ratio of each variable-frequency pump. , The system is a set of joint characteristic data points with the total system flow rate Q as the output, taking 51 values ​​for head (H∈[20,70]m, step size 1m) and 21 values ​​for speed ratio (k∈[0.60,1.00], step size 0.02). There are a total of 21×21=441 possible combinations of speed ratios for the two variable frequency pumps, and the total number of data points is 51×441=22491 sets.

[0213] Step 2: Training and Fitting the Neural Network Model

[0214] A fully connected neural network model is used to train and fit the joint characteristic data point set to obtain the joint characteristic curve of the power frequency variable frequency pump set, that is, the function relationship between the total system flow rate and the head and the speed ratio of each variable frequency pump. The input of the neural network model is the head H and the speed ratio of each variable frequency pump. , The output is the total system flow rate Q_total. After training, the total system flow rate can be quickly predicted given a combination of head and speed ratio.

[0215] Taking several typical working conditions as examples, the neural network predictions and analytical calculations are compared and verified:

[0216] Head H (m) (nr4,nr5) Analysis of Q_total (m³ / s) Neural Network Q_total (m³ / s) Relative error (%) 40 (0.80,0.80) 8.52 8.49 0.35 45 (0.85,0.80) 7.91 7.88 0.38 50 (0.90,0.85) 7.18 7.21 0.42 55 (0.95,0.90) 6.05 6.03 0.33 60 (1.00,1.00) 4.82 4.85 0.62

[0217] The verification results show that the relative error between the predicted value and the analytical calculation value of the neural network model is within 1%, which meets the engineering accuracy requirements.

[0218] Step 3: Construction of the joint power-flow characteristic curve

[0219] Based on the combined head-flow characteristic curve of the power frequency variable frequency pump set, the corresponding total system flow rate is calculated under a given head and speed ratio combination. Then, the total system flow rate is substituted into the power-flow characteristic curve of each pump set, and the total system power is obtained by summing them up. In this way, the correspondence between the total system power and the total system flow rate is established, and the combined power-flow characteristic curve of the power frequency variable frequency pump set is obtained by fitting.

[0220] Specifically, for a given (H, , After combining the components and using a neural network model to predict the total system flow Qtotal, based on the flow distribution scheme of each pump group (the flow rates of each pump in the power frequency pump group are qin and Q4 and Q5 in the variable frequency pump group), the power-flow characteristic curves of each pump group under the corresponding operating conditions are substituted to obtain the power of each pump shaft:

[0221] Power of industrial frequency pump ;

[0222] Variable frequency pump power

[0223] Total system power By summarizing the corresponding samples of each Q_total and N_total, and using quadratic polynomial fitting, the combined power-flow characteristic curve of the power frequency variable frequency pump set is obtained.

[0224] Step 4: Constructing the joint efficiency-flow characteristic curve

[0225] Based on the combined head-flow characteristic curve of the power frequency variable frequency pump set, the corresponding total system flow rate is calculated under a given head and speed ratio combination. Then, the total system flow rate is substituted into the efficiency-flow characteristic curve of each pump set, and the overall system efficiency is calculated by weighting by flow rate. Finally, the correspondence between the overall system efficiency and the total system flow rate is established, and the combined efficiency-flow characteristic curve of the power frequency variable frequency pump set is obtained by fitting.

[0226] Specifically, for a given By combining the pumps and substituting their flow rate distributions into the efficiency-flow characteristic curves of each pump group, the efficiency ηi of each pump is obtained. The overall system efficiency is calculated using a flow rate weighted average. ×100%; Summarize the corresponding samples of each Q total and η total, and use a quadratic polynomial fitting to obtain the combined efficiency and flow characteristic curve of the power frequency variable frequency pump set.

[0227] The aforementioned combined head-flow characteristic curve, power-flow characteristic curve, and efficiency-flow characteristic curve of the power frequency-variable frequency pump set constitute a pump station characteristic curve model under the mixed operation condition of the power frequency-variable frequency pump set. This model satisfies the physical constraint that the total system flow rate monotonically decreases with increasing head, consistent with the pump operating characteristics.

[0228] As a preferred implementation, this embodiment details the process of solving for the optimal forebay water level and the method for constructing the drift pattern database.

[0229] Given a fixed outlet water level and supply flow rate, while raising the forebay water level can reduce the system's static head and theoretically decrease the work done by the pumps against gravitational potential energy, it also causes the pumps' actual operating point to shift drastically along the performance curve towards higher flow rates. This forces the unit to deviate significantly from its high-efficiency operating range, leading not only to a sharp drop in pump efficiency but also to negative effects such as high-flow-rate overload and a surge in pipeline resistance. Ultimately, this results in an increase in actual shaft power instead of a decrease. Therefore, there exists an optimal forebay water level. The core objective of this step is to find the forebay water level that minimizes the total power of the pumping station system.

[0230] (1) Optimization of energy consumption and target conditions for forebay water level reduction

[0231] The total energy consumption of the pumping station is closely related to the forebay water level and flow distribution. The goal of establishing a correlation model between the forebay water level and the pump set energy consumption is to minimize the total energy consumption of the system.

[0232] 1) Total power calculation. Total power of the pumping station. The calculation formula is:

[0233]

[0234] in, The total power of the pumping station, The number of pump units put into operation. The density of water, It is the acceleration due to gravity. For the first The flow rate of the pump For the first Table pump in flow With rotational speed The efficiency is reduced for a fixed-speed industrial frequency pump set. This is the rated speed.

[0235] The system head consists of static head and dynamic head. The static head is determined by the water level in the forebay. and reservoir water level The pump head is determined by the head loss in the pipeline.

[0236]

[0237] When pump sets are operating in parallel, the head of each pump is equal, and equal to the system head:

[0238]

[0239] Analysis of the above power calculation formula shows that the forebay water level affects the static head, which in turn affects the total flow rate. The flow rate affects efficiency, which in turn affects power and energy consumption. When the decrease in efficiency exceeds the decrease in static head, the power actually increases. Therefore, there exists an optimal forebay water level that minimizes the energy consumption per unit of water transport, rather than a monotonically increasing relationship. The objective function of the forebay water level reduction optimization model is:

[0240]

[0241] As can be seen from the above, the power is affected by the water level of the forebay and the reservoir. Since the reservoir water level does not change much during the daily water supply process, the optimal forebay water level is calculated under the assumption that the reservoir water level remains constant.

[0242] 2) System constraints include:

[0243] These mainly include flow balance constraints, head matching constraints, water level safety constraints, flow distribution constraints, and rotational speed constraints.

[0244] Flow balance constraint: The basic flow constraint for parallel pump sets is that the total system flow must equal the demand flow.

[0245]

[0246] Head matching constraint: The basic head constraint for parallel pump sets is that the head of each pump must be equal to the system head.

[0247]

[0248] Water level safety constraints: The water level in the forebay must be within the safe range.

[0249]

[0250] Flow distribution constraints: The flow rate of each pump must be within the allowable range.

[0251]

[0252] Speed ​​constraints: The speed of each pump is within the allowable range.

[0253]

[0254] in, and These are the minimum and maximum safe values ​​for the forebay water level, respectively. and The first The minimum and maximum allowable flow rates of the pump. and The first Minimum and maximum permissible speeds of the trolley pump.

[0255] (2) Setting and discretization of the forebay water level traversal range

[0256] A range for the forebay water level is defined, with the upper and lower limits determined by the design maximum and minimum water levels of the forebay. In this embodiment, the design maximum water level of the forebay, H_design_max, is 52.0 m, and the design minimum water level, H_design_min, is 47.0 m, resulting in a range of [47.0, 52.0] m. Within this range, values ​​are discretely selected at a preset step size ΔH = 0.1 m, yielding 51 candidate forebay water levels {47.0, 47.1, 47.2, ..., 52.0} m.

[0257] (3) Solving the optimization model under three working conditions

[0258] Since the objective function calculation includes system head, flow rate, and efficiency, and system head and power are related to flow rate, and also involve solving for the operating point of the parallel operation of power frequency pumps and variable frequency pumps under hydraulic loss conditions, these factors are interdependent and correlated, resulting in complex coupling relationships during the solution process. This invention addresses the solution of the forebay water level reduction optimization model by employing an iterative method to accurately solve for the combined operating conditions of power frequency pump sets, variable frequency pump sets, and power frequency / variable frequency pump sets.

[0259] 3.1 Combined operating conditions of power frequency pump sets

[0260] Step 1: Set the forebay water level The static head of the system is calculated as the difference between the reservoir water level and the forebay water level, where the reservoir water level remains constant during the solution process.

[0261] Step 2: Solve for the given forebay water level The flow rates of each pump unit are calculated. For a power frequency pump, the pump unit's head-flow characteristic curve is a quadratic polynomial, and the dynamic head is also quadratic with respect to the flow rate. Therefore, given a static head, the unique flow rate corresponding to the power frequency pump can be calculated. As shown below:

[0262] = +

[0263] Calculate the given forebay water level Flow rates of each pump unit and calculate .

[0264] Step 3: Calculate the efficiency value of each frequency pump set. Determine if the flow constraint is met. If not, return to Step 1 and adjust the forebay water level. If it is met, calculate the efficiency value of each frequency pump set based on the efficiency-flow characteristic curve of the frequency pump set in Step S2, combined with the flow rate calculation of each pump set in the previous step.

[0265] Step 4: Calculate and sum the power of each pump. Based on the flow rate and efficiency calculated in the above steps, calculate the power of each pump group according to the power calculation formula for parallel operation of the pump group, and sum them to obtain the power of the parallel power frequency pump group.

[0266] Step 5: Add the forepool Discretize and iterate through the forebay water levels. And calculate the total power corresponding to the forebay water level according to steps 1-4. This allows us to obtain the mapping relationship between "forebay water level - speed of each pump unit (rated speed) - flow rate of each pump unit and total flow rate, efficiency of each pump unit, and power of each pump unit and total power".

[0267] Step 6: Retrieve from the mapping table The minimum water level corresponds to the optimal forebay water level, thus obtaining the optimal forebay water level under the power frequency combination.

[0268] Taking the deployment of two identical industrial frequency pumps with a required water flow of 8.0 m³ / s as an example, given the forebay water level H_forebay=49.5m, H_static=82.3-49.5=32.8m, the hydraulic balance equation is 32.8+0.002×(2q)²=72.8+1.35q-0.82q², solving for q=4.26m³ / s, Q_total=8.52m³ / s, the efficiency η=58.9%, and the total system power of 4650kW is the global optimum.

[0269] 3.2 Variable Frequency Pump Set Combined Operating Conditions

[0270] Step 1: Set the forebay water level The static head of the system is calculated as the difference between the reservoir water level and the forebay water level.

[0271] Step 2: Construct a speed optimization layer. For variable frequency pumps, the pump station characteristic curves differ at different speeds. Therefore, given a static head, it is necessary to determine the speed of the variable frequency pump unit in order to determine the operating point of each pump unit. Thus, a speed optimization layer is added to find the optimal speed that minimizes power at a given head. The objective function for speed optimization is as follows:

[0272]

[0273] Nested iterative optimization is used to determine the total power. The minimum, main steps are as follows:

[0274] [1] Within the allowable range of maximum and minimum speed of the pump set, given Solve for a given forebay water level The operating point is the flow rate and system head.

[0275] [2] According to the given And the power-flow characteristic curve formula is used to calculate the efficiency value of the corresponding flow rate;

[0276] [3] Calculate the power of each pump group and the total power according to the power calculation formula;

[0277] [4] Iterative optimization of different variable frequency pump sets According to [1]-[3], the power is calculated and the relationship mapping of "variable frequency pump group speed combination - flow rate, efficiency, power of each pump group and total flow rate and total power" is constructed under a given forebay water level;

[0278] [5] Take the total power from the above relationship mapping. The minimum corresponding combination of variable frequency pump speeds is the solution result of the speed optimization layer, corresponding to the combination of variable frequency pump unit speeds and the corresponding total power. .

[0279] Step 3: Add the forepool Discretize and iterate through the forebay water levels. The relationship mapping between "forebay water level - variable frequency pump unit speed combination - flow rate, efficiency, power of each pump unit and total flow rate, total power" is calculated according to steps 1-2. Furthermore, the set of solution results for the speed optimization layer of the discretized forebay water level is obtained, and the results from the set are taken. The minimum water level corresponds to the optimal forebay water level.

[0280] Taking the operation of two variable frequency pumps and a required water flow of 7.0 m³ / s as an example, with H_forebay = 49.5 m and H_static = 32.8 m, an optimization problem is established with the goal of minimizing the total power of the pumping station system, using the combined head-flow rate characteristic curve and the combined power-flow rate characteristic curve in the pumping station characteristic curve model as inputs to the constraints and cost function. The decision variable is the speed ratio of each variable frequency pump. The system's total flow rate and the flow distribution of each pump group are constrained by the following conditions: the total system flow rate equals the target water supply flow rate (Q_total = 7.0 m³ / s), the system head equals the current system head corresponding to the forebay water level, the speed ratio of each variable frequency pump is within the range of [0.60, 1.00], and the flow rate of each pump group is within the allowable operating range. An optimization algorithm is used to solve this problem, and the optimal speed combination that minimizes total power and satisfies the condition that the total flow rate equals the required flow rate is selected from all speed combinations. =0.84, =0.82), corresponding to a total power P_total=3795kW.

[0281] 3.3 Combined operation of power frequency and frequency conversion

[0282] Step 1: Given the forebay water level Z_fore, calculate the static head of the system, which is the difference between the reservoir water level and the forebay water level.

[0283] Step 2: Calculate the flow rate, efficiency, power, and total flow rate and total power of each power frequency pump group under a given forebay water level, according to the calculation steps under the parallel operation condition of power frequency.

[0284] Step 3: Construct a speed optimization layer. For variable frequency pumps, the pump station characteristic curves differ at different speeds. Therefore, given a static head, it is necessary to determine the speed of the variable frequency pump unit in order to determine the operating point of each pump unit. Thus, a speed optimization layer is added to find the optimal speed that minimizes power at a given head. The objective function for speed optimization is as follows:

[0285]

[0286] Nested iterative optimization is used to determine the total power. The minimum, main steps are as follows:

[0287] [1] Within the allowable range of maximum and minimum speed of the pump set, given Solve for a given forebay water level The operating point below, i.e., flow rate and system head.

[0288] [2] According to the given And the power-flow characteristic curve formula for calculating the efficiency value of the corresponding flow rate.

[0289] [3] Calculate the power of each pump group and the total power according to the power calculation formula.

[0290] [4] Iterative optimization of different variable frequency pump sets Based on [1]-[3], the power is calculated, and a mapping relationship is constructed for the "variable frequency pump group speed combination - flow rate, efficiency, power of each pump group and total flow rate, total power" under a given forebay water level.

[0291] [5] Take the total power from the above relationship mapping. The minimum corresponding combination of variable frequency pump speeds is the solution result of the speed optimization layer, corresponding to the combination of variable frequency pump unit speeds and the corresponding total power. .

[0292] Step 4: Based on the flow rate, efficiency, power, total flow rate, and total power of each power frequency pump group calculated in Step 2 under the power frequency parallel connection condition, and the solution results of the speed optimization layer calculated in Step 3, namely the flow rate, efficiency, power, and total flow rate of each variable frequency pump group, calculate the total power corresponding to the power frequency and variable frequency parallel combination according to the total power calculation formula.

[0293] Step 5: Add the forepool Discretize and iterate through the forebay water levels. The relationship mapping between "forebay water level - variable frequency pump unit speed combination - flow rate, efficiency, power of each industrial frequency variable frequency pump unit and total flow rate, total power" is calculated according to steps 1-4. The result set of the speed optimization layer for the discretized forebay water level is obtained, and the result set is taken from the set. The minimum water level corresponds to the optimal forebay water level.

[0294] Taking the operation of 2 fixed-frequency pumps + 2 variable-frequency pumps with a required water flow of 15.0 m³ / s as an example, when H_forebay = 49.5 m, the total power of the fixed-frequency pumps is approximately 4488 kW. The optimal speed combination for the variable-frequency pumps (k4 = 0.82, k5 = 0.80) is obtained through a speed optimization layer, resulting in a total power of approximately 3820 kW. The total system power is 8308 kW. After traversing all candidate forebay water levels, the optimal forebay water level is H_forebay = 49.3 m, corresponding to the minimum total power.

[0295] (4) Determination of U-shaped curve and optimal forebay water level (taking the combined operation of power frequency pump set as an example)

[0296] Taking the deployment of two identical industrial frequency pumps with a required water flow of 8.0 m³ / s as an example, we iterate through all 51 discrete forebay water levels and calculate the corresponding total power P_total(H_forebay_i) for each H_forebay_i using the above-mentioned solution method for combined industrial frequency pump conditions, thus establishing a mapping relationship between the forebay water level and the total system power:

[0297] Forebay water level (m) Headway (m) Single pump flow rate (m³ / s) Single pump efficiency (%) Total system power (kW) 47.0 35.3 4.52 57.2 5230 48.0 34.3 4.37 58.4 4950 49.0 33.3 4.18 59.2 4710 49.5 32.8 4.07 59.5 4650 50.0 32.3 3.95 59.1 4680 51.0 31.3 3.68 58.0 4820 52.0 30.3 3.38 56.5 5050

[0298] The table clearly shows a U-shaped curve in which the forebay water level and the total system power exhibit a trend of first decreasing and then increasing. When H_forebay increases from 47.0m to 49.5m, the static head decreases from 35.3m to 32.8m, a drop of 7.1%, and the total power decreases from 5230kW to 4650kW, a drop of 11.1%. However, when H_forebay continues to increase from 49.5m to 52.0m, the single pump flow rate decreases significantly, leading to a decrease in efficiency, while the total power actually increases to 5050kW. Therefore, H_forebay = 49.5m is the optimal forebay water level for this water supply flow rate. Please refer to [link / reference]. Figure 3 The curve showing the relationship between the forebay water level and the total power of the pumping station system exhibits a U-shaped characteristic of first decreasing and then increasing, indicating that there exists an optimal forebay water level that minimizes the energy consumption per unit of water transport.

[0299] (5) Construction of drift pattern library

[0300] Multiple typical water supply flow rates are set, covering the range from the minimum to the maximum water supply flow rate of the water diversion project. In this embodiment, 31 typical water supply flow rates are set within the range of the project's target water demand Q_demand∈[5.0,20.0]m³ / s with a step size of 0.5m³ / s. For each typical water supply flow rate, the forebay water level is traversed, and the minimum total power of the pumping station system corresponding to each candidate water level is calculated. The forebay water level corresponding to the minimum total power is selected as the optimal forebay water level under that water supply flow rate. Each typical water supply flow rate is associated and stored with its corresponding optimal forebay water level, minimum total system power, and corresponding optimal speed ratio to form a mapping relationship between water supply flow rate and optimal forebay water level, thereby constructing the drift law library. Taking several typical flow rates as examples:

[0301] Water supply flow rate (m³ / s) Optimal forebay water level (m) <![CDATA[Optimal rotational speed combination (k4, k5)]]> Minimum total power (kW) 5.0 50.8 (0.72,0.70) 2680 7.5 50.2 (0.78,0.76) 4120 10.0 49.8 (0.80,0.80) 5580 12.5 49.5 (0.81,0.80) 6940 15.0 49.3 (0.81,0.80) 8260 17.5 49.0 (0.83,0.82) 9680 20.0 48.7 (0.85,0.84) 11250

[0302] The drift pattern shows that the optimal forebay level decreases as the water supply flow rate increases. This is because under high flow conditions, the proportion of the dynamic head (sQ²) in the pipeline increases, while the weight of the static head decreases relatively. The system tends to control the single pump flow rate within the high-efficiency range by lowering the forebay level. This pattern verifies the "drift" characteristic of the forebay level: different water supply flow rates correspond to different optimal forebay levels, rather than a constant value.

[0303] (6) Sub-library of interpolation and time-segmented drift patterns

[0304] When the current water supply flow rate does not fall within the typical water supply flow rate value, an interpolation method is used to interpolate the corresponding optimal forebay water level from the mapping relationship. For example, when Q_demand = 8.3 m³ / s, linear interpolation between Q = 7.5 m³ / s (H_opt = 50.2 m) and Q = 10.0 m³ / s (H_opt = 49.8 m) yields H_opt ≈ 50.1 m.

[0305] Based on the time-of-use electricity price information of the power grid, the optimal forebay water level corresponding to different electricity price periods under each typical water supply flow is associated and stored in the drift pattern database, forming a time-of-use drift pattern sub-database. For example, during peak periods, the forebay water level can be appropriately increased to reduce the static head and thus reduce power consumption during high electricity price periods, while during off-peak periods, the forebay water level can be appropriately decreased to utilize the low electricity price period for more pumping and energy storage.

[0306] (7) Construct a database of drift patterns under different reservoir water levels

[0307] The optimal forebay water level mentioned above is calculated under the assumption that the reservoir water level remains constant. Since the reservoir water level varies at different times, the reservoir water level is also not a fixed value when generating schemes through the water supply scheduling model at different times. In order to facilitate the rapid determination of the optimal forebay water level in the water supply scheduling model, it is necessary to repeatedly construct a database of the drift law between water supply flow and optimal forebay water level at different reservoir water levels, following the process of steps (1)-(6) above.

[0308] Specifically, within the range H_reservoir∈[75.0,88.0]m, the above complete solution process is repeated with a step size of 1.0m to generate multiple sets of drift pattern libraries under different reservoir water levels, forming a two-dimensional lookup table "reservoir water level × water supply flow → optimal forebay water level", which provides a query basis for the optimal forebay water level of the scheduling model under the corresponding flow at different time periods.

[0309] The aforementioned database of drift patterns between water supply flow and optimal forebay water level provides crucial data support for the coordinated economic scheduling model of cascade pumping stations and gate valves. By traversing different combinations of forebay water level and variable frequency drive, a complete mapping relationship between forebay water level, drive speed, flow rate, and power was established. Furthermore, a database of drift patterns between water supply flow and optimal forebay water level was constructed under different reservoir water levels. During the rolling optimization process, the economic scheduling model needs to quickly retrieve the corresponding optimal forebay water level setpoint from this database based on the current water supply flow demand, using it as a benchmark reference for the dynamic constraint of the forebay water level.

[0310] As described above, this case transforms the forebay water level from a fixed parameter into a dynamic optimization decision variable by constructing an optimization model for reducing energy consumption at the forebay water level and accurately solving it under three operating conditions. This reveals a U-shaped relationship between the forebay water level and pump station energy consumption, characterized by an initial decrease followed by an increase. By constructing a database of drift patterns under different reservoir water levels, an architecture combining offline construction and online querying is formed. This enables the online scheduling process to quickly query the optimal forebay water level setpoint based on different water supply flows and reservoir water levels, significantly reducing the computational complexity of online optimization solutions and providing a data foundation for MPC rolling rescheduling to be completed within a minute-level timescale.

[0311] As a preferred implementation, this embodiment details the construction process of the coordinated economic scheduling model for gate valves in a cascade pumping station. Please refer to... Figure 4 This demonstrates the complete process of coordinated economic scheduling and rolling correction of gate valves in cascade pumping stations.

[0312] To address the challenges posed by the coupled influence of multiple factors during the daily operation of water diversion projects, including fluctuations in time-of-use electricity prices, dynamic matching of gate valve opening and pumping volume, and constraints on the recovery of the final reservoir's water level at the end of the day, this invention proposes a rolling optimization and deviation adaptive mechanism for the pump and gate valve water supply scheduling model based on model predictive control. Since changes in water supply flow demand at different times of the day drive the dynamic evolution of the forebay water level, and the optimal forebay water level under different flow rates exhibits drift characteristics, traditional static planning cannot cope with the predicted deviations and execution errors in actual operation.

[0313] Therefore, the overall implementation idea of ​​this embodiment is as follows: First, through the "water supply flow - optimal forebay water level" drift law library constructed above, the complex nonlinear hydraulic coupling is transformed into a benchmark mapping relationship; second, a multi-objective economic scheduling mathematical model including energy consumption cost, start-up and shutdown penalties and flow deviation penalties is established, and the forebay water level is included as a dynamic decision variable; finally, an online rolling rescheduling trigger mechanism is designed. When the deviation between the actual water supply and the plan exceeds a set threshold, the system uses the current actual forebay water level and the remaining water demand as the initial boundary conditions, and uses a fast solution algorithm combining decomposition coordination and piecewise linearization to regenerate the pump, gate, and valve linkage scheduling scheme with the lowest economic cost for the remaining time period of the day, thereby realizing real-time compensation and correction of operating errors.

[0314] This embodiment uses a scheduling step size of 1 hour (Δt=1h), with a total of T=24 time periods throughout the day. The following sections provide a detailed explanation from three aspects: objective function construction, constraint setting, and model solving.

[0315] (1) Construction of the objective function of the water supply optimization scheduling model

[0316] An objective function is constructed with the goal of minimizing the sum of the power consumption costs of the water pumps in each time period within the scheduling cycle. The power consumption costs of the water pumps are determined based on the shaft power of each pump group participating in operation in each time period, the time-of-use electricity price of the corresponding time period, and the duration of the time period. The specific formula for the objective function is as follows:

[0317]

[0318] In the formula: for Time-of-use electricity pricing; The scheduling time step; and They are power frequency pumps and variable frequency pump exist Shaft power during the time period and These represent collections of power frequency generators and variable frequency generators, respectively. This refers to the start / stop status variable of the power frequency pump. Specifically, in this embodiment, the price is 0.95 yuan / kWh during peak hours, 0.62 yuan / kWh during normal hours, and 0.32 yuan / kWh during off-peak hours.

[0319] (2) Dynamic safe operating range

[0320] The forebay water level at each time period is incorporated as a dynamic decision variable into the coordinated economic scheduling model of the cascade pumping station gate valves. The forebay water level at each time period continuously takes values ​​within the dynamic safe operating range of the corresponding time period. By setting the forebay water level as a dynamic decision variable, the scheduling model can actively select water level values ​​that are conducive to reducing energy consumption during the optimization process, rather than passively accepting fixed water level constraints, thereby achieving proactive optimization and control of the forebay water level.

[0321] The dynamic safe operating range is obtained from the drift law database based on the current water supply flow: the smaller value between the highest designed water level H_design_max=52.0m and the optimal forebay water level H_opt(Q) corresponding to the current water supply flow is used as the upper limit of the forebay water level, and the larger value between the lowest designed water level H_design_min=47.0m and the optimal forebay water level H_opt(Q) corresponding to the current water supply flow is used as the lower limit of the forebay water level.

[0322] For example, when Q_demand = 15.0 m³ / s, H_opt = 49.3 m is obtained from the drift law database. Therefore, the upper limit of the forebay water level is min(52.0, 49.3) = 49.3 m, and the lower limit of the forebay water level is max(47.0, 49.3) = 49.3 m. The dynamic safe operating range is [49.3 m, 49.3 m], meaning the forebay water level is constrained to operate near the optimal water level. To retain adjustment space and cope with fluctuations in actual operation, a safety margin bandwidth ΔH_safe = 1.5 m can be set near the optimal forebay water level. That is, the upper limit of the forebay water level is H_opt + ΔH_safe, and the lower limit is H*_opt - ΔH_safe, but neither exceeds the design maximum / minimum water level range. At this time, the dynamic safe operating range is extended to [47.8 m, 50.8 m].

[0323] (3) Constraint Construction

[0324] The cascade pump station gate valve coordinated economic scheduling model also includes the following constraints:

[0325] ① Hydraulic balance and dynamic constraints on forebay water level. The forebay water level changes dynamically with the difference between the inflow and outflow rates, and its safe operating boundary needs to be adaptively adjusted according to the current water supply flow rate:

[0326]

[0327]

[0328] In the formula: and They are respectively The forebay water level at the beginning and end of the time period, in meters. This refers to the cross-sectional area of ​​the forebay, expressed in square meters (m²). : The actual total pumping capacity of the pumping station system during a given time period, expressed in cubic meters per second. The outflow rate from the forebay to the downstream during a given period, expressed in cubic meters per second. The optimal forebay water level setting is given by the current water demand flow rate. The unit is meters. It is a dynamic function of the water demand flow rate and reflects the drift characteristics of the optimal water level. for Planned water demand for a given period, expressed in cubic meters per second. and These are the lower and upper limits of the safe forebay water level allowed under the corresponding flow rates, in meters.

[0329] ② Pump-valve-pipeline hydraulic coupling constraints

[0330] The pump station head needs to overcome the static head (water level difference), pipeline friction resistance, and local resistance of the gate valve:

[0331]

[0332] In the formula: Variable frequency pump exist The required head for a given period of time is expressed in meters (m). The water level of a downstream high-level pool or reservoir, in meters (m). The overall resistance coefficient (frictional resistance) of the pipeline is expressed in square seconds per fifth cubic meter. The local resistance coefficient of a gate valve is related to the valve opening degree. Nonlinear functions, dimensionless or without a specific unit. for The opening degree of the gate valve during the time period.

[0333] ③ Physical characteristic constraints of power frequency / variable frequency generator units

[0334] Industrial frequency units: There are only two discrete states, on and off. Their power is determined by the rated operating conditions. The power output of the industrial frequency pump depends entirely on its current operating state (on or off) and operating head, and it does not have continuous adjustment capability.

[0335] For the power frequency pump at the current forebay water level The shaft power characteristic function is given below, with units of kilowatts. For power frequency pump exist Start and stop status variables for a given time period.

[0336] The speed of the variable frequency unit is limited to a safe range and follows the similarity law:

[0337] For variable frequency pumps exist The actual rotational speed during the time period, in revolutions per minute; and These are the minimum and maximum permissible operating speed limits, respectively; This is the power characteristic function of the variable frequency pump at different speeds and water levels, in kilowatts.

[0338] ④ Complex sequential logic and rate control constraints

[0339] To ensure equipment lifespan and safety, the following constraints are introduced:

[0340] Minimum continuous running time and start / stop interval:

[0341] ,

[0342] The minimum continuous operating time after the unit starts up, in hours or scheduling steps; For the unit in The cumulative downtime prior to the current time; The minimum cooling interval required for restarting the unit after shutdown, in hours.

[0343] Maximum number of start-stop cycles:

[0344] The maximum number of start / stop operations allowed within a complete scheduling cycle, expressed in times. It is equal to 1 only when a state transition occurs, otherwise it is 0.

[0345] As mentioned above, this case incorporates the forebay water level as a dynamic decision variable into the economic dispatch model. By constraining the dynamic safe operating range, it keeps the system operating near the optimal water level, thus avoiding the increased energy consumption caused by traditional fixed water level constraints. Furthermore, these constraints comprehensively cover the engineering constraints involved in the coordinated dispatch of gate valves at cascade pumping stations, ensuring the feasibility of the dispatch scheme in actual engineering projects.

[0346] As a preferred implementation, this embodiment details the specific process of scheduling deviation monitoring and adaptive rolling correction. Specifically, it involves rolling rescheduling and fast solution based on MPC.

[0347] (1) Deviation monitoring and triggering mechanism

[0348] At each scheduling time, calculate the cumulative deviation between the actual cumulative water supply and the planned cumulative water supply up to the current time, and / or calculate the instantaneous deviation between the actual instantaneous water supply and the planned instantaneous water supply at the current time;

[0349] Deviation monitoring and triggering mechanism at each scheduling time Real-time monitoring of actual water supply Compared with planned value If determined If the deviation threshold is exceeded, a rescheduling procedure will be triggered immediately; otherwise, the original plan will continue to be executed.

[0350] In this embodiment, a dual monitoring mechanism of cumulative deviation and instantaneous deviation is specifically adopted:

[0351] Cumulative deviation: ;

[0352] Instantaneous deviation rate: %

[0353] When the absolute value of the cumulative deviation or the instantaneous deviation exceeds a preset threshold, a rolling correction mechanism is triggered. In this embodiment, the cumulative deviation threshold ΔV_threshold is set to 3.6 × 10⁻⁶. 4 m³ (equivalent to a water supply deficit of 15.0 m³ / s per hour), with an instantaneous deviation rate threshold ε_threshold = 5%. When the absolute value of the cumulative deviation exceeds ΔV_threshold, or the instantaneous deviation rate exceeds ε_threshold, a rolling correction mechanism is triggered. For example, the planned water supply at a certain moment... =15.0 m³ / s, actual water supply =14.1m³ / s, instantaneous deviation rate ε=|14.1-15.0| / 15.0×100%=6.0%>5%, triggering the rolling correction mechanism.

[0354] (2) State Reset and Vision Update

[0355] Once the rolling correction mechanism is triggered, the system performs the following state reset and view update operations:

[0356] [1] Update initial state: Set the current actual forebay water level. Set as the initial value for the optimization model, replacing the original plan. For example, if τ=10 (i.e., 10:00 AM), the originally planned water level at that time should be 49.5m, but the actual water level is 49.1m (due to an imbalance in the inflow and outflow of water in the forebay caused by a deviation in water supply). In this case, the rescheduling will use 49.1m as the new initial water level. At the same time, the actual operating status of each pump group is obtained: 2 fixed frequency pumps are running, 1 variable frequency pump is running at a speed ratio of 0.84, and another variable frequency pump is shut down for maintenance.

[0357] 【2】Update remaining tasks: Reallocate the water demand for the remaining time periods [τ+1,T] (i.e., 10:00-24:00, a total of 14 time periods), and add a hard constraint to the water balance constraint that "the total water supply must cover the accumulated deficit" to force the correction of the deviation:

[0358]

[0359] in This represents the cumulative water supply deficit as of time τ, which is the difference between the planned cumulative water supply and the actual cumulative water supply. For example, if the cumulative deficit as of time τ=10 is 3.6 × 10⁻⁶... 4 If the pumping volume is m³, then the total pumping volume of the pumping station in the remaining 14 time periods needs to make up for the deficit in addition to meeting the subsequent water demand.

[0360] [3] Extracting a new baseline: Based on the water demand for the remaining time periods after redistribution, extract the optimal forebay water level for each remaining time period t∈[τ+1,T] from the drift pattern library to form the corrected forebay water level setting trajectory.

[0361] (3) Resolve the economic scheduling model

[0362] Using the corrected forebay water level setting trajectory as a reference trajectory, the actual forebay water level at the current moment as the initial condition, and the actual pump group operating state at the current moment as the initial operating state, the coordinated economic scheduling model of the cascade pump station gate valve is re-solved to obtain the start-stop scheme, speed ratio setting value, flow distribution scheme and gate valve opening command for each pump group during the remaining time of the day.

[0363] In the re-solution process, for the mixed-integer nonlinear programming problem containing the start-stop state variables of the power frequency pump, a hierarchical iterative solver is designed to avoid the combinatorial explosion caused by the traditional branch-and-bound method:

[0364] [1] Upper layer (discrete layer dimensionality reduction: fixed water level) The start-stop combination matrix of the power frequency pump is determined preferentially using heuristic rules or genetic algorithms (GA). This step relaxes the complex MINLP problem into a nonlinear programming problem under given discrete states.

[0365] [2] Lower layer (continuous layer exact solution): For the nonlinear programming subproblem after dimensionality reduction, the alternating direction multiplier method is used for distributed solution. The global hydraulic coupling constraint is transformed into a local penalty term, so that the optimization problems of a single pump and a single valve are solved independently and in parallel; the main coordinator dynamically updates the Lagrange multipliers according to the global water level balance residual until it converges to the global feasible solution.

[0366] [3] Instruction issuance: The calculation is terminated when the improvement rate of the objective function is lower than the tolerance or the maximum number of iterations is reached, and only the current time step is output. The optimal forebay water level setpoint, target speed of each variable frequency pump, start / stop command of the fixed frequency pump, and valve adjustment step size are sent to the underlying control system for execution, and then enter the next control cycle.

[0367] As described above, this case establishes a deviation monitoring and adaptive triggering system, which automatically triggers rescheduling when the actual water supply deviates from the planned flow rate by a preset threshold. Through state reset (setting the current actual forebay water level as the initial value of the optimization model) and horizon update (redistributing the remaining water demand flow and adding a hard constraint to force the recovery of deviations), real-time compensation and correction of water supply prediction deviations and execution errors are achieved. Simultaneously, the hierarchical iterative solution architecture of discrete and continuous layers decomposes the mixed-integer nonlinear programming problem into two sub-problems: discrete combinatorial optimization and continuous parameter optimization. Distributed parallel solutions are achieved through the ADMM algorithm, effectively avoiding combinatorial explosion in traditional branch-and-bound methods. This allows rescheduling to be completed within a minute-level timescale, meeting the real-time scheduling requirements of the project.

[0368] As a preferred implementation, this embodiment details the steps of generating and rolling the day-ahead scheduling plan.

[0369] Before the start of the scheduling period, perform the day-ahead scheduling plan generation step:

[0370] First, based on the planned water supply for the day and the time-of-use electricity price information, the optimal forebay water level setpoint for each time period is retrieved from the drift pattern database to generate the daily forebay water level setpoint trajectory. For example, the planned water demand for each time period of the day is as follows:

[0371] Time period 0:00-8:00 (Valley) 8:00-9:00 (Standard) 9:00-12:00 (Peak) 12:00-17:00 (Standard) 17:00-22:00 (Peak) 22:00-24:00 (Standard) Q_demand(m³ / s) 10.0 12.0 8.0 14.0 9.0 11.0 H*_opt(m) 49.8 49.5 50.2 49.3 50.0 49.6

[0372] The aforementioned pre-day water level trajectory of the forebay is used as the input to the coordinated economic scheduling model of the gate valves of the cascade pumping station. With the objective of minimizing the power consumption cost of the pumps within the scheduling cycle, the pre-day scheduling scheme for each time period is solved and then issued for execution. The pre-day scheduling scheme includes the start-stop combination of the mains frequency pumps, the set value of the variable frequency pump speed ratio, and the gate valve opening command for each time period.

[0373] During intraday scheduling, if rolling correction is not triggered, the day-ahead scheduling plan continues to be executed, and the day-ahead water level trajectory of the forebay is tracked and corrected based on the actual forebay water level at the current moment. For example, at t=6, the planned forebay water level is 49.8m, and the actual forebay water level is 49.6m, with a deviation of 0.2m, which is within the allowable range. The water level is gradually brought back to the set trajectory by fine-tuning the variable frequency pump speed, without triggering rescheduling.

[0374] If a rolling correction is triggered, the scheduling instructions for the remaining time period in the daytime scheduling scheme are replaced with the re-solved collaborative scheduling scheme, and the setting values ​​for the remaining time period in the daytime forebay water level setting trajectory are replaced with the corrected forebay water level setting trajectory. For example, if a rolling correction is triggered at t=10, the scheduling instructions for 10:00-24:00 in the daytime scheduling scheme are replaced with the re-solved scheme, and the setting values ​​for 10:00-24:00 in the daytime forebay water level setting trajectory are replaced with the corrected setting trajectory.

[0375] As a preferred implementation, this embodiment details the dynamic updating of the pump station characteristic curve model during the scheduling process. Please refer to... Figure 5 This demonstrates the process of dynamically updating the characteristic curve model of the pumping station.

[0376] During the scheduling process, the pump station characteristic curve model is dynamically updated:

[0377] Each time a rolling correction is triggered, the actual operating flow rate, head, power, and efficiency data of each pump group at the current moment are recorded. For example, when the rolling correction is triggered at t=10, the actual operating data of pump No. 1 (stationary frequency pump) are recorded as follows: Qact=4.12m³ / s, Hact=33.2m, Pact=2395kW, ηact=58.5%; the actual operating data of pump No. 1 (variable frequency pump) are recorded as follows: Qact=3.38m³ / s, Hact=33.2m, Pact=1920kW, n r =0.81, ηact=57.2%.

[0378] When the accumulated actual operating data reaches a preset threshold (50 sets of data per pump group in this embodiment), the characteristic curve parameters of the corresponding pump group in the pump station characteristic curve model are corrected online using the actual operating data. Taking the head-flow characteristic curve of No. 1 power frequency pump as an example, the original fitting parameters are: =72.8, =1.35, =-0.82. The corrected parameters were obtained by re-fitting the least squares data using 50 sets of accumulated actual operating data. =73.1, =1.32, =-0.80, that is, H(Q)=73.1+1.32Q-0.80Q². The corrected curve parameters reflect the slight performance drift of the equipment during long-term operation (such as characteristic changes caused by impeller wear).

[0379] The corrected pump set characteristic curve parameters are updated in the pump station characteristic curve model for subsequent speed optimization and economic scheduling model solving. Through this dynamic update mechanism, the pump station characteristic curve model can adapt to performance drift caused by factors such as equipment aging and wear, ensuring the long-term effectiveness of scheduling optimization.

[0380] As described above, this invention solves the core problems in the coordinated economic scheduling of cascade pumping station gate valves, such as the inability of static plans to cope with dynamic deviations and the drift of model parameters as equipment ages, by constructing a multi-layer scheduling architecture that includes an offline drift pattern library, a day-ahead scheduling plan, online rolling correction, and dynamic model updates. This effectively ensures the economic scheduling performance of the cascade pumping station gate valve system under dynamic disturbance conditions.

[0381] In summary, this invention discloses a method and system for coordinated economic scheduling of a hybrid cascade pumping station and gate valves based on dynamic optimization of the forebay water level. The method collects static parameters and real-time operating data of the water diversion project; constructs a pumping station characteristic curve model under multiple parallel operating conditions, including single-pump operation, parallel operation of power frequency pumps, parallel operation of variable frequency pumps, and hybrid operation of power frequency and variable frequency pumps. Each pump in parallel operation has the same head at the same node, and the total system flow is equal to the sum of the flow rates of each parallel pump. Using the forebay water level as the optimization decision variable, different forebay water levels are traversed within the water level safety constraint range, and the corresponding total power of the pumping station system is calculated. The optimal speed combination corresponding to each forebay water level is determined through speed optimization, thereby obtaining the optimal forebay water level under different water supply flows, and constructing a database of the drift patterns between water supply flow and the optimal forebay water level. A coordinated economic scheduling model for cascade pumping stations and gate valves is established with the goal of minimizing the power consumption cost of water pumps within a scheduling cycle. The forebay water level is incorporated as a dynamic decision variable into the model, and the safe operating boundary of the forebay water level is obtained from a drift pattern database based on the current water supply flow. At each scheduling moment within the scheduling cycle, the deviation between the actual water supply and the planned water supply is compared with a preset threshold. When the deviation exceeds the preset threshold, the current actual forebay water level and the remaining water demand are used as initial boundary conditions. The corrected forebay water level trajectory is extracted from the drift pattern database, and the coordinated economic scheduling model for cascade pumping stations and gate valves is re-solved. This generates a coordinated scheduling scheme for pumping stations and gate valves for the remaining time period of the day, which is then issued for execution. This method overcomes the traditional conservative scheduling mode that treats the forebay water level as a fixed parameter, and overcomes the problem of decreased scheduling economy caused by water supply prediction deviations and execution errors. It significantly improves the economic scheduling performance and adaptive correction capability of the power-frequency hybrid cascade pumping station system under dynamic disturbance conditions.

[0382] Example 2

[0383] Please see Figure 5 , Figure 5This is a schematic diagram of a control system disclosed in an embodiment of the present invention. The control system may include:

[0384] Memory 201 storing executable program code;

[0385] Processor 202 coupled to memory 201;

[0386] Among them, the processor 202 calls the executable program code stored in the memory 201 to execute the economic scheduling method of the power and variable frequency hybrid cascade pump station and gate valve based on the dynamic optimization of the forebay water level.

[0387] As stated above, this case protects the method for coordinated economic dispatch of power and variable frequency hybrid cascade pump stations and gate valves based on dynamic optimization of forebay water level. All technical solutions that are the same as or similar to this case should be considered to fall within the scope of protection of this case.

Claims

1. A method for coordinated and economical scheduling of power-integrated variable frequency hybrid cascade pumping stations and gate valves based on dynamic optimization of forebay water level, characterized in that, Includes the following steps: Collect static parameters and real-time operating data of the water diversion project; the real-time operating data includes at least the forebay water level, reservoir water level, pipeline flow rate, and time-of-use electricity price of the power grid; A pump station characteristic curve model is constructed for parallel operation of power frequency pump sets under multiple operating conditions. The multiple operating conditions include single pump operation, parallel operation of power frequency pump sets, parallel operation of variable frequency pump sets, and mixed operation of power frequency and variable frequency pump sets. Among them, each pump set operating in parallel has the same head at the same node, and the total flow of the system is equal to the sum of the flow of each pump set in parallel. Based on the pump station characteristic curve model, the total system flow rate is obtained. The forebay water level is used as the optimization decision variable. Within the water level safety constraint range, different forebay water levels are traversed and the corresponding total power of the pump station system is calculated. The optimal speed combination corresponding to each forebay water level is determined by speed optimization, thereby obtaining the optimal forebay water level under different water supply flow rates and constructing a drift law library between water supply flow rate and optimal forebay water level. A coordinated economic scheduling model for gate valves of cascade pumping stations is established with the goal of minimizing the power consumption cost of water pumps within the scheduling cycle. The water level of the forebay is incorporated as a dynamic decision variable into the coordinated economic scheduling model for gate valves of cascade pumping stations, and the safe operating boundary of the water level of the forebay is obtained from the drift law library based on the current water supply flow. At each scheduling moment within the scheduling cycle, the deviation between the actual water supply and the planned water supply is compared with a preset threshold. When the deviation exceeds the preset threshold, the actual forebay water level and the remaining water demand are used as the initial boundary conditions. The corrected forebay water level setting trajectory is extracted from the drift law library, and the cascade pump station and gate valve coordinated economic scheduling model is re-solved to generate a pump station and gate valve coordinated scheduling scheme for the remaining time period of the day and issue it for execution.

2. The method according to claim 1, characterized in that, The static parameters of the project include: pump station unit fitting coefficient, pipeline length, pipeline diameter, pipeline friction coefficient, forebay surface area, reservoir characteristic water level, and valve flow coefficient; the real-time operating data include: forebay water level, high-level water tank water level, reservoir water level, pipeline flow, unit operating status, and grid time-of-use electricity price.

3. The method according to claim 1, characterized in that, The construction of the pump station characteristic curve model for the variable frequency pump set under multiple operating conditions in parallel includes: Generate single-pump characteristic curves for the power frequency pump set: Collect multiple sets of measured data on flow rate, head, power, and efficiency of a single power frequency pump at its rated speed, and establish flow rate-head characteristic curves, flow rate-power characteristic curves, and flow rate-efficiency characteristic curves using quadratic polynomials to obtain the single-pump characteristic curves of the power frequency pump set; the speed of the power frequency pump is fixed, and the fitted single-pump characteristic curves of the power frequency pump set are used for single-pump operating condition calculations. Variable frequency pump reference curve fitting and speed conversion: The reference characteristic curve is obtained by second fitting of the rated operating condition data of the variable frequency pump. The speed ratio is defined as the ratio of the actual speed to the rated speed. Based on the pump similarity law, the real-time characteristic curve of the variable frequency pump under different operating speeds is calculated. Based on the constraints of equal pump head and total system flow equal to the sum of flow rates of all parallel pump sets, characteristic curve models of the pump station are constructed for single-pump operation, parallel operation of power frequency pump sets, parallel operation of variable frequency pump sets, and mixed operation of power frequency and variable frequency pump sets. For single-pump operation, the single-pump characteristic curve of the power frequency pump set or the real-time characteristic curve of the variable frequency pump is directly used as the characteristic curve model of the pump station. For parallel operation of power frequency pump sets, the individual pump characteristic curves of each power frequency pump participating in the parallel operation are used as input. Under a given head condition, the flow rate of each pump is calculated using the flow-head characteristic curves of each power frequency pump set, and the total system flow rate is obtained by summing them. The data point set of head-to-flow rate is obtained by traversing different head values, and the head-flow rate joint characteristic curve of the power frequency pump set is obtained by fitting. The power-flow rate joint characteristic curve and the efficiency-flow rate joint characteristic curve of the power frequency pump set are obtained according to the same principle. The head-flow rate joint characteristic curve, the power-flow rate joint characteristic curve, and the efficiency-flow rate joint characteristic curve of the power frequency pump set constitute the pump station characteristic curve model. For parallel operation of variable frequency pump sets, the real-time characteristic curves of each variable frequency pump set at its respective operating speed are used as input. Based on parallel constraints, the flow rates of each pump are calculated and accumulated to obtain the total system flow rate under given head and actual speed ratio conditions. Different combinations of head and actual speed ratio are traversed to obtain data point sets and fit them to obtain the head-flow rate joint characteristic curve of the variable frequency pump set. The power-flow rate joint characteristic curve and the efficiency-flow rate joint characteristic curve of the variable frequency pump set are obtained according to the same principle. The head-flow rate joint characteristic curve, the power-flow rate joint characteristic curve, and the efficiency-flow rate joint characteristic curve of the variable frequency pump set constitute the pump station characteristic curve model. For the mixed operation of power frequency and variable frequency pump sets, the single pump characteristic curve of the power frequency pump set and the real-time characteristic curve of the variable frequency pump set are used as inputs. Based on parallel constraints, the total flow rate of the power frequency part and the variable frequency part are calculated separately and then added together to obtain the total system flow rate. Under the condition of setting the head calculation range and the speed ratio range, different head and speed ratio combinations are traversed to obtain the data point set, and a fully connected neural network model is used to fit the head-flow characteristic curve of the power frequency and variable frequency pump set pump station. Based on the same principle, the power-flow joint characteristic curve and the efficiency-flow joint characteristic curve of the power frequency and variable frequency pump set are obtained. The head-flow joint characteristic curve, the power-flow joint characteristic curve, and the efficiency-flow joint characteristic curve of the power frequency and variable frequency pump set constitute the pump station characteristic curve model.

4. The method according to claim 3, characterized in that, The acquired data point set is fitted using a fully connected neural network model to obtain the head-flow characteristic curve of the power frequency variable frequency pump unit. Based on the same principle, the power-flow joint characteristic curve and the efficiency-flow joint characteristic curve of the power frequency variable frequency pump unit are also obtained, including: The flow rates of each pump in the power frequency pump group and the variable frequency pump group at the same head are superimposed to obtain the total system flow rate corresponding to that head. All combinations within the set head calculation range and speed ratio range are traversed to form a set of joint characteristic data points with head and speed ratio of each variable frequency pump as input and total system flow rate as output. A fully connected neural network model is used to train and fit the set of joint characteristic data points to obtain the joint characteristic curve of the head and flow rate of the power frequency variable frequency pump set. Based on the combined head-flow characteristic curve of the power frequency variable frequency pump set, the corresponding total system flow is calculated under a given head and speed ratio combination. Then, the total system flow is substituted into the power-flow characteristic curve of each pump set, and the total system power is obtained by summing them up. In this way, the correspondence between the total system power and the total system flow is established, and the combined power-flow characteristic curve of the power frequency variable frequency pump set is obtained by fitting. Based on the combined head-flow characteristic curve of the power frequency variable frequency pump set, the corresponding total system flow rate is calculated under a given head and speed ratio combination. Then, the total system flow rate is substituted into the efficiency-flow characteristic curve of each pump set, and the overall system efficiency is calculated by weighting by flow rate. Finally, the correspondence between the overall system efficiency and the total system flow rate is established, and the combined efficiency-flow characteristic curve of the power frequency variable frequency pump set is obtained by fitting.

5. The method according to claim 1, characterized in that, The system's total flow rate is obtained based on the pump station characteristic curve model. The forebay water level is used as the optimization decision variable. Within the water level safety constraint range, different forebay water levels are traversed, and the corresponding total power of the pump station system is calculated. The optimal rotational speed combination corresponding to each forebay water level is determined through rotational speed optimization, thereby obtaining the optimal forebay water level under different water supply flows. A drift law library between water supply flow and optimal forebay water level is constructed, including: The range of water levels in the forebay is defined, and the upper and lower limits of the range are determined by the design maximum and design minimum water levels in the forebay. Within the traversal range, values ​​are discretely selected according to a preset step size to obtain multiple candidate forebay water levels; For each candidate forebay water level, based on the current water supply flow demand and the pump station characteristic curve model, and under the condition of satisfying the speed ratio constraints of each variable frequency pump, with the goal of minimizing the total power of the pump station system, the optimal speed ratio combination of each variable frequency pump is calculated using an optimization algorithm, so that the pump station system outputs the target flow with the minimum total power at the forebay water level. Record the minimum total power of the pumping station system corresponding to each candidate forebay water level and its corresponding optimal speed ratio combination; Multiple typical water supply flow values ​​are set, which cover the range from the minimum to the maximum water supply flow of the water diversion project; For each typical water supply flow, the forebay water level is traversed and the minimum total power of the pumping station system corresponding to each candidate water level is calculated. The forebay water level corresponding to the minimum total power is selected as the optimal forebay water level under that water supply flow. Each typical water supply flow rate is associated with and stored in conjunction with its corresponding optimal forebay water level, minimum total system power, and corresponding optimal speed ratio, forming a mapping relationship between water supply flow rate and optimal forebay water level, thereby constructing the drift law library.

6. The method according to claim 5, characterized in that, The optimal speed ratio combination for each variable frequency pump is calculated using an optimization algorithm, including: The head-flow combined characteristic curve and the power-flow combined characteristic curve in the pump station characteristic curve model are used as inputs for constraints and cost functions; An optimization problem is established with the goal of minimizing the total power of the pumping station system. The decision variables of the optimization problem are the speed ratio of each variable frequency pump and the flow distribution of each pump group. The constraints include the total system flow being equal to the target water supply flow, the system head being equal to the current system head corresponding to the forebay water level, the speed ratio of each variable frequency pump being within the allowable range, and the flow of each pump group being within the allowable operating range. The optimization problem is solved using an optimization algorithm to obtain the optimal speed ratio combination of each variable frequency pump and the optimal flow distribution scheme of each pump group; The construction of the drift pattern library also includes: When the current water supply flow does not fall within the typical water supply flow value, the corresponding optimal forebay water level is obtained by interpolation from the mapping relationship using an interpolation method. Based on the time-of-use electricity price information of the power grid, the optimal forebay water level corresponding to different electricity price periods under each typical water supply flow is associated and stored in the drift pattern database, forming a time-of-use drift pattern sub-database.

7. The method according to claim 1, characterized in that, The establishment of a coordinated economic scheduling model for cascade pumping station gate valves, aimed at minimizing the power consumption cost of water pumps within a scheduling cycle, incorporates the forebay water level as a dynamic decision variable into the model. It also obtains the safe operating boundary of the forebay water level from the drift pattern database based on the current water supply flow. This includes: An objective function is constructed with the goal of minimizing the sum of the power consumption costs of water pumps in each time period within the scheduling cycle. The power consumption costs of water pumps are determined based on the shaft power of each pump group participating in operation in each time period, the time-of-use electricity price of the corresponding time period, and the duration of the time period. The forebay water level at each time period is incorporated as a dynamic decision variable into the cascade pump station gate valve coordinated economic scheduling model. The forebay water level at each time period is continuously measured within the dynamic safe operation range of the corresponding time period. The dynamic safe operation range is obtained from the drift law database based on the current water supply flow: the smaller value between the highest designed water level of the forebay and the optimal water level of the forebay corresponding to the current water supply flow is used as the upper limit of the forebay water level, and the larger value between the lowest designed water level of the forebay and the optimal water level of the forebay corresponding to the current water supply flow is used as the lower limit of the forebay water level. The dynamic safe operation range is composed of the upper limit of the forebay water level and the lower limit of the forebay water level. The cascade pump station gate valve coordinated economic scheduling model also includes the following constraints: Hydraulic balance and dynamic constraints on forebay water level: the forebay water level changes dynamically with the difference between inflow and outflow rates, and the safe operating boundary is adaptively adjusted according to the current water supply flow rate. Hydraulic coupling constraints mean that the pump station head must overcome static head, pipeline friction resistance, and local resistance of gate valves. Due to the physical characteristics of the unit, the power of the fixed frequency pump is determined by the start-stop state and the working head, while the speed of the variable frequency pump is limited to a safe range and the power follows a similarity law. Complex timing logic and regulation rate constraints, including minimum continuous operating time constraints, start-stop interval constraints, and maximum number of start-stops limits.

8. The method according to claim 1, characterized in that, At each scheduling moment within the scheduling cycle, the deviation between the actual water supply and the planned water supply is compared with a preset threshold. When the deviation exceeds the preset threshold, using the current actual forebay water level and remaining water demand as initial boundary conditions, the corrected forebay water level setting trajectory is extracted from the drift pattern database. The coordinated economic scheduling model of the cascade pumping station and gate valves is re-solved, generating a coordinated scheduling scheme for the pumping station and gate valves for the remaining time period of the day, which is then issued for execution. At each scheduling moment, the deviation between the actual water supply and the planned water supply is monitored in real time; When the absolute value of the deviation between the actual water supply and the planned water supply exceeds a preset threshold, a rolling correction mechanism is triggered. Set the current actual water level in the forebay as the initial value of the optimization model, replacing the original planned value; The remaining water demand flow is reallocated, and a hard constraint on accumulated deficit is added to force the recovery of deviations; the accumulated deficit is the difference between the planned cumulative water supply and the actual cumulative water supply up to the current moment. Based on the redistributed remaining water demand flow rate, the forebay water level setting trajectory for each remaining time period is extracted from the drift pattern library to form the corrected forebay water level setting trajectory. Using the modified forebay water level setting trajectory as a reference trajectory, the actual forebay water level at the current moment as the initial condition, and the actual pump group operating state at the current moment as the initial operating state, the cascade pump station gate valve coordinated economic scheduling model is re-solved to obtain the start-stop scheme, speed ratio setting value, flow distribution scheme and gate valve opening command for each pump group during the remaining time of the day. The re-solved collaborative scheduling scheme is then sent to the pump station control system and the gate valve control system for execution.

9. The method according to claim 1, characterized in that, It also includes the steps for generating and rolling over the day-ahead scheduling plan: Before the start of the scheduling cycle, based on the planned water supply for the day and the time-of-use electricity price information of the power grid, the optimal forebay water level setting value for each time period is queried from the drift pattern database to generate the forebay water level daily setting trajectory. The daily set trajectory of the forebay water level is used as the input of the coordinated economic scheduling model of the gate valves of the cascade pumping station. With the goal of minimizing the power consumption cost of the pumps within the scheduling cycle, the daily scheduling scheme for each time period is solved and issued for execution. If rolling correction is not triggered during intraday scheduling, the day-ahead scheduling scheme will continue to be executed, and the day-ahead water level trajectory of the forebay will be tracked and corrected based on the actual forebay water level at the current moment. If a rolling correction is triggered, the scheduling instructions for the remaining time period in the daytime scheduling scheme are replaced with the re-solved collaborative scheduling scheme, and the setting value for the remaining time period in the daytime setting trajectory of the forebay water level is replaced with the corrected forebay water level setting trajectory.

10. The method according to claim 8, characterized in that, The pump station characteristic curve model is dynamically updated during the scheduling process: Each time a rolling correction is triggered, the actual operating flow rate, head, power, and efficiency data of each pump group at the current moment are recorded. When the accumulated actual operating data reaches a preset threshold, the actual operating data is used to correct the characteristic curve parameters of the corresponding pump group in the pump station characteristic curve model online. The corrected pump set characteristic curve parameters are updated to the pump station characteristic curve model for subsequent speed optimization and economic scheduling model solving.

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