A dynamic programming-based parallel pump group scheduling method and system

Abstract

This invention discloses a parallel pump group scheduling method and system based on dynamic programming, belonging to the technical field of intelligent pump group scheduling. The method involves data acquisition and preprocessing, discretizing and equivalently treating the variable frequency pumps as n equivalent fixed frequency pumps. Then, single-pump performance curves and pipeline network performance curves are fitted. Based on the single-pump performance curves, the high-efficiency operating range of each pump is determined. Then, using water supply flow demand, water supply head demand, and the high-efficiency operating range of each pump as hard constraints for pump group operation, candidate pump group combinations are selected. The start-up and shutdown costs and usage time of each pump are incorporated as soft constraints into the total cost, constructing a minimum objective function for the total cost. Finally, a dynamic programming algorithm is used to obtain the global optimal solution, generating the optimal pump group scheduling sequence within the scheduling cycle. This invention balances low energy consumption and equipment health, and is applicable to mixed pump group scenarios including fixed-frequency and variable frequency pumps, significantly reducing energy consumption in traditional scheduling and mitigating equipment wear.

Description

Technical Field

[0001] This invention belongs to the technical field of intelligent pump scheduling, specifically relating to a method and system for scheduling parallel pump groups based on dynamic programming. Background Technology

[0002] As a core component of municipal infrastructure, urban water supply pumping stations account for a high proportion of the total operating cost of the water supply system. They also suffer from problems such as frequent pump start-ups and shutdowns, prolonged heavy-duty operation, and operating conditions deviating from the efficient operating range of individual pumps, leading to increased equipment failure rates. However, existing technologies largely focus on the single objective of "minimizing energy consumption," employing biomimetic algorithms to solve pump scheduling schemes. These algorithms suffer from issues such as the inability to guarantee global optimality, coarse modeling of mixed pump groups, and a lack of equipment health constraints, making it difficult to simultaneously achieve energy consumption optimization and long-term equipment operation.

[0003] For example, Chinese patent CN116702611A discloses a pump group optimization method based on a genetic algorithm, aiming to solve the problems of excessive power consumption, long-term deviation of pumps from their efficient operating range, and unstable water supply caused by the reliance on manual experience in waterworks pumping stations. The method includes: Step S1, collecting and analyzing performance test reports and actual production data of each pump in the pumping station to obtain a pump group optimization model, which includes constraints and a fitness function; Step S2, applying the pump group optimization model to water distribution units; Step S3, constructing a genetic algorithm framework based on the problem to be optimized and the fitness function; Step S4, processing the outflow rate and pressure of the water distribution unit using the pump group optimization model and iterating using the genetic algorithm to obtain an optimized pump group combination. This technical solution aims to minimize energy consumption and enables the regulation and use of fixed-frequency or variable-frequency pumps.

[0004] Chinese patent CN119491828A discloses an energy efficiency optimization method for parallel pump sets based on an improved wolf-sparrow algorithm. This method aims to address the problems of slow convergence speed and susceptibility to local optima in single intelligent algorithms, as well as the high energy consumption of traditional "one-to-many" control modes. The method involves obtaining basic data of the target pipeline network through centrifugal pump hydraulic performance tests; establishing polynomial fitting equations for flow rate-head and flow rate-power at different pump speeds; constructing the objective function of the parallel pump set optimization model according to requirements; constructing and considering the constraints of the parallel pump set optimization model; and solving the problem using the improved wolf-sparrow algorithm to obtain the control scheme for the parallel pump set optimization model.

[0005] Chinese patent CN118309640A discloses a method and system for intelligent scheduling of pump sets based on evolutionary algorithms, aiming to solve the energy waste problem caused by the reliance on fixed rules or manual control in traditional pump set scheduling, which suffers from poor flexibility and insufficient real-time response. The system includes pump sets, a sensor unit group, a scheduling control unit, and a display unit. It uses a combination of input frequency ranges corresponding to the combination of inlet water pressure ranges for each variable frequency pump as an optimization resource library; calculates the working efficiency of each variable frequency pump at the current acquisition moment; determines whether the inlet or outlet water pressure of the variable frequency pump has changed; if not, no response is taken; if so, within the rated frequency range of each variable frequency pump, the optimal input frequency for each pump is obtained by comparing and matching the inlet water pressure and input frequency of each pump at the current moment within the optimization resource library, and then executing the algorithm.

[0006] However, the above method has the following problems:

[0007] (1) Algorithm level: Global optimality cannot be guaranteed and time-series adaptability is insufficient; existing technologies all use biomimetic algorithms such as genetic algorithms, improved gray wolf-sparrow algorithms, and evolutionary algorithms, which are essentially random heuristic search, can only approximate suboptimal solutions, and cannot theoretically prove global optimality; moreover, biomimetic algorithms need to solve through a large number of population iterations, which is difficult to adapt to the real-time scheduling requirements of pumping stations.

[0008] (2) Model level: The modeling of the hybrid pump set is rough and the performance adaptability of the variable frequency pump is poor. For the scenario of mixed combination of fixed frequency pump and variable frequency pump, the existing technology has not solved the problem of the difference in pump performance curves in the pump set at different speeds of the variable frequency pump. The lack of a "performance curve consistency verification" mechanism may lead to illegal schemes with mismatched flow rate / head of the combined pump set.

[0009] (3) Constraint level: Insufficient equipment health protection; Existing technologies all take "minimizing energy consumption" as the core objective, and only use the high-efficiency operating range of a single pump and the number of start-stop cycles as soft constraints, without avoiding the problem of long-term heavy-load operation of a single pump, and the equipment failure rate and life loss have not been effectively controlled. Summary of the Invention

[0010] The purpose of this invention is to provide a method and system for scheduling parallel pump groups based on dynamic programming, aiming to solve any of the above-mentioned problems.

[0011] This invention is mainly achieved through the following technical solutions:

[0012] A method for scheduling parallel pump sets based on dynamic programming includes the following steps:

[0013] Step S1: Data acquisition and preprocessing;

[0014] Step S2: Discretize and treat the variable frequency pump as an equivalent pump: Discretize the variable frequency pump as n equivalent fixed frequency pumps; then, fit the single pump performance curve and the pipeline network performance curve respectively.

[0015] Step S3: Determine the high-efficiency operating range of a single pump based on its performance curve. Then, using the water supply flow rate demand, water supply head demand, and the high-efficiency operating range of the single pump as hard constraints for pump group operation, candidate pump group combinations are selected. ;

[0016] Step S4: Incorporate the start-up and shutdown cost of a single pump and its usage duration as soft constraints into the total cost to construct an objective function that minimizes the total cost; finally, obtain the global optimal solution through a dynamic programming (DP) algorithm to generate the optimal pump group scheduling sequence within the scheduling cycle.

[0017] To better implement the present invention, step S1 further includes the following steps:

[0018] Step S11: First, collect data on the independent operation of a single pump, data on the main outlet pipe of the pumping station, and basic parameters of the single pump equipment;

[0019] The individual pump operation data includes pump outlet flow rate Q, pump inlet and outlet pressure difference ΔP, motor input voltage U, current I, and operating frequency f; the pump station outlet main pipe data includes the total flow rate of the main pipe. The basic parameters of the single pump equipment include the rated flow rate. Rated head Rated frequency Rated efficiency Rated power of motor ;

[0020] Step S12: Then, perform data preprocessing to unify the time granularity and ensure that the data remains consistent over time.

[0021] To better realize the present invention, step S2 further includes the following steps:

[0022] Step S21: Discretize the variable frequency pump as n equivalent fixed frequency pumps and derive the core performance parameters of each equivalent fixed frequency pump;

[0023] ;

[0024] in: These are the rated flow rate, rated head, and rated motor power of the equivalent fixed-frequency pump, respectively.

[0025] The discrete target frequency of the variable frequency pump;

[0026] Step S22: Single pump performance curve fitting;

[0027] (1) Fitting the flow-head curve based on a quadratic polynomial;

[0028] ;

[0029] Where: H is the head of a single pump;

[0030] Q is the pump outlet flow rate;

[0031] These are the fitting coefficients for the head curve;

[0032] (2) Fitting the flow-power curve based on quadratic polynomial fitting;

[0033] ;

[0034] Where: W is the motor input power;

[0035] Q is the pump outlet flow rate;

[0036] These are the power curve fitting coefficients;

[0037] Step S23: Pipeline performance curve fitting;

[0038] ;

[0039] in: To oversee Yang Cheng;

[0040] For total flow rate;

[0041] For the static head of the pipeline network;

[0042] This is the pipeline resistance coefficient.

[0043] To better realize the present invention, step S3 further includes the following steps:

[0044] Step S31: Defining the high-efficiency operating range of a single pump; based on the fact that the efficiency of a variable speed pump is approximately constant at different speeds, the efficiency of a single pump is limited. Operating within the high-efficiency operating range of a single pump, the fitting equations of the combined flow-head and flow-power curves are used to derive the quadratic equation for critical efficiency. Solving this equation yields the high-efficiency operating range of the single pump. ;

[0045] in: The maximum flow rate for the high-efficiency operating range;

[0046] This is the lower limit of the flow rate for the high-efficiency operating range;

[0047] Step S32: Calculate the equilibrium operating point; by analyzing the individual pump performance curves and pipeline characteristic curves of each pump in the combined pump set, the steady-state equilibrium operating point is obtained. , ),in, =General Manager's Head , =Total flow rate ;

[0048] Step S33: Establish hard constraints for the steady-state operating conditions of the pump set and screen out candidate pump set combinations. ;

[0049] The steady-state flow rate of a single pump is at Within the interval; and satisfying:

[0050] ;

[0051] in: , These represent the lower limit of flow demand and the lower limit of head demand for a certain period of time, respectively.

[0052] To better realize the present invention, further, in step S31, the single pump efficiency is limited. By combining the fitting equations of the flow-head curve and the flow-power curve, the quadratic equation for critical efficiency is obtained:

[0053] ;

[0054] in: The density of water;

[0055] This is the acceleration due to gravity.

[0056] To better implement this invention, in step S4, the X-hour scheduling period is further divided into 24 discrete time periods; the objective function to be minimized is constructed as follows:

[0057] ;

[0058] ;

[0059] ;

[0060] Where: J represents the total cost;

[0061] For the first Energy consumption of pump unit combination during different time periods;

[0062] For the first Pump start-stop switching losses during specific time periods;

[0063] For the first Loss during single-pump operation time;

[0064] Cost per pump per start-up and shutdown;

[0065] N() is a counting function;

[0066] This refers to the number of pumps that are shut down;

[0067] This refers to the number of pumps that are in operation.

[0068] This is a pre-assembled set of single pumps;

[0069] For a combination of single pumps;

[0070] For the first The operating status of the j-th pump during the time period;

[0071] For the first The cumulative runtime of the j-th pump during the time period;

[0072] This is the runtime loss factor;

[0073] m represents the total volume of the water pump.

[0074] To better implement the present invention, further, in step S4, the DP solving algorithm includes the following steps:

[0075] Step T1: Data and Parameter Initialization: Obtain Candidate Pump Set Combinations Initialize the DP state matrix and predecessor backtracking matrix with 24-hour time-series supply and demand data;

[0076] Step T2: Initial time period state assignment: Traverse all legal pump group combinations in hour 0, calculate initial energy consumption and initial operating loss, and complete the initial assignment of DP matrix;

[0077] Step T3: Forward recursion for each time period: From hour 1 to hour 23, traverse the legal combinations for each time period, compare with all previous legal combinations, calculate the total cost, and retain the decision and state corresponding to the minimum cost;

[0078] Step T4: Backtracking the optimal solution: Select the combination with the minimum total cost in the 23rd hour as the endpoint, backtrack the predecessor combination, and generate the optimal pump group scheduling sequence for 24 hours.

[0079] This invention is mainly achieved through the following technical solutions:

[0080] A parallel pump group scheduling system based on dynamic programming, which is based on the above-mentioned parallel pump group scheduling method based on dynamic programming, includes a data acquisition and preprocessing module, a variable frequency pump equivalent processing module, a hard constraint screening module, a soft constraint objective function module, and a DP solution module.

[0081] The data acquisition and preprocessing module is used to collect and preprocess data of independent operation of a single pump, data of the pump station outlet main pipe, and basic parameters of a single pump.

[0082] The variable frequency pump equivalent processing module is used to convert the discrete variable frequency pump into n equivalent fixed frequency pumps, and to fit the single pump performance curve and the pipeline network performance curve.

[0083] The hard constraint screening module is used to determine the high-efficiency operating range of a single pump and to construct hard constraints to screen candidate pump group combinations. ;

[0084] The soft-constraint objective function module is used to construct an objective function that minimizes the total cost, and the DP solution module is used to calculate the globally optimal solution by minimizing the objective function and generate the optimal pump group scheduling sequence within the scheduling cycle.

[0085] The beneficial effects of this invention are as follows:

[0086] (1) This invention balances low energy consumption and equipment health, and can be applied to mixed pump group scenarios that include fixed-frequency pumps and variable-frequency pumps. It solves the problems existing in the current water supply pump group scheduling technology, such as the bionic algorithm being prone to getting trapped in local optima, the modeling of fixed-frequency-variable-frequency mixed pump groups being coarse, and the failure to consider the long-term heavy-load operation of a single pump. This invention significantly reduces energy consumption in traditional scheduling and reduces the degree of equipment wear.

[0087] (2) Based on the core characteristics of dynamic programming, namely "optimal substructure + no aftereffect", this invention constructs an optimization framework of "hard constraints defining the boundary, soft constraints optimizing the cost and guiding the equilibrium": the hard constraints of water supply flow demand, water supply head demand, and single pump high-efficiency operation range are used as the pump group operation to limit the boundary of the algorithm solution; the start-up and shutdown cost of a single pump and the usage time are used as soft constraints to be integrated into the total cost, and finally the global optimal solution at the algorithm level is solved by DP, which takes into account both energy consumption and equipment health requirements and has good practicality.

[0088] (3) This invention employs a dynamic programming algorithm, relying on the characteristics of "optimal substructure + no aftereffect" to ensure the global optimal solution of the time-series scheduling, thus solving the problem of "suboptimal solution + random search" in biomimetic algorithms. This invention proposes a unified modeling method for the discretization of variable frequency pumps, discretizing the continuous speed of the variable frequency pump into n fixed speeds (equivalent to "virtual fixed frequency pumps"), forming a unified parallel combination system with the actual fixed frequency pumps, solving the problem of matching the performance curves of variable frequency pumps with those of fixed frequency pumps at different speeds, and improving the modeling accuracy of hybrid pump groups. This invention constructs equipment-friendly constraints, using the high-efficiency operating range of a single pump as a prerequisite for combination screening (hard constraint), and guiding each pump to participate in operation in a balanced manner through a penalty mechanism for frequent use of a single pump (soft constraint), thereby extending the service life of the equipment.

[0089] (4) Potential application scenarios of the present invention include:

[0090] Pump scheduling in municipal wastewater treatment plants: This is applied to the coordinated scheduling of multiple types of pumps, such as influent pumps, return pumps, and sludge pumps, in wastewater treatment plants. By taking into account the diurnal fluctuation characteristics of wastewater volume, the system balances the operating time of each pump while meeting the flow rate, pressure requirements, and energy consumption reduction targets of wastewater treatment processes. This can avoid problems such as blockage and wear caused by long-term heavy loads on a single pump.

[0091] Industrial Park Circulating Water / Water Supply System Scheduling: Adapted to circulating cooling water pumps and production water supply pump sets in industrial parks such as chemical, electronics, and pharmaceutical industries. In response to the dynamic changes in the production load of the park, the system protects industrial-grade pump set equipment through hard constraints on the number of start-stop cycles, and reduces equipment maintenance downtime by leveraging a single pump balancing mechanism.

[0092] Pump scheduling for secondary water supply in high-rise buildings: Applied to secondary pressurized water supply systems in high-rise buildings and commercial complexes, this system addresses the significant peak and valley differences in residential water consumption. Under the premise of meeting the standards for end-point water supply pressure and optimizing energy consumption, it avoids performance degradation caused by long-term idleness of some pumps by balancing the operating time of each pressurized pump. Attached Figure Description

[0093] Figure 1 This is a flowchart of the parallel pump group scheduling method based on dynamic programming according to the present invention. Detailed Implementation

[0094] Example 1:

[0095] A parallel pump scheduling method based on dynamic programming aims to address the following issues in existing water supply pump scheduling technologies: biomimetic algorithms are prone to getting trapped in local optima, the modeling of fixed-frequency-variable-frequency hybrid pump sets is coarse, and the problem of long-term heavy-load operation of a single pump is not considered. Figure 1 As shown, it includes the following steps:

[0096] Step S1: Data acquisition and preprocessing;

[0097] Step S2: Discretize and treat the variable frequency pump as an equivalent pump: Discretize the variable frequency pump as n equivalent fixed frequency pumps; then, fit the single pump performance curve and the pipeline network performance curve respectively.

[0098] Step S3: Determine the high-efficiency operating range of a single pump based on its performance curve. Then, using the water supply flow rate demand, water supply head demand, and the high-efficiency operating range of the single pump as hard constraints for pump group operation, candidate pump group combinations are selected. ;

[0099] Step S4: Incorporate the start-up and shutdown cost of a single pump and its usage duration as soft constraints into the total cost to construct an objective function that minimizes the total cost; finally, obtain the global optimal solution through a dynamic programming (DP) algorithm to generate the optimal pump group scheduling sequence within the scheduling cycle.

[0100] This invention introduces a dynamic programming algorithm: abandoning the biomimetic algorithm that is prone to getting trapped in local optima, it adopts dynamic programming to achieve the global optimal solution for 24-hour scheduling. Furthermore, through the lightweight state (time period × pump group combination) design, it reduces computational complexity and better adapts to the real-time scheduling needs of water plants.

[0101] This invention addresses the characteristics of hybrid pump sets by discretizing the continuous speed of a variable frequency pump into n fixed speeds and equating them to a virtual fixed frequency pump. This breaks down the modeling barriers between fixed frequency and variable frequency pumps, enabling unified adaptation and combination selection for the two types of pump sets.

[0102] This invention introduces a new single-pump usage time penalty mechanism: based on existing research on "reducing start-up and shutdown and improving pump efficiency", an additional single-pump usage time penalty item is introduced (the longer the usage time, the higher the penalty cost), which guides the balanced operation of each pump from the cost dimension and avoids the problem of long-term heavy load on a single pump from the root.

[0103] In summary, this invention, based on the core characteristics of dynamic programming—"optimal substructure + no aftereffect"—constructs an optimization framework of "hard constraints defining boundaries, soft constraints optimizing costs and guiding equilibrium." Hard constraints on pump operation include water supply flow demand, water supply head demand, and the high-efficiency operating range of a single pump, limiting the boundaries of the algorithm's solution. Soft constraints on single pump start-up and shutdown costs and usage time are incorporated into the total cost. Finally, the global optimal solution at the algorithm level is obtained through dynamic programming, balancing energy consumption and equipment health requirements, and demonstrating good practicality.

[0104] Example 2:

[0105] A method for scheduling parallel pump sets based on dynamic programming includes the following steps:

[0106] Step S1: Data acquisition and preprocessing;

[0107] Step S1: Collect independent operation data of a single pump, data of the pump station outlet main pipe, and basic parameters of the single pump equipment;

[0108] ①Single pump independent operation data: pump outlet flow rate Q (m³ / h), pump inlet and outlet pressure difference ΔP (MPa), motor input voltage U (kV), current I (A), operating frequency f (Hz);

[0109] ② Pump station outlet main pipe data: total flow rate of the main pipe (m³ / h), covering the entire water usage cycle;

[0110] ③ Basic parameters of a single pump: rated flow rate (m³ / h), rated head (m), rated frequency (Hz), rated efficiency (%), Rated power of motor (W).

[0111] Step S12: Data preprocessing, unifying the time granularity to ensure data consistency over time;

[0112] ①Outlier removal: The 3σ criterion is used to calculate the mean and standard deviation of a single class of data, and to remove extreme outliers that exceed the mean ± 3σ range;

[0113] ② Missing value completion: Linear interpolation is used to complete the missing values ​​while maintaining temporal continuity;

[0114] ③ Uniform time granularity: Unify the timestamps of all collected data and aggregate them by hourly granularity to ensure data consistency over time.

[0115] Step S2: Discretize and treat the variable frequency pump as an equivalent pump: Discretize the variable frequency pump as n equivalent fixed frequency pumps; then, fit the single pump performance curve and the pipeline network performance curve respectively.

[0116] Step S21: Discrete equivalent processing of the variable frequency pump;

[0117] If we consider the variable frequency pump as n equivalent fixed frequency pumps, and rely on the pump similarity law, the core performance parameters of each equivalent fixed frequency pump can be derived from the rated parameters of the equipment, as shown in the following formula:

[0118]

[0119] in: The rated flow rate, rated head, and rated motor power of the equivalent fixed-frequency pump are given. Let be the discrete target frequency of the variable frequency pump, and 'i' be the index. After the equivalence is completed, the variable frequency pump will be treated as a fixed frequency pump for subsequent calculations.

[0120] Step S22: Single pump performance curve fitting;

[0121] (1) Flow-head curve fitting: Quadratic polynomial fitting was used, and the coefficients were solved by the least squares method:

[0122] (1)

[0123] (2)

[0124] Where: H is the head of a single pump (m). This is the density of water (1000 kg / m³). The acceleration due to gravity is 9.81 m / s². These are the fitting coefficients for the head curve.

[0125] (2) Flow-power curve fitting: Quadratic polynomial fitting is used, and the solution method is the same as above:

[0126] (3)

[0127] ;

[0128] Where: W is the motor input power (W). This refers to the rated power factor of the motor (an inherent parameter of the equipment). These are the power curve fitting coefficients.

[0129] Step S23: Pipeline performance curve fitting;

[0130] Define the secondary resistance equation for the pipeline network and solve for the coefficients using the least squares method:

[0131] ;

[0132] in: The total head (m) is the head of the main pump. The static head of the pipeline (m, to be fitted). This is the pipeline resistance coefficient (a constant, to be fitted).

[0133] Data calculation explanation: Total flow rate of main pipe The head can be directly measured using a main pipe flow meter; when multiple pumps are running in parallel in steady state, the actual head of each individual pump is equal and consistent with the head of the main pipe, therefore the head of the main pipe is... The formula (2) can be used to derive the result from the measured pressure difference between the inlet and outlet of a single pump.

[0134] Step S3: Determine the high-efficiency operating range of a single pump based on its performance curve. Then, using the water supply flow rate demand, water supply head demand, and the high-efficiency operating range of the single pump as hard constraints for pump group operation, candidate pump group combinations are selected. ;

[0135] Step S31: Delineate the high-efficiency operating range of a single pump;

[0136] To ensure that the efficiency of the variable speed pump remains approximately constant at different speeds, the efficiency of a single pump can be limited. Operating within the high-efficiency operating range of a single pump: The upper and lower limits of the flow rate in the high-efficiency operating range are derived by using the performance curve of a single pump. , The operating efficiency of a single pump can be expressed by the following formula:

[0137] ;

[0138] Substitute the fitting equations from formulas (1) and (3) into... The quadratic equation for the critical efficiency is obtained as follows:

[0139] ;

[0140] The coefficient 0.008 is obtained from 0.8 / 100%, which means the unit of efficiency η is 0.008.

[0141] The equations are solved numerically, and ineffective roots are eliminated to obtain the high-efficiency operating range of a single pump:

[0142] Step S32: Solving for the balanced operating point of the pump set and pipeline network;

[0143] When m water pumps are connected in parallel, they follow the principle of equal head and superposition of flow rates. The operating head of each pump is... Equal to the head of the main pump Total flow rate of pump set Single pump flow rate sum:

[0144] ;

[0145] By combining the performance curves of a single pump unit with the characteristic curves of the pipeline network, the steady-state equilibrium operating point is determined. Taking three dissimilar pumps connected in parallel as an example, the head-flow curve coefficients of each pump are independent of each other, and are denoted as pump 1: Pump 2: Pump 3: Construct a system of equations:

[0146] ;

[0147] in: , These are the flow rates and equilibrium heads of pumps 1, 2, and 3 at the equilibrium point, respectively. Head at the equilibrium point Notation: , Notation: .

[0148] Step S33: Establish hard constraints for the steady-state operating conditions of the pump set and screen out candidate pump set combinations. ;

[0149] (1) Verify the hard constraints for high-efficiency operation of a single pump: Based on the high-efficiency operation range of the single pump obtained in step S31, check whether the steady-state flow rate of the single pump is within the range. Within the range, if all individual pumps meet the constraints of the high-efficiency operating range of a single pump, the pump group combination is a preliminary feasible combination; if the flow rate of any single pump exceeds the high-efficiency operating range of a single pump, it is judged as an inefficient combination and directly eliminated.

[0150] (2) Hard constraints on candidate combinations of supply and demand matching in time series: Based on the supply and demand targets of each time period (each hour is a time period), set flow rate and head tolerance constraints:

[0151] ;

[0152] Iterate through the initially feasible combinations, verify supply and demand constraints, and retain the combinations that satisfy both efficient operation and supply and demand matching, denoted as: t represents a certain time period. The feasible pump combinations for this period of time were recorded (e.g., [pump 1, pump 3, pump 5]). , These are the lower limits of flow demand and head demand for a certain period of time, which can be directly extracted from historical operating data. For example, the mode or 95th percentile of the historical flow and head data for the corresponding period can be selected to match the needs of regular water supply scheduling.

[0153] Step S4: Incorporate the start-up and shutdown cost of a single pump and its usage duration as soft constraints into the total cost to construct an objective function that minimizes the total cost; finally, obtain the global optimal solution through a dynamic programming (DP) algorithm to generate the optimal pump group scheduling sequence within the scheduling cycle.

[0154] Step S41: Soft constraint setting;

[0155] (1) Pump start-stop switching losses;

[0156] At time t, let the set of single pumps in the preceding combination be when switching between adjacent time periods. The combined single pump assembly is The total number of pumps started and stopped is the sum of the number of pumps stopped and the number of pumps started, and the total start-stop loss is... Calculation formula:

[0157] ;

[0158] in: Let N() be the cost of a single pump's start-stop cycle, and N() be a counting function. Number of pumps to be shut down This represents the number of pumps that are in operation.

[0159] (2) Losses during single pump operation;

[0160] At time t, let the cumulative running time of the j-th pump be . The current operating status is (Take 1 for operation, 0 for shutdown), formula for calculating marginal loss during single pump operation:

[0161] ;

[0162] in: is the runtime loss coefficient, and m is the total number of water pumps.

[0163] Step S42: DP solution;

[0164] (1) Initial definition;

[0165] ① Phase Division: Divide the X-hour scheduling cycle (taking X=24 as an example) into stages. There are a total of 24 discrete time periods, with each hour being an independent decision-making stage;

[0166] ②State variables: Two-dimensional states ,in The time period number. For candidate pump group combination index; store the cumulative minimum total cost in the state, and record the predecessor combination index and the cumulative runtime encoding of a single pump;

[0167] ③ Decision variables: The decision for each time period is to select the legal pump group combination screened in step S31. .

[0168] (2) Construction of the objective function;

[0169] With the core optimization objective of minimizing the total energy consumption over a 24-hour cycle, start-up and shutdown losses, and marginal losses over runtime, a function is constructed to minimize the total cost.

[0170]

[0171] Where: J represents the total cost;

[0172] For the first Energy consumption of pump sets during different time periods.

[0173] (3) State transition equation;

[0174] Based on the decision made in the current time period, the state for the next time period is updated, completing the update of the running state and the accumulation of the running time. The state transition equation is as follows:

[0175] ;

[0176] in: For the first Decision-making for different time periods; For the first Legal pump group combinations for +1 time period;

[0177] For the first The cumulative runtime of a single pump j in the +1 time period is only accumulated by 1 hour when the pump is running.

[0178] For the first The cumulative runtime of pump j during the time period;

[0179] For the first Operating status of single pump j during a given time period.

[0180] (4) DP optimization solution;

[0181] Based on the definitions in (1), (2), and (3) above, the general solution process of DP can be used to solve the problem. The main steps are as follows:

[0182] Step T1: Data and Parameter Initialization: Import the candidate pump group combinations selected in step S31 24-hour time-series supply and demand data, setting start-up and shutdown loss coefficients, runtime marginal loss coefficients, and initializing the DP state matrix and predecessor backtracking matrix;

[0183] Step T2: Initial time period state assignment: Traverse all legal pump group combinations in hour 0, calculate initial energy consumption and initial operating loss, and complete the initial assignment of DP matrix;

[0184] Step T3: Forward recursion for each time period: From hour 1 to hour 23, traverse all legal combinations for each time period, compare with all previous legal combinations, calculate the cumulative total cost (energy consumption + start-up and shutdown losses + operating losses), and retain the decision and state corresponding to the minimum cost;

[0185] Step T4: Backtracking the optimal solution: Select the combination with the minimum total cost in the 23rd hour as the endpoint, backtrack the predecessor combination, and generate the optimal pump group scheduling sequence for 24 hours;

[0186] Step T5: Result Statistics Output: Statistically calculate total energy consumption, total number of pump starts and stops, and cumulative runtime of each individual pump, and output complete scheduling plan and operation and maintenance indicators.

[0187] The effectiveness of this invention is evaluated as follows:

[0188] (1) Explanation of evaluation indicators;

[0189] ①Total energy consumption in 24 hours: refers to the cumulative input power of all operating water pumps within the scheduling cycle, in kW·h. It is the core indicator for measuring the economic efficiency of the scheduling plan and is directly related to the operating cost of the pump station. The lower the total energy consumption, the more significant the energy-saving benefits of the plan.

[0190] ② Average operating efficiency: refers to the weighted average of the pump set operating efficiency in each time period within the scheduling cycle. It reflects the quality of the pump set's operating conditions. The higher the average efficiency, the closer the pump set is to the high-efficiency operating range of a single pump, and the less hydraulic loss and energy waste.

[0191] ③ Cumulative number of start-stop operations: refers to the total number of start-stop operations of all water pumps within the scheduling cycle, reflecting the degree of mechanical wear and impact loss of the equipment. The fewer the number of start-stop operations, the lower the loss of the motor and pump body, the longer the service life of the equipment, and the lower the operation and maintenance costs.

[0192] ④ Single pump running time balance: refers to the dispersion of the cumulative running time of each pump. It is characterized by the range / mean ratio. The smaller the ratio, the more balanced the load distribution of each pump. This can avoid the problem of long-term overload operation of a single pump and long-term corrosion of idle pumps, and improve the overall service life of the pump set.

[0193] ⑤ Supply and demand satisfaction rate: refers to the percentage of time within the scheduling cycle that meets the hard constraints of flow and head, reflecting the adaptability of the scheme to the water demand of the pipeline network. It is necessary to ensure 100% supply and demand satisfaction and eliminate the working conditions of insufficient water supply and substandard head.

[0194] (2) Comparison of historical scheduling and the scheduling effect of the present invention;

[0195] Based on the manual experience-based scheduling records of Water Plant G from February 2025 to September 2025, and the scheduling records of this invention from September 2025 to February 2026, the 24-hour operating performance (mean) of both is shown in Table 1. The comparison reveals that this invention significantly reduces total energy consumption, cumulative start-stop times, and the balance of single-pump runtime, improving average operating efficiency and achieving 100% supply-demand satisfaction.

[0196] Table 1. 24-hour operational performance of Water Plant G

[0197]

[0198] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Any simple modifications or equivalent changes made to the above embodiments based on the technical essence of the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for scheduling parallel pump sets based on dynamic programming, characterized in that, Includes the following steps: Step S1: Data acquisition and preprocessing; Step S2: Discretize and treat the variable frequency pump as an equivalent pump: Discretize the variable frequency pump as n equivalent fixed frequency pumps; Then, the performance curves of a single pump and the pipeline network were fitted respectively; Step S3: Determine the high-efficiency operating range of a single pump based on its performance curve. Then, using the water supply flow rate demand, water supply head demand, and the high-efficiency operating range of the single pump as hard constraints for pump group operation, candidate pump group combinations are selected. ; Step S4: Incorporate the start-up and shutdown cost of a single pump and its usage duration as soft constraints into the total cost to construct an objective function that minimizes the total cost; finally, obtain the global optimal solution through a dynamic programming (DP) algorithm to generate the optimal pump group scheduling sequence within the scheduling cycle.

2. The parallel pump group scheduling method based on dynamic programming according to claim 1, characterized in that, Step S1 includes the following steps: Step S11: First, collect data on the independent operation of a single pump, data on the main outlet pipe of the pump station, and basic parameters of the single pump equipment; The individual pump operation data includes pump outlet flow rate Q, pump inlet and outlet pressure difference ΔP, motor input voltage U, current I, and operating frequency f; the pump station outlet main pipe data includes the total flow rate of the main pipe. The basic parameters of the single pump equipment include the rated flow rate. Rated head Rated frequency Rated efficiency Rated power of motor ; Step S12: Then, perform data preprocessing to unify the time granularity and ensure that the data remains consistent over time.

3. The parallel pump group scheduling method based on dynamic programming according to claim 2, characterized in that, Step S2 includes the following steps: Step S21: Discretize the variable frequency pump as n equivalent fixed frequency pumps and derive the core performance parameters of each equivalent fixed frequency pump; ； in: These are the rated flow rate, rated head, and rated motor power of the equivalent fixed-frequency pump, respectively. The discrete target frequency of the variable frequency pump; Step S22: Single pump performance curve fitting; (1) Fitting the flow-head curve based on a quadratic polynomial; ； Where: H is the head of a single pump; Q is the pump outlet flow rate; These are the fitting coefficients for the head curve; (2) Fitting the flow-power curve based on quadratic polynomial fitting; ； Where: W is the motor input power; These are the power curve fitting coefficients; Step S23: Pipeline performance curve fitting; ； in: To oversee Yang Cheng; For total flow rate; For the static head of the pipeline network; This is the pipeline resistance coefficient.

4. The parallel pump group scheduling method based on dynamic programming according to claim 3, characterized in that, Step S3 includes the following steps: Step S31: Defining the high-efficiency operating range of a single pump; based on the fact that the efficiency of a variable speed pump is approximately constant at different speeds, the efficiency of a single pump is limited. Operating within the high-efficiency operating range of a single pump, the fitting equations of the combined flow-head and flow-power curves are used to derive the quadratic equation for critical efficiency. Solving this equation yields the high-efficiency operating range of the single pump. ; in: The maximum flow rate for the high-efficiency operating range; The lower limit of flow rate for the high-efficiency operating range; Step S32: Calculate the equilibrium operating point; by analyzing the individual pump performance curves and pipeline characteristic curves of each pump in the combined pump set, the steady-state equilibrium operating point is obtained. , ),in, =General Manager's Head , =Total flow rate ; Step S33: Establish hard constraints for the steady-state operating conditions of the pump set and screen out candidate pump set combinations. ; The steady-state flow rate of a single pump is at Within the interval; and satisfying: ； in: , These represent the lower limit of flow demand and the lower limit of head demand for a certain period of time, respectively.

5. The parallel pump group scheduling method based on dynamic programming according to claim 4, characterized in that, In step S31, the single pump efficiency is limited. By combining the fitting equations of the flow-head curve and the flow-power curve, the quadratic equation for critical efficiency is obtained: ； in: The density of water; This is the acceleration due to gravity.

6. The parallel pump group scheduling method based on dynamic programming according to claim 4, characterized in that, In step S4, the X-hour scheduling period is divided into 24 discrete time periods; the objective function to be minimized is constructed as follows: ； ； ； Where: J represents the total cost; For the first Energy consumption of pump unit combination during different time periods; For the first Pump start-stop switching losses during specific time periods; For the first Loss during single-pump operation time; Cost per pump per start-up and shutdown; N() is a counting function; This refers to the number of pumps that are shut down; This refers to the number of pumps that are in operation. This is a pre-assembled set of single pumps; For a combination of single pumps; For the first The operating status of the j-th pump during the time period; For the first The cumulative runtime of the j-th pump during the time period; This is the runtime loss factor; m represents the total volume of the water pump.

7. A method for scheduling parallel pump groups based on dynamic programming according to claim 6, characterized in that, In step S4, the DP solution algorithm includes the following steps: Step T1: Data and Parameter Initialization: Obtain Candidate Pump Set Combinations Initialize the DP state matrix and predecessor backtracking matrix with 24-hour time-series supply and demand data; Step T2: Initial time period state assignment: Traverse all legal pump group combinations in hour 0, calculate initial energy consumption and initial operating loss, and complete the initial assignment of DP matrix; Step T3: Forward recursion for each time period: From hour 1 to hour 23, traverse the legal combinations for each time period, compare with all previous legal combinations, calculate the total cost, and retain the decision and state corresponding to the minimum cost; Step T4: Backtracking the optimal solution: Select the combination with the minimum total cost in the 23rd hour as the endpoint, backtrack the predecessor combination, and generate the optimal pump group scheduling sequence for 24 hours.

8. A parallel pump group scheduling system based on dynamic programming, implemented based on the parallel pump group scheduling method based on dynamic programming according to any one of claims 1-7, characterized in that, It includes a data acquisition and preprocessing module, a variable frequency pump equivalent processing module, a hard constraint screening module, a soft constraint objective function module, and a DP solution module; The data acquisition and preprocessing module is used to collect and preprocess data of independent operation of a single pump, data of the pump station outlet main pipe, and basic parameters of a single pump. The variable frequency pump equivalent processing module is used to convert the discrete variable frequency pump into n equivalent fixed frequency pumps, and to fit the single pump performance curve and the pipeline network performance curve. The hard constraint screening module is used to determine the high-efficiency operating range of a single pump and to construct hard constraints to screen candidate pump group combinations. ; The soft-constraint objective function module is used to construct an objective function that minimizes the total cost, and the DP solution module is used to calculate the globally optimal solution by minimizing the objective function and generate the optimal pump group scheduling sequence within the scheduling cycle.

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