Multi-objective optimization method for starting of impulse turbine based on kinetic model and NSGA-Ⅱ algorithm

Abstract

This application relates to a multi-objective optimization method for starting an impulse turbine based on a dynamic model and the NSGA-II algorithm. The method includes: establishing a starting dynamic model of the impulse turbine based on its kinetic equations and runner inertia equations, and determining the parameter conditions in the starting dynamic model according to the unit's geometric and performance parameters; establishing a multi-objective optimization model for the starting process of the impulse turbine, and determining the optimization objective function, optimization variables, and constraints; generating initial and stochastic solutions based on the starting process to be optimized, using a fast non-dominated sorting genetic algorithm to optimize and output a Pareto solution, adjusting the algorithm parameters to obtain the desired optimization result; and optimizing and selecting different nozzle starting strategies. This solves the problem of related technologies struggling to formulate scientific multi-nozzle cooperative starting strategies based on the dynamic characteristics under different operating conditions, and improves the starting speed and operational stability of the impulse turbine.

Description

Technical Field

[0001] This application relates to the field of fluid machinery engineering technology, and in particular to a multi-objective optimization method for starting up an impulse turbine based on a dynamic model and the NSGA-II algorithm. Background Technology

[0002] my country possesses enormous potential for the development of high-head hydropower resources, and impulse turbines are the main type of turbine used in high-head hydropower stations. During the startup process of impulse turbines, dynamic changes in unit parameters such as nozzle flow rate, runner speed, and bucket stress affect the rapid grid connection and stable operation of the impulse turbine unit. Developing a scientific and reasonable multi-nozzle coordinated startup strategy based on actual operating conditions is a key technical issue for ensuring startup quality.

[0003] In related technologies, the start-up process of impulse turbines mainly relies on fixed nozzle opening curves and empirical formulas for control. The nozzle flow rate is adjusted by the preset opening curve to realize the start-up process of the unit.

[0004] However, in related technologies, it is difficult to formulate a scientific multi-nozzle coordinated start-up strategy based on the dynamic characteristics under different working conditions due to the fixed nozzle opening curve and empirical formula. In the single-nozzle start-up mode, the unbalanced radial force on the impeller is large, which will affect the stability of operation and the service life of the equipment. In the multi-nozzle start-up mode, the switching time of different nozzles and the change of nozzle opening also determine the start-up time, water consumption and water bucket stress of the unit, which urgently need to be improved. Summary of the Invention

[0005] This application provides a multi-objective optimization method for starting an impulse turbine based on a dynamic model and the NSGA-II (Non-dominated Sorting Genetic Algorithm II) algorithm. This method addresses the challenges in related technologies, such as the difficulty in developing a scientific multi-nozzle coordinated start-up strategy based on the dynamic characteristics under different operating conditions. In single-nozzle start-up mode, the unbalanced radial force on the runner is large, which can affect operational stability and equipment lifespan. In multi-nozzle start-up mode, the switching time and nozzle opening of different nozzles determine the start-up time, water consumption, and bucket stress of the unit.

[0006] This application provides a multi-objective optimization method for starting an impulse turbine based on a dynamic model and the NSGA-II algorithm, comprising the following steps: establishing a starting dynamic model of the impulse turbine based on the impulse turbine's kinetic equations and runner inertia equations, and determining the parameter conditions in the starting dynamic model according to the geometric and performance parameters of the impulse turbine unit; establishing a multi-objective optimization model of the starting process of the impulse turbine based on the starting dynamic model and the parameter conditions, and determining the optimization objective function, optimization variables, and constraints of the multi-objective optimization model of the starting process; generating initial and random solutions according to the starting process to be optimized, and using a fast non-dominated sorting genetic algorithm to optimize and output Pareto solutions; adjusting the algorithm parameters of the fast non-dominated sorting genetic algorithm based on the optimization objective function, the optimization variables, and the constraints to obtain the required optimization results; optimizing different nozzle starting strategies of the impulse turbine, comparing the optimization results of the different nozzle starting strategies, and selecting a starting strategy that meets the requirements of the actual application scenario.

[0007] Optionally, in one embodiment of this application, establishing the start-up dynamics model of the impulse turbine based on the impulse turbine's kinetic equation and runner inertia equation includes: establishing the relationship between the unit's rotational speed change and the nozzle jet torque of the impulse turbine during start-up, wherein the runner inertia equation is: , in, The moment of inertia of the wheel. The rotational speed of the wheel, For time, The nozzle jet torque, The drag torque is given by the jet torque, which is caused by the tangential force generated by the jet and is calculated using the following formula: , in, For the first i The jet tangential force generated by the nozzle jet Z For the number of operating nozzles, Let be the pitch circle diameter of the impulse turbine runner; wherein, the jet tangential force is caused by the momentum change resulting from the relative velocity change between the nozzle jet and the water bucket, and the calculation formula is: , in, For water flow density, For the first i Nozzle jet flow rate of each nozzle The absolute velocity of the jet entering the water bucket Let be the circumferential velocity of the peg circle, whereθ The difference between the angle at which the water bucket is located and the angle at which the jet hits the water bucket perpendicularly; Let be the cosine of the relative angle at the jet outlet; since the relative incident angle of the impulse turbine is 0, where is the absolute velocity of the jet entering the water bucket. With nozzle jet exit velocity Equal to each other, the formulas for calculating the absolute velocity of the jet entering the water bucket and the circumferential velocity of the impeller pitch circle are: , , in Let be the angular velocity of the rotating wheel. Nozzle energy loss coefficient It is the acceleration due to gravity. For operating head.

[0008] The nozzle jet flow rate From relative needle stroke Y i Define the flow coefficient. The actual flow rate multiplied by the nozzle velocity and the nozzle diameter. D The ratio of 0 to the flow coefficient of a single nozzle under different numbers of nozzles. Relative needle stroke Y i The relationship was obtained by fitting a fourth-order polynomial to the experimental results. The formula for the flow coefficient of a single nozzle is as follows: ， in, The coefficients before each term of the fitted fourth-order polynomial are used to determine the jet flow rate for each nozzle, which is therefore expressed as: .

[0009] Optionally, in one embodiment of this application, the step of establishing a multi-objective optimization model for the startup process of the impulse turbine, and determining the optimization objective function, optimization variables, and constraints of the multi-objective optimization model for the startup process, includes three sets of optimization variables, the objective function, and the constraints; wherein, the first set of optimization variables is the total opening of all nozzles. The first set of optimization variables consists of a total opening curve generated by interpolation of N control points, with the initial total opening fixed at 0. The second set of optimization variables is the start and end times of nozzle switching. The number of variables in the second set is determined by the number of stages M in the startup strategy, and the number of variables is 2(M-1). The third set of optimization variables is the opening curve of a single nozzle within each stage, generated by n control points (the opening is fixed at the start and end). The total number of optimization variables in the multi-objective optimization model for the startup process is N-1 + 2(M-1) + M × (n-2) = M × n + N-3. The optimization objectives of the multi-objective optimization model for the startup process include minimizing the startup time of the impulse turbine, water consumption, and accumulated unbalanced radial force. The constraints of the multi-objective optimization model for the startup process include termination speed constraints, speed change rate constraints, termination torque constraints, nozzle opening constraints, opening change rate constraints, and nozzle switching constraints.

[0010] Optionally, in one embodiment of this application, the step of generating an initial solution and a random solution based on the startup process to be optimized, and using a fast non-dominated sorting genetic algorithm to optimize and output a Pareto solution, and adjusting the algorithm parameters of the fast non-dominated sorting genetic algorithm based on the optimization objective function, the optimization variables, and the constraints to obtain the optimization result that meets the requirements, includes: generating an initial population based on the startup curve to be optimized and then entering algorithm iteration; obtaining the target value through startup calculation; performing fast non-dominated sorting on the population to select non-dominated solutions and calculating crowding distance; using selection, crossover, and mutation to generate offspring; merging the parent and offspring populations; performing constraint verification on the new population and removing solutions that do not meet the constraints; outputting the Pareto front solution set after multiple rounds of iterative optimization; performing preliminary analysis on the results before and after optimization, and using the optimization effect to guide the adjustment of algorithm parameters to obtain the optimization result that meets the optimization requirements.

[0011] Optionally, in one embodiment of this application, the method further includes: classifying the start-up strategies of the six-nozzle impulse turbine according to the number of start-up nozzles, supporting the optimization comparison of different nozzle strategies, and selecting the start-up strategy that best meets the requirements according to the actual scenario. In a fast response scenario, the strategy with the shortest start-up time is selected; in a water resource efficiency utilization scenario, the strategy with the lowest water consumption is selected; or the strategy with comprehensive performance that meets the actual needs is selected.

[0012] This application can optimize the nozzle opening control strategy by establishing a dynamic model of the start-up of an impulse turbine and a multi-objective optimization model to achieve the following objectives: (1) Speed ​​objective: Minimize startup time and improve response speed; (2) Economic objectives: Minimize water consumption during startup and improve water resource utilization; (3) Stability objective: Minimize the peak value of unbalanced radial force during startup and extend the life of the unit.

[0013] This solves the problems in related technologies, such as the difficulty in formulating a scientific multi-nozzle coordinated start-up strategy based on the dynamic characteristics under different working conditions, the large unbalanced radial force on the impeller in the single-nozzle start-up mode, which will affect the stability of operation and the life of equipment, and the fact that the switching time of different nozzles and the change of nozzle opening in the multi-nozzle start-up mode also determine the start-up time, water consumption and water bucket stress of the unit.

[0014] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

[0015] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein: Figure 1 This is a flowchart illustrating a multi-objective optimization method for starting an impulse turbine based on a dynamic model and the NSGA-II algorithm, according to an embodiment of this application. Figure 2 The following is an optimization flowchart of the NSGA-II algorithm used in a multi-objective optimization model according to an embodiment of this application; Figure 3 This is a diagram showing the nozzle opening curve optimized according to a dual-nozzle start-up strategy provided in one embodiment of this application. Figure 4 This is a comparison chart of the wheel acceleration curves before and after optimization of the dual-nozzle start-up strategy according to an embodiment of this application; Figure 5 The Pareto front plot is obtained by optimizing a dual-nozzle start-up strategy according to an embodiment of this application. Detailed Implementation

[0016] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0017] The following describes, with reference to the accompanying drawings, a multi-objective optimization method for starting an impulse turbine based on a dynamic model and the NSGA-II algorithm, according to embodiments of this application. In response to the aforementioned background technologies, it is difficult to formulate a scientific multi-nozzle coordinated start-up strategy based on the dynamic characteristics under different operating conditions. In the single-nozzle start-up mode, the unbalanced radial force on the runner is large, which will affect the operational stability and equipment life. In the multi-nozzle start-up mode, the switching time of different nozzles and the change of nozzle opening also determine the start-up time, water consumption, and water bucket stress of the unit. This application provides a multi-objective optimization method for starting an impulse turbine based on a dynamic model and the NSGA-II algorithm. In this method, a dynamic model for starting an impulse turbine can be established based on the impulse turbine's kinetic equation and the runner's inertia equation. A multi-objective optimization model for the start-up process of the impulse turbine can be established to generate an initial solution based on the start-up process to be optimized. A fast non-dominated sorting genetic algorithm is used to optimize and output a Pareto solution. The algorithm parameters are adjusted to obtain the optimization results that meet the requirements. Different nozzle start-up strategies are optimized and selected, thereby formulating a more flexible and efficient nozzle start-up strategy and opening curve to achieve a comprehensive improvement in the start-up speed, water resource utilization, and operational stability of the impulse turbine. This solves the problems in related technologies, such as the difficulty in formulating a scientific multi-nozzle coordinated start-up strategy based on the dynamic characteristics under different working conditions, the large unbalanced radial force on the impeller in the single-nozzle start-up mode, which will affect the stability of operation and the life of equipment, and the fact that the switching time of different nozzles and the change of nozzle opening in the multi-nozzle start-up mode also determine the start-up time, water consumption and water bucket stress of the unit.

[0018] Specifically, Figure 1 This is a flowchart illustrating a multi-objective optimization method for starting an impulse turbine based on a dynamic model and the NSGA-II algorithm, provided in an embodiment of this application.

[0019] like Figure 1 As shown, the multi-objective optimization method for starting up an impulse turbine based on a dynamic model and the NSGA-II algorithm includes the following steps: In step S101, a startup dynamics model of the impulse turbine is established based on the impulse turbine's kinetic equation and runner inertia equation, and the parameter conditions in the startup dynamics model are determined according to the geometric parameters and performance parameters of the impulse turbine unit.

[0020] Optionally, in one embodiment of this application, a startup dynamics model of the impulse turbine is established based on the impulse turbine's kinetic equation and runner inertia equation, including: establishing the relationship between the unit's rotational speed change and the nozzle jet torque of the impulse turbine during startup, wherein the runner inertia equation is: , in, Let be the moment of inertia of the wheel. The rotational speed of the wheel, For time, This refers to the nozzle jet torque. The drag torque is given by the jet torque, which is caused by the tangential force generated by the jet and is calculated using the following formula: , in, For the first i The jet tangential force generated by the nozzle jet Z For the number of operating nozzles, Let be the pitch circle diameter of the impulse turbine runner; where the jet tangential force is caused by the momentum change resulting from the relative velocity change between the nozzle jet and the water bucket, and the calculation formula is: , in, For water flow density, For the first i Nozzle jet flow rate of each nozzle The absolute velocity of the jet entering the water bucket Let be the circumferential velocity of the peg circle, where θ The difference between the angle at which the water bucket is located and the angle at which the jet hits the water bucket perpendicularly; Let be the cosine of the relative angle at the jet outlet; since the relative incident angle of the impulse turbine is 0, where is the absolute velocity of the jet entering the water bucket. With nozzle jet exit velocity The formulas for calculating the absolute velocity of the jet entering the water bucket and the circumferential velocity of the impeller pitch circle are equal: , , in Let be the angular velocity of the rotating wheel. Nozzle energy loss coefficient It is the acceleration due to gravity. For operating head.

[0021] Nozzle jet flow rate From relative needle stroke Yi Define the flow coefficient. The actual flow rate multiplied by the nozzle velocity and the nozzle diameter. D The ratio of 0 to the flow coefficient of a single nozzle under different numbers of nozzles. Relative needle stroke Y i The relationship was obtained by fitting a fourth-order polynomial to the experimental results. The formula for the flow coefficient of a single nozzle is as follows: ， in, The coefficients before each term of the fitted fourth-order polynomial are used; therefore, the jet flow rate of each nozzle is expressed as: .

[0022] Specifically, in this embodiment, a dynamic model including hydraulic characteristics and mechanical inertia can be established during the startup process of a six-nozzle impulse turbine, and the geometric parameters and performance parameters of the impulse turbine selected in the embodiment can be input into the dynamic model for startup calculation.

[0023] First, the equation for the change in rotational speed of the impeller when it is impacted by the jet: ， in, The moment of inertia of the entire unit. The rotational speed of the wheel, For time, This refers to the nozzle jet torque. The moment of inertia J is the drag torque. Using the geometric parameters of the impulse turbine selected in this embodiment, the required rotational inertia J in the speed equation of the dynamic model can be calculated. In this embodiment, the moment of inertia of the unit is 214.4 kg·m. 2 .

[0024] Jet torque Caused by the tangential force generated by the jet, the calculation formula is: , in, For the first i The tangential force generated by the jet from each nozzle Z For the number of operating nozzles, The pitch circle diameter of the impulse turbine runner. Jet tangential force. It is caused by the change in momentum resulting from the change in the relative velocity between the nozzle jet and the water bucket. The calculation formula is: , in, For water flow density, For the first i Nozzle jet flow rate of each nozzle The absolute velocity of the jet entering the water bucket Let be the circumferential velocity of the peg circle, where θ The difference between the angle at which the water bucket is located and the angle at which the jet hits the water bucket perpendicularly; Let be the cosine of the relative angle at the jet outlet; since the relative incident angle of the impulse turbine is 0, where is the absolute velocity of the jet entering the water bucket. With nozzle jet exit velocity The formulas for calculating the absolute velocity of the jet entering the water bucket and the circumferential velocity of the impeller pitch circle are equal: , , in Let be the angular velocity of the rotating wheel. Nozzle energy loss coefficient It is the acceleration due to gravity. For operating head.

[0025] Nozzle jet flow rate From relative needle stroke Y i Decision. Define the flow coefficient. This is the ratio of the actual flow rate to the nozzle velocity multiplied by the nozzle diameter D0. Therefore, the flow coefficient of a single nozzle is calculated for different numbers of nozzles. Relative needle stroke Y i The relationship can be obtained by fitting the experimental results with a fourth-order polynomial, as shown in the following formula: , in, Let be the coefficients before each term of the fitted fourth-order polynomial. Therefore, the jet flow rate of each nozzle is expressed as: .

[0026] The flow coefficient of a single nozzle under different numbers of nozzles in the examples can be obtained through hydraulic tests. Relative needle stroke Y i The relationship. The example uses the fitting formula for the unit operating with 1 to 6 nozzles. As shown in Table 1. Table 1 shows the flow coefficient of a single nozzle under different numbers of nozzles. Relative needle stroke Y i Relationship table.

[0027] Table 1

[0028] The jet velocity can be obtained from the head and nozzle loss coefficient. Combined with the nozzle area A0, the jet flow rate at different nozzle openings can be obtained. Furthermore, the tangential force of the jet at each nozzle in the startup dynamics model can be derived. radial force and jet torque Important parameters such as...

[0029] After inputting the geometric and performance parameters of the startup process into the startup dynamics model, by setting an appropriate time step, the integral of nozzle flow rate, torque and force, as well as the change of runner angle in each time step can be calculated, thereby realizing the calculation of the startup process of the impulse turbine based on the dynamics model.

[0030] In step S102, based on the startup dynamics model and parameter conditions, a multi-objective optimization model for the startup process of the impulse turbine is established, and the optimization objective function, optimization variables, and constraints of the multi-objective optimization model for the startup process are determined.

[0031] Optionally, in one embodiment of this application, a multi-objective optimization model for the startup process of an impulse turbine is established, and the objective function, optimization variables, and constraints of the multi-objective optimization model for the startup process are determined, including three sets of optimization variables, objective functions, and constraints; wherein, the first set of optimization variables is the total opening of all nozzles. The first set of optimization variables is the total opening curve generated by interpolation of N control points, with the initial total opening fixed at 0. The second set of optimization variables is the start and end times of nozzle switching. The number of variables in the second set is determined by the number of stages M of the startup strategy, and the number of variables is 2(M-1). The third set of optimization variables is the opening curve of a single nozzle in each stage, generated by n control points (the opening is fixed at 0 at the start and at the end). The total number of optimization variables in the multi-objective optimization model for the startup process is N-1+2(M-1)+M×(n-2)=M×n+N-3. The optimization objectives of the multi-objective optimization model for the startup process include minimizing the startup time of the impulse turbine, water consumption, and accumulated unbalanced radial force. The constraints of the multi-objective optimization model for the startup process include termination speed constraints, speed change rate constraints, termination torque constraints, nozzle opening constraints and opening change rate constraints, and nozzle switching constraints.

[0032] In the embodiments of this application, the optimization variables include the number of nozzles and the change curve of nozzle opening over time during the startup process. The startup process can be controlled using three sets of control variables.

[0033] For example, in a two-stage startup strategy for switching from a single nozzle to a dual nozzle, 21 control points on the total nozzle opening curve can be selected for optimization. The first point is fixed at the origin, and the first set of optimization variables has 20. With 2 stages, the second set of variables represents the start and end times of the switch from a single nozzle to a dual nozzle, also with 2 optimization variables. The third set of optimization variables represents the nozzle opening curve within each stage. In this embodiment, 7 control points are selected. Since the start and end points are fixed, the third set of optimization variables has 2 × 5 = 10. Therefore, in this embodiment, the total number of optimization variables is determined to be 20 + 2 + 10 = 32. That is, the startup process is optimized by optimizing the selection of these 32 variables.

[0034] The optimization objectives for the start-up process of an impulse turbine include minimizing the start-up time, water consumption, and peak unbalanced radial force. Start-up time... It is the time it takes for the generator runner to accelerate from a standstill to its rated speed.

[0035] Water consumption during startup C The calculation formula can be expressed as: , Resultant force of unbalanced radial forces during startup The calculation formula can be expressed as: , in, for t Time of the first i The radial force exerted on the impeller by the jet from each nozzle. The unbalanced radial force of a single nozzle. The calculation formula is: , in, It is the tangent of the difference between the angle at which the water bucket is located and the angle at which the jet hits the water bucket perpendicularly.

[0036] The constraints during the start-up process of an impulse turbine include termination speed constraints, speed change rate constraints, termination torque constraints, nozzle opening constraints, opening change rate constraints, and nozzle switching constraints.

[0037] The constraints include termination speed constraints, speed change rate constraints, termination torque constraints, nozzle opening constraints and opening change rate constraints, nozzle switching constraints, etc.

[0038] To ensure stable grid connection, the unit speed should rise to near and stabilize at the rated speed at the end of the startup process. Therefore, the jet torque should be equal to the unit's resistance torque at the end of startup, ensuring a net torque of zero. Additionally, to protect the shaft system, the rate of change of speed over time should be limited.

[0039] Meanwhile, during startup, the relative opening of the nozzle should be between 0 and 1, and the rate of change of the nozzle opening over time should not exceed the maximum capacity of the actuator, as shown in the following formula: , in, The maximum allowable rate of change in nozzle opening.

[0040] Nozzle switching constraints include symmetrical switching and phased switching constraints. Symmetrical switching constraints prioritize opening nozzles symmetrical to those already in operation when increasing the number of nozzles, reducing unbalanced radial forces. Phased opening constraints ensure that the start time of the next nozzle switching phase is no earlier than the end time of the previous phase. When opening a new set of nozzles, the overall opening curve should be smooth and continuous, avoiding abrupt changes.

[0041] For example, in order to ensure that the unit can connect to the grid at a stable frequency upon startup, the rotor speed in this embodiment is... n end The engine speed needs to reach 214.3 rpm at the end of startup, and the rate of change of engine speed d during startup is... n / d t The relative nozzle opening value should not exceed 4 rpm / s. Y i Between 0 (fully closed) and 1 (fully open). The net torque at the end of startup should be close to zero to maintain stable speed, hence the setting. Additionally, when switching from a single nozzle to a dual nozzle, the nozzles at symmetrical positions of the operating nozzles are activated to accelerate the rotor, minimizing unbalanced radial forces and ensuring the correct start and end times of the switching period.

[0042] In step S103, an initial solution and a random solution are generated based on the startup process to be optimized, and a Pareto solution is output using a fast non-dominated sorting genetic algorithm. Based on the optimization objective function, optimization variables, and constraints, the algorithm parameters of the fast non-dominated sorting genetic algorithm are adjusted to obtain the optimization result that meets the requirements.

[0043] Optionally, in one embodiment of this application, an initial solution and a random solution are generated based on the startup process to be optimized, and a fast non-dominated sorting genetic algorithm is used to optimize and output a Pareto solution. Based on the optimization objective function, optimization variables, and constraints, the algorithm parameters of the fast non-dominated sorting genetic algorithm are adjusted to obtain the optimization result that meets the requirements. This includes: generating an initial population based on the startup curve to be optimized and then entering algorithm iteration; obtaining the target value through startup calculation; performing fast non-dominated sorting on the population to screen out non-dominated solutions and calculating crowding distance; using selection, crossover, and mutation to generate offspring; merging the parent and offspring populations; performing constraint verification on the new population and removing solutions that do not meet the constraints; outputting a Pareto front solution set after multiple rounds of iterative optimization; performing preliminary analysis on the results before and after optimization; and using the optimization effect to guide the adjustment of algorithm parameters to obtain an optimization result that meets the optimization requirements.

[0044] In this embodiment, the original nozzle opening curve of the startup process to be optimized can be input as an initial value into the startup dynamics model to calculate the objective function value of the initial value. Then, the initial strategy is input into the multi-objective optimization model of the startup process and optimized using the NSGA-II algorithm. The optimization process of the NSGA-II algorithm is as follows: Figure 2 As shown.

[0045] Specifically, the first step is to optimize the algorithm parameters, mainly including population and offspring size, number of iterations, crossover probability, mutation probability, and the weights of the three objective functions. Selecting appropriate algorithm parameters helps to obtain a solution that better meets the optimization requirements.

[0046] After setting the algorithm parameters, an initial population is first generated, including the initial solution to be optimized and random solutions. The initial solution is then input into the start-up dynamics model of the impulse turbine to calculate the objective function value and constraint violations. In this embodiment, the start-up time of the initial solution for the dual-nozzle strategy is 128.95 s, the water consumption is 1046.71 m³, the peak value of the unbalanced radial force is 14.20 N·s, and all constraints, such as the final rotational speed, final torque, maximum rotational speed change rate, and maximum opening change rate, are met.

[0047] After generating the initial population, the algorithm iterates, specifically by first obtaining the target value through initial computation, then performing a fast non-dominated sort on the population to filter out non-dominated solutions and calculating crowding distances. Next, a parent generation is selected, followed by binary crossover and polynomial mutation to generate offspring. After merging the parent and offspring populations, constraints are checked on the new population, and solutions that do not meet the constraints are removed. Finally, after multiple rounds of iterative optimization, the Pareto front solution set, i.e., the optimization result, is output. The NSGA-II algorithm flow is as follows: Figure 2 As shown, a preliminary analysis of the results before and after optimization is performed. The optimization effect guides the adjustment of algorithm parameters to obtain a solution that meets the optimization requirements and a startup scheme.

[0048] In this embodiment of the dual-nozzle strategy optimization, the optimized start-up time is 90.40 s, a reduction of approximately 29.90% compared to the original. Water consumption is 906.46 m³, a saving of 13.40% compared to the original. The peak value of the unbalanced radial force is 11.84 N·s, a reduction of 16.62% compared to the original. All constraints are met. The optimized nozzle opening curve of this embodiment is shown below. Figure 3 As shown, the comparison of the wheel acceleration curves before and after optimization is as follows: Figure 4 As shown, the Pareto front for optimization is as follows: Figure 5 As shown.

[0049] In step S104, different nozzle start-up strategies for the impulse turbine are optimized, and the optimization results of different nozzle start-up strategies are compared to select a start-up strategy that meets the requirements of the actual application scenario.

[0050] Optionally, in one embodiment of this application, the method further includes: classifying the start-up strategies of the six-nozzle impulse turbine according to the number of start-up nozzles, supporting the optimization comparison of different nozzle strategies, and selecting the start-up strategy that best meets the requirements according to the actual scenario. In a fast response scenario, the strategy with the shortest start-up time is selected; in a water resource efficiency utilization scenario, the strategy with the lowest water consumption is selected; or the strategy with comprehensive performance that meets the actual needs is selected.

[0051] This application also supports the optimization and comparison of different startup strategies. For example, switching from a single-nozzle to a dual-nozzle startup strategy. Under the same constraints, this application can also select other startup strategies, such as single-nozzle startup, dual-nozzle startup, switching from a single nozzle to a dual nozzle and then to a four-nozzle startup strategy, etc.

[0052] Specifically, the startup strategies of a six-nozzle impulse turbine can be classified according to the number of nozzles activated. Using the final number of activated nozzles as the classification criterion, there is only one single-nozzle startup strategy, denoted as Strategy A1. There are two dual-nozzle strategies: switching from a single nozzle to a dual nozzle and directly activating both nozzles, denoted as Strategy B1 and Strategy B2, respectively. Startup strategies for other numbers of nozzles are classified similarly. Therefore, the nozzle strategies for the startup process of a six-nozzle impulse turbine are described in Table 2 below.

[0053] Table 2

[0054] In this embodiment, strategies A1 (single-nozzle start-up), B2 (dual-nozzle start-up), and D2 (1-2-4-nozzle start-up), i.e., executing steps S101 to S103, were selected to optimize the start-up process of the impulse turbine in this embodiment, and the start-up objective function values ​​under different nozzle strategies were compared. Among the optimization results of strategies A1, B1, B2, and D2 selected in this embodiment, strategy D2 has the smallest start-up time and water consumption, while strategy B2 has the smallest unbalanced radial force.

[0055] Under the same parameter settings and constraints, the method of this application can be used to optimize and compare different nozzle start-up strategies, thereby selecting a start-up strategy that better meets the requirements based on the actual scenario. For example, in a rapid response scenario, the strategy with the shortest start-up time can be selected; in a water resource efficiency utilization scenario, the strategy with the lowest water consumption can be selected; or, based on actual needs, a strategy with better overall performance can be selected.

[0056] The multi-objective optimization method for starting an impulse turbine based on a dynamic model and the NSGA-II algorithm proposed in this application establishes a dynamic model for starting the impulse turbine based on the turbine's kinetic equations and runner inertia equations. A multi-objective optimization model for the turbine's starting process is then established to generate an initial solution based on the starting process to be optimized. The NSGA-II algorithm is used to optimize and output a Pareto solution. Algorithm parameters are adjusted to obtain the desired optimization results. Different nozzle starting strategies are optimized and selected, thereby developing more flexible and efficient nozzle starting strategies and opening curves to comprehensively improve the turbine's starting speed, water resource utilization, and operational stability. This solves the problems in related technologies, such as the difficulty in developing scientific multi-nozzle coordinated starting strategies based on the dynamic characteristics under different operating conditions, the large unbalanced radial force on the runner in single-nozzle starting mode which affects operational stability and equipment lifespan, and the fact that the switching time and nozzle opening changes of different nozzles in multi-nozzle starting mode determine the unit's starting time, water consumption, and bucket stress.

[0057] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0058] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "N" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0059] Any process or method described in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or N executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

[0060] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0061] It should be understood that the various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, the N steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. If implemented in hardware, as in another embodiment, it can be implemented using any one or more of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0062] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

[0063] Furthermore, the functional units in the various embodiments of this application can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0064] The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of this application.

Claims

1. A multi-objective optimization method for starting an impulse turbine based on a dynamic model and the NSGA-II algorithm, characterized in that, Includes the following steps: A startup dynamics model for an impulse turbine is established based on the impulse turbine's kinetic equation and runner inertia equation, and the parameter conditions in the startup dynamics model are determined based on the geometric and performance parameters of the impulse turbine unit. Based on the startup dynamics model and the parameter conditions, a multi-objective optimization model for the startup process of the impulse turbine is established, and the optimization objective function, optimization variables and constraints of the multi-objective optimization model for the startup process are determined. An initial solution and a random solution are generated based on the startup process to be optimized, and a Pareto solution is output using a fast non-dominated sorting genetic algorithm. Based on the optimization objective function, the optimization variables, and the constraints, the algorithm parameters of the fast non-dominated sorting genetic algorithm are adjusted to obtain the optimization result that meets the requirements. Different nozzle start-up strategies for the impulse turbine are optimized, and the optimization results of the different nozzle start-up strategies are compared to select a start-up strategy that meets the requirements of the actual application scenario.

2. The method according to claim 1, characterized in that, The starting dynamics model of the impulse turbine, based on the impulse turbine's kinetic equation and the runner's inertia equation, includes: Establish the relationship between the unit's rotational speed change and the nozzle jet torque of the impulse turbine during startup. The runner's inertia equation is: ， in, The moment of inertia of the wheel. The rotational speed of the wheel, For time, The nozzle jet torque, The drag torque is given by the jet torque, which is caused by the tangential force generated by the jet and is calculated using the following formula: ， in, For the first i The jet tangential force generated by the nozzle jet Z For the number of operating nozzles, Let be the pitch circle diameter of the impulse turbine runner; wherein, the jet tangential force is caused by the momentum change resulting from the relative velocity change between the nozzle jet and the water bucket, and the calculation formula is: ， in, For water flow density, For the first i Nozzle jet flow rate of each nozzle The absolute velocity of the jet entering the water bucket Let be the circumferential velocity of the impeller, where θ The difference between the angle at which the water bucket is located and the angle at which the jet hits the water bucket perpendicularly; Let be the cosine of the relative angle at the jet outlet; since the relative incident angle of the impulse turbine is 0, where is the absolute velocity of the jet entering the water bucket. With nozzle jet exit velocity Equal to each other, the formulas for calculating the absolute velocity of the jet entering the water bucket and the circumferential velocity of the impeller pitch circle are: ， ， in Let be the angular velocity of the rotating wheel. Nozzle energy loss coefficient It is the acceleration due to gravity. For operating head; The nozzle jet flow rate From relative needle stroke Y i Define the flow coefficient. The actual flow rate multiplied by the nozzle velocity and the nozzle diameter. D The ratio of 0 to the flow coefficient of a single nozzle under different numbers of nozzles. Relative needle stroke Y i The relationship was obtained by fitting a fourth-order polynomial to the experimental results. The formula for the flow coefficient of a single nozzle is as follows: ， in, The coefficients before each term of the fitted fourth-order polynomial, and the jet flow rate for each nozzle, are expressed as: 。 3. The method according to claim 1, characterized in that, The establishment of a multi-objective optimization model for the startup process of the impulse turbine, and the determination of the optimization objective function, optimization variables and constraints of the multi-objective optimization model for the startup process, including three sets of optimization variables, the objective function and the constraints; The first set of optimization variables is the total opening of all nozzles. The first set of optimization variables consists of a total opening curve generated by interpolation of N control points, with the initial total opening fixed at 0. The second set of optimization variables consists of the start and end times of nozzle switching, and the number of variables in the second set is determined by the number of stages M of the startup strategy, with a total number of variables of 2(M-1). The third set of optimization variables consists of the opening curve of a single nozzle within each stage, generated by n control points (the initial opening is fixed at 0, and the end opening is fixed). The total number of optimization variables in the multi-objective optimization model for the startup process is N-1 + 2(M-1) + M × (n-2) = M × n + N-3. The optimization objectives of the multi-objective optimization model for the startup process include minimizing the startup time, water consumption, and accumulated unbalanced radial force of the impulse turbine. The constraints of the multi-objective optimization model for the startup process include termination speed constraint, speed change rate constraint, termination torque constraint, nozzle opening constraint, opening change rate constraint, and nozzle switching constraint.

4. The method according to claim 1, characterized in that, The process of generating initial and random solutions based on the startup process to be optimized, and using a fast non-dominated sorting genetic algorithm to optimize and output a Pareto solution, and adjusting the algorithm parameters of the fast non-dominated sorting genetic algorithm based on the optimization objective function, the optimization variables, and the constraints to obtain the required optimization result, includes: After generating an initial population based on the starting curve to be optimized, the algorithm iterates, calculates the target value through starting calculations, performs fast non-dominated sorting on the population, filters out non-dominated solutions, and calculates crowding distance; selects, crossovers, and mutates to generate offspring, merges the parent and offspring populations, performs constraint verification on the new population, and removes solutions that do not meet the constraints; after multiple rounds of iterative optimization, the Pareto front solution set is output; a preliminary analysis of the results before and after optimization is performed, and the optimization effect guides the adjustment of algorithm parameters to obtain the optimization result that meets the optimization requirements.

5. The method according to claim 1, characterized in that, Also includes: The startup strategies of a six-nozzle impulse turbine are categorized based on the number of startup nozzles. The optimization and comparison of different nozzle strategies are supported, and the startup strategy that best meets the requirements is selected according to the actual scenario. In a fast response scenario, the strategy with the shortest startup time is selected. In a water resource efficiency scenario, the strategy with the lowest water consumption is selected, or the strategy whose comprehensive performance meets the actual needs is selected.

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