Water turbine PID parameter optimization method, system and device based on gravitational search algorithm and storage medium

Abstract

The invention discloses a water turbine PID parameter optimization method, system and device based on a gravitational search algorithm and a storage medium. The method comprises the steps that a mathematical model of a water turbine speed regulation system is established, and transfer functions of all parts in the mathematical model are determined; a low-pass filter is introduced on the basis of a traditional PID controller, and a mathematical model of a robust PID controller is obtained; taking the three parameters of the robust PID controller as optimization variables, establishing an objective function based on preset performance requirements of the water turbine speed regulation system, and constructing an optimization model based on a gravitational search algorithm; optimizing robust PID controller parameters by using a gravitational search algorithm; and finally, the optimized robust PID controller is applied to the water turbine speed regulation system. The method solves the problems of low convergence speed and easy falling into local optimum in the prior art, and has the characteristics of improving the global search capability, improving the optimization efficiency and improving the convergence speed by optimizing the parameters of the robust PID controller through the gravitational search algorithm.

Description

Technical Field

[0001] The present invention relates to the control technology of a hydroturbine governing system, and particularly to a method, system, device and storage medium for optimizing the PID parameters of a hydroturbine based on a gravitational search algorithm. Background Art

[0002] The hydroturbine governing system is an important part of a hydropower station, and its performance directly affects the safe, stable operation and power generation efficiency of the hydropower station. Although the traditional PID controller has been widely used in the hydroturbine governing system, due to the high complexity, nonlinear characteristics and variable operating conditions of the hydroturbine governing system, the traditional PID controller often fails to achieve an ideal control effect. Therefore, how to design a controller that can adapt to various operating conditions and disturbances and has higher performance has become a research hotspot.

[0003] At present, some researchers have tried to use intelligent algorithms such as CEP, FEP, MFEP and DCMEP to optimize the parameters of the PID controller and achieved certain results; however, these algorithms still have some deficiencies in solving complex multi-parameter optimization problems, such as slow convergence speed and easy to fall into local optimum; therefore, it is necessary to design a hydroturbine PID parameter optimization based on a gravitational search algorithm to solve the above problems. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method, system, device and storage medium for optimizing the PID parameters of a hydroturbine based on a gravitational search algorithm, aiming to solve the problems of slow convergence speed and easy to fall into local optimum in the prior art, optimize the parameters of a robust PID controller through the gravitational search algorithm, so as to improve the global search ability and enhance the optimization efficiency and convergence speed.

[0005] To achieve the above technical effects, the technical solution adopted by the present invention is: A method for optimizing the PID parameters of a hydroturbine based on a gravitational search algorithm, comprising: S1, establishing a mathematical model of the hydroturbine governing system and determining the transfer functions of each part in the mathematical model; each part in the mathematical model includes a mechanical hydraulic system, a governor, a water diversion system, a hydroturbine, a generator load and a hydroturbine generator set; S2, designing a robust PID controller: Introducing a low-pass filter on the basis of the traditional PID controller to eliminate the interference of high-frequency noise, and obtaining the mathematical model of the robust PID controller; S3, constructing a gravitational search algorithm optimization model: Taking the three parameters K P 、K I and KD Taking the optimized variables, an objective function is established based on the preset performance requirements of the hydraulic turbine governing system; An optimization model is constructed based on the gravitational search algorithm; S4. Optimize the parameters of the robust PID controller using the gravitational search algorithm: Input the optimization model constructed in step S3 into the gravitational search algorithm, and find the combination of parameters of the robust PID controller that makes the objective function reach the optimal value through iterative calculation; S5. Apply the optimized robust PID controller to the hydraulic turbine governing system: Apply the combination of parameters of the optimized robust PID controller obtained in step S4 to the hydraulic turbine governing system.

[0006] Preferably, in step S1, the transfer function of the mechanical hydraulic system is: ; where, is the reaction time constant of the auxiliary servomotor, , are the maximum displacement of the auxiliary servomotor and the maximum opening of the pilot valve respectively, , , are the piston area of the auxiliary servomotor, the flow velocity and width of the pilot valve window respectively, and s is the complex variable in the Laplace transform.

[0007] Preferably, in step S1, the transfer function of the governor is: ; where, K D , K P , K I are the PID adjustment coefficients, and b p is the permanent speed droop coefficient.

[0008] Preferably, in step S1, the transfer function of the water conveyance system is: ; where, T w is the water inertia time constant; H(s) is the Laplace transform of the head flow rate, and Q(s) is the Laplace transform of the flow rate out of the pipeline.

[0009] Preferably, in step S1, the transfer function of the hydraulic turbine is: ; ; where, e y is the transfer coefficient of the hydraulic turbine torque to the guide vane opening, e x is the transfer coefficient of the hydraulic turbine torque to the rotational speed, eh is the transfer coefficient of the turbine torque to the head, e qy is the transfer coefficient of the turbine flow rate to the guide vane opening, e qx is the transfer coefficient of the turbine flow rate to the rotational speed, e qh is the transfer coefficient of the turbine flow rate to the head, y is the relative value of the guide vane opening deviation, x is the relative value of the rotational speed deviation, h is the relative value of the head deviation, and Y(s), X(s), and H(s) are the Laplace transforms of y, x, and h respectively; M t (s) represents the Laplace transform of the turbine output torque.

[0010] Preferably, in step S1, the transfer function of the generator load is: ; where, e g represents the rate of change of the generator load torque with respect to the rotational speed, and its value is greater than 0; m go represents the load torque at the moment when ω = ω0 is cut off or connected at t = 0, and ω is the angular velocity of the turbine; The transfer function of the hydro turbine generator unit is: ; where, T a is the inertia time constant of the unit, T b is the inertia time constant of the load, e n is the comprehensive self-regulation coefficient of the hydro turbine generator unit; s is the complex variable in the Laplace transform.

[0011] Preferably, in step S2, obtaining the mathematical model of the robust PID controller specifically includes: S201, population initialization; generating an initial population, where each individual represents a set of possible PID parameters; S202, fitness evaluation; calculating the fitness value of each individual; S203, selection operation; selecting excellent individuals for reproduction according to the fitness value; S204, crossover operation; generating new individuals through the crossover operation to increase the diversity of the population; S205, mutation operation; randomly mutating individuals to explore new solution spaces; S206, repeated iteration; repeating the above steps until the preset number of evolutionary generations is reached or the termination condition is satisfied.

[0012] Preferably, a hydro turbine PID parameter optimization system based on the gravitational search algorithm is used to execute the above-mentioned hydro turbine PID parameter optimization method based on the gravitational search algorithm; the system includes a system model unit, a PID controller unit, an optimization model unit, a parameter adjustment unit, and an output unit; The system model unit is used to establish the mathematical model of the hydro-turbine governing system, including the mechanical hydraulic system, governor, water diversion system, hydro-turbine, generator load, and hydro-generator set, and determine the transfer function of each part; The PID controller unit is used to design a robust PID controller. Based on the traditional PID controller, a low-pass filter is introduced to obtain the mathematical model of the robust PID controller; The optimization model unit is used to construct a gravitational search algorithm optimization model: taking the three parameters KP, KI, and KD of the robust PID controller as optimization variables, establishing an objective function based on the preset performance requirements of the hydro-turbine governing system; constructing an optimization model based on the gravitational search algorithm; The parameter adjustment unit is used to optimize the parameters of the robust PID controller using the gravitational search algorithm. Input the constructed optimization model into the gravitational search algorithm, and find the parameter combination of the robust PID controller that makes the objective function reach the optimal value through iterative calculation; The output unit is used to apply the optimized robust PID controller to the hydro-turbine governing system.

[0013] Preferably, a computer device includes a memory and one or more processors; one or more programs are stored on the memory. When the one or more programs are executed by the one or more processors, the one or more processors implement the hydro-turbine PID parameter optimization method based on the gravitational search algorithm.

[0014] Preferably, a computer-readable storage medium stores a computer program, and the computer instructions are used to make a computer execute the hydro-turbine PID parameter optimization method based on the gravitational search algorithm.

[0015] The beneficial effects of the present invention are as follows: 1. By optimizing the parameters of the robust PID controller through the gravitational search algorithm, the present invention can enable the hydro-turbine governing system to have better static and dynamic performance under various operating conditions and disturbances.

[0016] 2. The gravitational search algorithm used in the present invention has the advantages of strong global search ability and fast convergence speed, can quickly find the optimal solution, and improves the optimization efficiency.

[0017] 3. The method of the present invention is not only applicable to a specific hydro-turbine governing system, but also can be extended to other similar complex control systems, and has wide applicability. Description of the Drawings

[0018] Figure 1 is the flow chart of the present invention; Figure 2 is the general flow chart of the gravitational search algorithm in the embodiment of the present invention.

[0019] Figure 3 This is a schematic flow chart of obtaining the mathematical model of the robust PID controller in the embodiments of the present invention. Detailed implementation manners

[0020] Embodiment 1: As Figure 1 shown, a method for optimizing the PID parameters of a hydraulic turbine based on the gravitational search algorithm includes: S1. Establish the mathematical model of the hydraulic turbine governing system and determine the transfer functions of each part in the mathematical model; each part in the mathematical model includes a mechanical hydraulic system, a governor, a water diversion system, a hydraulic turbine, a generator load, and a hydraulic turbine generator set; S2. Design a robust PID controller: Introduce a low-pass filter on the basis of the traditional PID controller to eliminate the interference of high-frequency noise, and obtain the mathematical model of the robust PID controller; S3. Construct a gravitational search algorithm optimization model: Take the three parameters K P , K I and K D of the robust PID controller as optimization variables, and establish an objective function based on the preset performance requirements of the hydraulic turbine governing system; Construct an optimization model based on the gravitational search algorithm; S4. Use the gravitational search algorithm to optimize the parameters of the robust PID controller: Input the optimization model constructed in step S3 into the gravitational search algorithm, and find the parameter combination of the robust PID controller that makes the objective function reach the optimal value through iterative calculation; S5. Apply the optimized robust PID controller to the hydraulic turbine governing system: Apply the parameter combination of the optimized robust PID controller obtained in step S4 to the hydraulic turbine governing system.

[0021] Preferably, in step S1, the transfer function of the mechanical hydraulic system is: ; where is the reaction time constant of the auxiliary servomotor, , are the maximum displacements of the auxiliary servomotor and the maximum opening of the pilot valve respectively, , , are the piston area of the auxiliary servomotor, the flow velocity and width of the pilot valve window respectively, and s is the complex variable in the Laplace transform.

[0022] Furthermore, in this embodiment, the value of s in the mechanical hydraulic system is , where is the spool valve displacement, is the maximum opening of the pilot valve; in other systems, s takes relevant data variables for calculation according to the adaptation situation.

[0023] Preferably, in step S1, the transfer function of the governor is: ; where K D , K P , K I are the PID adjustment coefficients, and b p is the permanent speed droop coefficient.

[0024] Preferably, in step S1, the transfer function of the water intake system is: ; where T w is the water flow inertia time constant; H(s) is the Laplace transform of the water head flow rate, Q(s) is the Laplace transform of the outflow pipeline flow rate, and s is the complex variable in the Laplace transform.

[0025] Preferably, in step S1, the transfer function of the water turbine is: ; ; where e y is the transfer coefficient of the water turbine torque to the guide vane opening, e x is the transfer coefficient of the water turbine torque to the rotational speed, e h is the transfer coefficient of the water turbine torque to the water head, e qy is the transfer coefficient of the water turbine flow rate to the guide vane opening, e qx is the transfer coefficient of the water turbine flow rate to the rotational speed, e qh is the transfer coefficient of the water turbine flow rate to the water head, y is the relative value of the guide vane opening deviation, x is the relative value of the rotational speed deviation, h is the relative value of the water head deviation, and Y(s), X(s), H(s) are the Laplace transforms of y, x, h respectively; M t (s) represents the Laplace transform of the water turbine output torque.

[0026] Preferably, in step S1, the transfer function of the generator load is: ; where e g represents the change rate of the generator load torque with respect to the rotational speed, and its value is greater than 0; m go represents the load torque at the moment when ω = ω0 is cut off or connected at t = 0, and ω is the angular velocity of the water turbine; The transfer function of the water turbine generator set is: ; wherein, T a is the inertia time constant of the unit, T b is the inertia time constant of the load, and e n is the comprehensive self-regulation coefficient of the hydro-generating unit; s is the complex variable in the Laplace transform.

[0027] As Figure 2 shown, the specific steps of the gravitational search algorithm are: generating the initial population, evaluating the suitability of each agent, updating the gravitational search constant G, the best and worst populations, calculating the mass M and acceleration a of each agent, updating the velocity and position, meeting the end criteria, and returning the best solution.

[0028] As Figure 3 shown, preferably, in step S2, obtaining the mathematical model of the robust PID controller specifically includes: S201, population initialization; generating the initial population, where each individual represents a set of possible PID parameters; S202, fitness evaluation; calculating the fitness value of each individual; S203, selection operation; selecting excellent individuals for reproduction according to the fitness value; S204, crossover operation; generating new individuals through the crossover operation to increase the diversity of the population; S205, mutation operation; randomly mutating individuals to explore new solution spaces; S206, repeated iteration; repeating the above steps until the preset number of evolution times is reached or the termination condition is met.

[0029] Preferably, a hydro-turbine PID parameter optimization system based on the gravitational search algorithm is used to execute the above-mentioned hydro-turbine PID parameter optimization method based on the gravitational search algorithm; the system includes a system model unit, a PID controller unit, an optimization model unit, a parameter adjustment unit, and an output unit; The system model unit is used to establish the mathematical model of the hydro-turbine speed regulation system: including the mechanical hydraulic system, governor, water diversion system, hydro-turbine, generator load, and hydro-generating unit, and determining the transfer function of each part; The PID controller unit is used to design a robust PID controller. On the basis of the traditional PID controller, a low-pass filter is introduced to obtain the mathematical model of the robust PID controller; The optimization model unit is used to construct a gravitational search algorithm optimization model: taking the three parameters KP, KI, and KD of the robust PID controller as optimization variables, establishing an objective function based on the preset performance requirements of the hydro-turbine speed regulation system; constructing an optimization model based on the gravitational search algorithm; The parameter adjustment unit is used to optimize the parameters of the robust PID controller by using the gravitational search algorithm. The constructed optimization model is input into the gravitational search algorithm, and the parameter combination of the robust PID controller that makes the objective function reach the optimal value is found through iterative calculation; The output unit is used to apply the optimized robust PID controller to the hydro turbine governing system.

[0030] Preferably, a computer device includes a memory and one or more processors; one or more programs are stored on the memory. When the one or more programs are executed by the one or more processors, the one or more processors implement the above-mentioned hydro turbine PID parameter optimization method based on the gravitational search algorithm.

[0031] Preferably, a computer-readable storage medium stores a computer program, and the computer instructions are used to make a computer execute the above-mentioned hydro turbine PID parameter optimization method based on the gravitational search algorithm.

[0032] Embodiment 2: For the optimization model of the gravitational search algorithm constructed in step S3 in this embodiment, a specific method for optimizing the parameters of the robust PID controller by using the gravitational search algorithm is provided; the implementation process is as follows: S301, Define the search space and individual coding: Take the parameters of the robust PID controller as the optimization variables to construct a three-dimensional search space; each individual is represented as: ; where N is the population size, and the parameter range satisfies the physical constraints: ; ; .

[0033] S302, Objective function design: Based on the dynamic performance requirements of the hydro turbine governing system, define the minimized comprehensive objective function J: ; where: represents the integral of time-weighted absolute error; is the maximum overshoot of the system response; is the adjustment time; is the weight coefficient, satisfying .

[0034] S303, Construct the core calculation framework of the gravitational search algorithm: Mass calculation: Individual mass is obtained by normalizing the fitness value as follows: ; where ; Gravitational force calculation: The gravitational force of an individual on in the th dimension ( d ) is: ; where, is the time-varying gravitational constant; is the initial value, is the attenuation coefficient, t is the current iteration number, and T is the total number of iterations; is the Euclidean distance, is a small constant to prevent division by zero; Resultant force and acceleration: The total acceleration of an individual in the d th dimension is: ; Position update: Update the velocity and position according to the acceleration: ; where rand is a uniform random number in [0, 1], used to increase randomness.

[0035] S304, Constraint handling: If the updated parameter exceeds the boundary, use reflection correction: .

[0036] S305, Termination condition: When the maximum number of iterations T is reached, or the change rate of the objective function , i.e., the threshold, the optimization is terminated.

[0037] Furthermore, the initial parameter settings are preferably: The initial population size N = 50 to 100; The gravitational constant G0 = 100G, λ = 20; The weight coefficients α = 0.6, β = 0.2, γ = 0.2.​

Claims

1. A method for optimizing the PID parameters of a hydraulic turbine based on the gravitational search algorithm, characterized in that Including: S1. Establish the mathematical model of the hydro - turbine governing system and determine the transfer functions of all parts in the mathematical model. All parts in the mathematical model include the mechanical - hydraulic system, governor, water - diversion system, hydro - turbine, generator load, and hydro - turbine generator set; S2. Design a robust PID controller: Based on the traditional PID controller, introduce a low - pass filter to obtain the mathematical model of the robust PID controller; S3. Construct a gravitational search algorithm optimization model: Take the three parameters K P 、K I and K D as the optimization variables, and establish an objective function based on the preset performance requirements of the hydraulic turbine governing system; Construct an optimization model based on the gravitational search algorithm; S4. Use the gravitational search algorithm to optimize the parameters of the robust PID controller: Input the optimization model constructed in step S3 into the gravitational search algorithm, and through iterative calculation, find the combination of robust PID controller parameters that makes the objective function reach the optimal value; S5. Apply the optimized robust PID controller to the hydro - turbine governing system: Apply the combination of optimized robust PID controller parameters obtained in step S4 to the hydro - turbine governing system.

2. The PID parameter optimization method for a water turbine based on the gravitational search algorithm according to claim 1, wherein In step S1, the transfer function of the mechanical - hydraulic system is: ； Among them, is the auxiliary servomotor response time constant, and are the maximum displacement of the auxiliary servomotor and the maximum opening of the pilot valve respectively, and and are the piston area of the auxiliary servomotor, the flow velocity and width of the pilot valve window respectively, and s is the complex variable in the Laplace transform.

3. The hydroturbine PID parameter optimization method based on the gravitational search algorithm according to claim 2, characterized in that, In step S1, the transfer function of the governor is: ； Among them, K D , K P , K I are PID adjustment coefficients, and b p is the permanent speed droop coefficient.

4. A method for optimizing the PID parameters of a water turbine based on the gravitational search algorithm according to claim 3, characterized in that, In step S1, the transfer function of the water - diversion system is: ； where T w is the water flow inertia time constant; H(s) is the Laplace transform of the water head flow rate, and Q(s) is the Laplace transform of the flow rate out of the pipeline.

5. A method for optimizing the PID parameters of a water turbine based on the gravitational search algorithm according to claim 4, characterized in that In step S1, the transfer function of the hydro - turbine is: ； ； where, e y is the transfer coefficient of the turbine torque to the guide vane opening, e x is the transfer coefficient of the turbine torque to the rotational speed, e h is the transfer coefficient of the turbine torque to the water head, e qy is the transfer coefficient of the turbine flow rate to the guide vane opening, e qx is the transfer coefficient of the turbine flow rate to the rotational speed, e qh is the transfer coefficient of the turbine flow rate to the water head, y is the relative value of the guide vane opening deviation, x is the relative value of the rotational speed deviation, h is the relative value of the water head deviation, Y(s), X(s), and H(s) are the Laplace transforms of y, x, and h respectively; Mt(s) represents the Laplace transform of the turbine output torque.

6. The optimization method for the PID parameters of a hydraulic turbine based on the gravitational search algorithm according to claim 5, characterized in that, In step S1, the transfer function of the generator load is: ； Among them, e g represents the change rate of the generator load torque with respect to the rotational speed, and its value is greater than 0; m go represents the load torque at the moment when ω = ω0 is cut off or put in at t = 0, where ω is the angular velocity of the water turbine; The transfer function of the hydro - turbine generator set is: ； Among them, T a is the inertia time constant of the unit, and T b is the inertia time constant of the load, and e n is the comprehensive self-regulation coefficient of the hydro-generator unit; s is the complex variable in the Laplace transform.

7. A method for optimizing the PID parameters of a hydraulic turbine based on a gravitational search algorithm according to claim 1, characterized in that In step S2, obtaining the mathematical model of the robust PID controller specifically includes: S201. Population initialization; Generate an initial population, and each individual represents a group of possible PID parameters; S202. Fitness evaluation; Calculate the fitness value of each individual; S203. Selection operation; Select excellent individuals for reproduction according to the fitness value; S204. Crossover operation; Generate new individuals through the crossover operation to increase the diversity of the population; S205. Mutation operation; Randomly mutate individuals to explore new solution spaces; S206. Repeat iteration; Repeat the above steps until the preset number of evolutionary times is reached or the termination condition is met.

8. A hydroturbine PID parameter optimization system based on the gravitational search algorithm, characterized in that, The system is used to execute a method for optimizing the PID parameters of a hydro - turbine based on the gravitational search algorithm according to any one of claims 1 - 7, and includes a system model unit, a PID controller unit, an optimization model unit, a parameter adjustment unit, and an output unit; The system model unit is used to establish the mathematical model of the hydro - turbine governing system: including the mechanical - hydraulic system, governor, water - diversion system, hydro - turbine, generator load, and hydro - turbine generator set, and determine the transfer functions of all parts; The PID controller unit is used to design a robust PID controller. Based on the traditional PID controller, introduce a low - pass filter to obtain the mathematical model of the robust PID controller; The optimization model unit is used to construct a gravitational search algorithm optimization model: Take the three parameters KP, KI, KD of the robust PID controller as optimization variables, and establish an objective function based on the preset performance requirements of the hydro - turbine governing system; Construct an optimization model based on the gravitational search algorithm; The parameter adjustment unit is used to optimize the parameters of the robust PID controller by using the gravitational search algorithm. Input the constructed optimization model into the gravitational search algorithm, and through iterative calculation, find the combination of robust PID controller parameters that makes the objective function reach the optimal value; The output unit is used to apply the optimized robust PID controller to the hydro-turbine speed regulation system.

9. A computer device, characterized in that, It includes a memory and one or more processors; one or more programs are stored on the memory, and when the one or more programs are executed by the one or more processors, the one or more processors implement the hydro-turbine PID parameter optimization method based on the gravitational search algorithm according to any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, A computer program is stored on a computer-readable storage medium, and the computer instructions are used to cause a computer to execute the hydro-turbine PID parameter optimization method based on the gravitational search algorithm according to any one of claims 1 to 7.

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