Water turbine governor parameter adjusting method based on fractal multi-objective optimization algorithm

Abstract

The invention relates to a water turbine speed regulator parameter adjusting method based on a fractal multi-objective optimization algorithm, which takes a water conservancy power station speed regulating system as a research background, establishes a water turbine speed regulating system control model based on a first principle, and constructs a water turbine speed regulating system parameter multi-objective optimization method. Different from a previous mode that only system accuracy or system speed regulation is considered, two conflicting targets of fractal dimension and integral time absolute error are taken as two targets of the optimization method, and a stability measurement index of the speed regulation system is refined. According to the optimization algorithm, complex geometric characteristics are introduced into variation of a candidate solution by utilizing fractal self-similarity, and the diversity or convergence of the algorithm is preferentially considered in a self-adaptive selection optimization process by utilizing fractal dimensions, so that a better solution is provided for research in the field of optimization of complex and difficult multi-target optimization problems.

Description

Technical Field

[0001] The invention belongs to the field of intelligent adjustment of turbine governor parameters, and in particular relates to a method for adjusting turbine governor parameters based on a fractal multi-objective optimization algorithm. Background Art

[0002] The turbine uses the kinetic energy or potential energy of the water flow to drive the impeller to rotate. It is a mechanical device that converts water energy into mechanical energy and is mainly used in hydroelectric power stations. Its basic principle is to introduce water into the turbine through the water diversion system. The water flow pushes the blades of the turbine to drive it to rotate, thereby driving the generator to generate electricity and achieve clean and efficient hydropower generation. The advantages of the turbine include high energy utilization efficiency, environmental protection, long life, strong load regulation ability and low operating cost, so it plays an important role in sustainable energy utilization. The turbine speed control system is the core control device in the hydropower generation system. It is responsible for adjusting the frequency of the generator and the speed of the turbine. By adjusting the water flow, the guide vane opening and the turbine load, it ensures that the turbine maintains a stable operating frequency under different working conditions, usually at 50Hz or 60Hz. The turbine speed control system plays an important role in the efficiency, safety and stability of the power system. Therefore, the basic task of turbine regulation is to control the speed and output power of the turbine by adjusting the water flow to ensure that the generator operates stably under different working conditions and meet the requirements of the power grid. The turbine regulating system is responsible for frequency regulation, power regulation and unit safety protection in hydropower generation. The main components of the turbine governor include: governor host, hydraulic operating mechanism, feedback and sensor system, and control unit.

[0003] The core task of the turbine speed governor is to maintain the stability of the turbine speed by monitoring and adjusting the water flow, ensuring that the generator output frequency matches the grid demand, and at the same time has protection and emergency regulation functions. This system ensures the safe and efficient operation of the hydropower station. For most units, the use of PID-based adaptive variable parameter regulation can make the static and dynamic characteristics of the turbine control system meet the requirements of the power system. Its transfer function is:

[0004]

[0005] Where K P , K I and K D are proportional, integral and differential gain coefficients respectively, T 1v is the inertia time constant of the acceleration link, b t , T n and T d They are transient difference coefficient, acceleration time constant and buffer time constant respectively.

[0006] In view of the challenges of turbine governor control and the models for different types of units, different types of runners and different water diversion systems, a lot of turbine commissioning experience and continuous experiments are needed on site to give recommended control system adjustment parameters. The Chinese patent with patent number CN201710152523.1 invented a method for optimizing the parameters of the PID governor of a hydro-turbine generator set. The TLBO algorithm is used to minimize the difference between time and system frequency, and the turbine governor parameters are optimized to ensure the convergence speed and optimization efficiency of the governor. However, the objective function in the invention only considers the speed of controller convergence. Therefore, most subsequent inventions in this field are centered on the two goals of ensuring the rapid response and stable control of the PID controller at the same time. The Chinese patent with patent number CN201910164611.2 uses a particle swarm algorithm to optimize the parameters of the hydro-turbine generator set governor with the weighted sum of the speed influence factor and the damping torque as the optimization target. After optimization, the governor system adjustment ability is more stable, and ultra-low frequency oscillation is suppressed. In the invention, a multi-objective problem is solved by a single-objective optimization method through a simple weighted summation method. This method is relatively simple to operate, but this simplification often loses some information, resulting in the solution being not the global optimal. In addition, there is a certain degree of subjectivity in how to determine the weights. The Chinese patent with patent number CN202211071531.0, in order to ensure the power regulation quality of the unit monitoring system, constructs a power control model, uses an improved multi-objective genetic algorithm to solve the control model, and designs a multi-objective optimization problem based on the power regulation performance and anti-regulation performance. However, from the results, the designed multi-objective problem cannot accurately reflect the regulation performance, and the performance of the optimization algorithm cannot meet the requirements of complex and difficult regulation tasks. Summary of the invention

[0007] The purpose of the present invention is to propose a method for adjusting parameters of a turbine speed governor based on a fractal multi-objective optimization algorithm, which can solve the multi-objective optimization problem with complex speed governor adjustment tasks and difficult solutions. The technical solution of the present invention includes the following steps:

[0008] S1. Construct mathematical model of turbine governor system;

[0009] S1.1, construct the parallel PID control model of the turbine governor system;

[0010] S1.2, construct a hydraulic servo system to realize the servo control of the speed governor;

[0011] S1.3. For the dynamic characteristics of the turbine speed control system, an idealized water diversion system simulation model is used to build a simulation model using various characteristic coefficients in the turbine;

[0012] S1.4, use a first-order link to simulate the operation of the hydropower station in the isolated grid mode and simulate the dynamic characteristics of the turbine speed control system;

[0013] S2, construct decision variables and objective functions of multi-objective optimization methods;

[0014] S2.1, proportional gain coefficient K P , integral gain coefficient K I , differential gain coefficient K D Decision variables for multi-objective optimization methods;

[0015] S2.2, the fractal dimension of the frequency-time curve of the F1 speed regulation system and the absolute error of the F2 integral time are used as the objective function of the optimization algorithm;

[0016] S3, construct a fractal-based multi-objective optimization algorithm;

[0017] S3.1, randomly generate an initialization population according to a pre-set range of the population;

[0018] S3.2, calculate the two objective function values ​​corresponding to each group of populations to form a fitness matrix, and perform fast non-dominated sorting based on crowding distance;

[0019] S3.3, mutating and updating the population through an iterative function system to generate a matrix composed of new candidate solutions, and expanding the matrix of the undetermined population to a three-dimensional fractal space to perform an affine transformation based on the iterative function system;

[0020] S3.4, transform the coordinate points in the fractal space into the solution space of the actual problem, and constrain the parameter specifications for generating candidate solutions;

[0021] S3.5. According to the fractal dimension value of the new fitness matrix and the fractal dimension change of the fitness matrix of the previous generation, adaptive selection prioritizes population convergence or selects offspring strategies based on population convergence;

[0022] S3.6, give priority to population convergence, first sort the population by non-dominance, retain the top individuals, then sort by crowding, retain the top individuals to fill the remaining individuals, and get the same population as the previous generation;

[0023] S3.7. Give priority to population convergence, first sort the population by non-dominance, retain the top individuals, then sort by crowding, retain the top individuals to fill the remaining individuals, and get the same population as the previous generation;

[0024] S3.8, repeat S3.2-S3.7 until the number of evaluations meets the set value;

[0025] S3.9. Select the best solution.

[0026] In the above-mentioned turbine governor parameter adjustment method based on fractal multi-objective optimization algorithm, the turbine governor system in S1.1 adopts a parallel PID control model, and the expression is:

[0027]

[0028] where σ c is the given opening of the relay, σ PID is the PID regulator control output, x c is the given speed of the unit, K D is the differential magnification factor, K P is the proportional magnification factor, T D is the differential time, K I is the integral magnification factor, b P is the permanent slip coefficient.

[0029] In the above-mentioned turbine governor parameter adjustment method based on fractal multi-objective optimization algorithm, the expression of the hydraulic follow-up system in S1.2 is:

[0030]

[0031] Where α is the guide vane opening, T y is the time constant of the relay.

[0032] In the above-mentioned turbine governor parameter adjustment method based on fractal multi-objective optimization algorithm, the water diversion system simulation model expression in S1.3 is:

[0033]

[0034]

[0035]

[0036]

[0037] Where n, y, q, h, m, and a are the relative values ​​of speed, guide vane opening, flow, head, torque, and speed, respectively. s )、WM(x s ) is the transformation curve describing the full characteristics, k1 = 10, k2 = 0.9, C y =0.2, C h =0.5.

[0038] In the above-mentioned turbine governor parameter adjustment method based on fractal multi-objective optimization algorithm, the dynamic characteristic process expression of the turbine speed control system in S1.4 is:

[0039]

[0040] where e n is the comprehensive self-regulation coefficient of the unit, T a is the unit inertia time constant.

[0041] In the above-mentioned turbine speed governor parameter adjustment method based on fractal multi-objective optimization algorithm, the optimization target of the parameter multi-objective optimization method in S2.2 is that F1 measures the stability of the speed control system, and F2 measures the accuracy of the speed control system. The specific formula is as follows:

[0042]

[0043] Where y(t) is the system output, r(t) is the reference signal, N is the number of data, and x i is the spatial coordinate of each point, θ(r) is 1 when r is a positive number, otherwise it is 0. The correlation dimension is used to approximate the fractal dimension of the frequency-time curve of the speed regulation system. All points with a spatial distance less than δ are considered to be related. These points are calculated and calculated in N 2 The proportion of t can be obtained to obtain the approximate fractal dimension, which reflects the fluctuation degree of the frequency-time curve of the speed regulation system. s is the speed rise time.

[0044] In the above-mentioned turbine governor parameter adjustment method based on fractal multi-objective optimization algorithm, the specific structure of the fractal multi-objective optimization algorithm in S3 is: 1. Initialize the population; 2. Non-dominated sorting with crowding distance and calculate the fractal dimension of the fitness matrix; 3. Perform fractal mutation; 4. Calculate the fitness of the mutated new population, the fractal dimension of the fitness matrix, the crowding and the dominance relationship; 5. Adaptively choose whether to give priority to the convergence or diversity of the generated population according to the change in the fractal dimension of the fitness matrix of the new and old populations; 6. Repeat steps 2-5 until the requirements are met.

[0045] In the above-mentioned turbine governor parameter adjustment method based on fractal multi-objective optimization algorithm, the specific formula of the new population in S3.3 is as follows:

[0046]

[0047] Where a, b, c, ..., i are the elements of the fractal diffusion matrix, which determine the rotation, shearing, scaling and other operations of the point in the three-dimensional space; j, k, l are the translation amounts, which control the translation of the point in the three-dimensional space. The present invention adopts the following two iterative function system parameters:

[0048]

[0049]

[0050] Where P is the probability of selecting the calculation formula. The process randomly selects one of the two for iterative calculation. When the number of iterations reaches the maximum, the iteration stops.

[0051] In the above-mentioned turbine governor parameter adjustment method based on fractal multi-objective optimization algorithm, the coordinate points in the fractal space are converted into the solution space of the actual problem in S3.4. The specific formula is:

[0052]

[0053] Among them, F∈[0,1] determines the amplitude of the variation introduced in the variation process, thus affecting the characteristics of the generated new individuals; s' i (j) is the new variable generated by the j-th mutation in the i-th group of candidate solutions, s i (j) is the jth original variable in the i-th group of candidate solutions, x, y, z are fractal space variables generated by the iterative function system, and the choice of x, y, or z is changed with the same probability p. The boundary correction method is used to ensure that the candidate solutions in the new population matrix are within the defined boundary range. The formula is as follows:

[0054] x new =max(x min ,min(x max ,x new ))

[0055] where x new is a candidate solution in the new population matrix, x min is the lower limit of the candidate solution, x max is the upper constraint limit of the candidate solution.

[0056] In the above-mentioned turbine governor parameter adjustment method based on fractal multi-objective optimization algorithm, S3.5 is based on whether the fractal dimension value of the new fitness matrix and the fractal dimension of the previous generation fitness matrix are greater than a certain threshold, so as to adaptively judge whether the current evolution gives priority to population diversity or population convergence. The fractal dimension calculation method is as follows:

[0057]

[0058] Beneficial effects:

[0059] The invention proposes a method for adjusting parameters of a turbine governor based on a fractal multi-objective optimization algorithm, which provides a better solution for the research of parameter adjustment of turbine speed control systems and other multi-objective, multi-variable and difficult multi-objective optimization problems. The innovative method can achieve the following technical effects:

[0060] 1. Different from the previous method of only considering system accuracy or system adjustment speed or the simple combination of the two, the multi-objective optimization method simultaneously considers the two conflicting goals of system accuracy and stability, and makes the other goal meet the expected requirements without significantly reducing one goal;

[0061] 2. Using the self-similarity of fractals to introduce complex geometric properties into the variation of candidate solutions, this variation method is more exploratory than traditional variation methods and can better cover the solution space, thus helping to optimize the convergence of the algorithm when solving nonlinear and complex problems;

[0062] 3. Use fractal dimension as an objective of the optimization algorithm to measure the stability of the algorithm, balance the performance and adaptability of the speed control system through a fractal-based multi-objective optimization algorithm, and make the control system achieve optimal operating performance in a given disturbance experiment;

[0063] 4. In order to improve the diversity and convergence of the optimization algorithm evolution process, the design adaptively chooses whether to prioritize algorithm diversity or convergence during the optimization process to enhance the performance of the optimization algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 It is the structure diagram of the parameter adjustment method of the turbine governor based on the fractal multi-objective optimization algorithm;

[0065] Figure 2 This is the parallel PID control structure diagram of the turbine governor system;

[0066] Figure 3 This is the structural diagram of the electro-hydraulic servo system;

[0067] Figure 4 It is the structural diagram of the generator and its load;

[0068] Figure 5 Flowchart of fractal-based multi-objective optimization algorithm;

[0069] Figure 6 (a) Iterated function system generates Sierpinski tetrahedron point distribution map;

[0070] Figure 6 (b) Iterative function system generates the distribution map of Barnsley fern points;

[0071] Figure 7 Schematic diagram of the best solution selection strategy;

[0072] Figure 8 (a) provides a solution set diagram based on the fractal multi-objective optimization algorithm;

[0073] Figure 8 (b) Graph of solution sets provided by traditional multi-objective optimization algorithms;

[0074] Figure 9 (a) Primary frequency disturbance response curve;

[0075] Fig.9(b) Response curves of two frequency disturbances. DETAILED DESCRIPTION

[0076] The present application is further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the protection scope of the present application.

[0077] The structure of the turbine governor parameter adjustment method based on fractal multi-objective optimization algorithm is as follows: Figure 1 , the specific implementation includes the following steps:

[0078] S1. Construct mathematical model of turbine governor system;

[0079] S1.1, the turbine speed governor system adopts a parallel PID control model, the specific structure is as follows Figure 2 , the expression is:

[0080]

[0081] where σ c is the given opening of the relay, σ PID is the PID regulator control output, x c is the given speed of the unit, K D is the differential magnification factor, K P is the proportional magnification factor, T D is the differential time, K I is the integral magnification factor, b P is the permanent slip coefficient;

[0082] S1.2. The hydraulic follow-up system of the turbine speed governor is a common control system used to adjust the speed of the turbine. Hydraulic components are used to achieve follow-up control of the speed governor. The specific structure is as follows: Figure 3 , the expression is:

[0083]

[0084] Where α is the guide vane opening, T y is the time constant of the servomotor;

[0085] S1.3. For the dynamic characteristics of the turbine speed control system, the water in the water diversion system has a large inertia. Especially in the long-distance water diversion pipeline, the water flow needs a certain amount of time to reach a completely stable state. When the power output or guide vane opening of the turbine is adjusted quickly, the water flow inertia in the water diversion system will cause pressure fluctuations. This phenomenon is called the water hammer effect, which causes oscillation and system instability. The simulation model built using the various characteristic coefficients in the turbine has the following specific structural expression:

[0086]

[0087]

[0088] Where n, y, q, h, m, and a are the relative values ​​of speed, guide vane opening, flow, head, torque, and speed, respectively. s )、WM(x s ) is the transformation curve describing the full characteristics, k1 = 10, k2 = 0.9, C y =0.2, C h =0.5;

[0089] S1.4. There are two main operating modes for turbine power generation systems: isolated grid mode and grid-connected mode. The operating characteristics and regulation requirements of these two modes are different, and they are adapted to different grid conditions and needs respectively. The grid-connected mode means that the turbine generator set is connected to the large grid for operation, and the generator is powered by the grid and other power sources together. The frequency and voltage of the turbine must be consistent with the grid, and the output power must be adjusted according to the requirements of the grid. The isolated grid mode means that the turbine generator set is not connected to the large grid, but supplies power to a certain area or an independent grid alone. When the hydropower station operates in the isolated grid mode, it is regarded as a first-order link in the process of analyzing and studying the dynamic characteristics of the turbine speed control system. The specific structure is as follows Figure 4 , the expression is:

[0090]

[0091] where e n is the comprehensive self-regulation coefficient of the unit, T a is the unit inertia time constant;

[0092] S2, construct decision variables and objective functions of multi-objective optimization methods;

[0093] S2.1. The decision variables of the turbine governor parameter adjustment method based on fractal multi-objective optimization algorithm are the same as those of the governor optimization model method, with the proportional gain coefficient K P , integral gain coefficient K I , differential gain coefficient K D Decision variables for multi-objective optimization methods;

[0094] S2.2. In order to construct a multi-objective problem, the multi-objective optimization method for turbine speed governor parameters based on the fractal multi-objective optimization algorithm selects the fractal dimension of the frequency-time curve of the F1 speed control system and the absolute error of the F2 integral time, and minimizes the two conflicting objectives as the objective function of the optimization algorithm. The F1 objective function represents the stability of the speed control system, and the F2 objective function represents the accuracy of the entire response process of the speed control system. The specific formula is as follows:

[0095]

[0096] Where y(t) is the system output, r(t) is the reference signal, N is the number of data, and x i is the spatial coordinate of each point, θ(r) is 1 when r is a positive number, otherwise it is 0; the correlation dimension is used to approximate the fractal dimension of the frequency-time curve of the speed regulation system. All points with a spatial distance less than δ are considered to be related, and these points are calculated and calculated in N 2 The proportion of t can be obtained to obtain the approximate fractal dimension, which reflects the fluctuation degree of the frequency-time curve of the speed regulation system. s is the speed rise time;

[0097] S3. Construct a multi-objective optimization algorithm based on fractals. The specific process is as follows: Figure 5 , where F represents the set fractal dimension change determination threshold;

[0098] S3.1. According to the pre-set range of the population, randomly generate the initial population, given the maximum number of iterations gen_max, the population size N, the number of objective functions n and the dimension of the decision space d, and randomly generate X in the decision space i (k), i = 1, 2, ..., N, the current iteration number is gen = 1;

[0099] S3.2. According to formula (7), the two objective function values ​​corresponding to each group of populations are calculated to form a fitness matrix, and a fast non-dominated sorting based on crowding distance is performed. The method is as follows: a group of fitness matrices are classified according to the dominance relationship. Solution A is called the dominated solution B. If A is not inferior to B in all objective functions and is better than B in at least one objective function, according to this definition, all solutions that are not dominated by other solutions belong to the first layer, that is, the non-dominated layer; remove the solutions of the first layer, and find a new non-dominated layer from the remaining solutions, and repeat this process until all solutions are sorted. If the dominance is at the same level, sort them from large to small according to the crowding distance. The formula is:

[0100]

[0101] where f i+1 j is the jth objective function of point i+1, id is the congestion degree of point i, f i-1 j is the j-th objective function value of point i-1;

[0102] S3.3, the population is mutated and updated through an iterative function system to generate a matrix composed of new candidate solutions, i.e., a new population. The two objective function values ​​corresponding to each group of individuals in the new population are calculated to form a fitness matrix. The iterative function system generates a complex fractal structure through simple rules. The specific scheme is as follows: In the present invention, the population is specifically the proportional gain coefficient K P , integral gain coefficient K I , differential gain coefficient K D The undetermined population matrix composed of these three is extended to the three-dimensional fractal space to perform affine transformation based on the iterated function system, and the complex geometric characteristics are introduced into the variation of the candidate solution to form many self-similar parts similar to the whole. The specific formula is as follows:

[0103]

[0104] Where a, b, c, ..., i are the elements of the fractal diffusion matrix, which determine the rotation, shearing, scaling and other operations of the point in the three-dimensional space; j, k, l are the translation amounts, which control the translation of the point in the three-dimensional space; the present invention adopts the following two iterative function system parameters:

[0105]

[0106] Where P is the probability of selecting the calculation formula. The process randomly selects one of the two for iterative calculation. When the number of iterations reaches the maximum, the iteration is stopped. In order to ensure the speed of calculation, the number of iterations is set to a random number between 500 and 5000. By generating fractal perturbations through the iterative function system, the design space can be effectively searched to find the optimal configuration. Figure 6(a) and Figure 6(b) respectively show the spatial structure formed by 10,000 iterations of the two transformations of function T1 and T2 with (0,0) as the starting point. The iterative function system generates complex fractal images through simple rules.

[0107] S3.4. Convert the coordinate points in the fractal space into the solution space of the actual problem. The specific formula is:

[0108]

[0109] Among them, F∈[0,1] determines the amplitude of the variation introduced in the variation process, thus affecting the characteristics of the generated new individuals; s' i (j) is the new variable generated by the j-th mutation in the i-th group of candidate solutions, s i(j) is the jth original variable in the i-th group of candidate solutions, x, y, z are fractal space variables generated by the iterative function system, and the same probability p is used to change the selection of x or y or z; in order to constrain the parameter specifications of the generated candidate solutions, the boundary correction method is used to ensure that the candidate solutions in the new population matrix are within the defined boundary range. The formula is as follows:

[0110] x new =max(x min ,min(x max ,x new ))(13)

[0111] where x new is a candidate solution in the new population matrix, x min is the lower limit of the candidate solution, x max is the upper constraint limit of the candidate solution;

[0112] S3.5, according to whether the fractal dimension value of the new fitness matrix and the fractal dimension of the previous fitness matrix are greater than a certain threshold, the current evolution is judged to give priority to population diversity or population convergence. If it is greater than the threshold, execute S3.6; otherwise, execute S3.7, and judge whether the current evolution strategy gives priority to the diversity or convergence of the offspring population by the change value of the fractal dimension of the current fitness matrix. The fractal dimension calculation method is as follows:

[0113]

[0114] S3.6. Give priority to the diversity of the population. First, sort the population by crowding degree, retain the individuals in the top 50% of the population, and then perform non-dominated sorting, using the top individuals to fill the remaining individuals to obtain the same population as the previous generation;

[0115] S3.7. Prioritize population convergence, sort the population by non-dominance, select the dominant individuals, then calculate the crowding degree and sort them, retain the individuals with the highest crowding degree to fill the remaining individuals, until the population size is the same as the previous generation;

[0116] S3.8, repeat S3.2-S3.7 until the number of evaluations meets the set value;

[0117] S3.9, Selection Strategy The present invention makes the best selection for multiple sets of parameter solutions in the multi-objective optimization algorithm. The main method is to find the limit points in the solution set. The line connecting two limit points is called the limit line. By finding the solution point with the largest distance from the limit line, the point represents the optimal solution, which means that one goal is slightly improved while the other goal is not significantly degraded. The specific selection method is as follows: Figure 7 ;

[0118] S4, conducting simulation experiments on the algorithm proposed by the present invention;

[0119] S4.1, Assume that the rated parameters of the unit are as follows: Rated head H r =500m, rated speed N r =500r / min, rated flow rate Q r =60m 3 / s, rated torque is M r =5×106Nm, rated guide vane opening α r =20°, hydraulic system time constant T y =0.5, unit inertia time constant T a =0.5, water flow inertia time constant T W =0.5;

[0120] S4.2. Specify the parameters of the multi-objective fractal evolution algorithm and the proportional gain coefficient K of the PID controller. P , K I , K D The adjustment range is set to (0, 15), the objective function is specifically formula (7), the population size is set to 200, the maximum evolutionary generation is 100, and the number of evaluations is 20,000;

[0121] The present invention uses a fractal-based multi-objective optimization algorithm to optimize the system under the condition that a 4% frequency disturbance signal is given at the 10th second when the system is running stably without load. The Pareto frontier and the compromise solution are shown in Figure 8(a). At the same time, in order to compare the superiority of the fractal-based multi-objective optimization algorithm, a multi-objective evolutionary algorithm based on decomposition is used and the algorithm uses a differential operator to perform a comparative experiment on the variation of the offspring population, as shown in Figure 8(b). It can be seen that for the optimization of the speed regulation system parameters for such difficult optimization problems, the performance of the optimization algorithm is very important. The traditional optimization algorithm has insufficient search ability and is prone to fall into local optimality, and the number of feasible solutions found is small. The specific values ​​of the best solution are shown in Table 1. The frequency disturbance response curve obtained based on the following parameters is shown in Figure 9(a). The overshoot is 0.01%, the overshoot time is 10.84s, and the integral time absolute error is 1.489. In order to verify the robustness of the model, Figure 9(b) shows that the model is given an 8% frequency disturbance signal at the 30th second, and the frequency disturbance response curve can still respond quickly and accurately.

[0122] Table 1 Controller parameters obtained by fractal multi-objective optimization algorithm model

[0123]

[0124] The above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the above embodiments, it should be clear to those skilled in the art that the technical solutions described in the above embodiments may be modified, or some or all of the technical features therein may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for adjusting parameters of a turbine governor based on a fractal multi-objective optimization algorithm, comprising the following steps: S1. Construct mathematical model of turbine governor system; S1.1, construct the parallel PID control model of the turbine governor system; S1.2, construct a hydraulic servo system to realize the servo control of the speed governor; S1.

3. For the dynamic characteristics of the turbine speed control system, an idealized water diversion system simulation model is used to build a simulation model using various characteristic coefficients in the turbine; S1.4, use a first-order link to simulate the operation of the hydropower station in the isolated grid mode and simulate the dynamic characteristics of the turbine speed control system; S2, construct decision variables and objective functions of multi-objective optimization methods; S2.1, proportional gain coefficient K P , integral gain coefficient K I , differential gain coefficient K D Decision variables for multi-objective optimization methods; S2.2, the fractal dimension of the frequency-time curve of the F1 speed regulation system and the absolute error of the F2 integral time are used as the objective function of the optimization algorithm; S3, construct a fractal-based multi-objective optimization algorithm; S3.1, randomly generate an initialization population according to a pre-set range of the population; S3.2, calculate the two objective function values ​​corresponding to each group of populations to form a fitness matrix, and perform fast non-dominated sorting based on crowding distance; S3.3, mutating and updating the population through an iterative function system to generate a matrix composed of new candidate solutions, and expanding the matrix of the undetermined population to a three-dimensional fractal space to perform an affine transformation based on the iterative function system; S3.4, transform the coordinate points in the fractal space into the solution space of the actual problem, and constrain the parameter specifications for generating candidate solutions; S3.

5. According to the fractal dimension value of the new fitness matrix and the fractal dimension change of the fitness matrix of the previous generation, adaptive selection prioritizes population convergence or selects offspring strategies based on population convergence; S3.6, give priority to population convergence, first sort the population by non-dominance, retain the top individuals, then sort by crowding, retain the top individuals to fill the remaining individuals, and get the same population as the previous generation; S3.

7. Give priority to population convergence, first sort the population by non-dominance, retain the top individuals, then sort by crowding, retain the top individuals to fill the remaining individuals, and get the same population as the previous generation; S3.8, repeat S3.2-S3.7 until the number of evaluations meets the set value; S3.

9. Select the best solution.

2. The method for adjusting parameters of a turbine governor based on a fractal multi-objective optimization algorithm according to claim 1 is characterized in that: The turbine governor system expression in S1.1 is: where σ c is the given opening of the relay, σ PID is the PID regulator control output, x c is the given speed of the unit, K D is the differential magnification factor, K P is the proportional magnification factor, T D is the differential time, K I is the integral magnification factor, b P is the permanent slip coefficient.

3. The method for adjusting parameters of a turbine governor based on a fractal multi-objective optimization algorithm according to claim 1 is characterized in that: The water diversion system simulation model expression in S1.3 is: Where n, y, q, h, m, and a are the relative values ​​of speed, guide vane opening, flow, head, torque, and speed, respectively. s )、WM(x s ) is the transformation curve describing the full characteristics, k1 = 10, k2 = 0.9, C y =0.2, C h =0.

5.

4. The method for adjusting parameters of a turbine governor based on a fractal multi-objective optimization algorithm according to claim 1 is characterized in that: The optimization objectives of the parameter multi-objective optimization method in S2.2 are as follows: F1 objective function represents the stability of the speed regulation system, and F2 objective function represents the accuracy of the entire response process of the speed regulation system. The specific formula is as follows: Where y(t) is the system output, r(t) is the reference signal, N is the number of data, and x i is the spatial coordinate of each point, θ(r) is 1 when r is a positive number, otherwise it is 0. The correlation dimension is used to approximate the fractal dimension of the frequency-time curve of the speed regulation system. All points with a spatial distance less than δ are considered to be related. These points are calculated and calculated in N 2 The proportion of t can be obtained to obtain the approximate fractal dimension, which reflects the fluctuation degree of the frequency-time curve of the speed regulation system. s is the speed rise time.

5. According to claim 1, the method for adjusting parameters of a turbine governor based on a fractal multi-objective optimization algorithm is characterized in that: The specific structure of the fractal-based multi-objective optimization algorithm in S3 is as follows:

1. Initialize the population; 2. Perform non-dominated sorting with crowding distance and calculate the fractal dimension of the fitness matrix; 3. Perform fractal mutation; 4. Calculate the fitness of the mutated new population, the fractal dimension of the fitness matrix, the crowding degree and the dominance relationship; 5. Adaptively choose whether to prioritize the convergence or diversity of the generated population according to the change in the shape dimension of the fitness matrix of the new and old populations; 6. Repeat steps 2-5 until the requirements are met.

6. According to claim 1, a method for adjusting parameters of a turbine governor based on a fractal multi-objective optimization algorithm is characterized in that: In S3.1, an initial population is randomly generated according to a preset range of the population, and given the maximum number of iterations gen_max, the population size N, the number of objective functions n, and the dimension d of the decision space, X is randomly generated in the decision space. i (k), i=1,2,…,N, the current iteration number is gen=1.

7. According to claim 1, the method for adjusting parameters of a turbine governor based on a fractal multi-objective optimization algorithm is characterized in that: In S3.2, the two objective function values ​​corresponding to each group of populations are calculated to form a fitness matrix, and the fitness matrix is ​​quickly non-dominated sorted based on the crowding distance. The method is as follows: a group of fitness matrices are classified according to the dominance relationship, and solution A is called the dominated solution B. If A is not inferior to B in all objective functions and is better than B in at least one objective function, according to this definition, all solutions that are not dominated by other solutions belong to the first layer, that is, the non-dominated layer. Remove the solutions of the first layer, and find a new non-dominated layer from the remaining solutions. Repeat this process until all solutions are sorted. If the dominance is at the same level, sort them from large to small according to the crowding distance. The formula is: where f i+1 j is the jth objective function of point i+1, i d is the congestion degree of point i, f i-1 j is the j-th objective function value at point i-1.

8. According to claim 1, the method for adjusting parameters of a turbine governor based on a fractal multi-objective optimization algorithm is characterized in that: In S3.3, the population is mutated and updated by an iterative function system to generate a matrix composed of new candidate solutions, i.e., a new population. The iterative function system generates a complex fractal structure through simple rules, and calculates the two objective function values ​​corresponding to each group of individuals in the new population to form a fitness matrix. The specific formula is as follows: Where a, b, c, ..., i are the elements of the fractal diffusion matrix, which determine the rotation, shearing, scaling and other operations of the point in the three-dimensional space; j, k, l are the translation amounts, which control the translation of the point in the three-dimensional space. The present invention adopts the following two iterative function system parameters: Where P is the probability of selecting the calculation formula. The process randomly selects one of the two for iterative calculation. When the number of iterations reaches the maximum, the iteration stops.

9. According to claim 1, a method for adjusting parameters of a turbine governor based on a fractal multi-objective optimization algorithm is characterized in that: In S3.4, the coordinate points in the fractal space are converted into the solution space of the actual problem. The specific formula is: Among them, F∈[0,1] determines the amplitude of the variation introduced in the variation process, thus affecting the characteristics of the generated new individuals; s' i (j) is the new variable generated by the j-th mutation in the i-th group of candidate solutions, s i (j) is the jth original variable in the i-th group of candidate solutions, x, y, z are fractal space variables generated by the iterative function system, and the same probability p is used to change the selection of x or y or z; in order to constrain the parameter specifications of the generated candidate solutions, the boundary correction method is used to ensure that the candidate solutions in the new population matrix are within the defined boundary range. The formula is as follows: x new =max(x min ,min(x max ,x new )) where x new is a candidate solution in the new population matrix, x min is the lower limit of the candidate solution, x max is the upper constraint limit of the candidate solution.

10. According to claim 1, the method for adjusting parameters of a turbine governor based on a fractal multi-objective optimization algorithm is characterized in that: In S3.5, the fractal dimension value of the new fitness matrix and the fractal dimension of the previous fitness matrix are greater than a certain threshold, so as to judge whether the current evolution should give priority to population diversity or population convergence. If it is greater than the threshold, S3.6 is executed; otherwise, S3.7 is executed, and the design is to judge whether the current evolution strategy gives priority to the diversity or convergence of the offspring population by the change value of the fractal dimension of the current fitness matrix. The fractal dimension calculation method is as follows:

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