Pumped storage unit speed regulation control optimization method based on PID mu control of tracking differentiator

Abstract

The invention discloses a pumped storage unit speed regulation control optimization method based on PID mu control of a tracking differentiator. The method comprises the steps that 1, a simulation model is built based on parameters of a pumped storage power station; 2, popularizing a PID control differential item from an integer order to a fractional order, and introducing a tracking differentiator to carry out smooth transition on a control signal; and step 3, optimizing the control parameters by adopting an intelligent algorithm. Through a good point set and a Levy flight improved dung beetle algorithm, an objective function is established through linear weighting of an ITAE index, an overshoot and a steady-state error. And 4, performing simulation verification. And performing simulation verification on each working condition of the pumped storage unit, and verifying a control effect through no-load and on-load rotating speed disturbance simulation under different water heads. The method provided by the invention is suitable for improving the control capability of the pumped storage unit under the background of a novel power system with new energy access, and has important significance for ensuring safe and stable operation of the power system.

Description

Technical Field

[0001] The present invention belongs to the field of speed control of pumped storage units, and specifically relates to a PID controller based on a tracking differentiator. μ Optimization method for speed control of pumped storage units based on control. Background Art

[0002] In recent years, with the advancement of the "dual carbon" goal and energy reform, new energy sources such as wind power and photovoltaics have been continuously connected to the grid, forming a complex new power system, and the control requirements for pumped storage units have been continuously improved. In order to ensure the safe and steady-state operation of the power grid and improve the peak and frequency regulation capabilities, it is necessary to study the speed control method of the unit and improve the control performance. Although the parallel PID control used in traditional control has the advantages of simple control structure and easy implementation, it has insufficient control accuracy in nonlinear systems and is difficult to meet the control requirements of new power systems under complex working conditions.

[0003] In order to solve this problem, existing studies have proposed various controls such as sliding mode control and H∞ robust control. Although the control effect can be improved in theory, there are also some shortcomings, such as the chattering problem of frequent switching of sliding mode control and the need for a large number of data sets for training of neural network control. Most methods based on modern control theory require the state equation of the system, but the complexity of pumped storage units makes such precise mathematical modeling difficult to achieve. Another hot spot in control optimization is parameter setting, such as orthogonal experimental method and particle swarm algorithm. However, they all have their shortcomings to a greater or lesser extent, such as the large error and initial parameter dependence of the orthogonal experimental method, and the particle swarm algorithm is prone to fall into the local optimal solution. Summary of the invention

[0004] In view of the above shortcomings, in order to improve the control effect while retaining the applicability and reliability of the control method, the present invention proposes a PID control method based on a tracking differentiator. μ The method proposed in the present invention is suitable for improving the control capability of pumped storage units under the background of new power systems with new energy access, and is of great significance for ensuring the safe and stable operation of power systems.

[0005] The technical solution adopted by the present invention is:

[0006] PID Based on Tracking Differentiator μ The speed control optimization method of a pumped storage unit controlled by the invention comprises the following steps:

[0007] Step 1: Establish the electro-hydraulic servo system, water flow system, turbine, generator and load model of the pumped storage unit;

[0008] Step 2: Improve PID control by introducing fractional-order differential control and tracking differential link;

[0009] Step 3: Improve the dung beetle algorithm, add good point set initialization and Levy flight variation, and find the optimal control parameters;

[0010] Step 4: Perform speed disturbance under different working conditions to verify the control effect.

[0011] In the step 1, based on the parameters of the pumped storage power station, the governor, the water flow system, the turbine, the generator and the load systems are modeled in blocks, and connected to form an overall simulation model according to the hydraulic and mechanical relationship;

[0012] The step 1 comprises:

[0013] Step 1.1: Model the electro-hydraulic servo system:

[0014] The electro-hydraulic servo system is the action mechanism of the speed regulator. The model is built by considering the time lag, saturation and limiting characteristics of the main pressure regulating valve and the main servomotor. Its transfer function is:

[0015]

[0016] In formula (1), y(s) is the guide vane opening; u(s) is the control signal; k is the mechanical / electrical signal conversion gain; T y1 T is the inertia time constant of the main pressure regulating valve; y is the inertia time constant of the main relay; s represents the Laplace operator.

[0017] Step 1.2: Model the turbine:

[0018] The logarithmic transformation method is used to process the comprehensive characteristic curve data of the turbine. The transformation formula is:

[0019]

[0020] In formula (2), α represents the per unit value of the unit speed; β represents the per unit value of the unit flow rate; x 11 is the unit speed; x 11r is the unit speed rating; Q 11 is the unit flow rate; Q 11r is the unit flow rating; X is the horizontal coordinate after projection; e is the base of the natural logarithm function.

[0021] The transformed data is divided into three parts: training set, test set and validation set; then, the BP neural network is used for model fitting, where the guide vane opening and the transformed coordinate value X are used as the input of the BP neural network, and the unit torque and unit flow are used as the output for iterative training. Through the training process, the weight and bias parameters of the BP neural network are optimized, thereby establishing a BP neural network model that can accurately reflect the mechanism of the turbine.

[0022] Step 1.3: Use the approximate elastic water hammer model to build the water hammer model:

[0023] The water diversion pipeline consists of upstream and downstream reservoir pipelines, turbine water inlet pipelines, and tailwater pipes. The approximate elastic water hammer model is used to represent the hydraulic relationship:

[0024]

[0025] In formula (3): G h (s) represents the transfer function of the water hammer model; Δh(s) is the head change value; Δq(s) is the flow change value; T w is the water flow inertia coefficient; T r is the water hammer phase; f is the pipe friction coefficient; s is the Laplace operator.

[0026] Step 1.4: Build the generator model:

[0027] First-order generator model described by the rotor rotation equations of motion:

[0028]

[0029] Where: G g (s) represents the transfer function of the first-order generator; x is the unit speed; T a is the inertia time constant of the unit; m t is the turbine torque; m g is the resistance torque, indicating the magnitude of the load; e n It is the comprehensive self-regulation coefficient of the unit.

[0030] In step 2, the PID control is improved by pushing the PID control differential term from integer order to fractional order, and introducing a tracking differentiator TD to perform a smooth transition on the control signal.

[0031] The step 2 comprises the following steps:

[0032] Step 2.1: Introducing PID μ Controller, PID μ The controller introduces a differential order, pushing the integer-order differential gain to a fractional order, and its expression is:

[0033]

[0034] In formula (6): G(s) represents PID μ Control system transfer function; k p is the proportional gain coefficient; k i is the integral gain coefficient; k dis the differential gain coefficient; u(s) is the control signal; e(s) is the deviation between the actual signal and the given signal; μ is the differential term order; s μ Represents the symbol for fractional differentiation.

[0035] Step 2.2: Introduce the tracking differentiator TD to make a smooth transition of the control signal:

[0036] A tracking differentiator is added before PID control to transition the target value and adjust the error feedback. The expression of the tracking differentiator is:

[0037]

[0038] In formula (7): f 1 (k) represents the tracking signal at the kth moment; f 2 (k) represents the differential signal of the tracking signal at the kth moment; f 1 (k+1) represents the tracking signal at the k+1th moment; f 2 (k+1) represents the differential signal of the tracking signal at the k+1th moment; u(k) represents the input signal at the kth moment; fh represents the abbreviation of the fastest function; r is the speed factor, which determines the tracking speed; h is the step size; and fhan is the fastest control function.

[0039] The step 3 comprises the following steps:

[0040] Step 3.1: When the population is initialized, the good point set theory is used to generate a uniformly distributed initial population, expressed as:

[0041]

[0042] In formula (8): r i j represents the best point value of the jth dimension; n is the population size; i represents the individual number; mod is the remainder function; k is the smallest prime number that satisfies 0.5(k-3)≥j;

[0043]

[0044] In formula (9): is the set of good points in the jth dimension; {r 1 j i} represents the product of the best point value of the first individual in the j-dimension and the individual sequence number; It represents the product of the best point value of the second individual in the j-dimension and the individual serial number; Represents the product of the best point value of the nth individual in the j-dimension and the individual sequence number.

[0045]

[0046] In formula (10): xi j The j-th dimension individual; represents the good point set of the jth dimension; ub j lb j Represents the upper and lower bounds of the jth dimension. Step 3.2: Introduce Levy flight for mutation, compare the original position and the individual position after Levy flight to obtain the optimal value, and jump out of the local optimum to the greatest extent;

[0047] x l (k)=x(k)+a.*Levy(β) (11);

[0048] In formula (11): x l (k) is the position after Levy flight mutation; x(k) represents the original position; a is the weight coefficient; Levy(β) is the random step length;

[0049]

[0050] In formula (12): r 1 ~N(0,σ 2 );r 2 ~N(0,1); β represents the Levy flight distribution parameter, and its value range is generally: 1≤β≤3; σ represents the standard deviation.

[0051]

[0052] In formula (13), Γ is the gamma function.

[0053] Step 3.3: Objective function selection:

[0054] By adding overshoot and steady-state error as evaluation quantities of the objective function, the objective function designed in this way comprehensively considers the dynamic performance and steady-state performance of the system during the adjustment process. By adjusting the weight coefficient, the relationship between overshoot and steady-state error can be balanced according to actual needs, thereby achieving the best control effect. The specific expression is:

[0055] f ITAE =∫e(t)tdt (14);

[0056] In formula (14): f ITAE is the ITAE index; e(t) is the error between the system given signal and the output signal; t represents time.

[0057] fit = f ITAE +ω 1 △f+ω 2 σ (15);

[0058] In formula (15), fit represents the comprehensive objective function; ω 1 ,ω2 is the weight coefficient; σ is the overshoot.

[0059] The step 4 comprises the following steps:

[0060] Step 4.1: Simulate the multiple operating conditions of startup, speed disturbance, and load shedding of the pumped storage unit to verify the simulation model;

[0061] Step 4.2: Carry out speed disturbance simulation under no-load and load conditions under different water head conditions.

[0062] The present invention is a PID based on tracking differentiator μ The speed control optimization method of the pumped storage unit controlled by the invention has the following technical effects: 1) The method of the invention introduces PID μ Control, improve the PID control differential link is sensitive to disturbances and easily cause response fluctuations, so that it has better anti-interference ability.

[0063] 2) The method of the present invention introduces a tracking differentiator transition target, improves the contradiction between easy overshoot and rapidity of PID control, adjusts error feedback, and realizes low overshoot and rapid tracking.

[0064] 3) The present invention introduces the DBO algorithm into the speed control of the pumped storage unit, and introduces the optimal point set initialization population and Levy flight theory for improvement. Compared with the DBO algorithm, the improved DBO algorithm (IDBO) improves the local optimal problem and has better optimization ability and convergence speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] The present invention will be further described below in conjunction with the accompanying drawings and examples;

[0066] Figure 1 It is the block diagram of the turbine simulation model.

[0067] Figure 2 It is a flow chart of the present invention.

[0068] Figure 3 It is a simulation diagram of various operating conditions of the pumped storage unit regulation system.

[0069] Figure 4 It is the simulation response curve of speed disturbance under no-load condition at a water head of 195 meters.

[0070] Figure 5 This is the simulation response curve of the speed disturbance under load condition at a water head of 195 meters.

[0071] Figure 6 It is the simulation response curve of speed disturbance under no-load condition under 200m head.

[0072] Figure 7It is the simulation response curve of speed disturbance under load condition with 200m head.

[0073] Figure 8 It is the simulation response curve of speed disturbance under no-load condition under 210m head.

[0074] Fig. 9 This is the simulation response curve of the speed disturbance under load condition at a water head of 210 meters. DETAILED DESCRIPTION

[0075] PID Based on Tracking Differentiator μ The speed control optimization method of pumped storage unit controlled by Figure 1 As shown, the specific steps include:

[0076] Step 1: Based on the parameters of the pumped storage power station, the governor, water flow system, turbine, generator and load are modeled separately and connected to form an overall simulation model according to the hydraulic and mechanical relationship;

[0077] Step 2: Extend the PID control differential term from integer order to fractional order, and introduce a tracking differentiator TD to make a smooth transition of the control signal;

[0078] Step 3: Optimize the control parameters based on the improved dung beetle algorithm;

[0079] Step 4: Perform speed disturbance under different working conditions to verify the proposed method.

[0080] In step 1: Based on the parameters of the pumped storage power station, the governor, water flow system, turbine, generator and load are modeled separately and connected according to the hydraulic and mechanical relationship to form an overall simulation model, such as Figure 2 The specific steps include:

[0081] Step 1-1: Model the electro-hydraulic servo system.

[0082] The electro-hydraulic servo system is the action mechanism of the speed regulator. The model is built by considering the time lag, saturation and limiting characteristics of the main pressure regulating valve and the main servomotor. Its transfer function is:

[0083]

[0084] Where: y(s) is the guide vane opening; u(s) is the control signal; k is the mechanical / electrical signal conversion gain; T y1 T is the inertia time constant of the main pressure regulating valve; y is the inertia time constant of the main servomotor; both the main pressure regulating valve and the main servomotor have saturation upper limits; s represents the Laplace operator.

[0085] Step 1-2: Process the comprehensive characteristic curve data of the turbine using logarithmic projection transformation.

[0086] The pumped storage unit turbine has "hump area" and "s" area at both ends of the comprehensive characteristic curve, and there are opening line twisting and crossing phenomena. If the interpolation calculation is performed directly, it will lead to interpolation calculation errors for one input corresponding to multiple outputs. Therefore, this paper adopts the "logarithmic transformation method" for processing. The converted full characteristic curve can extend the distorted and overlapping parts on both sides, which is convenient for interpolation calculation. The transformation formula is:

[0087]

[0088] Where: α represents the per unit speed; β represents the per unit flow rate; x 11 is the unit speed; x 11r is the unit speed rating; Q 11 is the unit flow rate; Q 11r is the unit flow rating; X is the horizontal coordinate after projection; e is the base of the natural logarithm function.

[0089] The transformed data is divided into three parts: training set, test set and validation set. Then, BP neural network is used for model fitting, where the guide vane opening and the transformed coordinate value X are used as the input of the neural network, and the unit torque and unit flow are used as the output for iterative training. Through the training process, the weight and bias parameters of the neural network are optimized, thereby establishing a BP neural network model that can accurately reflect the mechanism of the turbine.

[0090] Step 1-3: Use the approximate elastic water hammer model to build the water hammer model.

[0091] The water diversion pipeline is usually composed of upstream and downstream reservoir pipelines, turbine water inlet pipelines, tailwater pipes, etc. The approximate elastic water hammer model is used to represent the hydraulic relationship:

[0092]

[0093] Where: G h (s) represents the transfer function of the water hammer model; Δh(s) is the head change value; Δq(s) is the flow change value; T w is the water flow inertia coefficient; T r is the water hammer phase; f is the pipe friction coefficient; s is the Laplace operator.

[0094] Step 1-4: Establish a first-order generator model described by the rotor rotation equation of motion.

[0095] The generator model ignores its electromagnetic characteristics and only considers the rotation characteristics of the rotor. The first-order generator model described by the rotor rotation motion equation is adopted:

[0096]

[0097] Where: x is the unit speed; T a is the inertia time constant of the unit; m t is the turbine torque; m g is the resistance torque, indicating the magnitude of the load; e n It is the comprehensive self-regulation coefficient of the unit.

[0098] In step 2: the PID control differential term is pushed from integer order to fractional order, and a tracking differentiator TD is introduced to make a smooth transition of the control signal. Specifically, the following steps are included:

[0099] Step 2-1: Push the PID control differential term from integer order to fractional order.

[0100] At present, most domestic speed regulator models use parallel PID models. When the differential control link parameters are not appropriate, they are too sensitive to disturbances and easily cause unit speed fluctuations. Therefore, PID is introduced. μ Compared with the traditional PID model, PID μ The differential order is introduced to push the integer differential gain to the fractional order, which provides a larger search space and flexibility for parameter adjustment, and thus has a better upper limit for adjustment. Its expression is:

[0101]

[0102] Where: G(s) represents PID μ Control system transfer function; k p is the proportional gain coefficient; k i is the integral gain coefficient; k d is the differential gain coefficient; u(s) is the control signal; e(s) is the deviation between the actual signal and the given signal; μ is the order of the differential term.

[0103] Step 2-2: Introduce the tracking differentiator TD to make a smooth transition of the control signal.

[0104] Since the PID control of the pumped storage unit speed control system is prone to overshoot during rapid adjustment, a tracking differentiator is added before control to transition the target value and adjust the error feedback. The expression of the tracking differentiator is:

[0105]

[0106] Where: f 1 (k) represents the tracking signal at the kth moment; f 2 (k) represents the differential signal of the tracking signal at the kth moment; f 1(k+1) represents the tracking signal at the k+1th moment; f 2 (k+1) represents the differential signal of the tracking signal at the k+1th moment; u(k) represents the input signal at the kth moment; fh represents the abbreviation of the fastest function; r is the speed factor, which determines the tracking speed; h is the step size; and fhan is the fastest control function.

[0107] In step 3: optimize the control parameters based on the improved dung beetle algorithm (IDBO). The specific steps are as follows:

[0108] The DBO algorithm is inspired by the behavior of dung beetles and divides the population into four types of dung beetle populations: larval dung beetles, thief dung beetles, breeding dung beetles, and rolling dung beetles, representing different position update rules. It has good performance in optimization and iteration speed, but like other intelligent algorithms, it may have the disadvantages of local optimality and weak global exploration ability. In order to overcome this disadvantage and find better control parameters, the algorithm is now improved. The specific steps are as follows:

[0109] Step 3-1: When initializing the population, use the good point set theory to generate a uniformly distributed initial population.

[0110] The diversity of the initial population determines the superiority of the algorithm to some extent. Higher diversity can effectively improve the convergence speed of the algorithm. In order to improve the optimization ability of the DBO algorithm, the optimal point set initialization is introduced. The optimal point set theory can generate a globally uniformly distributed population. The generated population can be more evenly distributed in the solution space compared to the randomly initialized population of the original algorithm, making the initial optimal position of the population better, thereby reducing the possibility of falling into a local optimal solution due to the low diversity of the initial population. Its function is expressed as:

[0111]

[0112] Where: r i j represents the optimal point value of the jth dimension; mod is the remainder function; n is the population size; i represents the individual number; j represents the dimension; is the set of good points in the jth dimension; {r 1 j i} represents the product of the best point value of the first individual in the j-dimension and the individual sequence number; It represents the product of the best point value of the second individual in the j-dimension and the individual serial number; represents the product of the best point value and the individual number of the nth individual in the j-dimensional space; k is the smallest prime number that satisfies 0.5(k-3)≥j; x i j j-th dimension individual; ub j lb j Represents the upper and lower bounds of the j-th dimension.

[0113] Step 3-2: Introduce Levy flight for mutation, compare the original position and the individual position after Levy flight to obtain the optimal value, and jump out of the local optimum to the greatest extent.

[0114] Levy flight is a non-Gaussian random process that alternates short-distance and occasionally long-distance walking modes. The probability distribution of this heavy-tailed distribution characteristic makes the step value vary in a small range while occasionally varying in a large range. Therefore, it can help the DBO algorithm to jump out of the original optimal solution, better cover the search space and enhance the ability of global optimization. Its expression is:

[0115] x l (k) = x(k) + a.*Levy(β)(11);

[0116]

[0117] Where: x l (k) is the position after Levy flight mutation; x(k) is the original position; a is the weight coefficient; Levy(β) is the random step size; β is the Levy flight distribution parameter, usually 1≤β≤3; r 1 ~N(0,σ 2 );r 2 ~N(0,1); Γ is the gamma function; σ represents the standard deviation.

[0118] Step 3-2: Objective function selection.

[0119] The objective function is the key link in determining the optimization effect of the algorithm parameters. The objective function not only needs to consider the dynamic response characteristics of the system, but also needs to comprehensively consider the steady-state performance and control quality of the system. Therefore, in the optimization process, a comprehensive objective function should be constructed. In order to improve the control effect of the optimization parameters, improve the regulation performance of the system, reduce the overshoot, shorten the time to return to the steady state and meet the requirements of the steady-state error, in addition to selecting the integral value of the absolute value of the error and the time (ITAE) indicator, overshoot and steady-state error are added as the evaluation quantity of the objective function. The objective function designed in this way comprehensively considers the dynamic performance and steady-state performance of the system during the regulation process. By adjusting the weight coefficient, the relationship between overshoot and steady-state error can be balanced according to actual needs, so as to achieve the best control effect. The specific expression is:

[0120] f ITAE =∫e(t)tdt (14);

[0121] fit = f ITAE +ω 1 △f+ω 2 σ (15);

[0122] Where: e(t) is the error between the given signal and the output signal of the system; t represents time; f ITAE is the ITAE index; Δf is the steady-state error; fit represents the comprehensive objective function ω 1 ,ω 2 is the weight coefficient; σ is the overshoot;.

[0123] In step 4: speed disturbance is performed under different working conditions to verify the proposed method. The specific steps are as follows:

[0124] Based on the transfer functions of each object in the above pumped storage unit regulation system, a simulation model was established on the MATLAB / SIMULINK platform. The controllers were PID and PID improved based on tracking differentiator. μ Control (IPID μ ) model, in which the model data is imported into a hydropower station data as shown in Table 1.

[0125] Table 1 Simulation unit parameters

[0126]

[0127] In order to facilitate analysis, unit modeling is adopted to convert relevant parameters into per-unit values. The simulation mainly includes the following steps:

[0128] (1) Simulation model verification:

[0129] In order to verify the effectiveness of the model, multiple working condition simulations of startup, speed disturbance and load shedding were carried out. The startup adopts the general two-stage startup. When the speed reaches 95%, it is put into no-load mode, and a 3% speed disturbance is given at 60 seconds; 70% load is put into operation at 150 seconds, and load shedding is performed at 200 seconds. The simulation results are shown in the figure. Figure 3 As shown. Figure 3 It can be seen that the dynamic response characteristics of pumped storage during startup, speed disturbance, load switching and load shedding. In the startup phase, the variables rise rapidly and tend to stabilize, but there is an initial oscillation. When the speed is disturbed, the system shows a certain fluctuation, but it can gradually stabilize, showing good anti-interference ability. During the load input process, the fluctuations of various system variables are large, especially in the head change and speed response, reflecting that the load change has a significant impact on the system. After the load is shed, the system experienced obvious fluctuations again, but eventually gradually recovered and stabilized, and the speed decreased. The analysis shows that the simulation of each working condition is in line with the actual situation, verifying the effectiveness of the model.

[0130] (2) Speed ​​disturbance simulation:

[0131] Based on the model parameters, a 5% no-load speed disturbance experiment and a 5% speed disturbance experiment with 20% load were carried out respectively. μThe controller performs parameter optimization and the PSO algorithm performs parameter optimization on the PID controller. The optimization vectors are X 1 =[k p , k i , k d , μ] and X 2 =[k p , k i , k d ]. The population size is set to 30, the maximum number of iterations is set to 50, and the maximum simulation step is set to 0.005. The disturbance signal is:

[0132]

[0133] The initial parameters of the no-load disturbance simulation are shown in Table 2, and the initial parameters of the 20% load disturbance simulation are shown in Table 3.

[0134] Table 2 Initial parameters of no-load disturbance simulation

[0135]

[0136] Table 3 Initial parameters of load disturbance simulation

[0137]

[0138] Depend on Figures 4 to 9 It can be seen that in the speed disturbance simulation under different water head conditions, IDBO-IPID μ The control performs best under no-load and load conditions, with the smallest overshoot and the fastest settling speed, and the smallest oscillation amplitude. In contrast, the PSO-PID control has a larger initial overshoot, a longer oscillation time, and a slower response speed. μ Although the control is improved compared with PSO-PID control, it is still inferior to IDBO-IPID in overall performance. μ Therefore, IDBO-IPID μ The control has better anti-interference and stability under different head conditions.

[0139] The results of the no-load 5% speed disturbance experiment are shown in Table 4, and the results of the loaded 5% speed disturbance experiment are shown in Table 5. The controller parameters optimized by PSO, DBO, and IDBO algorithms can make the overshoot of the pumped storage unit less than 10%. In the 5% speed disturbance experiment, IDBO-IPD μ Control outperforms DBO-IPD under no-load and load conditions μand PSO-PID control. The objective function value of IDBO is lower than that of DBO and PSO. Under no-load conditions, the average value of IDBO's objective function value under different water heads is about 14.92% lower than that of DBO and about 37.81% lower than that of PSO; under load conditions, the average value of IDBO's objective function value under different water heads is about 26.82% lower than that of DBO and about 31.42% lower than that of PSO. In terms of overshoot, the IDBO average value is lower than that of DBO and PSO at all speeds. In terms of steady-state time, IDBO has the fastest response speed, and the average steady-state time under different water heads is about 11.83% lower than that of DBO and about 20.19% lower than that of PSO. Therefore, IDBO-IPD μ In terms of objective function value, overshoot and steady-state time, it can more effectively control the transition process of the system and improve the response speed and stability of the system.

[0140] Table 4 No-load 5% speed disturbance test results

[0141]

[0142] Table 5 Test results of 5% speed disturbance with load

[0143]

[0144] The PID based on tracking differentiator proposed by the present invention μ The speed control optimization method of pumped storage unit controlled by the control system has important reference significance for the speed control operation of pumped storage unit.

Claims

1. PID based on tracking differentiator μ The speed control optimization method of the pumped storage unit is characterized by The following steps are involved: Step 1: Establish the electro-hydraulic servo system, water flow system, turbine, generator and load model of the pumped storage unit; Step 2: Improve PID control by introducing fractional-order differential control and tracking differential link; Step 3: Improve the dung beetle algorithm, add good point set initialization and Levy flight mutation, and find the optimal control parameters.

2. The PID based on the tracking differentiator according to claim 1 μ The speed control optimization method of a pumped storage unit controlled by the invention is characterized by: It also includes step 4: performing speed disturbance under different working conditions to verify the control effect.

3. The PID based on tracking differentiator according to claim 1 μ The speed control optimization method of a pumped storage unit controlled by the invention is characterized by: In the step 1, based on the parameters of the pumped storage power station, the speed governor, water flow system, turbine, generator and load systems are modeled in blocks, and connected according to the hydraulic and mechanical relationship to form an overall simulation model.

4. The PID based on the tracking differentiator according to claim 3 μ The speed control optimization method of a pumped storage unit controlled by the invention is characterized by: The step 1 comprises: Step 1.1: Model the electro-hydraulic servo system: The electro-hydraulic servo system is the action mechanism of the speed regulator. The model is built by considering the time lag, saturation and limiting characteristics of the main pressure regulating valve and the main servomotor. Its transfer function is: In formula (1), y(s) is the guide vane opening; u(s) is the control signal; k is the mechanical / electrical signal conversion gain; T y1 T is the inertia time constant of the main pressure regulating valve; y is the inertia time constant of the main relay; s represents the Laplace operator; Step 1.2: Model the turbine: The logarithmic transformation method is used to process the comprehensive characteristic curve data of the turbine. The transformation formula is: In formula (2), α represents the per unit value of the unit speed; β represents the per unit value of the unit flow rate; x 11 is the unit speed; x 11r is the unit speed rating; Q 11 is the unit flow rate; Q 11r is the unit flow rating; X is the horizontal coordinate after projection; e is the base of the natural logarithm function; The transformed data is divided into three parts: training set, test set and validation set. Then, the BP neural network is used for model fitting, in which the guide vane opening and the transformed coordinate value X are used as the input of the BP neural network, and the unit torque and unit flow are used as the output, and iterative training is performed. Through the training process, the weight and bias parameters of the BP neural network are optimized, so as to establish a BP neural network model that can accurately reflect the mechanism of the turbine. Step 1.3: Use the approximate elastic water hammer model to build the water hammer model: The water diversion pipeline consists of upstream and downstream reservoir pipelines, turbine water inlet pipelines, and tailwater pipes. The approximate elastic water hammer model is used to represent the hydraulic relationship: In formula (3): G h (s) represents the transfer function of the water hammer model; Δh(s) is the head change value; Δq(s) is the flow change value; T w is the water flow inertia coefficient; T r is the water hammer phase; f is the pipe friction coefficient; s is the Laplace operator; Step 1.4: Build the generator model: First-order generator model described by the rotor rotation equations of motion: Where: G g (s) represents the transfer function of the first-order generator; x is the unit speed; T a is the inertia time constant of the unit; m t is the turbine torque; m g is the resistance torque, indicating the magnitude of the load; e n It is the comprehensive self-regulation coefficient of the unit.

5. The PID based on tracking differentiator according to claim 1 μ The speed control optimization method of a pumped storage unit controlled by the invention is characterized by: The step 2 comprises the following steps: Step 2.1: Introducing PID μ Controller, PID μ The controller introduces a differential order, pushing the integer-order differential gain to a fractional order, and its expression is: In formula (6): G(s) represents PID μ Control system transfer function; k p is the proportional gain coefficient; k i is the integral gain coefficient; k d is the differential gain coefficient; u(s) is the control signal; e(s) is the deviation between the actual signal and the given signal; μ is the differential term order; s μ Represents the symbol for fractional differentials; Step 2.2: Introduce the tracking differentiator TD to make a smooth transition of the control signal: A tracking differentiator is added before PID control to transition the target value and adjust the error feedback. The expression of the tracking differentiator is: In formula (7): f1(k) represents the tracking signal at the kth moment; f2(k) represents the differential signal of the tracking signal at the kth moment; f1(k+1) represents the tracking signal at the k+1th moment; f2(k+1) represents the differential signal of the tracking signal at the k+1th moment; u(k) represents the input signal at the kth moment; fh represents the abbreviation of the fastest function; r is the speed factor, which determines the tracking speed; h is the step size; fhan is the fastest control function.

6. The PID based on tracking differentiator according to claim 1 μ The speed control optimization method of a pumped storage unit controlled by the invention is characterized by: The step 3 comprises the following steps: Step 3.1: When the population is initialized, the good point set theory is used to generate a uniformly distributed initial population, expressed as: In formula (8): r i j represents the best point value of the jth dimension; n is the population size; i represents the individual number; mod is the remainder function; k is the smallest prime number that satisfies 0.5(k-3)≥j; In formula (9): is the good point set of the jth dimension; {r1 j i} represents the product of the best point value of the first individual in the j-dimension and the individual sequence number; It represents the product of the best point value of the second individual in the j-dimension and the individual serial number; It represents the product of the best point value and the individual number of the nth individual in the j-dimension; In formula (10): x i j The j-th dimension individual; represents the good point set of the jth dimension; ub j lb j Represents the upper and lower bounds of the j-th dimension; Step 3.2: Introduce Levy flight for mutation, compare the original position and the individual position after Levy flight to obtain the optimal value, and jump out of the local optimum to the greatest extent; x l (k)=x(k)+a.*Levy(β) (11); In formula (11): x l (k) is the position after Levy flight mutation; x(k) represents the original position; a is the weight coefficient; Levy(β) is the random step length; In formula (12): r1~N(0,σ 2 );r2~N(0,1);β represents the Levy flight distribution parameter;σ represents the standard deviation; In formula (13): Γ is the gamma function; Step 3.3: Objective function selection: By adding overshoot and steady-state error as evaluation quantities of the objective function, the objective function designed in this way comprehensively considers the dynamic performance and steady-state performance of the system during the adjustment process; by adjusting the weight coefficient, the relationship between overshoot and steady-state error can be balanced according to actual needs, so as to achieve the best control effect. The specific expression is: f ITAE =∫e(t)tdt (14); In formula (14): f ITAE is the ITAE index; e(t) is the error between the given signal and the output signal of the system; t represents time; fit=f ITAE +ω1△f+ω2σ (15); In formula (15), fit represents the comprehensive objective function; ω1 and ω2 are weight coefficients; σ is the overshoot.

7. The PID based on tracking differentiator according to claim 2 μ The speed control optimization method of a pumped storage unit controlled by the invention is characterized by: The step 4 comprises the following steps: Step 4.1: Simulate the multiple operating conditions of startup, speed disturbance, and load shedding of the pumped storage unit to verify the simulation model; Step 4.2: Carry out speed disturbance simulation under no-load and load conditions under different water head conditions.

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