PID Based on Tracking Differentiator μ Optimization method of speed regulation control of pumped storage units based on control

Abstract

PID Based on Tracking Differentiator μ The speed control optimization method of the pumped storage unit controlled by the control method includes the following steps: step 1: constructing a simulation model based on the parameters of the pumped storage power station; step 2: generalizing the PID control differential term from integer order to fractional order, and introducing a tracking differentiator to make a smooth transition of the control signal; step 3: optimizing the control parameters using an intelligent algorithm. By improving the dung beetle algorithm using the good point set and Levy flight, the objective function is established by linearly weighting the ITAE index, overshoot and steady-state error. Step 4: performing simulation verification. The simulation verification model is performed on each operating condition of the pumped storage unit, and the control effect is verified by simulating no-load and loaded speed disturbances under different water heads. The method proposed in the present invention is suitable for improving the control capability of the pumped storage unit in the context of a new power system with the access of new energy, and is of great significance for ensuring the safe and stable operation of the power system.

Description

Technical Field

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

[0002] In recent years, with the advancement of the "dual carbon" goals and energy reforms, new energy sources such as wind power and photovoltaics have been continuously integrated into the grid, forming a complex new power system and continuously increasing the control requirements for pumped storage units. To ensure the safe and stable operation of the power grid and improve peak and frequency regulation capabilities, it is essential to research unit speed control methods and improve control performance. Although the parallel PID control used in traditional control has the advantages of simple control structure and easy implementation, it suffers from insufficient control accuracy in nonlinear systems and cannot meet the control requirements of new power systems under complex operating conditions.

[0003] To address this issue, existing research has proposed various control methods, such as sliding mode control and H∞ robust control. While theoretically effective, these methods also suffer from drawbacks, such as chattering caused by frequent switching in sliding mode control and the large datasets required for training neural network control. Most methods based on modern control theory require the system's state equations, but the complexity of pumped-storage units makes precise mathematical modeling difficult. Another hot topic in control optimization is parameter tuning, such as orthogonal experimental methods and particle swarm optimization algorithms. However, these methods all have limitations, such as large errors and initial parameter dependence in orthogonal experimental methods, and the tendency of particle swarm optimization algorithms to become trapped in local optima. 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 this invention is suitable for the context of new power systems with the integration of renewable energy, and improves the control capability of pumped storage units, which 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 control method comprises the following steps:

[0007] Step 1: Establish the electro-hydraulic servo system, water flow system, turbine, generator and load models 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 by adding good point set initialization and Lévy flight mutation to find the optimal control parameters;

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

[0011] In 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 separately and connected to form an overall simulation model according to the hydraulic and mechanical relationships;

[0012] The step 1 comprises:

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

[0014] The electro-hydraulic servo system is the actuating mechanism of the speed regulator. It is modeled by considering the time lag, saturation, and limiting characteristics of the main pressure regulating valve and 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 rate rating; X is the horizontal coordinate after projection; e is the base of the natural logarithm function.

[0021] The transformed data was divided into a training set, a test set, and a validation set. A BP neural network was then used for model fitting. The guide vane opening and the transformed coordinate value X served as the BP neural network inputs, and the unit torque and unit flow rate were used as the outputs. Iterative training was performed. Through the training process, the weights and bias parameters of the BP neural network were optimized, resulting in a BP neural network model that accurately reflects the turbine's mechanism.

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

[0023] The water diversion pipeline consists of upstream and downstream reservoir pipelines, turbine inlet pipelines, and tailwater pipes. An 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 equation 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, which indicates the size of the load; e n 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 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 to push 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 fractional differential symbol.

[0035] Step 2.2: Introduce the tracking differentiator TD to smooth the 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), 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; and fhan is the fastest control function.

[0039] The step 3 comprises the following steps:

[0040] Step 3.1: When initializing the population, use the good point set theory 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 is 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; {r1 j i} represents the product of the best point value of the first individual in dimension j and the individual sequence number; It represents the product of the best point value and individual number of the second individual in the j-dimension; It represents the product of the best point value of the n-th individual in the j-dimension and the individual sequence number.

[0045]

[0046] In formula (10): x i j j-th dimension individual; represents the good point set of the jth dimension; ubj lb j Denote the upper and lower bounds of the j-th dimension. Step 3.2: Introduce Lévy flight for mutation, compare the original position and the individual position after Lévy 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 size;

[0049]

[0050] In formula (12): r1~N(0,σ 2 ); r2~N(0,1); β represents the parameter of the Levy flight distribution, 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 variables of the objective function, the designed objective function 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, 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 +ω1△f+ω2σ (15);

[0058] In formula (15), fit represents the comprehensive objective function; ω1 and ω2 are weight coefficients; σ is the overshoot.

[0059] The step 4 comprises the following steps:

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

[0061] Step 4.2: Perform 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 characteristics of PID control differential link that is sensitive to disturbances and easily causes 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 good 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 with reference to the accompanying drawings and examples;

[0066] Figure 1 This 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 working conditions of the pumped storage unit regulation system.

[0069] Figure 4 This is the simulation response curve of the 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 conditions at a water head of 195 meters.

[0071] Figure 6 This is the simulation response curve of the speed disturbance under no-load condition at a water head of 200 meters.

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

[0073] Figure 8 This is the simulation response curve of the speed disturbance under no-load condition at a water head of 210 meters.

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

[0075] PID Based on Tracking Differentiator μ Optimization method for speed control of pumped storage units 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 according to the hydraulic and mechanical relationships to form an overall simulation model;

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

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

[0079] Step 4: Perform speed disturbances 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 to form an overall simulation model according to the hydraulic and mechanical relationship. Figure 2 The specific steps include:

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

[0082] The electro-hydraulic servo system is the actuating mechanism of the speed regulator. It is modeled by considering the time lag, saturation, and limiting characteristics of the main pressure regulating valve and 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 phenomena such as opening line twisting and crossing. If the interpolation calculation is performed directly, it will lead to interpolation calculation errors where one input corresponds 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 is the per-unit speed value; β is the per-unit flow value; 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 rate rating; X is the horizontal coordinate after projection; e is the base of the natural logarithm function.

[0089] The transformed data is divided into a training set, a test set, and a validation set. A BP neural network is then used for model fitting, with the guide vane opening and the transformed coordinate value X serving as the neural network inputs, and the unit torque and unit flow rate serving as the outputs. Through the training process, the neural network's weights and bias parameters are optimized, resulting in a BP neural network model that accurately reflects the turbine's mechanism.

[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 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, which indicates the size of the load; e n 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 smooth the transition of the control signal. The specific steps include:

[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, it is too sensitive to disturbances and easily causes unit speed fluctuations. Therefore, PID is introduced. μ Controller. Compared with the traditional PID model, PID μ The differential order is introduced to push the integer-order 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 a tracking differentiator TD to smooth the 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: 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.

[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, inspired by the behavior of dung beetles, divides the population into four types: larval dung beetles, thief dung beetles, breeding dung beetles, and ball-rolling dung beetles. These types represent different position update rules and perform well in terms of optimization and iteration speed. However, like other intelligent algorithms, they may suffer from local optimality and weak global exploration capabilities. To overcome this shortcoming and find better control parameters, the algorithm has been 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 partially determines the superiority of the algorithm. Higher diversity can effectively improve the convergence speed of the algorithm. In order to improve the optimization ability of the DBO algorithm, the good point set initialization is introduced. The good point set theory can generate a globally uniformly distributed population. The generated population can be more evenly distributed in the solution space than 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 value of the j-th dimension; mod is the remainder function; n is the population size; i is the individual number; j is the dimension; is the set of good points in the jth dimension; {r1 j i} represents the product of the best point value of the first individual in dimension j and the individual sequence number; It represents the product of the best point value and individual number of the second individual in the j-dimension; 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 Lévy flight for mutation, compare the original position and the individual position after Lévy flight to obtain the optimal value, and jump out of the local optimum to the greatest extent.

[0114] Lévy flight is a non-Gaussian random process that alternates short-distance and occasionally long-distance walking patterns. This heavy-tailed probability distribution makes the step length 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; r1~N(0,σ 2 ); r2~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 effect of algorithm parameter optimization. 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 steady state and meet the requirements of 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 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 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. Its specific expression is

[0120] f ITAE =∫e(t)tdt (14);

[0121] fit=f ITAE +ω1△f+ω2σ (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, ω1 and ω2 are weight coefficients; σ is the overshoot;.

[0123] In step 4, the proposed method is verified by performing speed disturbances under different working conditions. The specific steps are as follows:

[0124] Based on the transfer functions of each object in the 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, where the model data is imported into a hydropower station data as shown in Table 1.

[0125] Table 1 Simulation unit parameters

[0126]

[0127] For the convenience of 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] To verify the effectiveness of the model, multiple working condition simulations of startup, speed disturbance, and load shedding were carried out. The startup adopted a common two-stage startup method. When the speed reached 95%, it was put into no-load mode, and a 3% speed disturbance was given at 60 seconds. At 150 seconds, 70% load was put into operation, and load shedding was performed at 200 seconds. The simulation results are shown as follows: Figure 3 As shown. Figure 3 The dynamic response characteristics of pumped storage during startup, speed disturbance, load switching, and load shedding are shown. During startup, various variables rise rapidly and stabilize, but there is initial oscillation. During speed disturbance, the system exhibits some fluctuations but gradually stabilizes, demonstrating good anti-interference capabilities. During load application, the system variables fluctuate significantly, particularly in head change and speed response, reflecting the significant impact of load changes on the system. After load shedding, the system again experiences significant fluctuations but eventually stabilizes, with the speed decreasing. Analysis shows that the simulations for each operating condition are consistent with actual conditions, verifying the effectiveness of the model.

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

[0131] Based on the model parameters, 5% no-load speed disturbance experiment and 5% speed disturbance experiment with 20% load were carried out respectively. μ The controller performs parameter optimization and the PSO algorithm is used to optimize the parameters of the PID controller. The optimization vectors are X1=[k p , k i , k d , μ] and X2=[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 size 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 head conditions, IDBO-IPID μ The control performs best under both no-load and load conditions, with the smallest overshoot and the fastest stabilization speed, while also having 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 load 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 The control performance is better than DBO-IPD under no-load and load conditions μ and 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 average value of IDBO 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-IPDμ In terms of objective function value, overshoot and steady-state time, it can more effectively control the system's transition process and improve the system's response speed and stability.

[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 the pumped storage unit controlled by this method has important reference significance for the speed control operation of the pumped storage unit.

Claims

1. PID based on tracking differentiator μ The speed control optimization method of 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 models 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 by adding good point set initialization and Lévy flight mutation to find the optimal control parameters; Step 4: Perform speed disturbances under different operating conditions to verify the control effect; The step 3 comprises the following steps: Step 3.1: When initializing the population, use the good point set theory to generate a uniformly distributed initial population, expressed as: （8）； In formula (8): Indicates the j The best point value of dimension; n is the population size; i represents the individual serial number; mod is the remainder function; k is the smallest prime number that satisfies 0.5(k-3)≥j; （9）； In formula (9): For the j The good point set of dimension; express j The product of the best point value of the first individual and the individual sequence number; express j The product of the best point value of the second individual and the individual sequence number; express j Vidi n The product of the best point value of each individual and the individual serial number; （10）； In formula (10): No. j Dimensional individual; Indicates the j The good point set of dimension; ub j 、 lb j Indicates the j The upper and lower bounds of the dimension; Step 3.2: Introduce Lévy flight for mutation, compare the original position and the individual position after Lévy flight to obtain the optimal value, and jump out of the local optimum to the greatest extent; （11）； In formula (11): This is the position after Levi's flight mutation; Indicates the original position; is the weight coefficient; Levy ( β ) is a random step size; （12）； In formula (12): r 1~ N (0,σ 2 ); r 2~ N (0,1); β represents the Lévy flight distribution parameter; represents the standard deviation; （13）； In formula (13): is the gamma function; Step 3.3: Objective function selection: By adding overshoot and steady-state error as evaluation variables of the objective function, the designed objective function 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, thereby achieving the best control effect. The specific expression is: （14）； In formula (14): It is the ITAE indicator; is the error between the system given signal and the output signal; Indicates time; （15）； In formula (15): represents the comprehensive objective function; 、 is the weight coefficient; is the overshoot.

2. The PID based on the tracking differentiator according to claim 1 μ The speed control optimization method of a pumped storage unit is characterized by: In 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.

3. The PID based on tracking differentiator according to claim 2 μ The speed control optimization method of a pumped storage unit is characterized by: The step 1 comprises: Step 1.1: Model the electro-hydraulic servo system: The electro-hydraulic servo system is the actuating mechanism of the speed regulator. It is modeled by considering the time lag, saturation, and limiting characteristics of the main pressure regulating valve and main servomotor. Its transfer function is: （1）； In formula (1): y ( s ) is the guide vane opening; u ( s ) is a control signal; k is the mechanical / electrical signal conversion gain; T y1 Inertia time constant of the main pressure regulating valve; T y is the inertia time constant of the main servomotor; 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: （2）； In formula (2): Expressed as per unit speed; Indicates the per unit value of unit flow; 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, BP neural network is used to fit the model, in which the guide vane opening and the transformed coordinate value X As the input of the BP neural network, the unit torque and unit flow are used as the output, and iterative training is carried out; 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; Step 1.3: Use the approximate elastic water hammer model to model the water hammer model: The water diversion pipeline consists of upstream and downstream reservoir pipelines, turbine inlet pipelines, and tailwater pipes. An approximate elastic water hammer model is used to represent the hydraulic relationship: （3）； In formula (3): represents the transfer function of the water hammer model; h ( s ) is the head change value; q ( s ) is the flow rate change value; T w is the water flow inertia coefficient; T r For water strikes each other; f is the pipeline friction coefficient; s is the Laplace operator; Step 1.4: Build the generator model: First-order generator model described by the rotor rotation equation of motion: （4）； （5）； Where: 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, which indicates the magnitude of the load; e n is the comprehensive self-regulation coefficient of the unit.

4. The PID based on tracking differentiator according to claim 1 μ The speed control optimization method of a pumped storage unit 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 to push the integer-order differential gain to a fractional order, and its expression is: （6）； In formula (6): Indicates 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 a control signal; e ( s ) is the deviation between the actual signal and the given signal; μ is the order of the differential term; Represents the symbol of fractional differential; Step 2.2: Introduce the tracking differentiator TD to smooth the 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: （7）； In formula (7): Indicates the k Tracking signal at all times; Indicates the k The differential signal of the tracking signal at the moment; Indicates the k +1 tracking signal; Indicates the k The differential signal of the tracking signal at time +1; Indicates the k Input signal at the moment; Abbreviation for the fastest function; r is the speed factor, which determines the tracking speed; h is the step length; fhan is the fastest control function.

5. The PID based on tracking differentiator according to claim 1 μ The speed control optimization method of a pumped storage unit is characterized by: The step 4 comprises the following steps: Step 4.1: Simulate the pumped storage unit under multiple operating conditions including startup, speed disturbance, and load rejection to verify the simulation model; Step 4.2: Perform speed disturbance simulation under no-load and load conditions under different water head conditions.

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