Hydroelectric generating set intelligent robust controller design method based on whale optimization algorithm and H infinity

Abstract

The invention discloses a hydroelectric generating set intelligent robust controller design method based on a whale optimization algorithm and H infinity. The method comprises the following steps: S1, constructing a nonlinear water turbine model; s2, constructing a numerical simulation model of the water turbine adjusting system based on an Octave tool; s3, obtaining a state space model of the water turbine adjusting system; s4, designing a robust controller structure based on H infinity; s5, constructing a comprehensive objective function of the whale optimization algorithm; and S6, optimizing parameters of the H-infinity controller by combining the whale optimization algorithm, the water turbine regulation system simulation model and the comprehensive objective function. According to the intelligent robust controller suitable for the hydroelectric generating set, the influence of uncertain disturbance on the adjusting quality of the controller can be fully considered, and safe and stable operation of the hydroelectric generating set is effectively guaranteed.

Description

Technical Field

[0001] The present invention belongs to the technical field of safe and stable operation of hydro-generating units, and particularly relates to a design method for an intelligent robust controller of a hydro-generating unit based on the whale optimization algorithm and H ∞ . Background Technique

[0002] As an important part of modern power systems, the operating efficiency and stability of hydro-generating units are directly related to the reliability and economy of power supply. However, the operating environment of hydro-generating units is complex and variable, with significant non-linearity, time-variation, and strong coupling characteristics. Traditional control methods, such as PID controllers, often struggle to ensure optimal performance when faced with these complex characteristics, easily leading to a decline in system stability and efficiency. Therefore, developing an intelligent robust controller that can adapt to complex operating conditions and improve control performance has become an urgent problem to be solved.

[0003] H ∞ control theory is a robust control method aimed at dealing with the stability and performance of systems in the presence of uncertainties and disturbances. By designing an H ∞ controller, the performance index of the system under the worst-case scenario can be guaranteed. Even when there are certain deviations in the system model and external disturbances, the system can still maintain stability and relatively good performance. The H ∞ control method is particularly suitable for dealing with uncertainty problems in complex industrial processes and is widely used in fields such as aerospace, robot control, and automated production. However, the H ∞ control contains hyperparameters that need to be given artificially, and it is necessary to conduct optimization research on these control parameters.

[0004] The whale optimization algorithm is a newly emerging swarm intelligence optimization algorithm that mimics the foraging behavior of humpback whales, especially its "bubble net attack" strategy, and searches for the global optimal solution by simulating the encirclement and spiral upward movement of whales. The whale optimization algorithm has been widely applied in fields such as function optimization, engineering design optimization, and machine learning due to its simple algorithm structure, strong global search ability, and fast convergence speed.

[0005] In view of the limitation that traditional PID controllers inadequately consider uncertain disturbances in complex operating environments, it is necessary to combine the whale optimization algorithm with H ∞ control theory to design an intelligent robust controller to significantly improve the control performance and robustness of the system. This optimization method is used to ensure the stability and performance of the hydraulic turbine regulating system in the presence of uncertainties and disturbances, thereby achieving long-term stable and efficient operation of hydro-generating units. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide an intelligent robust controller based on the whale optimization algorithm and H∞ The design method of the intelligent robust controller for hydropower units can fully consider the influence of uncertain disturbances on the regulation quality of the hydraulic turbine regulating system, and effectively ensure the safe and stable operation of hydropower units.

[0007] To solve the above technical problems, the technical solution adopted by the present invention is:

[0008] An intelligent robust controller design method for hydropower units based on the whale optimization algorithm and H ∞ The steps are as follows:

[0009] S1. Construct a non-linear hydraulic turbine model;

[0010] S2. Based on the Octave tool, construct a numerical simulation model of the hydraulic turbine regulating system;

[0011] S3. Obtain the state space model of the hydraulic turbine regulating system;

[0012] S4. Design a robust controller structure based on H ∞ ;

[0013] S5. Construct a comprehensive objective function of the whale optimization algorithm;

[0014] S6. Combine the whale optimization algorithm, the simulation model of the hydraulic turbine regulating system and the comprehensive objective function to optimize the parameters of the H ∞ controller.

[0015] Preferably, the method of step S1 is: based on the BP neural network, construct a flow characteristic neural network model with unit speed and guide vane opening as inputs and water turbine flow rate and torque as outputs respectively:

[0016] DCNN,Q 11 =Q 11 (n 11 , Y);

[0017] And a torque characteristic neural network model:

[0018] TCNN,M 11 =M 11 (n 11 , Y);

[0019] Wherein, n 11 is the unit speed, Y is the guide vane opening, Q 11 is the unit flow rate, M 11 is the unit torque, DCNN represents the flow characteristic neural network model, and TCNN represents the torque characteristic neural network model.

[0020] Preferably, the steps of constructing a flow characteristic neural network model and a torque characteristic neural network model with unit speed and guide vane opening as inputs and turbine flow rate and torque as outputs based on a neural network are as follows:

[0021] 1) Data collection: Collect the model comprehensive characteristic curve and operation data of the turbine. The operation data includes head, flow rate, and guide vane opening data. The operation data should cover various working conditions of the turbine to ensure the generalization ability of the flow characteristic neural network model and the torque characteristic neural network model;

[0022] 2) Data preprocessing: Preprocess the collected data. The preprocessing methods include removing outliers, filling missing values, and data normalization;

[0023] 3) Design the BP neural network structure: First, determine the number of nodes in the input layer and output layer of the neural network according to the input and output parameters of the turbine. The number of nodes in the input layer is equal to the number of input parameters, and the number of nodes in the output layer is equal to the number of output parameters; then, determine the number of hidden layers and the number of neurons in each layer;

[0024] 4) Train the BP neural network: First, randomly initialize the weights and biases of the network; then, input the input data into the neural network and calculate the output of each neuron; calculate the loss function according to the predicted output and the actual output; calculate the gradient of the loss function with respect to each parameter through the backpropagation algorithm; repeat the steps of forward propagation, loss calculation, backpropagation, and parameter update until the preset number of training epochs is reached or the loss function converges.

[0025] Preferably, in step S2, the numerical simulation model of the turbine governing system includes a water conveyance system model, a turbine model, a generator and power grid model, and a speed governor and servo system model; among them:

[0026] 1) Water conveyance system model:

[0027] The water conveyance system can adopt a rigid water hammer model, and its mathematical expression is:

[0028] G h (s)=-T w s (1);

[0029] In the formula, T w is the hydraulic time constant.

[0030] 2) Generator model:

[0031] Adopt a fifth-order generator model, and the expressions are formulas (2) and (3);

[0032]

[0033] Among them, ω is the angular velocity of the hydro-generator unit, Me is the electromagnetic torque, D t is the damping coefficient, δ is the power angle of the generator, ω 0 is the reference value of ω, H G is the generator inertia constant, E f is the excitation electromotive force; X d 、X d ', X d ”, E d ”, T d0 ', T d0 ”, I d and V d are the synchronous reactance, transient reactance, sub-transient reactance, sub-transient electromotive force, open-circuit transient time constant, sub-transient time constant, stator current component and terminal voltage V g component of the d-axis; X q 、X q ”, E q ', E q ”, T q0 ”, I q and V q are the synchronous reactance, transient reactance, sub-transient reactance, transient electromotive force, sub-transient electromotive force, open-circuit sub-transient time constant, stator current component and terminal voltage component of the q-axis; V g 2 =V d 2 +V q 2 ;

[0034] 3) Excitation system model:

[0035] Adopt a first-order excitation system model, as shown in Equation (4); considering the deviation of speed and electromagnetic power, a common power system stabilizer model is adopted in the power control mode, as shown in Equation (5); where, K a and T r are the excitation system gain and time constant respectively; K s is the gain of the power system stabilizer; T 0 、T 1 and T 2 are the time constants of the power system stabilizer;

[0036]

[0037] 4) Power network model:

[0038] The power network voltage can be expressed as:

[0039]

[0040] Among them: for an infinite power grid, Vs is almost a constant value; U x and U y are the network voltages; R l is the sum of the resistances of the transformer, line and load; X l is the sum of the impedances of the transformer, line and load; I x and I y are the network currents;

[0041] The generator and network coordinate transformation expressions are:

[0042]

[0043] 5) Governor model:

[0044] The transfer function of the linear part of the PID controller is:

[0045]

[0046] In the formula: T 1v is the time constant of the differential link; u is the controller output; e is the tracking error; K P , K I and K D are the proportional, integral and differential gains respectively;

[0047] 6) Servo system model:

[0048] The servo system expression is:

[0049]

[0050] Among them: K y is the comprehensive amplifier coefficient; T y are the reaction time constants of the main servomotor respectively;

[0051] 7) Turbine model:

[0052] Under small fluctuation conditions, the partial derivatives of the flow rate Q and torque M t at a certain operating point with respect to variables such as the guide vane opening Y, rotational speed X, and water head H are derived based on Taylor expansion, and high-order infinitesimals above the second order are ignored, that is, the constant coefficient algebraic equation at this operating point, namely the linear turbine model, is obtained:

[0053]

[0054] Among them, e qx , e qy and e qh are the transfer coefficients of Q with respect to X, Y, and H respectively; e x , e y and e h are M respectivelyt Transfer coefficients for X, Y, and H; q, m t , x, y, and h respectively represent the relative deviation values of Q, M t , X, Y, and H.

[0055] Preferably, the method of step S3 is: linearize the subsystem model with strong nonlinearity, and further obtain the state space model of the turbine governing system;

[0056] According to the equations of formulas (1)-(10), obtain the state space equation of the turbine governing system:

[0057]

[0058] where, I e is the output of the integral link of the PID controller; the coefficients K 1 ~K 10 The expressions are:

[0059]

[0060] Preferably, the method of step S4 is: design a robust controller structure based on H ∞ ;

[0061] Take the system control deviation e as shown in formula (12), obtain the new state space equation of the turbine governing system as shown in formula (13), and further design a robust controller of H ∞ ;

[0062] e = (ω d - ω) / e p + p d - p (12);

[0063]

[0064] where, ω d and ω are respectively the rotational speed reference value and the rotational speed; p d and p are respectively the reference value of the relative power value and the relative power value, and K i is the gain of the integral link after the system tracks the error e;

[0065] The state space model corresponding to formula (13) is:

[0066]

[0067] where, S = [y, x, h, E' q , E' q ', E' d ', E' f , δ, e iT ; U = [u, p d T ; A and B are state matrices;

[0068] Based on Equation (14), a robust controller for the hydropower unit based on H ∞ can be designed; for Equation (14), the design requirements of the H ∞ controller are required to satisfy:

[0069] (1) S = 0 is a locally asymptotically stable equilibrium point of the closed-loop hydropower turbine regulating system (HTRS), that is, for any initial state S(t) → 0;

[0070] (2) For any disturbance ω ∈ L 2 [0, +∞), the closed-loop HTRS has disturbance rejection performance, that is

[0071]

[0072] where, q i ≥ 0 (i = 1, 2,..., 9) and ρ > 0 are weighting coefficients;

[0073] Let D 11 = 0, take the control system performance evaluation signal z = C 1 S + D 11 ω + D 12 u, then Equation (15) is equivalent to:

[0074] ||z|| 2 < ||ω|| 2 (16);

[0075] Define T sω (s) as the closed-loop transfer function from ω to z, and the expression is:

[0076]

[0077] Then the disturbance rejection performance of the closed-loop HTRS is equivalent to ||T sω (s)|| ∞ < 1;

[0078] H ∞ The solution of the control problem is selected by the method based on linear matrix inequality (LMI). For this purpose, Theorem 1 is introduced:

[0079] Theorem 1: For Equation (15), given γ > 0, there exists P 1 = P 1 T > 0 and P 2 , if the inequality is satisfied: ​​

[0080]

[0081] Then the output of the state feedback robust controller is as follows:

[0082] u = KS = P 2 P 1 -1 S (19);

[0083] where K = [k 1 k 2 k 3 k 4 k 5 k 6 k 7 k 8 k 9 ;

[0084] When using Theorem 1 to solve for K in Equation (19), two LMIs are required, namely Equations (18) and (20);

[0085] -P 1 < 0 (20).

[0086] Preferably, the step S5 is specifically as follows:

[0087] Construct a comprehensive objective function considering overshoot, reverse overshoot, rise time, and the standard ITAE index J ITAE where J ITAE is a commonly used objective function for PID parameter optimization, as shown in the following equation:

[0088]

[0089] In the equation, t is the actual time; t s is the total simulation time; e(t) is the integral of the error of the turbine control signal;

[0090] The comprehensive objective function J ITAE including overshoot, reverse overshoot, rise time, and the standard ITAE index J 综合 is as shown in the following equation:

[0091]

[0092] In the equation, σ 1 is the overshoot; σ 2 is the reverse overshoot; t r is the rise time; ω 1 、ω 2 and ω 3 are weight coefficients.

[0093] Preferably, the step S6 is specifically as follows:

[0094] Combining the whale optimization algorithm, the turbine regulation system simulation model and the comprehensive objective function optimization H ∞ Controller parameters; The whale optimization algorithm simulates the hunting behavior of humpback whales, which mainly includes three stages: surrounding prey, attacking with a bubble net, and searching for prey. The formula for the prey surrounding stage is as follows:

[0095]

[0096] Where: t represents the number of iterations; t max Indicates the maximum number of iterations; is the coefficient vector; A random number between the range [0, 1]; represents the search particle, Represents the target prey, which is the position vector of the current optimal solution, and is continuously updated in iterations to obtain a better solution; is the convergence factor that decreases linearly from 2 to 0 during the iteration process;

[0097] The whale optimization algorithm mathematically models the bubble network attack behavior through the shrinking and surrounding mechanism and the spiral update mechanism. These two methods are used alternately according to the probability p. When p < 0.5, the shrinking and surrounding mechanism is used; when p > 0.5, the spiral mechanism is used to update the position of the search particle, that is:

[0098]

[0099] Where: b is the shape parameter of the logarithmic spiral, l is a random number between [-1, 1], Represents the distance between the search particle and the current optimal solution;

[0100] It decreases linearly, resulting in The value of will be Changes between Then the search particles gradually surround the current optimal solution, which belongs to the local optimization stage in the whale optimization algorithm; The distance data will be randomly updated, causing the whale to deviate from the original optimal individual and update the population according to the random position to perform a global search; in the process of searching for prey, its mathematical model is defined as follows:

[0101]

[0102] In the formula, represents a search particle randomly selected from the population.

[0103] A novel method based on whale optimization algorithm and H ∞The intelligent robust controller for a hydropower unit adopts the described one based on the whale optimization algorithm and H ∞ The design method of the intelligent robust controller for a hydropower unit includes:

[0104] A modeling tool for constructing a non - linear turbine model;

[0105] A simulation module for constructing a numerical simulation model of the turbine governing system based on the Octave tool;

[0106] A system identification and conversion tool for obtaining the state - space model of the turbine governing system;

[0107] A control design tool for designing the robust controller structure based on H ∞ ;

[0108] An optimization algorithm execution module for constructing the comprehensive objective function of the whale optimization algorithm;

[0109] A simulation environment integration module for optimizing the H ∞ controller parameters by combining the whale optimization algorithm, the simulation model of the turbine governing system and the comprehensive objective function.

[0110] A computer device includes:

[0111] One or more processors;

[0112] The said processor for storing one or more programs;

[0113] When the said one or more programs are executed by the said one or more processors, the design method of the intelligent robust controller for a hydropower unit as described is implemented. ∞

[0114] The present invention can achieve the following beneficial effects:

[0115] 1. The design method of the robust controller for a hydropower unit considering uncertain disturbances designed by the present invention can fully consider the influence of uncertain disturbances on the regulation quality of the turbine governing system, and effectively ensure the safe and stable operation of the hydropower unit.

[0116] 2. As the core equipment for power production in a hydropower station, the safe and stable operation of a hydropower unit has increasingly become a hot topic of concern in the industry. Aiming at the limitation that the traditional PID controller insufficiently considers uncertain disturbances in a complex operating environment, the present invention proposes a design method of an intelligent robust controller for a hydropower unit based on the whale optimization algorithm and H ∞ .

[0117] ​2. While ensuring the conventional regulation requirements of the hydropower unit, the intelligent robust controller designed by the present invention fully considers uncertain disturbances, effectively ensuring the long-term stable and efficient operation of the hydropower unit. BRIEF DESCRIPTION OF THE DRAWINGS

[0118] The present invention will be further described below in conjunction with the drawings and embodiments:

[0119] Figure 1 For the design steps of the method of the present invention;

[0120] Figure 2 Schematic diagram of the training process of the turbine model based on the BP neural network of the present invention;

[0121] Figure 3 Schematic diagram of the turbine model based on the BP neural network constructed by the present invention;

[0122] Figure 4 Calculation process of the whale optimization algorithm of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0123] The preferred solution is as Figures 1 to 4 shown, a design method of an intelligent robust controller for a hydropower unit based on the whale optimization algorithm and H ∞ In view of the limitation that the traditional PID controller insufficiently considers uncertain disturbances in a complex operating environment, the present invention proposes a new robust controller design method to comprehensively consider factors such as uncertain disturbances. This method will allow the hydropower unit to operate more efficiently and stably under different working conditions, thereby extending the equipment life, reducing the maintenance cost, and improving the power generation efficiency. The specific method is as follows:

[0124] (1) Construct a non-linear turbine model.

[0125] Based on the neural network, construct a flow characteristic neural network model (DCNN, Q 11 =Q 11 (n 11 , Y)) and a torque characteristic neural network model (TCNN, M 11 =M 11 (n 11 , Y)) with unit speed and guide vane opening as inputs and turbine flow and torque as outputs respectively. The steps include:

[0126] 1) Collect data

[0127] Collect the model comprehensive characteristic curves and operation data of the turbine, including data such as head, flow, and guide vane opening. These data should cover various working conditions of the turbine to ensure the generalization ability of the model.

[0128] 2) Data preprocessing

[0129] Preprocess the collected data, including removing outliers, filling in missing values, data normalization, etc. Normalization can scale the data to the same range (usually [0,1] or [-1,1]), which helps to speed up the training of the neural network and improve the model performance.

[0130] 3) Design the BP neural network structure

[0131] First, determine the number of nodes in the input layer and output layer of the neural network according to the input and output parameters of the water turbine. The number of nodes in the input layer is equal to the number of input parameters, and the number of nodes in the output layer is equal to the number of output parameters. Then, determine the number of hidden layers and the number of neurons in each layer. Generally, the number of neurons in the hidden layer needs to be determined through experiments. A common approach is to start with a small number of neurons and gradually increase it until the model performance no longer improves significantly. Further, select a suitable activation function for the hidden layer. Commonly used activation functions include Sigmoid, Tanh, and ReLU. The activation function of the output layer is selected according to the specific problem. For example, a linear activation function is commonly used in regression problems.

[0132] 4) Train the BP neural network

[0133] First, randomly initialize the weights and biases of the network, generally using small random values. Common methods include uniform distribution initialization and normal distribution initialization. Then, input the input data into the neural network and calculate the output of each neuron. Further, calculate the loss function according to the predicted output and the actual output. For example, the mean squared error (MSE) is commonly used as the loss function in regression problems. Further, calculate the gradient of the loss function with respect to each parameter through the backpropagation algorithm. Repeat the steps of forward propagation, calculating the loss, backpropagation, and parameter update until the preset number of training epochs is reached or the loss function converges.

[0134] (2) Build a numerical simulation model of the water turbine governing system based on the Octave tool.

[0135] Build a simulation model of the water turbine governing system based on the Octave tool. The simulation model includes a penstock system model, a water turbine model, a generator and power grid model, an excitation system, a governor and servo system model, etc.

[0136] 1) Penstock system model

[0137] The penstock system can adopt a rigid water hammer model, and its mathematical expression is:

[0138] G h (s)=-T w s (1)

[0139] 2) Generator model

[0140] A fifth-order generator model can be adopted, and the expressions are shown in Eqs. (2) and (3).

[0141]

[0142] Among them, ω is the angular velocity of the hydro-generator unit, M e is the electromagnetic torque, D t is the damping coefficient, δ is the power angle of the generator, ω 0 is the reference value of ω, H G is the generator inertia constant, E f is the excitation electromotive force. X d 、X d '、X d ”、E d ”、T d0 '、T d0 ”、I d and V d are the synchronous reactance, transient reactance, sub-transient reactance, sub-transient electromotive force, open-circuit transient time constant, sub-transient time constant, stator current component and terminal voltage V g component on the d-axis. X q 、X q ”、E q '、E q ”、T q0 ”、I q and V q are the synchronous reactance, transient reactance, sub-transient reactance, transient electromotive force, sub-transient electromotive force, open-circuit sub-transient time constant, stator current component and terminal voltage component on the q-axis. V g 2 =V d 2 +V q 2 .

[0143] 3) Excitation system model

[0144] Adopt a first-order excitation system (AVR) model as shown in Eq. (4). Considering the deviations of speed and electromagnetic power, a common power system stabilizer is adopted in the power control mode as shown in Eq. (5). Among them, K a and T r are the excitation system gain and time constant respectively; K s is the gain of the power system stabilizer; T 0 、T 1 and T 2 are the time constants of the power system stabilizer.

[0145]

[0146] 4) Power network model

[0147] The voltage of the power network can be expressed as:

[0148]

[0149] Among them: for an infinite power grid, V s is almost a constant value; U x and U y are the network voltages; R l is the sum of the resistances of the transformer, line, and load; X l is the sum of the impedances of the transformer, line, and load; I x and I y are the network currents.

[0150] The coordinate transformation expressions of the generator and the network are:

[0151]

[0152] 5) Governor model

[0153] The transfer function of the linear part of the PID controller is:

[0154]

[0155] In the formula: T 1v is the time constant of the differential link; u is the output of the controller; e is the tracking error; K P , K I and K D are the proportional, integral, and differential gains respectively.

[0156] 6) Servo system model

[0157] The expression of the servo system is:

[0158]

[0159] Among them: K y is the coefficient of the comprehensive amplifier; T y are the reaction time constants of the main servomotor respectively.

[0160] 7) Turbine model

[0161] Under small fluctuation conditions, based on Taylor expansion, the partial derivatives of the flow rate Q and torque M t at a certain operating point with respect to variables such as the guide vane opening Y, rotational speed X, and water head H are derived, and high-order infinitesimals above the second order are ignored, that is, the constant coefficient algebraic equation at this operating point, namely the linear turbine model, is obtained:

[0162]

[0163] Among them, eqx , e qy and e qh are the transfer coefficients of Q to X, Y, and H, respectively; e x , e y and e h are the transfer coefficients of M t to X, Y, and H, respectively; q, m t , x, y, and h represent the relative deviation values of Q, M t , X, Y, and H, respectively.

[0164] (3) Obtain the state - space model of the hydraulic turbine governing system.

[0165] According to the above equations, the state - space equation of the hydraulic turbine governing system is:

[0166]

[0167] where I e is the output of the integral link of the PID controller; the coefficients K 1 ~K 10 are expressed as:

[0168]

[0169] (4) Design the robust controller structure based on H ∞ .

[0170] Take the system control deviation e as shown in Equation (12), and obtain the new state - space equation of the hydraulic turbine governing system as shown in Equation (13), and further design the robust controller of H ∞ .

[0171] e = (ω d - ω) / e p + p d - p (12)

[0172]

[0173] where ω d and ω are the reference speed and the speed, respectively; p d and p are the reference value of the relative power and the relative power value, respectively, and K i is the gain of the integral link after the system tracking error e.

[0174] The state - space model corresponding to Equation (13) is:

[0175]

[0176] where S = [y, x, h, E' q , E' q ', E'd ',E' f ,δ,e i T ; U = [u, p d T ; A and B are state matrices.

[0177] Based on Equation (14), a robust controller for a hydropower unit can be designed. For Equation (14), the design requirements of the H ∞ controller are as follows: ∞ The controller design requirements are as follows:

[0178] (1) S = 0 is a locally asymptotically stable equilibrium point of the closed-loop hydropower turbine regulation system (HTRS), that is, for any initial state S(t) → 0;

[0179] (2) For any disturbance ω ∈ L 2 [0, +∞), the closed-loop HTRS has disturbance rejection performance, that is,

[0180]

[0181] where, q i ≥ 0 (i = 1, 2,..., 9) and ρ > 0 are weighting coefficients.

[0182] Let D 11 = 0, take the control system performance evaluation signal z = C 1 S + D 11 ω + D 12 u, then Equation (15) is equivalent to:

[0183] ||z|| 2 < ||ω|| 2 (16)

[0184] Define T sω (s) as the closed-loop transfer function from ω to z, and the expression is:

[0185]

[0186] Then the disturbance rejection performance of the closed-loop HTRS is equivalent to ||T sω (s)|| ∞ < 1.

[0187] H ∞ The solution to the control problem is selected to use the method based on linear matrix inequalities (LMI). For this purpose, Theorem 1 is introduced: Theorem 1 For Equation (15), given γ > 0, there exists P 1 = P 1 T > 0 and P​​2 , if the inequality is satisfied:

[0188]

[0189] Then the output of the state - feedback robust controller is:

[0190] u = KS = P 2 P 1 -1 S(19)

[0191] where K = [k 1 k 2 k 3 k 4 k 5 k 6 k 7 k 8 k 9 .

[0192] When using Theorem 1 to solve for K in Equation (19), two LMIs are required, namely Equation (18) and (20).

[0193] -P 1 <0 (20)

[0194] (5) Construct the comprehensive objective function of the whale optimization algorithm.

[0195] Obtain q i (i = 1, 2, …, 9) and ρ in the robust controller based on the whale optimization algorithm, where the objective function of the whale optimization algorithm is the comprehensive objective function.

[0196] Construct the comprehensive objective function considering overshoot, reverse overshoot, rise time, and the standard ITAE index (J ITAE ).

[0197] where J ITAE is the objective function commonly used for PID parameter optimization, as shown in the following equation:

[0198]

[0199] In the formula, t is the actual time; t s is the total simulation time; e(t) is the integral of the error of the turbine control signal.

[0200] The comprehensive objective function J ITAE including overshoot, reverse overshoot, rise time, and the standard ITAE index (J 综合 ) is as shown in the following equation:

[0201]

[0202] where, σ 1 is the overshoot; σ 2 is the inverse overshoot; t r is the rise time; ω 1 , ω 2 and ω 3 are the weight coefficients.

[0203] (6) Optimize the parameters of the H ∞ controller by combining the whale optimization algorithm, the simulation model of the hydraulic turbine governing system and the comprehensive objective function.

[0204] Optimize the parameters of the H ∞ controller based on the whale optimization algorithm with strong optimization ability. The whale optimization algorithm (WOA) is a natural meta-heuristic algorithm that searches for the optimal solution by simulating the bubble-net hunting behavior of humpback whales. This algorithm has few parameters, a simple mechanism, does not require relevant gradient information, and the local search and global search alternate according to the parameter changes, which can well avoid the emergence of local optimal solutions. The WOA algorithm simulates the hunting behavior of humpback whales mainly including three stages: surrounding the prey, bubble-net attacking, and searching for the prey. The formula for the stage of surrounding the prey is as follows:

[0205]

[0206]

[0207] where: t represents the number of iterations; t max represents the maximum number of iterations; is the coefficient vector; is a random number in the range of [0, 1]; represents the search particle, represents the target prey, that is, the position vector of the current optimal solution, which is continuously updated during the iteration to obtain a better solution; is the convergence factor that linearly decreases from 2 to 0 during the iteration.

[0208] WOA mathematically models the bubble-net attacking behavior through the shrinking encircling mechanism and the spiral updating mechanism. These two methods are alternately used according to the probability p (p is a probability randomly generated from [0, 1]). When p < 0.5, the shrinking encircling mechanism is adopted; while when p > 0.5, the spiral mechanism is used to update the position of the search particle, that is:

[0209]

[0210] where: b is the shape parameter of the logarithmic spiral, l is a random number between [-1, 1], represents the distance between the search particle and the current optimal solution.

[0211] Decrease linearly, resulting in The value of will be within Change between. Then the search particles gradually surround the current optimal solution, which belongs to the local optimization stage in WOA. When The distance data of will be randomly updated, causing the whale to deviate from the original optimal individual and updating the population according to the random position to perform global search. During the process of hunting for prey, its mathematical model is defined as follows:

[0212]

[0213] In the formula, Represents a search particle randomly selected from the population.

[0214] The execution of the WOA algorithm starts with a set of randomly initialized parameters, and the best solution is saved according to the calculation result of the fitness function. Then, the parameters are updated according to the above search mechanism, and the loop iterates until the maximum number of times. Finally, the WOA algorithm terminates and outputs the global optimal solution.

[0215] The above embodiments are only the preferred technical solutions of the present invention and should not be regarded as limitations on the present invention. The protection scope of the present invention should be the technical solutions recorded in the claims, including equivalent replacement solutions of the technical features in the technical solutions recorded in the claims. That is, equivalent replacement improvements within this scope are also within the protection scope of the present invention.

Claims

1. A novel method based on whale optimization algorithm and H ∞ The design method of intelligent robust controller for hydropower unit is characterized by The following steps are involved: S1, construct nonlinear turbine model; S2, build a numerical simulation model of the turbine regulation system based on Octave tool; S3, obtaining a state space model of a turbine regulating system; S4, designed based on H ∞ The robust controller structure of S5, construct the comprehensive objective function of the whale optimization algorithm; S6, combining the whale optimization algorithm, the turbine regulation system simulation model and the comprehensive objective function optimization H ∞ Controller parameters.

2. A method based on the whale optimization algorithm and H according to claim 1 ∞ The design method of intelligent robust controller for hydropower unit is characterized by: The method of step S1 is: constructing a flow characteristic neural network model based on the BP neural network with unit speed and guide vane opening as inputs and turbine flow and torque as outputs: DCNN,Q 11 =Q 11 (n 11 ,Y); And the torque characteristic neural network model: TCNN,M 11 =M 11 (n 11 ,Y); Among them, n 11 is the unit speed, Y is the guide vane opening, Q 11 is the unit flow rate, M 11 is the unit torque, DCNN represents the flow characteristic neural network model, and TCNN represents the torque characteristic neural network model.

3. A method based on the whale optimization algorithm and H according to claim 2 ∞ The intelligent robust controller design method for hydropower units is characterized by: The steps of constructing a flow characteristic neural network model and a torque characteristic neural network model based on a neural network with unit speed and guide vane opening as input and turbine flow and torque as output are as follows: 1) Data collection: Collect the comprehensive characteristic curve and operation data of the turbine model. The operation data includes water head, flow rate, and guide vane opening data. The operation data should cover various working conditions of the turbine to ensure the generalization ability of the flow characteristic neural network model and the torque characteristic neural network model; 2) Data preprocessing: preprocess the collected data. The preprocessing methods include removing outliers, filling missing values, and normalizing data. 3) Design the BP neural network structure: First, according to the input and output parameters of the turbine, determine the number of nodes in the input layer and output layer of the neural network. The number of nodes in the input layer is equal to the number of input parameters, and the number of nodes in the output layer is equal to the number of output parameters; then, determine the number of hidden layers and the number of neurons in each layer; 4) Training BP neural network: First, randomly initialize the weights and biases of the network; then, input data into the neural network and calculate the output of each neuron; calculate the loss function based on the predicted output and actual output; calculate the gradient of the loss function for each parameter through the back propagation algorithm; repeat the steps of forward propagation, loss calculation, back propagation and parameter update until the preset number of training rounds is reached or the loss function converges.

4. A method based on the whale optimization algorithm and H according to claim 1 ∞ A design method for an intelligent robust controller for a hydropower unit is provided; the method is characterized in that: In step S2, the numerical simulation model of the hydraulic turbine regulation system includes a water diversion system model, a hydraulic turbine model, a generator and power grid model, a speed regulator and a servo system model; wherein: 1) Water diversion system model: The water diversion system can adopt a rigid water hammer model, and the mathematical expression is: G h (s)=-T w s (1); Where, T w is the hydraulic time constant; 2) Generator model: Using the fifth-order generator model, the expressions are (2) and (3); Where ω is the angular velocity of the turbine generator set, M e is the electromagnetic torque, D t is the damping coefficient, δ is the power angle of the generator, ω0 is the reference value of ω, H G is the generator inertia constant, E f is the excitation electromotive force; X d , X d ', X d ”、E d ”、T d0 '、T d0 ”、I d and V d They are the synchronous reactance of the d-axis, transient reactance, subtransient reactance, subtransient potential, open-circuit transient time constant, subtransient time constant, stator current component and terminal voltage V g Weight; X q , X q ”、E q ', E q ”、T q0 ”、I q and V q They are the synchronous reactance, transient reactance, subtransient reactance, transient potential, subtransient potential, open circuit subtransient time constant, stator current component and terminal voltage component of q axis respectively; V g 2 =V d 2 +V q 2 ; 3) Excitation system model: The first-order excitation system model is adopted, as shown in formula (4); considering the deviation of speed and electromagnetic power, the commonly used power system stabilizer model is adopted in the power control mode, as shown in formula (5): Among them, K a and T r are the excitation system gain and time constant respectively; K s is the gain of the power system stabilizer; T0, T1 and T2 are the time constants of the power system stabilizer; 4) Power network model: The power network voltage can be expressed as: Where: For infinite power grid, V s Almost a constant value; U x and U y is the network voltage; R l is the sum of the resistance of the transformer, line and load; X l is the sum of the impedance of the transformer, line and load; I x and I y is the network current; The generator and network coordinate transformation expressions are: 5) Governor model: The transfer function of the linear part of the PID controller is: Where: T 1v is the time constant of the differential link; u is the controller output; e is the tracking error; K P , K I and K D are proportional, integral and derivative gains respectively; 6) Follow-up system model: The expression of the follow-up system is: Where: K y is the comprehensive amplifier coefficient; T y are the main servomotor reaction time constants respectively; 7) Turbine model: Under small fluctuation conditions, the flow Q and torque M at a certain operating point are derived based on Taylor expansion. t Taking partial derivatives of variables such as guide vane opening Y, speed X, and water head H, and ignoring higher-order traces above the second order, we can obtain a constant coefficient algebraic equation for this operating point, namely the linear turbine model: Among them, e qx 、e qy and e qh are the transmission coefficients of Q to X, Y and H respectively; e x 、e y and e h M t Transfer coefficients for X, Y and H; q, m t , x, y and h represent Q, M respectively t , relative values ​​of deviation of X, Y and H.

5. The method according to claim 1 based on the whale optimization algorithm and H ∞ A design method for an intelligent robust controller for a hydropower unit is provided; the method is characterized in that: The method of step S3 is: linearizing the subsystem model with strong nonlinearity to further obtain the state space model of the turbine regulation system; According to equations (1)-(10), the state space equation of the turbine regulation system is obtained: Among them, I e is the output of the integral link of the PID controller; coefficients K1~K 10 The expression is:

6. A method according to claim 1 based on the whale optimization algorithm and H ∞ The design method of intelligent robust controller for hydropower unit is characterized by: The method of step S4 is: designing a hydraulic turbine regulation system based on the state space model of H ∞ The robust controller structure of Taking the system control deviation e as shown in formula (12), the new state space equation of the turbine regulation system is obtained as shown in formula (13). ∞ Robust controller of e=(ω d -ω) / e p +p d -p (12); Among them, ω d and ω are the speed reference value and speed respectively; p d and p are the reference value and relative value of power respectively, K i is the gain of the integral link after the system tracks the error e; The state space model corresponding to formula (13) is: Where S = [y, x, h, E' q ,E' q ',E' d ',E' f ,δ,e i ] T ; U=[u,p d ] T ; A and B are state matrices; According to formula (14), the H ∞ The robust controller of the hydropower unit is: ∞ The controller design requirements meet: (1) S = 0 is the local asymptotically stable equilibrium point of the closed-loop hydraulic turbine regulating system (HTRS), that is, for any initial state S(t)→0; (2For any disturbance ω∈L2[0,+∞), the closed-loop HTRS has disturbance suppression performance, that is, Among them, q i ≥0(i=1,2,…,9) and ρ>0 are weighting coefficients; make D 11 =0, take the control system performance evaluation signal z=C1S+D 11 ω+D 12 u, then formula (15) is equivalent to: ||z||2<||ω||2 (16); Define T sω (s) is the closed-loop transfer function from ω to z, expressed as: Then the disturbance rejection performance of the closed-loop HTRS is equivalent to ||T sω (s)|| ∞ <1; H ∞ The solution to the control problem is based on the linear matrix inequality (LMI) method. For this purpose, Theorem 1 is introduced: Theorem 1: For equation (15), given γ>0, there exists P1=P1 T >0 and P2, if the inequality is satisfied: Then the output of the state feedback robust controller is: u=KS=P2P1 -1 S (19); Where, K = [k1 k2 k3 k4 k5 k6 k7 k8 k9]; When using Theorem 1 to solve K in equation (19), two LMIs are required, namely equations (18) and (20); -P1＜0 (20)。 7. The method according to claim 1 based on the whale optimization algorithm and H ∞ The design method of intelligent robust controller for hydropower unit is characterized by: The step S5 is specifically as follows: Construct J considering overshoot, reverse shoot, rise time and standard ITAE index ITAE The comprehensive objective function, where J ITAE It is a commonly used objective function for PID parameter optimization, as shown in the following formula: Where t is the actual time; t s is the total simulation time; e(t) is the integral of the turbine control signal error; Contains overshoot, reverse shoot, rise time and standard ITAE index J ITAE The comprehensive objective function J 综合 As shown below: In the formula, σ1 is the overshoot; σ2 is the backshoot; t r is the rise time; ω1, ω2 and ω3 are weight coefficients.

8. The method according to claim 1 based on the whale optimization algorithm and H ∞ The design method of intelligent robust controller for hydropower unit is characterized by: The step S6 is specifically as follows: Combining the whale optimization algorithm, the turbine regulation system simulation model and the comprehensive objective function optimization H ∞ Controller parameters; The whale optimization algorithm simulates the hunting behavior of humpback whales, which mainly includes three stages: surrounding prey, attacking with a bubble net, and searching for prey. The formula for the prey surrounding stage is as follows: Where: t represents the number of iterations; t max Indicates the maximum number of iterations; is the coefficient vector; A random number between the range [0, 1]; represents the search particle, Represents the target prey, which is the position vector of the current optimal solution, and is continuously updated in iterations to obtain a better solution; is the convergence factor that decreases linearly from 2 to 0 during the iteration process; The whale optimization algorithm mathematically models the bubble network attack behavior through the shrinking and surrounding mechanism and the spiral update mechanism. These two methods are used alternately according to the probability p. When p < 0.5, the shrinking and surrounding mechanism is used; when p > 0.5, the spiral mechanism is used to update the position of the search particle, that is: Where: b is the shape parameter of the logarithmic spiral, l is a random number between [-1, 1], Represents the distance between the search particle and the current optimal solution; It decreases linearly, resulting in The value of will be Changes between Then the search particles gradually surround the current optimal solution, which belongs to the local optimization stage in the whale optimization algorithm; The distance data will be randomly updated, causing the whale to deviate from the original optimal individual and update the population according to the random position to perform a global search; in the process of searching for prey, its mathematical model is defined as follows: In the formula, represents a search particle randomly selected from the population.

9. A novel method based on whale optimization algorithm and H ∞ The intelligent robust controller for hydropower units is characterized by: A method based on a whale optimization algorithm and H according to any one of claims 1 to 8 is adopted. ∞ The design method of intelligent robust controller for hydropower units includes: Modeling tools for building nonlinear turbine models; The simulation module is used to build a numerical simulation model of the turbine regulation system based on the Octave tool; System identification and conversion tools to obtain the state space model of the turbine regulation system; Control design tool for designing H-based ∞ The robust controller structure of The optimization algorithm execution module is used to construct the comprehensive objective function of the whale optimization algorithm; Simulation environment integration module, used to combine the whale optimization algorithm, turbine regulation system simulation model and comprehensive objective function optimization H ∞ Controller parameters.

10. A computer device, characterized in that: include: one or more processors; The processor is used to store one or more programs; When the one or more programs are executed by the one or more processors, a method based on the whale optimization algorithm and H as described in any one of claims 1 to 8 is implemented. ∞ Design method of intelligent robust controller for hydropower units.

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