A method for optimizing speed control of a hydraulic turbine based on multivariable feedback

Abstract

The application provides a water turbine speed regulation control optimization method based on multivariable feedback. The optimization method is based on an existing stable and feasible PID control method, introduces water head, flow, rotating speed and the like as input, constructs a new type of state feedback control, forms a new type of optimization control method, and is applied to a water turbine speed regulator to improve response speed and quality of speed regulation control.

Description

Technical Field

[0001] This invention relates to the field of hydro turbine speed regulation technology, and specifically to a hydro turbine speed regulation control optimization method based on multivariable feedback. Background Technology

[0002] New energy power generation, such as wind and solar power, is replacing traditional thermal power generation on a large scale. Unlike traditional synchronous generator units, new energy generator units have weak inertia support capabilities, and new energy resources are highly volatile. Under the background of large-scale new energy grid connection, the frequency problem of the power system is becoming increasingly severe. Hydropower turbine speed regulation has the advantages of large regulation capacity and flexible response, and is a key resource for suppressing new energy fluctuations and supporting power system frequency regulation.

[0003] However, to mitigate the rapid fluctuations in renewable energy generation and ensure that frequency regulation resources meet the dynamic demands of the system, grid connection criteria are placing increasingly higher demands on the response speed and quality of equipment involved in frequency regulation. However, the engineering application of turbine speed regulation technology has seen little development in the past two decades, primarily relying on single-feedback PID control based on output error. This control structure, which depends on engineering experience for parameter tuning, is increasingly unable to meet grid connection requirements and urgently needs upgrading.

[0004] Currently, the academic community has also proposed some novel speed control methods for hydro turbines, such as introducing artificial intelligence algorithms to optimize PID controller parameters, or proposing new control structures and parameter design methods based on theories such as adaptive control and sliding mode control. However, due to the complexity of hydro turbine speed control systems and their operating conditions, the robustness of these advanced control methods in practical engineering is difficult to fully verify, and their reliability is not as good as traditional PID control, so there are no typical engineering applications yet.

[0005] Compared to speed control designs that apply entirely new theories or methods, modifying and improving existing, stable, and feasible PID control methods is more significant in engineering practice. The three typical existing PID control modes are single-channel feedback control based on the error between commands such as frequency, power, and opening degree and the feedback values. However, information characterizing the operating status, such as head height, unit flow rate, speed, and load changes, which are monitored in actual operation, has not yet been utilized in the control. Summary of the Invention

[0006] Based on this, the purpose of this application is to provide an optimization method for turbine speed control based on multivariable feedback. This optimization method is based on the existing stable and feasible PID control method, and introduces variables such as head, flow rate, and speed as inputs to construct a new state feedback control, forming a new optimization control method, which is then applied to the turbine governor to improve the response speed and quality of speed control.

[0007] To achieve the above-mentioned technical features, the objective of this invention is as follows: A method for optimizing the speed control of a hydraulic turbine based on multivariable feedback, characterized by comprising the following steps:

[0008] Step 1: Establish a model of the turbine speed control system. Based on the model, obtain the transfer functions G for the governor, servo system, turbine and water intake system, generator and load, respectively. t G s G y and G f ;

[0009] Step 2: The open-loop transfer function G1 of the closed-loop system consisting of the governor, servo system, turbine and water intake system, generator and load is used to form output feedback with the output frequency of the speed regulation system as the feedback variable, and a traditional turbine speed regulation system model is established.

[0010] Step 3: Select the measurable variables in the actual operation of the turbine speed regulation system, and feed the selected variables back to the relay command value to form a multivariable feedback speed regulation system;

[0011] Step 4: Establish the multivariable feedback state space equation based on the multivariable feedback speed regulation system of the turbine. Based on the obtained system state matrix, improve the response speed of the turbine speed regulation system when meeting the primary frequency regulation requirements of the power grid by designing the parameters of the multivariable feedback loop, and reduce the power back-regulation that occurs during the system response to a certain extent, so that the multivariable feedback turbine speed regulation system can obtain better frequency response characteristics and higher response quality.

[0012] The turbine speed control system comprises four basic components: governor, servo system, turbine and water intake system, generator and load.

[0013] The speed governor section adopts the microcomputer speed governor commonly used in the operation of water turbine units. The input is a manually set frequency specification value. The output frequency of the generator and load is fed back to the input side through the frequency measurement circuit and the difference with the given frequency is used to obtain the frequency error signal of the speed governor system. When the amplitude of the error signal exceeds the manual frequency dead zone, the speed governor system will start to operate. After the error signal is adjusted by the PID controller, the relay stroke command value is output.

[0014] The follow-up system is the main operating link of the turbine. This part receives the stroke command value of the servo and adjusts the opening of the turbine guide vanes, thereby affecting the changes in head, flow rate and mechanical power parameters. Since the reaction time constant of the auxiliary servo is much smaller than that of the main servo, in order to simplify the turbine speed regulation system model, the inertial link dominated by the reaction time constant of the main servo is used to replace the follow-up system.

[0015] The turbine and entrainment system's flow rate and head parameters change due to variations in guide vane opening, which in turn affects the turbine's output torque. This part is modeled based on the turbine's external characteristic formula (1-1). Due to its strong nonlinearity, a linearized model is used for the study. To simplify the analysis, a rigid water hammer model is adopted for the entrainment system, and the influence of speed variation on the turbine's flow rate is ignored, i.e., e qx =0;

[0016] Formulas for the external characteristics of a water turbine:

[0017]

[0018] In the formula: s is the Laplace operator; M t To output mechanical torque for the prime mover of the water turbine; e y Y is the torque transfer coefficient of the turbine to the guide vane opening; Y is the turbine guide vane opening; e x The torque-to-speed transmission coefficient is given by X; X is the generator output speed; e h The torque-to-head transmission coefficient of the turbine; H is the head; Q is the flow rate; e qy e is the turbine flow rate transfer coefficient to the guide vane opening. qx e is the turbine flow rate to speed transfer coefficient; qh The turbine flow rate is the coefficient of head transfer.

[0019] The turbine changes the speed of the generator connected to it by changing the output mechanical torque, thereby affecting the generator's output power and output frequency;

[0020] The generator and load are modeled as a first-order generator, and the torque-to-speed transfer coefficient e is used. x With load self-adjustment coefficient e g Merge, and the merged result is adjusted by the coefficient e. n replace.

[0021] Multivariable feedback control adopts the design concept of state feedback loop, with proportional element as the main form of feedback loop. The selected variable is amplified by the proportional element and then input to the relay command value. Together with the output command of the original turbine speed regulation system PID governor, it changes the guide vane opening of the servo system, thereby achieving the effect of multivariable control system output frequency and output power, and thus improving the system response speed.

[0022] The specific process of the multivariable feedback control method is as follows:

[0023] Establish the state-space equations based on the traditional turbine speed control system:

[0024]

[0025] In the formula: t is time; Let A be the derivative of the state variable with respect to time; let x be the state variable; let B be the input matrix; let u be the input variable; let y be the output variable; let C be the output matrix; and let D be the feedforward matrix.

[0026] In order to improve the response speed and quality of the speed control system, proportional feedback control is introduced for the multiple variables contained in the speed control system, and the state space equation of the speed control system with multivariable feedback loop is established.

[0027] After introducing multivariable feedback control, the relationship between the input signal and the state variable is shown in equation (1-3):

[0028] u(t)=r(t)-Kx(t),K∈R 1×n (1-3)

[0029] In the formula, K is the coefficient matrix composed of the proportional coefficients of the multivariable feedback loop; r is the new input variable of the system defined after the introduction of feedback control;

[0030] Substituting equation (1-3) into equation (1-2), we obtain the state-space equation of the speed control system after introducing state feedback:

[0031]

[0032] According to formula (1-4), the system state matrix A-BK after introducing state feedback is obtained. Through analysis of the state matrix, it can be seen that the real and imaginary parts of the speed regulation system poles are related to the K matrix parameters. That is, the configuration of the turbine speed regulation system poles can be achieved by changing the proportional coefficient of the feedback loop. According to the correspondence between the speed regulation system poles and the system response characteristics, it can be seen that adjusting the leftward shift of the real part of the dominant oscillation pole can improve the response speed and ensure that the damping ratio is between 0.5 and 0.7 to prevent overshoot or oscillation. Therefore, the system response characteristics can be improved by adjusting the K matrix parameters.

[0033] In actual operation, measurable variables include guide vane opening, head, flow rate, mechanical power, and output frequency.

[0034] The specific process of modeling and simulating the speed control system after introducing multivariable feedback, by adding head, flow rate, and output frequency feedback control loops to the hydropower unit speed governor, is as follows:

[0035] In the turbine speed control system model, K p1 K I1 K D1 These are the PID parameters of the speed controller, T d1 b is the differential constant. p T is the permanent slip coefficient. y K is the reaction time constant of the relay. f1K f2 K f3 These are the proportional coefficients for the head feedback, flow feedback, and output frequency feedback loops, respectively. After introducing multivariable feedback control, the relationship between the system frequency deviation signal and the guide vane opening command value is as follows:

[0036]

[0037] In the formula: Δf is the frequency deviation signal; s is the Laplace operator; H is the head parameter; Q is the unit flow rate; f is the generator output frequency; y PID The PID controller outputs the opening command value;

[0038] The transfer function of the servo system is as follows:

[0039]

[0040] In the formula: G s T is the transfer function of the servo system; y s is the time constant of the relay action; s is the Laplace operator;

[0041] Considering the rigid water hammer model, the transfer function of the water diversion system is as follows:

[0042] G y =-T w s (1-7)

[0043] In the formula: G y T is the transfer function of the water diversion system; w Let be the time constant for the water hammer effect; s be the Laplace operator; where e y =1,e h =1.5, e qy =1,e qh =0.5;

[0044] The transfer function of the generator and load is:

[0045]

[0046] In the formula: G f T is the transfer function of the generator and load; a e is the inertial time constant; n e is the comprehensive self-regulation coefficient of the hydro-generator unit. n =e g -e x The value ranges from 0 to 2; e g e is the generator load self-regulation coefficient; x This is the torque-to-speed transmission coefficient;

[0047] Based on the above relationships, the transfer function of the multivariable feedback speed regulation system of the water turbine can be established, and simulation can be performed based on the model and the transfer function.

[0048] The simulation process of the turbine speed control system with multivariable feedback is as follows: The state-space equation of the multivariable feedback speed control system is established with the integrator output as the state variable. In this system, the differential element in the PID governor is equivalent to a parallel proportional element and an inertial element. For the turbine and water intake system, the head parameters are retained, and only the rigid water hammer model is transformed. When establishing the state-space equation, the algebraic relationship H = f(x2, x3) between the state variables x2 and x3 and the head is used to replace the head parameters. Due to the influence of the rigid water hammer model transfer function, the flow feedback loop is equivalent to an integral loop, operating in parallel with the head feedback loop. The state-space equation of the multivariable feedback control is shown below:

[0049]

[0050] In the formula: F is the input frequency setpoint, M g0 For load power disturbance;

[0051] Based on the state-space equations, the state matrix of the multivariable feedback turbine speed control system is obtained. The poles of the turbine speed control system can be solved using the formula sI-A. The positions of the system poles in the S-plane and K are then determined. f1 K f2 K f3 The value of is related to the position of the characteristic root of the speed control system in the S-plane, so the response performance of the speed control system can be adjusted by changing the parameters of the state feedback loop.

[0052] After adjusting the feedback loop parameters, the optimization effect of introducing multivariable feedback on the response characteristics of the turbine speed control system can be obtained based on the frequency response curve.

[0053] The beneficial effects of this invention are as follows:

[0054] The multivariable feedback turbine speed control method proposed in this invention introduces multivariable feedback into the traditional turbine governor, using proportional control in the feedback loop. By adjusting the parameters of the multivariable feedback loop, system pole configuration is achieved, the system damping ratio is adjusted, and the turbine frequency response speed is improved, thereby optimizing the turbine's performance in primary frequency regulation. Compared with new control structures and parameter design methods based on adaptive control and sliding mode control theories, this method features high reliability, convenient control, and ease of implementation. Attached Figure Description

[0055] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0056] Figure 1This is a schematic diagram illustrating the principle of multivariable feedback optimization of turbine speed regulation performance control according to the present invention.

[0057] Figure 2 This is a schematic diagram of the multivariable feedback control method used in this invention.

[0058] Figure 3 This is a simulated block diagram of the water turbine and its water intake system of the present invention.

[0059] Figure 4 The present invention is a multivariable feedback speed control system for a water turbine, which is composed of a speed governor, a servo system, a water turbine and a water intake system, a generator and a load model, and feedback loops for head, flow rate and output frequency.

[0060] Figure 5 The simulation structure diagram of the turbine speed regulation system that introduces multivariable feedback in this invention is shown.

[0061] Figure 6 To compare the frequency response process simulation curves of a traditional turbine speed control system and a speed control system that uses feedback of water head, flow rate, and output frequency variables. Detailed Implementation

[0062] The embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0063] Example 1:

[0064] This invention discloses a method for optimizing the speed regulation performance of a hydro turbine based on multivariable feedback control. The invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described are merely illustrative of the invention and are not intended to limit the invention.

[0065] A method for optimizing the speed control of a hydro turbine based on multivariable feedback includes the following steps:

[0066] Step 1: Establish a model of the turbine speed control system. Based on the model, obtain the transfer functions G for the governor, servo system, turbine and water intake system, generator and load, respectively. t G s G y and G f ;

[0067] Step 2: The open-loop transfer function G1 of the closed-loop system consisting of the governor, servo system, turbine and water intake system, generator and load is used to form output feedback with the output frequency of the speed regulation system as the feedback variable, and a traditional turbine speed regulation system model is established.

[0068] Step 3: Select the measurable variables in the actual operation of the turbine speed regulation system, and feed the selected variables back to the relay command value to form a multivariable feedback speed regulation system;

[0069] Step 4: Establish the multivariable feedback state space equation based on the multivariable feedback speed regulation system of the turbine. Based on the obtained system state matrix, improve the response speed of the turbine speed regulation system when meeting the primary frequency regulation requirements of the power grid by designing the parameters of the multivariable feedback loop, and reduce the power back-regulation that occurs during the system response to a certain extent, so that the multivariable feedback turbine speed regulation system can obtain better frequency response characteristics and higher response quality.

[0070] By employing the specific control optimization methods described above, this method primarily addresses the significant challenges posed to power system frequency stability by the vigorous development of new energy power generation, represented by wind and solar power. Pumped storage, as a major frequency regulation resource for the power system, has also experienced a surge in development. The rapid fluctuations in output from new energy power generation necessitate increased response speeds from grid-connected frequency regulation resources to ensure system frequency dynamics. However, industrial turbine speed control based on PID control struggles to meet grid connection standards and urgently requires upgrading. On the other hand, PID controllers, due to their simple control laws and robustness, are mature in industrial turbine regulator applications. However, the reliability of intelligent control optimization of PID parameters or entirely new control systems proposed by academia is difficult to guarantee, resulting in limited engineering applications. Based on this situation, this invention builds upon existing reliable PID control, introducing existing monitoring variables from turbine operation, such as head, flow rate, speed, and load, adding novel state feedback control, and constructing a state-space model to design compensating control parameters. This improves the response speed of turbine speed control and reduces power overshoot.

[0071] Example 2:

[0072] See Figure 1 A schematic diagram illustrating the control principle for optimizing the speed regulation performance of a hydro turbine using multivariable feedback. The hydro turbine speed regulation system comprises four basic structures: governor, servo system, turbine and water intake system, and generator and load.

[0073] The speed governor section adopts the microcomputer speed governor commonly used in the operation of water turbine units. The input is a manually set frequency specification value. The output frequency of the generator and load is fed back to the input side through the frequency measurement circuit and the difference with the given frequency is used to obtain the frequency error signal of the speed governor system. When the amplitude of the error signal exceeds the manual frequency dead zone, the speed governor system will start to operate (the water turbine speed governor system is operating in frequency mode and the dead zone is set to zero). After the error signal is regulated by the proportional-integral-derivative (PID) controller, the relay stroke command value is output.

[0074] The follow-up system is the main operating link of the turbine. This part receives the stroke command value of the servo and adjusts the opening of the turbine guide vanes, thereby affecting the changes in head, flow rate and mechanical power parameters. Since the reaction time constant of the auxiliary servo is much smaller than that of the main servo, in order to simplify the turbine speed regulation system model, the inertial link dominated by the reaction time constant of the main servo is used to replace the follow-up system.

[0075] The turbine and entrainment system's flow rate and head parameters change due to variations in guide vane opening, which in turn affects the turbine's output torque. This part is modeled based on the turbine's external characteristic formula (1-1). Due to its strong nonlinearity, a linearized model is used for the study. To simplify the analysis, a rigid water hammer model is adopted for the entrainment system, and the influence of speed variation on the turbine's flow rate is ignored, i.e., e qx =0;

[0076] Among them, the formula for the external characteristics of the water turbine is:

[0077]

[0078] In the formula: s is the Laplace operator; M t To output mechanical torque for the prime mover of the water turbine; e y Y is the torque transfer coefficient of the turbine to the guide vane opening; Y is the turbine guide vane opening; e x The torque-to-speed transmission coefficient is given by X; X is the generator output speed; e h The torque-to-head transmission coefficient of the turbine; H is the head; Q is the flow rate; e qy e is the turbine flow rate transfer coefficient to the guide vane opening. qx e is the turbine flow rate to speed transfer coefficient; qh The turbine flow rate is the coefficient of head transfer.

[0079] The turbine changes the rotational speed of the generator connected to it by altering the output mechanical torque, thereby affecting the generator's output power and frequency.

[0080] The generator and load are modeled as a first-order generator, and the torque-to-speed transfer coefficient e is used. x With load self-adjustment coefficient e g Merge, and the merged result is adjusted by the coefficient e. n replace.

[0081] The present invention proposes a design concept for multivariable feedback control that adopts state feedback loops. The proportional element is used as the main form of the feedback loop. The selected variable is amplified by the proportional element and then input to the relay command value. Together with the output command of the original turbine speed regulation system PID governor, it changes the guide vane opening of the servo system, thereby achieving the effect of multivariable control system output frequency and output power, and thus improving the system response speed.

[0082] Figure 2 This is a schematic diagram of the multivariable feedback control method used in this invention. The specific process of the multivariable feedback control method is as follows:

[0083] Establish the state-space equations based on the traditional turbine speed control system:

[0084]

[0085] In the formula: t is time; Let A be the derivative of the state variable with respect to time; let x be the state variable; let B be the input matrix; let u be the input variable; let y be the output variable; let C be the output matrix; and let D be the feedforward matrix.

[0086] In order to improve the response speed and quality of the speed control system, proportional feedback control is introduced for the multiple variables contained in the speed control system, and the state space equation of the speed control system with multivariable feedback loop is established.

[0087] After introducing multivariable feedback control, the relationship between the input signal and the state variable is shown in equation (1-3):

[0088] u(t)=r(t)-Kx(t),K∈R 1×n (1-3)

[0089] In the formula, K is the coefficient matrix composed of the proportional coefficients of the multivariable feedback loop; r is the new input variable of the system defined after the introduction of feedback control;

[0090] Substituting equation (1-3) into equation (1-2), we obtain the state-space equation of the speed control system after introducing state feedback:

[0091]

[0092] According to formula (1-4), the system state matrix A-BK after introducing state feedback is obtained. Through analysis of the state matrix, it can be seen that the real and imaginary parts of the speed regulation system poles are related to the K matrix parameters. That is, the configuration of the turbine speed regulation system poles can be achieved by changing the proportional coefficient of the feedback loop. According to the correspondence between the speed regulation system poles and the system response characteristics, it can be seen that adjusting the leftward shift of the real part of the dominant oscillation pole can improve the response speed and ensure that the damping ratio is between 0.5 and 0.7 to prevent overshoot or oscillation. Therefore, the system response characteristics can be improved by adjusting the K matrix parameters.

[0093] The multivariable feedback turbine speed control method proposed in this invention introduces multivariable feedback into the traditional turbine governor, using proportional control in the feedback loop. By adjusting the parameters of the multivariable feedback loop, system pole configuration is achieved, the system damping ratio is adjusted, and the turbine frequency response speed is improved, thereby optimizing the turbine's performance in primary frequency regulation. Compared with new control structures and parameter design methods based on adaptive control and sliding mode control theories, this method features high reliability, convenient control, and ease of implementation.

[0094] Example 3:

[0095] This invention discloses a control method for optimizing the speed regulation performance of a hydro turbine using multivariable feedback. This method comprises a traditional hydro turbine speed regulation system and a multivariable feedback control loop. The multivariable feedback control loop is designed based on a proportional element. The introduction of the multivariable feedback control loop can optimize the system's response characteristics based on the original system regulation, thereby improving the response speed of the hydro turbine speed regulation system during speed regulation and reducing system feedback.

[0096] To illustrate the effectiveness of this technical solution in more detail, specific engineering examples are provided below.

[0097] In actual operation, measurable variables include guide vane opening, head, flow rate, mechanical power, and output frequency.

[0098] Based on the speed governor of a certain hydropower unit, a feedback control loop for head, flow rate and output frequency was added. The speed regulation system after introducing multivariable feedback was modeled and simulated to verify the effectiveness of the invention.

[0099] In the turbine speed control system model, K p1 K I1 K D1 These are the PID parameters of the speed controller, T d1 b is the differential constant. p T is the permanent slip coefficient. y K is the reaction time constant of the relay. f1 K f2 K f3 These are the proportional coefficients for the head feedback, flow feedback, and output frequency feedback loops, respectively. After introducing multivariable feedback control, the relationship between the system frequency deviation signal and the guide vane opening command value is as follows:

[0100]

[0101] In the formula: Δf is the frequency deviation signal; s is the Laplace operator; H is the head parameter; Q is the unit flow rate; f is the generator output frequency; y PIDThe PID controller outputs the opening command value;

[0102] The transfer function of the servo system is as follows:

[0103]

[0104] In the formula: G s T is the transfer function of the servo system; y s is the time constant of the relay action; s is the Laplace operator;

[0105] Figure 3 The simulation block diagram of the water turbine and its water intake system is shown below. Considering the rigid water hammer model, the transfer function of the water intake system is as follows:

[0106] G y =-T w s (1-7)

[0107] In the formula: G y T is the transfer function of the water diversion system; w Let be the time constant for the water hammer effect; s be the Laplace operator; where e y =1,e h =1.5, e qy =1,e qh =0.5;

[0108] The transfer function of the generator and load is:

[0109]

[0110] In the formula: G f T is the transfer function of the generator and load; a e is the inertial time constant; n e is the comprehensive self-regulation coefficient of the hydro-generator unit. n =e g -e x The value ranges from 0 to 2; e g e is the generator load self-regulation coefficient; x This is the torque-to-speed transmission coefficient;

[0111] Based on the above relationships, the transfer function of the multivariable feedback speed regulation system of the water turbine can be established, and simulation can be performed based on the model and the transfer function.

[0112] Figure 4 The multivariable feedback speed control system for a water turbine is composed of the aforementioned governor, servo system, turbine and water intake system, generator and load model, as well as feedback loops for head, flow rate and output frequency.

[0113] Figure 5The diagram shows the simulation structure of a turbine speed control system incorporating multivariable feedback. Based on the above steps, the simulation process of the turbine speed control system with multivariable feedback is as follows: The state-space equation of the multivariable feedback speed control system is established using the integrator output as the state variable. In this process, the differential element in the PID controller is equivalent to a parallel proportional element and an inertial element. For the turbine and water intake system, the head parameters are retained, and only the rigid water hammer model is transformed. When establishing the state-space equation, the algebraic relationship H = f(x2, x3) between the state variables x2 and x3 and the head is used to replace the head parameters. Due to the influence of the rigid water hammer model transfer function, the flow feedback loop is equivalent to an integral loop, operating in parallel with the head feedback loop. The state-space equation of the multivariable feedback control is shown below:

[0114]

[0115] In the formula: F is the input frequency setpoint, M g0 For load power disturbance;

[0116] Based on the state-space equations, the state matrix of the multivariable feedback turbine speed control system is obtained. The poles of the turbine speed control system can be solved using the formula sI-A. The positions of the system poles in the S-plane and K are then determined. f1 K f2 K f3 The value of is related to the position of the characteristic root of the speed control system in the S-plane, so the response performance of the speed control system can be adjusted by changing the parameters of the state feedback loop.

[0117] After adjusting the feedback loop parameters, the optimization effect of introducing multivariable feedback on the response characteristics of the turbine speed control system can be obtained based on the frequency response curve.

[0118] Figure 6 Simulation curves of the frequency response process of a traditional turbine speed control system and a speed control system incorporating head, flow rate, and output frequency variable feedback are presented for comparison. The input frequency is set to 0.5 pu, and the output is the frequency response of the speed control system. The figures show that the traditional turbine speed control system, due to mechanical limitations, has a relatively slow frequency response, failing to meet the rapid frequency support requirements of the power grid for hydropower generation under large-scale renewable energy grid integration. However, with the introduction of multivariable feedback control, the turbine speed control system exhibits a significantly improved frequency response speed and better dynamic performance, enabling faster frequency dynamic response, thus improving the frequency support requirements of hydropower generation for the power grid and reducing the impact of frequency fluctuations caused by large-scale renewable energy grid integration.

Claims

1. A method for optimizing the speed control of a hydro turbine based on multivariable feedback, characterized in that, Includes the following steps: Step 1: Establish a model of the turbine speed control system. Based on the model, obtain the transfer functions G for the governor, servo system, turbine and water intake system, generator and load, respectively. t G s G y and G f ; Step 2: The open-loop transfer function G1 of the closed-loop system consisting of the governor, servo system, turbine and water intake system, generator and load is used to form output feedback with the output frequency of the speed regulation system as the feedback variable, and a traditional turbine speed regulation system model is established. Step 3: Select the measurable variables in the actual operation of the turbine speed regulation system, and feed the selected variables back to the relay command value to form a multivariable feedback speed regulation system; Step 4: Establish the multivariable feedback state space equation based on the multivariable feedback speed regulation system of the turbine. Based on the obtained system state matrix, improve the response speed of the turbine speed regulation system when meeting the primary frequency regulation requirements of the power grid by designing the parameters of the multivariable feedback loop, and reduce the power back-regulation that occurs during the system response to a certain extent, so that the multivariable feedback turbine speed regulation system can obtain better frequency response characteristics and higher response quality.

2. The method for optimizing turbine speed control based on multivariable feedback according to claim 1, characterized in that, The turbine speed control system comprises four basic components: governor, servo system, turbine and water intake system, generator and load. The speed governor section adopts the microcomputer speed governor commonly used in the operation of water turbine units. The input is a manually set frequency specification value. The output frequency of the generator and load is fed back to the input side through the frequency measurement circuit and the difference with the given frequency is used to obtain the frequency error signal of the speed governor system. When the amplitude of the error signal exceeds the manual frequency dead zone, the speed governor system will start to operate. After the error signal is adjusted by the PID controller, the relay stroke command value is output. The follow-up system is the main operating link of the turbine. This part receives the stroke command value of the servo and adjusts the opening of the turbine guide vanes, thereby affecting the changes in head, flow rate and mechanical power parameters. Since the reaction time constant of the auxiliary servo is much smaller than that of the main servo, in order to simplify the turbine speed regulation system model, the inertial link dominated by the reaction time constant of the main servo is used to replace the follow-up system.

3. The method for optimizing turbine speed control based on multivariable feedback according to claim 2, characterized in that, The turbine and entrainment system's flow rate and head parameters change due to variations in guide vane opening, which in turn affects the turbine's output torque. This part is modeled based on the turbine's external characteristic formula (1-1). Due to its strong nonlinearity, a linearized model is used for the study. To simplify the analysis, a rigid water hammer model is adopted for the entrainment system, and the influence of speed variation on the turbine's flow rate is ignored, i.e., e qx =0; Formulas for the external characteristics of a water turbine: In the formula: s is the Laplace operator; M t To output mechanical torque for the prime mover of the water turbine; e y Y is the torque transfer coefficient of the turbine to the guide vane opening; Y is the turbine guide vane opening; e x The torque-to-speed transmission coefficient is given by X; X is the generator output speed; e h The torque-to-head transmission coefficient of the turbine; H is the head; Q is the flow rate; e qy e is the turbine flow rate transfer coefficient to the guide vane opening. qx e is the turbine flow rate to speed transfer coefficient; qh The turbine flow rate is the coefficient of head transfer. The turbine changes the speed of the generator connected to it by changing the output mechanical torque, thereby affecting the generator's output power and output frequency; The generator and load are modeled as a first-order generator, and the torque-to-speed transfer coefficient e is used. x With load self-adjustment coefficient e g Merge, and the merged result is adjusted by the coefficient e. n replace.

4. The method for optimizing turbine speed control based on multivariable feedback according to claim 3, characterized in that, Multivariable feedback control adopts the design concept of state feedback loop, with proportional element as the main form of feedback loop. The selected variable is amplified by the proportional element and then input to the relay command value. Together with the output command of the original turbine speed regulation system PID governor, it changes the guide vane opening of the servo system, thereby achieving the effect of multivariable control system output frequency and output power, and thus improving the system response speed.

5. The method for optimizing turbine speed control based on multivariable feedback according to claim 4, characterized in that, The specific process of the multivariable feedback control method is as follows: Establish the state-space equations based on the traditional turbine speed control system: In the formula: t is time; Let A be the derivative of the state variable with respect to time; let x be the state variable; let B be the input matrix; let u be the input variable; let y be the output variable; let C be the output matrix; and let D be the feedforward matrix. In order to improve the response speed and quality of the speed control system, proportional feedback control is introduced for the multiple variables contained in the speed control system, and the state space equation of the speed control system with multivariable feedback loop is established. After introducing multivariable feedback control, the relationship between the input signal and the state variable is shown in equation (1-3): u(t)=r(t)-Kx(t),K∈R 1×n (1-3) In the formula, K is the coefficient matrix composed of the proportional coefficients of the multivariable feedback loop; r is the new input variable of the system defined after the introduction of feedback control; Substituting equation (1-3) into equation (1-2), we obtain the state-space equation of the speed control system after introducing state feedback: According to formula (1-4), the system state matrix A-BK after introducing state feedback is obtained. Through analysis of the state matrix, it can be seen that the real and imaginary parts of the speed regulation system poles are related to the K matrix parameters. That is, the configuration of the turbine speed regulation system poles can be achieved by changing the proportional coefficient of the feedback loop. According to the correspondence between the speed regulation system poles and the system response characteristics, it can be seen that adjusting the leftward shift of the real part of the dominant oscillation pole can improve the response speed and ensure that the damping ratio is between 0.5 and 0.7 to prevent overshoot or oscillation. Therefore, the system response characteristics can be improved by adjusting the K matrix parameters.

6. The method for optimizing turbine speed control based on multivariable feedback according to claim 5, characterized in that, In actual operation, measurable variables include guide vane opening, head, flow rate, mechanical power, and output frequency.

7. The method for optimizing turbine speed control based on multivariable feedback according to claim 6, characterized in that, The specific process of modeling and simulating the speed control system after introducing multivariable feedback, by adding head, flow rate, and output frequency feedback control loops to the hydropower unit speed governor, is as follows: In the turbine speed control system model, K p1 K I1 K D1 These are the PID parameters of the speed controller, T d1 b is the differential constant. p T is the permanent slip coefficient. y K is the reaction time constant of the relay. f1 K f2 K f3 These are the proportional coefficients for the head feedback, flow feedback, and output frequency feedback loops, respectively. After introducing multivariable feedback control, the relationship between the system frequency deviation signal and the guide vane opening command value is as follows: In the formula: Δf is the frequency deviation signal; s is the Laplace operator; H is the head parameter; Q is the unit flow rate; f is the generator output frequency; y PID The PID controller outputs the opening command value; The transfer function of the servo system is as follows: In the formula: G s T is the transfer function of the servo system; y s is the time constant of the relay action; s is the Laplace operator; Considering the rigid water hammer model, the transfer function of the water diversion system is as follows: G y =-T w s (1-7) In the formula: G y T is the transfer function of the water diversion system; w Let be the time constant for the water hammer effect; s be the Laplace operator; where e y =1,e h =1.5, e qy =1,e qh =0.5; The transfer function of the generator and load is: In the formula: G f T is the transfer function of the generator and load; a e is the inertial time constant; n e is the comprehensive self-regulation coefficient of the hydro-generator unit. n =e g -e x The value ranges from 0 to 2; e g e is the generator load self-regulation coefficient; x This is the torque-to-speed transmission coefficient; Based on the above relationships, the transfer function of the multivariable feedback speed regulation system of the water turbine can be established, and simulation can be performed based on the model and the transfer function.

8. The method for optimizing turbine speed control based on multivariable feedback according to claim 7, characterized in that, The simulation process of the turbine speed control system with multivariable feedback is as follows: The state-space equation of the multivariable feedback speed control system is established with the integrator output as the state variable. In this system, the differential element in the PID governor is equivalent to a parallel proportional element and an inertial element. For the turbine and water intake system, the head parameters are retained, and only the rigid water hammer model is transformed. When establishing the state-space equation, the algebraic relationship H = f(x2, x3) between the state variables x2 and x3 and the head is used to replace the head parameters. Due to the influence of the rigid water hammer model transfer function, the flow feedback loop is equivalent to an integral loop, operating in parallel with the head feedback loop. The state-space equation of the multivariable feedback control is shown below: In the formula: F is the input frequency setpoint, M g0 For load power disturbance; Based on the state-space equations, the state matrix of the multivariable feedback turbine speed control system is obtained. The poles of the turbine speed control system can be solved using the formula sI-A. The positions of the system poles in the S-plane and K are then determined. f1 K f2 K f3 The value of is related to the position of the characteristic root of the speed control system in the S-plane, so the response performance of the speed control system can be adjusted by changing the parameters of the state feedback loop. After adjusting the feedback loop parameters, the optimization effect of introducing multivariable feedback on the response characteristics of the turbine speed control system can be obtained based on the frequency response curve.

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