A method for quickly calculating parameter constraints of a hydroelectric generator controller considering nonlinearity of an object

Abstract

A kind of fast calculation method of considering the parameter constraint of hydroelectric generator set controller nonlinearity of object, comprising the following steps: S1, the mathematical model of nonlinear water turbine regulating system is built;S2, the linearization model of nonlinear water turbine regulating system mathematical model is built;S3, the state space equation of linear water turbine regulating system model is obtained;S4, the controller parameter constraint of linear water turbine regulating system model is calculated based on Hopf bifurcation theory;S5, Octave tool is used to build nonlinear water turbine regulating system model;S6, the controller parameter constraint of linear water turbine regulating system model is obtained in combination with dichotomy and the water turbine regulating system simulation model based on Octave tool built.The fast calculation method of considering the parameter constraint of hydroelectric generator set controller nonlinearity of object designed by the application can fully consider the influence of nonlinear link on controller parameter constraint, effectively guarantee the safe and stable operation of hydroelectric generator set.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of safe and stable operation of hydroelectric generating units, and particularly relates to a fast calculation method for parameter constraints of a hydroelectric generating unit controller considering object nonlinearity. BACKGROUND

[0002] As an important hydraulic energy conversion device, hydroelectric generating units play a crucial role in power systems. Parameter optimization of hydroelectric generating unit controllers is of great significance for improving their operating efficiency, stability, and reliability. Before conducting parameter optimization of hydroelectric generating unit controllers, the controller parameter constraints need to be determined first. The conventional approach is to use a simplified linear hydro-turbine governing system model, which results in a large deviation between the obtained controller parameter stability region and the actual one, i.e., it is not suitable as the upper limit of controller parameters in subsequent controller parameter optimization work.

[0003] The nonlinear characteristics of hydroelectric generating unit systems mainly manifest in the complex dynamic responses of hydro-turbine and generator components, the regulating characteristics of the governor, and the changes in factors such as reservoir water level. These nonlinear factors make it difficult for traditional controller parameter constraint calculation methods to meet the requirements of actual engineering, thus a new fast calculation method is needed to consider the impact of these nonlinear factors on controller parameter constraints.

[0004] In recent years, with the rapid development of computer science and artificial intelligence technology, simulation and optimization algorithm-based hydroelectric generating unit controller parameter calculation methods have attracted widespread attention. These methods establish complex mathematical models of hydroelectric generating units and use optimization algorithms to solve them, which can more accurately consider the nonlinear characteristics of the system, thereby obtaining more optimized controller parameters, but still have the problem of being unable to obtain accurate controller parameter upper limits.

[0005] In view of the problem of being unable to consider object nonlinearity in the calculation of hydroelectric generating unit controller parameter constraints, a fast calculation method with important theoretical significance and practical application value is proposed to solve the problem of being unable to fully consider object nonlinearity in the calculation of hydroelectric generating unit controller parameter constraints. SUMMARY

[0006] The technical problem to be solved by the present application is to provide a fast calculation method for parameter constraints of a hydroelectric generating unit controller considering object nonlinearity. The present application constructs a detailed nonlinear hydro-turbine governing system mathematical model and linearizes it to obtain a state space equation. Then, the Hopf bifurcation theory is used to calculate the controller parameter constraints under the linear model, and simulation is performed using the Octave tool, and finally a more accurate controller parameter constraint is obtained through the bisection method. This method can effectively ensure the safe and stable operation of hydroelectric generating units, and provides a general stability criterion applicable to various types of hydroelectric generating units.

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

[0008] A fast calculation method for parameter constraints of hydropower unit controller considering nonlinearity of the plant, the steps are as follows:

[0009] S1, construct the mathematical model of nonlinear turbine regulation system;

[0010] S2, constructing a linearized model of the mathematical model of the nonlinear turbine regulation system;

[0011] S3, obtain the state space equation of the linear turbine regulation system model;

[0012] S4, Calculate the controller parameter constraints of the linear turbine regulation system model based on Hopf bifurcation theory;

[0013] S5, using Octave tool to build nonlinear turbine regulation system model;

[0014] S6, combining the controller parameter constraints of the linear turbine regulation system model, the dichotomy method and the turbine regulation system simulation model built based on the Octave tool to obtain the controller parameter constraints of the hydropower unit.

[0015] Preferably, in step S1, the mathematical model of the nonlinear turbine regulating system constructed includes a nonlinear water diversion system model, a high-order generator model, an excitation system model, a power network model, a speed regulator model, a servo system model and a turbine model.

[0016] The method of step S1 is:

[0017] 1) The process of building the nonlinear water diversion system model is as follows:

[0018] In the one-dimensional simulation of the nonlinear water diversion system model, the nonlinear water diversion system model includes a rigid water hammer model, an elastic water hammer model, and a characteristic model, which can be selected according to the pipeline length and simulation requirements;

[0019] Starting from the basic equations of unsteady flow, the water hammer model of the nonlinear water diversion system model can be derived; the basic equations of unsteady flow include the equations of motion and the continuity equations, and their basic form is:

[0020]

[0021] Where V is the velocity of water in the pipe, H w is the piezometric tube head, f c is the friction coefficient, g is the acceleration due to gravity, D wis the pipe diameter, a is the water hammer velocity, L is the distance measured from the upstream position; α is the angle between the pipe axis and the horizontal plane (positive along the slope);

[0022] If a large fluctuation process is to be simulated, the characteristic line model is more appropriate. Therefore, the nonlinear water diversion system model of the complex turbine regulation system simulation platform adopts the characteristic line model. The characteristic line method solves the problem by introducing the Lagrange factor to transform Equation (1) into an ordinary differential equation. Then, the pipeline is segmented along the characteristic line, and the ordinary differential equation is solved in combination with the boundary conditions. The characteristic line model can be expressed as

[0023]

[0024] 2) The high-order generator model is constructed as follows:

[0025] Without considering the stator transient, taking into account the influence of the rotor damping winding, but ignoring the G winding of the q axis, the classic fifth-order generator model can be expressed as Equations (3) and (4);

[0026]

[0027] 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, transient reactance, subtransient reactance, subtransient potential, open circuit transient time constant, subtransient time constant, stator current component and terminal voltage V of the d-axis respectively. g Quantity; X q 、X q ”、E q '、E q ”、T q0 ”、I q and V q 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 the q-axis respectively; V g 2 =V d 2 +V q 2 ;

[0028] 3) The excitation system model is constructed as follows:

[0029] The first-order excitation system (AVR) model is adopted, as shown in formula (5); considering the deviation of speed and electromagnetic power, the commonly used power system stabilizer (PSS) is adopted in the power control mode, as shown in formula (6); where K a and T r are the excitation system gain and time constant respectively; K s is the gain of PSS; T0, T1 and T2 are the time constants of PSS;

[0030]

[0031]

[0032] 4) The power network model is constructed as follows:

[0033] The power network voltage can be expressed as:

[0034]

[0035] 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;

[0036] The generator and network coordinate transformation expressions are shown in Equation (8). Based on Equations (7) and (8), the overall generator and network model can be constructed in combination with the fifth-order generator model.

[0037]

[0038] 5) The speed regulator model is constructed as follows:

[0039] The speed governor structure of a hydropower station is generally: a controller implemented based on a programmable controller tool + an electro-hydraulic servo system with autonomous closed-loop control. The controller usually adopts a PID parallel structure.

[0040] The transfer function of the linear part of the PID controller is shown in formula (9);

[0041]

[0042] Where: T 1vis 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;

[0043] 6) The servo system model is constructed as follows:

[0044] The servo system contains nonlinear links such as delay, saturation, speed limit, and dead zone, and its linear part transfer function is shown in formula (10);

[0045]

[0046] Among them: K y is the comprehensive amplifier coefficient; T y1 and T y are the reaction time constants of the intermediate servomotor and the main servomotor respectively; t o is the guide vane fully open time; t c1 , t c2 , t c3 Y is the three-stage closing time of the guide vane; c1 and Y c2 The inflection point for the segmented closing of the guide vane opening;

[0047] 7) The turbine model is constructed as follows:

[0048] Based on the neural network, a flow characteristic neural network model (DCNN, Q 11 =Q 11 (n 11 , Y)) and torque characteristic neural network model (TCNN, M 11 =M 11 (n 11 , Y)).

[0049] Preferably, in step S2, the purpose of constructing a linearized model of the nonlinear hydraulic turbine regulating system mathematical model is to replace the complex, nonlinear submodules in the nonlinear hydraulic turbine regulating system mathematical model with linear modules;

[0050] Preferably, a linearized model of the mathematical model of the nonlinear turbine regulating system is constructed by:

[0051] To ensure accuracy, only the nonlinear water diversion system model and turbine model are linearized; the linearized water diversion system model can be expressed as:

[0052] G h (s)=-T w s (11);

[0053] Where: Tw is the water flow inertia time constant.

[0054] The dynamic characteristics of the hydraulic turbine can be expressed by DCNN and TCNN, which are equivalent to the nonlinear functions of guide vane opening Y, rotational speed X and water head H for a Francis turbine:

[0055]

[0056] Considering data conversion, the function relationship between the inputs and outputs of the hydraulic turbine can be expressed as:

[0057]

[0058] M t = f M (n 11 ,Y)D 3 H (14);

[0059] wherein f Q represents the DCNN, and f M represents the TCNN;

[0060] Under the condition of small fluctuation, the partial derivatives of Y, X and H with respect to Q and M t are derived based on Taylor expansion, and the high-order infinitesimal of the second order and above is ignored, so as to obtain the constant algebraic equation of the working point:

[0061]

[0062] wherein 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 the transfer coefficients of M t with respect to X, Y and H respectively; q, m t , x, y and h represent the deviation relative values of Q, M t , X, Y and H respectively.

[0063] Preferably, the specific process of step S3 is: firstly, the differential equations of each sub-module of the linear hydraulic turbine regulating system model are obtained, and then the state space equation of the hydraulic turbine regulating system is obtained by combining the differential equations of each sub-module of the linear hydraulic turbine regulating system model.

[0064] The differential form of the controller equation is:

[0065]

[0066] wherein I e is the output of the integral element, and pc is the power disturbance reference value, m e is the relative value of power change, f is the relative value of frequency change, e p is the adjustment rate;

[0067] According to the above equations, the state space equation of the turbine regulation system is obtained:

[0068]

[0069] Preferably, for the n-order linear turbine regulating system model L-HTRS, its differential equation can be Represented as follows, where x is the matrix of state variables and v is the Hopf bifurcation parameter; the characteristic equation of the Jacobian matrix of L-HTRS at the equilibrium point (x0, v0) is

[0070]

[0071] Where: p i It can be expressed by controller parameters at a specified operating point; λ is the characteristic root;

[0072] According to Hopf bifurcation theory, under critical stability conditions, Equation (18) contains n characteristic roots, of which 2 real parts are 0 and (n-2) real parts are not 0; that is, the L-HTRS characteristic polynomial can be expressed as:

[0073]

[0074] Where: w is the imaginary part of two purely imaginary conjugate complex roots; a i are the coefficients of a polynomial consisting of (n-2) characteristic roots whose real parts are not zero;

[0075] By combining equations (18) and (19), we can solve the characteristic roots that satisfy the critical stability constraints of the L-HTRS controller parameters, and further obtain any K D K is expressed as a fractional equation below P and K I The constraint equations.

[0076] Preferably, the controller parameter constraints of the hydropower unit are obtained by combining the controller parameter constraints of the linear turbine regulation system model, the dichotomy method and the turbine regulation system simulation model constructed based on the Octave tool;

[0077] The controller parameter constraint value of the linear turbine regulation system model is K times (1 <K<1.5)作为控制器参数初始边界条件,然后结合二分法和基于Octave工具构建的非线性水轮机调节系统仿真模型获取水电机组控制器参数约束值;其中,若HTRS的稳定性指标I s <NI , then the large range is stable; I s is the HTRS multivariable integral value in steady state, as shown in formula (20); this stability criterion is general and applicable to any type of hydropower unit; for a stable nonlinear HTRS model, N I = 0; for critically stable or unstable nonlinear HTRS models, N I >0; When applying this criterion, in order to reduce the controller parameter constraint calculation time, take N I =1, t max =100s, t lim =10s;

[0078]

[0079] Where Δx represents the relative change of x, Δm t Indicates m t Δq represents the relative change of q, and I1, I2, and I3 are weight coefficients;

[0080] A computer device comprising:

[0081] one or more processors;

[0082] The processor is configured to store one or more programs;

[0083] When the one or more programs are executed by the one or more processors, a method for quickly calculating parameter constraints of a hydropower unit controller considering object nonlinearity is implemented.

[0084] A computer-readable storage medium stores a computer program, which, when executed, implements a method for quickly calculating parameter constraints of a hydropower unit controller taking into account object nonlinearity.

[0085] The present invention can achieve the following beneficial effects:

[0086] The fast calculation method for controller parameter constraints of a hydropower unit designed in the present invention considering the nonlinearity of the object can fully consider the influence of nonlinear links on controller parameter constraints and effectively ensure the safe and stable operation of the hydropower unit.

[0087] As the core equipment for power generation in hydropower stations, the safe and stable operation of hydropower generators has become an increasingly important focus in the industry. This paper addresses the limitations of traditional PID controllers and advanced control methods and proposes a fast calculation method for hydropower generator controller parameter constraints that takes into account the nonlinearity of the object.

[0088] The beneficial effects of the present invention are that the calculated hydropower unit controller parameter constraints are more accurate, further ensuring the quality of controller parameter optimization work and effectively guaranteeing the safe and stable operation of the hydropower unit. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] The present invention will be further described below with reference to the accompanying drawings and examples:

[0090] Figure 1 Designing steps for the method of the present invention;

[0091] Figure 2 The neural network-based turbine model of the present invention;

[0092] Figure 3 Schematic diagram of the turbine regulating system model of the present invention;

[0093] Figure 4 This is the parameter constraint calculation process of the nonlinear turbine regulation system controller of the present invention. DETAILED DESCRIPTION

[0094] The preferred solution is Figures 1 to 4 As shown, a method for quickly calculating the parameter constraints of a hydropower unit controller considering the nonlinearity of the object is designed by the present invention. The method includes three parts: obtaining the state space equation of the turbine control system, calculating the controller parameter constraints of the linear turbine control system model based on the Hopf bifurcation theory, and obtaining the parameter constraints of the hydropower unit controller based on the nonlinear model. The implementation steps mainly include: constructing a mathematical model of the nonlinear turbine control system; constructing a linearized model of the mathematical model of the nonlinear turbine control system; obtaining the state space equation of the linear turbine control system model; calculating the controller parameter constraints of the linear turbine control system model based on the Hopf bifurcation theory; constructing a nonlinear turbine control system model using the Octave tool; combining the controller parameter constraints of the linear turbine control system model, the dichotomy method, and the turbine control system simulation model constructed based on the Octave tool to obtain the parameter constraints of the hydropower unit controller. The method for quickly calculating the parameter constraints of the hydropower unit controller considering the nonlinearity of the object can fully consider the influence of the nonlinear link on the controller parameter constraints, and effectively ensure the safe and stable operation of the hydropower unit. The specific steps are:

[0095] (1) Construct a mathematical model of the nonlinear turbine regulation system.

[0096] 1) Nonlinear water diversion system model

[0097] In the one-dimensional simulation of the water diversion system, nonlinear water diversion system models include rigid water hammer model, elastic water hammer model and characteristic model, which can be selected according to the pipeline length and simulation requirements.

[0098] Starting from the basic equations of unsteady flow, the water hammer model of the nonlinear water diversion system model can be derived. The basic equations of unsteady flow include the equation of motion and the continuity equation, and their basic form is:

[0099]

[0100] Where V is the velocity of water in the pipe, H w is the piezometric tube head, f c is the friction coefficient, g is the acceleration due to gravity, D w is the pipe diameter, a is the water hammer velocity, L is the distance measured from the upstream position; α is the angle between the pipe axis and the horizontal plane (positive along the slope).

[0101] If a large fluctuation process is to be simulated, the characteristic line model is more appropriate. Therefore, the nonlinear water diversion system model of the complex turbine regulation system simulation platform adopts the characteristic line model. The characteristic line method solves the problem by introducing the Lagrange factor to transform Equation (1) into an ordinary differential equation. Then, the pipeline is segmented along the characteristic line, and the ordinary differential equation is solved in combination with the boundary conditions. The characteristic line model can be expressed as

[0102]

[0103] 2) High-order generator model

[0104] Without considering the stator transient, taking into account the influence of the rotor damping winding, but ignoring the G winding of the q-axis, the classic fifth-order generator model can be expressed as Equations (3) and (4).

[0105]

[0106] 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, transient reactance, subtransient reactance, subtransient potential, open circuit transient time constant, subtransient time constant, stator current component and terminal voltage V of the d-axis respectively. g Quantity. X q 、X q ”、Eq '、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 the q axis respectively. g 2 =V d 2 +V q 2 .

[0107] 3) Excitation system model

[0108] The first-order excitation system (AVR) model is adopted, as shown in Equation (5). Considering the deviation of speed and electromagnetic power, the commonly used power system stabilizer (PSS) is adopted in the power control mode, as shown in Equation (6). a and T r are the excitation system gain and time constant respectively; K s is the gain of PSS; T0, T1, and T2 are the time constants of PSS.

[0109]

[0110] 4) Power network model

[0111] The power network voltage can be expressed as:

[0112]

[0113] 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.

[0114] The coordinate transformation expressions of the generator and network are shown in Equation (8). Based on Equations (7) and (8), the overall model of the generator and network can be constructed by combining the fifth-order generator model.

[0115]

[0116] 5) Governor model

[0117] The speed regulator structure of a hydropower station is generally: a controller implemented based on a programmable controller tool + an electro-hydraulic servo system with autonomous closed-loop control, and its controller mostly adopts a PID parallel structure.

[0118] The transfer function of the linear part of the PID controller is shown in formula (9).

[0119]

[0120] 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 the proportional, integral and derivative gains respectively.

[0121] 6) Servo system model

[0122] The servo system contains nonlinear links such as delay, saturation, speed limit, and dead zone. The transfer function of its linear part is shown in formula (10).

[0123]

[0124] Among them: K y is the comprehensive amplifier coefficient; T y1 and T y are the reaction time constants of the intermediate servomotor and the main servomotor respectively; t o is the guide vane fully open time; t c1 , t c2 , t c3 Y is the three-stage closing time of the guide vane; c1 and Y c2 It is the inflection point for the segmented closing of the guide vane opening.

[0125] 7) Turbine model

[0126] Based on the neural network, a flow characteristic neural network model (DCNN, Q 11 =Q 11 (n 11 , Y)) and torque characteristic neural network model (TCNN, M 11 =M 11 (n 11 , Y)).

[0127] (2) Construct a linearized model of the mathematical model of the nonlinear turbine regulation system.

[0128] To ensure accuracy, only the nonlinear water diversion system model and turbine model are linearized. The linearized model of the water diversion system can be expressed as:

[0129] G h (s)=-T w s (11);

[0130] Where: T w is the water flow inertia time constant.

[0131] The dynamic characteristics of a turbine can be approximated by DCNN and TCNN. For a Francis turbine, they are equivalent to nonlinear functions of guide vane opening Y, speed X, and water head H:

[0132]

[0133] Considering data conversion, the functional relationship between turbine input and output can be expressed as:

[0134]

[0135] M t =f M (n 11 ,Y)D 3 H (14);

[0136] Among them, f Q represents DCNN, f M represents TCNN.

[0137] 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 Y, X, and H, and ignoring higher-order traces above the second order, we can obtain the algebraic equation with constant coefficients at this operating point:

[0138]

[0139] 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.

[0140] (3) Obtain the state space equation of the linear turbine regulation system model.

[0141] The differential form of the controller equation is:

[0142]

[0143] Among them, Ie is the output of the integral link, p c is the power disturbance reference value, m e is the relative value of power change, f is the relative value of frequency change, e p The adjustment rate.

[0144] According to the above equations, the state space equation of the turbine regulation system is obtained:

[0145]

[0146] (4) Calculate the controller parameter constraints of the linear turbine regulation system model based on Hopf bifurcation theory.

[0147] For the n-order linear turbine regulating system model L-HTRS, its differential equation can be used Represented as follows, where x is the matrix of state variables and v is the Hopf bifurcation parameter [9] The characteristic equation of the Jacobian matrix of L-HTRS at the equilibrium point (x0, v0) is

[0148]

[0149] Where: p i It can be expressed by controller parameters at a specified operating point; λ is the characteristic root.

[0150] According to Hopf bifurcation theory, under critical stability conditions, Equation (18) contains n characteristic roots, of which 2 real parts are 0 and (n-2) real parts are not 0. That is, the L-HTRS characteristic polynomial can be expressed as:

[0151]

[0152] Where: w is the imaginary part of two purely imaginary conjugate complex roots; a i are the coefficients of a polynomial consisting of (n-2) characteristic roots whose real parts are not zero.

[0153] By combining equations (18) and (19), we can solve the characteristic roots that satisfy the critical stability constraints of the L-HTRS controller parameters, and further obtain any K D K is expressed as a fractional equation below P and K I The constraint equations.

[0154] (5) Use Octave tool to construct a nonlinear turbine regulation system model.

[0155] Octave tool is used to construct a nonlinear water diversion system model, a high-order generator model, an excitation system model, a power network model, a speed regulator model, a servo system model and a turbine model.

[0156] (6) The controller parameter constraints of the hydropower unit are obtained by combining the controller parameter constraints of the linear turbine regulation system model, the dichotomy method and the turbine regulation system simulation model built based on the Octave tool.

[0157] The controller parameter constraint value of the linear turbine regulation system model is K times (1 <K<1.5)作为控制器参数初始边界条件,然后结合二分法和基于Octave工具构建的非线性水轮机调节系统仿真模型获取水电机组控制器参数约束值。其中,若HTRS的稳定性指标I s <N I , then the large range is stable. s is the HTRS multivariable integral value in steady state, as shown in Equation (20). This stability criterion is general and applicable to any type of hydropower unit. For a stable nonlinear HTRS model, N I = 0; for critically stable or unstable nonlinear HTRS models, N I > 0. When applying this criterion, in order to reduce the controller parameter constraint calculation time, take N I =1, t max =100s, t lim =10s.

[0158]

[0159] Where Δx represents the relative change of x, Δm t Indicates m t , Δq represents the relative change of q, and I1, I2, and I3 are weight coefficients.

[0160] To address the limitations of traditional PID controllers and advanced control methods, this paper proposes a fast calculation method for hydropower unit controller parameter constraints that takes into account plant nonlinearity, facilitating controller parameter optimization. This method provides highly accurate controller parameter constraint values ​​for controller parameter optimization, thereby improving the quality of hydropower unit controller parameter optimization.

[0161] In addition, the present invention also protects a computer device, comprising:

[0162] one or more processors;

[0163] The processor is configured to store one or more programs;

[0164] When the one or more programs are executed by the one or more processors, a method for quickly calculating parameter constraints of a hydropower unit controller considering object nonlinearity is implemented.

[0165] A computer-readable storage medium stores a computer program, which, when executed, implements a method for quickly calculating parameter constraints of a hydropower unit controller taking into account object nonlinearity.

[0166] The above embodiments are merely preferred technical solutions of the present invention and should not be construed as limiting the present invention. The scope of protection of the present invention shall be the technical solutions set forth in the claims, including equivalent alternatives to the technical features of the technical solutions set forth in the claims. In other words, equivalent alternatives and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A method for quickly calculating the parameter constraints of a hydropower unit controller considering the nonlinearity of the plant, comprising the following steps: S1, construct the mathematical model of nonlinear turbine regulation system; S2, constructing a linearized model of the mathematical model of the nonlinear turbine regulation system; S3, obtain the state space equation of the linear turbine regulation system model; S4, Calculate the controller parameter constraints of the linear turbine regulation system model based on Hopf bifurcation theory; S5, using Octave tool to build nonlinear turbine regulation system model; S6, combining the controller parameter constraints of the linear turbine regulation system model, the dichotomy method and the turbine regulation system simulation model built based on the Octave tool to obtain the controller parameter constraints of the hydropower unit; In step S1, the mathematical model of the nonlinear hydraulic turbine regulating system is constructed, including a nonlinear water diversion system model, a high-order generator model, an excitation system model, a power network model, a speed governor model, a servo system model, and a hydraulic turbine model; In step S2, the linearization model of the nonlinear hydraulic turbine regulating system mathematical model is constructed for the purpose of replacing the complex and nonlinear submodules in the nonlinear hydraulic turbine regulating system mathematical model with linear modules.

2. A method for fast calculation of controller parameter constraints of a hydropower unit considering object nonlinearity according to claim 1, characterized in that: The method of step S1 is: 1) The process of building the nonlinear water diversion system model is as follows: In the one-dimensional simulation of nonlinear water diversion system model, the nonlinear water diversion system model includes rigid water hammer model, elastic water hammer model and characteristic model; Starting from the basic equations of unsteady flow, the water hammer model of the nonlinear water diversion system model is derived; the basic equations of unsteady flow include the equation of motion and the continuity equation, and their basic form is: (1)； in, V is the flow rate of water in the pipe, H w is the piezometric tube head, f c is the coefficient of friction, g is the acceleration due to gravity, D w is the pipe diameter, a is the water hammer velocity, L is the distance measured from the upstream location; α is the angle between the pipe axis and the horizontal plane; If a large fluctuation process is to be simulated, the characteristic line model is more appropriate. Therefore, the nonlinear water diversion system model of the complex turbine regulation system simulation platform adopts the characteristic line model. The characteristic line method solves the problem by introducing the Lagrange factor to transform Equation (1) into an ordinary differential equation. Then, the pipeline is segmented along the characteristic line and the ordinary differential equation is solved in combination with the boundary conditions. The characteristic line model is expressed as (2)； 2) The high-order generator model is constructed as follows: Without considering the stator transient, the influence of the rotor damping winding is considered, but the q Axis G Winding, the classic fifth-order generator model is expressed as Equations (3) and (4); (3)； (4)； in, ω is the angular velocity of the turbine generator set, is the electromagnetic torque, is the damping coefficient, is the generator power angle, yes ω The reference value, is the generator inertia constant, is the excitation electromotive force; 、 、 、 、 、 、 and They are d Axis synchronous reactance, transient reactance, subtransient reactance, subtransient potential, open-circuit transient time constant, subtransient time constant, stator current components, and terminal voltage Quantity; 、 、 、 、 、 and They are q Shaft synchronous reactance, transient reactance, subtransient reactance, transient emf, subtransient emf, open-circuit subtransient time constant, stator current components, and terminal voltage components; ; 3) The excitation system model is constructed as follows: The first-order excitation system model is adopted, as shown in formula (5); considering the deviation of speed and electromagnetic power, the commonly used power system stabilizer is adopted in the power control mode, as shown in formula (6); where, K a and T r are the excitation system gain and time constant respectively; K s is the gain of PSS; T 0. T 1 and T 2 is the time constant of PSS; (5)； (6)； 4) The power network model is constructed as follows: The power network voltage is expressed as: (7)； Among them: For infinite power grid, V s Almost a constant value; and is the network voltage; is the sum of the resistance of the transformer, line and load; is the sum of the impedances of the transformer, line, and load; and is the network current; The generator and network coordinate transformation expressions are shown in Equation (8). Based on Equations (7) and (8), the overall generator and network model is constructed in combination with the fifth-order generator model. (8)； 5) The speed regulator model is constructed as follows: The speed governor structure of the hydropower station is: a controller implemented based on a programmable controller tool + an electro-hydraulic servo system with autonomous closed-loop control. The controller mostly adopts a PID parallel structure. The transfer function of the linear part of the PID controller is shown in formula (9); (9)； 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 differential gains respectively; 6) The servo system model is constructed as follows: The servo system model contains nonlinear links including delay, saturation, speed limit, and dead zone. The transfer function of its linear part is shown in formula (10); (10)； in: K y is the comprehensive amplifier coefficient; T y1 and T y are the reaction time constants of the intermediate servomotor and the main servomotor respectively; t o is the guide vane fully open time; t c1 、 t c2 、 t c3 The three closing times of the guide vanes; Y c1 and Y c2 The inflection point for the segmented closing of the guide vane opening; 7) The turbine model is constructed as follows: Based on the neural network, a flow characteristic neural network model and a torque characteristic neural network model are constructed, which take the unit speed and guide vane opening as input and the turbine flow and torque as output respectively.

3. The method for fast calculation of controller parameter constraints of a hydropower unit considering object nonlinearity according to claim 2 is characterized by: In step S2, to ensure accuracy, only the nonlinear water diversion system model and the turbine model are linearized; the linearized water diversion system model is expressed as: (11)； Where: T w is the water flow inertia time constant; The dynamic characteristics of the turbine are approximately represented by DCNN and TCNN. For Francis turbines, they are equivalent to the guide vane opening. Y , speed X and water head H A nonlinear function of: (12)； Considering data conversion, the functional relationship between turbine input and output is expressed as: (13)； (14)； in, f Q represents DCNN, f M represents TCNN; Under small fluctuation conditions, the flow rate at a certain operating point is derived based on Taylor expansion Q and torque right Y 、 X and H Taking partial derivatives of equal variables and ignoring higher-order traces above the second order, we can obtain the algebraic equation with constant coefficients at this operating point: (15) in, 、 and They are Q right X 、 Y and H The transfer coefficient of 、 and They are right X 、 Y and H The transfer coefficient of q 、 、 x 、 y and h Respectively Q 、 、 X 、 Y and H The relative value of the deviation.

4. The method for fast calculation of controller parameter constraints of a hydropower unit considering nonlinearity of an object according to claim 1 is characterized by: The specific process of step S3 is as follows: first, the differential equations of each submodule of the linear turbine regulation system model are obtained, and then the differential equations of each submodule of the linear turbine regulation system model are combined to obtain the state space equation of the turbine regulation system; The differential form of the controller equation is: (16)； in, I e is the output of the integration link, p c is the power disturbance reference value, m e is the relative value of power change, f is the relative value of frequency change, e p is the adjustment rate; According to the above equations, the state space equation of the turbine regulation system is obtained: 。 5. The method for fast calculation of controller parameter constraints of a hydropower unit considering nonlinearity of an object according to claim 1, characterized in that: The method of step S4 is: for The differential equation of the L-HTRS is a linear turbine regulation system model. Indicates that is the matrix of state variables, yes Bifurcation parameter; L-HTRS at equilibrium The characteristic equation of the Jacobian matrix at is (18)； Where: It can be expressed by controller parameters at a specified operating point; is the characteristic root; According to Hopf bifurcation theory, under critical stability conditions, Equation (18) contains n characteristic roots, two of which have real parts equal to 0, The real part is not 0; that is, the L-HTRS characteristic polynomial can be expressed as: (19)； Where: w is the imaginary part of two purely imaginary conjugate complex roots; yes The coefficients of the polynomial consisting of the characteristic roots whose real parts are not 0; By combining equations (18) and (19), we can solve the characteristic roots that satisfy the critical stability constraints of the L-HTRS controller parameters, and further obtain any The following fractional equation is expressed as and The constraint equations.

6. The method for fast calculation of controller parameter constraints of a hydropower unit considering nonlinearity of an object according to claim 1, characterized in that: The method of step S6 is: The controller parameter constraint values ​​of the linear turbine regulation system model are K times, where 1< K <1.5, as the initial boundary condition of the controller parameters, and then combine the dichotomy method and the nonlinear turbine regulation system simulation model built based on Octave tool to obtain the constraint value of the hydropower unit controller parameters; Among them, if the stability index of HTRS , then the large range is stable; is the HTRS multivariable integral value in steady state, as shown in formula (20); this stability criterion is general and applicable to any type of hydropower unit; for a stable nonlinear HTRS model, ; For critically stable or unstable nonlinear HTRS models, ; When applying this criterion, in order to reduce the controller parameter constraint calculation time, take 、 、 ; (20)； Where, ∆ x express x The relative change, ∆ m t express m t The relative change, ∆ q express q The relative change of 、 and is the weight coefficient.

7. A computer device, characterized in that: include: one or more processors; The processor is configured to store one or more programs; When the one or more programs are executed by the one or more processors, a method for quickly calculating parameter constraints of a hydropower unit controller taking into account object nonlinearity as described in any one of claims 1 to 6 is implemented.

8. A computer-readable storage medium, characterized in that: A computer program is stored thereon, and when the computer program is executed, a method for quickly calculating parameter constraints of a hydropower unit controller considering object nonlinearity according to any one of claims 1 to 6 is implemented.

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