Method and device for analyzing uncertainty of adjusting process of doubly-fed pumped storage unit

Abstract

The invention belongs to the technical field of doubly-fed variable-speed pumped storage, and particularly discloses a doubly-fed pumped storage unit adjusting process uncertainty analysis method and device. The method comprises the following steps: firstly, establishing a speed regulation-excitation system state-space equation of the doubly-fed pumped storage unit considering initial rotating speed and rotor power response; setting uncertain parameters and distribution characteristics of the uncertain parameters, and substituting the uncertain parameters into the speed regulation-excitation system state-space equation to obtain a speed regulation-excitation system state-space equation under an uncertain framework; selecting an orthogonal polynomial, and performing generalized polynomial chaos expansion on the state-space equation of the speed regulation-excitation system; and finally, obtaining an approximate solution of each state vector in the state-space equation of the speed regulation-excitation system through a numerical solution method, and quantifying the output response statistical characteristics of the state-space equation of the speed regulation-excitation system. According to the method and the device, each state variable of the system can be quickly solved, so that statistical characteristics of output response of the control system are quantified.

Description

Technical Field

[0001] The present application belongs to the technical field of doubly-fed variable-speed pumped storage, and more specifically, relates to a method and device for analyzing uncertainty in the regulation process of a doubly-fed pumped storage unit. Background Art

[0002] With the large-scale integration of renewable energy into the grid, the power system's demand for flexible regulation resources is becoming increasingly urgent. Doubly-fed variable-speed pumped storage, as an advanced pumped storage technology, boasts rapid response and wide-range power regulation capabilities, playing a vital role in grid frequency regulation, peak load regulation, and backup capacity support. However, the regulation process of a doubly-fed variable-speed pumped storage unit involves complex hydro-mechanical-electrical coupled dynamics, often affected by multiple sources of uncertainty, such as hydraulic system nonlinearity, mechanical vibration randomness, and grid perturbation uncertainty. This makes its dynamic response difficult to accurately characterize, posing a potential threat to the unit's safety and reliability. Therefore, research on uncertainty quantification and analysis methods for the regulation process of doubly-fed variable-speed pumped storage units not only helps to reveal the propagation mechanism of multiple sources of uncertainty in the energy conversion process, but also provides theoretical support for high-precision modeling and optimized control. This is of great significance for improving unit operating efficiency and ensuring the safety and stability of the power system.

[0003] Specifically, the control system of a doubly-fed variable-speed pumped-storage unit primarily consists of a pump-turbine speed control subsystem and an excitation control subsystem. These two subsystems, coupled through electromagnetic torque and unit speed, collaboratively accomplish load frequency regulation. However, this regulation process is significantly affected by a variety of operating conditions, involving a large number of fundamental operating parameters. Furthermore, some operating parameters with clear physical meaning exhibit random, nonlinear, time-varying characteristics, exposing the unit's regulation dynamics to significant uncertainty. Therefore, to ensure safe unit operation, research is urgently needed to quantify and analyze the uncertainty of the unit's regulation process, adapting to various operating scenarios. Summary of the Invention

[0004] In response to the above defects or improvement needs of the existing technology, the present application provides a method and device for analyzing the uncertainty of the regulation process of a doubly fed pumped storage unit, the purpose of which is to solve the technical problem that the regulation process of the current doubly fed variable-speed pumped storage unit has great uncertainty.

[0005] To achieve the above objectives, in a first aspect, the present application provides a method for analyzing uncertainty in the regulation process of a doubly-fed pumped storage unit, comprising: Establish the state space equations of the speed regulation-excitation system of the doubly-fed pumped storage unit taking into account the initial speed and rotor power response; Setting uncertainty parameters and their distribution characteristics, bringing the uncertainty parameters into the state space equation of the speed regulation-excitation system, and obtaining the state space equation of the speed regulation-excitation system under the uncertainty framework; Selecting orthogonal polynomials to perform generalized polynomial chaos expansion on the state space equation of the speed regulation-excitation system; By using a numerical solution method, an approximate solution of each state vector in the state space equation of the speed regulation-excitation system is obtained, and the statistical characteristics of the output response of the state space equation of the speed regulation-excitation system are quantified.

[0006] Preferably, establishing a state space equation of the speed regulation-excitation system of a doubly-fed pumped storage unit taking into account the initial speed and rotor power response specifically includes the following sub-steps: Based on the transient hydraulic characteristics of the water diversion system, the water hammer equation is derived and simplified to obtain the transfer function, clarifying the dynamic relationship between head and flow within the water diversion system pipeline; the structure of the doubly fed pumped storage unit is determined, and the dynamic models of the speed governor and relay are established; the flow and torque characteristic equations of the pump turbine are linearized; The voltage-flux equation of the doubly-fed pumped storage unit is established based on the dq coordinate system. The relationship between the flux and current is simplified through the stator flux directional vector control strategy, and the rotor voltage dynamic equation is derived to clarify the control relationship between the electromagnetic torque, power and rotor current. A dual closed-loop control structure consisting of a power outer loop and a current inner loop is designed to achieve precise regulation by eliminating slip frequency interference. Finally, combined with the flow and torque characteristic equations of the pump-turbine, the state-space equation of the speed regulation-excitation system is constructed, which takes into account the initial speed and rotor power response.

[0007] Preferably, the water level change at the inlet section of the pipe section in the water diversion system and the hydraulic friction loss of the pipeline are ignored, and the water hammer equation is simplified to obtain the transfer function.

[0008] Preferably, the voltage-flux equation of the doubly fed pumped storage unit is established based on the dq coordinate system, specifically: combining the characteristics of the doubly fed pumped storage unit that the stator is directly connected to the power grid and the rotor is excited by the converter, ignoring the influence of the motor magnetic circuit saturation loss, hysteresis loss, eddy current and core loss on the motor performance parameters, and establishing the voltage-flux equation in the dq coordinate system.

[0009] Preferably, the stator flux oriented vector control strategy is specifically as follows: the d-axis in the synchronous rotating coordinate system coincides with the stator magnetic field of the motor, and the direction of 90° counterclockwise rotation is used as the q-axis direction.

[0010] Preferably, the dual closed-loop control structure of the power outer loop and the current inner loop is specifically as follows: In the power outer loop control, the power deviation is converted into the rotor current q-axis reference value and d-axis reference value through the PI controller; in the current inner loop control, the current coaxial dynamic term adopts the PI controller, and the non-coaxial interference term adopts the feedforward compensation algorithm to generate the rotor voltage control equation.

[0011] Preferably, the state space equation of the speed regulation-excitation system is specifically:

[0012]

[0013]

[0014]

[0015]

[0016]

[0017]

[0018]

[0019]

[0020]

[0021] matrix Other elements is zero; in, is the state vector; is the output vector; is the input vector, 、 and is the corresponding matrix; yes First derivative with respect to time; Represents matrix transpose; is the servomotor time constant; is the water flow inertia time constant; is the inertia constant of the unit; is the equivalent inertia constant of the power grid; is the initial value of the unit torque; is the turbine flow to speed transfer coefficient; is the transfer coefficient of turbine flow to guide vane opening; is the turbine flow to working head transfer coefficient; is the turbine torque to speed transfer coefficient; is the transfer coefficient of turbine torque to guide vane opening; is the transfer coefficient of turbine torque to working head; is the unit sub-regulation coefficient; is the stator flux amplitude; is the number of motor pole pairs; is the initial value of the unit speed; is the frequency adjustment coefficient; is the frequency controller proportional gain, is the frequency controller integral gain, is the power controller proportional gain, is the power controller integral gain.

[0022] Preferably, the uncertainty parameters and their distribution characteristics are set, specifically: the water flow inertia time constant is selected , relay time constant , initial value of unit torque , unit inertia constant , grid equivalent inertia constant , Initial value of unit speed and the unit sub-regulation coefficient As the uncertainty parameter, the uncertainty parameter satisfies the normal distribution.

[0023] Preferably, an orthogonal polynomial is selected to perform a generalized polynomial chaos expansion on the state space equation of the speed regulation-excitation system; specifically: After expanding all state vectors and inserting them into the state space equation of the speed regulation-excitation system, we can obtain:

[0024] in, is the orthogonal function expansion; is the state vector, yes The first derivative with respect to time, Represents the state vector Serial number, , is the order of expansion; is the finite order of the expansion; is a random variable that follows a specific distribution; It's about Orthogonal polynomials of ; Multiply both sides of the equation , using orthogonality, for random variables Taking the expectation of the support set of , we get:

[0025] definition As the mass matrix, the general coefficient equation reflecting the state of the control system is obtained:

[0026] in, are orthogonal polynomial basis functions, and Together they form an orthogonal basis for the random process; Express expectations.

[0027] In a second aspect, the present application provides a device for analyzing uncertainty in the regulation process of a doubly-fed pumped storage unit, comprising: A model building module for establishing the state-space equations of the speed regulation and excitation system of a doubly-fed pumped storage unit, taking into account the initial speed and rotor power response; An uncertainty introduction module is used to set uncertainty parameters and their distribution characteristics, and introduce the uncertainty parameters into the state space equation of the speed regulation-excitation system to obtain the state space equation of the speed regulation-excitation system under the uncertainty framework; An expansion module, used for selecting an orthogonal polynomial and performing a generalized polynomial chaos expansion on the state space equation of the speed regulation-excitation system; The state solving module is used to obtain the approximate solution of each state vector in the state space equation of the speed regulation-excitation system through a numerical solution method, and quantify the output response statistical characteristics of the state space equation of the speed regulation-excitation system.

[0028] In general, the above technical solutions conceived by this application have the following beneficial effects compared with the existing technologies: (1) This paper establishes the state space equations of the speed regulation-excitation control system of a doubly-fed variable-speed pumped storage unit. In the derivation process, the model fully considers the comprehensive influence of the initial speed and rotor power response on the dynamic behavior of the system, improves the dynamic analysis framework of the existing variable-speed pumped storage unit, and also lays a reliable mathematical foundation for the subsequent uncertainty quantification analysis. It has important theoretical value and engineering application significance.

[0029] (2) By constructing a comprehensive mathematical model and introducing a generalized polynomial chaos expansion method, this invention can rapidly solve the system's state variables, thereby quantifying the statistical characteristics of the output response of the speed-excitation control system of a doubly-fed variable-speed pumped-storage unit. Compared with the traditional Monte Carlo method, the calculation time is significantly reduced while ensuring accuracy, facilitating the analysis of the impact of multidimensional uncertainty parameters on the system's dynamic behavior, and providing a reliable quantitative basis for unit design and optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a flow chart of an uncertainty analysis method for a doubly-fed pumped storage unit regulation process provided in an embodiment of the present application.

[0031] Figure 2 This is a schematic diagram of the doubly-fed generator side power control system provided in an embodiment of the present application.

[0032] Figure 3 This is a block diagram of the linearized control of unit load regulation provided in an embodiment of the present application.

[0033] Figure 4 This is a block diagram of the linearized control of unit load regulation provided in an embodiment of the present application.

[0034] Figure 5 This is a diagram of the unit state polynomial expansion quantification and analysis framework provided in the embodiment of the present application.

[0035] Figure 6 This embodiment of the present application provides T w 、 T y 、 T e1 and Schematic diagram of parameter uncertainty set.

[0036] Figure 7 This embodiment of the present application provides T a 、 T a1 、 e g Schematic diagram of parameter uncertainty set.

[0037] Figure 8 This is a comparison chart of the mean values ​​of the unit speed uncertainty response provided in the embodiment of the present application.

[0038] Figure 9 This is a comparison chart of the unit speed uncertainty response variance provided by the embodiment of the present application.

[0039] Figure 10 This is an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0040] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0041] The embodiment of the present application provides a method for analyzing uncertainty in the regulation process of a doubly-fed pumped storage unit, the process of which is as follows: Figure 1 As shown, the following steps are included: Step 1: Establish mathematical models of the doubly-fed pumped storage unit's water diversion system, pump-turbine model, speed governor, servo system, and doubly-fed generator and its control system, and derive the speed regulation-excitation system control equations taking into account the initial speed and rotor power response.

[0042] Step 1.1: Based on the continuity equation and momentum equation for the hydraulic transient flow inside the unit water diversion system pipeline, the relationship between the flow rate and water hammer pressure at section ab of the water diversion system pressure pipe section is expressed as follows:

[0043]

[0044]

[0045] in, and It is a pressure pipe a Cross-section and b The water head of the cross section, and It is a pressure pipe a Cross-section and b Flow rate of the section; is the Laplace operator; It is a pressure pipe a Section to b distance of the cross section; is the propagation operator; is the characteristic impedance of the pipeline; is the hyperbolic sine function; is the hyperbolic cosine function; is the wave velocity of the water shock wave; is the hydraulic friction coefficient of the pipe; is the unit design flow rate; is the pipe diameter; is the cross-sectional area of ​​the pipe; is the acceleration due to gravity; It is the design water head of the unit.

[0046] Further ignoring the water level change at the pipe inlet section and the hydraulic friction loss of the pipeline, the transfer function expression of the water hammer equation of the water diversion system is obtained as follows:

[0047] in, is the pipeline characteristic parameter, ; The water hits each other, , is the pipe length.

[0048] The speed control system controller and servo subsystem of the doubly-fed pumped storage unit have the same structure as the conventional pumped storage unit, and its action equation can be written as:

[0049]

[0050] in, is the relative deviation value of the unit speed; It’s time; is the unit speed reference value; is the actual speed of the unit; It is the adjustment amount of the unit speed governor; is the governor proportional control gain; is the governor integral control gain; is the action equation of the relay; is the magnification factor; is the reaction time constant of the main relay; is the reaction time constant of the auxiliary servomotor; is the relative value of the guide vane opening deviation; is the guide vane opening correction function; It is the relay action state.

[0051] The linearized expression of the flow-torque characteristic equation of the pump-turbine is:

[0052] in, is the relative value of turbine flow deviation; is the turbine flow to speed transfer coefficient; is the transfer coefficient of turbine flow to guide vane opening; is the turbine flow to working head transfer coefficient; is the relative value of speed deviation; is the relative value of the guide vane opening deviation; is the relative value of turbine head deviation; is the relative value of turbine torque deviation; is the turbine torque to speed transfer coefficient; is the transfer coefficient of turbine torque to guide vane opening; It is the transfer coefficient of turbine torque to working head.

[0053] Step 1.2: Unlike the traditional way synchronous motors in pumped-storage units are connected to the grid, the three-phase stator windings of the doubly-fed motor in a variable-speed pumped-storage unit are directly connected to the grid, while the three-phase rotor windings are connected to the grid via a back-to-back converter for AC excitation, thus achieving bidirectional power feeding between the stator, rotor, and grid. Based on the symmetrical three-phase winding distribution and ignoring the effects of motor magnetic circuit saturation, hysteresis losses, eddy currents, and core losses on motor performance parameters, the voltage-flux equation for the doubly-fed motor in the dq coordinate system is obtained as follows:

[0054]

[0055] in, are the stator d-axis and q-axis voltage components of the doubly-fed machine; are the rotor d-axis and q-axis voltage components of the doubly-fed machine; are the stator d-axis and q-axis current components of the doubly-fed machine; are the rotor d-axis and q-axis current components of the doubly-fed machine; is the stator resistance; is the rotor resistance; is a differential function; is the stator angular frequency; is the electrical frequency corresponding to the rotor speed; is the slip angular frequency; is the stator d-axis and q-axis flux components; are the rotor d-axis and q-axis magnetic flux components.

[0056] Combined with the corresponding magnetic flux equation, the voltage / current control equation and electromagnetic torque expression are as follows:

[0057]

[0058]

[0059] in, is the motor stator self-inductance; is the motor rotor self-inductance; Mutual inductance between the motor stator and rotor; is the magnetic flux leakage coefficient; It is the control matrix that reflects the voltage / current of the unit; is the electromagnetic torque of the unit; is the number of motor pole pairs.

[0060] Adopting the stator flux orientation vector control strategy, the d-axis of the synchronous rotating coordinate system is aligned with the motor stator magnetic field, and the direction of the q-axis is rotated 90° counterclockwise. According to the conversion relationship between the coordinate systems, the vector in the synchronous rotating coordinate system is defined as , then the stator flux in the synchronous rotating coordinate system can be expressed as:

[0061] in, is the magnetic flux vector; is the stator flux amplitude; is the base of natural logarithms; , is the synchronous rotation angle, is the synchronous rotation angle estimate; is the imaginary number symbol; is a vector in the synchronously rotating coordinate system; is the q-axis component of the vector; is the d-axis component of the vector.

[0062] Further simplification yields the magnetic flux and current equations in the synchronously rotating coordinate system:

[0063]

[0064] in, is the stator flux amplitude; is the general excitation current; when the grid is operating normally, since the stator of the unit is directly connected to the grid, the stator voltage and stator flux amplitude is constant, so It can usually be considered a constant.

[0065] Substituting the simplified flux equation into the motor rotor voltage control equation, we get:

[0066] The corresponding torque and power expressions are:

[0067]

[0068] in, is the electromagnetic torque of the unit; is the active power; is the reactive power; is the number of motor pole pairs.

[0069] Step 1.3: Use corresponding controllers for the power outer loop and rotor current inner loop of the doubly fed generator to achieve set value tracking. The control variables of the active and reactive power outer loops are the q-axis and d-axis rotor currents, respectively. The control equations are:

[0070]

[0071] and are the q-axis and d-axis reference values ​​of the rotor current, is the power controller proportional gain, is the power controller integral gain, It is the reference value for the active power regulation of the unit. is the reactive power regulation reference value of the unit, and s is the Laplace operator.

[0072] In the current inner loop control, the current coaxial dynamic term adopts the PI controller, and the non-coaxial interference term adopts the feedforward compensation algorithm. The rotor voltage control equation is:

[0073] in, and is the control parameter of the current inner loop PI controller.

[0074] Further considering the frequency control module and ignoring the current command calculation process, the active power regulation linearization equation of the doubly fed machine excitation system is obtained as follows:

[0075] in, is the torque equation of the unit; is the unit frequency regulation equation; is the motor frequency regulation response equation; is the frequency controller proportional gain, is the frequency controller integral gain, is the power controller proportional gain, is the power controller integral gain; is the Laplace operator; is the frequency adjustment coefficient; is the initial value of the unit torque; and They are the initial value and relative value of the unit speed respectively.

[0076] Combined with the pump-turbine regulation system, the linearized state space equation of the speed regulation-excitation system of the doubly-fed variable-speed pumped storage unit under the deterministic system framework is obtained:

[0077]

[0078]

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086] other is zero; is the state vector; is the output vector; is the input vector; yes First derivative with respect to time; Represents matrix transpose; is the servomotor time constant; is the water flow inertia time constant; is the inertia constant of the unit; is the equivalent inertia constant of the power grid; is the initial value of the unit torque; is the turbine flow to speed transfer coefficient; is the transfer coefficient of turbine flow to guide vane opening; is the turbine flow to working head transfer coefficient; is the turbine torque to speed transfer coefficient; is the transfer coefficient of turbine torque to guide vane opening; is the transfer coefficient of turbine torque to working head; is the unit sub-regulation coefficient; is the stator flux amplitude; is the number of motor pole pairs; is the initial value of the unit speed; is the frequency adjustment coefficient; is the frequency controller proportional gain, is the frequency controller integral gain, is the power controller proportional gain, is the power controller integral gain.

[0087] Step 2: Set the uncertainty parameter range and distribution characteristics of the unit speed regulation-excitation control system, bring the generated uncertain parameter set into the deterministic motion equation, and obtain the dynamic equation of the regulation process of the doubly fed variable-speed pumped storage unit under the uncertain framework.

[0088] Due to the changes in operating conditions, vibrations of the pump-turbine and generator, unbalanced forces, and structural fatigue and aging, the structural and operating parameters are characterized by uncertainty. Based on these considerations, the following seven key operating parameters are selected: 、 、 、 、 、 and As uncertainty parameters, the dynamic response of the control system of the doubly-fed variable-speed pumped storage unit is studied. Since the above basic operating parameters all have original measurement and reference information, they are set to obey the normal distribution:

[0089] in, is a distribution function where the variable are the selected 7 uncertain parameters; is the mean; is the standard deviation; is a natural exponential function.

[0090] Substituting the uncertain parameter set into the unit control equation, the speed regulation-excitation control equation of the doubly-fed variable-speed pumped storage unit under the uncertain framework is obtained as follows:

[0091]

[0092]

[0093]

[0094]

[0095]

[0096]

[0097]

[0098]

[0099] in, represents load disturbance; 、 、 and There are 7 uncertain parameters 、 、 、 、 、 and Uncertain expression of is the state vector First derivative with respect to time; is the proportional gain of the unit speed control system; It is the integral gain of the unit speed control system.

[0100] Step 3: Select orthogonal polynomials, perform generalized polynomial chaos expansion on the uncertain response, and use the Galerkin projection method to obtain the expansion coefficients of each polynomial term.

[0101] Step 3.1: Use the generalized polynomial chaos expansion method to describe the uncertainty of the response state of the double-fed variable-speed pumped storage unit. First, for a state vector x i , we can use a set of orthogonal polynomials To expand:

[0102] in, is a random variable that follows a specific distribution; It's about Orthogonal polynomials of , such as Hermite polynomials or Legendre polynomials; is the expansion coefficient to be solved.

[0103] In actual calculations, the above expansion is truncated to a finite order P :

[0104] Expand all state vectors of the unit system and bring them into the control equation of the doubly fed pumped storage unit to obtain:

[0105] in, is the orthogonal function expansion, yes The first derivative with respect to time.

[0106] The Galerkin projection method is used to transform the governing equation into a deterministic differential equation. Specifically, the original equation is projected into the basis function space and the orthogonality is used to eliminate random variables. , we get the coefficients The deterministic equation.

[0107] Multiply both sides of the expanded control equation above , using orthogonality, for random variables Taking the expectation of the support set of , we get:

[0108]

[0109] in, are orthogonal polynomial basis functions, and Together they form an orthogonal basis for the random process. Express expectations.

[0110] Define the matrix: As the mass matrix, the general coefficient equations reflecting the state of the control system are as follows:

[0111] Step 3.2: Next, the speed state of the double-fed variable-speed pumped storage unit is x Taking 6 as an example, the polynomial expansion process is as follows: Due to the unit operating parameters 、 、 、 、 、 and All obey the normal distribution, so the parameters are defined separately T w 、 T y 、 w r1 、 T a1 、 T e1 、 T a and e g The random variables are as follows:

[0112] Expand the random variable into:

[0113]

[0114]

[0115] At the same time, the generalized polynomial chaos expansion is used for the unit speed and its related state variables: ,

[0116] ,

[0117] in, is a Hermite polynomial, and its general expression is:

[0118] The specific recursive formula is as follows:

[0119] Substituting the expanded form into the state equation, we obtain:

[0120] The superscript of the state vector is Represents an approximation of the state vector.

[0121] The mass matrix is: .

[0122] are polynomial basis functions, and Together they form an orthogonal basis for the random process. Express expectations.

[0123] Due to the orthogonality of Hermite polynomials:

[0124] in, yes The standard deviation of is the order of the Hermite polynomial. And consider and A first-order approximation of :

[0125] The chaotic polynomial expansion of the speed response of the double-fed variable-speed pumped storage unit is obtained as follows:

[0126] Its vector matrix form can be expressed as:

[0127] Among them are:

[0128]

[0129] in is the identity matrix.

[0130] Similarly, other state vectors of the control system can be expanded in sequence using the above process method.

[0131] Step 4: Use numerical solution methods to obtain approximate solutions for each state vector and quickly quantify the statistical characteristics of the output response of the unit speed regulation-excitation control system.

[0132] Considering the combined effect of uncertain parameters, the generalized polynomial chaos expansion method is used to perform uncertainty analysis, calculate the mean and variance of the system output response, achieve rapid quantitative statistical characteristics, and effectively evaluate the dynamic response characteristics of the unit speed regulation-excitation system under the influence of uncertainty.

[0133]

[0134]

[0135] in, is the variance function.

[0136] The technical solution of this application is now introduced through a specific example. Specific data preparation: Select the basic operating data of a double-fed variable-speed pumped storage unit and establish the pump-turbine side speed control system. Figure 2 As shown, the power regulation system on the doubly fed generator side is as follows Figure 3 As shown. Under the stator magnetic field oriented vector control strategy, further simplification results in the transfer function block diagram of current command calculation, current control and electromagnetic torque calculation, as well as the control block diagram of the unit participating in frequency regulation. Figure 4 As shown. Figure 4 It can be seen that the frequency load regulation process of the doubly-fed pumped storage unit takes into account the influence of the unit's initial operating state and rotor dynamic feedback. The obtained doubly-fed variable-speed pumped storage unit model is not only convenient for theoretical analysis and controller design, but also can improve the regulation performance analysis accuracy of the unit's load regulation process under different operating conditions to a certain extent.

[0137] Based on random probability theory, the following seven key operating parameters are selected: 、 、 、 、 、 and As uncertainty input, its parameter characteristics and description are shown in Table 1.

[0138] Table 1

[0139] The above uncertainty parameter set is expanded through Hermite polynomials and brought into the deterministic motion equation to obtain the state expansion of the unit regulation process under the uncertain framework. The inner product of the regulation process expansion is performed and Galerkin projection is performed to obtain the system deterministic differential equation with random input and output characteristics. Then, the Runge-Kutta numerical solution method is used to realize the rapid calculation of the mean and variance of each state quantity in the regulation process. The specific process is as follows: Figure 5 shown.

[0140] In order to illustrate the accuracy of the proposed quantitative analysis method, the Monte Carlo brute force simulation method was used to generate the above 7 parameters. Group parameter sets, , the distribution of the obtained uncertain parameter set is as follows Figure 6 and Figure 7At the same time, the Latin hypercube sampling method is used to jointly generate the parameter space N k Group samples, For each parameter, the cumulative distribution is divided into A value is randomly selected within each interval and the coordinates across the parameters are paired by random permutation to ensure space filling properties. For normally distributed parameters, samples are obtained by inverse transform sampling:

[0141] in, It is The order of the samples in Latin hypercube sampling; is the standard deviation of the normal distribution parameter; is the mean of the normal distribution parameters. are orthogonal polynomials.

[0142] Based on this, Monte Carlo simulation calculation is carried out, and the mean value calculation formula of the state response is obtained as follows:

[0143] in, It is In the Monte Carlo simulation, the system is in state and time The response function value under ; To find the mean function.

[0144] The simulation results obtained by Monte Carlo brute force simulation method are verified and compared with the proposed generalized chaos polynomial expansion method. The obtained dynamic results of the speed of the double-fed variable-speed pumped storage unit are as follows: Figure 8 and Figure 9 As shown. Among them, Figure 8 The time domain variation of the mean value of the unit speed uncertainty response is shown. As can be seen from the figure, the mean curves obtained by the two methods are highly consistent, and the maximum error is less than 3e-4. Figure 9 The variance of the uncertain response of the unit speed was further compared, and the error was maintained at the order of 10e-8. The above results show that the generalized chaos polynomial expansion method shows high accuracy in the random uncertainty analysis of the doubly-fed variable-speed pumped storage unit, can effectively approximate the mean response of high-dimensional random systems, and can effectively replace the more computationally expensive Monte Carlo brute force simulation method, thereby improving the calculation and analysis efficiency of complex random systems.

[0145] The following describes a device for analyzing uncertainty in the regulation process of a doubly-fed pumped-storage unit provided in the present application. The device for analyzing uncertainty in the regulation process of a doubly-fed pumped-storage unit described below and the method for analyzing uncertainty in the regulation process of a doubly-fed pumped-storage unit described above can be referenced to each other.

[0146] A device for analyzing uncertainty in a regulation process of a doubly-fed pumped storage unit, comprising: A model building module for establishing the state-space equations of the speed regulation and excitation system of a doubly-fed pumped storage unit, taking into account the initial speed and rotor power response; An uncertainty introduction module is used to set uncertainty parameters and their distribution characteristics, and introduce the uncertainty parameters into the state space equation of the speed regulation-excitation system to obtain the state space equation of the speed regulation-excitation system under the uncertainty framework; An expansion module, used for selecting an orthogonal polynomial and performing a generalized polynomial chaos expansion on the state space equation of the speed regulation-excitation system; The state solving module is used to obtain the approximate solution of each state vector in the state space equation of the speed regulation-excitation system through a numerical solution method, and quantify the output response statistical characteristics of the state space equation of the speed regulation-excitation system.

[0147] It should be understood that the above-mentioned device is used to execute the method in the above-mentioned embodiment. The implementation principle and technical effect of the corresponding program module in the device are similar to those described in the above-mentioned method. The working process of the device can refer to the corresponding process in the above-mentioned method and will not be repeated here.

[0148] Based on the method in the above embodiment, the embodiment of the present application provides an electronic device, such as Figure 10 As shown, the electronic device includes a processor, a communications interface, a memory, and a communication bus. The processor, the communications interface, and the memory communicate with each other via the communication bus. The processor can call logic instructions in the memory to execute the method of the above embodiment.

[0149] In addition, the logical instructions in the above-mentioned memory can be implemented in the form of a software functional unit and can be stored in a computer-readable storage medium when sold or used as an independent product. Based on this understanding, the technical solution of the present application, or the part that contributes to the existing technology, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes a number of instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present application.

[0150] Based on the method in the above embodiment, an embodiment of the present application provides a computer-readable storage medium, which stores a computer program. When the computer program runs on a processor, the processor executes the method in the above embodiment.

[0151] Based on the method in the above embodiment, an embodiment of the present application provides a computer program product. When the computer program product runs on a processor, the processor executes the method in the above embodiment.

[0152] It is understood that the processor in the embodiments of the present application may be a central processing unit (CPU), other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field programmable gate arrays (FPGA), other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. The general-purpose processor may be a microprocessor or any conventional processor.

[0153] The method steps in the embodiments of the present application can be implemented by hardware or by a processor executing software instructions. The software instructions can be composed of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, mobile hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor so that the processor can read information from the storage medium and write information to the storage medium. Of course, the storage medium can also be an integral part of the processor. The processor and storage medium can be located in an ASIC.

[0154] The above embodiments can be implemented in whole or in part using software, hardware, firmware, or any combination thereof. When implemented using software, they can be implemented in whole or in part in the form of a computer program product. The computer program product comprises one or more computer instructions. When loaded and executed on a computer, the computer program instructions fully or partially produce the processes or functions described in the embodiments of this application. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted via the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium accessible by a computer or a data storage device such as a server or data center that integrates one or more available media. The available medium can be magnetic media (e.g., floppy disk, hard disk, tape), optical media (e.g., DVD), or semiconductor media (e.g., solid-state drive (SSD)).

[0155] It will be understood that the various numerical numbers involved in the embodiments of the present application are merely distinctions for the convenience of description and are not intended to limit the scope of the embodiments of the present application.

[0156] It is easy for those skilled in the art to understand that the above is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present application should be included in the scope of protection of the present application.

Claims

1. A method for uncertainty analysis of the regulation process of a doubly-fed pumped storage unit, characterized in that: include: Establish the state space equations of the speed regulation-excitation system of the doubly-fed pumped storage unit taking into account the initial speed and rotor power response; Setting uncertainty parameters and their distribution characteristics, bringing the uncertainty parameters into the state space equation of the speed regulation-excitation system, and obtaining the state space equation of the speed regulation-excitation system under the uncertainty framework; Selecting orthogonal polynomials to perform generalized polynomial chaos expansion on the state space equation of the speed regulation-excitation system; By using a numerical solution method, an approximate solution of each state vector in the state space equation of the speed regulation-excitation system is obtained, and the statistical characteristics of the output response of the state space equation of the speed regulation-excitation system are quantified.

2. The uncertainty analysis method for the regulation process of a doubly-fed pumped storage unit according to claim 1 is characterized in that: Establishing the state-space equations of the speed regulation-excitation system of the doubly-fed pumped storage unit taking into account the initial speed and rotor power response includes the following sub-steps: Based on the transient hydraulic characteristics of the water diversion system, the water hammer equation is derived and simplified to obtain the transfer function, clarifying the dynamic relationship between head and flow within the water diversion system pipeline; the structure of the doubly fed pumped storage unit is determined, and the dynamic models of the speed governor and relay are established; the flow and torque characteristic equations of the pump turbine are linearized; The voltage-flux equation of the doubly-fed pumped storage unit is established based on the dq coordinate system. The relationship between the flux and current is simplified through the stator flux directional vector control strategy, and the rotor voltage dynamic equation is derived to clarify the control relationship between the electromagnetic torque, power and rotor current. A dual closed-loop control structure consisting of a power outer loop and a current inner loop is designed to achieve precise regulation by eliminating slip frequency interference. Finally, combined with the flow and torque characteristic equations of the pump-turbine, the state-space equation of the speed regulation-excitation system is constructed, which takes into account the initial speed and rotor power response.

3. The uncertainty analysis method for the regulation process of a doubly-fed pumped storage unit according to claim 2 is characterized in that: Ignoring the water level change at the inlet section of the pipe in the water diversion system and the hydraulic friction loss of the pipeline, the water hammer equation is simplified to obtain the transfer function.

4. The uncertainty analysis method for the regulation process of a doubly-fed pumped storage unit according to claim 2 is characterized in that: The voltage-flux equation of the doubly-fed pumped storage unit is established based on the dq coordinate system. Specifically, considering the characteristics of the doubly-fed pumped storage unit that the stator is directly connected to the power grid and the rotor is excited by the converter, the influence of the motor magnetic circuit saturation loss, hysteresis loss, eddy current and core loss on the motor performance parameters is ignored, and the voltage-flux equation in the dq coordinate system is established.

5. The uncertainty analysis method for the regulation process of a doubly-fed pumped storage unit according to claim 2 is characterized in that: The stator flux oriented vector control strategy is specifically as follows: the d-axis in the synchronous rotating coordinate system coincides with the motor stator magnetic field, and the direction rotated 90° counterclockwise is used as the q-axis direction.

6. The uncertainty analysis method for the regulation process of a doubly-fed pumped storage unit according to claim 2 is characterized in that: The dual closed-loop control structure of the power outer loop and the current inner loop is specifically as follows: In the power outer loop control, the power deviation is converted into the rotor current q-axis reference value and d-axis reference value through the PI controller; in the current inner loop control, the current coaxial dynamic term adopts the PI controller, and the non-coaxial interference term adopts the feedforward compensation algorithm to generate the rotor voltage control equation.

7. The uncertainty analysis method for the regulation process of a doubly-fed pumped storage unit according to claim 1 or 2, characterized in that: The state space equation of the speed regulation-excitation system is specifically: matrix Other elements is zero; in, is the state vector; is the output vector; is the input vector, 、 and is the corresponding matrix; yes First derivative with respect to time; Represents matrix transpose; is the servomotor time constant; is the water flow inertia time constant; is the inertia constant of the unit; is the equivalent inertia constant of the power grid; is the initial value of the unit torque; is the turbine flow to speed transfer coefficient; is the transfer coefficient of turbine flow to guide vane opening; is the turbine flow to working head transfer coefficient; is the turbine torque to speed transfer coefficient; is the transfer coefficient of turbine torque to guide vane opening; is the transfer coefficient of turbine torque to working head; is the unit sub-regulation coefficient; is the stator flux amplitude; is the number of motor pole pairs; is the initial value of the unit speed; is the frequency adjustment coefficient; is the frequency controller proportional gain, is the frequency controller integral gain, is the power controller proportional gain, is the power controller integral gain.

8. The uncertainty analysis method for the regulation process of a doubly-fed pumped storage unit according to claim 1 is characterized in that: Set the uncertainty parameters and their distribution characteristics, specifically: select the water flow inertia time constant , relay time constant , initial value of unit torque , unit inertia constant , grid equivalent inertia constant , Initial value of unit speed and the unit sub-regulation coefficient As the uncertainty parameter, the uncertainty parameter satisfies the normal distribution.

9. The uncertainty analysis method for the regulation process of a doubly-fed pumped storage unit according to claim 1 is characterized in that: Select an orthogonal polynomial and perform a generalized polynomial chaos expansion on the state space equation of the speed regulation-excitation system; specifically: After expanding all state vectors and inserting them into the state space equation of the speed regulation-excitation system, we can obtain: in, is the orthogonal function expansion; is the state vector, yes The first derivative with respect to time, Represents the state vector Serial number, , is the order of expansion; is the finite order of the expansion; is a random variable that follows a specific distribution; It's about Orthogonal polynomials of ; Multiply both sides of the equation , using orthogonality, for random variables Taking the expectation of the support set of , we get: definition As the mass matrix, the general coefficient equation reflecting the state of the control system is obtained: in, are orthogonal polynomial basis functions, and Together they form an orthogonal basis for the random process; Express expectations.

10. A device for analyzing uncertainty in the regulation process of a doubly-fed pumped storage unit, characterized in that: include: A model building module for establishing the state-space equations of the speed regulation and excitation system of a doubly-fed pumped storage unit, taking into account the initial speed and rotor power response; An uncertainty introduction module is used to set uncertainty parameters and their distribution characteristics, and introduce the uncertainty parameters into the state space equation of the speed regulation-excitation system to obtain the state space equation of the speed regulation-excitation system under the uncertainty framework; An expansion module, used for selecting an orthogonal polynomial and performing a generalized polynomial chaos expansion on the state space equation of the speed regulation-excitation system; The state solving module is used to obtain the approximate solution of each state vector in the state space equation of the speed regulation-excitation system through a numerical solution method, and quantify the output response statistical characteristics of the state space equation of the speed regulation-excitation system.

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