A method for suppressing shaft oscillation of a doubly-fed pumped storage unit based on non-optimal speed operation

Abstract

The present invention discloses a method for suppressing shaft oscillation of a doubly-fed pumped-storage unit operating at non-optimal speeds, comprising the following steps: 1. dividing the turbine operating region into an S region and a stable operating region; 2. constructing a linear model for the stable operating region; 3. constructing a refined model for the S region; 4. establishing a state equation for the doubly-fed pumped-storage unit; 5. setting an operating range and calculating a steady-state operating point; 6. linearizing the state equation near the steady-state operating point; 7. performing eigenvalue analysis to obtain a shaft oscillation damping ratio; 8. screening all dangerous operating points and formulating a risk assessment index based on the shaft oscillation damping ratio; 9. screening dominant control parameters; 10. establishing a dominant control parameter optimization model; and 11. introducing a risk assessment index to improve the NSGA-II algorithm and solve the optimization model. The present invention can effectively identify and suppress dangerous speed and flow ranges of doubly-fed pumped-storage units operating at non-optimal speeds, thereby improving the effectiveness of suppressing shaft oscillation.

Description

Technical Field

[0001] The present invention relates to the field of shaft oscillation suppression of a doubly-fed pumped storage unit, and in particular to a method for suppressing shaft oscillation of a doubly-fed pumped storage unit operating at a non-optimal speed. Background Art

[0002] With the rapid development of power systems and the increasing proportion of renewable energy, the power grid's demand for peak and frequency regulation continues to grow. As an important means of energy storage, pumped-storage power plants play a key role in power systems. Doubly-fed pumped-storage units have attracted widespread attention due to their efficient power regulation capabilities. Doubly-fed units can flexibly switch between pumping and power generation modes, and adjust their speed through variable speed operation to adapt to different operating conditions. Doubly-fed units not only offer efficient power conversion capabilities, but also significantly reduce mechanical losses, improving system response speed and regulation accuracy.

[0003] However, pumped-storage units are susceptible to shaft oscillation during operation, which not only affects the equipment's service life but can also cause mechanical failures, jeopardizing the safety of the entire unit. Traditional maximum power point tracking (MPPT) operation, by real-time monitoring and adjusting turbine parameters, can quickly adapt to changing operating conditions and help reduce shaft oscillation. However, in non-MPPT operation, since the unit maintains a fixed speed, it is prone to operating in the S region of the flow characteristic for extended periods, generating large dynamic loads and mechanical stresses, leading to material fatigue and damage. This exacerbates shaft instability and oscillation intensity, making oscillation more difficult to suppress. When the unit operates at different speeds and pump conditions, especially in the turbine's S region, the flow and torque characteristics vary significantly with guide vane opening and unit speed. Accurate analysis of pumped-storage unit shaft oscillation is difficult using traditional linear models. Summary of the Invention

[0004] The purpose of the present invention is to overcome the shortcomings of the above-mentioned technology and propose a method for suppressing the shaft system oscillation of a doubly fed pumped storage unit based on non-optimal speed operation, so as to improve the accuracy of the shaft system oscillation analysis of the doubly fed pumped storage unit under non-optimal speed operation, thereby optimizing the system control parameters according to the analysis results, reducing the dangerous speed range that causes the system shaft system oscillation, suppressing the shaft system oscillation, thereby improving the operating stability of the unit and extending the service life of the equipment.

[0005] The present invention adopts the following technical solutions to solve the technical problems:

[0006] The method for suppressing shaft oscillation of a doubly-fed pumped storage unit based on non-optimal speed operation of the present invention is characterized in that it comprises the following steps:

[0007] Step S1: using historical data of the turbine operating at a non-optimal speed, the slope of the flow characteristic curve at each point is calculated, and the area on the flow characteristic curve of the turbine where the slope is greater than or equal to zero is defined as the S area of ​​the turbine; the area where the slope is less than zero is defined as the stable operation area of ​​the turbine;

[0008] Step S2: constructing a linear model of the stable operation region of the turbine;

[0009] Step S3: Taylor expansion of the flow characteristic function and torque characteristic function of the turbine in region S to the second order is performed to obtain a refined model of the turbine; partial derivatives of the flow characteristic and torque characteristic curves are taken using historical data of the turbine operating at non-optimal speeds to obtain first-order parameters of the refined model; and based on the first-order parameters, the refined model is identified using a recursive least squares method with a discount factor to obtain second-order parameters of the refined model;

[0010] Step S4: establishing a shaft system state equation, a speed control system state equation, a head state equation, and a doubly-fed motor state equation of the doubly-fed pumped storage unit, which together constitute a state equation group of the doubly-fed pumped storage unit;

[0011] Step S5: Based on historical data of the turbine operating at a non-optimal speed, a speed range and a flow range are set; the speed range and the flow range are discretized according to the set step size to obtain a speed operating point set and a flow operating point set; and based on the comprehensive characteristic curve of the doubly-fed pumped storage unit, a steady-state operating point of each speed operating point and each flow operating point is calculated;

[0012] Step S6: linearizing the state equation group of the doubly-fed pumped storage unit near the steady-state operating point to obtain the linearized equation of the doubly-fed pumped storage unit, and obtaining a system matrix based on the linearized equation;

[0013] Step S7: using the system matrix to calculate the eigenvalue, oscillation frequency, damping ratio and participation factor of each state variable, and determining the shaft system oscillation mode according to the participation factor, thereby obtaining the shaft system oscillation damping ratio;

[0014] Step S8: Screening out all steady-state operating points where the shaft system oscillation damping ratio is less than a critical value, thereby forming a dangerous speed and flow range, and constructing a risk assessment index based on the shaft system oscillation damping ratio;

[0015] Step S9: calculating the sensitivity of the control parameters of the turbine PID speed control system, the doubly-fed generator speed control system, and the converter control system in the doubly-fed pumped storage unit to the eigenvalue and the damping ratio, respectively; and selecting the dominant control parameters based on the eigenvalue sensitivity and the damping ratio sensitivity of the control parameters;

[0016] Step S10: minimizing the dangerous speed range and dangerous flow range of non-optimal speed operation as the first objective function, minimizing the risk assessment index as the second objective function, and taking the upper and lower limits of the dominant control parameter as constraints, thereby constructing a dominant control parameter optimization model;

[0017] Step S11: According to the risk assessment index, the improved NSGA-II algorithm is used to solve the dominant control parameter optimization model to obtain the optimal dominant control parameters for suppressing the shaft oscillation of the doubly fed pumped storage unit.

[0018] The method for suppressing shaft oscillation of a doubly-fed pumped storage unit based on non-optimal speed operation according to the present invention is also characterized in that step S3 is performed as follows:

[0019] Step S3-1: Use formula (1) to obtain the refined model of the turbine in region S:

[0020]

[0021] In formula (1), m t represents the relative value of the torque deviation of the turbine in the S area; q represents the relative value of the flow deviation of the turbine in the S area; y represents the relative value of the guide vane opening deviation of the turbine in the S area; ω m represents the relative value of the speed deviation of the turbine in the S region; h represents the relative value of the head deviation of the turbine in the S region; ▽q(y,ω m ,h) and ▽m(y,ω m ,h) respectively represent the first-order coefficients of the flow characteristic and torque characteristic of the turbine in the S region; B m and B q are the two second-order coefficients to be identified;

[0022] Step S3-2: Use formula (2) to obtain the identification expression of the second-order coefficient of the refined model:

[0023]

[0024] In formula (2), Z m represents the flow output observation value of the turbine in area S; Z q represents the torque output observation value of the turbine in region S; α represents the input vector; ε1 and ε2 represent two error values; T represents the transpose, and:

[0025]

[0026] Step S3-3: Use the recursive least square method with discount factor to identify equation (2) and obtain the two second-order coefficients B of the turbine refinement model. m and B q .

[0027] Furthermore, step 4 is performed as follows:

[0028] Step S4-1: Use equation (4) to obtain the shaft system state equation of the doubly fed pumped storage unit:

[0029]

[0030] In formula (4), E m , E r They represent the inertia coefficients of the turbine and induction motor respectively; K represents the total shaft stiffness coefficient of the turbine; D represents the damping coefficient of the turbine; ω r Indicates the rotor speed of the induction motor; T e represents the electromagnetic torque of the induction motor; θ represents the rotor torsion angle of the induction motor; ω b represents the base value of the electrical angular velocity of the doubly-fed pumped storage unit; d represents the differential; t represents the time;

[0031] Step S4-2: Use equation (5) to obtain the state equation of the speed control system:

[0032]

[0033] In formula (5), k p1 、k i1 、k d1 Respectively represent the proportional coefficient, integral coefficient, and differential coefficient in the PID controller; T y represents the time constant of the relay; z represents the intermediate variable of the speed control system;

[0034] Step S4-3: Use equation (6) to obtain the hydraulic head state equation:

[0035]

[0036] In formula (6), T w is the time constant of water flow inertia; b q3 Indicates the second-order coefficient B q The row vector consisting of the third row elements of ;

[0037] Step S4-4: Use equation (7) to obtain the doubly-fed machine state equation:

[0038]

[0039] In formula (7), x DFIG is the state variable of the doubly fed machine, y DFIG is the algebraic variable of the doubly fed machine, f(x DFIG ,y DFIG ) represents the differential equation, g(x DFIG ,y DFIG ) represents an algebraic equation;

[0040] Step S4-5: Combine equations (4), (5), (6) and (7) to obtain the state equation of the doubly-fed pumped storage unit.

[0041] Furthermore, step S6 is performed as follows:

[0042] Step S6-1: Perform a neighborhood Taylor expansion of the state equation of the doubly-fed pumped storage unit at the steady-state operating point and ignore the high-order infinitesimal terms, thereby obtaining the linearized equation of the doubly-fed pumped storage unit using equation (8):

[0043]

[0044] In formula (8), y0 represents the guide vane opening of the turbine at the steady-state operating point; ω m0 represents the speed of the turbine at the steady-state operation point; h0 represents the water head at the steady-state operation point; F x represents the derivative of the doubly-fed machine differential equation with respect to the state variable x; F y represents the derivative of the doubly-fed machine differential equation with respect to the algebraic variable; G x The derivative G of the doubly-fed machine algebraic equation with respect to the state variable x y represents the derivative of the doubly-fed machine algebraic equation with respect to the algebraic variable; V, O, and N represent the three coefficients of the head linearization equation, and:

[0045]

[0046]

[0047] Step S6-2: Use equation (12) to obtain the system matrix A:

[0048]

[0049] In formula (12), x represents the state variable.

[0050] Furthermore, the step 8 includes:

[0051] Step S8-1: Use formula (13) to filter out all steady-state operating points where the shaft oscillation damping ratio is less than the critical value, thereby obtaining the dangerous speed and flow range:

[0052] ξ z,i <ξ stable (13)

[0053] In formula (13), ζ z,i represents the shaft oscillation damping ratio at the i-th steady-state operating point, ζ stable Indicates the critical value of the set dangerous damping ratio;

[0054] Step S8-2: Use formula (14) to obtain the risk assessment index a of the i-th steady-state operation point i , to quantify the degree of danger of shaft oscillation:

[0055]

[0056] In formula (14), β represents the weight coefficient of the risk assessment index.

[0057] Furthermore, in the improved NSGA-II algorithm of step 11, the binary crossover operator is constructed using formula (15):

[0058]

[0059] In formula (15), c p1 、c p2 Represents two parent individuals; c o1 、c o2 Represents two offspring individuals, where each individual is composed of the dominant control parameters selected; η c represents the cross-index, and has:

[0060]

[0061] In formula (16), μ represents a random number in the range [0,1].

[0062] An electronic device according to the present invention includes a memory and a processor, wherein the memory is used to store a program that supports the processor in executing the method for suppressing shaft oscillation of a doubly-fed pumped storage unit, and the processor is configured to execute the program stored in the memory.

[0063] The present invention provides a computer-readable storage medium, wherein a computer program is stored on the computer-readable storage medium. The computer-readable storage medium is characterized in that when the computer program is run by a processor, the steps of the method for suppressing shaft oscillation of a doubly-fed pumped storage unit are executed.

[0064] Compared with the prior art, the present invention has the following beneficial effects:

[0065] 1. This invention considers the problem of shaft oscillation under non-optimal speeds. By analyzing the dynamic characteristics under different speed and flow combinations, dangerous oscillation modes are screened out. The system control parameters are optimized using the NSGA-II algorithm, reducing the dangerous speed range that causes system shaft oscillation. This provides a more effective control method for the shaft oscillation problem under non-optimal speeds and significantly improves the stability of the pumped storage unit.

[0066] 2. Taking into account that the turbine characteristic curve varies strongly with the guide vane opening and unit speed in the S region, the present invention performs a second-order Taylor expansion on the turbine dynamic characteristic function in the S region to retain its second-order terms. The refined model is used to establish the state equation of the doubly-fed pumped-storage unit, and the equation is linearized to perform small signal analysis, thereby improving the dynamic response analysis accuracy of the doubly-fed pumped-storage unit.

[0067] 3. This paper develops a hazard assessment index based on the damping ratio to quantify the degree of hazard. This index is then used to improve the crossover operator in the NSGA-II algorithm to optimize control parameters. This reduces the dangerous speed and flow ranges of shaft oscillation in the doubly-fed pumped-storage unit, effectively suppresses shaft oscillations at suboptimal speeds, and improves the stability of the doubly-fed pumped-storage unit. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 This is a structural diagram of a doubly-fed pumped storage unit;

[0069] Figure 2 is a flow chart of the present invention;

[0070] Figure 3 This is the control model diagram of the speed regulation system of the pumped storage unit;

[0071] Figure 4 Flowchart for obtaining control parameters for NSGA-II. DETAILED DESCRIPTION

[0072] In this embodiment, a method for suppressing shaft oscillation of a doubly-fed pumped storage unit based on non-optimal speed operation is provided, wherein the structure of the doubly-fed pumped storage unit is as follows: Figure 1As shown. In this embodiment, the working area of ​​the turbine is divided into the S area and the stable operation area. After Taylor expansion of the flow characteristic function and torque characteristic function of the turbine in the S area to the second order, a refined model of the turbine is obtained to more accurately describe the dynamic characteristics of the turbine in the S area. Based on the refined model of the turbine, the linearization equation of the doubly fed pumped storage unit is established, and the eigenvalue analysis is used to obtain the shaft oscillation frequency and damping ratio of the doubly fed pumped storage unit. The risk assessment index is formulated, the dangerous speed and flow range are screened out, and the optimization model is established. The improved NSGA-Ⅱ algorithm is used to optimize the dominant control parameters, thereby reducing the dangerous speed and flow range under non-optimal speed operation and suppressing the shaft oscillation. Specifically, as Figure 2 As shown, the method includes the following steps:

[0073] Step S1: Using the historical data of the turbine operating at a non-optimal speed, the slope of the flow characteristic curve at each point is calculated, and the area on the flow characteristic curve of the turbine where the slope is greater than or equal to zero is defined as the S area of ​​the turbine; the area where the slope is less than zero is defined as the stable operation area of ​​the turbine.

[0074] Step S2: Use equation (1) to construct a linear model of the stable operation area of ​​the turbine:

[0075]

[0076] In formula (1), m tw Indicates the relative value of the torque deviation of the turbine in the stable operation area; q w Relative value of flow deviation of the turbine in the stable operation area; y w Indicates the relative value of the guide vane opening deviation of the turbine in the stable operation area; ω mw Indicates the relative value of the turbine speed deviation in the stable operation area; h w Indicates the relative value of the water head deviation of the turbine in the stable operation area; ▽q(y w ,ω mw ,h w ) and ▽m(y w ,ω mw ,h w ) represent the first-order coefficients of the flow characteristic and torque characteristic of the turbine in the stable operation area respectively.

[0077] Step S3: After Taylor expansion of the flow characteristic function and torque characteristic function of the turbine in the S region to the second order, a refined model of the turbine is obtained; after partial derivatives of the flow characteristic and torque characteristic curves are respectively obtained using historical data of the turbine running at non-optimal speed, the first-order parameters of the refined model are obtained, and then, based on the first-order parameters, the refined model is identified using the recursive least squares method with a discount factor to obtain the second-order parameters of the refined model.

[0078] Step S3-1: The flow characteristics and torque characteristics of the turbine operating in the S region vary greatly with the guide vane opening and unit speed. Therefore, the flow characteristic function and torque characteristic function of the turbine operating in the S region are Taylor expanded to the second order, and the refined model of the turbine in the S region is obtained using formula (2):

[0079]

[0080] In formula (2), m t represents the relative value of the torque deviation of the turbine in the S area; q represents the relative value of the flow deviation of the turbine in the S area; y represents the relative value of the guide vane opening deviation of the turbine in the S area; ω m represents the relative value of the speed deviation of the turbine in the S region; h represents the relative value of the head deviation of the turbine in the S region; ▽q(y,ω m ,h) and ▽m(y,ω m ,h) respectively represent the first-order coefficients of the flow characteristic and torque characteristic of the turbine in the S region; B m and B q are the two second-order coefficients to be identified.

[0081] Step S3-2: Use the historical data of the turbine running at non-optimal speed to calculate the partial derivatives of the flow characteristic and torque characteristic curves to obtain the first-order parameters of the refined model. The second-order parameters of the refined model cannot be directly obtained based on the flow characteristic and torque characteristic curves, so the least squares method is used to identify the second-order coefficients. Substitute the first-order coefficients into the refined model and use formula (4) to obtain the identification expression of the second-order coefficients of the refined model:

[0082]

[0083] In formula (3), Z m represents the flow output observation value of the turbine in area S; Z q represents the torque output observation value of the turbine in region S; α represents the input vector; ε1 and ε2 represent two error values; T represents the transpose, and:

[0084]

[0085] Step S3-3: Use the recursive least square method with discount factor to identify Equation (3) and obtain the two second-order coefficients B of the turbine refinement model. m and B q .

[0086] Step S3-3-1: In order to prevent the parameter hysteresis problem caused by data saturation, a dynamic discount factor τ is introduced into the index function J(α). The index function J(α) and the dynamic discount factor τ are obtained using equations (5) and (6) respectively:

[0087]

[0088] In formula (6), ρ(i) represents the weighting factor; r is a positive adjustable number close to and less than 1; l is a positive adjustable parameter.

[0089] Step S3-3-2: The least squares method requires the index function to be minimized. Formula (5) is minimized, and then the recursive least squares identification formula with discount factor is obtained using formula (7):

[0090]

[0091] In formula (7), S i represents the gain vector; W i is the covariance matrix.

[0092] Step S3-3-3: Set the initial value α0 to a sufficiently small positive real vector, and set W0 to a sufficiently large positive real matrix.

[0093] Step S3-3-4: By continuously acquiring historical data of the turbine operating at non-optimal speed, the newly acquired data is substituted into formula (7) for iteration, and the original estimation results are continuously corrected to obtain the two second-order coefficients B of the refined model of the turbine. m and B q .

[0094] Step S4: Establish the shaft system state equation, speed control system state equation, head state equation and doubly fed generator state equation of the doubly fed pumped storage unit, which together constitute the state equation of the doubly fed pumped storage unit.

[0095] Step S4-1: Use equation (8) to establish the axis equation of the two masses:

[0096]

[0097] In formula (8), E m , E r They represent the inertia coefficients of the turbine and induction motor respectively; K represents the total shaft stiffness coefficient of the turbine; D represents the damping coefficient of the turbine; ω r Indicates the rotor speed of the induction motor; T e represents the electromagnetic torque of the induction motor; θ represents the rotor torsion angle of the induction motor; ω b It represents the base value of the electrical angular velocity of the doubly-fed pumped storage unit; d represents the differential; and t represents time.

[0098] Substitute the refined model of the turbine into the two-mass shaft system equation, and then use Equation (9) to obtain the shaft system state equation of the doubly fed pumped storage unit:

[0099]

[0100] Step S4-2: The speed control system of the doubly-fed pumped storage unit is as follows: Figure 3 As shown, the transfer function of the speed control system is obtained using formula (10):

[0101]

[0102] In formula (10), k p1 、k i1 、k d1 They represent the proportional coefficient, integral coefficient, and differential coefficient of the PID controller respectively; s represents the Laplace operator, u represents the output of the PID controller; z represents the intermediate variable of the speed control system, and:

[0103]

[0104] In formula (11), ω de Indicates the target speed.

[0105] Using formula (12), the transfer function of the servo system is obtained:

[0106]

[0107] In formula (12), T y represents the servomotor time constant;

[0108] According to the transfer function of the speed control system and the transfer function of the servo system, the state equation of the speed control system is obtained using formula (13):

[0109]

[0110] Step S4-3: Use formula (14) to obtain the hydraulic head state equation:

[0111]

[0112] In formula (14), T w is the time constant of water flow inertia. q3 Indicates the second-order coefficient B q The row vector consisting of the third row of .

[0113] Step S4-4: Use formula (15) to obtain the doubly-fed machine state equation:

[0114]

[0115] In formula (15), x DFIG is the state variable of the doubly fed machine, y DFIG is the algebraic variable of the doubly fed machine, f(x DFIG ,y DFIG ) represents the differential equation, g(x DFIG ,y DFIG ) represents an algebraic equation;

[0116] Step S4-5: Combine equations (9), (11), (13), (14) and (15) to obtain the state equation of the doubly-fed pumped storage unit.

[0117] Step S5: Based on historical data of the turbine operating at a non-optimal speed, a speed range and a flow range are set; a step size is set, and the speed range and the flow range are discretized according to the step size to obtain a speed operating point set and a flow operating point set; based on the comprehensive characteristic curve of the doubly-fed pumped storage unit, a steady-state operating point of each speed operating point and each flow operating point is calculated;

[0118] Step S6: linearizing the state equation group of the doubly-fed pumped storage unit near the steady-state operation point to obtain the linearized equation of the doubly-fed pumped storage unit, and obtaining the system matrix according to the linearized equation.

[0119] Step S6-1: Perform a neighborhood Taylor expansion of the state equation of the doubly-fed pumped storage unit at the steady-state operating point and ignore the high-order infinitesimal terms, thereby obtaining the linearized equation of the doubly-fed pumped storage unit using equation (16):

[0120]

[0121] In formula (16), y0 represents the guide vane opening of the turbine at the steady-state operating point; ω m0 represents the speed of the turbine at the steady-state operation point; h0 represents the water head at the steady-state operation point; F x represents the derivative of the doubly-fed machine differential equation with respect to the state variable x; F y represents the derivative of the doubly-fed machine differential equation with respect to the algebraic variable; G x The derivative G of the doubly-fed machine algebraic equation with respect to the state variable x y represents the derivative of the doubly-fed machine algebraic equation with respect to the algebraic variable; V, O, and N represent the three coefficients of the head linearization equation, and:

[0122]

[0123]

[0124] Step S6-2: Use equation (20) to obtain the system matrix A:

[0125]

[0126] In formula (20), x represents the state variable.

[0127] Step S7: using the system matrix to calculate the eigenvalue, oscillation frequency, damping ratio and participation factor of each state variable, and determining the shaft system oscillation mode according to the participation factor, thereby obtaining the shaft system oscillation damping ratio;

[0128] Step S7-1: Calculate the eigenvalue, left eigenvector, and right eigenvector using equation (21):

[0129]

[0130] In formula (21), λ i represents the i-th eigenvalue; v i and u i Respectively represent the left and right eigenvectors corresponding to the i-th eigenvalue; σ i represents the attenuation factor corresponding to the i-th eigenvalue; ω i represents the angular frequency corresponding to the i-th eigenvalue.

[0131] Step S7-2: Use equation (22) to obtain the oscillation frequency, damping ratio, and participation factors of each state variable:

[0132]

[0133] In formula (22), f i represents the oscillation frequency corresponding to the i-th eigenvalue; ζ i represents the damping ratio corresponding to the i-th eigenvalue; v ki represents the kth state variable of the left eigenvector corresponding to the i-th eigenvalue, u ki represents the kth state variable of the right eigenvector corresponding to the i-th eigenvalue; p ki represents the participation factor of the kth state variable of the eigenvector corresponding to the i-th eigenvalue.

[0134] Step S7-3: Determine the shaft system oscillation mode according to the magnitude of the participation factor of the state variable related to the shaft system oscillation. The damping ratio corresponding to the shaft system oscillation mode is the shaft system oscillation damping ratio ζ z .

[0135] Step S8: Screening out all steady-state operating points where the shaft system oscillation damping ratio is less than a critical value, thereby forming a dangerous speed and flow range, and constructing a risk assessment index based on the shaft system oscillation damping ratio;

[0136] Step S8-1: Use formula (23) to filter out all steady-state operating points where the shaft oscillation damping ratio is less than the critical value, thereby obtaining the dangerous speed and flow range:

[0137] ξ z,i <ξ stable (twenty three)

[0138] In formula (23), ζ z,i represents the shaft oscillation damping ratio at the i-th steady-state operating point, ζ stable Indicates the critical value of the set dangerous damping ratio.

[0139] Step S8-2: Use formula (24) to obtain the risk assessment index a of the i-th steady-state operation point i , to quantify the degree of danger of shaft oscillation:

[0140]

[0141] In formula (24), β represents the weight coefficient of the risk assessment index.

[0142] Step S9: calculating the sensitivity of the control parameters of the turbine PID speed control system, the doubly-fed generator speed control system, and the converter control system in the doubly-fed pumped storage unit to the eigenvalue and the damping ratio, respectively; and selecting the dominant control parameters based on the eigenvalue sensitivity and the damping ratio sensitivity of the control parameters;

[0143] Step S9-1: Record the control parameters of the turbine PID speed control system, the doubly fed generator speed control system and the converter control system in the doubly fed pumped storage unit as vector γ = [γ1,γ2...γ p ...γ k ] T , γ p represents the pth control parameter of the doubly fed pumped storage unit. The eigenvalue sensitivity and damping ratio sensitivity of the pth control parameter are obtained using formula (25):

[0144]

[0145] In formula (25), λ z represents the eigenvalue corresponding to the shaft oscillation mode; v z and u z They represent the left and right eigenvectors corresponding to the shaft oscillation mode; σ z represents the attenuation factor corresponding to the shaft oscillation mode; ω i It represents the angular frequency corresponding to the shaft oscillation mode.

[0146] Select the control parameter with high eigenvalue sensitivity and damping ratio sensitivity as the dominant control parameter γ z .

[0147] Step S10: minimizing the dangerous speed range and dangerous flow range of non-optimal speed operation as the first objective function, minimizing the risk assessment index as the second objective function, and taking the upper and lower limits of the dominant control parameter as constraints, thereby constructing a dominant control parameter optimization model;

[0148] Step S10-1: Minimizing the dangerous speed range and dangerous flow range of non-optimal speed operation is the first objective function:

[0149]

[0150] In formula (26), w n,i represents the size of the i-th dangerous speed area; w q,i Indicates the size of the i-th dangerous flow area.

[0151] Step S10-2: Minimizing the risk assessment index is used as the second objective function:

[0152]

[0153] Step S10-3: Use equation (28) to obtain the constraint conditions of the dominant control parameters:

[0154]

[0155] In formula (28), γ z,i represents the i-th dominant control parameter; represents the maximum value of the i-th dominant control parameter; represents the minimum value of the i-th dominant control parameter.

[0156] Step S11: According to the risk assessment index, the improved NSGA-II algorithm is used to solve the dominant control parameter optimization model to obtain the optimal dominant control parameters for suppressing the shaft oscillation of the doubly fed pumped storage unit.

[0157] Step S11-1: The main process of NSGA-Ⅱ algorithm is as follows Figure 4 As shown, first set the population size and use formula (29) to get the i-th population individual;

[0158] c i ={γ z,1 ,γ z,2 ...γ z,i ...γ z,k} (29)

[0159] Step S11-2: For each individual, calculate two objective functions. If c i All objective function values ​​are not inferior to c jAnd at least one objective function value is better than c j , then c i Dominate c j Individuals that are not dominated by any other individual in the population are called non-dominated individuals. All non-dominated individuals in the population constitute the first class; when the first class is removed from the population, the non-dominated individuals in the remaining solutions constitute the second class, and so on.

[0160] Step S11-3: For each individual in the non-dominated level, calculate the crowding distance of the i-th individual using formula (30):

[0161]

[0162] In formula (30), represents the kth objective function value of the i+1th individual; represents the kth objective function value of the i-1th individual; represents the maximum value of the kth objective function; represents the minimum value of the kth objective function.

[0163] Step S11-4: Use the tournament selection method based on fast non-dominated sorting and congestion sorting to select individuals as parents.

[0164] Step S11-5: Introduce the risk assessment index to improve the binary crossover operator of the NSGA-II algorithm, and perform a crossover operation on the parent individuals. When the risk assessment index of the parent individuals is small, the crossover index takes a larger value to retain the characteristics of the parent, thereby giving priority to optimizing the steady-state operating point with a high risk level. Use formula (31) to construct the binary crossover operator:

[0165]

[0166] In formula (31), c p1 、c p2 Represents two parent individuals; c o1 、c o2 Represents two offspring individuals, where each individual is composed of the dominant control parameters selected; η c represents the cross-index, and has:

[0167]

[0168] In formula (32), μ represents a random number in the range [0,1].

[0169] Step S11-6: Use formula (33) to perform mutation operation on the individuals after the crossover operation:

[0170]

[0171] In formula (33), c i represents the individual after crossover; c′ represents the individual after mutation; c max and c min represents the upper and lower bounds of the individual; δ represents the disturbance factor; and:

[0172]

[0173] In formula (34), η m Represents the mutation index, which controls the intensity of the mutation.

[0174] Step S11-7: Update the population and merge the parent population with the child population. A new population is selected based on the non-dominated sorting and congestion sorting. Through repeated iterations, the population gradually evolves and eventually converges to the Pareto frontier to obtain the optimal dominant control parameters, which are used to suppress the shaft oscillation of the doubly fed pumped storage unit.

[0175] In this embodiment, an electronic device includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the above method, and the processor is configured to execute the program stored in the memory.

[0176] In this embodiment, a computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the above method are executed.

Claims

1. A method for suppressing shaft oscillation of a doubly-fed pumped storage unit based on non-optimal speed operation, characterized in that: The following steps are involved: Step S1: using historical data of the turbine operating at a non-optimal speed, the slope of the flow characteristic curve at each point is calculated, and the area on the flow characteristic curve of the turbine where the slope is greater than or equal to zero is defined as the S area of ​​the turbine; the area where the slope is less than zero is defined as the stable operation area of ​​the turbine; Step S2: constructing a linear model of the stable operation region of the turbine; Step S3: Taylor expansion of the flow characteristic function and torque characteristic function of the turbine in region S to the second order is performed to obtain a refined model of the turbine; partial derivatives of the flow characteristic and torque characteristic curves are taken using historical data of the turbine operating at non-optimal speeds to obtain first-order parameters of the refined model; and based on the first-order parameters, the refined model is identified using a recursive least squares method with a discount factor to obtain second-order parameters of the refined model; Step S4: establishing a shaft system state equation, a speed control system state equation, a head state equation, and a doubly-fed motor state equation of the doubly-fed pumped storage unit, which together constitute a state equation group of the doubly-fed pumped storage unit; Step S5: setting a speed range and a flow range based on historical data of the turbine operating at a non-optimal speed; and discretizing the speed range and the flow range according to the set step size to obtain a speed operating point set and a flow operating point set; And according to the comprehensive characteristic curve of the doubly-fed pumped storage unit, the steady-state operating point of each speed operating point and each flow operating point is calculated; Step S6: linearizing the state equation group of the doubly-fed pumped storage unit near the steady-state operating point to obtain the linearized equation of the doubly-fed pumped storage unit, and obtaining a system matrix based on the linearized equation; Step S7: using the system matrix to calculate the eigenvalue, oscillation frequency, damping ratio and participation factor of each state variable, and determining the shaft system oscillation mode according to the participation factor, thereby obtaining the shaft system oscillation damping ratio; Step S8: Screening out all steady-state operating points where the shaft system oscillation damping ratio is less than a critical value, thereby forming a dangerous speed and flow range, and constructing a risk assessment index based on the shaft system oscillation damping ratio; Step S9: calculating the sensitivity of the control parameters of the turbine PID speed control system, the doubly-fed generator speed control system, and the converter control system in the doubly-fed pumped storage unit to the eigenvalue and the damping ratio, respectively; and selecting the dominant control parameters based on the eigenvalue sensitivity and the damping ratio sensitivity of the control parameters; Step S10: minimizing the dangerous speed range and dangerous flow range of non-optimal speed operation as the first objective function, minimizing the risk assessment index as the second objective function, and taking the upper and lower limits of the dominant control parameter as constraints, thereby constructing a dominant control parameter optimization model; Step S11: According to the risk assessment index, the improved NSGA-II algorithm is used to solve the dominant control parameter optimization model to obtain the optimal dominant control parameters for suppressing the shaft oscillation of the doubly fed pumped storage unit.

2. The method for suppressing shaft oscillation of a doubly-fed pumped storage unit based on non-optimal speed operation according to claim 1, characterized in that: Described step S3 is carried out as follows: Step S3-1: Use formula (1) to obtain the refined model of the turbine in region S: In formula (1), m t represents the relative value of the torque deviation of the turbine in the S area; q represents the relative value of the flow deviation of the turbine in the S area; y represents the relative value of the guide vane opening deviation of the turbine in the S area; ω m It represents the relative value of the speed deviation of the turbine in the S area; h represents the relative value of the head deviation of the turbine in the S area; and Respectively represent the first-order coefficients of the flow characteristic and torque characteristic of the turbine in the S area; B m and B q are the two second-order coefficients to be identified; Step S3-2: Use formula (2) to obtain the identification expression of the second-order coefficient of the refined model: In formula (2), Z m represents the flow output observation value of the turbine in area S; Z q represents the torque output observation value of the turbine in region S; α represents the input vector; ε1 and ε2 represent two error values; T represents the transpose, and: Step S3-3: Use the recursive least square method with discount factor to identify equation (2) and obtain the two second-order coefficients B of the turbine refinement model. m and B q .

3. The method for suppressing shaft oscillation of a doubly-fed pumped storage unit based on non-optimal speed operation according to claim 2, characterized in that: Described step 4 is carried out as follows: Step S4-1: Use equation (4) to obtain the shaft system state equation of the doubly fed pumped storage unit: In formula (4), E m , E r They represent the inertia coefficients of the turbine and induction motor respectively; K represents the total shaft stiffness coefficient of the turbine; D represents the damping coefficient of the turbine; ω r Indicates the rotor speed of the induction motor; T e represents the electromagnetic torque of the induction motor; θ represents the rotor torsion angle of the induction motor; ω b represents the base value of the electrical angular velocity of the doubly-fed pumped storage unit; d represents the differential; t represents the time; Step S4-2: Use equation (5) to obtain the state equation of the speed control system: In formula (5), k p1 、k i1 、k d1 Respectively represent the proportional coefficient, integral coefficient, and differential coefficient in the PID controller; T y represents the time constant of the relay; z represents the intermediate variable of the speed control system; Step S4-3: Use formula (6) to obtain the hydraulic head state equation: In formula (6), T w is the time constant of water flow inertia; b q3 Indicates the second-order coefficient B q The row vector consisting of the third row elements of ; Step S4-4: Use equation (7) to obtain the doubly-fed machine state equation: In formula (7), x DFIG is the state variable of the doubly fed machine, y DFIG is the algebraic variable of the doubly fed machine, f(x DFIG ,y DFIG ) represents the differential equation, g(x DFIG ,y DFIG ) represents an algebraic equation; Step S4-5: Combine equations (4), (5), (6) and (7) to obtain the state equation of the doubly-fed pumped storage unit.

4. The method for suppressing shaft oscillation of a doubly-fed pumped storage unit based on non-optimal speed operation according to claim 3, characterized in that: Step S6 is performed as follows: Step S6-1: Perform a neighborhood Taylor expansion of the state equation of the doubly-fed pumped storage unit at the steady-state operating point and ignore the high-order infinitesimal terms, thereby obtaining the linearized equation of the doubly-fed pumped storage unit using equation (8): In formula (8), y0 represents the guide vane opening of the turbine at the steady-state operating point; ω m0 represents the speed of the turbine at the steady-state operation point; h0 represents the water head at the steady-state operation point; F x represents the derivative of the doubly-fed machine differential equation with respect to the state variable x; F y represents the derivative of the doubly-fed machine differential equation with respect to the algebraic variable; G x The derivative G of the doubly-fed machine algebraic equation with respect to the state variable x y represents the derivative of the doubly-fed machine algebraic equation with respect to the algebraic variable; V, O, and N represent the three coefficients of the head linearization equation, and: Step S6-2: Use equation (12) to obtain the system matrix A: In formula (12), x represents the state variable.

5. The method for suppressing shaft oscillation of a doubly-fed pumped storage unit based on non-optimal speed operation according to claim 4, characterized in that: The step 8 comprises: Step S8-1: Use formula (13) to filter out all steady-state operating points where the shaft oscillation damping ratio is less than the critical value, thereby obtaining the dangerous speed and flow range: x z,i <ξ stable (13) In formula (13), ζ z,i represents the shaft oscillation damping ratio at the i-th steady-state operating point, ζ stable Indicates the critical value of the set dangerous damping ratio; Step S8-2: Use formula (14) to obtain the risk assessment index a of the i-th steady-state operation point i , to quantify the degree of danger of shaft oscillation: In formula (14), β represents the weight coefficient of the risk assessment index.

6. A method for suppressing shaft oscillation of a doubly-fed pumped storage unit based on non-optimal speed operation according to claim 5, characterized in that: In the improved NSGA-II algorithm of step 11, the binary crossover operator is constructed using formula (15): In formula (15), c p1 、c p2 Represents two parent individuals; c o1 、c o2 Represents two offspring individuals, where each individual is composed of the dominant control parameters selected; η c represents the cross-index, and has: In formula (16), μ represents a random number in the range [0,1].

7. An electronic device comprising a memory and a processor, characterized in that: The memory is used to store a program that supports the processor to execute the method for suppressing shaft oscillation of a doubly-fed pumped storage unit as described in any one of claims 1 to 6, and the processor is configured to execute the program stored in the memory.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for suppressing shaft oscillation of a doubly-fed pumped storage unit according to any one of claims 1 to 6 are executed.

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