Shafting oscillation suppression method for doubly-fed pumped storage unit based on non-optimal rotating speed operation

Abstract

The invention discloses a doubly-fed pumped storage unit shafting oscillation suppression method based on non-optimal rotating speed operation. The method comprises the steps that 1, a working area of a water turbine is divided into an S area and a stable operation area; 2, constructing a linear model of a stable operation area; 3, constructing a refined model of the S region; 4, establishing a state equation of the doubly-fed pumped storage unit; 5, setting a working range, and calculating a steady-state working point; 6, linearizing the state equation near the steady-state working point; 7, analyzing characteristic values to obtain a shafting oscillation damping ratio; 8, all dangerous working points are screened out, and danger evaluation indexes are formulated according to the shafting 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 an NSGA-II algorithm, and solving an optimization model. According to the method, the dangerous rotating speed and the flow interval of the doubly-fed pumped storage unit running at the non-optimal rotating speed can be effectively identified and suppressed, and the shafting oscillation suppression effect is improved.

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 shaft oscillation suppression method of a doubly-fed pumped-storage unit based on non-optimal speed operation. Background Art

[0002] With the rapid development of the power system and the increase in the proportion of renewable energy, the power grid has a growing demand for peak load regulation and frequency regulation. As an important means of energy storage, pumped storage power stations play a key role in the power system. Doubly fed pumped storage units have attracted widespread attention due to their efficient power regulation capabilities. Doubly fed units can flexibly switch between pump mode and power generation mode, and adjust the speed through variable speed operation to adapt to different operating conditions. Doubly fed units not only have efficient power conversion capabilities, but also can significantly reduce mechanical losses and improve the response speed and regulation accuracy of the system.

[0003] However, there is a problem of shaft oscillation in the operation of pumped storage units, which not only affects the service life of the equipment, but may also cause mechanical failures and endanger the safety of the entire pumped storage unit. The traditional maximum power point tracking (MPPT) operation mode can quickly adapt to changes in working conditions by real-time monitoring and adjusting the parameters of the turbine, which helps to reduce shaft oscillation. However, in the non-MPPT operation mode, since the unit maintains a fixed speed, it is easy to work in the S area of ​​the flow characteristic for a long time, generating large dynamic loads and mechanical stresses, leading to material fatigue and damage, thereby aggravating the instability and oscillation intensity of the shaft system, making the oscillation more difficult to suppress. When the unit operates at different speeds and pump conditions, especially in the S area of ​​the turbine, the flow characteristics and torque characteristics change strongly with the guide vane opening and unit speed. It is difficult to accurately analyze the shaft oscillation of pumped storage units 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 shaft oscillation of a doubly-fed pumped-storage unit based on non-optimal speed operation, in order to improve the accuracy of shaft oscillation analysis of the doubly-fed pumped-storage unit under non-optimal speed operation, so as to optimize system control parameters according to the analysis results, reduce the dangerous speed range that causes system shaft oscillation, suppress shaft 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 the historical data of the turbine under the condition of non-optimal speed operation, 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: After Taylor expansion of the flow characteristic function and the 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 the torque characteristic curves are respectively obtained using historical data of the turbine running at a non-optimal speed, the first-order parameters of the refined model are obtained, and then the refined model is identified based on the first-order parameters using the recursive least squares method with a discount factor to obtain the second-order parameters of the refined model;

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

[0011] Step S5: according to the historical data of the turbine running at a non-optimal speed, the speed range and the flow range are set; and 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 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;

[0012] 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;

[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: Screen 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 construct a danger assessment index according to 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 motor speed control system and the converter control system in the doubly-fed pumped storage unit to the characteristic value and the damping ratio, respectively, and selecting the dominant control parameters according to the characteristic value sensitivity and the damping ratio sensitivity of the control parameters;

[0016] Step S10: Taking minimizing the dangerous speed range and dangerous flow range of non-optimal speed operation as the first objective function, taking minimizing the danger 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 dominant control parameter optimization model is solved using the improved NSGA-II algorithm 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 according to the following steps:

[0019] Step S3-1: Use equation (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 area; h represents the relative value of the head deviation of the turbine in the S area; ▽q(y,ω m ,h) and ▽m(y,ω m , h) represent the first-order coefficients of flow characteristics and moment characteristics of the turbine in region S respectively; 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 the S region; α represents the input vector; ε1 and ε2 represent two error values; T represents the transposition, and:

[0025]

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

[0027] Further, 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 the 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 water 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 state equation of the doubly-fed machine:

[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] Further, step S6 is performed as follows:

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

[0043]

[0044] In formula (8), y0 represents the guide vane opening of the turbine at the steady-state operation point; ω m0 represents the speed of the turbine at the steady-state operation point; h0 represents the water head of the turbine at the steady-state operation point; F x F represents the derivative of the doubly-fed machine differential equation with respect to the state variable x; 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] Further, the step 8 comprises:

[0051] Step S8-1: Use formula (13) to screen 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 of the ith steady-state operating point, ζ stable Indicates the critical value of the set dangerous damping ratio;

[0054] Step S8-2: Using formula (14) to obtain the risk assessment index a of the ith 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, each of which is composed of the selected dominant control parameters; η c represents the crossover index, and has:

[0060]

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

[0062] An electronic device of the present invention includes a memory and a processor, wherein 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, 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, and the computer program executes the steps of the method for suppressing shaft oscillation of a doubly-fed pumped storage unit when the computer program is executed by a processor.

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

[0065] 1. The present invention takes into account the shaft oscillation problem under non-optimal speed, screens out dangerous oscillation modes by analyzing the dynamic characteristics under different speed and flow combinations, and optimizes the system control parameters through the NSGA-Ⅱ algorithm, thereby reducing the dangerous speed range that causes the system shaft oscillation, providing a more effective control method for the shaft oscillation problem under non-optimal speed, and significantly improving the stability of the pumped storage unit.

[0066] 2. The present invention takes into account that the characteristic curve of the turbine changes greatly with the guide vane opening and unit speed in the S region. In the S region, the second-order terms of the dynamic characteristic function of the turbine are retained by performing a second-order Taylor expansion. The state equation of the doubly-fed pumped-storage unit is established using the refined model, 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. The present invention develops a hazard assessment index based on the damping ratio to quantify the degree of hazard, and introduces the hazard assessment index to improve the crossover operator in the NSGA-II algorithm to optimize the control parameters, reduce the dangerous speed and flow range of the shaft oscillation of the doubly fed pumped storage unit, effectively suppress the shaft oscillation of the system under non-optimal speed operation, and improve the stability of the doubly fed pumped storage unit. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 It is a structural schematic 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 an S area and a 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. The linearization equation of the doubly fed pumped storage unit is established based on the refined model of the turbine. The shaft oscillation frequency and damping ratio of the doubly fed pumped storage unit are obtained by eigenvalue analysis, and a hazard assessment index is formulated to screen out the dangerous speed and flow range, establish an optimization model, and use the improved NSGA-Ⅱ algorithm to optimize the dominant control parameters, thereby reducing the dangerous speed and flow range under non-optimal speed operation and suppressing shaft oscillation. Specifically, Figure 2 As shown, the method comprises the following steps:

[0073] Step S1: Using the historical data of the turbine under non-optimal speed operation, 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 Relative value of 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; w Relative value of 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 Represents 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 speeds, the first-order parameters of the refined model are obtained, and then the refined model is identified based on the first-order parameters 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 characteristic and torque characteristic of the turbine running 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 running 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 area; h represents the relative value of the head deviation of the turbine in the S area; ▽q(y,ω m ,h) and ▽m(y,ω m , h) represent the first-order coefficients of flow characteristics and moment characteristics of the turbine in region S respectively; 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 find 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 the S region; α represents the input vector; ε1 and ε2 represent two error values; T represents the transposition, and:

[0084]

[0085] Step S3-3: Use the recursive least square method with discount factor to identify equation (3) and obtain 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 square method requires the index function to be minimum, and equation (5) is minimized, so that the recursive least square identification formula with discount factor is obtained using equation (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 running at non-optimal speed, substituting the newly acquired data into equation (7) for iteration, and continuously correcting the original estimation results, the two second-order coefficients B of the refined model of the turbine are obtained. 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 mass blocks:

[0096]

[0097] In formula (8), E m , E r They represent the inertia coefficients of the turbine and the 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; t represents the 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 double-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), we can get the transfer function of the servo system:

[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 equation (13):

[0109]

[0110] Step S4-3: Use equation (14) to obtain the water 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 state equation of the doubly-fed machine:

[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: according to the historical data of the turbine running at a non-optimal speed, the speed range and the flow range are set; the 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; 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;

[0118] Step S6: linearize 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 obtain the system matrix according to the linearized equation.

[0119] Step S6-1: Perform a neighborhood Taylor expansion on the state equation of the doubly-fed pumped storage unit at the steady-state operation 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 of the turbine at the steady-state operation point; F x F represents the derivative of the doubly-fed machine differential equation with respect to the state variable x; 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 ith 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: Screen 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 construct a danger assessment index according to 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 of the ith steady-state operating point, ζ stable Indicates the critical value of the set dangerous damping ratio.

[0139] Step S8-2: Using formula (24) to obtain the risk assessment index a of the ith 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 motor speed control system and the converter control system in the doubly-fed pumped storage unit to the characteristic value and the damping ratio, respectively, and selecting the dominant control parameters according to the characteristic value 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 motor 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 characteristic value 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 system oscillation mode; v z and u z They represent the left and right eigenvectors corresponding to the shaft oscillation mode respectively; 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: Taking minimizing the dangerous speed range and dangerous flow range of non-optimal speed operation as the first objective function, taking minimizing the danger 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: Taking the dangerous speed range and dangerous flow range of minimizing non-optimal speed operation as 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: Taking minimizing the risk assessment index 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 ith dominant control parameter; represents the maximum value of the ith dominant control parameter; represents the minimum value of the ith dominant control parameter.

[0156] Step S11: According to the risk assessment index, the dominant control parameter optimization model is solved using the improved NSGA-II algorithm 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 Domination 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; remove the first class from the population, and 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, the crowding distance of the i-th individual is calculated by 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, each of which is composed of the selected dominant control parameters; η c represents the crossover 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 mutation.

[0174] Step S11-7: Update the population and merge the parent population with the child population, and reselect a new population based on the non-dominated sorting and crowding 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 on the computer-readable storage medium, and the computer program executes the steps of the above method when executed by a processor.

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 the historical data of the turbine under the condition of non-optimal speed operation, 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: After Taylor expansion of the flow characteristic function and the 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 the torque characteristic curves are respectively obtained using historical data of the turbine running at a non-optimal speed, the first-order parameters of the refined model are obtained, and then the refined model is identified based on the first-order parameters using the recursive least squares method with a discount factor to obtain the second-order parameters of the refined model; Step S4: establishing the shaft system state equation, the speed control system state equation, the head state equation and the doubly fed motor state equation of the doubly fed pumped storage unit, which together constitute the state equation group of the doubly fed pumped storage unit; Step S5: according to the historical data of the turbine running at a non-optimal speed, the speed range and the flow range are set; and 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 according to the comprehensive characteristic curve of the doubly-fed pumped storage unit, the steady-state operating point of each speed operating point combined with each flow operating point is calculated; 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; 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: Screen 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 construct a danger assessment index according to 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 motor speed control system and the converter control system in the doubly-fed pumped storage unit to the characteristic value and the damping ratio, respectively, and selecting the dominant control parameters according to the characteristic value sensitivity and the damping ratio sensitivity of the control parameters; Step S10: Taking minimizing the dangerous speed range and dangerous flow range of non-optimal speed operation as the first objective function, taking minimizing the danger 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 dominant control parameter optimization model is solved using the improved NSGA-II algorithm to obtain the optimal dominant control parameters for suppressing the shaft oscillation of the doubly-fed pumped storage unit.

2. According to claim 1, a method for suppressing shaft oscillation of a doubly-fed pumped storage unit based on non-optimal speed operation is characterized in that: The step S3 is performed as follows: Step S3-1: Use equation (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 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 are 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; 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 the S region; α represents the input vector; ε1 and ε2 represent two error values; T represents the transposition, and: Step S3-3: Use the recursive least square method with discount factor to identify equation (2) and obtain two second-order coefficients B of the turbine refinement model: m and B q .

3. According to claim 2, a method for suppressing shaft oscillation of a doubly-fed pumped storage unit based on non-optimal speed operation is 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 the 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 equation (6) to obtain the water 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 state equation of the doubly-fed machine: 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. According to claim 3, a method for suppressing shaft oscillation of a doubly-fed pumped storage unit based on non-optimal speed operation is characterized in that: The step S6 is performed as follows: Step S6-1: Perform a neighborhood Taylor expansion on the state equation of the doubly-fed pumped storage unit at the steady-state operation point and ignore the high-order infinitesimal terms, thereby using equation (8) to obtain the linearized equation of the doubly-fed pumped storage unit: 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 of the turbine at the steady-state operation point; F x F represents the derivative of the doubly-fed machine differential equation with respect to the state variable x; 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. According to claim 4, a method for suppressing shaft oscillation of a doubly-fed pumped storage unit based on non-optimal speed operation is characterized in that: The step 8 comprises: Step S8-1: Use formula (13) to screen 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 of the ith steady-state operating point, ζ stable Indicates the critical value of the set dangerous damping ratio; Step S8-2: Using formula (14) to obtain the risk assessment index a of the ith 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, each of which is composed of the selected dominant control parameters; η c represents the crossover 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 described in any one of claims 1 to 6 are executed.

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