Method for optimizing control parameters of doubly-fed wind turbine generator based on lowest frequency point of power system under low voltage ride through

Abstract

The invention discloses a doubly-fed wind turbine generator control parameter optimization method based on the lowest point of the frequency of a power system under low voltage ride through, and the method comprises the steps: 1, considering the influence of a wind speed, a pitch angle and a rotating speed on a capture coefficient, and solving the capture power; 2, providing a virtual synchronous machine control strategy for active compensation of the wind turbine generator, solving a transfer function between the rotating speed of the wind turbine generator and the system frequency, and deducing a power frequency response transfer function of the wind turbine generator; 3, solving the equivalent inertia time constant of the wind turbine generator based on the transfer function, considering the influence of different working conditions of the wind turbine generator in low voltage ride through, performing weighted calculation on the equivalent inertia time constant of the system, and quantifying the power frequency response characteristics of the wind turbine generator in different working conditions; 4, solving a frequency variation based on a system equivalent inertia time constant and a power frequency response characteristic; and 5, solving system trajectory sensitivity, constructing a Hessian matrix based on the sensitivity, solving a parameter optimal value by an interior point method, and raising a frequency lowest point. The calculation accuracy of the frequency variation of the power system is improved.

Description

Technical Field

[0001] The present invention relates to the field of analytical expression and control optimization of the lowest frequency point of an electric power system under low voltage ride-through conditions, and in particular to a control parameter optimization method for a doubly-fed wind turbine generator set based on the lowest frequency point of an electric power system under low voltage ride-through conditions. Background Art

[0002] my country's clean energy represented by wind power generation is expanding day by day, and the installed capacity is increasing steadily. Doubly-fed wind turbines have become one of the widely used models in wind farms because of their good operating characteristics, small converter capacity, and separate control of active and reactive power. As the proportion of wind power generation gradually increases, the impact of wind power generation on the safe and stable operation of the power system can no longer be ignored.

[0003] During the low voltage ride-through process, the system will be affected by continuous and non-step active power shortages, and the lowest frequency point may be too low, resulting in protection action, which poses a risk of frequency instability. Therefore, it is necessary to analyze the system frequency response under non-step disturbances caused by the low voltage ride-through process of wind turbines, and quantify and improve frequency characteristics such as the lowest point. In terms of considering the system frequency response during the low voltage ride-through process of wind turbines, most studies are only qualitative analysis and lack quantitative calculation of key factors affecting frequency stability such as the lowest frequency point. Summary of the invention

[0004] The present invention aims to solve the deficiencies of the above-mentioned prior art and proposes a control parameter optimization method for a doubly-fed wind turbine generator set based on the lowest frequency point of a power system under low voltage ride-through, so as to accurately analyze the relationship between the speed of the wind turbine generator set and the system frequency during the process of the wind turbine generator set participating in the frequency regulation of the power system by considering different working conditions of the wind turbine generator set under low voltage ride-through, so as to improve the frequency regulation accuracy of the wind turbine generator set with an additional virtual synchronous machine, and improve the lowest point of the frequency variation of the power system by optimizing the controller parameters to reduce the fluctuation of the system frequency, thereby improving the frequency stability of the power system.

[0005] In order to achieve the above-mentioned purpose, the present invention adopts the following technical scheme:

[0006] The invention provides a method for optimizing control parameters of a double-fed wind turbine generator set based on the lowest frequency point of a power system under low voltage ride-through, which comprises the following steps:

[0007] Step 1: Considering the influence of wind speed, pitch angle and rotation speed on the capture coefficient, Taylor expansion is performed on the captured power and the first-order partial derivative is retained to obtain the expression of the captured power variation of the doubly-fed wind turbine;

[0008] Based on the flux and torque equations of the induction motor, the expressions of the electromagnetic power variation and stator active power variation of the doubly-fed wind turbine are obtained;

[0009] Step 2: Establish the rotor d-axis current ΔI through the rotor motion equation rd and speed Δω r The transfer function between

[0010] Considering the active power compensation of the doubly-fed wind turbine generator set under low voltage ride-through by the virtual synchronous machine VSG, the speed Δω of the doubly-fed wind turbine generator set is derived. r The transfer function between the frequency change Δf of the power system ; Where s represents frequency domain calculation;

[0011] Based on Δω r The transfer function between Δf and Δf is used to obtain the stator active power ΔP of the doubly fed wind turbine. s The transfer function G between the frequency change Δf of the power system s ;

[0012] Based on ΔP s The transfer function between Δf and Δf, considering the active power compensation of the virtual synchronous machine VSG, is obtained as DFIG The transfer function between the frequency change Δf of the power system ;

[0013] Step 3: Based on ΔP DFIG The transfer function between Δf , the equivalent inertia time constant H of the doubly fed wind turbine is obtained eqDFIG Considering the rated capacity of the doubly-fed wind turbine generator set under different working conditions of grid disconnection and low voltage ride-through, and combining the rated capacity of the synchronous unit, the equivalent inertia time constant H of the power system is obtained. eq ;

[0014] The power-frequency response characteristics of the doubly-fed wind turbine generator system under non-step response are quantified, and based on the equivalent inertia time constant H eq , synchronous units, and double-fed wind turbine units, and obtain the frequency response model of the power system;

[0015] Based on the frequency response model of the power system and considering the unit power fluctuation caused by different operating conditions in the low voltage ride-through situation, the frequency domain expression of the frequency change Δf is obtained. ;

[0016] Step 4: Use the polynomial common denominator pole method to establish the relationship between the polynomial numerator, denominator coefficients and eigenvalues, and solve the eigenvalues ​​of the power system, so as to obtain the time domain expression of the frequency change through complex frequency domain conversion, and obtain the zero point after partial derivative of the time domain expression, bring the zero point into the time domain expression of the frequency change, and obtain the lowest frequency point of the power system;

[0017] Step 5: Calculate the trajectory sensitivity of the power system, and then construct the Hessian matrix based on the trajectory sensitivity, and optimize the control parameters of the power system in combination with the interior point method to obtain the optimal correction amount of the control parameters to improve the lowest frequency point of the power system.

[0018] The method for optimizing control parameters of a doubly-fed wind turbine generator system based on the lowest frequency point of a power system according to the present invention is also characterized in that step 1 comprises:

[0019] Step 1.1: Use equation (1) to obtain the captured power change The expression is:

[0020] (1)

[0021] In formula (1): ρ is the air density, R t is the radius of the wind turbine blade, λ de is the tip speed ratio in the load reduction mode, C p (λ de ,0) is the wind energy capture coefficient in load reduction mode, Δv w is the change in wind speed, Δω r is the change in rotor speed, Δβ is the change in pitch angle, v w is the wind speed, ω r is the rotor speed, β is the pitch angle, k1 is the coefficient of the first constant term;

[0022] Step 1.2: Use formula (2) to obtain the electromagnetic power change ΔP e The expression is:

[0023] (2)

[0024] In formula (2): L m0 is the initial value of the excitation inductance, L s0 is the initial value of the stator self-inductance, ω s0 is the initial speed of the stator, U s0 is the initial voltage of the wind turbine stator, ω r0 is the initial speed of the rotor, ΔT e is the change in electromagnetic torque, ΔI rd is the change of the rotor d-axis current, k2 is the coefficient of the second constant term;

[0025] Using formula (3), we can get the stator active power change ΔP s The expression is:

[0026] (3)

[0027] In formula (3): U sd0is the initial value of the stator d-axis voltage, and k3 is the coefficient of the third constant term.

[0028] Furthermore, the step 2 comprises:

[0029] Step 2.1: Use equation (4) to establish the rotor d-axis current ΔI rd and speed Δω r The transfer function G1 is:

[0030] (4)

[0031] In formula (4): H DFIG is the inertia time constant of the doubly-fed wind turbine; s represents frequency domain calculation;

[0032] Step 2.2: Use equation (5) to establish the speed reference value variation of the doubly-fed wind turbine generator set: and the speed change Δω r The relationship is:

[0033] (5)

[0034] In formula (5): D is the damping coefficient of the power system;

[0035] Step 2.3: Use equation (6) to establish the stator power reference value and the speed change Δω r The relationship :

[0036] (6)

[0037] In formula (6): K pω , K iω are two parameters of the PI controller of the rotor-side converter in the doubly-fed wind turbine; is the speed reference value change;

[0038] Step 2.4: Considering the compensation measures of VSG, the speed change Δω of the doubly-fed wind turbine is obtained using equation (7): r The transfer function between the frequency change Δf of the power system :

[0039] (7)

[0040] In formula (7): G i is the transfer function of the current inner loop controller in the rotor-side converter, G SI is the transfer function of the additional controller, k de is the load reduction factor of the doubly-fed wind turbine generator set, G w is the transfer function of the power loop controller;

[0041] Step 2.5: Use equation (8) to get the stator active power ΔP s The transfer function G between the frequency change Δf of the power system s :

[0042] (8)

[0043] Step 2.6: Use equation (9) to obtain the active power ΔP of the doubly-fed wind turbine generator system: DFIG The transfer function between the frequency change Δf of the power system :

[0044] (9)

[0045] In formula (9): f0 is the initial value of the frequency of the power system, P s0 is the initial value of the stator active power.

[0046] Furthermore, the step 3 comprises:

[0047] Step 3.1: Obtain the equivalent inertia time constant H by equation (10): eqDFIG :

[0048] (10)

[0049] In formula (10): sg0 is the initial speed of the synchronous machine, H DFIG is the inertia time constant of the doubly-fed wind turbine;

[0050] Step 3.2: During the low voltage ride-through process, calculate the inertia time constants of the doubly fed wind turbines and synchronous units in other states except the off-grid state and the low voltage ride-through state and perform weighted calculation to obtain the equivalent inertia time constant H of the power system. eq ;

[0051] Step 3.3: Use equation (11) to obtain the power-frequency response characteristics of the doubly-fed wind turbine generator system under non-step response:

[0052] (11)

[0053] In formula (11): G eq is the power-frequency response characteristic under the equivalent step response, is the equivalent step response; The power change of the doubly-fed wind turbine generator system under low voltage ride-through The non-step component in ;

[0054] Step 3.4: Based on the power frequency response characteristics of the doubly-fed wind turbine and synchronous generator and the equivalent inertia time constant H of the power system eq Considering the operating conditions of the doubly-fed wind turbine generator set under low voltage ride-through, different operating conditions cause different power shortages to the power system. The frequency domain expression of the power system frequency change Δf is obtained using formula (12): :

[0055] (12)

[0056] In formula (12): G SG,i is the power-frequency response characteristic of the ith synchronous unit, G DFIG,h is the power-frequency response characteristic of the h-th wind turbine, D is the damping coefficient of the system, Indicates the total number of synchronous machines, represents the total number of doubly-fed wind turbines, m represents the total number of doubly-fed wind turbines in off-grid conditions, and p represents the total number of doubly-fed wind turbines in low voltage ride-through conditions; is the equivalent step response of the nth unit under low voltage ride-through condition; is the equivalent step response of the e-th unit under off-grid condition;

[0057] Further, the step 4 comprises:

[0058] Step 4.1: Use equation (13) to establish the nth term numerator B in frequency domain calculation n and the relationship between eigenvalues ​​and constants;

[0059] (13)

[0060] In formula (13): R n+1 is the constant of the n+1th term, λ n+1 is the eigenvalue of the n+1th term, b k is the coefficient of the kth term in the numerator, a r is the coefficient of the rth term in the denominator; is the coefficient of the k-th term of the numerator after merging and simplification, and we have:

[0061] (14)

[0062] In formula (14): is the coefficient of the n-1th term in the numerator; is the coefficient of the k-1th term in the numerator; a0 and b0 are the constant term coefficients in the denominator and numerator respectively; a k is the coefficient of the kth term in the denominator;

[0063] Step 4.2: Use equation (15) to establish the denominator coefficient A of the n+1th term in the frequency domain calculation n+1And the relationship between the eigenvalue:

[0064] (15)

[0065] In formula (15): is the coefficient of the rth term of the denominator after merging and simplification, and we have:

[0066] (16)

[0067] In formula (16): is the coefficient of the r-1th term in the denominator; is the coefficient of the nth term in the denominator;

[0068] Step 4.3: For the denominator A of the n+1th term n+1 Through differentiation treatment, A n+1 The coefficients in determine the n+1 eigenvalues ​​λ1…λ n+1 ;

[0069] According to n+1 eigenvalues ​​λ1…λ n+1 and B n The coefficients in , we get n+1 constants R1…R n+1 ;

[0070] According to n eigenvalues ​​λ1…λ n , using formula (17) to calculate the frequency change Perform complex frequency domain transformation to obtain the time domain expression of frequency change :

[0071] (17)

[0072] In formula (17), t represents the time domain, represents the constant coefficient of the αth term; λ α represents the αth eigenvalue coefficient;

[0073] Step 4.4: By frequency variation Taking the derivative of t in the time domain, we get the frequency conversion rate ;

[0074] Find the rate of change of frequency The zero point is brought into the frequency variation expression to solve the maximum frequency variation of the power system. , thus obtaining the lowest frequency point ,in, Indicates the frequency of the power system.

[0075] Furthermore, the trajectory sensitivity of the power system in step 5 is calculated according to the following steps:

[0076] Step 5.1: Use equation (18) to construct the objective function J for optimizing the control parameters of the power system:

[0077] (18)

[0078] In formula (18), t0 is the initial time, t1 is the end time, f(t0) is the frequency at the initial time t0, and f(t) is the time domain frequency expression of the power system;

[0079] Step 5.2: Use formula (19) to obtain the first-order gradient information , and as trajectory sensitivity;

[0080] (19)

[0081] In formula (19): N p is the total number of moments, Δt is the time step, t u is the u-th moment, Find the first-order partial derivative of the frequency expression with respect to a, f(t u ) is the frequency at the u-th simulation moment; a is the control parameter to be optimized;

[0082] Step 5.3: Use formula (20) to obtain the second-order gradient information , and used to construct the Hessian matrix;

[0083] (20)

[0084] In formula (20): Find the second-order partial derivative of the frequency expression with respect to a.

[0085] 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 optimizing control parameters of a doubly-fed wind turbine set, and the processor is configured to execute the program stored in the memory.

[0086] 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 control parameter optimization method of the doubly-fed wind turbine set when the computer program is executed by a processor.

[0087] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0088] 1. The present invention proposes a power-frequency response characteristic based on a complete model of a wind turbine generator set, and considers the influence of wind turbines, back-to-back converters, etc. on the system frequency, thereby overcoming the complexity of the wind turbine generator set model, considering different working conditions of the wind turbine generator set under low voltage ride-through conditions, and obtaining the equivalent inertia time constant of the system, thereby overcoming the complexity of low voltage ride-through and improving the frequency response characteristic of the wind turbine generator set grid-connected system;

[0089] 2. The present invention distinguishes the difference between the equivalent inertia time constants of synchronous units and wind turbines, distinguishes the different operating conditions of wind turbines and the corresponding power fluctuations, performs weighted calculation based on this, and proposes the equivalent inertia time constant of the power system, thereby improving the accuracy of the calculation of the frequency change of the power system;

[0090] 3. The present invention considers optimizing the parameters of the controller to improve the lowest frequency point, extending the trajectory sensitivity to the entire power system, using gradient information to construct the Hessian matrix of the interior point method, and combining the interior point method to solve the optimal value of the control parameter to improve the lowest frequency point of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] Figure 1 The synchronous machine frequency response model of the present invention;

[0092] Figure 2 A frequency response model of a double-fed wind turbine system of a new energy power generation system of the present invention;

[0093] Figure 3 This is a structural diagram of a doubly-fed wind turbine generator system according to the present invention;

[0094] Figure 4 A flow chart for optimizing the control parameters of the present invention;

[0095] Figure 5 This is a complete model control block diagram of the doubly-fed wind turbine generator system of the present invention. DETAILED DESCRIPTION

[0096] In this embodiment, a method for optimizing control parameters of a doubly-fed wind turbine generator system based on the lowest frequency point of a power system under low voltage ride-through includes the following steps:

[0097] Step 1: Considering the influence of wind speed, pitch angle and rotation speed on the capture coefficient, Taylor expansion is performed on the captured power to retain the first-order partial derivative, and the expression of captured power variation is obtained. Based on the flux and torque equations of the induction motor, the expression of electromagnetic power variation and stator active power variation of the doubly-fed wind turbine are obtained;

[0098] Step 1.1: The complete structure control block diagram of the doubly-fed wind turbine is as follows: Figure 5As shown, it includes a wind turbine, a transmission system, an induction generator and a back-to-back converter module. In the following parameter representation, the subscript s represents the stator winding, and the subscript r represents the rotor winding;

[0099] When the wind speed is v w When the wind turbine captures power P wt The expression is as follows (1-1):

[0100] (1-1)

[0101] In formula (1-1): ρ is the air density, R t is the blade radius, C P is the wind energy capture coefficient, v w is the wind speed;

[0102] (1-2)

[0103] In formula (1-2), λ is the tip speed ratio, η is the speed increase ratio, β is the pitch angle, c1~c9 are the fitting coefficients, λ i is the intermediate variable, ω t is the wind turbine speed, ω B is the rated speed, p is the number of motor poles, s t is the wind turbine slip rate;

[0104] Step 1.2: Capture power is wind speed v w , speed ω r , a multivariate function of the pitch angle β, retains the first-order partial derivative through Taylor expansion, and the expression of the change in captured power is obtained as shown in formula (1-3): (1-3)

[0105] In formula (1-3): ρ is the air density; R t is the radius of the wind turbine blade; C p (λ de ,0) is the wind energy capture coefficient in load reduction mode, λ de is the tip speed ratio in load reduction mode; Δv w is the wind speed change, Δω r is the change in rotation speed, and Δβ is the change in pitch angle.

[0106] Step 1.3: Small signal linearization model of the induction motor and shaft part, convert the rotor motion equation into a small signal model;

[0107] Stator flux directional vector control is adopted, that is, the direction of stator flux coincides with the q-axis; the stator d-axis flux is 0, and the relationship between the stator d-axis and q-axis currents can be derived through the flux equation in the induction motor;

[0108] The electromagnetic power P is derived from the electromagnetic torque equation of the induction motor e The expression is as follows (1-4):

[0109] (1-4)

[0110] In formula (1-4): L m0 is the initial value of the excitation inductance, L s0 is the initial value of stator self-inductance, ω s0 is the initial speed of the wind turbine stator, U s0 is the initial voltage of the wind turbine stator, ω r0 is the initial speed of the wind turbine, T e is the electromagnetic torque, I rd is the rotor d-axis current, k2 is the constant term coefficient;

[0111] From formula (1-4), we can know that the change of electromagnetic torque of wind turbine is mainly caused by the change of rotor excitation current. The electromagnetic torque of DFIG unit can be further simplified to obtain the change of electromagnetic power ΔP e The expression of is as follows (1-5):

[0112] (1-5)

[0113] In formula (1-5): ΔT e is the change in electromagnetic torque, ΔI rd is the change of rotor d-axis current;

[0114] ΔP s The expression of wind turbine stator active power change is as follows:

[0115] (1-6)

[0116] In formula (1-6): U sd0 is the initial value of the stator d-axis voltage, k3 is the constant term coefficient;

[0117] Step 1.4: When the wind turbine is operating in the overspeed load reduction mode, the wind turbine operates at a load reduction rate, and the expression of the load reduction power change is as follows:

[0118] (1-7)

[0119] In formula (1-7): k de is the load shedding power factor.

[0120] Step 2: Based on the electromagnetic power variation and the rotor-side converter current inner loop controller, the rotor q-axis current ΔI is obtained. rq and speed Δωr Considering the active power compensation of VSG to the wind turbine, the speed Δω of the doubly fed wind turbine is constructed. r The transfer function between the frequency change of the power system Δf is obtained based on the transfer function: the stator active power of the wind turbine ΔP s The transfer function between the power system frequency change Δf is further used to obtain the wind turbine active power ΔP DFIG and the transfer function between the power system frequency change Δf.

[0121] Step 2.1: Establish a small signal linearization model for rotor-side converter control;

[0122] Wind turbine power outer loop control, rotor side power outer loop control such as Figure 3 As shown, the wind turbine adopts comprehensive inertia control and overspeed load reduction strategy, and a virtual synchronous machine is used to compensate the active reference value of the wind turbine stator. Through the additional controller, a compensated active power is output according to the system frequency change to obtain the equation group as shown in formula (2-1):

[0123] (2-1)

[0124] In formula (2-1): ΔI rdref is the change in the rotor d-axis current reference value; ΔP s is the stator power variation of the wind turbine; ΔP * s is the stator power reference value change of the wind turbine; ΔP de is the power change of the wind turbine in overspeed load reduction mode; ΔP SI G is the virtual inertia additional power change; w is the transfer function of the power loop controller; k pw and k iw are the proportional coefficient and integral coefficient in the PI controller respectively;

[0125] The wind turbine adopts an additional control strategy of comprehensive inertia, and the power change of the additional controller is derived as shown in formula (2-2):

[0126] (2-2)

[0127] In formula (2-2): k I represents the virtual inertia coefficient, k D It represents the droop control coefficient, G SI Transfer functions for additional controllers;

[0128] Use equation (2-3) to establish the rotor d-axis current ΔI rd and speed Δω r The transfer function G1 is:

[0129] (2-3)

[0130] In formula (2-3): H DFIG is the inertia time constant of the doubly-fed wind turbine; s represents frequency domain calculation;

[0131] Derivation of wind turbine speed reference value through VSG control structure and wind turbine speed Δω r The relationship is as follows (2-4):

[0132] (2-4)

[0133] In formula (2-4): D is the damping coefficient of the system;

[0134] A VSG low voltage ride-through control strategy with active power compensation is proposed to compensate DFIG for active power during low voltage ride-through. The virtual synchronous machine VSG is considered to be the reference value of the stator power of the wind turbine. The influence of the stator power is established by using formula (2-5) and wind turbine speed reference value , wind turbine speed Δω r Relationship :

[0135] (2-5)

[0136] In formula (2-5): K pω , K iω are the PI controller parameters of the rotor-side converter of the doubly-fed wind turbine;

[0137] The rotor flux inner loop current control transfer function G is obtained by decoupling the control model of formula (2-6): i for:

[0138] (2-6)

[0139] In formula (2-6): R r is the rotor resistance, k pc and k ic are the proportional coefficient and integral coefficient of the rotor current inner loop PI controller, L m is the magnetizing inductance, L s is the stator self-inductance, L r is the rotor self-inductance.

[0140] Step 2.2: Transfer function relationship between the speed of the doubly-fed wind turbine and the grid frequency;

[0141] Combining the power variation expression under comprehensive inertia control, wind turbine capture power, load reduction power and induction motor small signal equation, the wind turbine speed Δω is derived. r The transfer function relationship between G and the power system frequency change Δf r As shown in formula (2-7):

[0142] (2-7)

[0143] Step 2.3: Transfer function relationship between active power of doubly-fed wind turbine and grid frequency;

[0144] By wind turbine speed Δω r The transfer function relationship between the system frequency Δf and the wind turbine stator active power ΔP is obtained by combining the power change under comprehensive inertia control, wind turbine capture power, and load reduction power. s The transfer function relationship between G and system frequency Δf s (s) as formula (2-8):

[0145] (2-8)

[0146] According to formula (2-8), the transfer function relationship between the wind turbine stator active power and the system frequency is derived, and the closed-loop transfer function G of the power-frequency response characteristic is further derived. DFIG Formula (2-9):

[0147] (2-9)

[0148] In formula (2-9): ω r0 is the initial value of wind turbine speed, f0 is the initial value of system frequency, P s0 is the initial value of stator active power.

[0149] Step 2.4: The speed regulation model of the synchronous machine is as follows: Figure 1 As shown, the mechanical power expression is derived according to the speed regulation model as shown in formula (2-10):

[0150] (2-10)

[0151] The equivalent power-frequency response characteristics of the synchronous unit are obtained as shown in formula (2-11):

[0152] (2-11)

[0153] In formula (2-11): K ∑δ is the magnification of the equivalent centrifugal flying pendulum speed measuring component of the synchronous unit; T ∑ch and T ∑rh are the equivalent steam turbine steam time constant and superheat time constant of the synchronous unit respectively; α is the superheat coefficient; K∑m K is the equivalent power conversion factor of synchronous units; ∑i and T ∑s are the equivalent hard feedback gain and time constant of the synchronous unit respectively.

[0154] Step 3: Based on the wind turbine speed Δω r The transfer function between the frequency change Δf of the power system is obtained by considering the equivalent inertia time constant H of the complete model of the doubly fed wind turbine generator set. eqDFIG , considering the number of wind turbines under low penetration and grid withdrawal conditions, combined with the inertia time constant of the synchronous unit, the equivalent inertia time constant H of the power system is obtained eq , through the power system frequency response model, the frequency variation expression of wind turbines is derived;

[0155] Step 3.1: The kinetic energy change in the inertial response of the wind turbine is expressed by the rotor speed change and the inherent moment of inertia as shown in formula (3-1):

[0156] (3-1)

[0157] In formula (3-1): P, S N , J DFIG , Δω r They are the number of pole pairs, rated power, inherent moment of inertia and speed change of the wind turbine;

[0158] After applying virtual inertia control to the wind turbine, the speed of the wind turbine is coupled with the system speed. The change in kinetic energy during the inertial response process can also be expressed by the change in the system synchronous speed and the virtual moment of inertia as shown in formula (3-2):

[0159] (3-2)

[0160] In formula (3-2): J eqDF ,ω sg0 , Δω sg They are the virtual moment of inertia of wind turbine, the system initial synchronous machine speed and the system synchronous machine speed change;

[0161] According to formula (3-1) and formula (3-2), the virtual moment of inertia of the wind turbine relative to the change of the system synchronous speed is calculated as shown in formula (3-3):

[0162] (3-3)

[0163] The equivalent inertia time constant H based on the complete model of the wind turbine is obtained by formula (3-4): eqDF :

[0164] (3-4)

[0165] In formula (3-4): H DFIG is the inertia time constant of the wind turbine.

[0166] During the low voltage ride-through process, wind turbines in the off-grid state and low voltage ride-through state are not included in the calculation of the equivalent inertia time constant;

[0167] By classifying the inertia time constants of wind turbines and synchronous units and considering the wind turbine operating conditions under low voltage ride-through, the equivalent inertia time constant H of the wind power system is obtained. eq It is expressed as formula (3-5):

[0168] (3-5)

[0169] In formula (3-5): H eqDFh It represents the equivalent inertia time constant of the complete model of the h-th wind turbine unit, S eqDFh It represents the rated capacity of the h-th doubly-fed wind turbine generator set, H SGi It represents the inertia time constant of the ith synchronous unit, S SGi It represents the rated capacity of the i-th synchronous unit.

[0170] Step 3.2: Frequency change based on the wind turbine system frequency response model Expression, according to the frequency response model of the system, such as Figure 2 As shown, the change in mechanical power of the system is shown in formula (3-6):

[0171] (3-6)

[0172] Under low voltage ride-through, the wind turbine is in normal operation, low voltage ride-through state, and grid-off state. In the three states, the wind turbine will cause different power shortages to the system;

[0173] Power changes during low voltage ride-through As shown in formula (3-7), the power change in the off-grid state The expression is as follows (3-8):

[0174] (3-7)

[0175] In formula (3-7): represents the step response starting from time t0, represents the step response starting from time t1, P0 represents the initial power, k is a constant term, t0 is the fault start time, and t1 is the fault end time;

[0176] (3-8)

[0177] Consider converting the non-step response of the wind turbine in low voltage ride-through into a step response, solving the equivalent transfer function, and converting the non-step response into a step response, so that the frequency response of the original system under non-step disturbance can be obtained by a constructed equivalent system under step response;

[0178] Power changes during low voltage ride-through The non-step response term in Formula (3-9):

[0179] (3-9)

[0180] The equivalent power-frequency response characteristics of the wind turbine under low voltage ride-through conditions are solved by formula (3-10):

[0181] (3-10)

[0182] In formula (3-10): G eq The power frequency response characteristic under the equivalent step response is: is the equivalent step response;

[0183] According to the frequency response model of the system, such as Figure 2 As shown, the expression of the power system frequency change is shown in formula (3-11):

[0184] (3-11)

[0185] In formula (3-11): G SG,i is the power-frequency response characteristic of the ith synchronous unit, G DFIG,h is the power-frequency response characteristic of the h-th wind turbine, D is the damping coefficient of the system, Indicates the total number of synchronous machines, represents the total number of doubly-fed wind turbines, m represents the total number of doubly-fed wind turbines in off-grid conditions, and p represents the total number of doubly-fed wind turbines in low voltage ride-through conditions; is the equivalent step response of the nth unit under low voltage ride-through condition; is the equivalent step response of the e-th unit in off-grid condition.

[0186] Step 4: Use the polynomial common denominator pole method to establish the relationship between the numerator and denominator coefficients and eigenvalues ​​of the frequency variation polynomial, and solve the eigenvalue and constant term respectively; thus, the time domain expression of the frequency variation is obtained through complex frequency domain conversion, and the zero point is obtained after partial derivative of the expression, and the zero point is brought into the time domain expression of the frequency variation to obtain the lowest point of the frequency variation of the power system;

[0187] Step 4.1: Use formula (4-1) to get the expression of system frequency change Δf:

[0188] (4-1)

[0189] In formula (4-1): R i is the constant of the i-th low-order term, λ i For the eigenvalue of the i-th low-order term, expand the numerator and denominator after the common denominator to obtain the analytical expressions of their respective coefficients, A n+1 , B n are two polynomials, c i d i are the coefficients of the corresponding i-th order terms respectively;

[0190] Use formula (4-2) to establish the nth term numerator B in frequency domain calculation n and the relationship between eigenvalues ​​and constants;

[0191] (4-2)

[0192] In formula (4-2): R n+1 is the constant of the n+1th term, λ n+1 is the eigenvalue of the n+1th term, b k is the coefficient of the kth term in the numerator, a r is the coefficient of the rth term in the denominator; is the coefficient of the k-th term of the numerator after merging and simplification, and we have:

[0193] (4-3)

[0194] In formula (4-3): is the coefficient of the n-1th term in the numerator; is the coefficient of the k-1th term in the numerator; a0 and b0 are the constant term coefficients in the denominator and numerator respectively; a k is the coefficient of the kth term in the denominator;

[0195] Step 4.2: Use formula (4-4) to establish the denominator coefficient A of the n+1th term in the frequency domain calculation n+1 And the relationship between the eigenvalue:

[0196] (4-4)

[0197] In formula (4-4): is the coefficient of the rth term of the denominator after merging and simplification, and we have:

[0198] (4-5)

[0199] In formula (4-5): is the coefficient of the r-1th term in the denominator; is the coefficient of the nth term in the denominator;

[0200] Step 4.3: For the denominator A of the n+1th term n+1 Through differentiation treatment, A n+1 The coefficients in determine the n+1 eigenvalues ​​λ1…λ n+1 ;

[0201] According to n+1 eigenvalues ​​λ1…λ n+1 and B n The coefficients in , we get n+1 constants R1…R n+1 ;

[0202] According to n eigenvalues ​​λ1…λ n , use formula (4-6) to calculate the frequency change Perform complex frequency domain transformation to obtain the time domain expression of frequency change :

[0203] (4-6)

[0204] By frequency change Taking the derivative with respect to time t, we get the frequency conversion rate ;

[0205] By finding the frequency change rate The zero point is brought into the frequency variation expression to solve the maximum frequency variation of the power system. , thus finding the lowest frequency point ,in, Indicates the frequency of the power system.

[0206] Step 5: Expand the object of trajectory sensitivity to the entire power system, construct the Hessian matrix, and use the interior point method to obtain the optimal value of the control parameter to improve the lowest point of the power system frequency change.

[0207] Step 5.1: Extend the damping torque method to the entire power system, taking into account DFIG, SG, and VSG, and the transient state of the wind power grid-connected power system is described as formula (5-1):

[0208] (5-1)

[0209] In formula (5-1): f s is the differential equation of SG and its excitation and speed regulation system; f w is the DFIG and its frequency control differential equation; g s It consists of SG and the grid algebraic equation; g wIt consists of DFIG and its frequency control differential equation and interface equation; t0 is the simulation start time; x s 、x w ,y s ,y w are the state variables and algebraic variables of DFIG and SG, with initial values ​​of x s0 、x w0 ,y s0 ,y w0 ; a is the control parameter to be optimized.

[0210] Based on the sensitivity of each variable v at the previous moment to the trajectory of the DFIG control parameter to be optimized, and the Jacobian matrix of the current moment v+1 and the previous moment v, the sensitivity of each variable at the current moment v+1 to the trajectory of the control parameter to be optimized can be obtained as shown in formula (5-2):

[0211] (5-2)

[0212] In formula (5-2): , , , are the state variables and algebraic variables of SG and DFIG at time v+1 to the sensitivity of the variable a to be determined; , , , are the sensitivities of the state variables and algebraic variables of SG and DFIG at time v to the variable a to be determined; , , , They are the derivatives of the SG and DFIG differential equations at time v+1 with respect to the SG and DFIG state variables; , , , They are the derivatives of the SG and DFIG differential equations at time v with respect to the SG and DFIG state variables; , , , They are the derivatives of the SG and DFIG algebraic equations at time v+1 with respect to the SG and DFIG state variables; , , , They are the derivatives of the SG and DFIG differential equations at time v+1 with respect to the algebraic variables SG and DFIG respectively; , , , They are the derivatives of the SG and DFIG differential equations at time v with respect to the algebraic variables SG and DFIG; , , , They are the derivatives of the SG and DFIG algebraic equations at time v+1 with respect to the SG and DFIG state variables; The derivative of the DFIG and its frequency control differential equation with respect to the control parameters to be optimized at time v+1;

[0213] The deviation between the system frequency in the transient process and its initial steady-state value is used as the evaluation criterion to optimize the parameters as shown in formula (5-3):

[0214] (5-3)

[0215] In formula (5-3), t1 is the end time of system simulation, and f(t) is the frequency of the system at time t.

[0216] The gradient information at each hour is superimposed to obtain the gradient information of the objective function to a as shown in formula (5-4):

[0217] (5-4)

[0218] (5-5)

[0219] Through the above-mentioned gradient information, combined with the interior point method, the control parameters are optimized, and the result after the kth iteration is shown in formula (5-6):

[0220] (5-6)

[0221] In formula (5-7): α p and α d is the step size, Δx is the control parameter adjustment, Δu is the relaxation constant change, Δy and Δz are the Lagrange multipliers change; the overall optimization process is as follows Figure 4 As shown, through k max After iterations, the optimal value of the control parameter is obtained, and then the lowest frequency point is optimized. min The size of the optimization is used to evaluate the quality of the optimization effect. , , , They are the control parameter adjustment, relaxation constant change, and Lagrange multiplier change at the k+1th iteration respectively; , , , are the control parameter adjustment, relaxation constant change, and Lagrange multiplier change at the kth iteration respectively;

[0222] 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.

[0223] 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 optimizing control parameters of a doubly-fed wind turbine generator system based on the lowest frequency point of a power system under low voltage ride-through, characterized in that: The following steps are involved: Step 1: Considering the influence of wind speed, pitch angle and rotation speed on the capture coefficient, Taylor expansion is performed on the captured power and the first-order partial derivative is retained to obtain the expression of the captured power variation of the doubly-fed wind turbine; Based on the flux and torque equations of the induction motor, the expressions of the electromagnetic power variation and stator active power variation of the doubly-fed wind turbine are obtained; Step 2: Establish the rotor d-axis current ΔI through the rotor motion equation rd and speed Δω r The transfer function between Considering the active power compensation of the doubly-fed wind turbine generator set under low voltage ride-through by the virtual synchronous machine VSG, the speed Δω of the doubly-fed wind turbine generator set is derived. r The transfer function between the frequency change Δf of the power system ; Where s represents frequency domain calculation; Based on Δω r The transfer function between Δf and Δf is used to obtain the stator active power ΔP of the doubly fed wind turbine. s The transfer function G between the frequency change Δf of the power system s ; Based on ΔP s The transfer function between Δf and Δf, considering the active power compensation of the virtual synchronous machine VSG, is obtained as DFIG The transfer function between the frequency change Δf of the power system ; Step 3: Based on ΔP DFIG The transfer function between Δf , the equivalent inertia time constant H of the doubly fed wind turbine is obtained eqDFIG Considering the rated capacity of the doubly-fed wind turbine generator set under different working conditions of grid disconnection and low voltage ride-through, and combining the rated capacity of the synchronous unit, the equivalent inertia time constant H of the power system is obtained. eq ; The power-frequency response characteristics of the doubly-fed wind turbine generator system under non-step response are quantified, and based on the equivalent inertia time constant H eq , synchronous units, and double-fed wind turbine units, and obtain the frequency response model of the power system; Based on the frequency response model of the power system and considering the unit power fluctuation caused by different operating conditions in the low voltage ride-through situation, the frequency domain expression of the frequency change Δf is obtained. ; Step 4: Use the polynomial common denominator pole method to establish the relationship between the polynomial numerator, denominator coefficients and eigenvalues, and solve the eigenvalues ​​of the power system, so as to obtain the time domain expression of the frequency change through complex frequency domain conversion, and obtain the zero point after partial derivative of the time domain expression, bring the zero point into the time domain expression of the frequency change, and obtain the lowest frequency point of the power system; Step 5: Calculate the trajectory sensitivity of the power system, and then construct the Hessian matrix based on the trajectory sensitivity, and optimize the control parameters of the power system in combination with the interior point method to obtain the optimal correction amount of the control parameters to improve the lowest frequency point of the power system.

2. The control parameter optimization method of a doubly-fed wind turbine generator system based on the lowest frequency point of a power system according to claim 1, characterized in that: The step 1 comprises: Step 1.1: Use equation (1) to obtain the captured power change The expression is: (1) In formula (1): ρ is the air density, R t is the radius of the wind turbine blade, λ de is the tip speed ratio in the load reduction mode, C p (λ de ,0) is the wind energy capture coefficient in load reduction mode, Δv w is the change in wind speed, Δω r is the change in rotor speed, Δβ is the change in pitch angle, v w is the wind speed, ω r is the rotor speed, β is the pitch angle, k1 is the coefficient of the first constant term; Step 1.2: Use formula (2) to obtain the electromagnetic power change ΔP e The expression is: (2) In formula (2): L m0 is the initial value of the excitation inductance, L s0 is the initial value of the stator self-inductance, ω s0 is the initial speed of the stator, U s0 is the initial voltage of the wind turbine stator, ω r0 is the initial speed of the rotor, ΔT e is the change in electromagnetic torque, ΔI rd is the change of the rotor d-axis current, k2 is the coefficient of the second constant term; Using formula (3), we can get the stator active power change ΔP s The expression is: (3) In formula (3): U sd0 is the initial value of the stator d-axis voltage, and k3 is the coefficient of the third constant term.

3. The control parameter optimization method of a doubly-fed wind turbine generator system based on the lowest frequency point of a power system according to claim 2, characterized in that: The step 2 comprises: Step 2.1: Use equation (4) to establish the rotor d-axis current ΔI rd and speed Δω r The transfer function G1 is: (4) In formula (4): H DFIG is the inertia time constant of the doubly-fed wind turbine; s represents frequency domain calculation; Step 2.2: Use equation (5) to establish the speed reference value variation of the doubly-fed wind turbine generator set: and the speed change Δω r The relationship is: (5) In formula (5): D is the damping coefficient of the power system; Step 2.3: Use equation (6) to establish the stator power reference value and the speed change Δω r The relationship : (6) In formula (6): K pω , K iω are two parameters of the PI controller of the rotor-side converter in the doubly-fed wind turbine; is the speed reference value change; Step 2.4: Considering the compensation measures of VSG, the speed change Δω of the doubly-fed wind turbine is obtained using equation (7): r The transfer function between the frequency change Δf of the power system : (7) In formula (7): G i is the transfer function of the current inner loop controller in the rotor-side converter, G SI is the transfer function of the additional controller, k de is the load reduction factor of the doubly-fed wind turbine generator set, G w is the transfer function of the power loop controller; Step 2.5: Use equation (8) to get the stator active power ΔP s The transfer function G between the frequency change Δf of the power system s : (8) Step 2.6: Use equation (9) to obtain the active power ΔP of the doubly-fed wind turbine generator system: DFIG The transfer function between the frequency change Δf of the power system : (9) In formula (9): f0 is the initial value of the frequency of the power system, P s0 is the initial value of the stator active power.

4. The control parameter optimization method of a doubly-fed wind turbine generator system based on the lowest frequency point of a power system according to claim 3 is characterized in that: The step 3 comprises: Step 3.1: Obtain the equivalent inertia time constant H by equation (10): eqDFIG : (10) In formula (10): sg0 is the initial speed of the synchronous machine, H DFIG is the inertia time constant of the doubly-fed wind turbine; Step 3.2: During the low voltage ride-through process, calculate the inertia time constants of the doubly fed wind turbines and synchronous units in other states except the off-grid state and the low voltage ride-through state and perform weighted calculation to obtain the equivalent inertia time constant H of the power system. eq ; Step 3.3: Use equation (11) to obtain the power-frequency response characteristics of the doubly-fed wind turbine generator under non-step response: (11) In formula (11): G eq is the power-frequency response characteristic under the equivalent step response, is the equivalent step response; The power change of the doubly-fed wind turbine generator system under low voltage ride-through The non-step component in ; Step 3.4: Based on the power frequency response characteristics of the doubly-fed wind turbine and synchronous generator and the equivalent inertia time constant H of the power system eq Considering the operating conditions of the doubly-fed wind turbine generator set under low voltage ride-through, different operating conditions cause different power shortages to the power system. The frequency domain expression of the power system frequency change Δf is obtained using formula (12): : (12) In formula (12): G SG,i is the power-frequency response characteristic of the ith synchronous unit, G DFIG,h is the power-frequency response characteristic of the h-th wind turbine, D is the damping coefficient of the system, Indicates the total number of synchronous machines, represents the total number of doubly-fed wind turbines, m represents the total number of doubly-fed wind turbines in off-grid conditions, and p represents the total number of doubly-fed wind turbines in low voltage ride-through conditions; is the equivalent step response of the nth unit under low voltage ride-through condition; is the equivalent step response of the e-th unit in off-grid condition.

5. The control parameter optimization method of a doubly-fed wind turbine generator system based on the lowest frequency point of a power system according to claim 4, characterized in that: The step 4 comprises: Step 4.1: Use equation (13) to establish the nth term numerator B in frequency domain calculation n and the relationship between eigenvalues ​​and constants; (13) In formula (13): R n+1 is the constant of the n+1th term, λ n+1 is the eigenvalue of the n+1th term, b k is the coefficient of the kth term in the numerator, a r is the coefficient of the rth term in the denominator; is the coefficient of the k-th term of the numerator after merging and simplification, and we have: (14) In formula (14): is the coefficient of the n-1th term in the numerator; is the coefficient of the k-1th term in the numerator; a0 and b0 are the constant term coefficients in the denominator and numerator respectively; a k is the coefficient of the kth term in the denominator; Step 4.2: Use equation (15) to establish the denominator coefficient A of the n+1th term in the frequency domain calculation n+1 And the relationship between the eigenvalue: (15) In formula (15): is the coefficient of the rth term of the denominator after merging and simplification, and we have: (16) In formula (16): is the coefficient of the r-1th term in the denominator; is the coefficient of the nth term in the denominator; Step 4.3: For the denominator A of the n+1th term n+1 Through differentiation treatment, A n+1 The coefficients in determine the n+1 eigenvalues ​​λ1…λ n+1 ; According to n+1 eigenvalues ​​λ1…λ n+1 and B n The coefficients in , we get n+1 constants R1…R n+1 ; According to n eigenvalues ​​λ1…λ n , using formula (17) to calculate the frequency change Perform complex frequency domain transformation to obtain the time domain expression of frequency change : (17) In formula (17), t represents the time domain, represents the constant coefficient of the αth term; λ α represents the αth eigenvalue coefficient; Step 4.4: By frequency variation Taking the derivative of t in the time domain, we get the frequency conversion rate ; Find the rate of change of frequency The zero point is brought into the frequency variation expression to solve the maximum frequency variation of the power system. , thus obtaining the lowest frequency point ,in, Indicates the frequency of the power system.

6. The control parameter optimization method of a doubly-fed wind turbine generator system based on the lowest frequency point of a power system according to claim 5, characterized in that: The trajectory sensitivity of the power system in step 5 is calculated as follows: Step 5.1: Use equation (18) to construct the objective function J for optimizing the control parameters of the power system: (18) In formula (18), t0 is the initial time, t1 is the end time, f(t0) is the frequency at the initial time t0, and f(t) is the time domain frequency expression of the power system; Step 5.2: Use formula (19) to obtain the first-order gradient information , and as the trajectory sensitivity; (19) In formula (19): N p is the total number of moments, Δt is the time step, t u is the u-th moment, Find the first-order partial derivative of the frequency expression with respect to a, f(t u ) is the frequency at the u-th simulation moment; a is the control parameter to be optimized; Step 5.3: Use formula (20) to obtain the second-order gradient information , and used to construct the Hessian matrix; (20) In formula (20): Find the second-order partial derivative of the frequency expression with respect to a.

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 optimizing control parameters of a doubly-fed wind turbine set 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 optimizing control parameters of a doubly-fed wind turbine set according to any one of claims 1 to 6 are executed.

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